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2021-04-13T20:59:56Z
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https://www.bogleheads.org/w/index.php?title=Simba%27s_backtesting_spreadsheet&diff=72037
Simba's backtesting spreadsheet
2021-02-17T20:41:25Z
<p>Siamond: /* Spreadsheet overview and download instructions */ v20b link</p>
<hr />
<div><br />
'''{{PAGENAME}}''' describes a spreadsheet originally developed by forum member ''Simba'' for the purpose of acting as a reference for historical returns, and analyzing a portfolio based on such historical data. The spreadsheet is no longer maintained by Simba, but other forum members continue to support it and to expand functionality, as a Bogleheads community project.<br />
<br />
{{Notice|This spreadsheet and the information it contains is intended for your personal, non-commercial, use only (e.g. for educational purposes). This is a learning, researching and teaching tool, nothing more.}}<br />
<br />
==Backtesting==<br />
Backtesting is a term used in oceanography, meteorology and the financial industry to refer to testing a predictive model using existing historic data.<ref name="Wiki">[[wikipedia:Backtesting|Backtesting]], on Wikipedia</ref> It is also often used to analyze the past for research purposes. It is notably useful to quantitatively assess the impact [[asset allocation]] had (in known history) on possible investment strategies.<br />
<br />
Backtesting seeks to estimate the performance of a strategy if it had been employed during a past period. This requires simulating past conditions with sufficient detail, making one limitation of backtesting the need for detailed historical data. A second limitation is the inability to model strategies that would affect historic prices.<br />
<br />
Finally, backtesting, like other modeling, is limited by potential overfitting. That is, it is often possible to find a strategy that would have worked well in the past, but will not work well in the future. <br />
<br />
Despite these limitations, backtesting provides valuable information not available when models and strategies are tested on synthetic data.<br />
<br />
==Spreadsheet overview and download instructions==<br />
The spreadsheet is discussed in this {{Forum post|t=2520|title=Simba's backtesting spreadsheet <nowiki>[a Bogleheads community project]</nowiki>}}.<br />
<br />
The latest version and download instructions are in '''[{{{url|https://www.bogleheads.org/forum/viewtopic.php?p=5815123#p5815123}}} this post]'''.<br />
<br />
Detailed instructions, glossary and revision history can be found in the '''README''' tab. Here is a brief overview of the individual worksheets:<br />
<br />
*'''Analyze_Portfolio''' provides a simple way to customize the asset allocation of a single portfolio and study its historical performance over specific time periods. This worksheet compares a custom portfolio to a benchmark portfolio (e.g. 60/40) and provides charts and statistics to illustrate respective growth and drawdowns.<br />
*'''Compare_Portfolios''' allows to compare two sets of 5 different portfolios, with the ability to change the portfolios' composition, the time period being examined, and to check the impact on various metrics and charts.<br />
*'''Lazy_Portfolios''' compares 25 predefined portfolios and provides risk/return statistics and charts for all portfolios.<br />
*'''Portfolio_Math''' calculates portfolio returns for all combinations of interest and performs most of the 'under the hood' calculations. <br />
*'''Analyze_Series''' investigates annual returns for all selected data series. Various statistics are provided, as well as a correlation matrix and rolling returns over various time periods.<br />
*'''Data_Series''' provides a selection mechanism to choose the data series to be analyzed and combined in portfolios in the rest of the spreadsheet.<br />
*'''Raw_Data''' provides a dynamic splicing mechanism to combine raw data (e.g. funds, indices and synthetic models) into full data series, while applying expense ratio adjustments.<br />
*'''Data_Sources''' identifies the various data sources used in this spreadsheet. More details on a per data series basis can be found in Raw_Data.<br />
<br />
==Historical Returns==<br />
The spreadsheet provides an extensive set of historical returns for various types of passive index funds, plus a few active funds. Most funds are from Vanguard and all corresponding historical returns have been validated with Vanguard. All returns are expressed as total returns, i.e. including dividends. The perspective of a U.S. investor is assumed, with returns expressed in USD.<br />
<br />
When actual fund returns are not available (e.g. early years), attempts were made to provide credible numbers to extend the fund's history, using returns from corresponding indices, and in some cases, using a synthetic model. <br />
<br />
In general, fairly good quality data is available starting in 1927 for U.S. stocks and bonds. Most International returns are available starting in 1970. Most sector returns aren't available before 1985.<br />
<br />
The ''Raw_Data'' worksheet is the main repository for such historical data. The ''Data_Series'' worksheet assembles a synthetic list of data series returns and can be easily copied in another spreadsheet, allowing to perform other types of backtesting analysis than the tools provided by the Simba spreadsheet.<br />
<br />
==Telltale chart==<br />
{{Main article|Telltale chart}}<br />
<br />
<onlyinclude>John Bogle stated:<ref>[https://personal.vanguard.com/bogle_site/sp20020626.html The Telltale Chart], [[John C. Bogle]], Vanguard.com (Bogle_site), June 26, 2002.</ref><br />
<blockquote>''A telltale chart is devised simply by dividing the cumulative returns of one data series into another'' (the benchmark).</blockquote><br />
In the Simba spreadsheet, such a chart compares the trajectory of historical returns for the various portfolios of interest to a Telltale benchmark (itself a portfolio), in a relative manner.<br />
<br />
Using Telltale charts can be very informative, truly 'telling the tale' of what happened over time to portfolio trajectories, illustrating return to the mean properties, or lack thereof.<br />
<br />
It is interesting to observe that ''growth charts'' are actually a special form of ''telltale charts'', and can be generated by the same tool. <br />
<br />
A telltale/growth chart is provided in the ''Compare_Portfolios'' worksheet and can be used in multiple ways:<br />
<br />
* If the benchmark is defined as 100% cash, the telltale chart becomes a simple growth chart (i.e. showing the growth of an initial investment over time, in nominal terms).<br />
* If the benchmark is defined as 100% inflation, the telltale chart becomes an inflation-adjusted growth chart (i.e. showing the growth of an initial investment over time, in real terms).<br />
* If a more concrete benchmark is used (e.g. US Total Market, aka TSM), the telltale chart shows the relative growth over time of the portfolios of interest compared to the benchmark.<br />
<br />
Typical examples of Telltale charts generated with the Simba spreadsheet can be found here: [https://finpage.blog/2018/02/15/telling-tales-2017-update Telling Tales – 2017 update].<br />
</onlyinclude><br />
<br />
==Compatibility==<br />
The spreadsheet is maintained using Microsoft Excel 2011, and provided in XLSX format.<br />
<br />
It should work fairly well with recent versions of [https://www.libreoffice.org/discover/calc/ LibreOffice Calc], with some minor limitations (e.g. dynamic chart titles do not automatically update). Once the file has been downloaded from Google Drive, open the file and save it in the suggested "ODF" default format. Otherwise, the charts will not be preserved in the correct format.<br />
<br />
There is limited compatibility with Google Sheets. The calculations and statistics appear to work well, while the charts do not work properly.<br />
<br />
==Inner Workings==<br />
As any complex spreadsheet, the inner workings of the Simba spreadsheet may not be quite obvious by just looking at formulas. The following series of blog articles document various aspects of how it actually works.<br />
<br />
*[https://www.bogleheads.org/blog/2018/02/02/inner-workings-of-the-simba-backtesting-spreadsheet-a-layered-structure/ Simba backtesting spreadsheet: a layered structure], elaborating on how the spreadsheet is constructed, and providing an overview of its layered structure.<br />
*[https://www.bogleheads.org/blog/2018/02/04/simba-backtesting-spreadsheet-risk-metrics-risk-ratios Simba backtesting spreadsheet: risk metrics, risk ratios]: elaborating on how risk metrics (e.g. volatility, drawdowns, etc) and risk ratios (e.g. Sharpe, Sortino, etc) are computed.<br />
*[https://www.bogleheads.org/blog/2018/02/04/simba-backtesting-spreadsheet-advanced-topics Simba backtesting spreadsheet: advanced topics]: elaborating on more advanced topics (e.g. unbalancing, safe withdrawal rate).<br />
*[https://www.bogleheads.org/blog/2018/02/05/simba-backtesting-spreadsheet-miscellaneous-topics Simba backtesting spreadsheet: miscellaneous topics]: addressing a few miscellaneous topics (e.g. end label on charts, compatibility issues, spreadsheet analytics).<br />
<br />
==References==<br />
<references /><br />
<br />
==External links==<br />
*[http://www.bogleheads.org/forum/viewtopic.php?t=2520 Spreadsheet for backtesting (includes TrevH's data)], forum thread containing Simba's spreadsheet.<br />
*[[wikipedia:Backtesting|Backtesting]], on Wikipedia<br />
*[http://www.financialtrading.com/issues-related-to-back-testing/ Issues Related to Back Testing], from FinancialTrading.com<br />
*[http://www.investopedia.com/terms/b/backtesting.asp Backtesting], from Investopedia<br />
{{Resources and links}}<br />
{{Spreadsheets}}<br />
[[Category:Google Docs.spreadsheets]]<br />
[[Category:Resources and links]]</div>
Siamond
https://www.bogleheads.org/w/index.php?title=User:LadyGeek/Callan_periodic_table_of_investment_returns&diff=71574
User:LadyGeek/Callan periodic table of investment returns
2021-01-26T22:44:01Z
<p>Siamond: /* Putting the table into perspective */ Cosmetic</p>
<hr />
<div>{{Notice| The Callan Periodic Table is the best visual information showing the importance of [[:Category:Asset classes|asset class]] diversification and the [[Bogleheads® investment philosophy#Never try to time the market|futility of market timing]]. It is a primary reason for which many Bogleheads favor total market index funds.<ref>{{Forum post|p=4107872|title=Re: Playing with Callan's periodic tables of investment returns|author=LadyGeek|date=September 7, 2018}}</ref>}}<br />
<br />
The '''{{PAGENAME}}''' is patterned after Mendeleev's periodic table of the elements<ref>[https://en.wikipedia.org/wiki/Periodic_table Mendeleev's periodic table of the elements], Retrieved August 30, 2013</ref> and features well-known, industry-standard market indices as proxies for each asset class.<ref name="Callan" /> <br />
<br />
The table shows returns for ten asset classes, ranked from best to worst. Each asset class is color-coded for easy tracking.<ref name="Callan">{{cite web|url=https://www.callan.com/periodic-table/| title=Periodic Table - Callan| publisher=Callan Institute| accessdate=January 19, 2021}}</ref>. It was created in 1999 by Jay Kloepfer.<ref name="Callan" /><br />
<br />
==Overview==<br />
The chart is intended to show the importance of diversification across asset classes ([[stock]]s versus [[bond]]s), investment styles (growth versus value), capitalizations (large versus small) and equity markets (U.S. versus international).<ref>[https://www.callan.com/wp-content/uploads/2018/01/Callan-PeriodicTbl_KeyInd_2018.pdf The Callan Periodic Table of Investment Returns (Key Indices: 1998-2017)], viewed Sep 07, 2018.</ref> <br />
<br />
Refer to the table below. The rankings change every year, thereby demonstrating two key principles of investing:<br />
<br />
*Diversification: by owning the entire market (all of the asset classes), susceptibility to changes in market returns is minimized.<br />
*Past performance does not predict future performance.<br />
<br><br />
{| border="1" style="border-collapse: collapse;"<br />
|-<br />
||[[File:Callan Periodic Table of Investment Returns.png|600px]]<br />
[http://www.bogleheads.org/w/images/d/dc/Callan_Periodic_Table_of_Investment_Returns.png View full size]<br />
©2021 by Callan LLC. Reprinted with permission.<br />
|}<br />
<br />
==History and changes==<br />
The composition of the table has changed over the years. <br />
{| class="wikitable" <br />
|-<br />
! Year<br />
! Changes made<br />
|-<br />
| 1999<br />
| Created with eight (8) asset classes.<br />
|-<br />
| 2010<br />
| Emerging markets asset class added, bring number to nine.<br />
|-<br />
| 2013<br />
| the addition of Barclay's Corporate high yield brought the total to ten.<br />
|-<br />
| 2017<br />
| "MSCI World ex USA" replaced "MSCI EAFE". The entire table was rebuilt using "MSCI World ex USA".<br />
|-<br />
| 2019<br />
| The S&P 500 Growth, S&P 500 Value, Russel 2000 Growth, and Russel 2000 Value were replaced with Global Bonds ex-US, Cash equivalent (90 day T-Bills), and Real Estate. The entire table was rebuilt. <br />
|}<br />
The prior spreadsheets are at [https://docs.google.com/spreadsheets/d/1AjfXhdInFpt6QZf9HuNkgSZyN6IvVqAoFLTppPJsXlg/edit#gid=0 Callan Periodic Chart 2017: Dispersion of Asset Class Returns] and [https://docs.google.com/spreadsheets/d/118vPv6zokoI51X1hL2h5CoEIOQaYF1cqLOMYn7Hjxkk/edit#gid=0 Callan Periodic Table 2017: Statistics]<br />
<br />
==How to read the table==<br />
For example: Real estate (a measure of the stock performance of companies engaged in specific real estate activities in the North American, European, and Asian real estate markets). Starting at the left side, this measure ranked:<br />
<br />
*2001 - 7th<br />
*2002 - 2003 - 3rd (2 consecutive years)<br />
*2004 - 1st<br />
*2005 - 2nd<br />
*2006 - 1st<br />
*2007 - 9th<br />
*2008 - 8th<br />
*2009 - 3rd<br />
*2010 - 2nd<br />
*2011 - 7th<br />
*2012 - 1st<br />
*2013 - 5th<br />
*2014 - 1st<br />
*2015 - 4th<br />
*2016 - 5th<br />
*2017 - 2018 - 6th (2 consecutive years)<br />
*2019 - 4th<br />
*2020 - 9th<br />
<br />
==Putting the table into perspective==<br />
Periodic tables provide a great visual about diversification benefits, but tend to be more qualitative than quantitative. The simple ranking from best to worse notably does not allow one to easily appreciate the scaling of annual returns. The effect of compounding over the long-term is also hard to perceive with such per-annum table.<ref name="siamond">{{Forum post|p=5758819|title=Re: <nowiki>[wiki]</nowiki> Callan periodic table of investment returns|author=siamond|date=Jan 24, 2021}}</ref><br />
<br />
The following graphs are therefore useful to put such a periodic table in perspective.<br />
<br />
{| border="1" style="border-collapse: collapse;"<br />
|-<br />
|[[File:Callan table asset class performance 2001-2020.png|600px]]<br />
|-<br />
|Notes: Created with Python Jupyter Notebook. See: {{Forum post|p=5757965 | title = Re: <nowiki>[wiki]</nowiki> Callan periodic table of investment returns| author = jsprag | date = Jan 24, 2021}}<br />
|}<br />
<br><br />
{| border="1" style="border-collapse: collapse;"<br />
|-<br />
|[[File:Callan table annual returns.svg|600px]]<br />
|-<br />
|Source: [https://docs.google.com/spreadsheets/d/1Hbdwy9g4StOrs_I9lHrx6nPanS88jLnwTiDzPuTORno/edit#gid=6 Callan Periodic Table: Statistics - Google Sheets]<br />
|}<br />
<br><br />
{| border="1" style="border-collapse: collapse;"<br />
|-<br />
|[[File:Callan table CAGR starting at 2001.svg|600px]]<br />
|-<br />
|Source: [https://docs.google.com/spreadsheets/d/1Hbdwy9g4StOrs_I9lHrx6nPanS88jLnwTiDzPuTORno/edit#gid=58883975 Callan Periodic Table: Statistics - Google Sheets]<br />
|}<br />
<br><br />
{| border="1" style="border-collapse: collapse;"<br />
|-<br />
|[[File:Callan table growth of 10K since 2001.svg|600px]]<br />
|-<br />
|Source: [https://docs.google.com/spreadsheets/d/1Hbdwy9g4StOrs_I9lHrx6nPanS88jLnwTiDzPuTORno/edit#gid=1831322522 Callan Periodic Table: Statistics - Google Sheets]<br />
|}<br />
<br />
==Create your own periodic table==<br />
A spreadsheet for creating your own periodic table is available in this {{Forum post|t=257653|title=Playing with Callan's periodic tables of investment returns}}.<br />
<br />
The latest version and download instructions are in [https://www.bogleheads.org/forum/viewtopic.php?p=4098373#p4098373 this post], which is a direct download from Google Drive.<br />
<br />
Detailed instructions and revision history are in the "README" tab.<br />
<br />
==See also==<br />
*[[Risk and return: an introduction]]<br />
*[[Mean reversion | Reversion to the mean]]<br />
<br />
==References==<br />
{{reflist|30em}}<br />
<br />
==External links==<br />
*[[finiki:Periodic table of annual returns|Periodic table of annual returns]], on [http://www.finiki.org/wiki/Main_Page finiki, the Canadian financial wiki]. Total returns for Canadian investors.<br />
*[https://www.callan.com/periodic-table/ Periodic Tables], by [http://www.callan.com/about/ Callan LLC]. Includes links to the "classic" table, a collection of tables ("classic"and 10 additional versions including the indices relative to inflation, real estate indices, and hedge fund sub-strategies), and a table of monthly rankings.<br />
*[https://us.allianzgi.com/documents/Investor-Education-Importance-of-Diversification The Importance of Diversification], asset classes for the past ten years, from [https://us.allianzgi.com/en-us/advisors/resources/literature-center Allianz Global Investors - Literature Center].<br />
*[https://2deaa804a6dc693855a0-eba658c6bc03668a61900f643427d64d.ssl.cf1.rackcdn.com/Documents/channel/advisor/article/JH%20Periodic%20Table_FINAL_2018-01.pdf Periodic Table of Investments], asset classes for the past ten years, from [https://en-us.janushenderson.com/advisor/ Janus Henderson Investors]<br />
*[http://www.usfunds.com/media/files/pdfs/researchreports/2015/2015_Periodic-Table-of-Sector-Returns.pdf Periodic table of sector returns] from usfunds.com, covers years 2005 - 2014.<br />
*[http://www.usfunds.com/media/files/pdfs/researchreports/2011-research-pdfs/2010-Commodity_Returns_Table.pdf Periodic table of commodity returns] from usfunds.com, covers years 2001 - 2010.<br />
<br />
===Forum discussions===<br />
* {{forum post|t = 336650|title = <nowiki>[wiki]</nowiki> Callan periodic table of investment returns| date = Jan 16, 2021 | author = LadyGeek}}<br />
* {{forum post|t=237091|title=2017 Callan Periodic Table of Investment Returns|date = Jan 06, 2018|author = triceratop}}<br />
* {{forum post|t=180882|title=2015 Asset Class Returns|date = Jan 01, 2016|author = Tamales}}. A comprehensive list of asset class returns compiled by forum member Tamales.<br />
{{Bogleheads investing start-up kit}}</div>
Siamond
https://www.bogleheads.org/w/index.php?title=User:LadyGeek/Callan_periodic_table_of_investment_returns&diff=71573
User:LadyGeek/Callan periodic table of investment returns
2021-01-26T22:41:14Z
<p>Siamond: /* Putting the table into perspective */ Added compounding sentence.</p>
<hr />
<div>{{Notice| The Callan Periodic Table is the best visual information showing the importance of [[:Category:Asset classes|asset class]] diversification and the [[Bogleheads® investment philosophy#Never try to time the market|futility of market timing]]. It is a primary reason for which many Bogleheads favor total market index funds.<ref>{{Forum post|p=4107872|title=Re: Playing with Callan's periodic tables of investment returns|author=LadyGeek|date=September 7, 2018}}</ref>}}<br />
<br />
The '''{{PAGENAME}}''' is patterned after Mendeleev's periodic table of the elements<ref>[https://en.wikipedia.org/wiki/Periodic_table Mendeleev's periodic table of the elements], Retrieved August 30, 2013</ref> and features well-known, industry-standard market indices as proxies for each asset class.<ref name="Callan" /> <br />
<br />
The table shows returns for ten asset classes, ranked from best to worst. Each asset class is color-coded for easy tracking.<ref name="Callan">{{cite web|url=https://www.callan.com/periodic-table/| title=Periodic Table - Callan| publisher=Callan Institute| accessdate=January 19, 2021}}</ref>. It was created in 1999 by Jay Kloepfer.<ref name="Callan" /><br />
<br />
==Overview==<br />
The chart is intended to show the importance of diversification across asset classes ([[stock]]s versus [[bond]]s), investment styles (growth versus value), capitalizations (large versus small) and equity markets (U.S. versus international).<ref>[https://www.callan.com/wp-content/uploads/2018/01/Callan-PeriodicTbl_KeyInd_2018.pdf The Callan Periodic Table of Investment Returns (Key Indices: 1998-2017)], viewed Sep 07, 2018.</ref> <br />
<br />
Refer to the table below. The rankings change every year, thereby demonstrating two key principles of investing:<br />
<br />
*Diversification: by owning the entire market (all of the asset classes), susceptibility to changes in market returns is minimized.<br />
*Past performance does not predict future performance.<br />
<br><br />
{| border="1" style="border-collapse: collapse;"<br />
|-<br />
||[[File:Callan Periodic Table of Investment Returns.png|600px]]<br />
[http://www.bogleheads.org/w/images/d/dc/Callan_Periodic_Table_of_Investment_Returns.png View full size]<br />
©2021 by Callan LLC. Reprinted with permission.<br />
|}<br />
<br />
==History and changes==<br />
The composition of the table has changed over the years. <br />
{| class="wikitable" <br />
|-<br />
! Year<br />
! Changes made<br />
|-<br />
| 1999<br />
| Created with eight (8) asset classes.<br />
|-<br />
| 2010<br />
| Emerging markets asset class added, bring number to nine.<br />
|-<br />
| 2013<br />
| the addition of Barclay's Corporate high yield brought the total to ten.<br />
|-<br />
| 2017<br />
| "MSCI World ex USA" replaced "MSCI EAFE". The entire table was rebuilt using "MSCI World ex USA".<br />
|-<br />
| 2019<br />
| The S&P 500 Growth, S&P 500 Value, Russel 2000 Growth, and Russel 2000 Value were replaced with Global Bonds ex-US, Cash equivalent (90 day T-Bills), and Real Estate. The entire table was rebuilt. <br />
|}<br />
The prior spreadsheets are at [https://docs.google.com/spreadsheets/d/1AjfXhdInFpt6QZf9HuNkgSZyN6IvVqAoFLTppPJsXlg/edit#gid=0 Callan Periodic Chart 2017: Dispersion of Asset Class Returns] and [https://docs.google.com/spreadsheets/d/118vPv6zokoI51X1hL2h5CoEIOQaYF1cqLOMYn7Hjxkk/edit#gid=0 Callan Periodic Table 2017: Statistics]<br />
<br />
==How to read the table==<br />
For example: Real estate (a measure of the stock performance of companies engaged in specific real estate activities in the North American, European, and Asian real estate markets). Starting at the left side, this measure ranked:<br />
<br />
*2001 - 7th<br />
*2002 - 2003 - 3rd (2 consecutive years)<br />
*2004 - 1st<br />
*2005 - 2nd<br />
*2006 - 1st<br />
*2007 - 9th<br />
*2008 - 8th<br />
*2009 - 3rd<br />
*2010 - 2nd<br />
*2011 - 7th<br />
*2012 - 1st<br />
*2013 - 5th<br />
*2014 - 1st<br />
*2015 - 4th<br />
*2016 - 5th<br />
*2017 - 2018 - 6th (2 consecutive years)<br />
*2019 - 4th<br />
*2020 - 9th<br />
<br />
==Putting the table into perspective==<br />
Periodic tables provide a great visual about diversification benefits, but tend to be more qualitative than quantitative. The simple ranking from best to worse notably does not allow one to easily appreciate the scaling of annual returns. The effect of compounding over the long-term is also hard to perceive with such per-annum table.<ref name="siamond">{{Forum post|p=5758819|title=Re: [wiki] Callan periodic table of investment returns|author=siamond|date=Jan 24,2021}}</ref><br />
<br />
The following graphs are therefore useful to put such a periodic table in perspective.<br />
<br />
{| border="1" style="border-collapse: collapse;"<br />
|-<br />
|[[File:Callan table asset class performance 2001-2020.png|600px]]<br />
|-<br />
|Notes: Created with Python Jupyter Notebook. See: {{Forum post|p=5757965 | title = Re: <nowiki>[wiki]</nowiki> Callan periodic table of investment returns| author = jsprag | date = Jan 24, 2021}}<br />
|}<br />
<br><br />
{| border="1" style="border-collapse: collapse;"<br />
|-<br />
|[[File:Callan table annual returns.svg|600px]]<br />
|-<br />
|Source: [https://docs.google.com/spreadsheets/d/1Hbdwy9g4StOrs_I9lHrx6nPanS88jLnwTiDzPuTORno/edit#gid=6 Callan Periodic Table: Statistics - Google Sheets]<br />
|}<br />
<br><br />
{| border="1" style="border-collapse: collapse;"<br />
|-<br />
|[[File:Callan table CAGR starting at 2001.svg|600px]]<br />
|-<br />
|Source: [https://docs.google.com/spreadsheets/d/1Hbdwy9g4StOrs_I9lHrx6nPanS88jLnwTiDzPuTORno/edit#gid=58883975 Callan Periodic Table: Statistics - Google Sheets]<br />
|}<br />
<br><br />
{| border="1" style="border-collapse: collapse;"<br />
|-<br />
|[[File:Callan table growth of 10K since 2001.svg|600px]]<br />
|-<br />
|Source: [https://docs.google.com/spreadsheets/d/1Hbdwy9g4StOrs_I9lHrx6nPanS88jLnwTiDzPuTORno/edit#gid=1831322522 Callan Periodic Table: Statistics - Google Sheets]<br />
|}<br />
<br />
==Create your own periodic table==<br />
A spreadsheet for creating your own periodic table is available in this {{Forum post|t=257653|title=Playing with Callan's periodic tables of investment returns}}.<br />
<br />
The latest version and download instructions are in [https://www.bogleheads.org/forum/viewtopic.php?p=4098373#p4098373 this post], which is a direct download from Google Drive.<br />
<br />
Detailed instructions and revision history are in the "README" tab.<br />
<br />
==See also==<br />
*[[Risk and return: an introduction]]<br />
*[[Mean reversion | Reversion to the mean]]<br />
<br />
==References==<br />
{{reflist|30em}}<br />
<br />
==External links==<br />
*[[finiki:Periodic table of annual returns|Periodic table of annual returns]], on [http://www.finiki.org/wiki/Main_Page finiki, the Canadian financial wiki]. Total returns for Canadian investors.<br />
*[https://www.callan.com/periodic-table/ Periodic Tables], by [http://www.callan.com/about/ Callan LLC]. Includes links to the "classic" table, a collection of tables ("classic"and 10 additional versions including the indices relative to inflation, real estate indices, and hedge fund sub-strategies), and a table of monthly rankings.<br />
*[https://us.allianzgi.com/documents/Investor-Education-Importance-of-Diversification The Importance of Diversification], asset classes for the past ten years, from [https://us.allianzgi.com/en-us/advisors/resources/literature-center Allianz Global Investors - Literature Center].<br />
*[https://2deaa804a6dc693855a0-eba658c6bc03668a61900f643427d64d.ssl.cf1.rackcdn.com/Documents/channel/advisor/article/JH%20Periodic%20Table_FINAL_2018-01.pdf Periodic Table of Investments], asset classes for the past ten years, from [https://en-us.janushenderson.com/advisor/ Janus Henderson Investors]<br />
*[http://www.usfunds.com/media/files/pdfs/researchreports/2015/2015_Periodic-Table-of-Sector-Returns.pdf Periodic table of sector returns] from usfunds.com, covers years 2005 - 2014.<br />
*[http://www.usfunds.com/media/files/pdfs/researchreports/2011-research-pdfs/2010-Commodity_Returns_Table.pdf Periodic table of commodity returns] from usfunds.com, covers years 2001 - 2010.<br />
<br />
===Forum discussions===<br />
* {{forum post|t = 336650|title = <nowiki>[wiki]</nowiki> Callan periodic table of investment returns| date = Jan 16, 2021 | author = LadyGeek}}<br />
* {{forum post|t=237091|title=2017 Callan Periodic Table of Investment Returns|date = Jan 06, 2018|author = triceratop}}<br />
* {{forum post|t=180882|title=2015 Asset Class Returns|date = Jan 01, 2016|author = Tamales}}. A comprehensive list of asset class returns compiled by forum member Tamales.<br />
{{Bogleheads investing start-up kit}}</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Callan_periodic_table_of_investment_returns&diff=71342
Callan periodic table of investment returns
2021-01-19T14:13:59Z
<p>Siamond: /* External links */ Fixed Callan link</p>
<hr />
<div>{{Notice| The Callan Periodic Table is the best visual information showing the importance of [[:Category:Asset classes|asset class]] diversification and the [[Bogleheads® investment philosophy#Never try to time the market|futility of market timing]]. It is a primary reason for which many Bogleheads favor total market index funds.<ref>{{Forum post|p=4107872|title=Re: Playing with Callan's periodic tables of investment returns|author=LadyGeek|date=September 7, 2018}}</ref>}}<br />
<br />
First published in 1999,<ref group="note">Authored by Jay Kloepfer, Director of Callan’s Capital Markets and Alternatives Research.</ref> the '''{{PAGENAME}}''' is patterned after Mendeleev's periodic table of the elements<ref>[http://en.wikipedia.org/wiki/Periodic_table Mendeleev's periodic table of the elements]</ref> and shows returns for 10 asset classes, ranked from best to worst. Each asset class is color-coded for easy tracking.<ref name="Callan">[https://www.callan.com/periodic-table/ Periodic Tables], by [http://www.callan.com/about/ Callan LLC.]</ref><br />
<br />
==Overview==<br />
The chart is intended to show the importance of diversification across asset classes ([[stock]]s versus [[bond]]s), investment styles (growth versus value), capitalizations (large versus small) and equity markets (U.S. versus international).<ref>[https://www.callan.com/wp-content/uploads/2018/01/Callan-PeriodicTbl_KeyInd_2018.pdf The Callan Periodic Table of Investment Returns (Key Indices: 1998-2017)], viewed Sep 07, 2018.</ref> <br />
<br />
Refer to the table below. The rankings change every year, thereby demonstrating two key principles of investing:<br />
<br />
*Diversification: by owning the entire market (all of the asset classes), susceptibility to changes in market returns is minimized.<br />
*Past performance does not predict future performance.<br />
<br><br />
{| border="1" style="border-collapse: collapse;"<br />
|-<br />
||[[File:Callan Periodic Table of Investment Returns.png|600px]]<br />
[http://www.bogleheads.org/w/images/d/dc/Callan_Periodic_Table_of_Investment_Returns.png View full size]<br />
©2020 by Callan LLC. Reprinted with permission.<br />
|-<br />
|style = "width:600px;"|'''Notes:''' There were 8 asset classes until 2009. Emerging markets was added in 2010, for a total of 9 asset classes. In 2013, the addition of Barclay's Corporate high yield brought the total to 10.<br><br />
In 2017, "MSCI World ex USA" replaced "MSCI EAFE". The entire table was rebuilt using "MSCI World ex USA".<br><br />
In 2019, the S&P 500 Growth, S&P 500 Value, Russel 2000 Growth, and Russel 2000 Value were replaced with Global Bonds ex-US, Cash equivalent (90 day T-Bills), and Real Estate. The entire table was rebuilt. The prior spreadsheets are at [https://docs.google.com/spreadsheets/d/1AjfXhdInFpt6QZf9HuNkgSZyN6IvVqAoFLTppPJsXlg/edit#gid=0 Callan Periodic Chart 2017: Dispersion of Asset Class Returns] and [https://docs.google.com/spreadsheets/d/118vPv6zokoI51X1hL2h5CoEIOQaYF1cqLOMYn7Hjxkk/edit#gid=0 Callan Periodic Table 2017: Statistics]<br />
|}<br />
<br />
==How to read the table==<br />
For example: Real estate (a measure of the stock performance of companies engaged in specific real estate activities in the North American, European, and Asian real estate markets). Starting at the left side, this measure ranked:<br />
<br />
*2000 - 1st<br />
*2001 - 7th<br />
*2002 - 2003 - 3rd (2 consecutive years)<br />
*2004 - 1st<br />
*2005 - 2nd<br />
*2006 - 1st<br />
*2007 - 9th<br />
*2008 - 8th<br />
*2009 - 3rd<br />
*2010 - 2nd<br />
*2011 - 7th<br />
*2012 - 1st<br />
*2013 - 5th<br />
*2014 - 1st<br />
*2015 - 4th<br />
*2016 - 5th<br />
*2017 - 2018 - 6th (2 consecutive years)<br />
*2019 - 4th<br />
<br />
==Putting the table into perspective==<br />
Periodic tables provide a great visual about diversification benefits, but tend to be more qualitative than quantitative. The simple ranking from best to worse notably does not allow one to easily appreciate the scaling of annual returns.<ref name="siamond">{{Forum post|p=4107929|title=Re: Playing with Callan's periodic tables of investment returns|author=siamond|date=Sep 07,2018}}</ref><br />
<br />
The following dispersion graph (distribution spread of returns over time) is therefore useful to put such a periodic table in perspective. Notice how the difference between the highest return (blue) and lowest return (red) changes over time.<br />
<br />
{| class="wikitable"<br />
|-<br />
|<br />
{{#widget:Google Spreadsheet<br />
|key=11kyTuSCt2FgzrHvqfEC4mdZ70wQJbd_l9vyB64DiquM<br />
|width=600<br />
|height=400<br />
}} <br> {{spreadsheet|key=11kyTuSCt2FgzrHvqfEC4mdZ70wQJbd_l9vyB64DiquM}}<br />
|<br />
|}<br />
<br />
In addition, it is challenging to get a sense of returns averaged over a period of time with a periodic table. The following table of statistics is therefore useful to consider.<br />
<br />
{| class="wikitable"<br />
|-<br />
|<br />
{{#widget:Google Spreadsheet<br />
|key=1Hbdwy9g4StOrs_I9lHrx6nPanS88jLnwTiDzPuTORno<br />
|width=600<br />
|height=400<br />
}} <br> {{spreadsheet|key=1Hbdwy9g4StOrs_I9lHrx6nPanS88jLnwTiDzPuTORno}}<br />
|<br />
|}<br />
<br />
One statistic that is sometimes informative is the "Coefficient of Variation" (CV), which is simply the standard deviation divided by the mean. This is sometimes called the "coefficient of relative variation." It is the inverse of a signal-to-noise ratio, thus it's a noise to signal ratio.<ref>[[Wikipedia:Coefficient of variation|Coefficient of variation]], Wikipedia</ref> The lower the ratio of standard deviation to mean return, the better your risk-return tradeoff.<ref>{{Forum post|p=1596490|title= <nowiki>[Wiki]</nowiki> Callan periodic table of investment returns|date=Jan 27, 2013|author=Garco}}</ref><br />
<br />
Over the past 20 years (1998 - 2017), the lowest coefficient of variation is "Aggregate Bonds" (0.69); the highest is World Ex USA (2.77).<br />
<br />
==Create your own periodic table==<br />
A spreadsheet for creating your own periodic table is available in this {{Forum post|t=257653|title=Playing with Callan's periodic tables of investment returns}}.<br />
<br />
The latest version and download instructions are in [https://www.bogleheads.org/forum/viewtopic.php?p=4098373#p4098373 this post], which is a direct download from Google Drive.<br />
<br />
Detailed instructions and revision history are in the "README" tab.<br />
<br />
==See also==<br />
*[[Risk and return: an introduction]]<br />
*[[Mean reversion | Reversion to the mean]]<br />
<br />
==Notes==<br />
<references group="note" /><br />
<br />
==References==<br />
{{reflist|30em}}<br />
<br />
==External links==<br />
*[[finiki:Periodic table of annual returns|Periodic table of annual returns]], on [http://www.finiki.org/wiki/Main_Page finiki, the Canadian financial wiki]. Total returns for Canadian investors.<br />
*[https://www.callan.com/periodic-table/ Periodic Tables], by [http://www.callan.com/about/ Callan LLC]. Includes links to the "classic" table, a collection of tables ("classic"and 10 additional versions including the indices relative to inflation, real estate indices, and hedge fund sub-strategies), and a table of monthly rankings.<br />
*[https://us.allianzgi.com/documents/Investor-Education-Importance-of-Diversification The Importance of Diversification], asset classes for the past ten years, from [https://us.allianzgi.com/en-us/advisors/resources/literature-center Allianz Global Investors - Literature Center].<br />
*[https://2deaa804a6dc693855a0-eba658c6bc03668a61900f643427d64d.ssl.cf1.rackcdn.com/Documents/channel/advisor/article/JH%20Periodic%20Table_FINAL_2018-01.pdf Periodic Table of Investments], asset classes for the past ten years, from [https://en-us.janushenderson.com/advisor/ Janus Henderson Investors]<br />
*[http://www.usfunds.com/media/files/pdfs/researchreports/2015/2015_Periodic-Table-of-Sector-Returns.pdf Periodic table of sector returns] from usfunds.com, covers years 2005 - 2014.<br />
*[http://www.usfunds.com/media/files/pdfs/researchreports/2011-research-pdfs/2010-Commodity_Returns_Table.pdf Periodic table of commodity returns] from usfunds.com, covers years 2001 - 2010.<br />
<br />
===Forum discussions===<br />
* {{forum post|t = 336650|title = <nowiki>[wiki]</nowiki> Callan periodic table of investment returns| date = Jan 16, 2021 | author = LadyGeek}}<br />
* {{forum post|t=237091|title=2017 Callan Periodic Table of Investment Returns|date = Jan 06, 2018|author = triceratop}}<br />
* {{forum post|t=180882|title=2015 Asset Class Returns|date = Jan 01, 2016|author = Tamales}}. A comprehensive list of asset class returns compiled by forum member Tamales.<br />
{{Bogleheads investing start-up kit}}<br />
[[Category:Asset allocation]]<br />
[[Category:Annual updates]]</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Simba%27s_backtesting_spreadsheet&diff=71292
Simba's backtesting spreadsheet
2021-01-16T01:29:12Z
<p>Siamond: /* Spreadsheet overview and download instructions */ v20a link</p>
<hr />
<div><br />
'''{{PAGENAME}}''' describes a spreadsheet originally developed by forum member ''Simba'' for the purpose of acting as a reference for historical returns, and analyzing a portfolio based on such historical data. The spreadsheet is no longer maintained by Simba, but other forum members continue to support it and to expand functionality, as a Bogleheads community project.<br />
<br />
{{Notice|This spreadsheet and the information it contains is intended for your personal, non-commercial, use only (e.g. for educational purposes). This is a learning, researching and teaching tool, nothing more.}}<br />
<br />
==Backtesting==<br />
Backtesting is a term used in oceanography, meteorology and the financial industry to refer to testing a predictive model using existing historic data.<ref name="Wiki">[[wikipedia:Backtesting|Backtesting]], on Wikipedia</ref> It is also often used to analyze the past for research purposes. It is notably useful to quantitatively assess the impact [[asset allocation]] had (in known history) on possible investment strategies.<br />
<br />
Backtesting seeks to estimate the performance of a strategy if it had been employed during a past period. This requires simulating past conditions with sufficient detail, making one limitation of backtesting the need for detailed historical data. A second limitation is the inability to model strategies that would affect historic prices.<br />
<br />
Finally, backtesting, like other modeling, is limited by potential overfitting. That is, it is often possible to find a strategy that would have worked well in the past, but will not work well in the future. <br />
<br />
Despite these limitations, backtesting provides valuable information not available when models and strategies are tested on synthetic data.<br />
<br />
==Spreadsheet overview and download instructions==<br />
The spreadsheet is discussed in this {{Forum post|t=2520|title=Simba's backtesting spreadsheet <nowiki>[a Bogleheads community project]</nowiki>}}.<br />
<br />
The latest version and download instructions are in '''[{{{url|https://www.bogleheads.org/forum/viewtopic.php?p=5728638#p5728638}}} this post]'''.<br />
<br />
Detailed instructions, glossary and revision history can be found in the '''README''' tab. Here is a brief overview of the individual worksheets:<br />
<br />
*'''Analyze_Portfolio''' provides a simple way to customize the asset allocation of a single portfolio and study its historical performance over specific time periods. This worksheet compares a custom portfolio to a benchmark portfolio (e.g. 60/40) and provides charts and statistics to illustrate respective growth and drawdowns.<br />
*'''Compare_Portfolios''' allows to compare two sets of 5 different portfolios, with the ability to change the portfolios' composition, the time period being examined, and to check the impact on various metrics and charts.<br />
*'''Lazy_Portfolios''' compares 25 predefined portfolios and provides risk/return statistics and charts for all portfolios.<br />
*'''Portfolio_Math''' calculates portfolio returns for all combinations of interest and performs most of the 'under the hood' calculations. <br />
*'''Analyze_Series''' investigates annual returns for all selected data series. Various statistics are provided, as well as a correlation matrix and rolling returns over various time periods.<br />
*'''Data_Series''' provides a selection mechanism to choose the data series to be analyzed and combined in portfolios in the rest of the spreadsheet.<br />
*'''Raw_Data''' provides a dynamic splicing mechanism to combine raw data (e.g. funds, indices and synthetic models) into full data series, while applying expense ratio adjustments.<br />
*'''Data_Sources''' identifies the various data sources used in this spreadsheet. More details on a per data series basis can be found in Raw_Data.<br />
<br />
==Historical Returns==<br />
The spreadsheet provides an extensive set of historical returns for various types of passive index funds, plus a few active funds. Most funds are from Vanguard and all corresponding historical returns have been validated with Vanguard. All returns are expressed as total returns, i.e. including dividends. The perspective of a U.S. investor is assumed, with returns expressed in USD.<br />
<br />
When actual fund returns are not available (e.g. early years), attempts were made to provide credible numbers to extend the fund's history, using returns from corresponding indices, and in some cases, using a synthetic model. <br />
<br />
In general, fairly good quality data is available starting in 1927 for U.S. stocks and bonds. Most International returns are available starting in 1970. Most sector returns aren't available before 1985.<br />
<br />
The ''Raw_Data'' worksheet is the main repository for such historical data. The ''Data_Series'' worksheet assembles a synthetic list of data series returns and can be easily copied in another spreadsheet, allowing to perform other types of backtesting analysis than the tools provided by the Simba spreadsheet.<br />
<br />
==Telltale chart==<br />
{{Main article|Telltale chart}}<br />
<br />
<onlyinclude>John Bogle stated:<ref>[https://personal.vanguard.com/bogle_site/sp20020626.html The Telltale Chart], [[John C. Bogle]], Vanguard.com (Bogle_site), June 26, 2002.</ref><br />
<blockquote>''A telltale chart is devised simply by dividing the cumulative returns of one data series into another'' (the benchmark).</blockquote><br />
In the Simba spreadsheet, such a chart compares the trajectory of historical returns for the various portfolios of interest to a Telltale benchmark (itself a portfolio), in a relative manner.<br />
<br />
Using Telltale charts can be very informative, truly 'telling the tale' of what happened over time to portfolio trajectories, illustrating return to the mean properties, or lack thereof.<br />
<br />
It is interesting to observe that ''growth charts'' are actually a special form of ''telltale charts'', and can be generated by the same tool. <br />
<br />
A telltale/growth chart is provided in the ''Compare_Portfolios'' worksheet and can be used in multiple ways:<br />
<br />
* If the benchmark is defined as 100% cash, the telltale chart becomes a simple growth chart (i.e. showing the growth of an initial investment over time, in nominal terms).<br />
* If the benchmark is defined as 100% inflation, the telltale chart becomes an inflation-adjusted growth chart (i.e. showing the growth of an initial investment over time, in real terms).<br />
* If a more concrete benchmark is used (e.g. US Total Market, aka TSM), the telltale chart shows the relative growth over time of the portfolios of interest compared to the benchmark.<br />
<br />
Typical examples of Telltale charts generated with the Simba spreadsheet can be found here: [https://finpage.blog/2018/02/15/telling-tales-2017-update Telling Tales – 2017 update].<br />
</onlyinclude><br />
<br />
==Compatibility==<br />
The spreadsheet is maintained using Microsoft Excel 2011, and provided in XLSX format.<br />
<br />
It should work fairly well with recent versions of [https://www.libreoffice.org/discover/calc/ LibreOffice Calc], with some minor limitations (e.g. dynamic chart titles do not automatically update). Once the file has been downloaded from Google Drive, open the file and save it in the suggested "ODF" default format. Otherwise, the charts will not be preserved in the correct format.<br />
<br />
There is limited compatibility with Google Sheets. The calculations and statistics appear to work well, while the charts do not work properly.<br />
<br />
==Inner Workings==<br />
As any complex spreadsheet, the inner workings of the Simba spreadsheet may not be quite obvious by just looking at formulas. The following series of blog articles document various aspects of how it actually works.<br />
<br />
*[https://www.bogleheads.org/blog/2018/02/02/inner-workings-of-the-simba-backtesting-spreadsheet-a-layered-structure/ Simba backtesting spreadsheet: a layered structure], elaborating on how the spreadsheet is constructed, and providing an overview of its layered structure.<br />
*[https://www.bogleheads.org/blog/2018/02/04/simba-backtesting-spreadsheet-risk-metrics-risk-ratios Simba backtesting spreadsheet: risk metrics, risk ratios]: elaborating on how risk metrics (e.g. volatility, drawdowns, etc) and risk ratios (e.g. Sharpe, Sortino, etc) are computed.<br />
*[https://www.bogleheads.org/blog/2018/02/04/simba-backtesting-spreadsheet-advanced-topics Simba backtesting spreadsheet: advanced topics]: elaborating on more advanced topics (e.g. unbalancing, safe withdrawal rate).<br />
*[https://www.bogleheads.org/blog/2018/02/05/simba-backtesting-spreadsheet-miscellaneous-topics Simba backtesting spreadsheet: miscellaneous topics]: addressing a few miscellaneous topics (e.g. end label on charts, compatibility issues, spreadsheet analytics).<br />
<br />
==References==<br />
<references /><br />
<br />
==External links==<br />
*[http://www.bogleheads.org/forum/viewtopic.php?t=2520 Spreadsheet for backtesting (includes TrevH's data)], forum thread containing Simba's spreadsheet.<br />
*[[wikipedia:Backtesting|Backtesting]], on Wikipedia<br />
*[http://www.financialtrading.com/issues-related-to-back-testing/ Issues Related to Back Testing], from FinancialTrading.com<br />
*[http://www.investopedia.com/terms/b/backtesting.asp Backtesting], from Investopedia<br />
{{Resources and links}}<br />
{{Spreadsheets}}<br />
[[Category:Google Docs.spreadsheets]]<br />
[[Category:Resources and links]]</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Amortization_based_withdrawal&diff=70891
Amortization based withdrawal
2020-12-22T21:51:14Z
<p>Siamond: /* Estimating the expected return */ Rephrased the intro, using multiple citations from Investopedia</p>
<hr />
<div>{{Under construction| comment = Comments are being solicited in this {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}}}<br />
'''Amortization based withdrawal (ABW)''' uses amortization techniques to calculate portfolio withdrawals during retirement.<br />
==Amortization==<br />
<br />
===Understanding amortization===<br />
<br />
Amortization is the process of converting the value of a lump sum into a series of payments over time. Most people encounter it when they take out a mortgage or car loan. Amortization is used to calculate the monthly payment required to pay back the loan. The value of the monthly payments has to be made equal to the value of the initial loan.<br />
<br />
If the interest rate is zero, amortization is just simple division: If $100,000 has to be paid back over 10 years, then the payment is $100,000 ÷ 10 = $10,000 per year.<br />
<br />
But if the interest rate is positive, as is usually the case, then the payment in the above example would have to be more than $10,000 per year. That's because $10,000 in the future is worth less than $10,000 today. This is referred to as the time value of money. If the interest is 5% per year, then $10,000 today is worth:<br />
<br />
* <math>$10,000*1.05^1=$10,500</math> one year from now<br />
* <math>$10,000*1.05^2=$11,025</math> two years from now<br />
<br />
and so on. We will have to adjust for the differences in value. The amortization formula makes the necessary adjustments and tells us that if the interest rate is 5% per year, then the payments will have to be $12,950 per year for the next ten years for the total value of the payments to be equal in value to the $100,000 that was borrowed today.<br />
<br />
==Amortization based withdrawal==<br />
<br />
To calculate portfolio withdrawals, enter the following inputs in the ABW calculator ([[#ABW calculator|below]]):<br />
<br />
* <math>P=</math> current portfolio value<br />
* <math>n=</math> number of years over which withdrawals are to be spread out<br />
* <math>r=</math> expected return of the portfolio.<br />
<br />
===Example===<br />
<br />
A 65 year old retiree with a $1 million portfolio expected to earn 3% per year and seeking to spread out withdrawals over 36 years (ages 65 to 100), would enter <math>P=$1,000,000, n=36, r=3%</math>. The amortization calculator says that this retiree can withdraw $44,470 per year. This means that if the portfolio actual rate of return remains constant at 3% per year and the retiree withdraws $44,470 every year, then the portfolio will be fully depleted after 36 years.<br />
<br />
===Real vs nominal rate of return===<br />
<br />
If a real (inflation adjusted) rate of return is used, the withdrawal strategy becomes automatically adjusted for inflation. In the above example, if the real rate of return is 3%, the retiree will be able to take out $44,470 (inflation adjusted) each year. If instead, the retiree enters a nominal interest rate of 5%, the calculator says that they can take out $60,434 per year. But that's in nominal dollars, so real consumption will decline each year by the inflation rate. In practice, it is strongly recommended to use a real rate of return.<br />
<br />
===Update and adapt===<br />
<br />
Withdrawals are recalculated each year with updated information about portfolio value, expected rate of return, and number of years left. This allows withdrawals to continually adapt to new information and mitigates the impact of past incorrect assumptions. Amortization spreads the course correction required across all remaining years, thereby minimizing the impact on any one year.<br />
<br />
====Example====<br />
<br />
Consider what happens in our earlier example if, instead of gaining 3% as expected, the portfolio actually loses 10%. The shortfall relative to expectations is <math>(1-.10)/(1+.03)-1=-12.6%</math>. Our retiree had expected to start age 66 with $984,196 in the portfolio. Instead, the portfolio contains only $859,977, which is 12.6% less. Consider what happens in the following two scenarios:<br />
<br />
=====Scenario 1: Expected return stays the same=====<br />
Suppose that the retiree believes that this market drop has not impacted future expected returns, which in the retiree's opinion, remains at 3%. The retiree enters the new reduced portfolio value, <math>P=$859,977</math>, number of years remaining <math>n=35</math>, and expected real return <math>r=3%</math>. The withdrawal is now reduced to $38,857 per year. That is a 12.6% reduction relative to the previously planned withdrawal of $44,470. So the 12.6% portfolio loss is being matched by a 12.6% spending cut across all remaining years.<br />
<br />
=====Scenario 2: Expected return increases=====<br />
If the market drop was due to a pure valuation change and the underlying earnings of the portfolio are not impacted, then the retiree might expect a higher rate of return going forward.<br />
<br />
If expected return is based on an earnings yield model (e.g. 1/CAPE) for stocks and yield to maturity for bonds, a 12.6% reduction in valuation will result in a higher expected real return of <math>.03/(1-.126)=3.43%</math>. With the higher expected return, the withdrawal becomes $41,181. That is a reduction of only 7.4% relative to the original plan of $44,470. A 12.6% reduction in the portfolio led to only a 7.4% reduction in income, because the higher expected return partially offset the loss in portfolio value.<br />
<br />
So to the extent that market volatility is caused by valuation changes and gets incorporated into expected returns, withdrawals from the portfolio will be less volatile than the portfolio itself.<br />
<br />
==Adding a terminal balance==<br />
<br />
Instead of fully depleting the portfolio, the amortization can be modified to leave behind a terminal balance. This could be used to fund end of life care or a bequest, or it could simply serve as a general financial cushion. <br />
<br />
In the ABW calculator, enter:<br />
* <math>B=</math> terminal balance<br />
<br />
===Example===<br />
<br />
The 65 year old retiree in the earlier example wants to have $200,000 left at the end for a bequest. Enter <math>B=$200,000</math> in the calculator to get a withdrawal of $41,401 per year. If the actual rate of return matches expectations, then after withdrawing $41,401 for 36 years (ages 65 to 100), the retiree will have $200,000 remaining in the portfolio at the end of age 100.<br />
<br />
==Rising or falling withdrawal schedules==<br />
<br />
Instead of aiming at a constant withdrawal schedule, some retirees may prefer to aim at a rising or falling withdrawal schedule. Retirees worried about incurring unexpected expenses or generally running out of money in later years may want to use a rising withdrawal schedule - take less early so they can have more later. Those wanting to fund an active early retirement may want to use a declining withdrawal schedule - take more early but have less later. (Note the similarity with savings. This can be viewed as a decision about how much to save in the early retirement years in order to fund late retirement consumption.)<br />
<br />
In the ABW calculator, enter:<br />
* <math>g=</math> rate of growth of the withdrawal schedule<br />
<br />
<math>g>0</math> generates a rising withdrawal schedule, <math>g<0</math> generates a declining withdrawal schedule, and <math>g=0</math> generates a constant withdrawal schedule.<br />
<br />
===Example===<br />
<br />
If the 65 year old retiree in the earlier example wants withdrawals to grow at 1% per year, set <math>g=1%</math> to get a withdrawal of $38,349. Withdrawals are scheduled to grow 1% per year, rising to $54,325 at age 100.<br />
<br />
If instead the retiree wishes to spend more in early retirement and wants withdrawals to fall by 1% per year, set <math>g=-1%</math> to get a withdrawal of $51,118. Withdrawals are scheduled to fall 1% per year, declining to $35,959 at age 100.<br />
<br />
==Asset allocation==<br />
<br />
===Fixed asset allocation===<br />
<br />
The amortization formula assumes an expected rate of return on the portfolio which stays consistent over the retirement period. This is easier to justify if the retiree plans to maintain a fixed asset allocation (AA). If instead the retiree is planning to change the AA over time (e.g. glide down from 60/40 to 30/70 over the course of the retirement), then the expected return will display more variations over time, skewing the amortization computation. The calculator provided here is not designed for such case. Entering the average expected return in the calculator may provide a rough estimate, but due to the potential for significant errors, more precise modeling is recommended.<br />
<br />
===Fixed asset allocation with sub-portfolios===<br />
<br />
The portfolio can be divided into multiple sub-portfolios and a different fixed allocation applied to each sub-portfolio.<br />
<br />
Suppose the retiree is more risk averse over certain categories of consumption (e.g. food and housing), and less risk averse over other categories (e.g. vacations). The portfolio can be subdivided into a safer portfolio to fund food and housing and a riskier portfolio to fund vacations. The safe portfolio would get a safe fixed AA like 30/70, and the riskier portfolio would get a riskier fixed AA like 80/20. Multiple sub-portfolios could be created to fund different consumption goals, each with a different AA that matches the risk-reward considerations for that goal. Withdrawals would be calculated separately for each sub-portfolio.<br />
<br />
An example of a strategy that uses sub-portfolios is the Liability Matched Portfolio (LMP) strategy. The portfolio is divided into a "liability matched portfolio" and a "risk portfolio". The liability matched portfolio has an AA of 0/100 and is used to fund non-negotiable consumption. The risk portfolio is given a riskier AA and is used to fund discretionary "nice to have" consumption.<br />
<br />
==Estimating the expected return==<br />
<br />
The expected return is the amount of profit or loss an investor can anticipate receiving on an investment. An expected return is calculated by multiplying potential outcomes by the odds of them occurring and then totaling these results.<ref name="investopedia">[https://www.investopedia.com/terms/e/expectedreturn.asp Expected Return] - Investopedia</ref> The expected return can be expanded to analyze a portfolio containing many investments. If the expected return for each investment is known, the portfolio's overall expected return is a weighted average of the expected returns of its components.<ref name="investopedia"/><br />
<br />
The expected return is usually based on historical data and is therefore not guaranteed into the future; however, it does often set reasonable expectations.<ref name="investopedia"/> Some models rely more on current data (e.g. market price).<br />
<br />
The ABW calculation requires the user to input the expected rate of return of the portfolio. ABW does not recommend a specific model for this purpose. The user is free to use whatever model of expected return they prefer. Regardless of the method, the user must be aware if the estimate is in real (inflation-adjusted) or nominal (not inflation-adjusted) terms. Examples of models that can be used include:<br />
<br />
===Models based on historical returns===<br />
<br />
This model uses a fixed value equal to the long-term weighted average of historical results. The weights are the same as the components of the portfolio's asset allocation, applied to historical averages of each market segment of interest. <br />
<br />
For example, the Credit Suisse Global Investment Returns Yearbook provides 120 years of data on stocks, bonds, bills, inflation and currency for 23 national markets and for the world as a whole<ref>[https://www.credit-suisse.com/about-us-news/en/articles/media-releases/credit-suisse-global-investment-returns-yearbook-2020-202002.html Credit Suisse Global Investment Returns Yearbook] - 2020 edition</ref>. As a rule of thumb, in real (inflation-adjusted) terms, stocks returned approximately 5% worldwide and bonds returned approximately 2%. If one's portfolio uses a 60/40 asset allocation, then the expected return would be 5% x 60% + 2% x 40% = 3.8%.<br />
<br />
===Models based on current yields===<br />
<br />
This model uses a value computed on a periodic basis (e.g. annual) derived from recent yields metrics. Such variable model historically displayed useful smoothing properties when used in the context of an amortization based withdrawal method, as illustrated in [[#Update_and_adapt|scenario 2 above]]. <br />
<br />
For stocks, the earnings yield E/P (the inverse of a price to earnings ratio P/E) can be used. Given earnings volatility, it is typically preferred to average earnings over a longer time period than just one year. The inverse of the [[P/E#Shiller PE10|Shiller PE10 ratio]] (aka CAPE) for a given stock market gives an earnings yield that averages earnings over the last 10 years. For the US, [https://www.multpl.com/shiller-pe multpl.com] provides the latest CAPE. For international markets, [https://www.starcapital.de/en/research/stock-market-valuation/ Star Capital] provides a monthly update. Stocks earning yields are real (inflation-adjusted) values.<br />
<br />
For bonds, the [[SEC Yield]] can be used. Yields for regular bonds are nominal values and need to be adjusted for expected inflation (e.g. the US Federal Reserve 2% target) to obtain a real value. For [[TIPS]], the SEC Yield is a real value. As bonds yields tend to provide short to mid term expected returns (e.g. a decade at most), it might be beneficial to compute the average of historical returns and current yields.<br />
<br />
===Models based on experts estimates===<br />
<br />
Multiple well-known expert sources provide expected returns for various market segments, while regularly updating corresponding models. Care should be exercised about the exact nature of such estimates (e.g. real vs. nominal, mid-term vs. long-term, etc.)<br />
<br />
As an example, [https://institutional.vanguard.com/VGApp/iip/site/institutional/researchcommentary/article/InvResVEMO2021 Vanguard] and [https://interactive.researchaffiliates.com/asset-allocation#!/?category=Multi-Country&currency=USD&group=all&model=ERYPG&scale=LINEAR&selected=32&terms=REAL&type=Equities Research Affiliates] are often cited as credible sources.<br />
<br />
==Extra income and expenses==<br />
<br />
Besides their savings portfolio, retirees may have other sources of present or future income such as social security, pensions, annuities, rental income, part-time wages and lump sum payouts ("extra income"). Retirees may also plan for exceptional expenses such as college tuition, a lingering home mortgage or long-term care expenses that may require funds beyond what is provided by regular budgeting ("extra expenses"). Such future extra income and expenses can be amortized by computing the present value of such future sums (see Wiki article on calculating present value by discounting future cash flows: [[Comparing_investments#Present_value|Comparing Investments]]) and converting in an additional series of payments, beyond the regular payment derived from the savings portfolio's balance. It is strongly recommended to perform such computations in real (inflation-adjusted) terms. Funding such additional payments in the short-term can be achieved in different ways, e.g. structuring financial assets according to the retiree's personal risks/rewards goals. ABW is neutral and does not take a position on how best to do it. Below are some of the strategies which can be used:<br />
<br />
===Separate sub-portfolio focused approach===<br />
<br />
The retiree can choose to keep funds for some or all of the extra income and expenses outside the regular amortization process. They can allocate extra income and budget for extra expenses, separate from the ABW calculation. This is effectively a partitioned portfolio approach where extra income and expenses are being handled in a separate safe sub-portfolio.<br />
<br />
A retiree formally pursuing the separate portfolio approach described [[User:Willthrill81/Amortization_based_withdrawal#Fixed_asset_allocation_with_sub-portfolios|earlier]] may find it convenient to use conservative estimates of social security and pensions to fund the safe sub-portfolios. For more complex cases, sizing the sub-portfolio can be achieved by a present value computation of future extra income and expenses (e.g. when using a bonds ladder, use the bonds interest rate to discount future income/expenses). The income streams are typically duration matched. Gaps remaining can be filled with duration matched bonds. Depending on the asset allocation, there may be little to no rebalancing needed in safe sub-portfolios.<br />
<br />
===Savings portfolio focused approach===<br />
<br />
The retiree funds the additional payments through additional withdrawals from the savings portfolio, while maintaining a fixed asset allocation on the savings portfolio. The discounting and amortization rate used should then be the savings portfolio's expected rate of return. Care should be exercised about the additional burden on one's savings portfolio and possible consequences of market crises before steady future income (e.g. SS/Pensions) materializes.<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using the portfolio's expected rate of return <ref>[https://www.kitces.com/blog/net-present-value-discount-rate-formula-retirement-plan-pension-lump-sum-or-social-security-breakeven/ Choosing An Appropriate Discount Rate For Retirement Planning Strategies] Michael Kitces, July 2017</ref>. Calculate amortized additional withdrawals based on such present value, in the same manner as the savings portfolio balance is amortized. Such computation is independent from the portfolio's rebalancing procedure and doesn't change the expected return computation. More information on this approach is available here: [https://www.bogleheads.org/blog/2019/02/01/early-retirement-and-time-value-of-money/ Early Retirement and Time Value of Money], a blog article which comes with a [http://bit.ly/2WuNmvf companion spreadsheet].<br />
<br />
===Total portfolio focused approach===<br />
<br />
The retiree adds the present value of safe extra net income (extra income minus extra expenses) to the savings portfolio to arrive at the value of the total portfolio. Asset allocation and withdrawal calculations are done on the total portfolio, counting the value of the safe extra net income as a bond. When the withdrawal scheduled for a given year exceeds the extra net income for that year, the difference is withdrawn from the savings portfolio. Conversely, when the withdrawal scheduled for a given year is less than the extra net income for that year, the difference is contributed to the savings portfolio.<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using bond interest rates. Add this value to the savings portfolio for all calculations, counting it as a bond. Include it when calculating withdrawals. Include it when calculating the asset allocation of the total portfolio (for rebalancing) and the expected return of the total portfolio (to enter into the amortized payment computation). More information on this approach is available here: [[User:Ben_Mathew/Total_portfolio_allocation_and_withdrawal|Total portfolio allocation and withdrawal]].<br />
<br />
==ABW calculator==<br />
<br />
===Basic calculator===<br />
<br />
The Excel spreadsheet to calculate withdrawals in on Google Drive: [https://drive.google.com/file/d/1XOnBaUspLX_oaM2rquTPmLj5AKOm6yxV/view?usp=sharing ABW Calculator]<br />
<br />
[[User:Ben Mathew/Formulas for Amortization Based Withdrawal (ABW)]] describes the formulas used in the calculator.<br />
<br />
===Advanced calculators===<br />
<br />
These calculators expand the basic functionality to include other considerations.<br />
<br />
An Excel spreadsheet that incorporates extra income and expenses using the "total portfolio focused approach" is available on Google Drive: [https://drive.google.com/file/d/1n4eGYbejArntB6IvuhcSycyh41bxaGbd/view?usp=sharing Total portfolio allocation and withdrawal]. <br />
<br />
A Google Sheets spreadsheet that incorporates extra income and expenses using the "savings portfolio focused approach" is available here (please make a copy): [http://bit.ly/2WuNmvf Amortized Spending Budget - Savings Portfolio Approach]. This spreadsheet also provides various backtesting capabilities.<br />
<br />
==Support==<br />
On-going discussion and support is in {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}.<br />
<br />
==See also==<br />
*[[Comparing investments]] - Tutorial on ''Time Value of Money'' equations<br />
*[https://howmuchcaniaffordtospendinretirement.blogspot.com/ How Much Can I Afford to Spend in Retirement] - Blog and spreadsheets from Ken Steiner (actuarial approach for determining reasonable spending budgets)<br />
<br />
==References==<br />
{{Reflist}}</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Amortization_based_withdrawal&diff=70867
Amortization based withdrawal
2020-12-20T20:35:22Z
<p>Siamond: /* Models based on current yields */ Fixed anchor link</p>
<hr />
<div>{{Under construction| comment = Comments are being solicited in this {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}}}<br />
'''Amortization based withdrawal (ABW)''' uses amortization techniques to calculate portfolio withdrawals during retirement.<br />
==Amortization==<br />
<br />
===Understanding amortization===<br />
<br />
Amortization is the process of converting the value of a lump sum into a series of payments over time. Most people encounter it when they take out a mortgage or car loan. Amortization is used to calculate the monthly payment required to pay back the loan. The value of the monthly payments has to be made equal to the value of the initial loan.<br />
<br />
If the interest rate is zero, amortization is just simple division: If $100,000 has to be paid back over 10 years, then the payment is $100,000 ÷ 10 = $10,000 per year.<br />
<br />
But if the interest rate is positive, as is usually the case, then the payment in the above example would have to be more than $10,000 per year. That's because $10,000 in the future is worth less than $10,000 today. This is referred to as the time value of money. If the interest is 5% per year, then $10,000 today is worth:<br />
<br />
* <math>$10,000*1.05^1=$10,500</math> one year from now<br />
* <math>$10,000*1.05^2=$11,025</math> two years from now<br />
<br />
and so on. We will have to adjust for the differences in value. The amortization formula makes the necessary adjustments and tells us that if the interest rate is 5% per year, then the payments will have to be $12,950 per year for the next ten years for the total value of the payments to be equal in value to the $100,000 that was borrowed today.<br />
<br />
==Amortization based withdrawal==<br />
<br />
To calculate portfolio withdrawals, enter the following inputs in the ABW calculator ([[#ABW calculator|below]]):<br />
<br />
* <math>P=</math> current portfolio value<br />
* <math>n=</math> number of years over which withdrawals are to be spread out<br />
* <math>r=</math> expected return of the portfolio.<br />
<br />
===Example===<br />
<br />
A 65 year old retiree with a $1 million portfolio expected to earn 3% per year and seeking to spread out withdrawals over 36 years (ages 65 to 100), would enter <math>P=$1,000,000, n=36, r=3%</math>. The amortization calculator says that this retiree can withdraw $44,470 per year. This means that if the portfolio actual rate of return remains constant at 3% per year and the retiree withdraws $44,470 every year, then the portfolio will be fully depleted after 36 years.<br />
<br />
===Real vs nominal rate of return===<br />
<br />
If a real (inflation adjusted) rate of return is used, the withdrawal strategy becomes automatically adjusted for inflation. In the above example, if the real rate of return is 3%, the retiree will be able to take out $44,470 (inflation adjusted) each year. If instead, the retiree enters a nominal interest rate of 5%, the calculator says that they can take out $60,434 per year. But that's in nominal dollars, so real consumption will decline each year by the inflation rate. In practice, it is strongly recommended to use a real rate of return.<br />
<br />
===Update and adapt===<br />
<br />
Withdrawals are recalculated each year with updated information about portfolio value, expected rate of return, and number of years left. This allows withdrawals to continually adapt to new information and mitigates the impact of past incorrect assumptions. Amortization spreads the course correction required across all remaining years, thereby minimizing the impact on any one year.<br />
<br />
====Example====<br />
<br />
Consider what happens in our earlier example if, instead of gaining 3% as expected, the portfolio actually loses 10%. The shortfall relative to expectations is <math>(1-.10)/(1+.03)-1=-12.6%</math>. Our retiree had expected to start age 66 with $984,196 in the portfolio. Instead, the portfolio contains only $859,977, which is 12.6% less. Consider what happens in the following two scenarios:<br />
<br />
=====Scenario 1: Expected return stays the same=====<br />
Suppose that the retiree believes that this market drop has not impacted future expected returns, which in the retiree's opinion, remains at 3%. The retiree enters the new reduced portfolio value, <math>P=$859,977</math>, number of years remaining <math>n=35</math>, and expected real return <math>r=3%</math>. The withdrawal is now reduced to $38,857 per year. That is a 12.6% reduction relative to the previously planned withdrawal of $44,470. So the 12.6% portfolio loss is being matched by a 12.6% spending cut across all remaining years.<br />
<br />
=====Scenario 2: Expected return increases=====<br />
If the market drop was due to a pure valuation change and the underlying earnings of the portfolio are not impacted, then the retiree might expect a higher rate of return going forward.<br />
<br />
If expected return is based on an earnings yield model (e.g. 1/CAPE) for stocks and yield to maturity for bonds, a 12.6% reduction in valuation will result in a higher expected real return of <math>.03/(1-.126)=3.43%</math>. With the higher expected return, the withdrawal becomes $41,181. That is a reduction of only 7.4% relative to the original plan of $44,470. A 12.6% reduction in the portfolio led to only a 7.4% reduction in income, because the higher expected return partially offset the loss in portfolio value.<br />
<br />
So to the extent that market volatility is caused by valuation changes and gets incorporated into expected returns, withdrawals from the portfolio will be less volatile than the portfolio itself.<br />
<br />
==Adding a terminal balance==<br />
<br />
Instead of fully depleting the portfolio, the amortization can be modified to leave behind a terminal balance. This could be used to fund end of life care or a bequest, or it could simply serve as a general financial cushion. <br />
<br />
In the ABW calculator, enter:<br />
* <math>B=</math> terminal balance<br />
<br />
===Example===<br />
<br />
The 65 year old retiree in the earlier example wants to have $200,000 left at the end for a bequest. Enter <math>B=$200,000</math> in the calculator to get a withdrawal of $41,401 per year. If the actual rate of return matches expectations, then after withdrawing $41,401 for 36 years (ages 65 to 100), the retiree will have $200,000 remaining in the portfolio at the end of age 100.<br />
<br />
==Rising or falling withdrawal schedules==<br />
<br />
Instead of aiming at a constant withdrawal schedule, some retirees may prefer to aim at a rising or falling withdrawal schedule. Retirees worried about incurring unexpected expenses or generally running out of money in later years may want to use a rising withdrawal schedule - take less early so they can have more later. Those wanting to fund an active early retirement may want to use a declining withdrawal schedule - take more early but have less later. (Note the similarity with savings. This can be viewed as a decision about how much to save in the early retirement years in order to fund late retirement consumption.)<br />
<br />
In the ABW calculator, enter:<br />
* <math>g=</math> rate of growth of the withdrawal schedule<br />
<br />
<math>g>0</math> generates a rising withdrawal schedule, <math>g<0</math> generates a declining withdrawal schedule, and <math>g=0</math> generates a constant withdrawal schedule.<br />
<br />
===Example===<br />
<br />
If the 65 year old retiree in the earlier example wants withdrawals to grow at 1% per year, set <math>g=1%</math> to get a withdrawal of $38,349. Withdrawals are scheduled to grow 1% per year, rising to $54,325 at age 100.<br />
<br />
If instead the retiree wishes to spend more in early retirement and wants withdrawals to fall by 1% per year, set <math>g=-1%</math> to get a withdrawal of $51,118. Withdrawals are scheduled to fall 1% per year, declining to $35,959 at age 100.<br />
<br />
==Asset allocation==<br />
<br />
===Fixed asset allocation===<br />
<br />
The amortization formula assumes an expected rate of return on the portfolio which stays consistent over the retirement period. This is easier to justify if the retiree plans to maintain a fixed asset allocation (AA). If instead the retiree is planning to change the AA over time (e.g. glide down from 60/40 to 30/70 over the course of the retirement), then the expected return will display more variations over time, skewing the amortization computation. The calculator provided here is not designed for such case. Entering the average expected return in the calculator may provide a rough estimate, but due to the potential for significant errors, more precise modeling is recommended.<br />
<br />
===Fixed asset allocation with sub-portfolios===<br />
<br />
The portfolio can be divided into multiple sub-portfolios and a different fixed allocation applied to each sub-portfolio.<br />
<br />
Suppose the retiree is more risk averse over certain categories of consumption (e.g. food and housing), and less risk averse over other categories (e.g. vacations). The portfolio can be subdivided into a safer portfolio to fund food and housing and a riskier portfolio to fund vacations. The safe portfolio would get a safe fixed AA like 30/70, and the riskier portfolio would get a riskier fixed AA like 80/20. Multiple sub-portfolios could be created to fund different consumption goals, each with a different AA that matches the risk-reward considerations for that goal. Withdrawals would be calculated separately for each sub-portfolio.<br />
<br />
An example of a strategy that uses sub-portfolios is the Liability Matched Portfolio (LMP) strategy. The portfolio is divided into a "liability matched portfolio" and a "risk portfolio". The liability matched portfolio has an AA of 0/100 and is used to fund non-negotiable consumption. The risk portfolio is given a riskier AA and is used to fund discretionary "nice to have" consumption.<br />
<br />
==Estimating the expected return==<br />
<br />
The expected return is the profit or loss that an investor anticipates on an investment that has known historical rates of return. It is calculated by multiplying potential outcomes by the chances of them occurring and then totaling these results. The expected return is usually based on historical data and is therefore not guaranteed into the future; however, it does often set reasonable expectations.<ref name="investopedia">[https://www.investopedia.com/terms/e/expectedreturn.asp Expected Return] - Investopedia</ref><br />
<br />
The expected return [...] can be expanded to analyze a portfolio containing many investments. If the expected return for each investment is known, the portfolio's overall expected return is a weighted average of the expected returns of its components.<ref name="investopedia" /><br />
<br />
The ABW calculation requires the user to input the expected rate of return of the portfolio. ABW does not recommend a specific model for this purpose. The user is free to use whatever model of expected return they prefer. Regardless of the method, the user must be aware if the estimate is in real (inflation-adjusted) or nominal (not inflation-adjusted) terms. Examples of models that can be used include:<br />
<br />
===Models based on historical returns===<br />
<br />
This model uses a fixed value equal to the long-term weighted average of historical results. The weights are the same as the components of the portfolio's asset allocation, applied to historical averages of each market segment of interest. <br />
<br />
For example, the Credit Suisse Global Investment Returns Yearbook provides 120 years of data on stocks, bonds, bills, inflation and currency for 23 national markets and for the world as a whole<ref>[https://www.credit-suisse.com/about-us-news/en/articles/media-releases/credit-suisse-global-investment-returns-yearbook-2020-202002.html Credit Suisse Global Investment Returns Yearbook] - 2020 edition</ref>. In real (inflation-adjusted) terms, stocks returned approximately 5% worldwide and bonds returned approximately 2%. If one's portfolio uses a 60/40 asset allocation, then the expected return would be 5% x 60% + 2% x 40% = 3.8%.<br />
<br />
===Models based on current yields===<br />
<br />
This model uses a value computed on a periodic basis (e.g. annual) derived from recent yields metrics. Such variable model historically displayed useful smoothing properties when used in the context of an amortization based withdrawal method, as illustrated in [[#Update_and_adapt|scenario 2 above]]. <br />
<br />
For stocks, the earnings yield E/P (the inverse of a price to earnings ratio P/E) can be used. Given earnings volatility, it is typically preferred to average earnings over a longer time period than just one year. The inverse of the [[P/E#Shiller PE10|Shiller PE10 ratio]] (aka CAPE) for a given stock market gives an earnings yield that averages earnings over the last 10 years. For the US, [https://www.multpl.com/shiller-pe multpl.com] provides the latest CAPE. For international markets, [https://www.starcapital.de/en/research/stock-market-valuation/ Star Capital] provides a monthly update. Stocks earning yields are real (inflation-adjusted) values.<br />
<br />
For bonds, the [[SEC Yield]] can be used. Yields for regular bonds are nominal values and need to be adjusted for expected inflation (e.g. the US Federal Reserve 2% target) to obtain a real value. For [[TIPS]], the SEC Yield is a real value. As bonds yields tend to provide short to mid term expected returns (e.g. a decade at most), it might be beneficial to compute the average of historical returns and current yields.<br />
<br />
===Models based on experts estimates===<br />
<br />
Multiple well-known expert sources provide expected returns for various market segments, while regularly updating corresponding models. Care should be exercised about the exact nature of such estimates (e.g. real vs. nominal, mid-term vs. long-term, etc.)<br />
<br />
As an example, [https://institutional.vanguard.com/VGApp/iip/site/institutional/researchcommentary/article/InvResVEMO2021 Vanguard] and [https://interactive.researchaffiliates.com/asset-allocation#!/?category=Multi-Country&currency=USD&group=all&model=ERYPG&scale=LINEAR&selected=32&terms=REAL&type=Equities Research Affiliates] are often cited as credible sources.<br />
<br />
==Extra income and expenses==<br />
<br />
Besides their savings portfolio, retirees may have other sources of present or future income such as social security, pensions, annuities, rental income, part-time wages and lump sum payouts ("extra income"). Retirees may also plan for exceptional expenses such as college tuition, a lingering home mortgage or long-term care expenses that may require funds beyond what is provided by regular budgeting ("extra expenses"). Such future extra income and expenses can be amortized by computing the present value of such future sums (see Wiki article on calculating present value by discounting future cash flows: [[Comparing_investments#Present_value|Comparing Investments]]) and converting in an additional series of payments, beyond the regular payment derived from the savings portfolio's balance. It is strongly recommended to perform such computations in real (inflation-adjusted) terms. Funding such additional payments in the short-term can be achieved in different ways, e.g. structuring financial assets according to the retiree's personal risks/rewards goals. ABW is neutral and does not take a position on how best to do it. Below are some of the strategies which can be used:<br />
<br />
===Separate sub-portfolio focused approach===<br />
<br />
The retiree can choose to keep funds for some or all of the extra income and expenses outside the regular amortization process. They can allocate extra income and budget for extra expenses, separate from the ABW calculation. This is effectively a partitioned portfolio approach where extra income and expenses are being handled in a separate safe sub-portfolio.<br />
<br />
A retiree formally pursuing the separate portfolio approach described [[User:Willthrill81/Amortization_based_withdrawal#Fixed_asset_allocation_with_sub-portfolios|earlier]] may find it convenient to use conservative estimates of social security and pensions to fund the safe sub-portfolios. For more complex cases, sizing the sub-portfolio can be achieved by a present value computation of future extra income and expenses (e.g. when using a bonds ladder, use the bonds interest rate to discount future income/expenses). The income streams are typically duration matched. Gaps remaining can be filled with duration matched bonds. Depending on the asset allocation, there may be little to no rebalancing needed in safe sub-portfolios.<br />
<br />
===Savings portfolio focused approach===<br />
<br />
The retiree funds the additional payments through additional withdrawals from the savings portfolio, while maintaining a fixed asset allocation on the savings portfolio. The discounting and amortization rate used should then be the savings portfolio's expected rate of return. Care should be exercised about the additional burden on one's savings portfolio and possible consequences of market crises before steady future income (e.g. SS/Pensions) materializes.<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using the portfolio's expected rate of return <ref>[https://www.kitces.com/blog/net-present-value-discount-rate-formula-retirement-plan-pension-lump-sum-or-social-security-breakeven/ Choosing An Appropriate Discount Rate For Retirement Planning Strategies] Michael Kitces, July 2017</ref>. Calculate amortized additional withdrawals based on such present value, in the same manner as the savings portfolio balance is amortized. Such computation is independent from the portfolio's rebalancing procedure and doesn't change the expected return computation. More information on this approach is available here: [https://www.bogleheads.org/blog/2019/02/01/early-retirement-and-time-value-of-money/ Early Retirement and Time Value of Money], a blog article which comes with a [http://bit.ly/2WuNmvf companion spreadsheet].<br />
<br />
===Total portfolio focused approach===<br />
<br />
The retiree adds the present value of safe extra net income (extra income minus extra expenses) to the savings portfolio to arrive at the value of the total portfolio. Asset allocation and withdrawal calculations are done on the total portfolio, counting the value of the safe extra net income as a bond. When the withdrawal scheduled for a given year exceeds the extra net income for that year, the difference is withdrawn from the savings portfolio. Conversely, when the withdrawal scheduled for a given year is less than the extra net income for that year, the difference is contributed to the savings portfolio.<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using bond interest rates. Add this value to the savings portfolio for all calculations, counting it as a bond. Include it when calculating withdrawals. Include it when calculating the asset allocation of the total portfolio (for rebalancing) and the expected return of the total portfolio (to enter into the amortized payment computation). More information on this approach is available here: [[User:Ben_Mathew/Total_portfolio_allocation_and_withdrawal|Total portfolio allocation and withdrawal]].<br />
<br />
==ABW calculator==<br />
<br />
===Basic calculator===<br />
<br />
The Excel spreadsheet to calculate withdrawals in on Google Drive: [https://drive.google.com/file/d/1XOnBaUspLX_oaM2rquTPmLj5AKOm6yxV/view?usp=sharing ABW Calculator]<br />
<br />
[[User:Ben Mathew/Formulas for Amortization Based Withdrawal (ABW)]] describes the formulas used in the calculator.<br />
<br />
===Advanced calculators===<br />
<br />
These calculators expand the basic functionality to include other considerations.<br />
<br />
An Excel spreadsheet that incorporates extra income and expenses using the "total portfolio focused approach" is available on Google Drive: [https://drive.google.com/file/d/1oSxquKLlGtYociWUy19nbStQnYpcuey0/view?usp=sharing Total portfolio allocation and withdrawal]. <br />
<br />
A Google Sheets spreadsheet that incorporates extra income and expenses using the "savings portfolio focused approach" is available here (please make a copy): [http://bit.ly/2WuNmvf Amortized Spending Budget - Savings Portfolio Approach]. This spreadsheet also provides various backtesting capabilities.<br />
<br />
==Support==<br />
On-going discussion and support is in {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}.<br />
<br />
==See also==<br />
*[[Comparing investments]] - Tutorial on ''Time Value of Money'' equations<br />
*[https://howmuchcaniaffordtospendinretirement.blogspot.com/ How Much Can I Afford to Spend in Retirement] - Blog and spreadsheets from Ken Steiner (actuarial approach for determining reasonable spending budgets)<br />
<br />
==References==<br />
{{Reflist}}</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Amortization_based_withdrawal&diff=70862
Amortization based withdrawal
2020-12-19T17:51:29Z
<p>Siamond: /* Models based on current yields */ Adopted Ben's rewording</p>
<hr />
<div>{{Under construction| comment = Comments are being solicited in this {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}}}<br />
'''Amortization based withdrawal (ABW)''' uses amortization techniques to calculate portfolio withdrawals during retirement. Examples of withdrawals that use amortization include [[Variable percentage withdrawal | Variable Percentage Withdrawal]] (VPW) and the [[Required Minimum Distribution]] (RMD) rules for traditional retirement accounts.<br />
<br />
==Amortization==<br />
<br />
===Understanding amortization===<br />
<br />
Amortization is the process of converting the value of a lump sum into a series of payments over time. Most people encounter it when they take out a mortgage or car loan. Amortization is used to calculate the monthly payment required to pay back the loan. The value of the monthly payments has to be made equal to the value of the initial loan.<br />
<br />
If the interest rate is zero, amortization is just simple division: If $100,000 has to be paid back over 10 years, then the payment is $100,000 ÷ 10 = $10,000 per year.<br />
<br />
But if the interest rate is positive, as is usually the case, then the payment in the above example would have to be more than $10,000 per year. That's because $10,000 in the future is worth less than $10,000 today. This is referred to as the time value of money. If the interest is 5% per year, then $10,000 today is worth:<br />
<br />
* <math>$10,000*1.05^1=$10,500</math> one year from now<br />
* <math>$10,000*1.05^2=$11,025</math> two years from now<br />
<br />
and so on. We will have to adjust for the differences in value. The amortization formula makes the necessary adjustments and tells us that if the interest rate is 5% per year, then the payments will have to be $12,950 per year for the next ten years for the total value of the payments to be equal in value to the $100,000 that was borrowed today.<br />
<br />
==Amortization based withdrawal==<br />
<br />
To calculate portfolio withdrawals, enter the following inputs in the ABW calculator ([[#ABW calculator|below]]):<br />
<br />
* <math>P=</math> current portfolio value<br />
* <math>n=</math> number of years over which withdrawals are to be spread out<br />
* <math>r=</math> expected return of the portfolio.<br />
<br />
===Example===<br />
<br />
A 65 year old retiree with a $1 million portfolio expected to earn 3% per year and seeking to spread out withdrawals over 36 years (ages 65 to 100), would enter <math>P=$1,000,000, n=36, r=3%</math>. The amortization calculator says that this retiree can withdraw $44,470 per year. This means that if the portfolio actual rate of return remains constant at 3% per year and the retiree withdraws $44,470 every year, then the portfolio will be fully depleted after 36 years.<br />
<br />
===Real vs nominal rate of return===<br />
<br />
If a real (inflation adjusted) rate of return is used, the withdrawal strategy becomes automatically adjusted for inflation. In the above example, if the real rate of return is 3%, the retiree will be able to take out $44,470 (inflation adjusted) each year. If instead, the retiree enters a nominal interest rate of 5%, the calculator says that they can take out $60,434 per year. But that's in nominal dollars, so real consumption will decline each year by the inflation rate. In practice, it is strongly recommended to use a real rate of return.<br />
<br />
===Update and adapt===<br />
<br />
Withdrawals are recalculated each year with updated information about portfolio value, expected rate of return, and number of years left. This allows withdrawals to continually adapt to new information and mitigates the impact of past incorrect assumptions. Amortization spreads the course correction required across all remaining years, thereby minimizing the impact on any one year.<br />
<br />
====Example====<br />
<br />
Consider what happens in our earlier example if, instead of gaining 3% as expected, the portfolio actually loses 10%. The shortfall relative to expectations is <math>(1-.10)/(1+.03)-1=-12.6%</math>. Our retiree had expected to start age 66 with $984,196 in the portfolio. Instead, the portfolio contains only $859,977, which is 12.6% less. Consider what happens in the following two scenarios:<br />
<br />
=====Scenario 1: Expected return stays the same=====<br />
Suppose that the retiree believes that this market drop has not impacted future expected returns, which in the retiree's opinion, remains at 3%. The retiree enters the new reduced portfolio value, <math>P=$859,977</math>, number of years remaining <math>n=35</math>, and expected real return <math>r=3%</math>. The withdrawal is now reduced to $38,857 per year. That is a 12.6% reduction relative to the previously planned withdrawal of $44,470. So the 12.6% portfolio loss is being matched by a 12.6% spending cut across all remaining years.<br />
<br />
=====Scenario 2: Expected return increases=====<br />
If the market drop was due to a pure valuation change and the underlying earnings of the portfolio are not impacted, then the retiree might expect a higher rate of return going forward.<br />
<br />
If expected return is based on an earnings yield model (e.g. 1/CAPE) for stocks and yield to maturity for bonds, a 12.6% reduction in valuation will result in a higher expected real return of <math>.03/(1-.126)=3.43%</math>. With the higher expected return, the withdrawal becomes $41,181. That is a reduction of only 7.4% relative to the original plan of $44,470. A 12.6% reduction in the portfolio led to only a 7.4% reduction in income, because the higher expected return partially offset the loss in portfolio value.<br />
<br />
So to the extent that market volatility is caused by valuation changes and gets incorporated into expected returns, withdrawals from the portfolio will be less volatile than the portfolio itself.<br />
<br />
==Adding a terminal balance==<br />
<br />
Instead of fully depleting the portfolio, the amortization can be modified to leave behind a terminal balance. This could be used to fund end of life care or a bequest, or it could simply serve as a general financial cushion. <br />
<br />
In the ABW calculator, enter:<br />
* <math>B=</math> terminal balance<br />
<br />
===Example===<br />
<br />
The 65 year old retiree in the earlier example wants to have $200,000 left at the end for a bequest. Enter <math>B=$200,000</math> in the calculator to get a withdrawal of $41,401 per year. If the actual rate of return matches expectations, then after withdrawing $41,401 for 36 years (ages 65 to 100), the retiree will have $200,000 remaining in the portfolio at the end of age 100.<br />
<br />
==Rising or falling withdrawal schedules==<br />
<br />
Instead of aiming at a constant withdrawal schedule, some retirees may prefer to aim at a rising or falling withdrawal schedule. Retirees worried about incurring unexpected expenses or generally running out of money in later years may want to use a rising withdrawal schedule - take less early so they can have more later. Those wanting to fund an active early retirement may want to use a declining withdrawal schedule - take more early but have less later. (Note the similarity with savings. This can be viewed as a decision about how much to save in the early retirement years in order to fund late retirement consumption.)<br />
<br />
In the ABW calculator, enter:<br />
* <math>g=</math> rate of growth of the withdrawal schedule<br />
<br />
<math>g>0</math> generates a rising withdrawal schedule, <math>g<0</math> generates a declining withdrawal schedule, and <math>g=0</math> generates a constant withdrawal schedule.<br />
<br />
===Example===<br />
<br />
If the 65 year old retiree in the earlier example wants withdrawals to grow at 1% per year, set <math>g=1%</math> to get a withdrawal of $38,349. Withdrawals are scheduled to grow 1% per year, rising to $54,325 at age 100.<br />
<br />
If instead the retiree wishes to spend more in early retirement and wants withdrawals to fall by 1% per year, set <math>g=-1%</math> to get a withdrawal of $51,118. Withdrawals are scheduled to fall 1% per year, declining to $35,959 at age 100.<br />
<br />
==Asset allocation==<br />
<br />
===Fixed asset allocation===<br />
<br />
The amortization formula assumes an expected rate of return on the portfolio which stays consistent over the retirement period. This is easier to justify if the retiree plans to maintain a fixed asset allocation (AA). If instead the retiree is planning to change the AA over time (e.g. glide down from 60/40 to 30/70 over the course of the retirement), then the expected return will display more variations over time, skewing the amortization computation. The calculator provided here is not designed for such case. Entering the average expected return in the calculator may provide a rough estimate, but due to the potential for significant errors, more precise modeling is recommended.<br />
<br />
===Fixed asset allocation with sub-portfolios===<br />
<br />
The portfolio can be divided into multiple sub-portfolios and a different fixed allocation applied to each sub-portfolio.<br />
<br />
Suppose the retiree is more risk averse over certain categories of consumption (e.g. food and housing), and less risk averse over other categories (e.g. vacations). The portfolio can be subdivided into a safer portfolio to fund food and housing and a riskier portfolio to fund vacations. The safe portfolio would get a safe fixed AA like 30/70, and the riskier portfolio would get a riskier fixed AA like 80/20. Multiple sub-portfolios could be created to fund different consumption goals, each with a different AA that matches the risk-reward considerations for that goal. Withdrawals would be calculated separately for each sub-portfolio.<br />
<br />
An example of a strategy that uses sub-portfolios is the Liability Matched Portfolio (LMP) strategy. The portfolio is divided into a "liability matched portfolio" and a "risk portfolio". The liability matched portfolio has an AA of 0/100 and is used to fund non-negotiable consumption. The risk portfolio is given a riskier AA and is used to fund discretionary "nice to have" consumption.<br />
<br />
==Estimating the expected return==<br />
<br />
The expected return is the profit or loss that an investor anticipates on an investment that has known historical rates of return. It is calculated by multiplying potential outcomes by the chances of them occurring and then totaling these results. The expected return is usually based on historical data and is therefore not guaranteed into the future; however, it does often set reasonable expectations.<ref name="investopedia">[https://www.investopedia.com/terms/e/expectedreturn.asp Expected Return] - Investopedia</ref><br />
<br />
The expected return [...] can be expanded to analyze a portfolio containing many investments. If the expected return for each investment is known, the portfolio's overall expected return is a weighted average of the expected returns of its components.<ref name="investopedia" /><br />
<br />
The ABW calculation requires the user to input the expected rate of return of the portfolio. ABW does not recommend a specific model for this purpose. The user is free to use whatever model of expected return they prefer. Regardless of the method, the user must be aware if the estimate is in real (inflation-adjusted) or nominal (not inflation-adjusted) terms. Examples of models that can be used include:<br />
<br />
===Models based on historical returns===<br />
<br />
This model uses a fixed value equal to the long-term weighted average of historical results. The weights are the same as the components of the portfolio's asset allocation, applied to historical averages of each market segment of interest. <br />
<br />
For example, the Credit Suisse Global Investment Returns Yearbook provides 120 years of data on stocks, bonds, bills, inflation and currency for 23 national markets and for the world as a whole<ref>[https://www.credit-suisse.com/about-us-news/en/articles/media-releases/credit-suisse-global-investment-returns-yearbook-2020-202002.html Credit Suisse Global Investment Returns Yearbook] - 2020 edition</ref>. In real (inflation-adjusted) terms, stocks returned approximately 5% worldwide and bonds returned approximately 2%. If one's portfolio uses a 60/40 asset allocation, then the expected return would be 5% x 60% + 2% x 40% = 3.8%.<br />
<br />
===Models based on current yields===<br />
<br />
This model uses a value computed on a periodic basis (e.g. annual) derived from recent yields metrics. Such variable model historically displayed useful smoothing properties when used in the context of an amortization based withdrawal method, as illustrated in scenario 2 [[ABW#Update_and_adapt|above]]. <br />
<br />
For stocks, the earnings yield E/P (the inverse of a price to earnings ratio P/E) can be used. Given earnings volatility, it is typically preferred to average earnings over a longer time period than just one year. The inverse of the [[P/E#Shiller PE10|Shiller PE10 ratio]] (aka CAPE) for a given stock market gives an earnings yield that averages earnings over the last 10 years. For the US, [https://www.multpl.com/shiller-pe multpl.com] provides the latest CAPE. For international markets, [https://www.starcapital.de/en/research/stock-market-valuation/ Star Capital] provides a monthly update. Stocks earning yields are real (inflation-adjusted) values.<br />
<br />
For bonds, the [[SEC Yield]] can be used. Yields for regular bonds are nominal values and need to be adjusted for expected inflation (e.g. the US Federal Reserve 2% target) to obtain a real value. For [[TIPS]], the SEC Yield is a real value. As bonds yields tend to provide short to mid term expected returns (e.g. a decade at most), it might be beneficial to compute the average of historical returns and current yields.<br />
<br />
===Models based on experts estimates===<br />
<br />
Multiple well-known expert sources provide expected returns for various market segments, while regularly updating corresponding models. Care should be exercised about the exact nature of such estimates (e.g. real vs. nominal, mid-term vs. long-term, etc.)<br />
<br />
As an example, [https://institutional.vanguard.com/VGApp/iip/site/institutional/researchcommentary/article/InvResVEMO2021 Vanguard] and [https://interactive.researchaffiliates.com/asset-allocation#!/?category=Multi-Country&currency=USD&group=all&model=ERYPG&scale=LINEAR&selected=32&terms=REAL&type=Equities Research Affiliates] are often cited as credible sources.<br />
<br />
==Extra income and expenses==<br />
<br />
Besides their savings portfolio, retirees may have other sources of present or future income such as social security, pensions, annuities, rental income, part-time wages and lump sum payouts ("extra income"). Retirees may also plan for exceptional expenses such as college tuition, a lingering home mortgage or long-term care expenses that may require funds beyond what is provided by regular budgeting ("extra expenses"). Such future extra income and expenses can be amortized by computing the present value of such future sums (see Wiki article on calculating present value by discounting future cash flows: [[Comparing_investments#Present_value|Comparing Investments]]) and converting in an additional series of payments, beyond the regular payment derived from the savings portfolio's balance. It is strongly recommended to perform such computations in real (inflation-adjusted) terms. Funding such additional payments in the short-term can be achieved in different ways, e.g. structuring financial assets according to the retiree's personal risks/rewards goals. ABW is neutral and does not take a position on how best to do it. Below are some of the strategies which can be used:<br />
<br />
===Separate sub-portfolio focused approach===<br />
<br />
The retiree can choose to keep funds for some or all of the extra income and expenses outside the regular amortization process. They can allocate extra income and budget for extra expenses, separate from the ABW calculation. This is effectively a partitioned portfolio approach where extra income and expenses are being handled in a separate safe sub-portfolio.<br />
<br />
A retiree formally pursuing the separate portfolio approach described [[User:Willthrill81/Amortization_based_withdrawal#Fixed_asset_allocation_with_sub-portfolios|earlier]] may find it convenient to use conservative estimates of social security and pensions to fund the safe sub-portfolios. For more complex cases, sizing the sub-portfolio can be achieved by a present value computation of future extra income and expenses (e.g. when using a bonds ladder, use the bonds interest rate to discount future income/expenses). The income streams are typically duration matched. Gaps remaining can be filled with duration matched bonds. Depending on the asset allocation, there may be little to no rebalancing needed in safe sub-portfolios.<br />
<br />
===Savings portfolio focused approach===<br />
<br />
The retiree funds the additional payments through additional withdrawals from the savings portfolio, while maintaining a fixed asset allocation on the savings portfolio. The discounting and amortization rate used should then be the savings portfolio's expected rate of return. Care should be exercised about the additional burden on one's savings portfolio and possible consequences of market crises before steady future income (e.g. SS/Pensions) materializes.<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using the portfolio's expected rate of return <ref>[https://www.kitces.com/blog/net-present-value-discount-rate-formula-retirement-plan-pension-lump-sum-or-social-security-breakeven/ Choosing An Appropriate Discount Rate For Retirement Planning Strategies] Michael Kitces, July 2017</ref>. Calculate amortized additional withdrawals based on such present value, in the same manner as the savings portfolio balance is amortized. Such computation is independent from the portfolio's rebalancing procedure and doesn't change the expected return computation. More information on this approach is available here: [https://www.bogleheads.org/blog/2019/02/01/early-retirement-and-time-value-of-money/ Early Retirement and Time Value of Money], a blog article which comes with a [http://bit.ly/2WuNmvf companion spreadsheet].<br />
<br />
===Total portfolio focused approach===<br />
<br />
The retiree adds the present value of safe extra net income (extra income minus extra expenses) to the savings portfolio to arrive at the value of the total portfolio. Asset allocation and withdrawal calculations are done on the total portfolio, counting the value of the safe extra net income as a bond. When the withdrawal scheduled for a given year exceeds the extra net income for that year, the difference is withdrawn from the savings portfolio. Conversely, when the withdrawal scheduled for a given year is less than the extra net income for that year, the difference is contributed to the savings portfolio.<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using bond interest rates. Add this value to the savings portfolio for all calculations, counting it as a bond. Include it when calculating withdrawals. Include it when calculating the asset allocation of the total portfolio (for rebalancing) and the expected return of the total portfolio (to enter into the amortized payment computation). More information on this approach is available here: [[User:Ben_Mathew/Total_portfolio_allocation_and_withdrawal|Total portfolio allocation and withdrawal]].<br />
<br />
==ABW calculator==<br />
<br />
===Basic calculator===<br />
<br />
The Excel spreadsheet to calculate withdrawals in on Google Drive: [https://drive.google.com/file/d/1XOnBaUspLX_oaM2rquTPmLj5AKOm6yxV/view?usp=sharing ABW Calculator]<br />
<br />
[[User:Ben Mathew/Formulas for Amortization Based Withdrawal (ABW)]] describes the formulas used in the calculator.<br />
<br />
===Advanced calculators===<br />
<br />
These calculators expand the basic functionality to include other considerations.<br />
<br />
An Excel spreadsheet that incorporates extra income and expenses using the "total portfolio focused approach" is available on Google Drive: [https://drive.google.com/file/d/1oSxquKLlGtYociWUy19nbStQnYpcuey0/view?usp=sharing Total portfolio allocation and withdrawal]. <br />
<br />
A Google Sheets spreadsheet that incorporates extra income and expenses using the "savings portfolio focused approach" is available here (please make a copy): [http://bit.ly/2WuNmvf Amortized Spending Budget - Savings Portfolio Approach]. This spreadsheet also provides various backtesting capabilities.<br />
<br />
==Support==<br />
On-going discussion and support is in {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}.<br />
<br />
==See also==<br />
*[[Comparing investments]] - Tutorial on ''Time Value of Money'' equations<br />
*[https://howmuchcaniaffordtospendinretirement.blogspot.com/ How Much Can I Afford to Spend in Retirement] - Blog and spreadsheets from Ken Steiner (actuarial approach for determining reasonable spending budgets)<br />
<br />
==References==<br />
{{Reflist}}</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Amortization_based_withdrawal&diff=70859
Amortization based withdrawal
2020-12-19T17:02:14Z
<p>Siamond: /* Estimating the expected return */ Extended intro (portfolio weighted average + real vs nominal terms; added 'care' sentence to experts section</p>
<hr />
<div>{{Under construction| comment = Comments are being solicited in this {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}}}<br />
'''Amortization based withdrawal (ABW)''' uses amortization techniques to calculate portfolio withdrawals during retirement. Examples of withdrawals that use amortization include [[Variable percentage withdrawal | Variable Percentage Withdrawal]] (VPW) and the [[Required Minimum Distribution]] (RMD) rules for traditional retirement accounts.<br />
<br />
==Amortization==<br />
<br />
===Understanding amortization===<br />
<br />
Amortization is the process of converting the value of a lump sum into a series of payments over time. Most people encounter it when they take out a mortgage or car loan. Amortization is used to calculate the monthly payment required to pay back the loan. The value of the monthly payments has to be made equal to the value of the initial loan.<br />
<br />
If the interest rate is zero, amortization is just simple division: If $100,000 has to be paid back over 10 years, then the payment is $100,000 ÷ 10 = $10,000 per year.<br />
<br />
But if the interest rate is positive, as is usually the case, then the payment in the above example would have to be more than $10,000 per year. That's because $10,000 in the future is worth less than $10,000 today. This is referred to as the time value of money. If the interest is 5% per year, then $10,000 today is worth:<br />
<br />
* <math>$10,000*1.05^1=$10,500</math> one year from now<br />
* <math>$10,000*1.05^2=$11,025</math> two years from now<br />
<br />
and so on. We will have to adjust for the differences in value. The amortization formula makes the necessary adjustments and tells us that if the interest rate is 5% per year, then the payments will have to be $12,950 per year for the next ten years for the total value of the payments to be equal in value to the $100,000 that was borrowed today.<br />
<br />
==Amortization based withdrawal==<br />
<br />
To calculate portfolio withdrawals, enter the following inputs in the ABW calculator ([[#ABW calculator|below]]):<br />
<br />
* <math>P=</math> current portfolio value<br />
* <math>n=</math> number of years over which withdrawals are to be spread out<br />
* <math>r=</math> expected return of the portfolio.<br />
<br />
===Example===<br />
<br />
A 65 year old retiree with a $1 million portfolio expected to earn 3% per year and seeking to spread out withdrawals over 36 years (ages 65 to 100), would enter <math>P=$1,000,000, n=36, r=3%</math>. The amortization calculator says that this retiree can withdraw $44,470 per year. This means that if the portfolio actual rate of return remains constant at 3% per year and the retiree withdraws $44,470 every year, then the portfolio will be fully depleted after 36 years.<br />
<br />
===Real vs nominal rate of return===<br />
<br />
If a real (inflation adjusted) rate of return is used, the withdrawal strategy becomes automatically adjusted for inflation. In the above example, if the real rate of return is 3%, the retiree will be able to take out $44,470 (inflation adjusted) each year. If instead, the retiree enters a nominal interest rate of 5%, the calculator says that they can take out $60,434 per year. But that's in nominal dollars, so real consumption will decline each year by the inflation rate. In practice, it is strongly recommended to use a real rate of return.<br />
<br />
===Update and adapt===<br />
<br />
Withdrawals are recalculated each year with updated information about portfolio value, expected rate of return, and number of years left. This allows withdrawals to continually adapt to new information and mitigates the impact of past incorrect assumptions. Amortization spreads the course correction required across all remaining years, thereby minimizing the impact on any one year.<br />
<br />
====Example====<br />
<br />
Consider what happens in our earlier example if, instead of gaining 3% as expected, the portfolio actually loses 10%. The shortfall relative to expectations is <math>(1-.10)/(1+.03)-1=-12.6%</math>. Our retiree had expected to start age 66 with $984,196 in the portfolio. Instead, the portfolio contains only $859,977, which is 12.6% less. Consider what happens in the following two scenarios:<br />
<br />
=====Scenario 1: Expected return stays the same=====<br />
Suppose that the retiree believes that this market drop has not impacted future expected returns, which in the retiree's opinion, remains at 3%. The retiree enters the new reduced portfolio value, <math>P=$859,977</math>, number of years remaining <math>n=35</math>, and expected real return <math>r=3%</math>. The withdrawal is now reduced to $38,857 per year. That is a 12.6% reduction relative to the previously planned withdrawal of $44,470. So the 12.6% portfolio loss is being matched by a 12.6% spending cut across all remaining years.<br />
<br />
=====Scenario 2: Expected return increases=====<br />
If the market drop was due to a pure valuation change and the underlying earnings of the portfolio are not impacted, then the retiree might expect a higher rate of return going forward.<br />
<br />
If expected return is based on an earnings yield model (e.g. 1/CAPE) for stocks and yield to maturity for bonds, a 12.6% reduction in valuation will result in a higher expected real return of <math>.03/(1-.126)=3.43%</math>. With the higher expected return, the withdrawal becomes $41,181. That is a reduction of only 7.4% relative to the original plan of $44,470. A 12.6% reduction in the portfolio led to only a 7.4% reduction in income, because the higher expected return partially offset the loss in portfolio value.<br />
<br />
So to the extent that market volatility is caused by valuation changes and gets incorporated into expected returns, withdrawals from the portfolio will be less volatile than the portfolio itself.<br />
<br />
==Adding a terminal balance==<br />
<br />
Instead of fully depleting the portfolio, the amortization can be modified to leave behind a terminal balance. This could be used to fund end of life care or a bequest, or it could simply serve as a general financial cushion. <br />
<br />
In the ABW calculator, enter:<br />
* <math>B=</math> terminal balance<br />
<br />
===Example===<br />
<br />
The 65 year old retiree in the earlier example wants to have $200,000 left at the end for a bequest. Enter <math>B=$200,000</math> in the calculator to get a withdrawal of $41,401 per year. If the actual rate of return matches expectations, then after withdrawing $41,401 for 36 years (ages 65 to 100), the retiree will have $200,000 remaining in the portfolio at the end of age 100.<br />
<br />
==Rising or falling withdrawal schedules==<br />
<br />
Instead of aiming at a constant withdrawal schedule, some retirees may prefer to aim at a rising or falling withdrawal schedule. Retirees worried about incurring unexpected expenses or generally running out of money in later years may want to use a rising withdrawal schedule - take less early so they can have more later. Those wanting to fund an active early retirement may want to use a declining withdrawal schedule - take more early but have less later. (Note the similarity with savings. This can be viewed as a decision about how much to save in the early retirement years in order to fund late retirement consumption.)<br />
<br />
In the ABW calculator, enter:<br />
* <math>g=</math> rate of growth of the withdrawal schedule<br />
<br />
<math>g>0</math> generates a rising withdrawal schedule, <math>g<0</math> generates a declining withdrawal schedule, and <math>g=0</math> generates a constant withdrawal schedule.<br />
<br />
===Example===<br />
<br />
If the 65 year old retiree in the earlier example wants withdrawals to grow at 1% per year, set <math>g=1%</math> to get a withdrawal of $38,349. Withdrawals are scheduled to grow 1% per year, rising to $54,325 at age 100.<br />
<br />
If instead the retiree wishes to spend more in early retirement and wants withdrawals to fall by 1% per year, set <math>g=-1%</math> to get a withdrawal of $51,118. Withdrawals are scheduled to fall 1% per year, declining to $35,959 at age 100.<br />
<br />
==Asset allocation==<br />
<br />
===Fixed asset allocation===<br />
<br />
The amortization formula assumes an expected rate of return on the portfolio which stays consistent over the retirement period. This is easier to justify if the retiree plans to maintain a fixed asset allocation (AA). If instead the retiree is planning to change the AA over time (e.g. glide down from 60/40 to 30/70 over the course of the retirement), then the expected return will display more variations over time, skewing the amortization computation. The calculator provided here is not designed for such case. Entering the average expected return in the calculator may provide a rough estimate, but due to the potential for significant errors, more precise modeling is recommended.<br />
<br />
===Fixed asset allocation with sub-portfolios===<br />
<br />
The portfolio can be divided into multiple sub-portfolios and a different fixed allocation applied to each sub-portfolio.<br />
<br />
Suppose the retiree is more risk averse over certain categories of consumption (e.g. food and housing), and less risk averse over other categories (e.g. vacations). The portfolio can be subdivided into a safer portfolio to fund food and housing and a riskier portfolio to fund vacations. The safe portfolio would get a safe fixed AA like 30/70, and the riskier portfolio would get a riskier fixed AA like 80/20. Multiple sub-portfolios could be created to fund different consumption goals, each with a different AA that matches the risk-reward considerations for that goal. Withdrawals would be calculated separately for each sub-portfolio.<br />
<br />
An example of a strategy that uses sub-portfolios is the Liability Matched Portfolio (LMP) strategy. The portfolio is divided into a "liability matched portfolio" and a "risk portfolio". The liability matched portfolio has an AA of 0/100 and is used to fund non-negotiable consumption. The risk portfolio is given a riskier AA and is used to fund discretionary "nice to have" consumption.<br />
<br />
==Estimating the expected return==<br />
<br />
The expected return is the profit or loss that an investor anticipates on an investment that has known historical rates of return. It is calculated by multiplying potential outcomes by the chances of them occurring and then totaling these results. The expected return is usually based on historical data and is therefore not guaranteed into the future; however, it does often set reasonable expectations.<ref name="investopedia">[https://www.investopedia.com/terms/e/expectedreturn.asp Expected Return] - Investopedia</ref><br />
<br />
The expected return [...] can be expanded to analyze a portfolio containing many investments. If the expected return for each investment is known, the portfolio's overall expected return is a weighted average of the expected returns of its components.<ref name="investopedia" /><br />
<br />
The ABW calculation requires the user to input the expected rate of return of the portfolio. ABW does not recommend a specific model for this purpose. The user is free to use whatever model of expected return they prefer. Regardless of the method, the user must be aware if the estimate is in real (inflation-adjusted) or nominal (not inflation-adjusted) terms. Examples of models that can be used include:<br />
<br />
===Models based on historical returns===<br />
<br />
This model uses a fixed value equal to the long-term weighted average of historical results. The weights are the same as the components of the portfolio's asset allocation, applied to historical averages of each market segment of interest. <br />
<br />
For example, the Credit Suisse Global Investment Returns Yearbook provides 120 years of data on stocks, bonds, bills, inflation and currency for 23 national markets and for the world as a whole<ref>[https://www.credit-suisse.com/about-us-news/en/articles/media-releases/credit-suisse-global-investment-returns-yearbook-2020-202002.html Credit Suisse Global Investment Returns Yearbook] - 2020 edition</ref>. In real (inflation-adjusted) terms, stocks returned approximately 5% worldwide and bonds returned approximately 2%. If one's portfolio uses a 60/40 asset allocation, then the expected return would be 5% x 60% + 2% x 40% = 3.8%.<br />
<br />
===Models based on current yields===<br />
<br />
This model uses a value computed on a periodic basis (e.g. annual) derived from recent yields metrics. Such variable model historically displayed useful smoothing properties when used in the context of an amortization based withdrawal method, as illustrated in scenario 2 [[ABW#Update_and_adapt|above]]. <br />
<br />
For stocks, the E/P yield (the inverse of a price to earnings ratio) can be used, but given earnings volatility, it is typically preferred to use the inverse of the [[P/E#Shiller PE10|Shiller PE10 ratio]] (aka CAPE) for a given stock market. For the US, [https://www.multpl.com/shiller-pe multpl.com] provides the latest CAPE. For international markets, [https://www.starcapital.de/en/research/stock-market-valuation/ Star Capital] provides a monthly update. Stocks earning yields are real (inflation-adjusted) values.<br />
<br />
For bonds, the [[SEC Yield]] can be used. Yields for regular bonds are nominal values and need to be adjusted for expected inflation (e.g. the US Federal Reserve 2% target) to obtain a real value. For [[TIPS]], the SEC Yield is a real value. As bonds yields tend to provide short to mid term expected returns (e.g. a decade at most), it might be beneficial to compute the average of historical returns and current yields.<br />
<br />
===Models based on experts estimates===<br />
<br />
Multiple well-known expert sources provide expected returns for various market segments, while regularly updating corresponding models. Care should be exercised about the exact nature of such estimates (e.g. real vs. nominal, mid-term vs. long-term, etc.)<br />
<br />
As an example, [https://institutional.vanguard.com/VGApp/iip/site/institutional/researchcommentary/article/InvResVEMO2021 Vanguard] and [https://interactive.researchaffiliates.com/asset-allocation#!/?category=Multi-Country&currency=USD&group=all&model=ERYPG&scale=LINEAR&selected=32&terms=REAL&type=Equities Research Affiliates] are often cited as credible sources.<br />
<br />
==Extra income and expenses==<br />
<br />
Besides their savings portfolio, retirees may have other sources of present or future income such as social security, pensions, annuities, rental income, part-time wages and lump sum payouts ("extra income"). Retirees may also plan for exceptional expenses such as college tuition, a lingering home mortgage or long-term care expenses that may require funds beyond what is provided by regular budgeting ("extra expenses"). Such future extra income and expenses can be amortized by computing the present value of such future sums (see Wiki article on calculating present value by discounting future cash flows: [[Comparing_investments#Present_value|Comparing Investments]]) and converting in an additional series of payments, beyond the regular payment derived from the savings portfolio's balance. It is strongly recommended to perform such computations in real (inflation-adjusted) terms. Funding such additional payments in the short-term can be achieved in different ways, e.g. structuring financial assets according to the retiree's personal risks/rewards goals. ABW is neutral and does not take a position on how best to do it. Below are some of the strategies which can be used:<br />
<br />
===Separate sub-portfolio focused approach===<br />
<br />
The retiree can choose to keep funds for some or all of the extra income and expenses outside the regular amortization process. They can allocate extra income and budget for extra expenses, separate from the ABW calculation. This is effectively a partitioned portfolio approach where extra income and expenses are being handled in a separate safe sub-portfolio.<br />
<br />
A retiree formally pursuing the separate portfolio approach described [[User:Willthrill81/Amortization_based_withdrawal#Fixed_asset_allocation_with_sub-portfolios|earlier]] may find it convenient to use conservative estimates of social security and pensions to fund the safe sub-portfolios. For more complex cases, sizing the sub-portfolio can be achieved by a present value computation of future extra income and expenses (e.g. when using a bonds ladder, use the bonds interest rate to discount future income/expenses). The income streams are typically duration matched. Gaps remaining can be filled with duration matched bonds. Depending on the asset allocation, there may be little to no rebalancing needed in safe sub-portfolios.<br />
<br />
===Savings portfolio focused approach===<br />
<br />
The retiree funds the additional payments through additional withdrawals from the savings portfolio, while maintaining a fixed asset allocation on the savings portfolio. The discounting and amortization rate used should then be the savings portfolio's expected rate of return. Care should be exercised about the additional burden on one's savings portfolio and possible consequences of market crises before steady future income (e.g. SS/Pensions) materializes.<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using the portfolio's expected rate of return <ref>[https://www.kitces.com/blog/net-present-value-discount-rate-formula-retirement-plan-pension-lump-sum-or-social-security-breakeven/ Choosing An Appropriate Discount Rate For Retirement Planning Strategies] Michael Kitces, July 2017</ref>. Calculate amortized additional withdrawals based on such present value, in the same manner as the savings portfolio balance is amortized. Such computation is independent from the portfolio's rebalancing procedure and doesn't change the expected return computation. More information on this approach is available here: [https://www.bogleheads.org/blog/2019/02/01/early-retirement-and-time-value-of-money/ Early Retirement and Time Value of Money], a blog article which comes with a [http://bit.ly/2WuNmvf companion spreadsheet].<br />
<br />
===Total portfolio focused approach===<br />
<br />
The retiree adds the present value of safe extra net income (extra income minus extra expenses) to the savings portfolio to arrive at the value of the total portfolio. Asset allocation and withdrawal calculations are done on the total portfolio, counting the value of the safe extra net income as a bond. When the withdrawal scheduled for a given year exceeds the extra net income for that year, the difference is withdrawn from the savings portfolio. Conversely, when the withdrawal scheduled for a given year is less than the extra net income for that year, the difference is contributed to the savings portfolio.<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using bond interest rates. Add this value to the savings portfolio for all calculations, counting it as a bond. Include it when calculating withdrawals. Include it when calculating the asset allocation of the total portfolio (for rebalancing) and the expected return of the total portfolio (to enter into the amortized payment computation). More information on this approach is available here: [[User:Ben_Mathew/Total_portfolio_allocation_and_withdrawal|Total portfolio allocation and withdrawal]].<br />
<br />
==ABW calculator==<br />
<br />
===Basic calculator===<br />
<br />
The Excel spreadsheet to calculate withdrawals in on Google Drive: [https://drive.google.com/file/d/1XOnBaUspLX_oaM2rquTPmLj5AKOm6yxV/view?usp=sharing ABW Calculator]<br />
<br />
[[User:Ben Mathew/Formulas for Amortization Based Withdrawal (ABW)]] describes the formulas used in the calculator.<br />
<br />
===Advanced calculators===<br />
<br />
These calculators expand the basic functionality to include other considerations.<br />
<br />
An Excel spreadsheet that incorporates extra income and expenses using the "total portfolio focused approach" is available on Google Drive: [https://drive.google.com/file/d/1oSxquKLlGtYociWUy19nbStQnYpcuey0/view?usp=sharing Total portfolio allocation and withdrawal]. <br />
<br />
A Google Sheets spreadsheet that incorporates extra income and expenses using the "savings portfolio focused approach" is available here (please make a copy): [http://bit.ly/2WuNmvf Amortized Spending Budget - Savings Portfolio Approach]. This spreadsheet also provides various backtesting capabilities.<br />
<br />
==Support==<br />
On-going discussion and support is in {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}.<br />
<br />
==See also==<br />
*[[Comparing investments]] - Tutorial on ''Time Value of Money'' equations<br />
*[https://howmuchcaniaffordtospendinretirement.blogspot.com/ How Much Can I Afford to Spend in Retirement] - Blog and spreadsheets from Ken Steiner (actuarial approach for determining reasonable spending budgets)<br />
<br />
==References==<br />
{{Reflist}}</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Amortization_based_withdrawal&diff=70858
Amortization based withdrawal
2020-12-19T16:23:00Z
<p>Siamond: /* Models based on current yields */ Minor rewording</p>
<hr />
<div>{{Under construction| comment = Comments are being solicited in this {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}}}<br />
'''Amortization based withdrawal (ABW)''' uses amortization techniques to calculate portfolio withdrawals during retirement. Examples of withdrawals that use amortization include [[Variable percentage withdrawal | Variable Percentage Withdrawal]] (VPW) and the [[Required Minimum Distribution]] (RMD) rules for traditional retirement accounts.<br />
<br />
==Amortization==<br />
<br />
===Understanding amortization===<br />
<br />
Amortization is the process of converting the value of a lump sum into a series of payments over time. Most people encounter it when they take out a mortgage or car loan. Amortization is used to calculate the monthly payment required to pay back the loan. The value of the monthly payments has to be made equal to the value of the initial loan.<br />
<br />
If the interest rate is zero, amortization is just simple division: If $100,000 has to be paid back over 10 years, then the payment is $100,000 ÷ 10 = $10,000 per year.<br />
<br />
But if the interest rate is positive, as is usually the case, then the payment in the above example would have to be more than $10,000 per year. That's because $10,000 in the future is worth less than $10,000 today. This is referred to as the time value of money. If the interest is 5% per year, then $10,000 today is worth:<br />
<br />
* <math>$10,000*1.05^1=$10,500</math> one year from now<br />
* <math>$10,000*1.05^2=$11,025</math> two years from now<br />
<br />
and so on. We will have to adjust for the differences in value. The amortization formula makes the necessary adjustments and tells us that if the interest rate is 5% per year, then the payments will have to be $12,950 per year for the next ten years for the total value of the payments to be equal in value to the $100,000 that was borrowed today.<br />
<br />
==Amortization based withdrawal==<br />
<br />
To calculate portfolio withdrawals, enter the following inputs in the ABW calculator ([[#ABW calculator|below]]):<br />
<br />
* <math>P=</math> current portfolio value<br />
* <math>n=</math> number of years over which withdrawals are to be spread out<br />
* <math>r=</math> expected return of the portfolio.<br />
<br />
===Example===<br />
<br />
A 65 year old retiree with a $1 million portfolio expected to earn 3% per year and seeking to spread out withdrawals over 36 years (ages 65 to 100), would enter <math>P=$1,000,000, n=36, r=3%</math>. The amortization calculator says that this retiree can withdraw $44,470 per year. This means that if the portfolio actual rate of return remains constant at 3% per year and the retiree withdraws $44,470 every year, then the portfolio will be fully depleted after 36 years.<br />
<br />
===Real vs nominal rate of return===<br />
<br />
If a real (inflation adjusted) rate of return is used, the withdrawal strategy becomes automatically adjusted for inflation. In the above example, if the real rate of return is 3%, the retiree will be able to take out $44,470 (inflation adjusted) each year. If instead, the retiree enters a nominal interest rate of 5%, the calculator says that they can take out $60,434 per year. But that's in nominal dollars, so real consumption will decline each year by the inflation rate. In practice, it is strongly recommended to use a real rate of return.<br />
<br />
===Update and adapt===<br />
<br />
Withdrawals are recalculated each year with updated information about portfolio value, expected rate of return, and number of years left. This allows withdrawals to continually adapt to new information and mitigates the impact of past incorrect assumptions. Amortization spreads the course correction required across all remaining years, thereby minimizing the impact on any one year.<br />
<br />
====Example====<br />
<br />
Consider what happens in our earlier example if, instead of gaining 3% as expected, the portfolio actually loses 10%. The shortfall relative to expectations is <math>(1-.10)/(1+.03)-1=-12.6%</math>. Our retiree had expected to start age 66 with $984,196 in the portfolio. Instead, the portfolio contains only $859,977, which is 12.6% less. Consider what happens in the following two scenarios:<br />
<br />
=====Scenario 1: Expected return stays the same=====<br />
Suppose that the retiree believes that this market drop has not impacted future expected returns, which in the retiree's opinion, remains at 3%. The retiree enters the new reduced portfolio value, <math>P=$859,977</math>, number of years remaining <math>n=35</math>, and expected real return <math>r=3%</math>. The withdrawal is now reduced to $38,857 per year. That is a 12.6% reduction relative to the previously planned withdrawal of $44,470. So the 12.6% portfolio loss is being matched by a 12.6% spending cut across all remaining years.<br />
<br />
=====Scenario 2: Expected return increases=====<br />
If the market drop was due to a pure valuation change and the underlying earnings of the portfolio are not impacted, then the retiree might expect a higher rate of return going forward.<br />
<br />
If expected return is based on an earnings yield model (e.g. 1/CAPE) for stocks and yield to maturity for bonds, a 12.6% reduction in valuation will result in a higher expected real return of <math>.03/(1-.126)=3.43%</math>. With the higher expected return, the withdrawal becomes $41,181. That is a reduction of only 7.4% relative to the original plan of $44,470. A 12.6% reduction in the portfolio led to only a 7.4% reduction in income, because the higher expected return partially offset the loss in portfolio value.<br />
<br />
So to the extent that market volatility is caused by valuation changes and gets incorporated into expected returns, withdrawals from the portfolio will be less volatile than the portfolio itself.<br />
<br />
==Adding a terminal balance==<br />
<br />
Instead of fully depleting the portfolio, the amortization can be modified to leave behind a terminal balance. This could be used to fund end of life care or a bequest, or it could simply serve as a general financial cushion. <br />
<br />
In the ABW calculator, enter:<br />
* <math>B=</math> terminal balance<br />
<br />
===Example===<br />
<br />
The 65 year old retiree in the earlier example wants to have $200,000 left at the end for a bequest. Enter <math>B=$200,000</math> in the calculator to get a withdrawal of $41,401 per year. If the actual rate of return matches expectations, then after withdrawing $41,401 for 36 years (ages 65 to 100), the retiree will have $200,000 remaining in the portfolio at the end of age 100.<br />
<br />
==Rising or falling withdrawal schedules==<br />
<br />
Instead of aiming at a constant withdrawal schedule, some retirees may prefer to aim at a rising or falling withdrawal schedule. Retirees worried about incurring unexpected expenses or generally running out of money in later years may want to use a rising withdrawal schedule - take less early so they can have more later. Those wanting to fund an active early retirement may want to use a declining withdrawal schedule - take more early but have less later. (Note the similarity with savings. This can be viewed as a decision about how much to save in the early retirement years in order to fund late retirement consumption.)<br />
<br />
In the ABW calculator, enter:<br />
* <math>g=</math> rate of growth of the withdrawal schedule<br />
<br />
<math>g>0</math> generates a rising withdrawal schedule, <math>g<0</math> generates a declining withdrawal schedule, and <math>g=0</math> generates a constant withdrawal schedule.<br />
<br />
===Example===<br />
<br />
If the 65 year old retiree in the earlier example wants withdrawals to grow at 1% per year, set <math>g=1%</math> to get a withdrawal of $38,349. Withdrawals are scheduled to grow 1% per year, rising to $54,325 at age 100.<br />
<br />
If instead the retiree wishes to spend more in early retirement and wants withdrawals to fall by 1% per year, set <math>g=-1%</math> to get a withdrawal of $51,118. Withdrawals are scheduled to fall 1% per year, declining to $35,959 at age 100.<br />
<br />
==Asset allocation==<br />
<br />
===Fixed asset allocation===<br />
<br />
The amortization formula assumes an expected rate of return on the portfolio which stays consistent over the retirement period. This is easier to justify if the retiree plans to maintain a fixed asset allocation (AA). If instead the retiree is planning to change the AA over time (e.g. glide down from 60/40 to 30/70 over the course of the retirement), then the expected return will display more variations over time, skewing the amortization computation. The calculator provided here is not designed for such case. Entering the average expected return in the calculator may provide a rough estimate, but due to the potential for significant errors, more precise modeling is recommended.<br />
<br />
===Fixed asset allocation with sub-portfolios===<br />
<br />
The portfolio can be divided into multiple sub-portfolios and a different fixed allocation applied to each sub-portfolio.<br />
<br />
Suppose the retiree is more risk averse over certain categories of consumption (e.g. food and housing), and less risk averse over other categories (e.g. vacations). The portfolio can be subdivided into a safer portfolio to fund food and housing and a riskier portfolio to fund vacations. The safe portfolio would get a safe fixed AA like 30/70, and the riskier portfolio would get a riskier fixed AA like 80/20. Multiple sub-portfolios could be created to fund different consumption goals, each with a different AA that matches the risk-reward considerations for that goal. Withdrawals would be calculated separately for each sub-portfolio.<br />
<br />
An example of a strategy that uses sub-portfolios is the Liability Matched Portfolio (LMP) strategy. The portfolio is divided into a "liability matched portfolio" and a "risk portfolio". The liability matched portfolio has an AA of 0/100 and is used to fund non-negotiable consumption. The risk portfolio is given a riskier AA and is used to fund discretionary "nice to have" consumption.<br />
<br />
==Estimating the expected return==<br />
<br />
The expected return is the profit or loss that an investor anticipates on an investment that has known historical rates of return. It is calculated by multiplying potential outcomes by the chances of them occurring and then totaling these results. The expected return is usually based on historical data and is therefore not guaranteed into the future; however, it does often set reasonable expectations.<ref>[https://www.investopedia.com/terms/e/expectedreturn.asp Expected Return] - Investopedia</ref><br />
<br />
The ABW calculation requires the user to input the expected rate of return of the portfolio. ABW does not recommend a specific model for this purpose. The user is free to use whatever model of expected return they prefer. Examples of models that can be used include:<br />
<br />
===Models based on historical returns===<br />
<br />
This model uses a fixed value equal to the long-term weighted average of historical results. The weights are the same as the components of the portfolio's asset allocation, applied to historical averages of each market segment of interest. <br />
<br />
For example, the Credit Suisse Global Investment Returns Yearbook provides 120 years of data on stocks, bonds, bills, inflation and currency for 23 national markets and for the world as a whole<ref>[https://www.credit-suisse.com/about-us-news/en/articles/media-releases/credit-suisse-global-investment-returns-yearbook-2020-202002.html Credit Suisse Global Investment Returns Yearbook] - 2020 edition</ref>. In real (inflation-adjusted) terms, stocks returned approximately 5% worldwide and bonds returned approximately 2%. If one's portfolio uses a 60/40 asset allocation, then the expected return would be 5% x 60% + 2% x 40% = 3.8%.<br />
<br />
===Models based on current yields===<br />
<br />
This model uses a value computed on a periodic basis (e.g. annual) derived from recent yields metrics. Such variable model historically displayed useful smoothing properties when used in the context of an amortization based withdrawal method, as illustrated in scenario 2 [[ABW#Update_and_adapt|above]]. <br />
<br />
For stocks, the E/P yield (the inverse of a price to earnings ratio) can be used, but given earnings volatility, it is typically preferred to use the inverse of the [[P/E#Shiller PE10|Shiller PE10 ratio]] (aka CAPE) for a given stock market. For the US, [https://www.multpl.com/shiller-pe multpl.com] provides the latest CAPE. For international markets, [https://www.starcapital.de/en/research/stock-market-valuation/ Star Capital] provides a monthly update. Stocks earning yields are real (inflation-adjusted) values.<br />
<br />
For bonds, the [[SEC Yield]] can be used. Yields for regular bonds are nominal values and need to be adjusted for expected inflation (e.g. the US Federal Reserve 2% target) to obtain a real value. For [[TIPS]], the SEC Yield is a real value. As bonds yields tend to provide short to mid term expected returns (e.g. a decade at most), it might be beneficial to compute the average of historical returns and current yields.<br />
<br />
===Models based on experts estimates===<br />
<br />
Multiple well-known expert sources provide expected returns for various market segments, while regularly updating corresponding models. <br />
<br />
As an example, [https://institutional.vanguard.com/VGApp/iip/site/institutional/researchcommentary/article/InvResVEMO2021 Vanguard] and [https://interactive.researchaffiliates.com/asset-allocation#!/?category=Multi-Country&currency=USD&group=all&model=ERYPG&scale=LINEAR&selected=32&terms=REAL&type=Equities Research Affiliates] are often cited as credible sources.<br />
<br />
==Extra income and expenses==<br />
<br />
Besides their savings portfolio, retirees may have other sources of present or future income such as social security, pensions, annuities, rental income, part-time wages and lump sum payouts ("extra income"). Retirees may also plan for exceptional expenses such as college tuition, a lingering home mortgage or long-term care expenses that may require funds beyond what is provided by regular budgeting ("extra expenses"). Such future extra income and expenses can be amortized by computing the present value of such future sums (see Wiki article on calculating present value by discounting future cash flows: [[Comparing_investments#Present_value|Comparing Investments]]) and converting in an additional series of payments, beyond the regular payment derived from the savings portfolio's balance. It is strongly recommended to perform such computations in real (inflation-adjusted) terms. Funding such additional payments in the short-term can be achieved in different ways, e.g. structuring financial assets according to the retiree's personal risks/rewards goals. ABW is neutral and does not take a position on how best to do it. Below are some of the strategies which can be used:<br />
<br />
===Separate sub-portfolio focused approach===<br />
<br />
The retiree can choose to keep funds for some or all of the extra income and expenses outside the regular amortization process. They can allocate extra income and budget for extra expenses, separate from the ABW calculation. This is effectively a partitioned portfolio approach where extra income and expenses are being handled in a separate safe sub-portfolio.<br />
<br />
A retiree formally pursuing the separate portfolio approach described [[User:Willthrill81/Amortization_based_withdrawal#Fixed_asset_allocation_with_sub-portfolios|earlier]] may find it convenient to use conservative estimates of social security and pensions to fund the safe sub-portfolios. For more complex cases, sizing the sub-portfolio can be achieved by a present value computation of future extra income and expenses (e.g. when using a bonds ladder, use the bonds interest rate to discount future income/expenses). The income streams are typically duration matched. Gaps remaining can be filled with duration matched bonds. Depending on the asset allocation, there may be little to no rebalancing needed in safe sub-portfolios.<br />
<br />
===Savings portfolio focused approach===<br />
<br />
The retiree funds the additional payments through additional withdrawals from the savings portfolio, while maintaining a fixed asset allocation on the savings portfolio. The discounting and amortization rate used should then be the savings portfolio's expected rate of return. Care should be exercised about the additional burden on one's savings portfolio and possible consequences of market crises before steady future income (e.g. SS/Pensions) materializes.<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using the portfolio's expected rate of return <ref>[https://www.kitces.com/blog/net-present-value-discount-rate-formula-retirement-plan-pension-lump-sum-or-social-security-breakeven/ Choosing An Appropriate Discount Rate For Retirement Planning Strategies] Michael Kitces, July 2017</ref>. Calculate amortized additional withdrawals based on such present value, in the same manner as the savings portfolio balance is amortized. Such computation is independent from the portfolio's rebalancing procedure and doesn't change the expected return computation. More information on this approach is available here: [https://www.bogleheads.org/blog/2019/02/01/early-retirement-and-time-value-of-money/ Early Retirement and Time Value of Money], a blog article which comes with a [http://bit.ly/2WuNmvf companion spreadsheet].<br />
<br />
===Total portfolio focused approach===<br />
<br />
The retiree adds the present value of safe extra net income (extra income minus extra expenses) to the savings portfolio to arrive at the value of the total portfolio. Asset allocation and withdrawal calculations are done on the total portfolio, counting the value of the safe extra net income as a bond. When the withdrawal scheduled for a given year exceeds the extra net income for that year, the difference is withdrawn from the savings portfolio. Conversely, when the withdrawal scheduled for a given year is less than the extra net income for that year, the difference is contributed to the savings portfolio.<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using bond interest rates. Add this value to the savings portfolio for all calculations, counting it as a bond. Include it when calculating withdrawals. Include it when calculating the asset allocation of the total portfolio (for rebalancing) and the expected return of the total portfolio (to enter into the amortized payment computation). More information on this approach is available here: [[User:Ben_Mathew/Total_portfolio_allocation_and_withdrawal|Total portfolio allocation and withdrawal]].<br />
<br />
==ABW calculator==<br />
<br />
===Basic calculator===<br />
<br />
The Excel spreadsheet to calculate withdrawals in on Google Drive: [https://drive.google.com/file/d/1XOnBaUspLX_oaM2rquTPmLj5AKOm6yxV/view?usp=sharing ABW Calculator]<br />
<br />
[[User:Ben Mathew/Formulas for Amortization Based Withdrawal (ABW)]] describes the formulas used in the calculator.<br />
<br />
===Advanced calculators===<br />
<br />
These calculators expand the basic functionality to include other considerations.<br />
<br />
An Excel spreadsheet that incorporates extra income and expenses using the "total portfolio focused approach" is available on Google Drive: [https://drive.google.com/file/d/1oSxquKLlGtYociWUy19nbStQnYpcuey0/view?usp=sharing Total portfolio allocation and withdrawal]. <br />
<br />
A Google Sheets spreadsheet that incorporates extra income and expenses using the "savings portfolio focused approach" is available here (please make a copy): [http://bit.ly/2WuNmvf Amortized Spending Budget - Savings Portfolio Approach]. This spreadsheet also provides various backtesting capabilities.<br />
<br />
==Support==<br />
On-going discussion and support is in {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}.<br />
<br />
==See also==<br />
*[[Comparing investments]] - Tutorial on ''Time Value of Money'' equations<br />
*[https://howmuchcaniaffordtospendinretirement.blogspot.com/ How Much Can I Afford to Spend in Retirement] - Blog and spreadsheets from Ken Steiner (actuarial approach for determining reasonable spending budgets)<br />
<br />
==References==<br />
{{Reflist}}</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Amortization_based_withdrawal&diff=70851
Amortization based withdrawal
2020-12-18T14:54:18Z
<p>Siamond: /* Estimating the expected return */ First draft</p>
<hr />
<div>{{Under construction| comment = Comments are being solicited in this {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}}}<br />
'''Amortization based withdrawal (ABW)''' uses amortization techniques to calculate portfolio withdrawals during retirement. Examples of withdrawals that use amortization include [[Variable percentage withdrawal | Variable Percentage Withdrawal]] (VPW) and the [[Required Minimum Distribution]] (RMD) rules for traditional retirement accounts.<br />
<br />
==Amortization==<br />
<br />
===Understanding amortization===<br />
<br />
Amortization is the process of converting the value of a lump sum into a series of payments over time. Most people encounter it when they take out a mortgage or car loan. Amortization is used to calculate the monthly payment required to pay back the loan. The value of the monthly payments has to be made equal to the value of the initial loan.<br />
<br />
If the interest rate is zero, amortization is just simple division: If $100,000 has to be paid back over 10 years, then the payment is $100,000 ÷ 10 = $10,000 per year.<br />
<br />
But if the interest rate is positive, as is usually the case, then the payment in the above example would have to be more than $10,000 per year. That's because $10,000 in the future is worth less than $10,000 today. This is referred to as the time value of money. If the interest is 5% per year, then $10,000 today is worth:<br />
<br />
* <math>$10,000*1.05^1=$10,500</math> one year from now<br />
* <math>$10,000*1.05^2=$11,025</math> two years from now<br />
<br />
and so on. We will have to adjust for the differences in value. The amortization formula makes the necessary adjustments and tells us that if the interest rate is 5% per year, then the payments will have to be $12,950 per year for the next ten years for the total value of the payments to be equal in value to the $100,000 that was borrowed today.<br />
<br />
==Amortization based withdrawal==<br />
<br />
To calculate portfolio withdrawals, enter the following inputs in the ABW calculator ([[#ABW calculator|below]]):<br />
<br />
* <math>P=</math> current portfolio value<br />
* <math>n=</math> number of years over which withdrawals are to be spread out<br />
* <math>r=</math> expected return of the portfolio.<br />
<br />
===Example===<br />
<br />
A 65 year old retiree with a $1 million portfolio expected to earn 3% per year and seeking to spread out withdrawals over 36 years (ages 65 to 100), would enter <math>P=$1,000,000, n=36, r=3%</math>. The amortization calculator says that this retiree can withdraw $44,470 per year. This means that if the portfolio actual rate of return remains constant at 3% per year and the retiree withdraws $44,470 every year, then the portfolio will be fully depleted after 36 years.<br />
<br />
===Real vs nominal rate of return===<br />
<br />
If a real (inflation adjusted) rate of return is used, the withdrawal strategy becomes automatically adjusted for inflation. In the above example, if the real rate of return is 3%, the retiree will be able to take out $44,470 (inflation adjusted) each year. If instead, the retiree enters a nominal interest rate of 5%, the calculator says that they can take out $60,434 per year. But that's in nominal dollars, so real consumption will decline each year by the inflation rate. In practice, it is strongly recommended to use a real rate of return.<br />
<br />
===Update and adapt===<br />
<br />
Withdrawals are recalculated each year with updated information about portfolio value, expected rate of return, and number of years left. This allows withdrawals to continually adapt to new information and mitigates the impact of past incorrect assumptions. Amortization spreads the course correction required across all remaining years, thereby minimizing the impact on any one year.<br />
<br />
====Example====<br />
<br />
Consider what happens in our earlier example if, instead of gaining 3% as expected, the portfolio actually loses 10%. The shortfall relative to expectations is <math>(1-.10)/(1+.03)-1=-12.6%</math>. Our retiree had expected to start age 66 with $984,196 in the portfolio. Instead, the portfolio contains only $859,977, which is 12.6% less. Consider what happens in the following two scenarios:<br />
<br />
=====Scenario 1: Expected return stays the same=====<br />
Suppose that the retiree believes that this market drop has not impacted future expected returns, which in the retiree's opinion, remains at 3%. The retiree enters the new reduced portfolio value, <math>P=$859,977</math>, number of years remaining <math>n=35</math>, and expected real return <math>r=3%</math>. The withdrawal is now reduced to $38,857 per year. That is a 12.6% reduction relative to the previously planned withdrawal of $44,470. So the 12.6% portfolio loss is being matched by a 12.6% spending cut across all remaining years.<br />
<br />
=====Scenario 2: Expected return increases=====<br />
If the market drop was due to a pure valuation change and the underlying earnings of the portfolio are not impacted, then the retiree might expect a higher rate of return going forward.<br />
<br />
If expected return is based on an earnings yield model (e.g. 1/CAPE) for stocks and yield to maturity for bonds, a 12.6% reduction in valuation will result in a higher expected real return of <math>.03/(1-.126)=3.43%</math>. With the higher expected return, the withdrawal becomes $41,181. That is a reduction of only 7.4% relative to the original plan of $44,470. A 12.6% reduction in the portfolio led to only a 7.4% reduction in income, because the higher expected return partially offset the loss in portfolio value.<br />
<br />
So to the extent that market volatility is caused by valuation changes and gets incorporated into expected returns, withdrawals from the portfolio will be less volatile than the portfolio itself.<br />
<br />
==Adding a terminal balance==<br />
<br />
Instead of fully depleting the portfolio, the amortization can be modified to leave behind a terminal balance. This could be used to fund end of life care or a bequest, or it could simply serve as a general financial cushion. <br />
<br />
In the ABW calculator, enter:<br />
* <math>B=</math> terminal balance<br />
<br />
===Example===<br />
<br />
The 65 year old retiree in the earlier example wants to have $200,000 left at the end for a bequest. Enter <math>B=$200,000</math> in the calculator to get a withdrawal of $41,401 per year. If the actual rate of return matches expectations, then after withdrawing $41,401 for 36 years (ages 65 to 100), the retiree will have $200,000 remaining in the portfolio at the end of age 100.<br />
<br />
==Rising or falling withdrawal schedules==<br />
<br />
Instead of aiming at a constant withdrawal schedule, some retirees may prefer to aim at a rising or falling withdrawal schedule. Retirees worried about incurring unexpected expenses or generally running out of money in later years may want to use a rising withdrawal schedule - take less early so they can have more later. Those wanting to fund an active early retirement may want to use a declining withdrawal schedule - take more early but have less later. (Note the similarity with savings. This can be viewed as a decision about how much to save in the early retirement years in order to fund late retirement consumption.)<br />
<br />
In the ABW calculator, enter:<br />
* <math>g=</math> rate of growth of the withdrawal schedule<br />
<br />
<math>g>0</math> generates a rising withdrawal schedule, <math>g<0</math> generates a declining withdrawal schedule, and <math>g=0</math> generates a constant withdrawal schedule.<br />
<br />
===Example===<br />
<br />
If the 65 year old retiree in the earlier example wants withdrawals to grow at 1% per year, set <math>g=1%</math> to get a withdrawal of $38,349. Withdrawals are scheduled to grow 1% per year, rising to $54,325 at age 100.<br />
<br />
If instead the retiree wishes to spend more in early retirement and wants withdrawals to fall by 1% per year, set <math>g=-1%</math> to get a withdrawal of $51,118. Withdrawals are scheduled to fall 1% per year, declining to $35,959 at age 100.<br />
<br />
==Asset allocation==<br />
<br />
===Fixed asset allocation===<br />
<br />
The amortization formula assumes an expected rate of return on the portfolio which stays consistent over the retirement period. This is easier to justify if the retiree plans to maintain a fixed asset allocation (AA). If instead the retiree is planning to change the AA over time (e.g. glide down from 60/40 to 30/70 over the course of the retirement), then the expected return will display more variations over time, skewing the amortization computation. The calculator provided here is not designed for such case. Entering the average expected return in the calculator may provide a rough estimate, but due to the potential for significant errors, more precise modeling is recommended.<br />
<br />
===Fixed asset allocation with sub-portfolios===<br />
<br />
The portfolio can be divided into multiple sub-portfolios and a different fixed allocation applied to each sub-portfolio.<br />
<br />
Suppose the retiree is more risk averse over certain categories of consumption (e.g. food and housing), and less risk averse over other categories (e.g. vacations). The portfolio can be subdivided into a safer portfolio to fund food and housing and a riskier portfolio to fund vacations. The safe portfolio would get a safe fixed AA like 30/70, and the riskier portfolio would get a riskier fixed AA like 80/20. Multiple sub-portfolios could be created to fund different consumption goals, each with a different AA that matches the risk-reward considerations for that goal. Withdrawals would be calculated separately for each sub-portfolio.<br />
<br />
An example of a strategy that uses sub-portfolios is the Liability Matched Portfolio (LMP) strategy. The portfolio is divided into a "liability matched portfolio" and a "risk portfolio". The liability matched portfolio has an AA of 0/100 and is used to fund non-negotiable consumption. The risk portfolio is given a riskier AA and is used to fund discretionary "nice to have" consumption.<br />
<br />
==Estimating the expected return==<br />
<br />
The expected return is the profit or loss that an investor anticipates on an investment that has known historical rates of return. It is calculated by multiplying potential outcomes by the chances of them occurring and then totaling these results. The expected return is usually based on historical data and is therefore not guaranteed into the future; however, it does often set reasonable expectations.<ref>[https://www.investopedia.com/terms/e/expectedreturn.asp Expected Return] - Investopedia</ref><br />
<br />
The ABW calculation requires the user to input the expected rate of return of the portfolio. ABW does not recommend a specific model for this purpose. The user is free to use whatever model of expected return they prefer. Examples of models that can be used include:<br />
<br />
===Models based on historical returns===<br />
<br />
This model uses a fixed value equal to the long-term weighted average of historical results. The weights are the same as the components of the portfolio's asset allocation, applied to historical averages of each market segment of interest. <br />
<br />
For example, the Credit Suisse Global Investment Returns Yearbook provides 120 years of data on stocks, bonds, bills, inflation and currency for 23 national markets and for the world as a whole<ref>[https://www.credit-suisse.com/about-us-news/en/articles/media-releases/credit-suisse-global-investment-returns-yearbook-2020-202002.html Credit Suisse Global Investment Returns Yearbook] - 2020 edition</ref>. In real (inflation-adjusted) terms, stocks returned approximately 5% worldwide and bonds returned approximately 2%. If one's portfolio uses a 60/40 asset allocation, then the expected return would be 5% x 60% + 2% x 40% = 3.8%.<br />
<br />
===Models based on current yields===<br />
<br />
This model uses a value computed on a periodic basis (e.g. annual) derived from recent yields metrics. Such variable model historically displayed useful smoothing properties when used in the context of an amortization based withdrawal method, as illustrated in scenario 2 [[ABW#Update_and_adapt|above]]. <br />
<br />
For stocks, the Earnings Yield (the inverse of a price to earnings ratio) can be used, but given earnings volatility, it is typically preferred to use the inverse of the [[P/E#Shiller PE10|Shiller PE10 ratio]] (aka CAPE) for a given stock market. For the US, [https://www.multpl.com/shiller-pe multpl.com] provides the latest CAPE. For international markets, [https://www.starcapital.de/en/research/stock-market-valuation/ Star Capital] provides a monthly update. Stocks earning yields are real (inflation-adjusted) values.<br />
<br />
For bonds, the [[SEC Yield]] can be used. Yields for regular bonds are nominal values and need to be adjusted for expected inflation (e.g. the US Federal Reserve 2% target) to obtain a real value. For [[TIPS]], the SEC Yield is a real value. As bonds yields tend to provide short to mid term expected returns (e.g. a decade at most), it might be beneficial to compute the average of historical returns and current yields.<br />
<br />
===Models based on experts estimates===<br />
<br />
Multiple well-known expert sources provide expected returns for various market segments, while regularly updating corresponding models. <br />
<br />
As an example, [https://institutional.vanguard.com/VGApp/iip/site/institutional/researchcommentary/article/InvResVEMO2021 Vanguard] and [https://interactive.researchaffiliates.com/asset-allocation#!/?category=Multi-Country&currency=USD&group=all&model=ERYPG&scale=LINEAR&selected=32&terms=REAL&type=Equities Research Affiliates] are often cited as credible sources.<br />
<br />
==Extra income and expenses==<br />
<br />
Besides their savings portfolio, retirees may have other sources of present or future income such as social security, pensions, annuities, rental income, part-time wages and lump sum payouts ("extra income"). Retirees may also plan for exceptional expenses such as college tuition, a lingering home mortgage or long-term care expenses that may require funds beyond what is provided by regular budgeting ("extra expenses"). Such future extra income and expenses can be amortized by computing the present value of such future sums (see Wiki article on calculating present value by discounting future cash flows: [[Comparing_investments#Present_value|Comparing Investments]]) and converting in an additional series of payments, beyond the regular payment derived from the savings portfolio's balance. It is strongly recommended to perform such computations in real (inflation-adjusted) terms. Funding such additional payments in the short-term can be achieved in different ways, e.g. structuring financial assets according to the retiree's personal risks/rewards goals. ABW is neutral and does not take a position on how best to do it. Below are some of the strategies which can be used:<br />
<br />
===Separate sub-portfolio focused approach===<br />
<br />
The retiree can choose to keep funds for some or all of the extra income and expenses outside the regular amortization process. They can allocate extra income and budget for extra expenses, separate from the ABW calculation. This is effectively a partitioned portfolio approach where extra income and expenses are being handled in a separate safe sub-portfolio.<br />
<br />
A retiree formally pursuing the separate portfolio approach described [[User:Willthrill81/Amortization_based_withdrawal#Fixed_asset_allocation_with_sub-portfolios|earlier]] may find it convenient to use conservative estimates of social security and pensions to fund the safe sub-portfolios. For more complex cases, sizing the sub-portfolio can be achieved by a present value computation of future extra income and expenses (e.g. when using a bonds ladder, use the bonds interest rate to discount future income/expenses). The income streams are typically duration matched. Gaps remaining can be filled with duration matched bonds. Depending on the asset allocation, there may be little to no rebalancing needed in safe sub-portfolios.<br />
<br />
===Savings portfolio focused approach===<br />
<br />
The retiree funds the additional payments through additional withdrawals from the savings portfolio, while maintaining a fixed asset allocation on the savings portfolio. The discounting and amortization rate used should then be the savings portfolio's expected rate of return. Care should be exercised about the additional burden on one's savings portfolio and possible consequences of market crises before steady future income (e.g. SS/Pensions) materializes.<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using the portfolio's expected rate of return <ref>[https://www.kitces.com/blog/net-present-value-discount-rate-formula-retirement-plan-pension-lump-sum-or-social-security-breakeven/ Choosing An Appropriate Discount Rate For Retirement Planning Strategies] Michael Kitces, July 2017</ref>. Calculate amortized additional withdrawals based on such present value, in the same manner as the savings portfolio balance is amortized. Such computation is independent from the portfolio's rebalancing procedure and doesn't change the expected return computation. More information on this approach is available here: [https://www.bogleheads.org/blog/2019/02/01/early-retirement-and-time-value-of-money/ Early Retirement and Time Value of Money], a blog article which comes with a [http://bit.ly/2WuNmvf companion spreadsheet].<br />
<br />
===Total portfolio focused approach===<br />
<br />
The retiree adds the present value of safe extra net income (extra income minus extra expenses) to the savings portfolio to arrive at the value of the total portfolio. Asset allocation and withdrawal calculations are done on the total portfolio, counting the value of the safe extra net income as a bond. When the withdrawal scheduled for a given year exceeds the extra net income for that year, the difference is withdrawn from the savings portfolio. Conversely, when the withdrawal scheduled for a given year is less than the extra net income for that year, the difference is contributed to the savings portfolio.<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using bond interest rates. Add this value to the savings portfolio for all calculations, counting it as a bond. Include it when calculating withdrawals. Include it when calculating the asset allocation of the total portfolio (for rebalancing) and the expected return of the total portfolio (to enter into the amortized payment computation). More information on this approach is available here: [[User:Ben_Mathew/Total_portfolio_allocation_and_withdrawal|Total portfolio allocation and withdrawal]].<br />
<br />
==ABW calculator==<br />
<br />
===Basic calculator===<br />
<br />
The Excel spreadsheet to calculate withdrawals in on Google Drive: [https://drive.google.com/file/d/1XOnBaUspLX_oaM2rquTPmLj5AKOm6yxV/view?usp=sharing ABW Calculator]<br />
<br />
[[User:Ben Mathew/Formulas for Amortization Based Withdrawal (ABW)]] describes the formulas used in the calculator.<br />
<br />
===Advanced calculators===<br />
<br />
These calculators expand the basic functionality to include other considerations.<br />
<br />
An Excel spreadsheet that incorporates extra income and expenses using the "total portfolio focused approach" is available on Google Drive: [https://drive.google.com/file/d/1oSxquKLlGtYociWUy19nbStQnYpcuey0/view?usp=sharing Total portfolio allocation and withdrawal]. <br />
<br />
A Google Sheets spreadsheet that incorporates extra income and expenses using the "savings portfolio focused approach" is available here (please make a copy): [http://bit.ly/2WuNmvf Amortized Spending Budget - Savings Portfolio Approach]. This spreadsheet also provides various backtesting capabilities.<br />
<br />
==Support==<br />
On-going discussion and support is in {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}.<br />
<br />
==See also==<br />
*[[Comparing investments]] - Tutorial on ''Time Value of Money'' equations<br />
*[https://howmuchcaniaffordtospendinretirement.blogspot.com/ How Much Can I Afford to Spend in Retirement] - Blog and spreadsheets from Ken Steiner (actuarial approach for determining reasonable spending budgets)<br />
<br />
==References==<br />
{{Reflist}}</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Amortization_based_withdrawal&diff=70723
Amortization based withdrawal
2020-12-03T22:46:58Z
<p>Siamond: /* See also */ Added reference to Ken Steiner work</p>
<hr />
<div>{{Under construction| comment = Comments are being solicited in this {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}}}<br />
'''Amortization based withdrawal (ABW)''' uses amortization techniques to calculate portfolio withdrawals during retirement. Examples of withdrawals that use amortization include [[Variable percentage withdrawal | Variable Percentage Withdrawal]] (VPW) and the [[Required Minimum Distribution]] (RMD) rules for traditional retirement accounts.<br />
<br />
==Amortization==<br />
<br />
===Understanding amortization===<br />
<br />
Amortization is the process of converting the value of a lump sum into a series of payments over time. Most people encounter it when they take out a mortgage or car loan. Amortization is used to calculate the monthly payment required to pay back the loan. The value of the monthly payments has to be made equal to the value of the initial loan.<br />
<br />
If the interest rate is zero, amortization is just simple division: If $100,000 has to be paid back over 10 years, then the payment is $100,000 ÷ 10 = $10,000 per year.<br />
<br />
But if the interest rate is positive, as is usually the case, then the payment in the above example would have to be more than $10,000 per year. That's because $10,000 in the future is worth less than $10,000 today. This is referred to as the time value of money. If the interest is 5% per year, then $10,000 today is worth:<br />
<br />
* <math>$10,000*1.05^1=$10,500</math> one year from now<br />
* <math>$10,000*1.05^2=$11,025</math> two years from now<br />
<br />
and so on. We will have to adjust for the differences in value. The amortization formula makes the necessary adjustments and tells us that if the interest rate is 5% per year, then the payments will have to be $12,950 per year for the next ten years for the total value of the payments to be equal in value to the $100,000 that was borrowed today.<br />
<br />
==Amortization based withdrawal==<br />
<br />
To calculate portfolio withdrawals, enter the following inputs in the ABW calculator ([[#ABW calculator|below]]):<br />
<br />
* <math>P=</math> current portfolio value<br />
* <math>n=</math> number of years over which withdrawals are to be spread out<br />
* <math>r=</math> expected return of the portfolio.<br />
<br />
===Example===<br />
<br />
A 65 year old retiree with a $1 million portfolio expected to earn 3% per year and seeking to spread out withdrawals over 36 years (ages 65 to 100), would enter <math>P=$1,000,000, n=36, r=3%</math>. The amortization calculator says that this retiree can withdraw $44,470 per year. This means that if the portfolio actual rate of return remains constant at 3% per year and the retiree withdraws $44,470 every year, then the portfolio will be fully depleted after 36 years.<br />
<br />
===Real vs nominal rate of return===<br />
<br />
If a real (inflation adjusted) rate of return is used, the withdrawal strategy becomes automatically adjusted for inflation. In the above example, if the real rate of return is 3%, the retiree will be able to take out $44,470 (inflation adjusted) each year. If instead, the retiree enters a nominal interest rate of 5%, the calculator says that they can take out $60,434 per year. But that's in nominal dollars, so real consumption will decline each year by the inflation rate. In practice, it is strongly recommended to use a real rate of return.<br />
<br />
===Update and adapt===<br />
<br />
Withdrawals are recalculated each year with updated information about portfolio value, expected rate of return, and number of years left. This allows withdrawals to continually adapt to new information and mitigates the impact of past incorrect assumptions. Amortization spreads the course correction required across all remaining years, thereby minimizing the impact on any one year.<br />
<br />
====Example====<br />
<br />
Consider what happens in our earlier example if, instead of gaining 3% as expected, the portfolio actually loses 10%. The shortfall relative to expectations is <math>(1-.10)/(1+.03)-1=-12.6%</math>. Our retiree had expected to start age 66 with $984,196 in the portfolio. Instead, the portfolio contains only $859,977, which is 12.6% less. Consider what happens in the following two scenarios:<br />
<br />
=====Scenario 1: Expected return stays the same=====<br />
Suppose that the retiree believes that this market drop has not impacted future expected returns, which in the retiree's opinion, remains at 3%. The retiree enters the new reduced portfolio value, <math>P=$859,977</math>, number of years remaining <math>n=35</math>, and expected real return <math>r=3%</math>. The withdrawal is now reduced to $38,857 per year. That is a 12.6% reduction relative to the previously planned withdrawal of $44,470. So the 12.6% portfolio loss is being matched by a 12.6% spending cut across all remaining years.<br />
<br />
=====Scenario 2: Expected return increases=====<br />
If the market drop was due to a pure valuation change and the underlying earnings of the portfolio are not impacted, then the retiree might expect a higher rate of return going forward.<br />
<br />
If expected return is based on an earnings yield model (e.g. 1/CAPE) for stocks and yield to maturity for bonds, a 12.6% reduction in valuation will result in a higher expected real return of <math>.03/(1-.126)=3.43%</math>. With the higher expected return, the withdrawal becomes $41,181. That is a reduction of only 7.4% relative to the original plan of $44,470. A 12.6% reduction in the portfolio led to only a 7.4% reduction in income, because the higher expected return partially offset the loss in portfolio value.<br />
<br />
So to the extent that market volatility is caused by valuation changes and gets incorporated into expected returns, withdrawals from the portfolio will be less volatile than the portfolio itself.<br />
<br />
==Adding a terminal balance==<br />
<br />
Instead of fully depleting the portfolio, the amortization can be modified to leave behind a terminal balance. This could be used to fund end of life care or a bequest, or it could simply serve as a general financial cushion. <br />
<br />
In the ABW calculator, enter:<br />
* <math>B=</math> terminal balance<br />
<br />
===Example===<br />
<br />
The 65 year old retiree in the earlier example wants to have $200,000 left at the end for a bequest. Enter <math>B=$200,000</math> in the calculator to get a withdrawal of $41,401 per year. If the actual rate of return matches expectations, then after withdrawing $41,401 for 36 years (ages 65 to 100), the retiree will have $200,000 remaining in the portfolio at the end of age 100.<br />
<br />
==Rising or falling withdrawal schedules==<br />
<br />
Instead of aiming at a constant withdrawal schedule, some retirees may prefer to aim at a rising or falling withdrawal schedule. Retirees worried about incurring unexpected expenses or generally running out of money in later years may want to use a rising withdrawal schedule - take less early so they can have more later. Those wanting to fund an active early retirement may want to use a declining withdrawal schedule - take more early but have less later. (Note the similarity with savings. This can be viewed as a decision about how much to save in the early retirement years in order to fund late retirement consumption.)<br />
<br />
In the ABW calculator, enter:<br />
* <math>g=</math> rate of growth of the withdrawal schedule<br />
<br />
<math>g>0</math> generates a rising withdrawal schedule, <math>g<0</math> generates a declining withdrawal schedule, and <math>g=0</math> generates a constant withdrawal schedule.<br />
<br />
===Example===<br />
<br />
If the 65 year old retiree in the earlier example wants withdrawals to grow at 1% per year, set <math>g=1%</math> to get a withdrawal of $38,349. Withdrawals are scheduled to grow 1% per year, rising to $54,325 at age 100.<br />
<br />
If instead the retiree wishes to spend more in early retirement and wants withdrawals to fall by 1% per year, set <math>g=-1%</math> to get a withdrawal of $51,118. Withdrawals are scheduled to fall 1% per year, declining to $35,959 at age 100.<br />
<br />
==Asset allocation==<br />
<br />
===Fixed asset allocation===<br />
<br />
The amortization formula assumes an expected rate of return on the portfolio which stays consistent over the retirement period. This is easier to justify if the retiree plans to maintain a fixed asset allocation (AA). If instead the retiree is planning to change the AA over time (e.g. glide down from 60/40 to 30/70 over the course of the retirement), then the expected return will display more variations over time, skewing the amortization computation. The calculator provided here is not designed for such case. Entering the average expected return in the calculator may provide a rough estimate, but due to the potential for significant errors, more precise modeling is recommended.<br />
<br />
===Fixed asset allocation with sub-portfolios===<br />
<br />
The portfolio can be divided into multiple sub-portfolios and a different fixed allocation applied to each sub-portfolio.<br />
<br />
Suppose the retiree is more risk averse over certain categories of consumption (e.g. food and housing), and less risk averse over other categories (e.g. vacations). The portfolio can be subdivided into a safer portfolio to fund food and housing and a riskier portfolio to fund vacations. The safe portfolio would get a safe fixed AA like 30/70, and the riskier portfolio would get a riskier fixed AA like 80/20. Multiple sub-portfolios could be created to fund different consumption goals, each with a different AA that matches the risk-reward considerations for that goal. Withdrawals would be calculated separately for each sub-portfolio.<br />
<br />
An example of a strategy that uses sub-portfolios is the Liability Matched Portfolio (LMP) strategy. The portfolio is divided into a "liability matched portfolio" and a "risk portfolio". The liability matched portfolio has an AA of 0/100 and is used to fund non-negotiable consumption. The risk portfolio is given a riskier AA and is used to fund discretionary "nice to have" consumption.<br />
<br />
==Estimating the expected return==<br />
<br />
The ABW calculation requires the user to input the expected rate of return of the portfolio. ABW does not recommend a specific model for this purpose. The user is free to use whatever model of expected return they prefer. Examples of models that can be used include:<br />
<br />
===Models based on earnings yields (e.g. 1/CAPE)===<br />
<Enter info><br />
<br />
===Models based on historical returns===<br />
<Enter info><br />
<br />
==Extra income and expenses==<br />
<br />
Besides their savings portfolio, retirees may have other sources of present or future income such as social security, pensions, annuities, rental income, part-time wages and lump sum payouts ("extra income"). Retirees may also plan for exceptional expenses such as college tuition, a lingering home mortgage or long-term care expenses that may require funds beyond what is provided by regular budgeting ("extra expenses"). Such future extra income and expenses can be amortized by computing the present value of such future sums (see Wiki article on calculating present value by discounting future cash flows: [[Comparing_investments#Present_value|Comparing Investments]]) and converting in an additional series of payments, beyond the regular payment derived from the savings portfolio's balance. It is strongly recommended to perform such computations in real (inflation-adjusted) terms. Funding such additional payments in the short-term can be achieved in different ways, e.g. structuring financial assets according to the retiree's personal risks/rewards goals. ABW is neutral and does not take a position on how best to do it. Below are some of the strategies which can be used:<br />
<br />
===Separate sub-portfolio focused approach===<br />
<br />
The retiree can choose to keep funds for some or all of the extra income and expenses outside the regular amortization process. They can allocate extra income and budget for extra expenses, separate from the ABW calculation. This is effectively a partitioned portfolio approach where extra income and expenses are being handled in a separate safe sub-portfolio.<br />
<br />
A retiree formally pursuing the separate portfolio approach described [[User:Willthrill81/Amortization_based_withdrawal#Fixed_asset_allocation_with_sub-portfolios|earlier]] may find it convenient to use conservative estimates of social security and pensions to fund the safe sub-portfolios. For more complex cases, sizing the sub-portfolio can be achieved by a present value computation of future extra income and expenses (e.g. when using a bonds ladder, use the bonds interest rate to discount future income/expenses). The income streams are typically duration matched. Gaps remaining can be filled with duration matched bonds. Depending on the asset allocation, there may be little to no rebalancing needed in safe sub-portfolios.<br />
<br />
===Savings portfolio focused approach===<br />
<br />
The retiree funds the additional payments through additional withdrawals from the savings portfolio, while maintaining a fixed asset allocation on the savings portfolio. The discounting and amortization rate used should then be the savings portfolio's expected rate of return. Care should be exercised about the additional burden on one's savings portfolio and possible consequences of market crises before steady future income (e.g. SS/Pensions) materializes.<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using the portfolio's expected rate of return <ref>[https://www.kitces.com/blog/net-present-value-discount-rate-formula-retirement-plan-pension-lump-sum-or-social-security-breakeven/ Choosing An Appropriate Discount Rate For Retirement Planning Strategies] Michael Kitces, July 2017</ref>. Calculate amortized additional withdrawals based on such present value, in the same manner as the savings portfolio balance is amortized. Such computation is independent from the portfolio's rebalancing procedure and doesn't change the expected return computation. More information on this approach is available here: [https://www.bogleheads.org/blog/2019/02/01/early-retirement-and-time-value-of-money/ Early Retirement and Time Value of Money], a blog article which comes with a [http://bit.ly/2WuNmvf companion spreadsheet].<br />
<br />
===Total portfolio focused approach===<br />
<br />
The retiree funds the additional payments through... <<Ben to elaborate, including a brief explanation of "total portfolio" concept>>. <br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using bond interest rates. Add this value to the regular portfolio's balance for all calculations, counting it as a bond. Include it when calculating withdrawals. Include it when calculating the asset allocation of the total portfolio (for rebalancing) and the expected return of the total portfolio (to enter into the amortized payment computation). More information on this approach is available here: [[User:Ben_Mathew/Total_portfolio_allocation_and_withdrawal|Total portfolio allocation and withdrawal]].<br />
<br />
==ABW calculator==<br />
<br />
===Basic calculator===<br />
<br />
The Excel spreadsheet to calculate withdrawals in on Google Drive: [https://drive.google.com/file/d/1XOnBaUspLX_oaM2rquTPmLj5AKOm6yxV/view?usp=sharing ABW Calculator]<br />
<br />
[[User:Ben Mathew/Formulas for Amortization Based Withdrawal (ABW)]] describes the formulas used in the calculator.<br />
<br />
===Advanced calculators===<br />
<br />
These calculators expand the basic functionality to include other considerations.<br />
<br />
An Excel spreadsheet that incorporates extra income and expenses using the "total portfolio focused approach" is available on Google Drive: [https://drive.google.com/file/d/1oSxquKLlGtYociWUy19nbStQnYpcuey0/view?usp=sharing Total portfolio allocation and withdrawal]. <br />
<br />
A Google Sheets spreadsheet that incorporates extra income and expenses using the "savings portfolio focused approach" is available here (please make a copy): [http://bit.ly/2WuNmvf Amortized Spending Budget - Savings Portfolio Approach]. This spreadsheet also provides various backtesting capabilities.<br />
<br />
==Support==<br />
On-going discussion and support is in {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}.<br />
<br />
==See also==<br />
*[[Comparing investments]] - Tutorial on ''Time Value of Money'' equations<br />
*[https://howmuchcaniaffordtospendinretirement.blogspot.com/ How Much Can I Afford to Spend in Retirement] - Blog and spreadsheets from Ken Steiner (actuarial approach for determining reasonable spending budgets)<br />
<br />
==References==<br />
{{Reflist}}</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Amortization_based_withdrawal&diff=70718
Amortization based withdrawal
2020-12-01T03:56:07Z
<p>Siamond: /* Savings portfolio focused approach */ More explicit reference to blog's title</p>
<hr />
<div>{{Under construction| comment = Comments are being solicited in this {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}}}<br />
'''Amortization based withdrawal (ABW)''' uses amortization techniques to calculate portfolio withdrawals during retirement. Examples of withdrawals that use amortization include [[Variable percentage withdrawal | Variable Percentage Withdrawal]] (VPW) and the [[Required Minimum Distribution]] (RMD) rules for traditional retirement accounts.<br />
<br />
==Amortization==<br />
<br />
===Understanding amortization===<br />
<br />
Amortization is the process of converting the value of a lump sum into a series of payments over time. Most people encounter it when they take out a mortgage or car loan. Amortization is used to calculate the monthly payment required to pay back the loan. The value of the monthly payments has to be made equal to the value of the initial loan.<br />
<br />
If the interest rate is zero, amortization is just simple division: If $100,000 has to be paid back over 10 years, then the payment is $100,000 ÷ 10 = $10,000 per year.<br />
<br />
But if the interest rate is positive, as is usually the case, then the payment in the above example would have to be more than $10,000 per year. That's because $10,000 in the future is worth less than $10,000 today. This is referred to as the time value of money. If the interest is 5% per year, then $10,000 today is worth:<br />
<br />
* <math>$10,000*1.05^1=$10,500</math> one year from now<br />
* <math>$10,000*1.05^2=$11,025</math> two years from now<br />
<br />
and so on. We will have to adjust for the differences in value. The amortization formula makes the necessary adjustments and tells us that if the interest rate is 5% per year, then the payments will have to be $12,950 per year for the next ten years for the total value of the payments to be equal in value to the $100,000 that was borrowed today.<br />
<br />
==Amortization based withdrawal==<br />
<br />
To calculate portfolio withdrawals, enter the following inputs in the ABW calculator ([[#ABW calculator|below]]):<br />
<br />
* <math>P=</math> current portfolio value<br />
* <math>n=</math> number of years over which withdrawals are to be spread out<br />
* <math>r=</math> expected return of the portfolio.<br />
<br />
===Example===<br />
<br />
A 65 year old retiree with a $1 million portfolio expected to earn 3% per year and seeking to spread out withdrawals over 36 years (ages 65 to 100), would enter <math>P=$1,000,000, n=36, r=3%</math>. The amortization calculator says that this retiree can withdraw $44,470 per year. This means that if the portfolio actual rate of return remains constant at 3% per year and the retiree withdraws $44,470 every year, then the portfolio will be fully depleted after 36 years.<br />
<br />
===Real vs nominal rate of return===<br />
<br />
If a real (inflation adjusted) rate of return is used, the withdrawal strategy becomes automatically adjusted for inflation. In the above example, if the real rate of return is 3%, the retiree will be able to take out $44,470 (inflation adjusted) each year. If instead, the retiree enters a nominal interest rate of 5%, the calculator says that they can take out $60,434 per year. But that's in nominal dollars, so real consumption will decline each year by the inflation rate. In practice, it is strongly recommended to use a real rate of return.<br />
<br />
===Update and adapt===<br />
<br />
Withdrawals are recalculated each year with updated information about portfolio value, expected rate of return, and number of years left. This allows withdrawals to continually adapt to new information and mitigates the impact of past incorrect assumptions. Amortization spreads the course correction required across all remaining years, thereby minimizing the impact on any one year.<br />
<br />
====Example====<br />
<br />
Consider what happens in our earlier example if, instead of gaining 3% as expected, the portfolio actually loses 10%. The shortfall relative to expectations is <math>(1-.10)/(1+.03)-1=-12.6%</math>. Our retiree had expected to start age 66 with $984,196 in the portfolio. Instead, the portfolio contains only $859,977, which is 12.6% less. Consider what happens in the following two scenarios:<br />
<br />
=====Scenario 1: Expected return stays the same=====<br />
Suppose that the retiree believes that this market drop has not impacted future expected returns, which in the retiree's opinion, remains at 3%. The retiree enters the new reduced portfolio value, <math>P=$859,977</math>, number of years remaining <math>n=35</math>, and expected real return <math>r=3%</math>. The withdrawal is now reduced to $38,857 per year. That is a 12.6% reduction relative to the previously planned withdrawal of $44,470. So the 12.6% portfolio loss is being matched by a 12.6% spending cut across all remaining years.<br />
<br />
=====Scenario 2: Expected return increases=====<br />
If the market drop was due to a pure valuation change and the underlying earnings of the portfolio are not impacted, then the retiree might expect a higher rate of return going forward.<br />
<br />
If expected return is based on an earnings yield model (e.g. 1/CAPE) for stocks and yield to maturity for bonds, a 12.6% reduction in valuation will result in a higher expected real return of <math>.03/(1-.126)=3.43%</math>. With the higher expected return, the withdrawal becomes $41,181. That is a reduction of only 7.4% relative to the original plan of $44,470. A 12.6% reduction in the portfolio led to only a 7.4% reduction in income, because the higher expected return partially offset the loss in portfolio value.<br />
<br />
So to the extent that market volatility is caused by valuation changes and gets incorporated into expected returns, withdrawals from the portfolio will be less volatile than the portfolio itself.<br />
<br />
==Adding a terminal balance==<br />
<br />
Instead of fully depleting the portfolio, the amortization can be modified to leave behind a terminal balance. This could be used to fund end of life care or a bequest, or it could simply serve as a general financial cushion. <br />
<br />
In the ABW calculator, enter:<br />
* <math>B=</math> terminal balance<br />
<br />
===Example===<br />
<br />
The 65 year old retiree in the earlier example wants to have $200,000 left at the end for a bequest. Enter <math>B=$200,000</math> in the calculator to get a withdrawal of $41,401 per year. If the actual rate of return matches expectations, then after withdrawing $41,401 for 36 years (ages 65 to 100), the retiree will have $200,000 remaining in the portfolio at the end of age 100.<br />
<br />
==Rising or falling withdrawal schedules==<br />
<br />
Instead of aiming at a constant withdrawal schedule, some retirees may prefer to aim at a rising or falling withdrawal schedule. Retirees worried about incurring unexpected expenses or generally running out of money in later years may want to use a rising withdrawal schedule - take less early so they can have more later. Those wanting to fund an active early retirement may want to use a declining withdrawal schedule - take more early but have less later. (Note the similarity with savings. This can be viewed as a decision about how much to save in the early retirement years in order to fund late retirement consumption.)<br />
<br />
In the ABW calculator, enter:<br />
* <math>g=</math> rate of growth of the withdrawal schedule<br />
<br />
<math>g>0</math> generates a rising withdrawal schedule, <math>g<0</math> generates a declining withdrawal schedule, and <math>g=0</math> generates a constant withdrawal schedule.<br />
<br />
===Example===<br />
<br />
If the 65 year old retiree in the earlier example wants withdrawals to grow at 1% per year, set <math>g=1%</math> to get a withdrawal of $38,349. Withdrawals are scheduled to grow 1% per year, rising to $54,325 at age 100.<br />
<br />
If instead the retiree wishes to spend more in early retirement and wants withdrawals to fall by 1% per year, set <math>g=-1%</math> to get a withdrawal of $51,118. Withdrawals are scheduled to fall 1% per year, declining to $35,959 at age 100.<br />
<br />
==Asset allocation==<br />
<br />
===Fixed asset allocation===<br />
<br />
The amortization formula assumes an expected rate of return on the portfolio which stays consistent over the retirement period. This is easier to justify if the retiree plans to maintain a fixed asset allocation (AA). If instead the retiree is planning to change the AA over time (e.g. glide down from 60/40 to 30/70 over the course of the retirement), then the expected return will display more variations over time, skewing the amortization computation. The calculator provided here is not designed for such case. Entering the average expected return in the calculator may provide a rough estimate, but due to the potential for significant errors, more precise modeling is recommended.<br />
<br />
===Fixed asset allocation with sub-portfolios===<br />
<br />
The portfolio can be divided into multiple sub-portfolios and a different fixed allocation applied to each sub-portfolio.<br />
<br />
Suppose the retiree is more risk averse over certain categories of consumption (e.g. food and housing), and less risk averse over other categories (e.g. vacations). The portfolio can be subdivided into a safer portfolio to fund food and housing and a riskier portfolio to fund vacations. The safe portfolio would get a safe fixed AA like 30/70, and the riskier portfolio would get a riskier fixed AA like 80/20. Multiple sub-portfolios could be created to fund different consumption goals, each with a different AA that matches the risk-reward considerations for that goal. Withdrawals would be calculated separately for each sub-portfolio.<br />
<br />
An example of a strategy that uses sub-portfolios is the Liability Matched Portfolio (LMP) strategy. The portfolio is divided into a "liability matched portfolio" and a "risk portfolio". The liability matched portfolio has an AA of 0/100 and is used to fund non-negotiable consumption. The risk portfolio is given a riskier AA and is used to fund discretionary "nice to have" consumption.<br />
<br />
==Estimating the expected return==<br />
<br />
The ABW calculation requires the user to input the expected rate of return of the portfolio. ABW does not recommend a specific model for this purpose. The user is free to use whatever model of expected return they prefer. Examples of models that can be used include:<br />
<br />
===Models based on earnings yields (e.g. 1/CAPE)===<br />
<Enter info><br />
<br />
===Models based on historical returns===<br />
<Enter info><br />
<br />
==Extra income and expenses==<br />
<br />
Besides their savings portfolio, retirees may have other sources of present or future income such as social security, pensions, annuities, rental income, part-time wages and lump sum payouts ("extra income"). Retirees may also plan for exceptional expenses such as college tuition, a lingering home mortgage or long-term care expenses that may require funds beyond what is provided by regular budgeting ("extra expenses"). Such future extra income and expenses can be amortized by computing the present value of such future sums (see Wiki article on calculating present value by discounting future cash flows: [[Comparing_investments#Present_value|Comparing Investments]]) and converting in an additional series of payments, beyond the regular payment derived from the savings portfolio's balance. It is strongly recommended to perform such computations in real (inflation-adjusted) terms. Funding such additional payments in the short-term can be achieved in different ways, e.g. structuring financial assets according to the retiree's personal risks/rewards goals. ABW is neutral and does not take a position on how best to do it. Below are some of the strategies which can be used:<br />
<br />
===Separate sub-portfolio focused approach===<br />
<br />
The retiree can choose to keep funds for some or all of the extra income and expenses outside the regular amortization process. They can allocate extra income and budget for extra expenses, separate from the ABW calculation. This is effectively a partitioned portfolio approach where extra income and expenses are being handled in a separate safe sub-portfolio.<br />
<br />
A retiree formally pursuing the separate portfolio approach described [[User:Willthrill81/Amortization_based_withdrawal#Fixed_asset_allocation_with_sub-portfolios|earlier]] may find it convenient to use conservative estimates of social security and pensions to fund the safe sub-portfolios. For more complex cases, sizing the sub-portfolio can be achieved by a present value computation of future extra income and expenses (e.g. when using a bonds ladder, use the bonds interest rate to discount future income/expenses). The income streams are typically duration matched. Gaps remaining can be filled with duration matched bonds. Depending on the asset allocation, there may be little to no rebalancing needed in safe sub-portfolios.<br />
<br />
===Savings portfolio focused approach===<br />
<br />
The retiree funds the additional payments through additional withdrawals from the savings portfolio, while maintaining a fixed asset allocation on the savings portfolio. The discounting and amortization rate used should then be the savings portfolio's expected rate of return. Care should be exercised about the additional burden on one's savings portfolio and possible consequences of market crises before steady future income (e.g. SS/Pensions) materializes.<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using the portfolio's expected rate of return <ref>[https://www.kitces.com/blog/net-present-value-discount-rate-formula-retirement-plan-pension-lump-sum-or-social-security-breakeven/ Choosing An Appropriate Discount Rate For Retirement Planning Strategies] Michael Kitces, July 2017</ref>. Calculate amortized additional withdrawals based on such present value, in the same manner as the savings portfolio balance is amortized. Such computation is independent from the portfolio's rebalancing procedure and doesn't change the expected return computation. More information on this approach is available here: [https://www.bogleheads.org/blog/2019/02/01/early-retirement-and-time-value-of-money/ Early Retirement and Time Value of Money], a blog article which comes with a [http://bit.ly/2WuNmvf companion spreadsheet].<br />
<br />
===Total portfolio focused approach===<br />
<br />
The retiree funds the additional payments through... <<Ben to elaborate, including a brief explanation of "total portfolio" concept>>. <br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using bond interest rates. Add this value to the regular portfolio's balance for all calculations, counting it as a bond. Include it when calculating withdrawals. Include it when calculating the asset allocation of the total portfolio (for rebalancing) and the expected return of the total portfolio (to enter into the amortized payment computation). More information on this approach is available here: [[User:Ben_Mathew/Total_portfolio_allocation_and_withdrawal|Total portfolio allocation and withdrawal]].<br />
<br />
==ABW calculator==<br />
<br />
===Basic calculator===<br />
<br />
The Excel spreadsheet to calculate withdrawals in on Google Drive: [https://drive.google.com/file/d/1XOnBaUspLX_oaM2rquTPmLj5AKOm6yxV/view?usp=sharing ABW Calculator]<br />
<br />
[[User:Ben Mathew/Formulas for Amortization Based Withdrawal (ABW)]] describes the formulas used in the calculator.<br />
<br />
===Advanced calculators===<br />
<br />
These calculators expand the basic functionality to include other considerations.<br />
<br />
An Excel spreadsheet that incorporates extra income and expenses using the "total portfolio focused approach" is available on Google Drive: [https://drive.google.com/file/d/1odW_PvhVrefzGp_sG41WOd_1UaqtR0iq/view?usp=sharing Total portfolio allocation and withdrawal]. <br />
<br />
A Google Sheets spreadsheet that incorporates extra income and expenses using the "savings portfolio focused approach" is available here (please make a copy): [http://bit.ly/2WuNmvf Amortized Spending Budget - Savings Portfolio Approach]. This spreadsheet also provides various backtesting capabilities.<br />
<br />
==Support==<br />
On-going discussion and support is in {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}.<br />
<br />
==See also==<br />
*[[Comparing investments]] - Tutorial on ''Time Value of Money'' equations<br />
<br />
==References==<br />
{{Reflist}}</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Amortization_based_withdrawal&diff=70717
Amortization based withdrawal
2020-12-01T03:51:10Z
<p>Siamond: /* References */ Minor formatting issue</p>
<hr />
<div>{{Under construction| comment = Comments are being solicited in this {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}}}<br />
'''Amortization based withdrawal (ABW)''' uses amortization techniques to calculate portfolio withdrawals during retirement. Examples of withdrawals that use amortization include [[Variable percentage withdrawal | Variable Percentage Withdrawal]] (VPW) and the [[Required Minimum Distribution]] (RMD) rules for traditional retirement accounts.<br />
<br />
==Amortization==<br />
<br />
===Understanding amortization===<br />
<br />
Amortization is the process of converting the value of a lump sum into a series of payments over time. Most people encounter it when they take out a mortgage or car loan. Amortization is used to calculate the monthly payment required to pay back the loan. The value of the monthly payments has to be made equal to the value of the initial loan.<br />
<br />
If the interest rate is zero, amortization is just simple division: If $100,000 has to be paid back over 10 years, then the payment is $100,000 ÷ 10 = $10,000 per year.<br />
<br />
But if the interest rate is positive, as is usually the case, then the payment in the above example would have to be more than $10,000 per year. That's because $10,000 in the future is worth less than $10,000 today. This is referred to as the time value of money. If the interest is 5% per year, then $10,000 today is worth:<br />
<br />
* <math>$10,000*1.05^1=$10,500</math> one year from now<br />
* <math>$10,000*1.05^2=$11,025</math> two years from now<br />
<br />
and so on. We will have to adjust for the differences in value. The amortization formula makes the necessary adjustments and tells us that if the interest rate is 5% per year, then the payments will have to be $12,950 per year for the next ten years for the total value of the payments to be equal in value to the $100,000 that was borrowed today.<br />
<br />
==Amortization based withdrawal==<br />
<br />
To calculate portfolio withdrawals, enter the following inputs in the ABW calculator ([[#ABW calculator|below]]):<br />
<br />
* <math>P=</math> current portfolio value<br />
* <math>n=</math> number of years over which withdrawals are to be spread out<br />
* <math>r=</math> expected return of the portfolio.<br />
<br />
===Example===<br />
<br />
A 65 year old retiree with a $1 million portfolio expected to earn 3% per year and seeking to spread out withdrawals over 36 years (ages 65 to 100), would enter <math>P=$1,000,000, n=36, r=3%</math>. The amortization calculator says that this retiree can withdraw $44,470 per year. This means that if the portfolio actual rate of return remains constant at 3% per year and the retiree withdraws $44,470 every year, then the portfolio will be fully depleted after 36 years.<br />
<br />
===Real vs nominal rate of return===<br />
<br />
If a real (inflation adjusted) rate of return is used, the withdrawal strategy becomes automatically adjusted for inflation. In the above example, if the real rate of return is 3%, the retiree will be able to take out $44,470 (inflation adjusted) each year. If instead, the retiree enters a nominal interest rate of 5%, the calculator says that they can take out $60,434 per year. But that's in nominal dollars, so real consumption will decline each year by the inflation rate. In practice, it is strongly recommended to use a real rate of return.<br />
<br />
===Update and adapt===<br />
<br />
Withdrawals are recalculated each year with updated information about portfolio value, expected rate of return, and number of years left. This allows withdrawals to continually adapt to new information and mitigates the impact of past incorrect assumptions. Amortization spreads the course correction required across all remaining years, thereby minimizing the impact on any one year.<br />
<br />
====Example====<br />
<br />
Consider what happens in our earlier example if, instead of gaining 3% as expected, the portfolio actually loses 10%. The shortfall relative to expectations is <math>(1-.10)/(1+.03)-1=-12.6%</math>. Our retiree had expected to start age 66 with $984,196 in the portfolio. Instead, the portfolio contains only $859,977, which is 12.6% less. Consider what happens in the following two scenarios:<br />
<br />
=====Scenario 1: Expected return stays the same=====<br />
Suppose that the retiree believes that this market drop has not impacted future expected returns, which in the retiree's opinion, remains at 3%. The retiree enters the new reduced portfolio value, <math>P=$859,977</math>, number of years remaining <math>n=35</math>, and expected real return <math>r=3%</math>. The withdrawal is now reduced to $38,857 per year. That is a 12.6% reduction relative to the previously planned withdrawal of $44,470. So the 12.6% portfolio loss is being matched by a 12.6% spending cut across all remaining years.<br />
<br />
=====Scenario 2: Expected return increases=====<br />
If the market drop was due to a pure valuation change and the underlying earnings of the portfolio are not impacted, then the retiree might expect a higher rate of return going forward.<br />
<br />
If expected return is based on an earnings yield model (e.g. 1/CAPE) for stocks and yield to maturity for bonds, a 12.6% reduction in valuation will result in a higher expected real return of <math>.03/(1-.126)=3.43%</math>. With the higher expected return, the withdrawal becomes $41,181. That is a reduction of only 7.4% relative to the original plan of $44,470. A 12.6% reduction in the portfolio led to only a 7.4% reduction in income, because the higher expected return partially offset the loss in portfolio value.<br />
<br />
So to the extent that market volatility is caused by valuation changes and gets incorporated into expected returns, withdrawals from the portfolio will be less volatile than the portfolio itself.<br />
<br />
==Adding a terminal balance==<br />
<br />
Instead of fully depleting the portfolio, the amortization can be modified to leave behind a terminal balance. This could be used to fund end of life care or a bequest, or it could simply serve as a general financial cushion. <br />
<br />
In the ABW calculator, enter:<br />
* <math>B=</math> terminal balance<br />
<br />
===Example===<br />
<br />
The 65 year old retiree in the earlier example wants to have $200,000 left at the end for a bequest. Enter <math>B=$200,000</math> in the calculator to get a withdrawal of $41,401 per year. If the actual rate of return matches expectations, then after withdrawing $41,401 for 36 years (ages 65 to 100), the retiree will have $200,000 remaining in the portfolio at the end of age 100.<br />
<br />
==Rising or falling withdrawal schedules==<br />
<br />
Instead of aiming at a constant withdrawal schedule, some retirees may prefer to aim at a rising or falling withdrawal schedule. Retirees worried about incurring unexpected expenses or generally running out of money in later years may want to use a rising withdrawal schedule - take less early so they can have more later. Those wanting to fund an active early retirement may want to use a declining withdrawal schedule - take more early but have less later. (Note the similarity with savings. This can be viewed as a decision about how much to save in the early retirement years in order to fund late retirement consumption.)<br />
<br />
In the ABW calculator, enter:<br />
* <math>g=</math> rate of growth of the withdrawal schedule<br />
<br />
<math>g>0</math> generates a rising withdrawal schedule, <math>g<0</math> generates a declining withdrawal schedule, and <math>g=0</math> generates a constant withdrawal schedule.<br />
<br />
===Example===<br />
<br />
If the 65 year old retiree in the earlier example wants withdrawals to grow at 1% per year, set <math>g=1%</math> to get a withdrawal of $38,349. Withdrawals are scheduled to grow 1% per year, rising to $54,325 at age 100.<br />
<br />
If instead the retiree wishes to spend more in early retirement and wants withdrawals to fall by 1% per year, set <math>g=-1%</math> to get a withdrawal of $51,118. Withdrawals are scheduled to fall 1% per year, declining to $35,959 at age 100.<br />
<br />
==Asset allocation==<br />
<br />
===Fixed asset allocation===<br />
<br />
The amortization formula assumes an expected rate of return on the portfolio which stays consistent over the retirement period. This is easier to justify if the retiree plans to maintain a fixed asset allocation (AA). If instead the retiree is planning to change the AA over time (e.g. glide down from 60/40 to 30/70 over the course of the retirement), then the expected return will display more variations over time, skewing the amortization computation. The calculator provided here is not designed for such case. Entering the average expected return in the calculator may provide a rough estimate, but due to the potential for significant errors, more precise modeling is recommended.<br />
<br />
===Fixed asset allocation with sub-portfolios===<br />
<br />
The portfolio can be divided into multiple sub-portfolios and a different fixed allocation applied to each sub-portfolio.<br />
<br />
Suppose the retiree is more risk averse over certain categories of consumption (e.g. food and housing), and less risk averse over other categories (e.g. vacations). The portfolio can be subdivided into a safer portfolio to fund food and housing and a riskier portfolio to fund vacations. The safe portfolio would get a safe fixed AA like 30/70, and the riskier portfolio would get a riskier fixed AA like 80/20. Multiple sub-portfolios could be created to fund different consumption goals, each with a different AA that matches the risk-reward considerations for that goal. Withdrawals would be calculated separately for each sub-portfolio.<br />
<br />
An example of a strategy that uses sub-portfolios is the Liability Matched Portfolio (LMP) strategy. The portfolio is divided into a "liability matched portfolio" and a "risk portfolio". The liability matched portfolio has an AA of 0/100 and is used to fund non-negotiable consumption. The risk portfolio is given a riskier AA and is used to fund discretionary "nice to have" consumption.<br />
<br />
==Estimating the expected return==<br />
<br />
The ABW calculation requires the user to input the expected rate of return of the portfolio. ABW does not recommend a specific model for this purpose. The user is free to use whatever model of expected return they prefer. Examples of models that can be used include:<br />
<br />
===Models based on earnings yields (e.g. 1/CAPE)===<br />
<Enter info><br />
<br />
===Models based on historical returns===<br />
<Enter info><br />
<br />
==Extra income and expenses==<br />
<br />
Besides their savings portfolio, retirees may have other sources of present or future income such as social security, pensions, annuities, rental income, part-time wages and lump sum payouts ("extra income"). Retirees may also plan for exceptional expenses such as college tuition, a lingering home mortgage or long-term care expenses that may require funds beyond what is provided by regular budgeting ("extra expenses"). Such future extra income and expenses can be amortized by computing the present value of such future sums (see Wiki article on calculating present value by discounting future cash flows: [[Comparing_investments#Present_value|Comparing Investments]]) and converting in an additional series of payments, beyond the regular payment derived from the savings portfolio's balance. It is strongly recommended to perform such computations in real (inflation-adjusted) terms. Funding such additional payments in the short-term can be achieved in different ways, e.g. structuring financial assets according to the retiree's personal risks/rewards goals. ABW is neutral and does not take a position on how best to do it. Below are some of the strategies which can be used:<br />
<br />
===Separate sub-portfolio focused approach===<br />
<br />
The retiree can choose to keep funds for some or all of the extra income and expenses outside the regular amortization process. They can allocate extra income and budget for extra expenses, separate from the ABW calculation. This is effectively a partitioned portfolio approach where extra income and expenses are being handled in a separate safe sub-portfolio.<br />
<br />
A retiree formally pursuing the separate portfolio approach described [[User:Willthrill81/Amortization_based_withdrawal#Fixed_asset_allocation_with_sub-portfolios|earlier]] may find it convenient to use conservative estimates of social security and pensions to fund the safe sub-portfolios. For more complex cases, sizing the sub-portfolio can be achieved by a present value computation of future extra income and expenses (e.g. when using a bonds ladder, use the bonds interest rate to discount future income/expenses). The income streams are typically duration matched. Gaps remaining can be filled with duration matched bonds. Depending on the asset allocation, there may be little to no rebalancing needed in safe sub-portfolios.<br />
<br />
===Savings portfolio focused approach===<br />
<br />
The retiree funds the additional payments through additional withdrawals from the savings portfolio, while maintaining a fixed asset allocation on the savings portfolio. The discounting and amortization rate used should then be the savings portfolio's expected rate of return. Care should be exercised about the additional burden on one's savings portfolio and possible consequences of market crises before steady future income (e.g. SS/Pensions) materializes.<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using the portfolio's expected rate of return <ref>[https://www.kitces.com/blog/net-present-value-discount-rate-formula-retirement-plan-pension-lump-sum-or-social-security-breakeven/ Choosing An Appropriate Discount Rate For Retirement Planning Strategies] Michael Kitces, July 2017</ref>. Calculate amortized additional withdrawals based on such value, in the same manner as the savings portfolio balance is amortized. Such computation is independent from the portfolio's rebalancing procedure and doesn't change the expected return computation. More information on this approach is available on this [https://www.bogleheads.org/blog/2019/02/01/early-retirement-and-time-value-of-money/ blog article], which comes with a [http://bit.ly/2WuNmvf companion spreadsheet].<br />
<br />
===Total portfolio focused approach===<br />
<br />
The retiree funds the additional payments through... <<Ben to elaborate, including a brief explanation of "total portfolio" concept>>. <br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using bond interest rates. Add this value to the regular portfolio's balance for all calculations, counting it as a bond. Include it when calculating withdrawals. Include it when calculating the asset allocation of the total portfolio (for rebalancing) and the expected return of the total portfolio (to enter into the amortized payment computation). More information on this approach is available here: [[User:Ben_Mathew/Total_portfolio_allocation_and_withdrawal|Total portfolio allocation and withdrawal]].<br />
<br />
==ABW calculator==<br />
<br />
===Basic calculator===<br />
<br />
The Excel spreadsheet to calculate withdrawals in on Google Drive: [https://drive.google.com/file/d/1XOnBaUspLX_oaM2rquTPmLj5AKOm6yxV/view?usp=sharing ABW Calculator]<br />
<br />
[[User:Ben Mathew/Formulas for Amortization Based Withdrawal (ABW)]] describes the formulas used in the calculator.<br />
<br />
===Advanced calculators===<br />
<br />
These calculators expand the basic functionality to include other considerations.<br />
<br />
An Excel spreadsheet that incorporates extra income and expenses using the "total portfolio focused approach" is available on Google Drive: [https://drive.google.com/file/d/1odW_PvhVrefzGp_sG41WOd_1UaqtR0iq/view?usp=sharing Total portfolio allocation and withdrawal]. <br />
<br />
A Google Sheets spreadsheet that incorporates extra income and expenses using the "savings portfolio focused approach" is available here (please make a copy): [http://bit.ly/2WuNmvf Amortized Spending Budget - Savings Portfolio Approach]. This spreadsheet also provides various backtesting capabilities.<br />
<br />
==Support==<br />
On-going discussion and support is in {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}.<br />
<br />
==See also==<br />
*[[Comparing investments]] - Tutorial on ''Time Value of Money'' equations<br />
<br />
==References==<br />
{{Reflist}}</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Amortization_based_withdrawal&diff=70716
Amortization based withdrawal
2020-12-01T03:49:04Z
<p>Siamond: /* See also */ Added reference section</p>
<hr />
<div>{{Under construction| comment = Comments are being solicited in this {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}}}<br />
'''Amortization based withdrawal (ABW)''' uses amortization techniques to calculate portfolio withdrawals during retirement. Examples of withdrawals that use amortization include [[Variable percentage withdrawal | Variable Percentage Withdrawal]] (VPW) and the [[Required Minimum Distribution]] (RMD) rules for traditional retirement accounts.<br />
<br />
==Amortization==<br />
<br />
===Understanding amortization===<br />
<br />
Amortization is the process of converting the value of a lump sum into a series of payments over time. Most people encounter it when they take out a mortgage or car loan. Amortization is used to calculate the monthly payment required to pay back the loan. The value of the monthly payments has to be made equal to the value of the initial loan.<br />
<br />
If the interest rate is zero, amortization is just simple division: If $100,000 has to be paid back over 10 years, then the payment is $100,000 ÷ 10 = $10,000 per year.<br />
<br />
But if the interest rate is positive, as is usually the case, then the payment in the above example would have to be more than $10,000 per year. That's because $10,000 in the future is worth less than $10,000 today. This is referred to as the time value of money. If the interest is 5% per year, then $10,000 today is worth:<br />
<br />
* <math>$10,000*1.05^1=$10,500</math> one year from now<br />
* <math>$10,000*1.05^2=$11,025</math> two years from now<br />
<br />
and so on. We will have to adjust for the differences in value. The amortization formula makes the necessary adjustments and tells us that if the interest rate is 5% per year, then the payments will have to be $12,950 per year for the next ten years for the total value of the payments to be equal in value to the $100,000 that was borrowed today.<br />
<br />
==Amortization based withdrawal==<br />
<br />
To calculate portfolio withdrawals, enter the following inputs in the ABW calculator ([[#ABW calculator|below]]):<br />
<br />
* <math>P=</math> current portfolio value<br />
* <math>n=</math> number of years over which withdrawals are to be spread out<br />
* <math>r=</math> expected return of the portfolio.<br />
<br />
===Example===<br />
<br />
A 65 year old retiree with a $1 million portfolio expected to earn 3% per year and seeking to spread out withdrawals over 36 years (ages 65 to 100), would enter <math>P=$1,000,000, n=36, r=3%</math>. The amortization calculator says that this retiree can withdraw $44,470 per year. This means that if the portfolio actual rate of return remains constant at 3% per year and the retiree withdraws $44,470 every year, then the portfolio will be fully depleted after 36 years.<br />
<br />
===Real vs nominal rate of return===<br />
<br />
If a real (inflation adjusted) rate of return is used, the withdrawal strategy becomes automatically adjusted for inflation. In the above example, if the real rate of return is 3%, the retiree will be able to take out $44,470 (inflation adjusted) each year. If instead, the retiree enters a nominal interest rate of 5%, the calculator says that they can take out $60,434 per year. But that's in nominal dollars, so real consumption will decline each year by the inflation rate. In practice, it is strongly recommended to use a real rate of return.<br />
<br />
===Update and adapt===<br />
<br />
Withdrawals are recalculated each year with updated information about portfolio value, expected rate of return, and number of years left. This allows withdrawals to continually adapt to new information and mitigates the impact of past incorrect assumptions. Amortization spreads the course correction required across all remaining years, thereby minimizing the impact on any one year.<br />
<br />
====Example====<br />
<br />
Consider what happens in our earlier example if, instead of gaining 3% as expected, the portfolio actually loses 10%. The shortfall relative to expectations is <math>(1-.10)/(1+.03)-1=-12.6%</math>. Our retiree had expected to start age 66 with $984,196 in the portfolio. Instead, the portfolio contains only $859,977, which is 12.6% less. Consider what happens in the following two scenarios:<br />
<br />
=====Scenario 1: Expected return stays the same=====<br />
Suppose that the retiree believes that this market drop has not impacted future expected returns, which in the retiree's opinion, remains at 3%. The retiree enters the new reduced portfolio value, <math>P=$859,977</math>, number of years remaining <math>n=35</math>, and expected real return <math>r=3%</math>. The withdrawal is now reduced to $38,857 per year. That is a 12.6% reduction relative to the previously planned withdrawal of $44,470. So the 12.6% portfolio loss is being matched by a 12.6% spending cut across all remaining years.<br />
<br />
=====Scenario 2: Expected return increases=====<br />
If the market drop was due to a pure valuation change and the underlying earnings of the portfolio are not impacted, then the retiree might expect a higher rate of return going forward.<br />
<br />
If expected return is based on an earnings yield model (e.g. 1/CAPE) for stocks and yield to maturity for bonds, a 12.6% reduction in valuation will result in a higher expected real return of <math>.03/(1-.126)=3.43%</math>. With the higher expected return, the withdrawal becomes $41,181. That is a reduction of only 7.4% relative to the original plan of $44,470. A 12.6% reduction in the portfolio led to only a 7.4% reduction in income, because the higher expected return partially offset the loss in portfolio value.<br />
<br />
So to the extent that market volatility is caused by valuation changes and gets incorporated into expected returns, withdrawals from the portfolio will be less volatile than the portfolio itself.<br />
<br />
==Adding a terminal balance==<br />
<br />
Instead of fully depleting the portfolio, the amortization can be modified to leave behind a terminal balance. This could be used to fund end of life care or a bequest, or it could simply serve as a general financial cushion. <br />
<br />
In the ABW calculator, enter:<br />
* <math>B=</math> terminal balance<br />
<br />
===Example===<br />
<br />
The 65 year old retiree in the earlier example wants to have $200,000 left at the end for a bequest. Enter <math>B=$200,000</math> in the calculator to get a withdrawal of $41,401 per year. If the actual rate of return matches expectations, then after withdrawing $41,401 for 36 years (ages 65 to 100), the retiree will have $200,000 remaining in the portfolio at the end of age 100.<br />
<br />
==Rising or falling withdrawal schedules==<br />
<br />
Instead of aiming at a constant withdrawal schedule, some retirees may prefer to aim at a rising or falling withdrawal schedule. Retirees worried about incurring unexpected expenses or generally running out of money in later years may want to use a rising withdrawal schedule - take less early so they can have more later. Those wanting to fund an active early retirement may want to use a declining withdrawal schedule - take more early but have less later. (Note the similarity with savings. This can be viewed as a decision about how much to save in the early retirement years in order to fund late retirement consumption.)<br />
<br />
In the ABW calculator, enter:<br />
* <math>g=</math> rate of growth of the withdrawal schedule<br />
<br />
<math>g>0</math> generates a rising withdrawal schedule, <math>g<0</math> generates a declining withdrawal schedule, and <math>g=0</math> generates a constant withdrawal schedule.<br />
<br />
===Example===<br />
<br />
If the 65 year old retiree in the earlier example wants withdrawals to grow at 1% per year, set <math>g=1%</math> to get a withdrawal of $38,349. Withdrawals are scheduled to grow 1% per year, rising to $54,325 at age 100.<br />
<br />
If instead the retiree wishes to spend more in early retirement and wants withdrawals to fall by 1% per year, set <math>g=-1%</math> to get a withdrawal of $51,118. Withdrawals are scheduled to fall 1% per year, declining to $35,959 at age 100.<br />
<br />
==Asset allocation==<br />
<br />
===Fixed asset allocation===<br />
<br />
The amortization formula assumes an expected rate of return on the portfolio which stays consistent over the retirement period. This is easier to justify if the retiree plans to maintain a fixed asset allocation (AA). If instead the retiree is planning to change the AA over time (e.g. glide down from 60/40 to 30/70 over the course of the retirement), then the expected return will display more variations over time, skewing the amortization computation. The calculator provided here is not designed for such case. Entering the average expected return in the calculator may provide a rough estimate, but due to the potential for significant errors, more precise modeling is recommended.<br />
<br />
===Fixed asset allocation with sub-portfolios===<br />
<br />
The portfolio can be divided into multiple sub-portfolios and a different fixed allocation applied to each sub-portfolio.<br />
<br />
Suppose the retiree is more risk averse over certain categories of consumption (e.g. food and housing), and less risk averse over other categories (e.g. vacations). The portfolio can be subdivided into a safer portfolio to fund food and housing and a riskier portfolio to fund vacations. The safe portfolio would get a safe fixed AA like 30/70, and the riskier portfolio would get a riskier fixed AA like 80/20. Multiple sub-portfolios could be created to fund different consumption goals, each with a different AA that matches the risk-reward considerations for that goal. Withdrawals would be calculated separately for each sub-portfolio.<br />
<br />
An example of a strategy that uses sub-portfolios is the Liability Matched Portfolio (LMP) strategy. The portfolio is divided into a "liability matched portfolio" and a "risk portfolio". The liability matched portfolio has an AA of 0/100 and is used to fund non-negotiable consumption. The risk portfolio is given a riskier AA and is used to fund discretionary "nice to have" consumption.<br />
<br />
==Estimating the expected return==<br />
<br />
The ABW calculation requires the user to input the expected rate of return of the portfolio. ABW does not recommend a specific model for this purpose. The user is free to use whatever model of expected return they prefer. Examples of models that can be used include:<br />
<br />
===Models based on earnings yields (e.g. 1/CAPE)===<br />
<Enter info><br />
<br />
===Models based on historical returns===<br />
<Enter info><br />
<br />
==Extra income and expenses==<br />
<br />
Besides their savings portfolio, retirees may have other sources of present or future income such as social security, pensions, annuities, rental income, part-time wages and lump sum payouts ("extra income"). Retirees may also plan for exceptional expenses such as college tuition, a lingering home mortgage or long-term care expenses that may require funds beyond what is provided by regular budgeting ("extra expenses"). Such future extra income and expenses can be amortized by computing the present value of such future sums (see Wiki article on calculating present value by discounting future cash flows: [[Comparing_investments#Present_value|Comparing Investments]]) and converting in an additional series of payments, beyond the regular payment derived from the savings portfolio's balance. It is strongly recommended to perform such computations in real (inflation-adjusted) terms. Funding such additional payments in the short-term can be achieved in different ways, e.g. structuring financial assets according to the retiree's personal risks/rewards goals. ABW is neutral and does not take a position on how best to do it. Below are some of the strategies which can be used:<br />
<br />
===Separate sub-portfolio focused approach===<br />
<br />
The retiree can choose to keep funds for some or all of the extra income and expenses outside the regular amortization process. They can allocate extra income and budget for extra expenses, separate from the ABW calculation. This is effectively a partitioned portfolio approach where extra income and expenses are being handled in a separate safe sub-portfolio.<br />
<br />
A retiree formally pursuing the separate portfolio approach described [[User:Willthrill81/Amortization_based_withdrawal#Fixed_asset_allocation_with_sub-portfolios|earlier]] may find it convenient to use conservative estimates of social security and pensions to fund the safe sub-portfolios. For more complex cases, sizing the sub-portfolio can be achieved by a present value computation of future extra income and expenses (e.g. when using a bonds ladder, use the bonds interest rate to discount future income/expenses). The income streams are typically duration matched. Gaps remaining can be filled with duration matched bonds. Depending on the asset allocation, there may be little to no rebalancing needed in safe sub-portfolios.<br />
<br />
===Savings portfolio focused approach===<br />
<br />
The retiree funds the additional payments through additional withdrawals from the savings portfolio, while maintaining a fixed asset allocation on the savings portfolio. The discounting and amortization rate used should then be the savings portfolio's expected rate of return. Care should be exercised about the additional burden on one's savings portfolio and possible consequences of market crises before steady future income (e.g. SS/Pensions) materializes.<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using the portfolio's expected rate of return <ref>[https://www.kitces.com/blog/net-present-value-discount-rate-formula-retirement-plan-pension-lump-sum-or-social-security-breakeven/ Choosing An Appropriate Discount Rate For Retirement Planning Strategies] Michael Kitces, July 2017</ref>. Calculate amortized additional withdrawals based on such value, in the same manner as the savings portfolio balance is amortized. Such computation is independent from the portfolio's rebalancing procedure and doesn't change the expected return computation. More information on this approach is available on this [https://www.bogleheads.org/blog/2019/02/01/early-retirement-and-time-value-of-money/ blog article], which comes with a [http://bit.ly/2WuNmvf companion spreadsheet].<br />
<br />
===Total portfolio focused approach===<br />
<br />
The retiree funds the additional payments through... <<Ben to elaborate, including a brief explanation of "total portfolio" concept>>. <br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using bond interest rates. Add this value to the regular portfolio's balance for all calculations, counting it as a bond. Include it when calculating withdrawals. Include it when calculating the asset allocation of the total portfolio (for rebalancing) and the expected return of the total portfolio (to enter into the amortized payment computation). More information on this approach is available here: [[User:Ben_Mathew/Total_portfolio_allocation_and_withdrawal|Total portfolio allocation and withdrawal]].<br />
<br />
==ABW calculator==<br />
<br />
===Basic calculator===<br />
<br />
The Excel spreadsheet to calculate withdrawals in on Google Drive: [https://drive.google.com/file/d/1XOnBaUspLX_oaM2rquTPmLj5AKOm6yxV/view?usp=sharing ABW Calculator]<br />
<br />
[[User:Ben Mathew/Formulas for Amortization Based Withdrawal (ABW)]] describes the formulas used in the calculator.<br />
<br />
===Advanced calculators===<br />
<br />
These calculators expand the basic functionality to include other considerations.<br />
<br />
An Excel spreadsheet that incorporates extra income and expenses using the "total portfolio focused approach" is available on Google Drive: [https://drive.google.com/file/d/1odW_PvhVrefzGp_sG41WOd_1UaqtR0iq/view?usp=sharing Total portfolio allocation and withdrawal]. <br />
<br />
A Google Sheets spreadsheet that incorporates extra income and expenses using the "savings portfolio focused approach" is available here (please make a copy): [http://bit.ly/2WuNmvf Amortized Spending Budget - Savings Portfolio Approach]. This spreadsheet also provides various backtesting capabilities.<br />
<br />
==Support==<br />
On-going discussion and support is in {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}.<br />
<br />
==See also==<br />
*[[Comparing investments]] - Tutorial on ''Time Value of Money'' equations<br />
<br />
==References==<br />
{{Reflist|30em}}</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Amortization_based_withdrawal&diff=70715
Amortization based withdrawal
2020-12-01T03:47:21Z
<p>Siamond: /* Savings portfolio focused approach */ Added reference to Kitces article</p>
<hr />
<div>{{Under construction| comment = Comments are being solicited in this {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}}}<br />
'''Amortization based withdrawal (ABW)''' uses amortization techniques to calculate portfolio withdrawals during retirement. Examples of withdrawals that use amortization include [[Variable percentage withdrawal | Variable Percentage Withdrawal]] (VPW) and the [[Required Minimum Distribution]] (RMD) rules for traditional retirement accounts.<br />
<br />
==Amortization==<br />
<br />
===Understanding amortization===<br />
<br />
Amortization is the process of converting the value of a lump sum into a series of payments over time. Most people encounter it when they take out a mortgage or car loan. Amortization is used to calculate the monthly payment required to pay back the loan. The value of the monthly payments has to be made equal to the value of the initial loan.<br />
<br />
If the interest rate is zero, amortization is just simple division: If $100,000 has to be paid back over 10 years, then the payment is $100,000 ÷ 10 = $10,000 per year.<br />
<br />
But if the interest rate is positive, as is usually the case, then the payment in the above example would have to be more than $10,000 per year. That's because $10,000 in the future is worth less than $10,000 today. This is referred to as the time value of money. If the interest is 5% per year, then $10,000 today is worth:<br />
<br />
* <math>$10,000*1.05^1=$10,500</math> one year from now<br />
* <math>$10,000*1.05^2=$11,025</math> two years from now<br />
<br />
and so on. We will have to adjust for the differences in value. The amortization formula makes the necessary adjustments and tells us that if the interest rate is 5% per year, then the payments will have to be $12,950 per year for the next ten years for the total value of the payments to be equal in value to the $100,000 that was borrowed today.<br />
<br />
==Amortization based withdrawal==<br />
<br />
To calculate portfolio withdrawals, enter the following inputs in the ABW calculator ([[#ABW calculator|below]]):<br />
<br />
* <math>P=</math> current portfolio value<br />
* <math>n=</math> number of years over which withdrawals are to be spread out<br />
* <math>r=</math> expected return of the portfolio.<br />
<br />
===Example===<br />
<br />
A 65 year old retiree with a $1 million portfolio expected to earn 3% per year and seeking to spread out withdrawals over 36 years (ages 65 to 100), would enter <math>P=$1,000,000, n=36, r=3%</math>. The amortization calculator says that this retiree can withdraw $44,470 per year. This means that if the portfolio actual rate of return remains constant at 3% per year and the retiree withdraws $44,470 every year, then the portfolio will be fully depleted after 36 years.<br />
<br />
===Real vs nominal rate of return===<br />
<br />
If a real (inflation adjusted) rate of return is used, the withdrawal strategy becomes automatically adjusted for inflation. In the above example, if the real rate of return is 3%, the retiree will be able to take out $44,470 (inflation adjusted) each year. If instead, the retiree enters a nominal interest rate of 5%, the calculator says that they can take out $60,434 per year. But that's in nominal dollars, so real consumption will decline each year by the inflation rate. In practice, it is strongly recommended to use a real rate of return.<br />
<br />
===Update and adapt===<br />
<br />
Withdrawals are recalculated each year with updated information about portfolio value, expected rate of return, and number of years left. This allows withdrawals to continually adapt to new information and mitigates the impact of past incorrect assumptions. Amortization spreads the course correction required across all remaining years, thereby minimizing the impact on any one year.<br />
<br />
====Example====<br />
<br />
Consider what happens in our earlier example if, instead of gaining 3% as expected, the portfolio actually loses 10%. The shortfall relative to expectations is <math>(1-.10)/(1+.03)-1=-12.6%</math>. Our retiree had expected to start age 66 with $984,196 in the portfolio. Instead, the portfolio contains only $859,977, which is 12.6% less. Consider what happens in the following two scenarios:<br />
<br />
=====Scenario 1: Expected return stays the same=====<br />
Suppose that the retiree believes that this market drop has not impacted future expected returns, which in the retiree's opinion, remains at 3%. The retiree enters the new reduced portfolio value, <math>P=$859,977</math>, number of years remaining <math>n=35</math>, and expected real return <math>r=3%</math>. The withdrawal is now reduced to $38,857 per year. That is a 12.6% reduction relative to the previously planned withdrawal of $44,470. So the 12.6% portfolio loss is being matched by a 12.6% spending cut across all remaining years.<br />
<br />
=====Scenario 2: Expected return increases=====<br />
If the market drop was due to a pure valuation change and the underlying earnings of the portfolio are not impacted, then the retiree might expect a higher rate of return going forward.<br />
<br />
If expected return is based on an earnings yield model (e.g. 1/CAPE) for stocks and yield to maturity for bonds, a 12.6% reduction in valuation will result in a higher expected real return of <math>.03/(1-.126)=3.43%</math>. With the higher expected return, the withdrawal becomes $41,181. That is a reduction of only 7.4% relative to the original plan of $44,470. A 12.6% reduction in the portfolio led to only a 7.4% reduction in income, because the higher expected return partially offset the loss in portfolio value.<br />
<br />
So to the extent that market volatility is caused by valuation changes and gets incorporated into expected returns, withdrawals from the portfolio will be less volatile than the portfolio itself.<br />
<br />
==Adding a terminal balance==<br />
<br />
Instead of fully depleting the portfolio, the amortization can be modified to leave behind a terminal balance. This could be used to fund end of life care or a bequest, or it could simply serve as a general financial cushion. <br />
<br />
In the ABW calculator, enter:<br />
* <math>B=</math> terminal balance<br />
<br />
===Example===<br />
<br />
The 65 year old retiree in the earlier example wants to have $200,000 left at the end for a bequest. Enter <math>B=$200,000</math> in the calculator to get a withdrawal of $41,401 per year. If the actual rate of return matches expectations, then after withdrawing $41,401 for 36 years (ages 65 to 100), the retiree will have $200,000 remaining in the portfolio at the end of age 100.<br />
<br />
==Rising or falling withdrawal schedules==<br />
<br />
Instead of aiming at a constant withdrawal schedule, some retirees may prefer to aim at a rising or falling withdrawal schedule. Retirees worried about incurring unexpected expenses or generally running out of money in later years may want to use a rising withdrawal schedule - take less early so they can have more later. Those wanting to fund an active early retirement may want to use a declining withdrawal schedule - take more early but have less later. (Note the similarity with savings. This can be viewed as a decision about how much to save in the early retirement years in order to fund late retirement consumption.)<br />
<br />
In the ABW calculator, enter:<br />
* <math>g=</math> rate of growth of the withdrawal schedule<br />
<br />
<math>g>0</math> generates a rising withdrawal schedule, <math>g<0</math> generates a declining withdrawal schedule, and <math>g=0</math> generates a constant withdrawal schedule.<br />
<br />
===Example===<br />
<br />
If the 65 year old retiree in the earlier example wants withdrawals to grow at 1% per year, set <math>g=1%</math> to get a withdrawal of $38,349. Withdrawals are scheduled to grow 1% per year, rising to $54,325 at age 100.<br />
<br />
If instead the retiree wishes to spend more in early retirement and wants withdrawals to fall by 1% per year, set <math>g=-1%</math> to get a withdrawal of $51,118. Withdrawals are scheduled to fall 1% per year, declining to $35,959 at age 100.<br />
<br />
==Asset allocation==<br />
<br />
===Fixed asset allocation===<br />
<br />
The amortization formula assumes an expected rate of return on the portfolio which stays consistent over the retirement period. This is easier to justify if the retiree plans to maintain a fixed asset allocation (AA). If instead the retiree is planning to change the AA over time (e.g. glide down from 60/40 to 30/70 over the course of the retirement), then the expected return will display more variations over time, skewing the amortization computation. The calculator provided here is not designed for such case. Entering the average expected return in the calculator may provide a rough estimate, but due to the potential for significant errors, more precise modeling is recommended.<br />
<br />
===Fixed asset allocation with sub-portfolios===<br />
<br />
The portfolio can be divided into multiple sub-portfolios and a different fixed allocation applied to each sub-portfolio.<br />
<br />
Suppose the retiree is more risk averse over certain categories of consumption (e.g. food and housing), and less risk averse over other categories (e.g. vacations). The portfolio can be subdivided into a safer portfolio to fund food and housing and a riskier portfolio to fund vacations. The safe portfolio would get a safe fixed AA like 30/70, and the riskier portfolio would get a riskier fixed AA like 80/20. Multiple sub-portfolios could be created to fund different consumption goals, each with a different AA that matches the risk-reward considerations for that goal. Withdrawals would be calculated separately for each sub-portfolio.<br />
<br />
An example of a strategy that uses sub-portfolios is the Liability Matched Portfolio (LMP) strategy. The portfolio is divided into a "liability matched portfolio" and a "risk portfolio". The liability matched portfolio has an AA of 0/100 and is used to fund non-negotiable consumption. The risk portfolio is given a riskier AA and is used to fund discretionary "nice to have" consumption.<br />
<br />
==Estimating the expected return==<br />
<br />
The ABW calculation requires the user to input the expected rate of return of the portfolio. ABW does not recommend a specific model for this purpose. The user is free to use whatever model of expected return they prefer. Examples of models that can be used include:<br />
<br />
===Models based on earnings yields (e.g. 1/CAPE)===<br />
<Enter info><br />
<br />
===Models based on historical returns===<br />
<Enter info><br />
<br />
==Extra income and expenses==<br />
<br />
Besides their savings portfolio, retirees may have other sources of present or future income such as social security, pensions, annuities, rental income, part-time wages and lump sum payouts ("extra income"). Retirees may also plan for exceptional expenses such as college tuition, a lingering home mortgage or long-term care expenses that may require funds beyond what is provided by regular budgeting ("extra expenses"). Such future extra income and expenses can be amortized by computing the present value of such future sums (see Wiki article on calculating present value by discounting future cash flows: [[Comparing_investments#Present_value|Comparing Investments]]) and converting in an additional series of payments, beyond the regular payment derived from the savings portfolio's balance. It is strongly recommended to perform such computations in real (inflation-adjusted) terms. Funding such additional payments in the short-term can be achieved in different ways, e.g. structuring financial assets according to the retiree's personal risks/rewards goals. ABW is neutral and does not take a position on how best to do it. Below are some of the strategies which can be used:<br />
<br />
===Separate sub-portfolio focused approach===<br />
<br />
The retiree can choose to keep funds for some or all of the extra income and expenses outside the regular amortization process. They can allocate extra income and budget for extra expenses, separate from the ABW calculation. This is effectively a partitioned portfolio approach where extra income and expenses are being handled in a separate safe sub-portfolio.<br />
<br />
A retiree formally pursuing the separate portfolio approach described [[User:Willthrill81/Amortization_based_withdrawal#Fixed_asset_allocation_with_sub-portfolios|earlier]] may find it convenient to use conservative estimates of social security and pensions to fund the safe sub-portfolios. For more complex cases, sizing the sub-portfolio can be achieved by a present value computation of future extra income and expenses (e.g. when using a bonds ladder, use the bonds interest rate to discount future income/expenses). The income streams are typically duration matched. Gaps remaining can be filled with duration matched bonds. Depending on the asset allocation, there may be little to no rebalancing needed in safe sub-portfolios.<br />
<br />
===Savings portfolio focused approach===<br />
<br />
The retiree funds the additional payments through additional withdrawals from the savings portfolio, while maintaining a fixed asset allocation on the savings portfolio. The discounting and amortization rate used should then be the savings portfolio's expected rate of return. Care should be exercised about the additional burden on one's savings portfolio and possible consequences of market crises before steady future income (e.g. SS/Pensions) materializes.<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using the portfolio's expected rate of return <ref>[https://www.kitces.com/blog/net-present-value-discount-rate-formula-retirement-plan-pension-lump-sum-or-social-security-breakeven/ Choosing An Appropriate Discount Rate For Retirement Planning Strategies] Michael Kitces, July 2017</ref>. Calculate amortized additional withdrawals based on such value, in the same manner as the savings portfolio balance is amortized. Such computation is independent from the portfolio's rebalancing procedure and doesn't change the expected return computation. More information on this approach is available on this [https://www.bogleheads.org/blog/2019/02/01/early-retirement-and-time-value-of-money/ blog article], which comes with a [http://bit.ly/2WuNmvf companion spreadsheet].<br />
<br />
===Total portfolio focused approach===<br />
<br />
The retiree funds the additional payments through... <<Ben to elaborate, including a brief explanation of "total portfolio" concept>>. <br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using bond interest rates. Add this value to the regular portfolio's balance for all calculations, counting it as a bond. Include it when calculating withdrawals. Include it when calculating the asset allocation of the total portfolio (for rebalancing) and the expected return of the total portfolio (to enter into the amortized payment computation). More information on this approach is available here: [[User:Ben_Mathew/Total_portfolio_allocation_and_withdrawal|Total portfolio allocation and withdrawal]].<br />
<br />
==ABW calculator==<br />
<br />
===Basic calculator===<br />
<br />
The Excel spreadsheet to calculate withdrawals in on Google Drive: [https://drive.google.com/file/d/1XOnBaUspLX_oaM2rquTPmLj5AKOm6yxV/view?usp=sharing ABW Calculator]<br />
<br />
[[User:Ben Mathew/Formulas for Amortization Based Withdrawal (ABW)]] describes the formulas used in the calculator.<br />
<br />
===Advanced calculators===<br />
<br />
These calculators expand the basic functionality to include other considerations.<br />
<br />
An Excel spreadsheet that incorporates extra income and expenses using the "total portfolio focused approach" is available on Google Drive: [https://drive.google.com/file/d/1odW_PvhVrefzGp_sG41WOd_1UaqtR0iq/view?usp=sharing Total portfolio allocation and withdrawal]. <br />
<br />
A Google Sheets spreadsheet that incorporates extra income and expenses using the "savings portfolio focused approach" is available here (please make a copy): [http://bit.ly/2WuNmvf Amortized Spending Budget - Savings Portfolio Approach]. This spreadsheet also provides various backtesting capabilities.<br />
<br />
==Support==<br />
On-going discussion and support is in {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}.<br />
<br />
==See also==<br />
*[[Comparing investments]] - Tutorial on ''Time Value of Money'' equations</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Amortization_based_withdrawal&diff=70714
Amortization based withdrawal
2020-12-01T03:30:16Z
<p>Siamond: /* Advanced calculators */ Tweaked the name of the 2nd calculator, aligned descriptions</p>
<hr />
<div>{{Under construction| comment = Comments are being solicited in this {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}}}<br />
'''Amortization based withdrawal (ABW)''' uses amortization techniques to calculate portfolio withdrawals during retirement. Examples of withdrawals that use amortization include [[Variable percentage withdrawal | Variable Percentage Withdrawal]] (VPW) and the [[Required Minimum Distribution]] (RMD) rules for traditional retirement accounts.<br />
<br />
==Amortization==<br />
<br />
===Understanding amortization===<br />
<br />
Amortization is the process of converting the value of a lump sum into a series of payments over time. Most people encounter it when they take out a mortgage or car loan. Amortization is used to calculate the monthly payment required to pay back the loan. The value of the monthly payments has to be made equal to the value of the initial loan.<br />
<br />
If the interest rate is zero, amortization is just simple division: If $100,000 has to be paid back over 10 years, then the payment is $100,000 ÷ 10 = $10,000 per year.<br />
<br />
But if the interest rate is positive, as is usually the case, then the payment in the above example would have to be more than $10,000 per year. That's because $10,000 in the future is worth less than $10,000 today. This is referred to as the time value of money. If the interest is 5% per year, then $10,000 today is worth:<br />
<br />
* <math>$10,000*1.05^1=$10,500</math> one year from now<br />
* <math>$10,000*1.05^2=$11,025</math> two years from now<br />
<br />
and so on. We will have to adjust for the differences in value. The amortization formula makes the necessary adjustments and tells us that if the interest rate is 5% per year, then the payments will have to be $12,950 per year for the next ten years for the total value of the payments to be equal in value to the $100,000 that was borrowed today.<br />
<br />
==Amortization based withdrawal==<br />
<br />
To calculate portfolio withdrawals, enter the following inputs in the ABW calculator ([[#ABW calculator|below]]):<br />
<br />
* <math>P=</math> current portfolio value<br />
* <math>n=</math> number of years over which withdrawals are to be spread out<br />
* <math>r=</math> expected return of the portfolio.<br />
<br />
===Example===<br />
<br />
A 65 year old retiree with a $1 million portfolio expected to earn 3% per year and seeking to spread out withdrawals over 36 years (ages 65 to 100), would enter <math>P=$1,000,000, n=36, r=3%</math>. The amortization calculator says that this retiree can withdraw $44,470 per year. This means that if the portfolio actual rate of return remains constant at 3% per year and the retiree withdraws $44,470 every year, then the portfolio will be fully depleted after 36 years.<br />
<br />
===Real vs nominal rate of return===<br />
<br />
If a real (inflation adjusted) rate of return is used, the withdrawal strategy becomes automatically adjusted for inflation. In the above example, if the real rate of return is 3%, the retiree will be able to take out $44,470 (inflation adjusted) each year. If instead, the retiree enters a nominal interest rate of 5%, the calculator says that they can take out $60,434 per year. But that's in nominal dollars, so real consumption will decline each year by the inflation rate. In practice, it is strongly recommended to use a real rate of return.<br />
<br />
===Update and adapt===<br />
<br />
Withdrawals are recalculated each year with updated information about portfolio value, expected rate of return, and number of years left. This allows withdrawals to continually adapt to new information and mitigates the impact of past incorrect assumptions. Amortization spreads the course correction required across all remaining years, thereby minimizing the impact on any one year.<br />
<br />
====Example====<br />
<br />
Consider what happens in our earlier example if, instead of gaining 3% as expected, the portfolio actually loses 10%. The shortfall relative to expectations is <math>(1-.10)/(1+.03)-1=-12.6%</math>. Our retiree had expected to start age 66 with $984,196 in the portfolio. Instead, the portfolio contains only $859,977, which is 12.6% less. Consider what happens in the following two scenarios:<br />
<br />
=====Scenario 1: Expected return stays the same=====<br />
Suppose that the retiree believes that this market drop has not impacted future expected returns, which in the retiree's opinion, remains at 3%. The retiree enters the new reduced portfolio value, <math>P=$859,977</math>, number of years remaining <math>n=35</math>, and expected real return <math>r=3%</math>. The withdrawal is now reduced to $38,857 per year. That is a 12.6% reduction relative to the previously planned withdrawal of $44,470. So the 12.6% portfolio loss is being matched by a 12.6% spending cut across all remaining years.<br />
<br />
=====Scenario 2: Expected return increases=====<br />
If the market drop was due to a pure valuation change and the underlying earnings of the portfolio are not impacted, then the retiree might expect a higher rate of return going forward.<br />
<br />
If expected return is based on an earnings yield model (e.g. 1/CAPE) for stocks and yield to maturity for bonds, a 12.6% reduction in valuation will result in a higher expected real return of <math>.03/(1-.126)=3.43%</math>. With the higher expected return, the withdrawal becomes $41,181. That is a reduction of only 7.4% relative to the original plan of $44,470. A 12.6% reduction in the portfolio led to only a 7.4% reduction in income, because the higher expected return partially offset the loss in portfolio value.<br />
<br />
So to the extent that market volatility is caused by valuation changes and gets incorporated into expected returns, withdrawals from the portfolio will be less volatile than the portfolio itself.<br />
<br />
==Adding a terminal balance==<br />
<br />
Instead of fully depleting the portfolio, the amortization can be modified to leave behind a terminal balance. This could be used to fund end of life care or a bequest, or it could simply serve as a general financial cushion. <br />
<br />
In the ABW calculator, enter:<br />
* <math>B=</math> terminal balance<br />
<br />
===Example===<br />
<br />
The 65 year old retiree in the earlier example wants to have $200,000 left at the end for a bequest. Enter <math>B=$200,000</math> in the calculator to get a withdrawal of $41,401 per year. If the actual rate of return matches expectations, then after withdrawing $41,401 for 36 years (ages 65 to 100), the retiree will have $200,000 remaining in the portfolio at the end of age 100.<br />
<br />
==Rising or falling withdrawal schedules==<br />
<br />
Instead of aiming at a constant withdrawal schedule, some retirees may prefer to aim at a rising or falling withdrawal schedule. Retirees worried about incurring unexpected expenses or generally running out of money in later years may want to use a rising withdrawal schedule - take less early so they can have more later. Those wanting to fund an active early retirement may want to use a declining withdrawal schedule - take more early but have less later. (Note the similarity with savings. This can be viewed as a decision about how much to save in the early retirement years in order to fund late retirement consumption.)<br />
<br />
In the ABW calculator, enter:<br />
* <math>g=</math> rate of growth of the withdrawal schedule<br />
<br />
<math>g>0</math> generates a rising withdrawal schedule, <math>g<0</math> generates a declining withdrawal schedule, and <math>g=0</math> generates a constant withdrawal schedule.<br />
<br />
===Example===<br />
<br />
If the 65 year old retiree in the earlier example wants withdrawals to grow at 1% per year, set <math>g=1%</math> to get a withdrawal of $38,349. Withdrawals are scheduled to grow 1% per year, rising to $54,325 at age 100.<br />
<br />
If instead the retiree wishes to spend more in early retirement and wants withdrawals to fall by 1% per year, set <math>g=-1%</math> to get a withdrawal of $51,118. Withdrawals are scheduled to fall 1% per year, declining to $35,959 at age 100.<br />
<br />
==Asset allocation==<br />
<br />
===Fixed asset allocation===<br />
<br />
The amortization formula assumes an expected rate of return on the portfolio which stays consistent over the retirement period. This is easier to justify if the retiree plans to maintain a fixed asset allocation (AA). If instead the retiree is planning to change the AA over time (e.g. glide down from 60/40 to 30/70 over the course of the retirement), then the expected return will display more variations over time, skewing the amortization computation. The calculator provided here is not designed for such case. Entering the average expected return in the calculator may provide a rough estimate, but due to the potential for significant errors, more precise modeling is recommended.<br />
<br />
===Fixed asset allocation with sub-portfolios===<br />
<br />
The portfolio can be divided into multiple sub-portfolios and a different fixed allocation applied to each sub-portfolio.<br />
<br />
Suppose the retiree is more risk averse over certain categories of consumption (e.g. food and housing), and less risk averse over other categories (e.g. vacations). The portfolio can be subdivided into a safer portfolio to fund food and housing and a riskier portfolio to fund vacations. The safe portfolio would get a safe fixed AA like 30/70, and the riskier portfolio would get a riskier fixed AA like 80/20. Multiple sub-portfolios could be created to fund different consumption goals, each with a different AA that matches the risk-reward considerations for that goal. Withdrawals would be calculated separately for each sub-portfolio.<br />
<br />
An example of a strategy that uses sub-portfolios is the Liability Matched Portfolio (LMP) strategy. The portfolio is divided into a "liability matched portfolio" and a "risk portfolio". The liability matched portfolio has an AA of 0/100 and is used to fund non-negotiable consumption. The risk portfolio is given a riskier AA and is used to fund discretionary "nice to have" consumption.<br />
<br />
==Estimating the expected return==<br />
<br />
The ABW calculation requires the user to input the expected rate of return of the portfolio. ABW does not recommend a specific model for this purpose. The user is free to use whatever model of expected return they prefer. Examples of models that can be used include:<br />
<br />
===Models based on earnings yields (e.g. 1/CAPE)===<br />
<Enter info><br />
<br />
===Models based on historical returns===<br />
<Enter info><br />
<br />
==Extra income and expenses==<br />
<br />
Besides their savings portfolio, retirees may have other sources of present or future income such as social security, pensions, annuities, rental income, part-time wages and lump sum payouts ("extra income"). Retirees may also plan for exceptional expenses such as college tuition, a lingering home mortgage or long-term care expenses that may require funds beyond what is provided by regular budgeting ("extra expenses"). Such future extra income and expenses can be amortized by computing the present value of such future sums (see Wiki article on calculating present value by discounting future cash flows: [[Comparing_investments#Present_value|Comparing Investments]]) and converting in an additional series of payments, beyond the regular payment derived from the savings portfolio's balance. It is strongly recommended to perform such computations in real (inflation-adjusted) terms. Funding such additional payments in the short-term can be achieved in different ways, e.g. structuring financial assets according to the retiree's personal risks/rewards goals. ABW is neutral and does not take a position on how best to do it. Below are some of the strategies which can be used:<br />
<br />
===Separate sub-portfolio focused approach===<br />
<br />
The retiree can choose to keep funds for some or all of the extra income and expenses outside the regular amortization process. They can allocate extra income and budget for extra expenses, separate from the ABW calculation. This is effectively a partitioned portfolio approach where extra income and expenses are being handled in a separate safe sub-portfolio.<br />
<br />
A retiree formally pursuing the separate portfolio approach described [[User:Willthrill81/Amortization_based_withdrawal#Fixed_asset_allocation_with_sub-portfolios|earlier]] may find it convenient to use conservative estimates of social security and pensions to fund the safe sub-portfolios. For more complex cases, sizing the sub-portfolio can be achieved by a present value computation of future extra income and expenses (e.g. when using a bonds ladder, use the bonds interest rate to discount future income/expenses). The income streams are typically duration matched. Gaps remaining can be filled with duration matched bonds. Depending on the asset allocation, there may be little to no rebalancing needed in safe sub-portfolios.<br />
<br />
===Savings portfolio focused approach===<br />
<br />
The retiree funds the additional payments through additional withdrawals from the savings portfolio, while maintaining a fixed asset allocation on the savings portfolio. The discounting and amortization rate used should then be the savings portfolio's expected rate of return. Care should be exercised about the additional burden on one's savings portfolio and possible consequences of market crises before steady future income (e.g. SS/Pensions) materializes.<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using the portfolio's expected rate of return. Calculate amortized additional withdrawals based on such value, in the same manner as the savings portfolio balance is amortized. Such computation is independent from the portfolio's rebalancing procedure and doesn't change the expected return computation. More information on this approach is available on this [https://www.bogleheads.org/blog/2019/02/01/early-retirement-and-time-value-of-money/ blog article], which comes with a [http://bit.ly/2WuNmvf companion spreadsheet].<br />
<br />
===Total portfolio focused approach===<br />
<br />
The retiree funds the additional payments through... <<Ben to elaborate, including a brief explanation of "total portfolio" concept>>. <br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using bond interest rates. Add this value to the regular portfolio's balance for all calculations, counting it as a bond. Include it when calculating withdrawals. Include it when calculating the asset allocation of the total portfolio (for rebalancing) and the expected return of the total portfolio (to enter into the amortized payment computation). More information on this approach is available here: [[User:Ben_Mathew/Total_portfolio_allocation_and_withdrawal|Total portfolio allocation and withdrawal]].<br />
<br />
==ABW calculator==<br />
<br />
===Basic calculator===<br />
<br />
The Excel spreadsheet to calculate withdrawals in on Google Drive: [https://drive.google.com/file/d/1XOnBaUspLX_oaM2rquTPmLj5AKOm6yxV/view?usp=sharing ABW Calculator]<br />
<br />
[[User:Ben Mathew/Formulas for Amortization Based Withdrawal (ABW)]] describes the formulas used in the calculator.<br />
<br />
===Advanced calculators===<br />
<br />
These calculators expand the basic functionality to include other considerations.<br />
<br />
An Excel spreadsheet that incorporates extra income and expenses using the "total portfolio focused approach" is available on Google Drive: [https://drive.google.com/file/d/1odW_PvhVrefzGp_sG41WOd_1UaqtR0iq/view?usp=sharing Total portfolio allocation and withdrawal]. <br />
<br />
A Google Sheets spreadsheet that incorporates extra income and expenses using the "savings portfolio focused approach" is available here (please make a copy): [http://bit.ly/2WuNmvf Amortized Spending Budget - Savings Portfolio Approach]. This spreadsheet also provides various backtesting capabilities.<br />
<br />
==Support==<br />
On-going discussion and support is in {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}.<br />
<br />
==See also==<br />
*[[Comparing investments]] - Tutorial on ''Time Value of Money'' equations</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Amortization_based_withdrawal&diff=70693
Amortization based withdrawal
2020-11-28T15:13:27Z
<p>Siamond: /* Extra income and expenses */ Minor editing to capture forum feedback</p>
<hr />
<div>{{Under construction| comment = Comments are being solicited in this {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}}}<br />
'''Amortization based withdrawal (ABW)''' uses amortization techniques to calculate portfolio withdrawals during retirement. Examples of withdrawals that use amortization include [[Variable percentage withdrawal | Variable Percentage Withdrawal]] (VPW) and the [[Required Minimum Distribution]] (RMD) rules for traditional retirement accounts.<br />
<br />
==Amortization==<br />
<br />
===Understanding amortization===<br />
<br />
Amortization is the process of converting the value of a lump sum into a series of payments over time. Most people encounter it when they take out a mortgage or car loan. Amortization is used to calculate the monthly payment required to pay back the loan. The value of the monthly payments has to be made equal to the value of the initial loan.<br />
<br />
If the interest rate is zero, amortization is just simple division: If $100,000 has to be paid back over 10 years, then the payment is $100,000 ÷ 10 = $10,000 per year.<br />
<br />
But if the interest rate is positive, as is usually the case, then the payment in the above example would have to be more than $10,000 per year. That's because $10,000 in the future is worth less than $10,000 today. This is referred to as the time value of money. If the interest is 5% per year, then $10,000 today is worth:<br />
<br />
* <math>$10,000*1.05^1=$10,500</math> one year from now<br />
* <math>$10,000*1.05^2=$11,025</math> two years from now<br />
<br />
and so on. We will have to adjust for the differences in value. The amortization formula makes the necessary adjustments and tells us that if the interest rate is 5% per year, then the payments will have to be $12,950 per year for the next ten years for the total value of the payments to be equal in value to the $100,000 that was borrowed today.<br />
<br />
==Amortization based withdrawal==<br />
<br />
To calculate portfolio withdrawals, enter the following inputs in the ABW calculator ([[#ABW calculator|below]]):<br />
<br />
* <math>P=</math> current portfolio value<br />
* <math>n=</math> number of years over which withdrawals are to be spread out<br />
* <math>r=</math> expected return of the portfolio.<br />
<br />
===Example===<br />
<br />
A 65 year old retiree with a $1 million portfolio expected to earn 3% per year and seeking to spread out withdrawals over 36 years (ages 65 to 100), would enter <math>P=$1,000,000, n=36, r=3%</math>. The amortization calculator says that this retiree can withdraw $44,470 per year. This means that if the portfolio actual rate of return remains constant at 3% per year and the retiree withdraws $44,470 every year, then the portfolio will be fully depleted after 36 years.<br />
<br />
===Real vs nominal rate of return===<br />
<br />
If a real (inflation adjusted) rate of return is used, the withdrawal strategy becomes automatically adjusted for inflation. In the above example, if the real rate of return is 3%, the retiree will be able to take out $44,470 (inflation adjusted) each year. If instead, the retiree enters a nominal interest rate of 5%, the calculator says that they can take out $60,434 per year. But that's in nominal dollars, so real consumption will decline each year by the inflation rate. In practice, it is strongly recommended to use a real rate of return.<br />
<br />
===Update and adapt===<br />
<br />
Withdrawals are recalculated each year with updated information about portfolio value, expected rate of return, and number of years left. This allows withdrawals to continually adapt to new information and mitigates the impact of past incorrect assumptions. Amortization spreads the course correction required across all remaining years, thereby minimizing the impact on any one year.<br />
<br />
====Example====<br />
<br />
Consider what happens in our earlier example if, instead of gaining 3% as expected, the portfolio actually loses 10%. The shortfall relative to expectations is <math>(1-.10)/(1+.03)-1=-12.6%</math>. Our retiree had expected to start age 66 with $984,196 in the portfolio. Instead, the portfolio contains only $859,977, which is 12.6% less. Consider what happens in the following two scenarios:<br />
<br />
=====Scenario 1: Expected return stays the same=====<br />
Suppose that the retiree believes that this market drop has not impacted future expected returns, which in the retiree's opinion, remains at 3%. The retiree enters the new reduced portfolio value, <math>P=$859,977</math>, number of years remaining <math>n=35</math>, and expected real return <math>r=3%</math>. The withdrawal is now reduced to $38,857 per year. That is a 12.6% reduction relative to the previously planned withdrawal of $44,470. So the 12.6% portfolio loss is being matched by a 12.6% spending cut across all remaining years.<br />
<br />
=====Scenario 2: Expected return increases=====<br />
If the market drop was due to a pure valuation change and the underlying earnings of the portfolio are not impacted, then the retiree might expect a higher rate of return going forward.<br />
<br />
If expected return is based on an earnings yield model (e.g. 1/CAPE) for stocks and yield to maturity for bonds, a 12.6% reduction in valuation will result in a higher expected real return of <math>.03/(1-.126)=3.43%</math>. With the higher expected return, the withdrawal becomes $41,181. That is a reduction of only 7.4% relative to the original plan of $44,470. A 12.6% reduction in the portfolio led to only a 7.4% reduction in income, because the higher expected return partially offset the loss in portfolio value.<br />
<br />
So to the extent that market volatility is caused by valuation changes and gets incorporated into expected returns, withdrawals from the portfolio will be less volatile than the portfolio itself.<br />
<br />
==Adding a terminal balance==<br />
<br />
Instead of fully depleting the portfolio, the amortization can be modified to leave behind a terminal balance. This could be used to fund end of life care or a bequest, or it could simply serve as a general financial cushion. <br />
<br />
In the ABW calculator, enter:<br />
* <math>B=</math> terminal balance<br />
<br />
===Example===<br />
<br />
The 65 year old retiree in the earlier example wants to have $200,000 left at the end for a bequest. Enter <math>B=$200,000</math> in the calculator to get a withdrawal of $41,401 per year. If the actual rate of return matches expectations, then after withdrawing $41,401 for 36 years (ages 65 to 100), the retiree will have $200,000 remaining in the portfolio at the end of age 100.<br />
<br />
==Rising or falling withdrawal schedules==<br />
<br />
Instead of aiming at a constant withdrawal schedule, some retirees may prefer to aim at a rising or falling withdrawal schedule. Retirees worried about incurring unexpected expenses or generally running out of money in later years may want to use a rising withdrawal schedule - take less early so they can have more later. Those wanting to fund an active early retirement may want to use a declining withdrawal schedule - take more early but have less later. (Note the similarity with savings. This can be viewed as a decision about how much to save in the early retirement years in order to fund late retirement consumption.)<br />
<br />
In the ABW calculator, enter:<br />
* <math>g=</math> rate of growth of the withdrawal schedule<br />
<br />
<math>g>0</math> generates a rising withdrawal schedule, <math>g<0</math> generates a declining withdrawal schedule, and <math>g=0</math> generates a constant withdrawal schedule.<br />
<br />
===Example===<br />
<br />
If the 65 year old retiree in the earlier example wants withdrawals to grow at 1% per year, set <math>g=1%</math> to get a withdrawal of $38,349. Withdrawals are scheduled to grow 1% per year, rising to $54,325 at age 100.<br />
<br />
If instead the retiree wishes to spend more in early retirement and wants withdrawals to fall by 1% per year, set <math>g=-1%</math> to get a withdrawal of $51,118. Withdrawals are scheduled to fall 1% per year, declining to $35,959 at age 100.<br />
<br />
==Asset allocation==<br />
<br />
===Fixed asset allocation===<br />
<br />
The amortization formula assumes an expected rate of return on the portfolio which stays consistent over the retirement period. This is easier to justify if the retiree plans to maintain a fixed asset allocation (AA). If instead the retiree is planning to change the AA over time (e.g. glide down from 60/40 to 30/70 over the course of the retirement), then the expected return will display more variations over time, skewing the amortization computation. The calculator provided here is not designed for such case. Entering the average expected return in the calculator may provide a rough estimate, but due to the potential for significant errors, more precise modeling is recommended.<br />
<br />
===Fixed asset allocation with sub-portfolios===<br />
<br />
The portfolio can be divided into multiple sub-portfolios and a different fixed allocation applied to each sub-portfolio.<br />
<br />
Suppose the retiree is more risk averse over certain categories of consumption (e.g. food and housing), and less risk averse over other categories (e.g. vacations). The portfolio can be subdivided into a safer portfolio to fund food and housing and a riskier portfolio to fund vacations. The safe portfolio would get a safe fixed AA like 30/70, and the riskier portfolio would get a riskier fixed AA like 80/20. Multiple sub-portfolios could be created to fund different consumption goals, each with a different AA that matches the risk-reward considerations for that goal. Withdrawals would be calculated separately for each sub-portfolio.<br />
<br />
An example of a strategy that uses sub-portfolios is the Liability Matched Portfolio (LMP) strategy. The portfolio is divided into a "liability matched portfolio" and a "risk portfolio". The liability matched portfolio has an AA of 0/100 and is used to fund non-negotiable consumption. The risk portfolio is given a riskier AA and is used to fund discretionary "nice to have" consumption.<br />
<br />
==Estimating the expected return==<br />
<br />
The ABW calculation requires the user to input the expected rate of return of the portfolio. ABW does not recommend a specific model for this purpose. The user is free to use whatever model of expected return they prefer. Examples of models that can be used include:<br />
<br />
===Models based on earnings yields (e.g. 1/CAPE)===<br />
<Enter info><br />
<br />
===Models based on historical returns===<br />
<Enter info><br />
<br />
==Extra income and expenses==<br />
<br />
Besides their savings portfolio, retirees may have other sources of present or future income such as social security, pensions, annuities, rental income, part-time wages and lump sum payouts ("extra income"). Retirees may also plan for exceptional expenses such as college tuition, a lingering home mortgage or long-term care expenses that may require funds beyond what is provided by regular budgeting ("extra expenses"). Such future extra income and expenses can be amortized by computing the present value of such future sums (see Wiki article on calculating present value by discounting future cash flows: [[Comparing_investments#Present_value|Comparing Investments]]) and converting in an additional series of payments, beyond the regular payment derived from the savings portfolio's balance. It is strongly recommended to perform such computations in real (inflation-adjusted) terms. Funding such additional payments in the short-term can be achieved in different ways, e.g. structuring financial assets according to the retiree's personal risks/rewards goals. ABW is neutral and does not take a position on how best to do it. Below are some of the strategies which can be used:<br />
<br />
===Separate sub-portfolio focused approach===<br />
<br />
The retiree can choose to keep funds for some or all of the extra income and expenses outside the regular amortization process. They can allocate extra income and budget for extra expenses, separate from the ABW calculation. This is effectively a partitioned portfolio approach where extra income and expenses are being handled in a separate safe sub-portfolio.<br />
<br />
A retiree formally pursuing the separate portfolio approach described [[User:Willthrill81/Amortization_based_withdrawal#Fixed_asset_allocation_with_sub-portfolios|earlier]] may find it convenient to use conservative estimates of social security and pensions to fund the safe sub-portfolios. For more complex cases, sizing the sub-portfolio can be achieved by a present value computation of future extra income and expenses (e.g. when using a bonds ladder, use the bonds interest rate to discount future income/expenses). The income streams are typically duration matched. Gaps remaining can be filled with duration matched bonds. Depending on the asset allocation, there may be little to no rebalancing needed in safe sub-portfolios.<br />
<br />
===Savings portfolio focused approach===<br />
<br />
The retiree funds the additional payments through additional withdrawals from the savings portfolio, while maintaining a fixed asset allocation on the savings portfolio. The discounting and amortization rate used should then be the savings portfolio's expected rate of return. Care should be exercised about the additional burden on one's savings portfolio and possible consequences of market crises before steady future income (e.g. SS/Pensions) materializes.<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using the portfolio's expected rate of return. Calculate amortized additional withdrawals based on such value, in the same manner as the savings portfolio balance is amortized. Such computation is independent from the portfolio's rebalancing procedure and doesn't change the expected return computation. More information on this approach is available on this [https://www.bogleheads.org/blog/2019/02/01/early-retirement-and-time-value-of-money/ blog article], which comes with a [http://bit.ly/2WuNmvf companion spreadsheet].<br />
<br />
===Total portfolio focused approach===<br />
<br />
The retiree funds the additional payments through... <<Ben to elaborate, including a brief explanation of "total portfolio" concept>>. <br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using bond interest rates. Add this value to the regular portfolio's balance for all calculations, counting it as a bond. Include it when calculating withdrawals. Include it when calculating the asset allocation of the total portfolio (for rebalancing) and the expected return of the total portfolio (to enter into the amortized payment computation). More information on this approach is available here: <insert link><br />
<br />
==ABW calculator==<br />
<br />
===Basic calculator===<br />
<br />
The Excel spreadsheet to calculate withdrawals in on Google Drive: [https://drive.google.com/file/d/1XOnBaUspLX_oaM2rquTPmLj5AKOm6yxV/view?usp=sharing ABW Calculator]<br />
<br />
[[User:Ben Mathew/Formulas for Amortization Based Withdrawal (ABW)]] describes the formulas used in the calculator.<br />
<br />
===Advanced calculators===<br />
<br />
These calculators expand the basic functionality to include other considerations.<br />
<br />
An Excel spreadsheet that incorporates extra income and expenses is available on Google Drive: [https://drive.google.com/file/d/1v8KZfXMCnIJXjy0e3RkZ-Uap4OiaXCpu/view?usp=sharing ABW Calculator with Extra Income and Expenses]. <br />
<br />
Another calculator performing similar amortization functions and providing some backtesting capabilities is formatted as a Google sheet and is available here (please make a copy): [http://bit.ly/2WuNmvf Amortized Spending Budget - Fixed Asset Allocation].<br />
<br />
==Support==<br />
On-going discussion and support is in {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}.<br />
<br />
==See also==<br />
*[[Comparing investments]] - Tutorial on ''Time Value of Money'' equations</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Amortization_based_withdrawal&diff=70682
Amortization based withdrawal
2020-11-27T19:41:34Z
<p>Siamond: /* Extra income and expenses */ Minor consistency improvement</p>
<hr />
<div>{{Under construction| comment = Comments are being solicited in this {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}}}<br />
'''Amortization based withdrawal (ABW)''' uses amortization techniques to calculate portfolio withdrawals during retirement. Examples of withdrawals that use amortization include [[Variable percentage withdrawal | Variable Percentage Withdrawal]] (VPW) and the [[Required Minimum Distribution]] (RMD) rules for traditional retirement accounts.<br />
<br />
==Amortization==<br />
<br />
===Understanding amortization===<br />
<br />
Amortization is the process of converting the value of a lump sum into a series of payments over time. Most people encounter it when they take out a mortgage or car loan. Amortization is used to calculate the monthly payment required to pay back the loan. The value of the monthly payments has to be made equal to the value of the initial loan.<br />
<br />
If the interest rate is zero, amortization is just simple division: If $100,000 has to be paid back over 10 years, then the payment is $100,000 ÷ 10 = $10,000 per year.<br />
<br />
But if the interest rate is positive, as is usually the case, then the payment in the above example would have to be more than $10,000 per year. That's because $10,000 in the future is worth less than $10,000 today. This is referred to as the time value of money. If the interest is 5% per year, then $10,000 today is worth:<br />
<br />
* <math>$10,000*1.05^1=$10,500</math> one year from now<br />
* <math>$10,000*1.05^2=$11,025</math> two years from now<br />
<br />
and so on. We will have to adjust for the differences in value. The amortization formula makes the necessary adjustments and tells us that if the interest rate is 5% per year, then the payments will have to be $12,950 per year for the next ten years for the total value of the payments to be equal in value to the $100,000 that was borrowed today.<br />
<br />
==Amortization based withdrawal==<br />
<br />
To calculate portfolio withdrawals, enter the following inputs in the ABW calculator ([[#ABW calculator|below]]):<br />
<br />
* <math>P=</math> current portfolio value<br />
* <math>n=</math> number of years over which withdrawals are to be spread out<br />
* <math>r=</math> expected return of the portfolio.<br />
<br />
===Example===<br />
<br />
A 65 year old retiree with a $1 million portfolio expected to earn 3% per year and seeking to spread out withdrawals over 36 years (ages 65 to 100), would enter <math>P=$1,000,000, n=36, r=3%</math>. The amortization calculator says that this retiree can withdraw $44,470 per year. This means that if the portfolio actual rate of return remains constant at 3% per year and the retiree withdraws $44,470 every year, then the portfolio will be fully depleted after 36 years.<br />
<br />
===Real vs nominal rate of return===<br />
<br />
If a real (inflation adjusted) rate of return is used, the withdrawal strategy becomes automatically adjusted for inflation. In the above example, if the real rate of return is 3%, the retiree will be able to take out $44,470 (inflation adjusted) each year. If instead, the retiree enters a nominal interest rate of 5%, the calculator says that they can take out $60,434 per year. But that's in nominal dollars, so real consumption will decline each year by the inflation rate. In practice, it is strongly recommended to use a real rate of return.<br />
<br />
===Update and adapt===<br />
<br />
Withdrawals are recalculated each year with updated information about portfolio value, expected rate of return, and number of years left. This allows withdrawals to continually adapt to new information and mitigates the impact of past incorrect assumptions. Amortization spreads the course correction required across all remaining years, thereby minimizing the impact on any one year.<br />
<br />
====Example====<br />
<br />
Consider what happens in our earlier example if, instead of gaining 3% as expected, the portfolio actually loses 10%. The shortfall relative to expectations is <math>(1-.10)/(1+.03)-1=-12.6%</math>. Our retiree had expected to start age 66 with $984,196 in the portfolio. Instead, the portfolio contains only $859,977, which is 12.6% less. Consider what happens in the following two scenarios:<br />
<br />
=====Scenario 1: Expected return stays the same=====<br />
Suppose that the retiree believes that this market drop has not impacted future expected returns, which in the retiree's opinion, remains at 3%. The retiree enters the new reduced portfolio value, <math>P=$859,977</math>, number of years remaining <math>n=35</math>, and expected real return <math>r=3%</math>. The withdrawal is now reduced to $38,857 per year. That is a 12.6% reduction relative to the previously planned withdrawal of $44,470. So the 12.6% portfolio loss is being matched by a 12.6% spending cut across all remaining years.<br />
<br />
=====Scenario 2: Expected return increases=====<br />
If the market drop was due to a pure valuation change and the underlying earnings of the portfolio are not impacted, then the retiree might expect a higher rate of return going forward.<br />
<br />
If expected return is based on an earnings yield model (e.g. 1/CAPE) for stocks and yield to maturity for bonds, a 12.6% reduction in valuation will result in a higher expected real return of <math>.03/(1-.126)=3.43%</math>. With the higher expected return, the withdrawal becomes $41,181. That is a reduction of only 7.4% relative to the original plan of $44,470. A 12.6% reduction in the portfolio led to only a 7.4% reduction in income, because the higher expected return partially offset the loss in portfolio value.<br />
<br />
So to the extent that market volatility is caused by valuation changes and gets incorporated into expected returns, withdrawals from the portfolio will be less volatile than the portfolio itself.<br />
<br />
==Adding a terminal balance==<br />
<br />
Instead of fully depleting the portfolio, the amortization can be modified to leave behind a terminal balance. This could be used to fund end of life care or a bequest, or it could simply serve as a general financial cushion. <br />
<br />
In the ABW calculator, enter:<br />
* <math>B=</math> terminal balance<br />
<br />
===Example===<br />
<br />
The 65 year old retiree in the earlier example wants to have $200,000 left at the end for a bequest. Enter <math>B=$200,000</math> in the calculator to get a withdrawal of $41,401 per year. If the actual rate of return matches expectations, then after withdrawing $41,401 for 36 years (ages 65 to 100), the retiree will have $200,000 remaining in the portfolio at the end of age 100.<br />
<br />
==Rising or falling withdrawal schedules==<br />
<br />
Instead of aiming at a constant withdrawal schedule, some retirees may prefer to aim at a rising or falling withdrawal schedule. Retirees worried about incurring unexpected expenses or generally running out of money in later years may want to use a rising withdrawal schedule - take less early so they can have more later. Those wanting to fund an active early retirement may want to use a declining withdrawal schedule - take more early but have less later. (Note the similarity with savings. This can be viewed as a decision about how much to save in the early retirement years in order to fund late retirement consumption.)<br />
<br />
In the ABW calculator, enter:<br />
* <math>g=</math> rate of growth of the withdrawal schedule<br />
<br />
<math>g>0</math> generates a rising withdrawal schedule, <math>g<0</math> generates a declining withdrawal schedule, and <math>g=0</math> generates a constant withdrawal schedule.<br />
<br />
===Example===<br />
<br />
If the 65 year old retiree in the earlier example wants withdrawals to grow at 1% per year, set <math>g=1%</math> to get a withdrawal of $38,349. Withdrawals are scheduled to grow 1% per year, rising to $54,325 at age 100.<br />
<br />
If instead the retiree wishes to spend more in early retirement and wants withdrawals to fall by 1% per year, set <math>g=-1%</math> to get a withdrawal of $51,118. Withdrawals are scheduled to fall 1% per year, declining to $35,959 at age 100.<br />
<br />
==Asset allocation==<br />
<br />
===Fixed asset allocation===<br />
<br />
The amortization formula assumes an expected rate of return on the portfolio which stays consistent over the retirement period. This is easier to justify if the retiree plans to maintain a fixed asset allocation (AA). If instead the retiree is planning to change the AA over time (e.g. glide down from 60/40 to 30/70 over the course of the retirement), then the expected return will display more variations over time, skewing the amortization computation. The calculator provided here is not designed for such case. Entering the average expected return in the calculator may provide a rough estimate, but due to the potential for significant errors, more precise modeling is recommended.<br />
<br />
===Fixed asset allocation with sub-portfolios===<br />
<br />
The portfolio can be divided into multiple sub-portfolios and a different fixed allocation applied to each sub-portfolio.<br />
<br />
Suppose the retiree is more risk averse over certain categories of consumption (e.g. food and housing), and less risk averse over other categories (e.g. vacations). The portfolio can be subdivided into a safer portfolio to fund food and housing and a riskier portfolio to fund vacations. The safe portfolio would get a safe fixed AA like 30/70, and the riskier portfolio would get a riskier fixed AA like 80/20. Multiple sub-portfolios could be created to fund different consumption goals, each with a different AA that matches the risk-reward considerations for that goal. Withdrawals would be calculated separately for each sub-portfolio.<br />
<br />
An example of a strategy that uses sub-portfolios is the Liability Matched Portfolio (LMP) strategy. The portfolio is divided into a "liability matched portfolio" and a "risk portfolio". The liability matched portfolio has an AA of 0/100 and is used to fund non-negotiable consumption. The risk portfolio is given a riskier AA and is used to fund discretionary "nice to have" consumption.<br />
<br />
==Estimating the expected return==<br />
<br />
The ABW calculation requires the user to input the expected rate of return of the portfolio. ABW does not recommend a specific model for this purpose. The user is free to use whatever model of expected return they prefer. Examples of models that can be used include:<br />
<br />
===Models based on earnings yields (e.g. 1/CAPE)===<br />
<Enter info><br />
<br />
===Models based on historical returns===<br />
<Enter info><br />
<br />
==Extra income and expenses==<br />
<br />
Besides their savings portfolio, retirees may have other sources of present or future income such as social security, pensions, annuities, rental income, part-time wages and lump sum payouts ("extra income"). Retirees may also plan for exceptional expenses such as college tuition, a lingering home mortgage or long-term care expenses that may require funds beyond what is provided by regular budgeting ("extra expenses"). Such future extra income and expenses can be amortized by computing the present value of such future sums (see Wiki article on calculating present value by discounting future cash flows: [[Comparing_investments#Present_value|Comparing Investments]]) and converting in an additional series of payments, beyond the regular payment derived from the savings portfolio's balance. It is strongly recommended to perform such computations in real (inflation-adjusted) terms. Funding such additional payments in the short-term can be achieved in different ways, e.g. structuring financial assets according to the retiree's personal risks/rewards goals. ABW is neutral and does not take a position on how best to do it. Below are some of the strategies which can be used:<br />
<br />
===Separate sub-portfolio approach===<br />
<br />
The retiree can choose to keep funds for some or all of the extra income and expenses outside the regular amortization process. They can allocate extra income and budget for extra expenses, separate from the ABW calculation. This is effectively a partitioned portfolio approach where extra income and expenses are being handled in a separate safe sub-portfolio.<br />
<br />
A retiree formally pursuing the separate portfolio approach described [[User:Willthrill81/Amortization_based_withdrawal#Fixed_asset_allocation_with_sub-portfolios|earlier]] may find it convenient to use conservative estimates of social security and pensions to fund the safe sub-portfolios. For more complex cases, sizing the sub-portfolio can be achieved by a present value computation of future extra income and expenses (e.g. when using a bonds ladder, use the bonds interest rate to discount future income/expenses). The income streams are typically duration matched. Gaps remaining can be filled with duration matched bonds. Depending on the asset allocation, there may be little to no rebalancing needed in safe sub-portfolios.<br />
<br />
===Savings portfolio (fixed asset allocation) approach===<br />
<br />
The retiree can choose to fund the additional payments through additional withdrawals from the savings portfolio, using a fixed asset allocation. The discounting and amortization rate should then be the savings portfolio's expected rate of return, reflecting the savings portfolio's risks/rewards profile. Care should be exercised about the additional burden on one's savings portfolio and possible consequences of market crises before steady future income (e.g. SS/Pensions) materializes.<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using the portfolio's expected rate of return. Calculate amortized additional withdrawals based on such value, in the same manner as the savings portfolio balance is amortized. Such computation is independent from the portfolio's rebalancing procedure and doesn't change the expected return computation. More information on this approach is available on this [https://www.bogleheads.org/blog/2019/02/01/early-retirement-and-time-value-of-money/ blog article], which comes with a [http://bit.ly/2WuNmvf companion spreadsheet].<br />
<br />
===Total portfolio approach===<br />
<br />
The retiree can choose to fund the additional payments through... <<Ben to elaborate, including a brief explanation of "total portfolio" concept>>. <br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using bond interest rates. Add this value to the regular portfolio's balance for all calculations, counting it as a bond. Include it when calculating withdrawals. Include it when calculating the asset allocation of the total portfolio (for rebalancing) and the expected return of the total portfolio (to enter into the amortized payment computation). More information on this approach is available here: <insert link><br />
<br />
==ABW calculator==<br />
<br />
===Basic calculator===<br />
<br />
The Excel spreadsheet to calculate withdrawals in on Google Drive: [https://drive.google.com/file/d/1XOnBaUspLX_oaM2rquTPmLj5AKOm6yxV/view?usp=sharing ABW Calculator]<br />
<br />
[[User:Ben Mathew/Formulas for Amortization Based Withdrawal (ABW)]] describes the formulas used in the calculator.<br />
<br />
===Advanced calculators===<br />
<br />
These calculators expand the basic functionality to include other considerations.<br />
<br />
An Excel spreadsheet that incorporates extra income and expenses is available on Google Drive: [https://drive.google.com/file/d/1v8KZfXMCnIJXjy0e3RkZ-Uap4OiaXCpu/view?usp=sharing ABW Calculator with Extra Income and Expenses]. <br />
<br />
Another calculator performing similar amortization functions and providing some backtesting capabilities is formatted as a Google sheet and is available here (please make a copy): [http://bit.ly/2WuNmvf Amortized Spending Budget - Fixed Asset Allocation].<br />
<br />
==Support==<br />
On-going discussion and support is in {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}.<br />
<br />
==See also==<br />
*[[Comparing investments]] - Tutorial on ''Time Value of Money'' equations</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Amortization_based_withdrawal&diff=70681
Amortization based withdrawal
2020-11-27T19:12:13Z
<p>Siamond: /* Regular portfolio approach */ Minor tweaking</p>
<hr />
<div>{{Under construction| comment = Comments are being solicited in this {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}}}<br />
'''Amortization based withdrawal (ABW)''' uses amortization techniques to calculate portfolio withdrawals during retirement. Examples of withdrawals that use amortization include [[Variable percentage withdrawal | Variable Percentage Withdrawal]] (VPW) and the [[Required Minimum Distribution]] (RMD) rules for traditional retirement accounts.<br />
<br />
==Amortization==<br />
<br />
===Understanding amortization===<br />
<br />
Amortization is the process of converting the value of a lump sum into a series of payments over time. Most people encounter it when they take out a mortgage or car loan. Amortization is used to calculate the monthly payment required to pay back the loan. The value of the monthly payments has to be made equal to the value of the initial loan.<br />
<br />
If the interest rate is zero, amortization is just simple division: If $100,000 has to be paid back over 10 years, then the payment is $100,000 ÷ 10 = $10,000 per year.<br />
<br />
But if the interest rate is positive, as is usually the case, then the payment in the above example would have to be more than $10,000 per year. That's because $10,000 in the future is worth less than $10,000 today. This is referred to as the time value of money. If the interest is 5% per year, then $10,000 today is worth:<br />
<br />
* <math>$10,000*1.05^1=$10,500</math> one year from now<br />
* <math>$10,000*1.05^2=$11,025</math> two years from now<br />
<br />
and so on. We will have to adjust for the differences in value. The amortization formula makes the necessary adjustments and tells us that if the interest rate is 5% per year, then the payments will have to be $12,950 per year for the next ten years for the total value of the payments to be equal in value to the $100,000 that was borrowed today.<br />
<br />
==Amortization based withdrawal==<br />
<br />
To calculate portfolio withdrawals, enter the following inputs in the ABW calculator ([[#ABW calculator|below]]):<br />
<br />
* <math>P=</math> current portfolio value<br />
* <math>n=</math> number of years over which withdrawals are to be spread out<br />
* <math>r=</math> expected return of the portfolio.<br />
<br />
===Example===<br />
<br />
A 65 year old retiree with a $1 million portfolio expected to earn 3% per year and seeking to spread out withdrawals over 36 years (ages 65 to 100), would enter <math>P=$1,000,000, n=36, r=3%</math>. The amortization calculator says that this retiree can withdraw $44,470 per year. This means that if the portfolio actual rate of return remains constant at 3% per year and the retiree withdraws $44,470 every year, then the portfolio will be fully depleted after 36 years.<br />
<br />
===Real vs nominal rate of return===<br />
<br />
If a real (inflation adjusted) rate of return is used, the withdrawal strategy becomes automatically adjusted for inflation. In the above example, if the real rate of return is 3%, the retiree will be able to take out $44,470 (inflation adjusted) each year. If instead, the retiree enters a nominal interest rate of 5%, the calculator says that they can take out $60,434 per year. But that's in nominal dollars, so real consumption will decline each year by the inflation rate. In practice, it is strongly recommended to use a real rate of return.<br />
<br />
===Update and adapt===<br />
<br />
Withdrawals are recalculated each year with updated information about portfolio value, expected rate of return, and number of years left. This allows withdrawals to continually adapt to new information and mitigates the impact of past incorrect assumptions. Amortization spreads the course correction required across all remaining years, thereby minimizing the impact on any one year.<br />
<br />
====Example====<br />
<br />
Consider what happens in our earlier example if, instead of gaining 3% as expected, the portfolio actually loses 10%. The shortfall relative to expectations is <math>(1-.10)/(1+.03)-1=-12.6%</math>. Our retiree had expected to start age 66 with $984,196 in the portfolio. Instead, the portfolio contains only $859,977, which is 12.6% less. Consider what happens in the following two scenarios:<br />
<br />
=====Scenario 1: Expected return stays the same=====<br />
Suppose that the retiree believes that this market drop has not impacted future expected returns, which in the retiree's opinion, remains at 3%. The retiree enters the new reduced portfolio value, <math>P=$859,977</math>, number of years remaining <math>n=35</math>, and expected real return <math>r=3%</math>. The withdrawal is now reduced to $38,857 per year. That is a 12.6% reduction relative to the previously planned withdrawal of $44,470. So the 12.6% portfolio loss is being matched by a 12.6% spending cut across all remaining years.<br />
<br />
=====Scenario 2: Expected return increases=====<br />
If the market drop was due to a pure valuation change and the underlying earnings of the portfolio are not impacted, then the retiree might expect a higher rate of return going forward.<br />
<br />
If expected return is based on an earnings yield model (e.g. 1/CAPE) for stocks and yield to maturity for bonds, a 12.6% reduction in valuation will result in a higher expected real return of <math>.03/(1-.126)=3.43%</math>. With the higher expected return, the withdrawal becomes $41,181. That is a reduction of only 7.4% relative to the original plan of $44,470. A 12.6% reduction in the portfolio led to only a 7.4% reduction in income, because the higher expected return partially offset the loss in portfolio value.<br />
<br />
So to the extent that market volatility is caused by valuation changes and gets incorporated into expected returns, withdrawals from the portfolio will be less volatile than the portfolio itself.<br />
<br />
==Adding a terminal balance==<br />
<br />
Instead of fully depleting the portfolio, the amortization can be modified to leave behind a terminal balance. This could be used to fund end of life care or a bequest, or it could simply serve as a general financial cushion. <br />
<br />
In the ABW calculator, enter:<br />
* <math>B=</math> terminal balance<br />
<br />
===Example===<br />
<br />
The 65 year old retiree in the earlier example wants to have $200,000 left at the end for a bequest. Enter <math>B=$200,000</math> in the calculator to get a withdrawal of $41,401 per year. If the actual rate of return matches expectations, then after withdrawing $41,401 for 36 years (ages 65 to 100), the retiree will have $200,000 remaining in the portfolio at the end of age 100.<br />
<br />
==Rising or falling withdrawal schedules==<br />
<br />
Instead of aiming at a constant withdrawal schedule, some retirees may prefer to aim at a rising or falling withdrawal schedule. Retirees worried about incurring unexpected expenses or generally running out of money in later years may want to use a rising withdrawal schedule - take less early so they can have more later. Those wanting to fund an active early retirement may want to use a declining withdrawal schedule - take more early but have less later. (Note the similarity with savings. This can be viewed as a decision about how much to save in the early retirement years in order to fund late retirement consumption.)<br />
<br />
In the ABW calculator, enter:<br />
* <math>g=</math> rate of growth of the withdrawal schedule<br />
<br />
<math>g>0</math> generates a rising withdrawal schedule, <math>g<0</math> generates a declining withdrawal schedule, and <math>g=0</math> generates a constant withdrawal schedule.<br />
<br />
===Example===<br />
<br />
If the 65 year old retiree in the earlier example wants withdrawals to grow at 1% per year, set <math>g=1%</math> to get a withdrawal of $38,349. Withdrawals are scheduled to grow 1% per year, rising to $54,325 at age 100.<br />
<br />
If instead the retiree wishes to spend more in early retirement and wants withdrawals to fall by 1% per year, set <math>g=-1%</math> to get a withdrawal of $51,118. Withdrawals are scheduled to fall 1% per year, declining to $35,959 at age 100.<br />
<br />
==Asset allocation==<br />
<br />
===Fixed asset allocation===<br />
<br />
The amortization formula assumes an expected rate of return on the portfolio which stays consistent over the retirement period. This is easier to justify if the retiree plans to maintain a fixed asset allocation (AA). If instead the retiree is planning to change the AA over time (e.g. glide down from 60/40 to 30/70 over the course of the retirement), then the expected return will display more variations over time, skewing the amortization computation. The calculator provided here is not designed for such case. Entering the average expected return in the calculator may provide a rough estimate, but due to the potential for significant errors, more precise modeling is recommended.<br />
<br />
===Fixed asset allocation with sub-portfolios===<br />
<br />
The portfolio can be divided into multiple sub-portfolios and a different fixed allocation applied to each sub-portfolio.<br />
<br />
Suppose the retiree is more risk averse over certain categories of consumption (e.g. food and housing), and less risk averse over other categories (e.g. vacations). The portfolio can be subdivided into a safer portfolio to fund food and housing and a riskier portfolio to fund vacations. The safe portfolio would get a safe fixed AA like 30/70, and the riskier portfolio would get a riskier fixed AA like 80/20. Multiple sub-portfolios could be created to fund different consumption goals, each with a different AA that matches the risk-reward considerations for that goal. Withdrawals would be calculated separately for each sub-portfolio.<br />
<br />
An example of a strategy that uses sub-portfolios is the Liability Matched Portfolio (LMP) strategy. The portfolio is divided into a "liability matched portfolio" and a "risk portfolio". The liability matched portfolio has an AA of 0/100 and is used to fund non-negotiable consumption. The risk portfolio is given a riskier AA and is used to fund discretionary "nice to have" consumption.<br />
<br />
==Estimating the expected return==<br />
<br />
The ABW calculation requires the user to input the expected rate of return of the portfolio. ABW does not recommend a specific model for this purpose. The user is free to use whatever model of expected return they prefer. Examples of models that can be used include:<br />
<br />
===Models based on earnings yields (e.g. 1/CAPE)===<br />
<Enter info><br />
<br />
===Models based on historical returns===<br />
<Enter info><br />
<br />
==Extra income and expenses==<br />
<br />
Besides their savings portfolio, retirees may have other sources of present or future income such as social security, pensions, annuities, rental income, part-time wages and lump sum payouts ("extra income"). Retirees may also plan for exceptional expenses such as college tuition, a lingering home mortgage or long-term care expenses that may require funds beyond what is provided by regular budgeting ("extra expenses"). Such future extra income and expenses can be amortized by computing the present value of such future sums (see Wiki article on calculating present value by discounting future cash flows: [[Comparing_investments#Present_value|Comparing Investments]]) and converting in an additional series of payments, beyond the regular payment derived from the savings portfolio's balance. It is strongly recommended to perform such computations in real (inflation-adjusted) terms. Funding such additional payments in the short-term can be achieved in different ways, structuring financial assets according to the retiree's personal risks/rewards goals. ABW is neutral and does not take a position on how best to do it. Below are some of the strategies which can be used:<br />
<br />
===Separate sub-portfolio approach===<br />
<br />
The retiree can choose to keep funds for some or all of the extra income and expenses outside the regular amortization process. They can allocate extra income and budget for extra expenses, separate from the ABW calculation. This is effectively a partitioned portfolio approach where extra income and expenses are being handled in a separate safe sub-portfolio.<br />
<br />
A retiree formally pursuing the separate portfolio approach described [[User:Willthrill81/Amortization_based_withdrawal#Fixed_asset_allocation_with_sub-portfolios|earlier]] may find it convenient to use conservative estimates of social security and pensions to fund the safe sub-portfolios. For more complex cases, sizing the sub-portfolio can be achieved by a present value computation of future extra income and expenses (e.g. when using a TIPS ladder, use the bonds interest rate to discount future income/expenses). The income streams are typically duration matched. Gaps remaining can be filled with duration matched bonds. Depending on the asset allocation, there may be little to no rebalancing needed in safe sub-portfolios.<br />
<br />
===Regular portfolio (fixed asset allocation) approach===<br />
<br />
The retiree can choose to fund the additional payments through additional withdrawals from the regular savings portfolio, using a fixed asset allocation. The discounting and amortization rate should then be the savings portfolio's expected rate of return, reflecting the regular portfolio's risks/rewards profile. Care should be exercised about the additional burden on one's savings portfolio and possible consequences of market crises before steady future income (e.g. SS/Pensions) materializes.<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using the portfolio's expected rate of return. Calculate amortized additional withdrawals based on such value, in the same manner as the savings portfolio balance is amortized. Such computation is independent from the portfolio's rebalancing procedure and doesn't change the expected return computation. More information on this approach is available on this [https://www.bogleheads.org/blog/2019/02/01/early-retirement-and-time-value-of-money/ blog article], which comes with a [http://bit.ly/2WuNmvf companion spreadsheet].<br />
<br />
===Total portfolio approach===<br />
<br />
The retiree can choose to fund the additional payments through... <<Ben to elaborate, including a brief explanation of "total portfolio" concept>>. <br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using bond interest rates. Add this value to the regular portfolio's balance for all calculations, counting it as a bond. Include it when calculating withdrawals. Include it when calculating the asset allocation of the total portfolio (for rebalancing) and the expected return of the total portfolio (to enter into the amortized payment computation). More information on this approach is available here: <insert link><br />
<br />
==ABW calculator==<br />
<br />
===Basic calculator===<br />
<br />
The Excel spreadsheet to calculate withdrawals in on Google Drive: [https://drive.google.com/file/d/1XOnBaUspLX_oaM2rquTPmLj5AKOm6yxV/view?usp=sharing ABW Calculator]<br />
<br />
[[User:Ben Mathew/Formulas for Amortization Based Withdrawal (ABW)]] describes the formulas used in the calculator.<br />
<br />
===Advanced calculators===<br />
<br />
These calculators expand the basic functionality to include other considerations.<br />
<br />
An Excel spreadsheet that incorporates extra income and expenses is available on Google Drive: [https://drive.google.com/file/d/1v8KZfXMCnIJXjy0e3RkZ-Uap4OiaXCpu/view?usp=sharing ABW Calculator with Extra Income and Expenses]. <br />
<br />
Another calculator performing similar amortization functions and providing some backtesting capabilities is formatted as a Google sheet and is available here (please make a copy): [http://bit.ly/2WuNmvf Amortized Spending Budget - Fixed Asset Allocation].<br />
<br />
==Support==<br />
On-going discussion and support is in {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}.<br />
<br />
==See also==<br />
*[[Comparing investments]] - Tutorial on ''Time Value of Money'' equations</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Amortization_based_withdrawal&diff=70680
Amortization based withdrawal
2020-11-27T19:08:42Z
<p>Siamond: /* Separate sub-portfolio approach */ Trying to reduce disagreements...</p>
<hr />
<div>{{Under construction| comment = Comments are being solicited in this {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}}}<br />
'''Amortization based withdrawal (ABW)''' uses amortization techniques to calculate portfolio withdrawals during retirement. Examples of withdrawals that use amortization include [[Variable percentage withdrawal | Variable Percentage Withdrawal]] (VPW) and the [[Required Minimum Distribution]] (RMD) rules for traditional retirement accounts.<br />
<br />
==Amortization==<br />
<br />
===Understanding amortization===<br />
<br />
Amortization is the process of converting the value of a lump sum into a series of payments over time. Most people encounter it when they take out a mortgage or car loan. Amortization is used to calculate the monthly payment required to pay back the loan. The value of the monthly payments has to be made equal to the value of the initial loan.<br />
<br />
If the interest rate is zero, amortization is just simple division: If $100,000 has to be paid back over 10 years, then the payment is $100,000 ÷ 10 = $10,000 per year.<br />
<br />
But if the interest rate is positive, as is usually the case, then the payment in the above example would have to be more than $10,000 per year. That's because $10,000 in the future is worth less than $10,000 today. This is referred to as the time value of money. If the interest is 5% per year, then $10,000 today is worth:<br />
<br />
* <math>$10,000*1.05^1=$10,500</math> one year from now<br />
* <math>$10,000*1.05^2=$11,025</math> two years from now<br />
<br />
and so on. We will have to adjust for the differences in value. The amortization formula makes the necessary adjustments and tells us that if the interest rate is 5% per year, then the payments will have to be $12,950 per year for the next ten years for the total value of the payments to be equal in value to the $100,000 that was borrowed today.<br />
<br />
==Amortization based withdrawal==<br />
<br />
To calculate portfolio withdrawals, enter the following inputs in the ABW calculator ([[#ABW calculator|below]]):<br />
<br />
* <math>P=</math> current portfolio value<br />
* <math>n=</math> number of years over which withdrawals are to be spread out<br />
* <math>r=</math> expected return of the portfolio.<br />
<br />
===Example===<br />
<br />
A 65 year old retiree with a $1 million portfolio expected to earn 3% per year and seeking to spread out withdrawals over 36 years (ages 65 to 100), would enter <math>P=$1,000,000, n=36, r=3%</math>. The amortization calculator says that this retiree can withdraw $44,470 per year. This means that if the portfolio actual rate of return remains constant at 3% per year and the retiree withdraws $44,470 every year, then the portfolio will be fully depleted after 36 years.<br />
<br />
===Real vs nominal rate of return===<br />
<br />
If a real (inflation adjusted) rate of return is used, the withdrawal strategy becomes automatically adjusted for inflation. In the above example, if the real rate of return is 3%, the retiree will be able to take out $44,470 (inflation adjusted) each year. If instead, the retiree enters a nominal interest rate of 5%, the calculator says that they can take out $60,434 per year. But that's in nominal dollars, so real consumption will decline each year by the inflation rate. In practice, it is strongly recommended to use a real rate of return.<br />
<br />
===Update and adapt===<br />
<br />
Withdrawals are recalculated each year with updated information about portfolio value, expected rate of return, and number of years left. This allows withdrawals to continually adapt to new information and mitigates the impact of past incorrect assumptions. Amortization spreads the course correction required across all remaining years, thereby minimizing the impact on any one year.<br />
<br />
====Example====<br />
<br />
Consider what happens in our earlier example if, instead of gaining 3% as expected, the portfolio actually loses 10%. The shortfall relative to expectations is <math>(1-.10)/(1+.03)-1=-12.6%</math>. Our retiree had expected to start age 66 with $984,196 in the portfolio. Instead, the portfolio contains only $859,977, which is 12.6% less. Consider what happens in the following two scenarios:<br />
<br />
=====Scenario 1: Expected return stays the same=====<br />
Suppose that the retiree believes that this market drop has not impacted future expected returns, which in the retiree's opinion, remains at 3%. The retiree enters the new reduced portfolio value, <math>P=$859,977</math>, number of years remaining <math>n=35</math>, and expected real return <math>r=3%</math>. The withdrawal is now reduced to $38,857 per year. That is a 12.6% reduction relative to the previously planned withdrawal of $44,470. So the 12.6% portfolio loss is being matched by a 12.6% spending cut across all remaining years.<br />
<br />
=====Scenario 2: Expected return increases=====<br />
If the market drop was due to a pure valuation change and the underlying earnings of the portfolio are not impacted, then the retiree might expect a higher rate of return going forward.<br />
<br />
If expected return is based on an earnings yield model (e.g. 1/CAPE) for stocks and yield to maturity for bonds, a 12.6% reduction in valuation will result in a higher expected real return of <math>.03/(1-.126)=3.43%</math>. With the higher expected return, the withdrawal becomes $41,181. That is a reduction of only 7.4% relative to the original plan of $44,470. A 12.6% reduction in the portfolio led to only a 7.4% reduction in income, because the higher expected return partially offset the loss in portfolio value.<br />
<br />
So to the extent that market volatility is caused by valuation changes and gets incorporated into expected returns, withdrawals from the portfolio will be less volatile than the portfolio itself.<br />
<br />
==Adding a terminal balance==<br />
<br />
Instead of fully depleting the portfolio, the amortization can be modified to leave behind a terminal balance. This could be used to fund end of life care or a bequest, or it could simply serve as a general financial cushion. <br />
<br />
In the ABW calculator, enter:<br />
* <math>B=</math> terminal balance<br />
<br />
===Example===<br />
<br />
The 65 year old retiree in the earlier example wants to have $200,000 left at the end for a bequest. Enter <math>B=$200,000</math> in the calculator to get a withdrawal of $41,401 per year. If the actual rate of return matches expectations, then after withdrawing $41,401 for 36 years (ages 65 to 100), the retiree will have $200,000 remaining in the portfolio at the end of age 100.<br />
<br />
==Rising or falling withdrawal schedules==<br />
<br />
Instead of aiming at a constant withdrawal schedule, some retirees may prefer to aim at a rising or falling withdrawal schedule. Retirees worried about incurring unexpected expenses or generally running out of money in later years may want to use a rising withdrawal schedule - take less early so they can have more later. Those wanting to fund an active early retirement may want to use a declining withdrawal schedule - take more early but have less later. (Note the similarity with savings. This can be viewed as a decision about how much to save in the early retirement years in order to fund late retirement consumption.)<br />
<br />
In the ABW calculator, enter:<br />
* <math>g=</math> rate of growth of the withdrawal schedule<br />
<br />
<math>g>0</math> generates a rising withdrawal schedule, <math>g<0</math> generates a declining withdrawal schedule, and <math>g=0</math> generates a constant withdrawal schedule.<br />
<br />
===Example===<br />
<br />
If the 65 year old retiree in the earlier example wants withdrawals to grow at 1% per year, set <math>g=1%</math> to get a withdrawal of $38,349. Withdrawals are scheduled to grow 1% per year, rising to $54,325 at age 100.<br />
<br />
If instead the retiree wishes to spend more in early retirement and wants withdrawals to fall by 1% per year, set <math>g=-1%</math> to get a withdrawal of $51,118. Withdrawals are scheduled to fall 1% per year, declining to $35,959 at age 100.<br />
<br />
==Asset allocation==<br />
<br />
===Fixed asset allocation===<br />
<br />
The amortization formula assumes an expected rate of return on the portfolio which stays consistent over the retirement period. This is easier to justify if the retiree plans to maintain a fixed asset allocation (AA). If instead the retiree is planning to change the AA over time (e.g. glide down from 60/40 to 30/70 over the course of the retirement), then the expected return will display more variations over time, skewing the amortization computation. The calculator provided here is not designed for such case. Entering the average expected return in the calculator may provide a rough estimate, but due to the potential for significant errors, more precise modeling is recommended.<br />
<br />
===Fixed asset allocation with sub-portfolios===<br />
<br />
The portfolio can be divided into multiple sub-portfolios and a different fixed allocation applied to each sub-portfolio.<br />
<br />
Suppose the retiree is more risk averse over certain categories of consumption (e.g. food and housing), and less risk averse over other categories (e.g. vacations). The portfolio can be subdivided into a safer portfolio to fund food and housing and a riskier portfolio to fund vacations. The safe portfolio would get a safe fixed AA like 30/70, and the riskier portfolio would get a riskier fixed AA like 80/20. Multiple sub-portfolios could be created to fund different consumption goals, each with a different AA that matches the risk-reward considerations for that goal. Withdrawals would be calculated separately for each sub-portfolio.<br />
<br />
An example of a strategy that uses sub-portfolios is the Liability Matched Portfolio (LMP) strategy. The portfolio is divided into a "liability matched portfolio" and a "risk portfolio". The liability matched portfolio has an AA of 0/100 and is used to fund non-negotiable consumption. The risk portfolio is given a riskier AA and is used to fund discretionary "nice to have" consumption.<br />
<br />
==Estimating the expected return==<br />
<br />
The ABW calculation requires the user to input the expected rate of return of the portfolio. ABW does not recommend a specific model for this purpose. The user is free to use whatever model of expected return they prefer. Examples of models that can be used include:<br />
<br />
===Models based on earnings yields (e.g. 1/CAPE)===<br />
<Enter info><br />
<br />
===Models based on historical returns===<br />
<Enter info><br />
<br />
==Extra income and expenses==<br />
<br />
Besides their savings portfolio, retirees may have other sources of present or future income such as social security, pensions, annuities, rental income, part-time wages and lump sum payouts ("extra income"). Retirees may also plan for exceptional expenses such as college tuition, a lingering home mortgage or long-term care expenses that may require funds beyond what is provided by regular budgeting ("extra expenses"). Such future extra income and expenses can be amortized by computing the present value of such future sums (see Wiki article on calculating present value by discounting future cash flows: [[Comparing_investments#Present_value|Comparing Investments]]) and converting in an additional series of payments, beyond the regular payment derived from the savings portfolio's balance. It is strongly recommended to perform such computations in real (inflation-adjusted) terms. Funding such additional payments in the short-term can be achieved in different ways, structuring financial assets according to the retiree's personal risks/rewards goals. ABW is neutral and does not take a position on how best to do it. Below are some of the strategies which can be used:<br />
<br />
===Separate sub-portfolio approach===<br />
<br />
The retiree can choose to keep funds for some or all of the extra income and expenses outside the regular amortization process. They can allocate extra income and budget for extra expenses, separate from the ABW calculation. This is effectively a partitioned portfolio approach where extra income and expenses are being handled in a separate safe sub-portfolio.<br />
<br />
A retiree formally pursuing the separate portfolio approach described [[User:Willthrill81/Amortization_based_withdrawal#Fixed_asset_allocation_with_sub-portfolios|earlier]] may find it convenient to use conservative estimates of social security and pensions to fund the safe sub-portfolios. For more complex cases, sizing the sub-portfolio can be achieved by a present value computation of future extra income and expenses (e.g. when using a TIPS ladder, use the bonds interest rate to discount future income/expenses). The income streams are typically duration matched. Gaps remaining can be filled with duration matched bonds. Depending on the asset allocation, there may be little to no rebalancing needed in safe sub-portfolios.<br />
<br />
===Regular portfolio approach===<br />
<br />
The retiree can choose to fund the additional payments through additional withdrawals from the regular savings portfolio. The discounting and amortization rate should then be the savings portfolio's expected rate of return, reflecting the regular portfolio's risks/rewards profile. Care should be exercised about the additional burden on one's savings portfolio and possible consequences of market crises before steady future income (e.g. SS/Pensions) materializes.<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using the portfolio's expected rate of return. Calculate amortized additional withdrawals based on such value, in the same manner as the savings portfolio balance is amortized. Such computation is independent from the portfolio's rebalancing procedure and doesn't change the expected return computation. More information on this approach is available on this [https://www.bogleheads.org/blog/2019/02/01/early-retirement-and-time-value-of-money/ blog article], which comes with a [http://bit.ly/2WuNmvf companion spreadsheet].<br />
<br />
===Total portfolio approach===<br />
<br />
The retiree can choose to fund the additional payments through... <<Ben to elaborate, including a brief explanation of "total portfolio" concept>>. <br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using bond interest rates. Add this value to the regular portfolio's balance for all calculations, counting it as a bond. Include it when calculating withdrawals. Include it when calculating the asset allocation of the total portfolio (for rebalancing) and the expected return of the total portfolio (to enter into the amortized payment computation). More information on this approach is available here: <insert link><br />
<br />
==ABW calculator==<br />
<br />
===Basic calculator===<br />
<br />
The Excel spreadsheet to calculate withdrawals in on Google Drive: [https://drive.google.com/file/d/1XOnBaUspLX_oaM2rquTPmLj5AKOm6yxV/view?usp=sharing ABW Calculator]<br />
<br />
[[User:Ben Mathew/Formulas for Amortization Based Withdrawal (ABW)]] describes the formulas used in the calculator.<br />
<br />
===Advanced calculators===<br />
<br />
These calculators expand the basic functionality to include other considerations.<br />
<br />
An Excel spreadsheet that incorporates extra income and expenses is available on Google Drive: [https://drive.google.com/file/d/1v8KZfXMCnIJXjy0e3RkZ-Uap4OiaXCpu/view?usp=sharing ABW Calculator with Extra Income and Expenses]. <br />
<br />
Another calculator performing similar amortization functions and providing some backtesting capabilities is formatted as a Google sheet and is available here (please make a copy): [http://bit.ly/2WuNmvf Amortized Spending Budget - Fixed Asset Allocation].<br />
<br />
==Support==<br />
On-going discussion and support is in {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}.<br />
<br />
==See also==<br />
*[[Comparing investments]] - Tutorial on ''Time Value of Money'' equations</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Amortization_based_withdrawal&diff=70679
Amortization based withdrawal
2020-11-27T16:58:44Z
<p>Siamond: /* Fixed asset allocation */ reworded to avoid the 'constant return' wording</p>
<hr />
<div>{{Under construction| comment = Comments are being solicited in this {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}}}<br />
'''Amortization based withdrawal (ABW)''' uses amortization techniques to calculate portfolio withdrawals during retirement. Examples of withdrawals that use amortization include [[Variable percentage withdrawal | Variable Percentage Withdrawal]] (VPW) and the [[Required Minimum Distribution]] (RMD) rules for traditional retirement accounts.<br />
<br />
==Amortization==<br />
<br />
===Understanding amortization===<br />
<br />
Amortization is the process of converting the value of a lump sum into a series of payments over time. Most people encounter it when they take out a mortgage or car loan. Amortization is used to calculate the monthly payment required to pay back the loan. The value of the monthly payments has to be made equal to the value of the initial loan.<br />
<br />
If the interest rate is zero, amortization is just simple division: If $100,000 has to be paid back over 10 years, then the payment is $100,000 ÷ 10 = $10,000 per year.<br />
<br />
But if the interest rate is positive, as is usually the case, then the payment in the above example would have to be more than $10,000 per year. That's because $10,000 in the future is worth less than $10,000 today. This is referred to as the time value of money. If the interest is 5% per year, then $10,000 today is worth:<br />
<br />
* <math>$10,000*1.05^1=$10,500</math> one year from now<br />
* <math>$10,000*1.05^2=$11,025</math> two years from now<br />
<br />
and so on. We will have to adjust for the differences in value. The amortization formula makes the necessary adjustments and tells us that if the interest rate is 5% per year, then the payments will have to be $12,950 per year for the next ten years for the total value of the payments to be equal in value to the $100,000 that was borrowed today.<br />
<br />
==Amortization based withdrawal==<br />
<br />
To calculate portfolio withdrawals, enter the following inputs in the ABW calculator ([[#ABW calculator|below]]):<br />
<br />
* <math>P=</math> current portfolio value<br />
* <math>n=</math> number of years over which withdrawals are to be spread out<br />
* <math>r=</math> expected return of the portfolio.<br />
<br />
===Example===<br />
<br />
A 65 year old retiree with a $1 million portfolio expected to earn 3% per year and seeking to spread out withdrawals over 36 years (ages 65 to 100), would enter <math>P=$1,000,000, n=36, r=3%</math>. The amortization calculator says that this retiree can withdraw $44,470 per year. This means that if the portfolio actual rate of return remains constant at 3% per year and the retiree withdraws $44,470 every year, then the portfolio will be fully depleted after 36 years.<br />
<br />
===Real vs nominal rate of return===<br />
<br />
If a real (inflation adjusted) rate of return is used, the withdrawal strategy becomes automatically adjusted for inflation. In the above example, if the real rate of return is 3%, the retiree will be able to take out $44,470 (inflation adjusted) each year. If instead, the retiree enters a nominal interest rate of 5%, the calculator says that they can take out $60,434 per year. But that's in nominal dollars, so real consumption will decline each year by the inflation rate. In practice, it is strongly recommended to use a real rate of return.<br />
<br />
===Update and adapt===<br />
<br />
Withdrawals are recalculated each year with updated information about portfolio value, expected rate of return, and number of years left. This allows withdrawals to continually adapt to new information and mitigates the impact of past incorrect assumptions. Amortization spreads the course correction required across all remaining years, thereby minimizing the impact on any one year.<br />
<br />
====Example====<br />
<br />
Consider what happens in our earlier example if, instead of gaining 3% as expected, the portfolio actually loses 10%. The shortfall relative to expectations is <math>(1-.10)/(1+.03)-1=-12.6%</math>. Our retiree had expected to start age 66 with $984,196 in the portfolio. Instead, the portfolio contains only $859,977, which is 12.6% less. Consider what happens in the following two scenarios:<br />
<br />
=====Scenario 1: Expected return stays the same=====<br />
Suppose that the retiree believes that this market drop has not impacted future expected returns, which in the retiree's opinion, remains at 3%. The retiree enters the new reduced portfolio value, <math>P=$859,977</math>, number of years remaining <math>n=35</math>, and expected real return <math>r=3%</math>. The withdrawal is now reduced to $38,857 per year. That is a 12.6% reduction relative to the previously planned withdrawal of $44,470. So the 12.6% portfolio loss is being matched by a 12.6% spending cut across all remaining years.<br />
<br />
=====Scenario 2: Expected return increases=====<br />
If the market drop was due to a pure valuation change and the underlying earnings of the portfolio are not impacted, then the retiree might expect a higher rate of return going forward.<br />
<br />
If expected return is based on an earnings yield model (e.g. 1/CAPE) for stocks and yield to maturity for bonds, a 12.6% reduction in valuation will result in a higher expected real return of <math>.03/(1-.126)=3.43%</math>. With the higher expected return, the withdrawal becomes $41,181. That is a reduction of only 7.4% relative to the original plan of $44,470. A 12.6% reduction in the portfolio led to only a 7.4% reduction in income, because the higher expected return partially offset the loss in portfolio value.<br />
<br />
So to the extent that market volatility is caused by valuation changes and gets incorporated into expected returns, withdrawals from the portfolio will be less volatile than the portfolio itself.<br />
<br />
==Adding a terminal balance==<br />
<br />
Instead of fully depleting the portfolio, the amortization can be modified to leave behind a terminal balance. This could be used to fund end of life care or a bequest, or it could simply serve as a general financial cushion. <br />
<br />
In the ABW calculator, enter:<br />
* <math>B=</math> terminal balance<br />
<br />
===Example===<br />
<br />
The 65 year old retiree in the earlier example wants to have $200,000 left at the end for a bequest. Enter <math>B=$200,000</math> in the calculator to get a withdrawal of $41,401 per year. If the actual rate of return matches expectations, then after withdrawing $41,401 for 36 years (ages 65 to 100), the retiree will have $200,000 remaining in the portfolio at the end of age 100.<br />
<br />
==Rising or falling withdrawal schedules==<br />
<br />
Instead of aiming at a constant withdrawal schedule, some retirees may prefer to aim at a rising or falling withdrawal schedule. Retirees worried about incurring unexpected expenses or generally running out of money in later years may want to use a rising withdrawal schedule - take less early so they can have more later. Those wanting to fund an active early retirement may want to use a declining withdrawal schedule - take more early but have less later. (Note the similarity with savings. This can be viewed as a decision about how much to save in the early retirement years in order to fund late retirement consumption.)<br />
<br />
In the ABW calculator, enter:<br />
* <math>g=</math> rate of growth of the withdrawal schedule<br />
<br />
<math>g>0</math> generates a rising withdrawal schedule, <math>g<0</math> generates a declining withdrawal schedule, and <math>g=0</math> generates a constant withdrawal schedule.<br />
<br />
===Example===<br />
<br />
If the 65 year old retiree in the earlier example wants withdrawals to grow at 1% per year, set <math>g=1%</math> to get a withdrawal of $38,349. Withdrawals are scheduled to grow 1% per year, rising to $54,325 at age 100.<br />
<br />
If instead the retiree wishes to spend more in early retirement and wants withdrawals to fall by 1% per year, set <math>g=-1%</math> to get a withdrawal of $51,118. Withdrawals are scheduled to fall 1% per year, declining to $35,959 at age 100.<br />
<br />
==Asset allocation==<br />
<br />
===Fixed asset allocation===<br />
<br />
The amortization formula assumes an expected rate of return on the portfolio which stays consistent over the retirement period. This is easier to justify if the retiree plans to maintain a fixed asset allocation (AA). If instead the retiree is planning to change the AA over time (e.g. glide down from 60/40 to 30/70 over the course of the retirement), then the expected return will display more variations over time, skewing the amortization computation. The calculator provided here is not designed for such case. Entering the average expected return in the calculator may provide a rough estimate, but due to the potential for significant errors, more precise modeling is recommended.<br />
<br />
===Fixed asset allocation with sub-portfolios===<br />
<br />
The portfolio can be divided into multiple sub-portfolios and a different fixed allocation applied to each sub-portfolio.<br />
<br />
Suppose the retiree is more risk averse over certain categories of consumption (e.g. food and housing), and less risk averse over other categories (e.g. vacations). The portfolio can be subdivided into a safer portfolio to fund food and housing and a riskier portfolio to fund vacations. The safe portfolio would get a safe fixed AA like 30/70, and the riskier portfolio would get a riskier fixed AA like 80/20. Multiple sub-portfolios could be created to fund different consumption goals, each with a different AA that matches the risk-reward considerations for that goal. Withdrawals would be calculated separately for each sub-portfolio.<br />
<br />
An example of a strategy that uses sub-portfolios is the Liability Matched Portfolio (LMP) strategy. The portfolio is divided into a "liability matched portfolio" and a "risk portfolio". The liability matched portfolio has an AA of 0/100 and is used to fund non-negotiable consumption. The risk portfolio is given a riskier AA and is used to fund discretionary "nice to have" consumption.<br />
<br />
==Estimating the expected return==<br />
<br />
The ABW calculation requires the user to input the expected rate of return of the portfolio. ABW does not recommend a specific model for this purpose. The user is free to use whatever model of expected return they prefer. Examples of models that can be used include:<br />
<br />
===Models based on earnings yields (e.g. 1/CAPE)===<br />
<Enter info><br />
<br />
===Models based on historical returns===<br />
<Enter info><br />
<br />
==Extra income and expenses==<br />
<br />
Besides their savings portfolio, retirees may have other sources of present or future income such as social security, pensions, annuities, rental income, part-time wages and lump sum payouts ("extra income"). Retirees may also plan for exceptional expenses such as college tuition, a lingering home mortgage or long-term care expenses that may require funds beyond what is provided by regular budgeting ("extra expenses"). Such future extra income and expenses can be amortized by computing the present value of such future sums (see Wiki article on calculating present value by discounting future cash flows: [[Comparing_investments#Present_value|Comparing Investments]]) and converting in an additional series of payments, beyond the regular payment derived from the savings portfolio's balance. It is strongly recommended to perform such computations in real (inflation-adjusted) terms. Funding such additional payments in the short-term can be achieved in different ways, structuring financial assets according to the retiree's personal risks/rewards goals. ABW is neutral and does not take a position on how best to do it. Below are some of the strategies which can be used:<br />
<br />
===Separate sub-portfolio approach===<br />
<br />
The retiree can choose to keep funds for some or all of the extra income and expenses outside the regular amortization process. They can allocate extra income and budget for extra expenses, separate from the ABW calculation. This is effectively a partitioned portfolio approach where extra income and expenses are being handled in a separate safe sub-portfolio.<br />
<br />
A retiree formally pursuing the separate portfolio approach described [[User:Willthrill81/Amortization_based_withdrawal#Fixed_asset_allocation_with_sub-portfolios|earlier]] may find it convenient to use conservative estimates of social security and pensions to fund the safe sub-portfolios. For more complex cases, sizing the sub-portfolio can be achieved by a present value computation of future extra income and expenses, using a discounting rate equal to the sub-portfolio's expected rate of return (e.g. when using a TIPS ladder, use the bonds interest rate). The income streams are typically duration matched. Gaps remaining can be filled with duration matched bonds. Depending on the asset allocation, there may be little to no rebalancing needed in safe sub-portfolios.<br />
<br />
===Regular portfolio approach===<br />
<br />
The retiree can choose to fund the additional payments through additional withdrawals from the regular savings portfolio. The discounting and amortization rate should then be the savings portfolio's expected rate of return, reflecting the regular portfolio's risks/rewards profile. Care should be exercised about the additional burden on one's savings portfolio and possible consequences of market crises before steady future income (e.g. SS/Pensions) materializes.<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using the portfolio's expected rate of return. Calculate amortized additional withdrawals based on such value, in the same manner as the savings portfolio balance is amortized. Such computation is independent from the portfolio's rebalancing procedure and doesn't change the expected return computation. More information on this approach is available on this [https://www.bogleheads.org/blog/2019/02/01/early-retirement-and-time-value-of-money/ blog article], which comes with a [http://bit.ly/2WuNmvf companion spreadsheet].<br />
<br />
===Total portfolio approach===<br />
<br />
The retiree can choose to fund the additional payments through... <<Ben to elaborate, including a brief explanation of "total portfolio" concept>>. <br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using bond interest rates. Add this value to the regular portfolio's balance for all calculations, counting it as a bond. Include it when calculating withdrawals. Include it when calculating the asset allocation of the total portfolio (for rebalancing) and the expected return of the total portfolio (to enter into the amortized payment computation). More information on this approach is available here: <insert link><br />
<br />
==ABW calculator==<br />
<br />
===Basic calculator===<br />
<br />
The Excel spreadsheet to calculate withdrawals in on Google Drive: [https://drive.google.com/file/d/1XOnBaUspLX_oaM2rquTPmLj5AKOm6yxV/view?usp=sharing ABW Calculator]<br />
<br />
[[User:Ben Mathew/Formulas for Amortization Based Withdrawal (ABW)]] describes the formulas used in the calculator.<br />
<br />
===Advanced calculators===<br />
<br />
These calculators expand the basic functionality to include other considerations.<br />
<br />
An Excel spreadsheet that incorporates extra income and expenses is available on Google Drive: [https://drive.google.com/file/d/1v8KZfXMCnIJXjy0e3RkZ-Uap4OiaXCpu/view?usp=sharing ABW Calculator with Extra Income and Expenses]. <br />
<br />
Another calculator performing similar amortization functions and providing some backtesting capabilities is formatted as a Google sheet and is available here (please make a copy): [http://bit.ly/2WuNmvf Amortized Spending Budget - Fixed Asset Allocation].<br />
<br />
==Support==<br />
On-going discussion and support is in {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}.<br />
<br />
==See also==<br />
*[[Comparing investments]] - Tutorial on ''Time Value of Money'' equations</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Amortization_based_withdrawal&diff=70678
Amortization based withdrawal
2020-11-27T16:51:03Z
<p>Siamond: /* Advanced calculators */ Adding Siamond's calculator</p>
<hr />
<div>{{Under construction| comment = Comments are being solicited in this {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}}}<br />
'''Amortization based withdrawal (ABW)''' uses amortization techniques to calculate portfolio withdrawals during retirement. Examples of withdrawals that use amortization include [[Variable percentage withdrawal | Variable Percentage Withdrawal]] (VPW) and the [[Required Minimum Distribution]] (RMD) rules for traditional retirement accounts.<br />
<br />
==Amortization==<br />
<br />
===Understanding amortization===<br />
<br />
Amortization is the process of converting the value of a lump sum into a series of payments over time. Most people encounter it when they take out a mortgage or car loan. Amortization is used to calculate the monthly payment required to pay back the loan. The value of the monthly payments has to be made equal to the value of the initial loan.<br />
<br />
If the interest rate is zero, amortization is just simple division: If $100,000 has to be paid back over 10 years, then the payment is $100,000 ÷ 10 = $10,000 per year.<br />
<br />
But if the interest rate is positive, as is usually the case, then the payment in the above example would have to be more than $10,000 per year. That's because $10,000 in the future is worth less than $10,000 today. This is referred to as the time value of money. If the interest is 5% per year, then $10,000 today is worth:<br />
<br />
* <math>$10,000*1.05^1=$10,500</math> one year from now<br />
* <math>$10,000*1.05^2=$11,025</math> two years from now<br />
<br />
and so on. We will have to adjust for the differences in value. The amortization formula makes the necessary adjustments and tells us that if the interest rate is 5% per year, then the payments will have to be $12,950 per year for the next ten years for the total value of the payments to be equal in value to the $100,000 that was borrowed today.<br />
<br />
==Amortization based withdrawal==<br />
<br />
To calculate portfolio withdrawals, enter the following inputs in the ABW calculator ([[#ABW calculator|below]]):<br />
<br />
* <math>P=</math> current portfolio value<br />
* <math>n=</math> number of years over which withdrawals are to be spread out<br />
* <math>r=</math> expected return of the portfolio.<br />
<br />
===Example===<br />
<br />
A 65 year old retiree with a $1 million portfolio expected to earn 3% per year and seeking to spread out withdrawals over 36 years (ages 65 to 100), would enter <math>P=$1,000,000, n=36, r=3%</math>. The amortization calculator says that this retiree can withdraw $44,470 per year. This means that if the portfolio actual rate of return remains constant at 3% per year and the retiree withdraws $44,470 every year, then the portfolio will be fully depleted after 36 years.<br />
<br />
===Real vs nominal rate of return===<br />
<br />
If a real (inflation adjusted) rate of return is used, the withdrawal strategy becomes automatically adjusted for inflation. In the above example, if the real rate of return is 3%, the retiree will be able to take out $44,470 (inflation adjusted) each year. If instead, the retiree enters a nominal interest rate of 5%, the calculator says that they can take out $60,434 per year. But that's in nominal dollars, so real consumption will decline each year by the inflation rate. In practice, it is strongly recommended to use a real rate of return.<br />
<br />
===Update and adapt===<br />
<br />
Withdrawals are recalculated each year with updated information about portfolio value, expected rate of return, and number of years left. This allows withdrawals to continually adapt to new information and mitigates the impact of past incorrect assumptions. Amortization spreads the course correction required across all remaining years, thereby minimizing the impact on any one year.<br />
<br />
====Example====<br />
<br />
Consider what happens in our earlier example if, instead of gaining 3% as expected, the portfolio actually loses 10%. The shortfall relative to expectations is <math>(1-.10)/(1+.03)-1=-12.6%</math>. Our retiree had expected to start age 66 with $984,196 in the portfolio. Instead, the portfolio contains only $859,977, which is 12.6% less. Consider what happens in the following two scenarios:<br />
<br />
=====Scenario 1: Expected return stays the same=====<br />
Suppose that the retiree believes that this market drop has not impacted future expected returns, which in the retiree's opinion, remains at 3%. The retiree enters the new reduced portfolio value, <math>P=$859,977</math>, number of years remaining <math>n=35</math>, and expected real return <math>r=3%</math>. The withdrawal is now reduced to $38,857 per year. That is a 12.6% reduction relative to the previously planned withdrawal of $44,470. So the 12.6% portfolio loss is being matched by a 12.6% spending cut across all remaining years.<br />
<br />
=====Scenario 2: Expected return increases=====<br />
If the market drop was due to a pure valuation change and the underlying earnings of the portfolio are not impacted, then the retiree might expect a higher rate of return going forward.<br />
<br />
If expected return is based on an earnings yield model (e.g. 1/CAPE) for stocks and yield to maturity for bonds, a 12.6% reduction in valuation will result in a higher expected real return of <math>.03/(1-.126)=3.43%</math>. With the higher expected return, the withdrawal becomes $41,181. That is a reduction of only 7.4% relative to the original plan of $44,470. A 12.6% reduction in the portfolio led to only a 7.4% reduction in income, because the higher expected return partially offset the loss in portfolio value.<br />
<br />
So to the extent that market volatility is caused by valuation changes and gets incorporated into expected returns, withdrawals from the portfolio will be less volatile than the portfolio itself.<br />
<br />
==Adding a terminal balance==<br />
<br />
Instead of fully depleting the portfolio, the amortization can be modified to leave behind a terminal balance. This could be used to fund end of life care or a bequest, or it could simply serve as a general financial cushion. <br />
<br />
In the ABW calculator, enter:<br />
* <math>B=</math> terminal balance<br />
<br />
===Example===<br />
<br />
The 65 year old retiree in the earlier example wants to have $200,000 left at the end for a bequest. Enter <math>B=$200,000</math> in the calculator to get a withdrawal of $41,401 per year. If the actual rate of return matches expectations, then after withdrawing $41,401 for 36 years (ages 65 to 100), the retiree will have $200,000 remaining in the portfolio at the end of age 100.<br />
<br />
==Rising or falling withdrawal schedules==<br />
<br />
Instead of aiming at a constant withdrawal schedule, some retirees may prefer to aim at a rising or falling withdrawal schedule. Retirees worried about incurring unexpected expenses or generally running out of money in later years may want to use a rising withdrawal schedule - take less early so they can have more later. Those wanting to fund an active early retirement may want to use a declining withdrawal schedule - take more early but have less later. (Note the similarity with savings. This can be viewed as a decision about how much to save in the early retirement years in order to fund late retirement consumption.)<br />
<br />
In the ABW calculator, enter:<br />
* <math>g=</math> rate of growth of the withdrawal schedule<br />
<br />
<math>g>0</math> generates a rising withdrawal schedule, <math>g<0</math> generates a declining withdrawal schedule, and <math>g=0</math> generates a constant withdrawal schedule.<br />
<br />
===Example===<br />
<br />
If the 65 year old retiree in the earlier example wants withdrawals to grow at 1% per year, set <math>g=1%</math> to get a withdrawal of $38,349. Withdrawals are scheduled to grow 1% per year, rising to $54,325 at age 100.<br />
<br />
If instead the retiree wishes to spend more in early retirement and wants withdrawals to fall by 1% per year, set <math>g=-1%</math> to get a withdrawal of $51,118. Withdrawals are scheduled to fall 1% per year, declining to $35,959 at age 100.<br />
<br />
==Asset allocation==<br />
<br />
===Fixed asset allocation===<br />
<br />
The amortization formula assumes a constant rate of return on the portfolio. This is easier to justify if the retiree plans to maintain a fixed asset allocation (AA). If instead the retiree is planning to change AA over time (e.g. glide down from 60/40 to 30/70 over the course of the retirement), then the expected return is not constant. Amortization can still be performed, but it will require manual modeling. The calculator provided here cannot be used. Entering the average expected return in the calculator may provide a rough estimate, but due to the potential for significant errors, more precise modeling is recommended.<br />
<br />
===Fixed asset allocation with sub-portfolios===<br />
<br />
The portfolio can be divided into multiple sub-portfolios and a different fixed allocation applied to each sub-portfolio.<br />
<br />
Suppose the retiree is more risk averse over certain categories of consumption (e.g. food and housing), and less risk averse over other categories (e.g. vacations). The portfolio can be subdivided into a safer portfolio to fund food and housing and a riskier portfolio to fund vacations. The safe portfolio would get a safe fixed AA like 30/70, and the riskier portfolio would get a riskier fixed AA like 80/20. Multiple sub-portfolios could be created to fund different consumption goals, each with a different AA that matches the risk-reward considerations for that goal. Withdrawals would be calculated separately for each sub-portfolio.<br />
<br />
An example of a strategy that uses sub-portfolios is the Liability Matched Portfolio (LMP) strategy. The portfolio is divided into a "liability matched portfolio" and a "risk portfolio". The liability matched portfolio has an AA of 0/100 and is used to fund non-negotiable consumption. The risk portfolio is given a riskier AA and is used to fund discretionary "nice to have" consumption.<br />
<br />
==Estimating the expected return==<br />
<br />
The ABW calculation requires the user to input the expected rate of return of the portfolio. ABW does not recommend a specific model for this purpose. The user is free to use whatever model of expected return they prefer. Examples of models that can be used include:<br />
<br />
===Models based on earnings yields (e.g. 1/CAPE)===<br />
<Enter info><br />
<br />
===Models based on historical returns===<br />
<Enter info><br />
<br />
==Extra income and expenses==<br />
<br />
Besides their savings portfolio, retirees may have other sources of present or future income such as social security, pensions, annuities, rental income, part-time wages and lump sum payouts ("extra income"). Retirees may also plan for exceptional expenses such as college tuition, a lingering home mortgage or long-term care expenses that may require funds beyond what is provided by regular budgeting ("extra expenses"). Such future extra income and expenses can be amortized by computing the present value of such future sums (see Wiki article on calculating present value by discounting future cash flows: [[Comparing_investments#Present_value|Comparing Investments]]) and converting in an additional series of payments, beyond the regular payment derived from the savings portfolio's balance. It is strongly recommended to perform such computations in real (inflation-adjusted) terms. Funding such additional payments in the short-term can be achieved in different ways, structuring financial assets according to the retiree's personal risks/rewards goals. ABW is neutral and does not take a position on how best to do it. Below are some of the strategies which can be used:<br />
<br />
===Separate sub-portfolio approach===<br />
<br />
The retiree can choose to keep funds for some or all of the extra income and expenses outside the regular amortization process. They can allocate extra income and budget for extra expenses, separate from the ABW calculation. This is effectively a partitioned portfolio approach where extra income and expenses are being handled in a separate safe sub-portfolio.<br />
<br />
A retiree formally pursuing the separate portfolio approach described [[User:Willthrill81/Amortization_based_withdrawal#Fixed_asset_allocation_with_sub-portfolios|earlier]] may find it convenient to use conservative estimates of social security and pensions to fund the safe sub-portfolios. For more complex cases, sizing the sub-portfolio can be achieved by a present value computation of future extra income and expenses, using a discounting rate equal to the sub-portfolio's expected rate of return (e.g. when using a TIPS ladder, use the bonds interest rate). The income streams are typically duration matched. Gaps remaining can be filled with duration matched bonds. Depending on the asset allocation, there may be little to no rebalancing needed in safe sub-portfolios.<br />
<br />
===Regular portfolio approach===<br />
<br />
The retiree can choose to fund the additional payments through additional withdrawals from the regular savings portfolio. The discounting and amortization rate should then be the savings portfolio's expected rate of return, reflecting the regular portfolio's risks/rewards profile. Care should be exercised about the additional burden on one's savings portfolio and possible consequences of market crises before steady future income (e.g. SS/Pensions) materializes.<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using the portfolio's expected rate of return. Calculate amortized additional withdrawals based on such value, in the same manner as the savings portfolio balance is amortized. Such computation is independent from the portfolio's rebalancing procedure and doesn't change the expected return computation. More information on this approach is available on this [https://www.bogleheads.org/blog/2019/02/01/early-retirement-and-time-value-of-money/ blog article], which comes with a [http://bit.ly/2WuNmvf companion spreadsheet].<br />
<br />
===Total portfolio approach===<br />
<br />
The retiree can choose to fund the additional payments through... <<Ben to elaborate, including a brief explanation of "total portfolio" concept>>. <br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using bond interest rates. Add this value to the regular portfolio's balance for all calculations, counting it as a bond. Include it when calculating withdrawals. Include it when calculating the asset allocation of the total portfolio (for rebalancing) and the expected return of the total portfolio (to enter into the amortized payment computation). More information on this approach is available here: <insert link><br />
<br />
==ABW calculator==<br />
<br />
===Basic calculator===<br />
<br />
The Excel spreadsheet to calculate withdrawals in on Google Drive: [https://drive.google.com/file/d/1XOnBaUspLX_oaM2rquTPmLj5AKOm6yxV/view?usp=sharing ABW Calculator]<br />
<br />
[[User:Ben Mathew/Formulas for Amortization Based Withdrawal (ABW)]] describes the formulas used in the calculator.<br />
<br />
===Advanced calculators===<br />
<br />
These calculators expand the basic functionality to include other considerations.<br />
<br />
An Excel spreadsheet that incorporates extra income and expenses is available on Google Drive: [https://drive.google.com/file/d/1v8KZfXMCnIJXjy0e3RkZ-Uap4OiaXCpu/view?usp=sharing ABW Calculator with Extra Income and Expenses]. <br />
<br />
Another calculator performing similar amortization functions and providing some backtesting capabilities is formatted as a Google sheet and is available here (please make a copy): [http://bit.ly/2WuNmvf Amortized Spending Budget - Fixed Asset Allocation].<br />
<br />
==Support==<br />
On-going discussion and support is in {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}.<br />
<br />
==See also==<br />
*[[Comparing investments]] - Tutorial on ''Time Value of Money'' equations</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Amortization_based_withdrawal&diff=70677
Amortization based withdrawal
2020-11-27T16:31:16Z
<p>Siamond: /* Extra income and expenses */ Reworded with more emphasis on assets structure and ways to fund additional payments.</p>
<hr />
<div>{{Under construction| comment = Comments are being solicited in this {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}}}<br />
'''Amortization based withdrawal (ABW)''' uses amortization techniques to calculate portfolio withdrawals during retirement. Examples of withdrawals that use amortization include [[Variable percentage withdrawal | Variable Percentage Withdrawal]] (VPW) and the [[Required Minimum Distribution]] (RMD) rules for traditional retirement accounts.<br />
<br />
==Amortization==<br />
<br />
===Understanding amortization===<br />
<br />
Amortization is the process of converting the value of a lump sum into a series of payments over time. Most people encounter it when they take out a mortgage or car loan. Amortization is used to calculate the monthly payment required to pay back the loan. The value of the monthly payments has to be made equal to the value of the initial loan.<br />
<br />
If the interest rate is zero, amortization is just simple division: If $100,000 has to be paid back over 10 years, then the payment is $100,000 ÷ 10 = $10,000 per year.<br />
<br />
But if the interest rate is positive, as is usually the case, then the payment in the above example would have to be more than $10,000 per year. That's because $10,000 in the future is worth less than $10,000 today. This is referred to as the time value of money. If the interest is 5% per year, then $10,000 today is worth:<br />
<br />
* <math>$10,000*1.05^1=$10,500</math> one year from now<br />
* <math>$10,000*1.05^2=$11,025</math> two years from now<br />
<br />
and so on. We will have to adjust for the differences in value. The amortization formula makes the necessary adjustments and tells us that if the interest rate is 5% per year, then the payments will have to be $12,950 per year for the next ten years for the total value of the payments to be equal in value to the $100,000 that was borrowed today.<br />
<br />
==Amortization based withdrawal==<br />
<br />
To calculate portfolio withdrawals, enter the following inputs in the ABW calculator ([[#ABW calculator|below]]):<br />
<br />
* <math>P=</math> current portfolio value<br />
* <math>n=</math> number of years over which withdrawals are to be spread out<br />
* <math>r=</math> expected return of the portfolio.<br />
<br />
===Example===<br />
<br />
A 65 year old retiree with a $1 million portfolio expected to earn 3% per year and seeking to spread out withdrawals over 36 years (ages 65 to 100), would enter <math>P=$1,000,000, n=36, r=3%</math>. The amortization calculator says that this retiree can withdraw $44,470 per year. This means that if the portfolio actual rate of return remains constant at 3% per year and the retiree withdraws $44,470 every year, then the portfolio will be fully depleted after 36 years.<br />
<br />
===Real vs nominal rate of return===<br />
<br />
If a real (inflation adjusted) rate of return is used, the withdrawal strategy becomes automatically adjusted for inflation. In the above example, if the real rate of return is 3%, the retiree will be able to take out $44,470 (inflation adjusted) each year. If instead, the retiree enters a nominal interest rate of 5%, the calculator says that they can take out $60,434 per year. But that's in nominal dollars, so real consumption will decline each year by the inflation rate. In practice, it is strongly recommended to use a real rate of return.<br />
<br />
===Update and adapt===<br />
<br />
Withdrawals are recalculated each year with updated information about portfolio value, expected rate of return, and number of years left. This allows withdrawals to continually adapt to new information and mitigates the impact of past incorrect assumptions. Amortization spreads the course correction required across all remaining years, thereby minimizing the impact on any one year.<br />
<br />
====Example====<br />
<br />
Consider what happens in our earlier example if, instead of gaining 3% as expected, the portfolio actually loses 10%. The shortfall relative to expectations is <math>(1-.10)/(1+.03)-1=-12.6%</math>. Our retiree had expected to start age 66 with $984,196 in the portfolio. Instead, the portfolio contains only $859,977, which is 12.6% less. Consider what happens in the following two scenarios:<br />
<br />
=====Scenario 1: Expected return stays the same=====<br />
Suppose that the retiree believes that this market drop has not impacted future expected returns, which in the retiree's opinion, remains at 3%. The retiree enters the new reduced portfolio value, <math>P=$859,977</math>, number of years remaining <math>n=35</math>, and expected real return <math>r=3%</math>. The withdrawal is now reduced to $38,857 per year. That is a 12.6% reduction relative to the previously planned withdrawal of $44,470. So the 12.6% portfolio loss is being matched by a 12.6% spending cut across all remaining years.<br />
<br />
=====Scenario 2: Expected return increases=====<br />
If the market drop was due to a pure valuation change and the underlying earnings of the portfolio are not impacted, then the retiree might expect a higher rate of return going forward.<br />
<br />
If expected return is based on an earnings yield model (e.g. 1/CAPE) for stocks and yield to maturity for bonds, a 12.6% reduction in valuation will result in a higher expected real return of <math>.03/(1-.126)=3.43%</math>. With the higher expected return, the withdrawal becomes $41,181. That is a reduction of only 7.4% relative to the original plan of $44,470. A 12.6% reduction in the portfolio led to only a 7.4% reduction in income, because the higher expected return partially offset the loss in portfolio value.<br />
<br />
So to the extent that market volatility is caused by valuation changes and gets incorporated into expected returns, withdrawals from the portfolio will be less volatile than the portfolio itself.<br />
<br />
==Adding a terminal balance==<br />
<br />
Instead of fully depleting the portfolio, the amortization can be modified to leave behind a terminal balance. This could be used to fund end of life care or a bequest, or it could simply serve as a general financial cushion. <br />
<br />
In the ABW calculator, enter:<br />
* <math>B=</math> terminal balance<br />
<br />
===Example===<br />
<br />
The 65 year old retiree in the earlier example wants to have $200,000 left at the end for a bequest. Enter <math>B=$200,000</math> in the calculator to get a withdrawal of $41,401 per year. If the actual rate of return matches expectations, then after withdrawing $41,401 for 36 years (ages 65 to 100), the retiree will have $200,000 remaining in the portfolio at the end of age 100.<br />
<br />
==Rising or falling withdrawal schedules==<br />
<br />
Instead of aiming at a constant withdrawal schedule, some retirees may prefer to aim at a rising or falling withdrawal schedule. Retirees worried about incurring unexpected expenses or generally running out of money in later years may want to use a rising withdrawal schedule - take less early so they can have more later. Those wanting to fund an active early retirement may want to use a declining withdrawal schedule - take more early but have less later. (Note the similarity with savings. This can be viewed as a decision about how much to save in the early retirement years in order to fund late retirement consumption.)<br />
<br />
In the ABW calculator, enter:<br />
* <math>g=</math> rate of growth of the withdrawal schedule<br />
<br />
<math>g>0</math> generates a rising withdrawal schedule, <math>g<0</math> generates a declining withdrawal schedule, and <math>g=0</math> generates a constant withdrawal schedule.<br />
<br />
===Example===<br />
<br />
If the 65 year old retiree in the earlier example wants withdrawals to grow at 1% per year, set <math>g=1%</math> to get a withdrawal of $38,349. Withdrawals are scheduled to grow 1% per year, rising to $54,325 at age 100.<br />
<br />
If instead the retiree wishes to spend more in early retirement and wants withdrawals to fall by 1% per year, set <math>g=-1%</math> to get a withdrawal of $51,118. Withdrawals are scheduled to fall 1% per year, declining to $35,959 at age 100.<br />
<br />
==Asset allocation==<br />
<br />
===Fixed asset allocation===<br />
<br />
The amortization formula assumes a constant rate of return on the portfolio. This is easier to justify if the retiree plans to maintain a fixed asset allocation (AA). If instead the retiree is planning to change AA over time (e.g. glide down from 60/40 to 30/70 over the course of the retirement), then the expected return is not constant. Amortization can still be performed, but it will require manual modeling. The calculator provided here cannot be used. Entering the average expected return in the calculator may provide a rough estimate, but due to the potential for significant errors, more precise modeling is recommended.<br />
<br />
===Fixed asset allocation with sub-portfolios===<br />
<br />
The portfolio can be divided into multiple sub-portfolios and a different fixed allocation applied to each sub-portfolio.<br />
<br />
Suppose the retiree is more risk averse over certain categories of consumption (e.g. food and housing), and less risk averse over other categories (e.g. vacations). The portfolio can be subdivided into a safer portfolio to fund food and housing and a riskier portfolio to fund vacations. The safe portfolio would get a safe fixed AA like 30/70, and the riskier portfolio would get a riskier fixed AA like 80/20. Multiple sub-portfolios could be created to fund different consumption goals, each with a different AA that matches the risk-reward considerations for that goal. Withdrawals would be calculated separately for each sub-portfolio.<br />
<br />
An example of a strategy that uses sub-portfolios is the Liability Matched Portfolio (LMP) strategy. The portfolio is divided into a "liability matched portfolio" and a "risk portfolio". The liability matched portfolio has an AA of 0/100 and is used to fund non-negotiable consumption. The risk portfolio is given a riskier AA and is used to fund discretionary "nice to have" consumption.<br />
<br />
==Estimating the expected return==<br />
<br />
The ABW calculation requires the user to input the expected rate of return of the portfolio. ABW does not recommend a specific model for this purpose. The user is free to use whatever model of expected return they prefer. Examples of models that can be used include:<br />
<br />
===Models based on earnings yields (e.g. 1/CAPE)===<br />
<Enter info><br />
<br />
===Models based on historical returns===<br />
<Enter info><br />
<br />
==Extra income and expenses==<br />
<br />
Besides their savings portfolio, retirees may have other sources of present or future income such as social security, pensions, annuities, rental income, part-time wages and lump sum payouts ("extra income"). Retirees may also plan for exceptional expenses such as college tuition, a lingering home mortgage or long-term care expenses that may require funds beyond what is provided by regular budgeting ("extra expenses"). Such future extra income and expenses can be amortized by computing the present value of such future sums (see Wiki article on calculating present value by discounting future cash flows: [[Comparing_investments#Present_value|Comparing Investments]]) and converting in an additional series of payments, beyond the regular payment derived from the savings portfolio's balance. It is strongly recommended to perform such computations in real (inflation-adjusted) terms. Funding such additional payments in the short-term can be achieved in different ways, structuring financial assets according to the retiree's personal risks/rewards goals. ABW is neutral and does not take a position on how best to do it. Below are some of the strategies which can be used:<br />
<br />
===Separate sub-portfolio approach===<br />
<br />
The retiree can choose to keep funds for some or all of the extra income and expenses outside the regular amortization process. They can allocate extra income and budget for extra expenses, separate from the ABW calculation. This is effectively a partitioned portfolio approach where extra income and expenses are being handled in a separate safe sub-portfolio.<br />
<br />
A retiree formally pursuing the separate portfolio approach described [[User:Willthrill81/Amortization_based_withdrawal#Fixed_asset_allocation_with_sub-portfolios|earlier]] may find it convenient to use conservative estimates of social security and pensions to fund the safe sub-portfolios. For more complex cases, sizing the sub-portfolio can be achieved by a present value computation of future extra income and expenses, using a discounting rate equal to the sub-portfolio's expected rate of return (e.g. when using a TIPS ladder, use the bonds interest rate). The income streams are typically duration matched. Gaps remaining can be filled with duration matched bonds. Depending on the asset allocation, there may be little to no rebalancing needed in safe sub-portfolios.<br />
<br />
===Regular portfolio approach===<br />
<br />
The retiree can choose to fund the additional payments through additional withdrawals from the regular savings portfolio. The discounting and amortization rate should then be the savings portfolio's expected rate of return, reflecting the regular portfolio's risks/rewards profile. Care should be exercised about the additional burden on one's savings portfolio and possible consequences of market crises before steady future income (e.g. SS/Pensions) materializes.<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using the portfolio's expected rate of return. Calculate amortized additional withdrawals based on such value, in the same manner as the savings portfolio balance is amortized. Such computation is independent from the portfolio's rebalancing procedure and doesn't change the expected return computation. More information on this approach is available on this [https://www.bogleheads.org/blog/2019/02/01/early-retirement-and-time-value-of-money/ blog article], which comes with a [http://bit.ly/2WuNmvf companion spreadsheet].<br />
<br />
===Total portfolio approach===<br />
<br />
The retiree can choose to fund the additional payments through... <<Ben to elaborate, including a brief explanation of "total portfolio" concept>>. <br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period, using conservative estimates of extra income and exceptional expenses. Calculate its aggregate present value using bond interest rates. Add this value to the regular portfolio's balance for all calculations, counting it as a bond. Include it when calculating withdrawals. Include it when calculating the asset allocation of the total portfolio (for rebalancing) and the expected return of the total portfolio (to enter into the amortized payment computation). More information on this approach is available here: <insert link><br />
<br />
==ABW calculator==<br />
<br />
===Basic calculator===<br />
<br />
The Excel spreadsheet to calculate withdrawals in on Google Drive: [https://drive.google.com/file/d/1XOnBaUspLX_oaM2rquTPmLj5AKOm6yxV/view?usp=sharing ABW Calculator]<br />
<br />
[[User:Ben Mathew/Formulas for Amortization Based Withdrawal (ABW)]] describes the formulas used in the calculator.<br />
<br />
===Advanced calculators===<br />
<br />
These calculators expand the basic functionality to include other considerations.<br />
<br />
An Excel spreadsheet that incorporates extra income and expenses in on Google Drive: [https://drive.google.com/file/d/1v8KZfXMCnIJXjy0e3RkZ-Uap4OiaXCpu/view?usp=sharing ABW Calculator with Extra Income and Expenses]<br />
<br />
==Support==<br />
On-going discussion and support is in {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}.<br />
<br />
==See also==<br />
*[[Comparing investments]] - Tutorial on ''Time Value of Money'' equations</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Amortization_based_withdrawal&diff=70623
Amortization based withdrawal
2020-11-20T00:44:15Z
<p>Siamond: /* Extra income and expenses */ Incremental rewording to add emphasis on amortization and future years</p>
<hr />
<div>{{Under construction| comment = Comments are being solicited in this {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}}}<br />
'''Amortization based withdrawal (ABW)''' uses amortization techniques to calculate portfolio withdrawals during retirement. Examples of withdrawals that use amortization include [[Variable percentage withdrawal | Variable Percentage Withdrawal]] (VPW) and the [[Required Minimum Distribution]] (RMD) rules for traditional retirement accounts.<br />
<br />
==Amortization==<br />
<br />
===Understanding amortization===<br />
<br />
Amortization is the process of converting the value of a lump sum into a series of payments over time. Most people encounter it when they take out a mortgage or car loan. Amortization is used to calculate the monthly payment required to pay back the loan. The value of the monthly payments has to be made equal to the value of the initial loan.<br />
<br />
If the interest rate is zero, amortization is just simple division: If $100,000 has to be paid back over 10 years, then the payment is $100,000 ÷ 10 = $10,000 per year.<br />
<br />
But if the interest rate is positive, as is usually the case, then the payment in the above example would have to be more than $10,000 per year. That's because $10,000 in the future is worth less than $10,000 today. This is referred to as the time value of money. If the interest is 5% per year, then $10,000 today is worth:<br />
<br />
* <math>$10,000*1.05^1=$10,500</math> one year from now<br />
* <math>$10,000*1.05^2=$11,025</math> two years from now<br />
<br />
and so on. We will have to adjust for the differences in value. The amortization formula makes the necessary adjustments and tells us that if the interest rate is 5% per year, then the payments will have to be $12,950 per year for the next ten years for the total value of the payments to be equal in value to the $100,000 that was borrowed today.<br />
<br />
==Amortization based withdrawal==<br />
<br />
To calculate portfolio withdrawals, enter the following inputs in the ABW calculator ([[#ABW calculator|below]]):<br />
<br />
* <math>P=</math> current portfolio value<br />
* <math>n=</math> number of years over which withdrawals are to be spread out<br />
* <math>r=</math> expected return of the portfolio.<br />
<br />
===Example===<br />
<br />
A 65 year old retiree with a $1 million portfolio expected to earn 3% per year and seeking to spread out withdrawals over 36 years (ages 65 to 100), would enter <math>P=$1,000,000, n=36, r=3%</math>. The amortization calculator says that this retiree can withdraw $44,470 per year. This means that if the portfolio actual rate of return remains constant at 3% per year and the retiree withdraws $44,470 every year, then the portfolio will be fully depleted after 36 years.<br />
<br />
===Real vs nominal rate of return===<br />
<br />
If a real (inflation adjusted) rate of return is used, the withdrawal strategy becomes automatically adjusted for inflation. In the above example, if the real rate of return is 3%, the retiree will be able to take out $44,470 (inflation adjusted) each year. If instead, the retiree enters a nominal interest rate of 5%, the calculator says that they can take out $60,434 per year. But that's in nominal dollars, so real consumption will decline each year by the inflation rate. In practice, it is strongly recommended to use a real rate of return.<br />
<br />
===Update and adapt===<br />
<br />
Withdrawals are recalculated each year with updated information about portfolio value, expected rate of return, and number of years left. This allows withdrawals to continually adapt to new information and mitigates the impact of past incorrect assumptions. Amortization spreads the course correction required across all remaining years, thereby minimizing the impact on any one year.<br />
<br />
====Example====<br />
<br />
Consider what happens in our earlier example if, instead of gaining 3% as expected, the portfolio actually loses 10%. The shortfall relative to expectations is <math>(1-.10)/(1+.03)-1=-12.6%</math>. Our retiree had expected to start age 66 with $984,196 in the portfolio. Instead, the portfolio contains only $859,977, which is 12.6% less. Consider what happens in the following two scenarios:<br />
<br />
=====Scenario 1: Expected return stays the same=====<br />
Suppose that the retiree believes that this market drop has not impacted future expected returns, which in the retiree's opinion, remains at 3%. The retiree enters the new reduced portfolio value, <math>P=$859,977</math>, number of years remaining <math>n=35</math>, and expected real return <math>r=3%</math>. The withdrawal is now reduced to $38,857 per year. That is a 12.6% reduction relative to the previously planned withdrawal of $44,470. So the 12.6% portfolio loss is being matched by a 12.6% spending cut across all remaining years.<br />
<br />
=====Scenario 2: Expected return increases=====<br />
If the market drop was due to a pure valuation change and the underlying earnings of the portfolio are not impacted, then the retiree might expect a higher rate of return going forward.<br />
<br />
If expected return is based on an earnings yield model (e.g. 1/CAPE) for stocks and yield to maturity for bonds, a 12.6% reduction in valuation will result in a higher expected real return of <math>.03/(1-.126)=3.43%</math>. With the higher expected return, the withdrawal becomes $41,181. That is a reduction of only 7.4% relative to the original plan of $44,470. A 12.6% reduction in the portfolio led to only a 7.4% reduction in income, because the higher expected return partially offset the loss in portfolio value.<br />
<br />
So to the extent that market volatility is caused by valuation changes and gets incorporated into expected returns, withdrawals from the portfolio will be less volatile than the portfolio itself.<br />
<br />
==Adding a terminal balance==<br />
<br />
Instead of fully depleting the portfolio, the amortization can be modified to leave behind a terminal balance. This could be used to fund end of life care or a bequest, or it could simply serve as a general financial cushion. <br />
<br />
In the ABW calculator, enter:<br />
* <math>B=</math> terminal balance<br />
<br />
===Example===<br />
<br />
The 65 year old retiree in the earlier example wants to have $200,000 left at the end for a bequest. Enter <math>B=$200,000</math> in the calculator to get a withdrawal of $41,401 per year. If the actual rate of return matches expectations, then after withdrawing $41,401 for 36 years (ages 65 to 100), the retiree will have $200,000 remaining in the portfolio at the end of age 100.<br />
<br />
==Rising or falling withdrawal schedules==<br />
<br />
Instead of aiming at a constant withdrawal schedule, some retirees may prefer to aim at a rising or falling withdrawal schedule. Retirees worried about incurring unexpected expenses or generally running out of money in later years may want to use a rising withdrawal schedule - take less early so they can have more later. Those wanting to fund an active early retirement may want to use a declining withdrawal schedule - take more early but have less later. (Note the similarity with savings. This can be viewed as a decision about how much to save in the early retirement years in order to fund late retirement consumption.)<br />
<br />
In the ABW calculator, enter:<br />
* <math>g=</math> rate of growth of the withdrawal schedule<br />
<br />
<math>g>0</math> generates a rising withdrawal schedule, <math>g<0</math> generates a declining withdrawal schedule, and <math>g=0</math> generates a constant withdrawal schedule.<br />
<br />
===Example===<br />
<br />
If the 65 year old retiree in the earlier example wants withdrawals to grow at 1% per year, set <math>g=1%</math> to get a withdrawal of $38,349. Withdrawals are scheduled to grow 1% per year, rising to $54,325 at age 100.<br />
<br />
If instead the retiree wishes to spend more in early retirement and wants withdrawals to fall by 1% per year, set <math>g=-1%</math> to get a withdrawal of $51,118. Withdrawals are scheduled to fall 1% per year, declining to $35,959 at age 100.<br />
<br />
==Asset allocation==<br />
<br />
===Fixed asset allocation===<br />
<br />
The amortization formula assumes a constant rate of return on the portfolio. This is easier to justify if the retiree plans to maintain a fixed asset allocation (AA). If instead the retiree is planning to change AA over time (e.g. glide down from 60/40 to 30/70 over the course of the retirement), then the expected return is not constant. Amortization can still be performed, but it will require manual modeling. The calculator provided here cannot be used. Entering the average expected return in the calculator may provide a rough estimate, but due to the potential for significant errors, more precise modeling is recommended.<br />
<br />
===Fixed asset allocation with sub-portfolios===<br />
<br />
The portfolio can be divided into multiple sub-portfolios and a different fixed allocation applied to each sub-portfolio.<br />
<br />
Suppose the retiree is more risk averse over certain categories of consumption (e.g. food and housing), and less risk averse over other categories (e.g. vacations). The portfolio can be subdivided into a safer portfolio to fund food and housing and a riskier portfolio to fund vacations. The safe portfolio would get a safe fixed AA like 30/70, and the riskier portfolio would get a riskier fixed AA like 80/20. Multiple sub-portfolios could be created to fund different consumption goals, each with a different AA that matches the risk-reward considerations for that goal. Withdrawals would be calculated separately for each sub-portfolio.<br />
<br />
An example of a strategy that uses sub-portfolios is the Liability Matched Portfolio (LMP) strategy. The portfolio is divided into a "liability matched portfolio" and a "risk portfolio". The liability matched portfolio has an AA of 0/100 and is used to fund non-negotiable consumption. The risk portfolio is given a riskier AA and is used to fund discretionary "nice to have" consumption.<br />
<br />
==Extra income and expenses==<br />
<br />
Besides their savings portfolio, retirees may have other sources of present or future income such as social security, pensions, annuities, rental income, and lump sum payouts ("extra income"). They may also have exceptional expenses planned such as college tuition or a lingering home mortgage or long-term care expenses that may require funds beyond what is provided by the basic amortization process ("extra expenses"). Such extra income and expenses can be dealt with in different ways. ABW is neutral and does not take a position on how best to do it. Below are some of the strategies that have been used:<br />
<br />
===Keep it separate===<br />
<br />
The retiree can choose to keep some or all of the extra income and expenses outside the amortization process. They can allocate the extra income, and budget for the extra expenses, separate from the ABW calculation. This is effectively a sub-portfolio approach where the extra income and expenses are being handled in a separate portfolio.<br />
<br />
A retiree formally pursuing the sub-portfolio approach described earlier may indeed find it convenient to use conservative estimates of social security and pensions to fund the safe sub-portfolios. The income streams are already duration matched. Gaps remaining can be filled with duration matched bonds. Depending on the asset allocation, there may be little to no rebalancing needed in the safe sub-portfolios.<br />
<br />
===Incorporate it using the portfolio rate of return to amortize all income and expenses===<br />
<br />
Calculate the extra net income (extra income minus extra expenses) for each year of the planned withdrawal period. Calculate its present value using the portfolio's expected rate of return. (See Wiki article on calculating present value by discounting future cash flows: [[Comparing_investments#Present_value|Comparing Investments]]). Add this value to the savings portfolio to calculate withdrawals. Such computation is independent from savings portfolio rebalancing and expected return computation. More information on this approach is available here: <insert link><br />
<br />
===Incorporate it using bond interest rates to amortize safe income and essential expenses===<br />
<br />
Create a conservatively low estimate of safe extra income and a conservatively high estimate of essential extra expenses, for each year of the planned withdrawal period. Subtract the latter from the former to obtain a conservatively low estimate of safe extra net income. Calculate its present value using bond interest rates. Add this value to the portfolio for all calculations, counting it as a bond. Include it when calculating withdrawals. Include it when calculating the asset allocation of the portfolio (for rebalancing) and the expected return of the portfolio (to enter into the ABW calculator). More information on this approach is available here: <insert link><br />
<br />
==Estimating the expected return==<br />
<br />
The ABW calculation requires the user to input the expected rate of return of the portfolio. ABW does not recommend a specific model for this purpose. The user is free to use whatever model of expected return they prefer. Examples of models that can be used include:<br />
<br />
===Models based on earnings yields (e.g. 1/CAPE)===<br />
<Enter info><br />
<br />
===Models based on historical returns===<br />
<Enter info><br />
<br />
==ABW calculator==<br />
<br />
===Basic calculator===<br />
<br />
The Excel spreadsheet to calculate withdrawals in on Google Drive: [https://drive.google.com/file/d/1XOnBaUspLX_oaM2rquTPmLj5AKOm6yxV/view?usp=sharing ABW Calculator]<br />
<br />
[[User:Ben Mathew/Formulas for Amortization Based Withdrawal (ABW)]] describes the formulas used in the calculator.<br />
<br />
===Advanced calculators===<br />
<br />
These calculators expand the basic functionality to include other considerations.<br />
<br />
An Excel spreadsheet that incorporates extra income and expenses in on Google Drive: [https://drive.google.com/file/d/1v8KZfXMCnIJXjy0e3RkZ-Uap4OiaXCpu/view?usp=sharing ABW Calculator with Extra Income and Expenses]<br />
<br />
==Support==<br />
On-going discussion and support is in {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}.<br />
<br />
==See also==<br />
*[[Comparing investments]] - Tutorial on ''Time Value of Money'' equations</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Amortization_based_withdrawal&diff=70622
Amortization based withdrawal
2020-11-20T00:31:40Z
<p>Siamond: /* Extra income and expenses */ Reworded the intro a tad</p>
<hr />
<div>{{Under construction| comment = Comments are being solicited in this {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}}}<br />
'''Amortization based withdrawal (ABW)''' uses amortization techniques to calculate portfolio withdrawals during retirement. Examples of withdrawals that use amortization include [[Variable percentage withdrawal | Variable Percentage Withdrawal]] (VPW) and the [[Required Minimum Distribution]] (RMD) rules for traditional retirement accounts.<br />
<br />
==Amortization==<br />
<br />
===Understanding amortization===<br />
<br />
Amortization is the process of converting the value of a lump sum into a series of payments over time. Most people encounter it when they take out a mortgage or car loan. Amortization is used to calculate the monthly payment required to pay back the loan. The value of the monthly payments has to be made equal to the value of the initial loan.<br />
<br />
If the interest rate is zero, amortization is just simple division: If $100,000 has to be paid back over 10 years, then the payment is $100,000 ÷ 10 = $10,000 per year.<br />
<br />
But if the interest rate is positive, as is usually the case, then the payment in the above example would have to be more than $10,000 per year. That's because $10,000 in the future is worth less than $10,000 today. This is referred to as the time value of money. If the interest is 5% per year, then $10,000 today is worth:<br />
<br />
* <math>$10,000*1.05^1=$10,500</math> one year from now<br />
* <math>$10,000*1.05^2=$11,025</math> two years from now<br />
<br />
and so on. We will have to adjust for the differences in value. The amortization formula makes the necessary adjustments and tells us that if the interest rate is 5% per year, then the payments will have to be $12,950 per year for the next ten years for the total value of the payments to be equal in value to the $100,000 that was borrowed today.<br />
<br />
==Amortization based withdrawal==<br />
<br />
To calculate portfolio withdrawals, enter the following inputs in the ABW calculator ([[#ABW calculator|below]]):<br />
<br />
* <math>P=</math> current portfolio value<br />
* <math>n=</math> number of years over which withdrawals are to be spread out<br />
* <math>r=</math> expected return of the portfolio.<br />
<br />
===Example===<br />
<br />
A 65 year old retiree with a $1 million portfolio expected to earn 3% per year and seeking to spread out withdrawals over 36 years (ages 65 to 100), would enter <math>P=$1,000,000, n=36, r=3%</math>. The amortization calculator says that this retiree can withdraw $44,470 per year. This means that if the portfolio actual rate of return remains constant at 3% per year and the retiree withdraws $44,470 every year, then the portfolio will be fully depleted after 36 years.<br />
<br />
===Real vs nominal rate of return===<br />
<br />
If a real (inflation adjusted) rate of return is used, the withdrawal strategy becomes automatically adjusted for inflation. In the above example, if the real rate of return is 3%, the retiree will be able to take out $44,470 (inflation adjusted) each year. If instead, the retiree enters a nominal interest rate of 5%, the calculator says that they can take out $60,434 per year. But that's in nominal dollars, so real consumption will decline each year by the inflation rate. In practice, it is strongly recommended to use a real rate of return.<br />
<br />
===Update and adapt===<br />
<br />
Withdrawals are recalculated each year with updated information about portfolio value, expected rate of return, and number of years left. This allows withdrawals to continually adapt to new information and mitigates the impact of past incorrect assumptions. Amortization spreads the course correction required across all remaining years, thereby minimizing the impact on any one year.<br />
<br />
====Example====<br />
<br />
Consider what happens in our earlier example if, instead of gaining 3% as expected, the portfolio actually loses 10%. The shortfall relative to expectations is <math>(1-.10)/(1+.03)-1=-12.6%</math>. Our retiree had expected to start age 66 with $984,196 in the portfolio. Instead, the portfolio contains only $859,977, which is 12.6% less. Consider what happens in the following two scenarios:<br />
<br />
=====Scenario 1: Expected return stays the same=====<br />
Suppose that the retiree believes that this market drop has not impacted future expected returns, which in the retiree's opinion, remains at 3%. The retiree enters the new reduced portfolio value, <math>P=$859,977</math>, number of years remaining <math>n=35</math>, and expected real return <math>r=3%</math>. The withdrawal is now reduced to $38,857 per year. That is a 12.6% reduction relative to the previously planned withdrawal of $44,470. So the 12.6% portfolio loss is being matched by a 12.6% spending cut across all remaining years.<br />
<br />
=====Scenario 2: Expected return increases=====<br />
If the market drop was due to a pure valuation change and the underlying earnings of the portfolio are not impacted, then the retiree might expect a higher rate of return going forward.<br />
<br />
If expected return is based on an earnings yield model (e.g. 1/CAPE) for stocks and yield to maturity for bonds, a 12.6% reduction in valuation will result in a higher expected real return of <math>.03/(1-.126)=3.43%</math>. With the higher expected return, the withdrawal becomes $41,181. That is a reduction of only 7.4% relative to the original plan of $44,470. A 12.6% reduction in the portfolio led to only a 7.4% reduction in income, because the higher expected return partially offset the loss in portfolio value.<br />
<br />
So to the extent that market volatility is caused by valuation changes and gets incorporated into expected returns, withdrawals from the portfolio will be less volatile than the portfolio itself.<br />
<br />
==Adding a terminal balance==<br />
<br />
Instead of fully depleting the portfolio, the amortization can be modified to leave behind a terminal balance. This could be used to fund end of life care or a bequest, or it could simply serve as a general financial cushion. <br />
<br />
In the ABW calculator, enter:<br />
* <math>B=</math> terminal balance<br />
<br />
===Example===<br />
<br />
The 65 year old retiree in the earlier example wants to have $200,000 left at the end for a bequest. Enter <math>B=$200,000</math> in the calculator to get a withdrawal of $41,401 per year. If the actual rate of return matches expectations, then after withdrawing $41,401 for 36 years (ages 65 to 100), the retiree will have $200,000 remaining in the portfolio at the end of age 100.<br />
<br />
==Rising or falling withdrawal schedules==<br />
<br />
Instead of aiming at a constant withdrawal schedule, some retirees may prefer to aim at a rising or falling withdrawal schedule. Retirees worried about incurring unexpected expenses or generally running out of money in later years may want to use a rising withdrawal schedule - take less early so they can have more later. Those wanting to fund an active early retirement may want to use a declining withdrawal schedule - take more early but have less later. (Note the similarity with savings. This can be viewed as a decision about how much to save in the early retirement years in order to fund late retirement consumption.)<br />
<br />
In the ABW calculator, enter:<br />
* <math>g=</math> rate of growth of the withdrawal schedule<br />
<br />
<math>g>0</math> generates a rising withdrawal schedule, <math>g<0</math> generates a declining withdrawal schedule, and <math>g=0</math> generates a constant withdrawal schedule.<br />
<br />
===Example===<br />
<br />
If the 65 year old retiree in the earlier example wants withdrawals to grow at 1% per year, set <math>g=1%</math> to get a withdrawal of $38,349. Withdrawals are scheduled to grow 1% per year, rising to $54,325 at age 100.<br />
<br />
If instead the retiree wishes to spend more in early retirement and wants withdrawals to fall by 1% per year, set <math>g=-1%</math> to get a withdrawal of $51,118. Withdrawals are scheduled to fall 1% per year, declining to $35,959 at age 100.<br />
<br />
==Asset allocation==<br />
<br />
===Fixed asset allocation===<br />
<br />
The amortization formula assumes a constant rate of return on the portfolio. This is easier to justify if the retiree plans to maintain a fixed asset allocation (AA). If instead the retiree is planning to change AA over time (e.g. glide down from 60/40 to 30/70 over the course of the retirement), then the expected return is not constant. Amortization can still be performed, but it will require manual modeling. The calculator provided here cannot be used. Entering the average expected return in the calculator may provide a rough estimate, but due to the potential for significant errors, more precise modeling is recommended.<br />
<br />
===Fixed asset allocation with sub-portfolios===<br />
<br />
The portfolio can be divided into multiple sub-portfolios and a different fixed allocation applied to each sub-portfolio.<br />
<br />
Suppose the retiree is more risk averse over certain categories of consumption (e.g. food and housing), and less risk averse over other categories (e.g. vacations). The portfolio can be subdivided into a safer portfolio to fund food and housing and a riskier portfolio to fund vacations. The safe portfolio would get a safe fixed AA like 30/70, and the riskier portfolio would get a riskier fixed AA like 80/20. Multiple sub-portfolios could be created to fund different consumption goals, each with a different AA that matches the risk-reward considerations for that goal. Withdrawals would be calculated separately for each sub-portfolio.<br />
<br />
An example of a strategy that uses sub-portfolios is the Liability Matched Portfolio (LMP) strategy. The portfolio is divided into a "liability matched portfolio" and a "risk portfolio". The liability matched portfolio has an AA of 0/100 and is used to fund non-negotiable consumption. The risk portfolio is given a riskier AA and is used to fund discretionary "nice to have" consumption.<br />
<br />
==Extra income and expenses==<br />
<br />
Besides their savings portfolio, retirees may have other sources of present or future income such as social security, pensions, annuities, rental income, and lump sum payouts ("extra income"). They may also have exceptional expenses planned such as college tuition or a lingering home mortgage or long-term care expenses that may require funds beyond what is provided by the basic amortization process ("extra expenses"). Such extra income and expenses can be dealt with in different ways. ABW is neutral and does not take a position on how best to do it. Below are some of the strategies that have been used:<br />
<br />
===Keep it separate===<br />
<br />
The retiree can choose to keep some or all of the extra income and expenses outside the amortization process. They can allocate the extra income, and budget for the extra expenses, separate from the ABW calculation. This is effectively a sub-portfolio approach where the extra income and expenses are being handled in a separate portfolio.<br />
<br />
A retiree formally pursuing the sub-portfolio approach described earlier may indeed find it convenient to use conservative estimates of social security and pensions to fund the safe sub-portfolios. The income streams are already duration matched. Gaps remaining can be filled with duration matched bonds. Depending on the asset allocation, there may be little to no rebalancing needed in the safe sub-portfolios.<br />
<br />
===Incorporate it using the portfolio rate of return to value all income and expenses===<br />
<br />
Calculate the extra net income (extra income minus extra expenses). Calculate its present value using the portfolio rate of return. (See Wiki article on calculating present value by discounting future cash flows: [[Comparing_investments#Present_value|Comparing Investments]]). Add this value to the portfolio to calculate withdrawals. Exclude it when calculating the asset allocation of the portfolio (for rebalancing) and the expected return of the portfolio (to enter into the ABW calculator). More information on this approach is available here: <insert link><br />
<br />
===Incorporate it using bond interest rates to value safe income and essential expenses===<br />
<br />
Create a conservatively low estimate of safe extra income and a conservatively high estimate of essential extra expenses. Subtract the latter from the former to obtain a conservatively low estimate of safe extra net income. Calculate its present value using bond interest rates. Add this value to the portfolio for all calculations, counting it as a bond. Include it when calculating withdrawals. Include it when calculating the asset allocation of the portfolio (for rebalancing) and the expected return of the portfolio (to enter into the ABW calculator). More information on this approach is available here: <insert link><br />
<br />
==Estimating the expected return==<br />
<br />
The ABW calculation requires the user to input the expected rate of return of the portfolio. ABW does not recommend a specific model for this purpose. The user is free to use whatever model of expected return they prefer. Examples of models that can be used include:<br />
<br />
===Models based on earnings yields (e.g. 1/CAPE)===<br />
<Enter info><br />
<br />
===Models based on historical returns===<br />
<Enter info><br />
<br />
==ABW calculator==<br />
<br />
===Basic calculator===<br />
<br />
The Excel spreadsheet to calculate withdrawals in on Google Drive: [https://drive.google.com/file/d/1XOnBaUspLX_oaM2rquTPmLj5AKOm6yxV/view?usp=sharing ABW Calculator]<br />
<br />
[[User:Ben Mathew/Formulas for Amortization Based Withdrawal (ABW)]] describes the formulas used in the calculator.<br />
<br />
===Advanced calculators===<br />
<br />
These calculators expand the basic functionality to include other considerations.<br />
<br />
An Excel spreadsheet that incorporates extra income and expenses in on Google Drive: [https://drive.google.com/file/d/1v8KZfXMCnIJXjy0e3RkZ-Uap4OiaXCpu/view?usp=sharing ABW Calculator with Extra Income and Expenses]<br />
<br />
==Support==<br />
On-going discussion and support is in {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}.<br />
<br />
==See also==<br />
*[[Comparing investments]] - Tutorial on ''Time Value of Money'' equations</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Amortization_based_withdrawal&diff=70621
Amortization based withdrawal
2020-11-20T00:18:50Z
<p>Siamond: /* Example */ Minor rewording</p>
<hr />
<div>{{Under construction| comment = Comments are being solicited in this {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}}}<br />
'''Amortization based withdrawal (ABW)''' uses amortization techniques to calculate portfolio withdrawals during retirement. Examples of withdrawals that use amortization include [[Variable percentage withdrawal | Variable Percentage Withdrawal]] (VPW) and the [[Required Minimum Distribution]] (RMD) rules for traditional retirement accounts.<br />
<br />
==Amortization==<br />
<br />
===Understanding amortization===<br />
<br />
Amortization is the process of converting the value of a lump sum into a series of payments over time. Most people encounter it when they take out a mortgage or car loan. Amortization is used to calculate the monthly payment required to pay back the loan. The value of the monthly payments has to be made equal to the value of the initial loan.<br />
<br />
If the interest rate is zero, amortization is just simple division: If $100,000 has to be paid back over 10 years, then the payment is $100,000 ÷ 10 = $10,000 per year.<br />
<br />
But if the interest rate is positive, as is usually the case, then the payment in the above example would have to be more than $10,000 per year. That's because $10,000 in the future is worth less than $10,000 today. This is referred to as the time value of money. If the interest is 5% per year, then $10,000 today is worth:<br />
<br />
* <math>$10,000*1.05^1=$10,500</math> one year from now<br />
* <math>$10,000*1.05^2=$11,025</math> two years from now<br />
<br />
and so on. We will have to adjust for the differences in value. The amortization formula makes the necessary adjustments and tells us that if the interest rate is 5% per year, then the payments will have to be $12,950 per year for the next ten years for the total value of the payments to be equal in value to the $100,000 that was borrowed today.<br />
<br />
==Amortization based withdrawal==<br />
<br />
To calculate portfolio withdrawals, enter the following inputs in the ABW calculator ([[#ABW calculator|below]]):<br />
<br />
* <math>P=</math> current portfolio value<br />
* <math>n=</math> number of years over which withdrawals are to be spread out<br />
* <math>r=</math> expected return of the portfolio.<br />
<br />
===Example===<br />
<br />
A 65 year old retiree with a $1 million portfolio expected to earn 3% per year and seeking to spread out withdrawals over 36 years (ages 65 to 100), would enter <math>P=$1,000,000, n=36, r=3%</math>. The amortization calculator says that this retiree can withdraw $44,470 per year. This means that if the portfolio actual rate of return remains constant at 3% per year and the retiree withdraws $44,470 every year, then the portfolio will be fully depleted after 36 years.<br />
<br />
===Real vs nominal rate of return===<br />
<br />
If a real (inflation adjusted) rate of return is used, the withdrawal strategy becomes automatically adjusted for inflation. In the above example, if the real rate of return is 3%, the retiree will be able to take out $44,470 (inflation adjusted) each year. If instead, the retiree enters a nominal interest rate of 5%, the calculator says that they can take out $60,434 per year. But that's in nominal dollars, so real consumption will decline each year by the inflation rate. In practice, it is strongly recommended to use a real rate of return.<br />
<br />
===Update and adapt===<br />
<br />
Withdrawals are recalculated each year with updated information about portfolio value, expected rate of return, and number of years left. This allows withdrawals to continually adapt to new information and mitigates the impact of past incorrect assumptions. Amortization spreads the course correction required across all remaining years, thereby minimizing the impact on any one year.<br />
<br />
====Example====<br />
<br />
Consider what happens in our earlier example if, instead of gaining 3% as expected, the portfolio actually loses 10%. The shortfall relative to expectations is <math>(1-.10)/(1+.03)-1=-12.6%</math>. Our retiree had expected to start age 66 with $984,196 in the portfolio. Instead, the portfolio contains only $859,977, which is 12.6% less. Consider what happens in the following two scenarios:<br />
<br />
=====Scenario 1: Expected return stays the same=====<br />
Suppose that the retiree believes that this market drop has not impacted future expected returns, which in the retiree's opinion, remains at 3%. The retiree enters the new reduced portfolio value, <math>P=$859,977</math>, number of years remaining <math>n=35</math>, and expected real return <math>r=3%</math>. The withdrawal is now reduced to $38,857 per year. That is a 12.6% reduction relative to the previously planned withdrawal of $44,470. So the 12.6% portfolio loss is being matched by a 12.6% spending cut across all remaining years.<br />
<br />
=====Scenario 2: Expected return increases=====<br />
If the market drop was due to a pure valuation change and the underlying earnings of the portfolio are not impacted, then the retiree might expect a higher rate of return going forward.<br />
<br />
If expected return is based on an earnings yield model (e.g. 1/CAPE) for stocks and yield to maturity for bonds, a 12.6% reduction in valuation will result in a higher expected real return of <math>.03/(1-.126)=3.43%</math>. With the higher expected return, the withdrawal becomes $41,181. That is a reduction of only 7.4% relative to the original plan of $44,470. A 12.6% reduction in the portfolio led to only a 7.4% reduction in income, because the higher expected return partially offset the loss in portfolio value.<br />
<br />
So to the extent that market volatility is caused by valuation changes and gets incorporated into expected returns, withdrawals from the portfolio will be less volatile than the portfolio itself.<br />
<br />
==Adding a terminal balance==<br />
<br />
Instead of fully depleting the portfolio, the amortization can be modified to leave behind a terminal balance. This could be used to fund end of life care or a bequest, or it could simply serve as a general financial cushion. <br />
<br />
In the ABW calculator, enter:<br />
* <math>B=</math> terminal balance<br />
<br />
===Example===<br />
<br />
The 65 year old retiree in the earlier example wants to have $200,000 left at the end for a bequest. Enter <math>B=$200,000</math> in the calculator to get a withdrawal of $41,401 per year. If the actual rate of return matches expectations, then after withdrawing $41,401 for 36 years (ages 65 to 100), the retiree will have $200,000 remaining in the portfolio at the end of age 100.<br />
<br />
==Rising or falling withdrawal schedules==<br />
<br />
Instead of aiming at a constant withdrawal schedule, some retirees may prefer to aim at a rising or falling withdrawal schedule. Retirees worried about incurring unexpected expenses or generally running out of money in later years may want to use a rising withdrawal schedule - take less early so they can have more later. Those wanting to fund an active early retirement may want to use a declining withdrawal schedule - take more early but have less later. (Note the similarity with savings. This can be viewed as a decision about how much to save in the early retirement years in order to fund late retirement consumption.)<br />
<br />
In the ABW calculator, enter:<br />
* <math>g=</math> rate of growth of the withdrawal schedule<br />
<br />
<math>g>0</math> generates a rising withdrawal schedule, <math>g<0</math> generates a declining withdrawal schedule, and <math>g=0</math> generates a constant withdrawal schedule.<br />
<br />
===Example===<br />
<br />
If the 65 year old retiree in the earlier example wants withdrawals to grow at 1% per year, set <math>g=1%</math> to get a withdrawal of $38,349. Withdrawals are scheduled to grow 1% per year, rising to $54,325 at age 100.<br />
<br />
If instead the retiree wishes to spend more in early retirement and wants withdrawals to fall by 1% per year, set <math>g=-1%</math> to get a withdrawal of $51,118. Withdrawals are scheduled to fall 1% per year, declining to $35,959 at age 100.<br />
<br />
==Asset allocation==<br />
<br />
===Fixed asset allocation===<br />
<br />
The amortization formula assumes a constant rate of return on the portfolio. This is easier to justify if the retiree plans to maintain a fixed asset allocation (AA). If instead the retiree is planning to change AA over time (e.g. glide down from 60/40 to 30/70 over the course of the retirement), then the expected return is not constant. Amortization can still be performed, but it will require manual modeling. The calculator provided here cannot be used. Entering the average expected return in the calculator may provide a rough estimate, but due to the potential for significant errors, more precise modeling is recommended.<br />
<br />
===Fixed asset allocation with sub-portfolios===<br />
<br />
The portfolio can be divided into multiple sub-portfolios and a different fixed allocation applied to each sub-portfolio.<br />
<br />
Suppose the retiree is more risk averse over certain categories of consumption (e.g. food and housing), and less risk averse over other categories (e.g. vacations). The portfolio can be subdivided into a safer portfolio to fund food and housing and a riskier portfolio to fund vacations. The safe portfolio would get a safe fixed AA like 30/70, and the riskier portfolio would get a riskier fixed AA like 80/20. Multiple sub-portfolios could be created to fund different consumption goals, each with a different AA that matches the risk-reward considerations for that goal. Withdrawals would be calculated separately for each sub-portfolio.<br />
<br />
An example of a strategy that uses sub-portfolios is the Liability Matched Portfolio (LMP) strategy. The portfolio is divided into a "liability matched portfolio" and a "risk portfolio". The liability matched portfolio has an AA of 0/100 and is used to fund non-negotiable consumption. The risk portfolio is given a riskier AA and is used to fund discretionary "nice to have" consumption.<br />
<br />
==Extra income and expenses==<br />
<br />
Besides their savings portfolio, retirees may have other sources of income such as social security, pensions, annuities, rental income, and lump sum payouts ("extra income"). They may also have atypical expenses such as college tuition or a home remodel that may require funds beyond what is provided by the basic amortization process ("extra expenses"). This extra income and expenses can be dealt with in different ways. ABW is neutral, and does not take a position on how best to do it. Below are some of the strategies that have been used:<br />
<br />
===Keep it separate===<br />
<br />
The retiree can choose to keep some or all of the extra income and expenses outside the amortization process. They can allocate the extra income, and budget for the extra expenses, separate from the ABW calculation. This is effectively a sub-portfolio approach where the extra income and expenses are being handled in a separate portfolio.<br />
<br />
A retiree formally pursuing the sub-portfolio approach described earlier may indeed find it convenient to use conservative estimates of social security and pensions to fund the safe sub-portfolios. The income streams are already duration matched. Gaps remaining can be filled with duration matched bonds. Depending on the asset allocation, there may be little to no rebalancing needed in the safe sub-portfolios.<br />
<br />
===Incorporate it using the portfolio rate of return to value all income and expenses===<br />
<br />
Calculate the extra net income (extra income minus extra expenses). Calculate its present value using the portfolio rate of return. (See Wiki article on calculating present value by discounting future cash flows: [[Comparing_investments#Present_value|Comparing Investments]]). Add this value to the portfolio to calculate withdrawals. Exclude it when calculating the asset allocation of the portfolio (for rebalancing) and the expected return of the portfolio (to enter into the ABW calculator). More information on this approach is available here: <insert link><br />
<br />
===Incorporate it using bond interest rates to value safe income and essential expenses===<br />
<br />
Create a conservatively low estimate of safe extra income and a conservatively high estimate of essential extra expenses. Subtract the latter from the former to obtain a conservatively low estimate of safe extra net income. Calculate its present value using bond interest rates. Add this value to the portfolio for all calculations, counting it as a bond. Include it when calculating withdrawals. Include it when calculating the asset allocation of the portfolio (for rebalancing) and the expected return of the portfolio (to enter into the ABW calculator). More information on this approach is available here: <insert link><br />
<br />
==Estimating the expected return==<br />
<br />
The ABW calculation requires the user to input the expected rate of return of the portfolio. ABW does not recommend a specific model for this purpose. The user is free to use whatever model of expected return they prefer. Examples of models that can be used include:<br />
<br />
===Models based on earnings yields (e.g. 1/CAPE)===<br />
<Enter info><br />
<br />
===Models based on historical returns===<br />
<Enter info><br />
<br />
==ABW calculator==<br />
<br />
===Basic calculator===<br />
<br />
The Excel spreadsheet to calculate withdrawals in on Google Drive: [https://drive.google.com/file/d/1XOnBaUspLX_oaM2rquTPmLj5AKOm6yxV/view?usp=sharing ABW Calculator]<br />
<br />
[[User:Ben Mathew/Formulas for Amortization Based Withdrawal (ABW)]] describes the formulas used in the calculator.<br />
<br />
===Advanced calculators===<br />
<br />
These calculators expand the basic functionality to include other considerations.<br />
<br />
An Excel spreadsheet that incorporates extra income and expenses in on Google Drive: [https://drive.google.com/file/d/1v8KZfXMCnIJXjy0e3RkZ-Uap4OiaXCpu/view?usp=sharing ABW Calculator with Extra Income and Expenses]<br />
<br />
==Support==<br />
On-going discussion and support is in {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}.<br />
<br />
==See also==<br />
*[[Comparing investments]] - Tutorial on ''Time Value of Money'' equations</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Amortization_based_withdrawal&diff=70620
Amortization based withdrawal
2020-11-20T00:17:12Z
<p>Siamond: /* Understanding amortization */ removed "today" as amortized lump sum may be in the future</p>
<hr />
<div>{{Under construction| comment = Comments are being solicited in this {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}}}<br />
'''Amortization based withdrawal (ABW)''' uses amortization techniques to calculate portfolio withdrawals during retirement. Examples of withdrawals that use amortization include [[Variable percentage withdrawal | Variable Percentage Withdrawal]] (VPW) and the [[Required Minimum Distribution]] (RMD) rules for traditional retirement accounts.<br />
<br />
==Amortization==<br />
<br />
===Understanding amortization===<br />
<br />
Amortization is the process of converting the value of a lump sum into a series of payments over time. Most people encounter it when they take out a mortgage or car loan. Amortization is used to calculate the monthly payment required to pay back the loan. The value of the monthly payments has to be made equal to the value of the initial loan.<br />
<br />
If the interest rate is zero, amortization is just simple division: If $100,000 has to be paid back over 10 years, then the payment is $100,000 ÷ 10 = $10,000 per year.<br />
<br />
But if the interest rate is positive, as is usually the case, then the payment in the above example would have to be more than $10,000 per year. That's because $10,000 in the future is worth less than $10,000 today. This is referred to as the time value of money. If the interest is 5% per year, then $10,000 today is worth:<br />
<br />
* <math>$10,000*1.05^1=$10,500</math> one year from now<br />
* <math>$10,000*1.05^2=$11,025</math> two years from now<br />
<br />
and so on. We will have to adjust for the differences in value. The amortization formula makes the necessary adjustments and tells us that if the interest rate is 5% per year, then the payments will have to be $12,950 per year for the next ten years for the total value of the payments to be equal in value to the $100,000 that was borrowed today.<br />
<br />
==Amortization based withdrawal==<br />
<br />
To calculate portfolio withdrawals, enter the following inputs in the ABW calculator ([[#ABW calculator|below]]):<br />
<br />
* <math>P=</math> current portfolio value<br />
* <math>n=</math> number of years over which withdrawals are to be spread out<br />
* <math>r=</math> expected return of the portfolio.<br />
<br />
===Example===<br />
<br />
A 65 year old retiree with a $1 million portfolio earning 3% per year and seeking to spread out withdrawals over 36 years (ages 65 to 100), would enter <math>P=$1,000,000, n=36, r=3%</math>. The amortization calculator says that this retiree can withdraw $44,470 per year. This means that if the portfolio actual rate of return remains constant at 3% per year and the retiree withdraws $44,470 every year, then the portfolio will be fully depleted after 36 years.<br />
<br />
===Real vs nominal rate of return===<br />
<br />
If a real (inflation adjusted) rate of return is used, the withdrawal strategy becomes automatically adjusted for inflation. In the above example, if the real rate of return is 3%, the retiree will be able to take out $44,470 (inflation adjusted) each year. If instead, the retiree enters a nominal interest rate of 5%, the calculator says that they can take out $60,434 per year. But that's in nominal dollars, so real consumption will decline each year by the inflation rate. In practice, it is strongly recommended to use a real rate of return.<br />
<br />
===Update and adapt===<br />
<br />
Withdrawals are recalculated each year with updated information about portfolio value, expected rate of return, and number of years left. This allows withdrawals to continually adapt to new information and mitigates the impact of past incorrect assumptions. Amortization spreads the course correction required across all remaining years, thereby minimizing the impact on any one year.<br />
<br />
====Example====<br />
<br />
Consider what happens in our earlier example if, instead of gaining 3% as expected, the portfolio actually loses 10%. The shortfall relative to expectations is <math>(1-.10)/(1+.03)-1=-12.6%</math>. Our retiree had expected to start age 66 with $984,196 in the portfolio. Instead, the portfolio contains only $859,977, which is 12.6% less. Consider what happens in the following two scenarios:<br />
<br />
=====Scenario 1: Expected return stays the same=====<br />
Suppose that the retiree believes that this market drop has not impacted future expected returns, which in the retiree's opinion, remains at 3%. The retiree enters the new reduced portfolio value, <math>P=$859,977</math>, number of years remaining <math>n=35</math>, and expected real return <math>r=3%</math>. The withdrawal is now reduced to $38,857 per year. That is a 12.6% reduction relative to the previously planned withdrawal of $44,470. So the 12.6% portfolio loss is being matched by a 12.6% spending cut across all remaining years.<br />
<br />
=====Scenario 2: Expected return increases=====<br />
If the market drop was due to a pure valuation change and the underlying earnings of the portfolio are not impacted, then the retiree might expect a higher rate of return going forward.<br />
<br />
If expected return is based on an earnings yield model (e.g. 1/CAPE) for stocks and yield to maturity for bonds, a 12.6% reduction in valuation will result in a higher expected real return of <math>.03/(1-.126)=3.43%</math>. With the higher expected return, the withdrawal becomes $41,181. That is a reduction of only 7.4% relative to the original plan of $44,470. A 12.6% reduction in the portfolio led to only a 7.4% reduction in income, because the higher expected return partially offset the loss in portfolio value.<br />
<br />
So to the extent that market volatility is caused by valuation changes and gets incorporated into expected returns, withdrawals from the portfolio will be less volatile than the portfolio itself.<br />
<br />
==Adding a terminal balance==<br />
<br />
Instead of fully depleting the portfolio, the amortization can be modified to leave behind a terminal balance. This could be used to fund end of life care or a bequest, or it could simply serve as a general financial cushion. <br />
<br />
In the ABW calculator, enter:<br />
* <math>B=</math> terminal balance<br />
<br />
===Example===<br />
<br />
The 65 year old retiree in the earlier example wants to have $200,000 left at the end for a bequest. Enter <math>B=$200,000</math> in the calculator to get a withdrawal of $41,401 per year. If the actual rate of return matches expectations, then after withdrawing $41,401 for 36 years (ages 65 to 100), the retiree will have $200,000 remaining in the portfolio at the end of age 100.<br />
<br />
==Rising or falling withdrawal schedules==<br />
<br />
Instead of aiming at a constant withdrawal schedule, some retirees may prefer to aim at a rising or falling withdrawal schedule. Retirees worried about incurring unexpected expenses or generally running out of money in later years may want to use a rising withdrawal schedule - take less early so they can have more later. Those wanting to fund an active early retirement may want to use a declining withdrawal schedule - take more early but have less later. (Note the similarity with savings. This can be viewed as a decision about how much to save in the early retirement years in order to fund late retirement consumption.)<br />
<br />
In the ABW calculator, enter:<br />
* <math>g=</math> rate of growth of the withdrawal schedule<br />
<br />
<math>g>0</math> generates a rising withdrawal schedule, <math>g<0</math> generates a declining withdrawal schedule, and <math>g=0</math> generates a constant withdrawal schedule.<br />
<br />
===Example===<br />
<br />
If the 65 year old retiree in the earlier example wants withdrawals to grow at 1% per year, set <math>g=1%</math> to get a withdrawal of $38,349. Withdrawals are scheduled to grow 1% per year, rising to $54,325 at age 100.<br />
<br />
If instead the retiree wishes to spend more in early retirement and wants withdrawals to fall by 1% per year, set <math>g=-1%</math> to get a withdrawal of $51,118. Withdrawals are scheduled to fall 1% per year, declining to $35,959 at age 100.<br />
<br />
==Asset allocation==<br />
<br />
===Fixed asset allocation===<br />
<br />
The amortization formula assumes a constant rate of return on the portfolio. This is easier to justify if the retiree plans to maintain a fixed asset allocation (AA). If instead the retiree is planning to change AA over time (e.g. glide down from 60/40 to 30/70 over the course of the retirement), then the expected return is not constant. Amortization can still be performed, but it will require manual modeling. The calculator provided here cannot be used. Entering the average expected return in the calculator may provide a rough estimate, but due to the potential for significant errors, more precise modeling is recommended.<br />
<br />
===Fixed asset allocation with sub-portfolios===<br />
<br />
The portfolio can be divided into multiple sub-portfolios and a different fixed allocation applied to each sub-portfolio.<br />
<br />
Suppose the retiree is more risk averse over certain categories of consumption (e.g. food and housing), and less risk averse over other categories (e.g. vacations). The portfolio can be subdivided into a safer portfolio to fund food and housing and a riskier portfolio to fund vacations. The safe portfolio would get a safe fixed AA like 30/70, and the riskier portfolio would get a riskier fixed AA like 80/20. Multiple sub-portfolios could be created to fund different consumption goals, each with a different AA that matches the risk-reward considerations for that goal. Withdrawals would be calculated separately for each sub-portfolio.<br />
<br />
An example of a strategy that uses sub-portfolios is the Liability Matched Portfolio (LMP) strategy. The portfolio is divided into a "liability matched portfolio" and a "risk portfolio". The liability matched portfolio has an AA of 0/100 and is used to fund non-negotiable consumption. The risk portfolio is given a riskier AA and is used to fund discretionary "nice to have" consumption.<br />
<br />
==Extra income and expenses==<br />
<br />
Besides their savings portfolio, retirees may have other sources of income such as social security, pensions, annuities, rental income, and lump sum payouts ("extra income"). They may also have atypical expenses such as college tuition or a home remodel that may require funds beyond what is provided by the basic amortization process ("extra expenses"). This extra income and expenses can be dealt with in different ways. ABW is neutral, and does not take a position on how best to do it. Below are some of the strategies that have been used:<br />
<br />
===Keep it separate===<br />
<br />
The retiree can choose to keep some or all of the extra income and expenses outside the amortization process. They can allocate the extra income, and budget for the extra expenses, separate from the ABW calculation. This is effectively a sub-portfolio approach where the extra income and expenses are being handled in a separate portfolio.<br />
<br />
A retiree formally pursuing the sub-portfolio approach described earlier may indeed find it convenient to use conservative estimates of social security and pensions to fund the safe sub-portfolios. The income streams are already duration matched. Gaps remaining can be filled with duration matched bonds. Depending on the asset allocation, there may be little to no rebalancing needed in the safe sub-portfolios.<br />
<br />
===Incorporate it using the portfolio rate of return to value all income and expenses===<br />
<br />
Calculate the extra net income (extra income minus extra expenses). Calculate its present value using the portfolio rate of return. (See Wiki article on calculating present value by discounting future cash flows: [[Comparing_investments#Present_value|Comparing Investments]]). Add this value to the portfolio to calculate withdrawals. Exclude it when calculating the asset allocation of the portfolio (for rebalancing) and the expected return of the portfolio (to enter into the ABW calculator). More information on this approach is available here: <insert link><br />
<br />
===Incorporate it using bond interest rates to value safe income and essential expenses===<br />
<br />
Create a conservatively low estimate of safe extra income and a conservatively high estimate of essential extra expenses. Subtract the latter from the former to obtain a conservatively low estimate of safe extra net income. Calculate its present value using bond interest rates. Add this value to the portfolio for all calculations, counting it as a bond. Include it when calculating withdrawals. Include it when calculating the asset allocation of the portfolio (for rebalancing) and the expected return of the portfolio (to enter into the ABW calculator). More information on this approach is available here: <insert link><br />
<br />
==Estimating the expected return==<br />
<br />
The ABW calculation requires the user to input the expected rate of return of the portfolio. ABW does not recommend a specific model for this purpose. The user is free to use whatever model of expected return they prefer. Examples of models that can be used include:<br />
<br />
===Models based on earnings yields (e.g. 1/CAPE)===<br />
<Enter info><br />
<br />
===Models based on historical returns===<br />
<Enter info><br />
<br />
==ABW calculator==<br />
<br />
===Basic calculator===<br />
<br />
The Excel spreadsheet to calculate withdrawals in on Google Drive: [https://drive.google.com/file/d/1XOnBaUspLX_oaM2rquTPmLj5AKOm6yxV/view?usp=sharing ABW Calculator]<br />
<br />
[[User:Ben Mathew/Formulas for Amortization Based Withdrawal (ABW)]] describes the formulas used in the calculator.<br />
<br />
===Advanced calculators===<br />
<br />
These calculators expand the basic functionality to include other considerations.<br />
<br />
An Excel spreadsheet that incorporates extra income and expenses in on Google Drive: [https://drive.google.com/file/d/1v8KZfXMCnIJXjy0e3RkZ-Uap4OiaXCpu/view?usp=sharing ABW Calculator with Extra Income and Expenses]<br />
<br />
==Support==<br />
On-going discussion and support is in {{Forum post|t = 274243| title = Amortization Based Withdrawal (ABW)}}.<br />
<br />
==See also==<br />
*[[Comparing investments]] - Tutorial on ''Time Value of Money'' equations</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Amortization_based_withdrawal&diff=70570
Amortization based withdrawal
2020-11-06T21:18:39Z
<p>Siamond: Fixed a few typos, added a couple of minor clarifications</p>
<hr />
<div>{{Under construction| comment = Comments are being solicited in this {{Forum post|t = 274243| title = Using the Time Value of Money Formula to Determine Withdrawals: Year 2000 Retiree Example}}}}<br />
'''Amortization based withdrawal (ABW)''' uses amortization techniques to calculate portfolio withdrawal methods during retirement. Examples of withdrawals that use amortization include [[Variable percentage withdrawal | Variable Percentage Withdrawal]] (VPW) and the [[Required Minimum Distribution]] (RMD) rules for traditional retirement accounts.<br />
<br />
==Amortization==<br />
<br />
===Understanding amortization===<br />
<br />
Amortization is the process of converting the value of a lump sum today into a series of payments over time. Most people encounter it when they take out a mortgage or car loan. Amortization is used to calculate the monthly payment required to pay back the loan. The value of the monthly payments has to be made equal to the value of the initial loan.<br />
<br />
If the interest rate is zero, amortization is just simple division: If $100,000 has to be paid back over 10 years, then the payment is $100,000 ÷ 10 = $10,000 per year.<br />
<br />
But if the interest rate is positive, as is usually the case, then the payment in the above example would have to be more than $10,000 per year. That's because $10,000 in the future is worth less than $10,000 today. This is referred to as the time value of money. If the interest is 5% per year, then $10,000 today is worth:<br />
<br />
* <math>$10,000*1.05^1=$10,500</math> one year from now<br />
* <math>$10,000*1.05^2=$11,025</math> two years from now<br />
<br />
and so on. We will have to adjust for the differences in value. The amortization formula makes the necessary adjustments and tells us that if the interest rate is 5% per year, then the payments will have to be $12,950 per year for the next ten years for the total value of the payments to be equal in value to the $100,000 that was borrowed today.<br />
<br />
==Amortization based withdrawal==<br />
<br />
To calculate portfolio withdrawals, enter the following inputs in the ABW calculator ([[#ABW calculator|below]]):<br />
<br />
* <math>P=</math> current portfolio value<br />
* <math>n=</math> number of years over which withdrawals are to be spread out<br />
* <math>r=</math> expected return of the portfolio.<br />
<br />
===Example===<br />
<br />
A 65 year old retiree with a $1 million portfolio earning 3% per year and seeking to spread out withdrawals over 36 years (ages 65 to 100), would enter <math>P=$1,000,000, n=36, r=3%</math>. The amortization calculator says that this retiree can withdraw $44,470 per year. This means that if the portfolio actual rate of return remains constant at 3% per year and the retiree withdraws $44,470 every year, then the portfolio will be fully depleted after 36 years.<br />
<br />
===Real vs nominal rate of return===<br />
<br />
If a real (inflation adjusted) rate of return is used, the withdrawal strategy becomes automatically adjusted for inflation. In the above example, if the real rate of return is 3%, the retiree will be able to take out $44,470 (inflation adjusted) each year. If instead, the retiree enters a nominal interest rate of 5%, the calculator says that they can take out $60,434 per year. But that's in nominal dollars, so real consumption will decline each year by the inflation rate. In practice, it is strongly recommended to use a real rate of return.<br />
<br />
===Update and adapt===<br />
<br />
Withdrawals are recalculated each year with updated information about portfolio value, expected rate of return, and number of years left. This allows withdrawals to continually adapt to new information and mitigates the impact of past incorrect assumptions. Amortization spreads the course correction required across all remaining years, thereby minimizing the impact on any one year.<br />
<br />
====Example====<br />
<br />
Consider what happens in our earlier example if, instead of gaining 3% as expected, the portfolio actually loses 10%. The shortfall relative to expectations is <math>(1-.10)/(1+.03)-1=-12.6%</math>. Our retiree had expected to start age 66 with $984,196 in the portfolio. Instead, the portfolio contains only $859,977, which is 12.6% less. Consider what happens in the following two scenarios:<br />
<br />
=====Scenario 1: Expected return stays the same=====<br />
Suppose that the retiree believes that this market drop has not impacted future expected returns, which in the retiree's opinion, remains at 3%. The retiree enters the new reduced portfolio value, <math>P=$859,977</math>, number of years remaining <math>n=35</math>, and expected real return <math>r=3%</math>. The withdrawal is now reduced to $38,857 per year. That is a 12.6% reduction relative to the previously planned withdrawal of $44,470. So the 12.6% portfolio loss is being matched by a 12.6% spending cut across all remaining years.<br />
<br />
=====Scenario 2: Expected return increases=====<br />
If the market drop was due to a pure valuation change and the underlying earnings of the portfolio are not impacted, then the retiree might expect a higher rate of return going forward. If expected return is based on an earnings yield model (e.g. 1/CAPE) for stocks and yield to maturity for bonds, a 12.6% reduction in valuation will result in a higher expected real return of <math>.03/(1-.126)=3.43%</math>. With the higher expected return, the withdrawal becomes $41,181. That is a reduction of only 7.4% relative to the original plan of $44,470. A 12.6% reduction in the portfolio led to only a 7.4% reduction in income, because the higher expected return partially offset the loss in portfolio value. So to the extent that market volatility is caused by valuation changes and gets incorporated into expected returns, withdrawals from the portfolio will be less volatile than the portfolio itself.<br />
<br />
==Adding a terminal balance==<br />
<br />
Instead of fully depleting the portfolio, the amortization can be modified to leave behind a terminal balance. This could be used to fund end of life care or a bequest, or it could simply serve as a general financial cushion. <br />
<br />
In the ABW calculator, enter:<br />
* <math>B=</math> terminal balance<br />
<br />
===Example===<br />
<br />
The 65 year old retiree in the earlier example wants to have $200,000 left at the end for a bequest. Enter <math>B=$200,000</math> in the calculator to get a withdrawal of $41,401 per year. If the actual rate of return matches expectations, then after withdrawing $41,401 for 36 years (ages 65 to 100), the retiree will have $200,000 remaining in the portfolio at the end of age 100.<br />
<br />
==Rising or falling withdrawal schedules==<br />
<br />
Instead of aiming at a constant withdrawal schedule, some retirees may prefer to aim at a rising or falling withdrawal schedule. Retirees worried about incurring unexpected expenses or running out of money in later years may want to use a rising withdrawal schedule - take less early so they can have more later. Those wanting to fund an active early retirement may want to use a declining withdrawal schedule - take more early but have less later. (Note the similarity with savings. This can be viewed as a decision about how much to save in the early retirement years in order to fund late retirement consumption.)<br />
<br />
In the ABW calculator, enter:<br />
* <math>g=</math> rate of growth of the withdrawal schedule<br />
<br />
<math>g>0</math> generates a rising withdrawal schedule, <math>g<0</math> generates a declining withdrawal schedule, and <math>g=0</math> generates a constant withdrawal schedule.<br />
<br />
===Example===<br />
<br />
If the 65 year old retiree in the earlier example wants withdrawals to grow at 1% per year, set <math>g=1%</math> to get a withdrawal of $38,349. Withdrawals are scheduled to grow 1% per year, rising to $54,325 at age 100.<br />
<br />
If instead the retiree wishes to spend more in early retirement and wants withdrawals to fall by 1% per year, set <math>g=-1%</math> to get a withdrawal of $51,118. Withdrawals are scheduled to fall 1% per year, declining to $35,959 at age 100.<br />
<br />
==Asset allocation==<br />
<br />
The amortization formula assumes a constant rate of return on the portfolio. This is easier to justify if the retiree plans to maintain a fixed asset allocation (AA). If instead the retiree is planning to change AA over time (e.g. glide down from 60/40 to 30/70 over the course of the retirement), then the expected return is not constant. Amortization can still be performed, but it will require manual modeling. The calculator provided here cannot be used. Entering the average expected return in the calculator may provide a rough estimate, but due to the potential for significant errors, more precise modeling is recommended.<br />
<br />
===Fixed asset allocation===<br />
<br />
Fixed asset allocations are optimal under the following conditions:<br />
<br />
* The retiree has a constant relative risk aversion (CRRA) utility function, at least for the consumption funded by portfolio withdrawals.<br />
* Returns are independent and identically distributed. That implies no mean reversion, for example.<br />
<br />
If these conditions hold, the retiree will choose to place the same fraction of the portfolio at risk every year. So the allocation is fixed.<br />
<br />
===Fixed asset allocation with sub-portfolios===<br />
<br />
Fixed asset allocations can be adapted to more general (non CRRA) utility functions by dividing the portfolio into multiple sub-portfolios and maintaining a different fixed allocation on each sub-portfolio.<br />
<br />
Suppose the retiree is more risk averse over certain categories of consumption (e.g. food and housing), and less risk averse over other categories (e.g. vacations). The portfolio can be subdivided into a safer portfolio to fund food and housing and a riskier portfolio to fund vacations. The safe portfolio would get a safe fixed AA like 30/70, and the riskier portfolio would get a riskier fixed AA like 80/20. Multiple sub-portfolios could be created to fund different consumption goals, each with a different AA that matches the risk-reward considerations for that goal. Withdrawals would be calculated separately for each sub-portfolio.<br />
<br />
An example of a strategy that uses sub-portfolios is the Liability Matched Portfolio (LMP) strategy. The portfolio is divided into a "liability matched portfolio" and a "risk portfolio". The liability matched portfolio has an AA of 0/100 and is used to fund non-negotiable consumption. The risk portfolio is given a riskier AA and is used to fund discretionary "nice to have" consumption. This strategy is consistent with a utility function that exhibits infinite risk aversion for consumption below some threshold (funded by the liability matched portfolio) and finite risk aversion for consumption above the threshold (funded by the risk portfolio).<br />
<br />
==Including other sources of income==<br />
<br />
The retiree can choose to include income from social security, pensions, annuities, and other sources into the portfolio and incorporate it into the withdrawal strategy. The payouts promised by these income sources can be viewed as bond payouts. The present value of the income is calculated by discounting the promised payouts using bond interest rates, and is included in the portfolio as a bond. Asset allocation and withdrawal calculations are done on this total portfolio.<br />
<br />
One way that these income sources differ from actual bonds is that they cannot be sold. If stocks perform badly, the retiree would need to sell bonds to maintain the target AA. If stock returns are poor enough, the retiree may reach a point where all of the actual bonds have already been sold and rebalancing to the target AA requires selling the income stream that is being counted as a bond. Since that is not possible, rebalancing cannot proceed and the AA will remain too safe relative to the target AA.<br />
<br />
A retiree pursuing the sub-portfolio approach described earlier may find it convenient to use these income streams to fund the safe sub-portfolios. The income streams are already duration matched. Gaps remaining can be filled with duration matched bonds. Depending on the AA, there may be little to no rebalancing needed in the safe sub-portfolios.<br />
<br />
==ABW calculator==<br />
<br />
The Excel spreadsheet to calculate withdrawals in on Google Drive: [https://drive.google.com/file/d/1XOnBaUspLX_oaM2rquTPmLj5AKOm6yxV/view?usp=sharing ABW Calculator]<br />
<br />
[[User:Ben Mathew/Formulas for Amortization Based Withdrawal (ABW)]] describes the formulas used in the calculator.<br />
<br />
==See also==<br />
*[[Comparing investments]] - Tutorial on ''Time Value of Money'' equations<br />
<br />
==External links==<br />
*{{Forum post|t = 274243| title = Using the Time Value of Money Formula to Determine Withdrawals: Year 2000 Retiree Example | author = willthrill81, date = February 27, 2019}}</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Bogleheads%C2%AE_financial_literacy_project&diff=70136
Bogleheads® financial literacy project
2020-09-13T16:33:53Z
<p>Siamond: /* General audience */ Added rebalancing presentation</p>
<hr />
<div><br />
{{Notice|To assist with education on financial topics, this article departs from the wiki's policy of neutrality. Contributions and discussion are being solicited in [{{{url|http://www.bogleheads.org/forum/viewtopic.php?f=2&t=117735}}} Help create a Financial Presentation: Calling all Bogleheads]}}<br />
The '''Bogleheads® financial literacy project''' is an effort to create a repository of PowerPoint on several very focused investing topics so that someone wanting to give a presentation could pick and choose and create a sub-set of the master group to suit their needs. Currently, a lot of material exists online to be read, but it is difficult to find PowerPoint presentations or other slide decks to be used for presenting to larger audiences. This article attempts to address that need.<br />
{{Quote|quote =<br />
'''Financial literacy:''' The ability to use knowledge and skills to manage financial resources effectively for a lifetime of financial well-being.<br><br />
'''Financial education:''' The process by which people improve their understanding of financial products, services and concepts, so they are empowered to make informed choices, avoid pitfalls, know where to go for help and take other actions to improve their present and long-term financial well-being.<br><br />
~President’s Advisory Council on Financial Literacy<ref>[http://www.treasury.gov/about/organizational-structure/offices/Domestic-Finance/Documents/exec_sum.pdf President’s Advisory Council on Financial Literacy], 2008 Annual Report to the President</ref>}}<br />
<br />
==Approach==<br />
Your target audience may need a specialized teaching environment or presentation style.<br />
<br />
===For parents===<br />
Many parents are interested in teaching their children about personal finance. While it is possible for parents to use accounts at financial institutions as instruments in the service of personal finance education, some account types accelerate a journey towards retirement savings. [[Accounts for children]] describes how.<br />
<br />
===Students===<br />
{{Empty section}}<br />
<br />
===Military===<br />
Try an informal seating arrangement (maybe around a table) with as little structure as possible. The service members who are ready to start saving for financial independence tend to be allergic to PowerPoint... or put to sleep by it. A two-page handout that's just text with plenty of space for taking notes will work.<br />
<br />
===Medical professionals===<br />
:''See also: [http://www.bogleheads.org/forum/viewtopic.php?p=1728504#p1728504 this post] by forum member czeckers.''<br />
<br />
Give an informal talk over 2 days. Much of the 1st day is specific to a target audience of young professionals who are late in the game with respect to saving, will have a high income, usually have a high loan burden. The second day is much more generalizable to the population at large.<br />
<br />
{| class="wikitable" style="text-align:left"<br />
|+ Two Day Talk<br />
! Day One (1 hour)<br />
! Day Two (Focused on Investing)<br />
|-<br />
|valign="top"|<br />
*Basics of personal finance<br />
*[[Insurance]]<br />
*Loan repayment -- pay off highest interest rate loans first<br />
|valign="top"|<br />
*Investing vs speculation, long-term view<br />
*[[:Category:Asset classes | Asset classes]], [[Risk and return: an introduction | risk]], [[Asset allocation | asset allocation]], time horizon<br />
*Diversification<br />
*Modern portfolio theory, further discussion of diversification<br />
*Periodic investing and effect of [[Dollar cost averaging | dollar cost averaging]]<br />
*[[Rebalancing]]<br />
|}<br />
<br />
===Young professionals===<br />
{{Empty section}}<br />
<br />
==Member supplied material==<br />
===General audience===<br />
Below are the forum member contributions for a general audience. The table can be sorted by clicking on the appropriate heading.<br />
<br />
{| class="wikitable sortable" style="text-align:left"<br />
|+ Bogleheads Forum Contributions for a General Audience<br />
! align="center" width="30%" | Title<br />
! align="center" width="25%" | Topics<br />
! align="center" width="35%" | Comments<br />
! align="center" width="5%" | Contributor<br />
|-<br />
||All-In-One Funds ([https://drive.google.com/file/d/0B8VSNcUR-B6ILW1IUUlGa1pkaE0/view?usp=sharing PowerPoint])||<br />
* Target Date Funds<br />
* Target Risk funds<br />
* Balanced Funds<br />
|| An overview of Vanguard offerings.<br />
||Milwaukee WI Bogleheads<br />
|-<br />
|| Bogleheads® Investment philosophy ([https://drive.google.com/file/d/0B8VSNcUR-B6IMk1DTWVBaktlOFE/view?usp=sharing PowerPoint])||<br />
See: [[Bogleheads® investment philosophy]]<br />
|| PowerPoint includes notes. Intended for new investors.<br />
||Milwaukee WI Bogleheads<br />
|-<br />
|| Charitable Donor Funds ([https://drive.google.com/file/d/0B8VSNcUR-B6IRU9ONTJkb0taQVk/view?usp=sharing PowerPoint])||<br />
See: [[Donor advised fund]].<br />
|| How to, why to, when to use these tools for tax and estate planning.<br />
||Milwaukee WI Bogleheads<br />
|-<br />
|| Fidelity's Income Investing Tools ([https://drive.google.com/file/d/0B8VSNcUR-B6IdEtXVnExWnRNMG8/view?usp=sharing PowerPoint])||<br />
How to use Fidelity's [https://www.fidelity.com/investment-guidance/overview Investment Guidance] tools.<br />
|| A supplemental guide.<br />
||Milwaukee WI Bogleheads<br />
|-<br />
|| Investment Policy Statement ([https://drive.google.com/file/d/0B8VSNcUR-B6IWVVTTlVIMWFERlU/view?usp=sharing PowerPoint])||<br />
See: [[Investment policy statement]]<br />
|| Intended for new investors.<br />
||Milwaukee WI Bogleheads<br />
|-<br />
|| Morningstar Style Boxes ([https://drive.google.com/file/d/0B8VSNcUR-B6INzhmTFhneE9vdGc/view?usp=sharing PowerPoint])||<br />
See: [[Stock basics#Style boxes|Stock style boxes]]<br />
|| Does not cover [[Bond_basics#Style_boxes|fixed income style boxes]].<br />
||Milwaukee WI Bogleheads<br />
|-<br />
|| Asset allocation during withdrawal ([https://drive.google.com/file/d/0B8VSNcUR-B6IMlZtemc2bjl1UzA/view?usp=sharing PowerPoint])||<br />
Managing portfolio withdrawal by asset allocation, reverse dollar cost averaging.<br />
|| MS PowerPoint, includes notes. Intended for experienced investors.<br />
||Milwaukee WI Bogleheads<br />
|-<br />
|| Retirement Funds: Will you still love me tomorrow? ([https://drive.google.com/file/d/0B8VSNcUR-B6IVVZrVGdqcThrbnc/view?usp=sharing PowerPoint])||<br />
Withdrawal strategy<br />
||A look at Jim Otar's zones and Guyton's rules. Intended for experienced investors.<br />
||Milwaukee WI Bogleheads<br />
|-<br />
|| Perspective: Keeping your head when all around you are losing theirs? ([https://drive.google.com/file/d/0B8VSNcUR-B6IOFFJZEtUSE5fMW8/view?usp=sharing PowerPoint])<br />
||Emotional impacts.<br />
|| An actual case study of why you should "Stay the course". Intended for new investors.<br />
||Milwaukee WI Bogleheads<br />
|-<br />
|| Rebalancing: How and When ([https://drive.google.com/file/d/0B8VSNcUR-B6IOUtSUlRTY1JMUG8/view?usp=sharing PowerPoint])||<br />
See: [[Rebalancing]]<br />
||LeeMKE's spreadsheet is available for download at the bottom of the [[Rebalancing]] article ("Spreadsheets").<br />
||Milwaukee WI Bogleheads<br />
|-<br />
|| Preparing for retirement: Streamline, simplify, document ([https://drive.google.com/file/d/0B8VSNcUR-B6IdHhMZ3AyeW82TTg/view?usp=sharing/view?usp=sharing PowerPoint])<br />
|| Retirement planning.<br />
|| How to prepare for retirement. Also see: [[Preparing for retirement]] and [[Checklist of important retirement dates]]<br />
||Milwaukee WI Bogleheads<br />
|-<br />
|| What's your number? How to know when you've "made it" ([https://drive.google.com/file/d/0B8VSNcUR-B6IMk92VmhILUl2ZTg/view?usp=sharing PowerPoint])<br />
||Retirement planning.<br />
||How to determine if you have enough saved to retire.<br />
||Milwaukee WI Bogleheads<br />
|-<br />
||Boglehead Basics and the IPS ([https://docs.google.com/file/d/0B1YvJ1_nL1hAYVJiZkttdGd6ZUE/edit?pli=1 PowerPoint]) ||<br />
*What is a Boglehead?<br />
*[[Investment policy statement]]<br />
||<br />
||Peter Foley<br />
|-<br />
||The Bogleheads community: an introduction ([https://drive.google.com/open?id=0B0svRQGBG_eabFdKXzkwN0U0dzg Powerpoint]) ||<br />
*Who are the Bogleheads?<br />
*Who is John C. Bogle?<br />
*Bogleheads’ Investment Philosophy<br />
||Use the presentation in full screen mode (some PowerPoint are animated).<br />
||Siamond<br />
|-<br />
||Bogleheads' Guide to Retirement Planning<br />
Available as:[https://docs.google.com/presentation/d/18HUa0XqhKnkouraTjERnKJMpMxkB4q61OUL1oRijlFk/edit?usp=sharing PowerPoint], [https://docs.google.com/file/d/0B8VSNcUR-B6ISERYdUhZTnhkOFE/edit PowerPoint]<br><br />
Spreadsheet source for graphs: [https://docs.google.com/file/d/0B8VSNcUR-B6IcWdZNTlFNDY0ZWs/edit Excel]<br />
||<br />
*What is a Boglehead?<br />
*Investment plans<br />
*Investing concepts<br />
*Income needed for retirement<br />
*Withdrawal strategies<br />
||Chapter 1 of the [[Bogleheads' Guide to Retirement Planning]]<br />
Neither Google PowerPoint nor its PowerPoint viewer render the content accurately. Use the viewers as a guide, then download the PowerPoint file.<br><br />
Most of the PowerPoint contain embedded notes. Be sure they are visible.<br />
||Peter Foley<br />
|-<br />
||Bogleheads Investment Philosophy<br />
Available as: [https://docs.google.com/presentation/d/1Rw-4urmFdFISfQsG-a_eu_0JsjoOa_K_U6iZgUlNST8/edit?pli=1#slide=id.p PowerPoint]<br />
||<br />
*[[Bogleheads® investment philosophy]]<br />
|| Open for anyone to edit. No login required.<br />
||Barry Barnitz<br />
|-<br />
||Credit Scores<br />
Available as: [https://docs.google.com/file/d/0B9DIxuYLRo-bWGFPNlYxQUpTaUU/edit?pli=1 PowerPoint]<br />
||<br />
*The high cost and risks of bad credit<br />
|| A few PowerPoint which show how your payment changes when you don't have good credit. Intended for high school students.<br />
|| sls239<br />
|-<br />
||Glide Path and Target Retirement Date Fund Primer<br />
Available as: [https://drive.google.com/file/d/0B8VSNcUR-B6IUEJFNnlBV3ZiYVk/view?usp=sharing PowerPoint]<br />
||<br />
*Asset Allocation<br />
*Glide path<br />
*Target date funds<br />
*Comparisons and considerations<br />
*Alternative glide paths<br />
|| Covers both Vanguard and Fidelity funds.<br />
||MN Bogleheads<br />
|-<br />
||S&P 500 index<br />
Available as: [https://docs.google.com/presentation/d/1Jo7RjF27flvO4iSXvRu5GlYF5UhcTMOXv97ylq2kFcI/edit?pli=1#slide=id.p PowerPoint]<br />
||<br />
*[[Indexing]]<br />
*[[Stock Market Indexing]]<br />
|| Open for anyone to edit. No login required.<br />
||Barry Barnitz<br />
|-<br />
||Long Term investing<br />
Available as: [https://docs.google.com/file/d/0B0JsVeBpjf_cYTh2U1Z2VjlueU0/edit?usp=sharing PowerPoint] <br><br />
Accompanying Handout: [https://docs.google.com/file/d/0B0JsVeBpjf_cZk9pSlRPdm1MNjA/edit?usp=sharing Doc File]<br />
||<br />
*Asset Allocation<br />
*Diversification<br />
*Tax Considerations<br />
*Asset Classes<br />
*Saving/Budgeting<br />
|| Google's viewer will not display the slide content correctly.<br />
PowerPoint 19 through 23 do not display correctly in LibreOffice Impress.<br />
||Steve Thorpe<br />
|-<br />
||Understanding Taxes<br />
Available as: [https://docs.google.com/presentation/d/12cO1ztxeRrParoHULyXiaBxAiuXJbJ5Fyq15qMqTdrE/edit?usp=sharing PowerPoint]<br />
||<br />
*Marginal Tax Rates<br />
*Accumulation Considerations<br />
*Withdrawal Considerations<br />
||Covers:<br />
*Rates and Sources of Income, Marginal Rates and tax brackets<br />
*Advantages of deferred accounts, asset placement for maximum efficiency<br />
*Withdrawal phase: Pre Social Security, Post Social Security<br />
||Peter Foley<br />
|-<br />
|| Withdrawal Methods 101<br />
Available as: [https://drive.google.com/open?id=0B0svRQGBG_eaWnctY0d6Y2Y3czQ Powerpoint]<br />
||<br />
*[[Withdrawal methods]]<br />
||Covers:<br />
*Basic Mechanics and Charts<br />
*Fixed and Variable Methods<br />
|| siamond<br />
|-<br />
|| Introduction to Index Funds<br />
Available as: [https://drive.google.com/open?id=0B0svRQGBG_eaRnN5dW1HUVFCeFk Powerpoint]<br />
||<br />
*[[Stock market indexing]]<br />
||Covers:<br />
*What is an Index?<br />
*What is an Index Fund?<br />
*Active vs. Passive Funds<br />
*Investigating Funds<br />
|| siamond<br />
|-<br />
|| Introduction to Asset Allocation<br />
Part 1<br />
Available as: [https://drive.google.com/open?id=0B0svRQGBG_eadXlZNUZLSWptbUU Powerpoint]<br />
||<br />
*[[Asset Allocation]]<br />
||Covers:<br />
*Goals, Fears and Risks<br />
*Stocks vs. Bonds<br />
*Domestic vs. International<br />
|| siamond<br />
|-<br />
|| Introduction to Asset Allocation<br />
Part 2<br />
Available as: [https://drive.google.com/open?id=0B0svRQGBG_eaTFlzNXdPUk1Bc0U Powerpoint]<br />
||<br />
*[[Asset Allocation]]<br />
||Covers:<br />
*Rebalancing<br />
*Factor Investing<br />
*International and Emerging<br />
*Special Markets<br />
*Types of Bonds<br />
|| siamond<br />
|-<br />
|| Treasury Inflation Protected Securities (TIPS)<br />
Available as: [https://goo.gl/iTrE9U Powerpoint]<br />
||Presentation Goals:<br />
*Education only<br />
*Objectivity<br />
*Clarity<br />
||Covers:<br />
*How TIPS work<br />
*Arguments for TIPS<br />
*Arguments against TIPS<br />
*Buying TIPS<br />
|| Metro-Boston Bogleheads<br />
|-<br />
|| Time Value of Money: a Short Introduction<br />
Available as: [https://tinyurl.com/y8gbb9fl Powerpoint]<br />
||<br />
*[[Comparing Investments]]<br />
||Covers:<br />
*Calculating Forwards<br />
*Calculating Backwards<br />
*Social Security Considerations<br />
|| Siamond<br />
|-<br />
|| 2018 Individual Income Taxes<br />
Available as: [http://bit.ly/2CjhxNw Powerpoint]<br />
||<br />
*[[Tax basics]]<br />
*[[Progressive tax]]<br />
*2017 Tax Reform<br />
||Covers:<br />
*PART I: Income Tax Basics<br />
*PART II: What’s Changed For 2018?<br />
|| Metro-Boston Bogleheads<br />
|-<br />
|| Required Minimum Distributions (RMDs)<br />
Available as: [https://tinyurl.com/y9pvgeln Powerpoint]<br />
||<br />
*[[Required Minimum Distribution vs annuitization]]<br />
||Covers:<br />
*What are RMDs<br />
*Calculating RMDs<br />
*Taxation of RMDs<br />
*Integrating RMDs into Your Finances<br />
|| Metro-Boston Bogleheads<br />
|-<br />
|| Rebalancing: staying the course with your target Asset Allocation<br />
Available as: [https://bit.ly/33dOcRp Powerpoint]<br />
||<br />
*[[Rebalancing]]<br />
||Covers:<br />
*Rebalancing basics<br />
*When to rebalance<br />
*Short summary of rebalancing blog study<br />
|| Metro-Boston Bogleheads<br />
|}<br />
<br />
===Medical professionals===<br />
Below are the forum member contributions for medical professionals. The table can be sorted by clicking on the appropriate heading.<br />
<br />
{| class="wikitable sortable" style="text-align:left"<br />
|+ Bogleheads Forum Contributions for Medical Professionals<br />
! align="center" width="30%" | Title<br />
! align="center" width="25%" | Topics<br />
! align="center" width="35%" | Comments<br />
! align="center" width="5%" | Contributor<br />
|-<br />
|| Personal Finance for Resident Physicians<br />
Available as: [https://docs.google.com/file/d/0B6JxEBt51v8AYWtsYTZzUnlWRzQ/edit PowerPoint]<br />
||<br />
* Life insurance<br />
* Disability insurance<br />
* Home ownership and mortgages<br />
* [[Asset protection]]<br />
* Taxes<br />
* Why doctors don't get rich<br />
* Investing<br />
||<br />
|| zzcooper123 <br />
|-<br />
|| Financial Literacy for Medical Professionals Talk #1 of 3<br />
Available as: [https://docs.google.com/file/d/0B6SoAmi6m0vnc2ZHeGxsS1JpaDg/edit?pli=1 PDF] [https://docs.google.com/file/d/0B6SoAmi6m0vnSktibnc0QVhBMXM/edit?pli=1 PowerPoint]<br />
||<br />
*Live below your means<br />
*Buy disability insurance (the focus of today’s talk)<br />
*Start an emergency fund<br />
*Determine a loan repayment strategy<br />
*Open a Roth IRA (if at all possible)<br />
*Begin to contribute to your 401k (icing on the cake if you can manage to do all of the above on your resident/fellow salary!)<br />
|| Download from the File --> Download menu.<br />
|| Neurosphere<br />
|-<br />
|| Financial Literacy for Medical Professionals Talk #2 of 3<br />
Available as: [https://docs.google.com/file/d/0B6SoAmi6m0vnSXNQT3ZKTzJsWWM/edit?pli=1 PDF] [https://docs.google.com/file/d/0B6SoAmi6m0vnVUJMRmRfNm9uTlk/edit?pli=1 PowerPoint]<br />
||<br />
*Tax code basics<br />
*Why does one need to invest at all?<br />
*The benefits of contributing to retirement accounts vs. taxable accounts<br />
*Introduction to the major asset classes (stock, bonds, etc)<br />
*Risk/volatility vs. reward/return<br />
*How investor psychology and behavior leads to poor investment performance<br />
*Constructing a diversified portfolio<br />
|| Download from the File --> Download menu.<br />
|| Neurosphere<br />
|-<br />
|| Financial Literacy for Medical Professionals Talk #3 of 3<br />
Available as: [https://docs.google.com/file/d/0B6SoAmi6m0vnQVBzWVIxSS1YUnc/edit?pli=1 PDF] [https://docs.google.com/file/d/0B6SoAmi6m0vnU2NfdTY3OWJLd1U/edit?pli=1 PowerPoint]<br />
||<br />
*What is retirement? Why would I ever want to retire?<br />
*How do I figure out how/when I can retire?<br />
*How much do I need to save each year in order to achieve my goals?<br />
*Why minimizing your investment costs are critical<br />
*How to find and interpret the cost of your investments (and your investment professional)<br />
*Why indexed mutual funds (aka passive funds) outperform actively managed investments<br />
*Do you need an investment advisor (most people don’t)<br />
*How/where to get help (if you feel you need it)<br />
*Pros and cons of various ways one can get financial help (financial planner, investment advisor, stock broker, insurance salesperson, etc.)<br />
|| Download from the File --> Download menu.<br />
|| Neurosphere<br />
|}<br />
<br />
===US Military===<br />
The first six months of forum member Nords' blog [http://the-military-guide.com/ The-Military-Guide.com] were used to create his book, [http://the-military-guide.com/about-2/about/ The Military Guide to Financial Independence and Retirement].<ref>See: [http://www.bogleheads.org/forum/viewtopic.php?f=2&t=117735&p=1723950#p1723950 Help create a Financial Presentation: Calling all Bogleheads], direct link to post.</ref> The blogs can be found in the chronological index at [http://the-military-guide.com/post-titles-by-month/ Post titles by month], and the applicable posts are from September 2010 - March 2011, with a few diversions for other topics.<br />
<br />
The top three blogs for military basic financial literacy (Marines & other services) would be:<br />
#[http://the-military-guide.com/2010/12/27/where-to-put-your-savings-in-the-militar/ Where to put your savings while you’re in the military]<br />
#[http://the-military-guide.com/2010/12/30/tailor-your-investments-to-your-military-pay-and-your-pension/ Tailor your investments to your military pay and your pension]<br />
#[http://the-military-guide.com/2011/03/16/saving-base-pay-and-promotion-raises/ Saving base pay and promotion raises]<br />
<br />
Another military financial literacy tool is the Total Pay iPhone/iPad app developed by Marine 1LT Matt Pagan at [http://totalpayapp.com/ Total Pay]. A review can be found at [http://the-military-guide.com/2013/04/18/total-pay-how-much-will-your-next-paycheck-be/ Total Pay: How much will your next paycheck be?]. It covers active-duty & Reserve pay tables as well as federal civil service.<br />
<br />
Below are the forum member contributions. The table can be sorted by clicking on the appropriate heading.<br />
{| class="wikitable sortable" style="text-align:left"<br />
|+ Bogleheads Forum Contributions for US Military<br />
! align="center" width="30%" | Title<br />
! align="center" width="25%" | Topics<br />
! align="center" width="35%" | Comments<br />
! align="center" width="5%" | Contributor<br />
|-<br />
||Military Financial Independence and Retirement<br />
Available as:[https://docs.google.com/document/d/1t4a6gVwf7XLh3K7qYJ2UpwAUKfrVzpBCvJsnMowOm-k/edit?usp=sharing Docs]<br />
||<br />
*Get ready<br />
*The process<br />
*The "fog of work"<br />
*Frugal living is not deprivation<br />
||A hand-out which discusses how to get ready for financial independence.<br />
||Nords<br />
|- valign="top"<br />
|| Personal Financial Management Basics for U.S. Military <br />
PowerPoint presentation available from:<br />
*[https://docs.google.com/file/d/0B8VSNcUR-B6IbVh5TnV0X1dhSEk/edit?usp=sharing Google Drive]<br />
*[http://the-military-guide.com/wp-content/uploads/2013/06/Personal-Financial-Management-Basics.ppt the-military-guide.com] (direct link to file)<br />
||<br />
*Assessment - Where am I now?<br />
*Goal setting - Where do I want to go?<br />
*Planning – How do I get there?<br />
*Budget<br />
*Organize<br />
*Debt & Credit<br />
*Adequate Protection (Insurance)<br />
**General<br />
**Property (Home/Renters, Car)<br />
**Liability<br />
**Death<br />
**Disability<br />
**Health<br />
**Long-term care (LTC)<br />
*Tax planning<br />
*Saving & Investment Planning<br />
*Retirement planning<br />
*Estate planning<br />
*Execute (the plan)<br />
*Monitor / Reassess<br />
||This PowerPoint presentation is a comprehensive 70-slide overview of the basics of financial management for U.S. military servicemembers. It was created in 2012 by retired Marine Mark Hensen and may be freely shared. <br><br>Because it covers so many topics, you may wish to edit your own copy for a shorter seminar. You'll also need to update some PowerPoint for new contribution limits or changes to the Roth Thrift Savings Plan.<br><br><br />
See: [http://the-military-guide.com/2013/06/27/mixed-plate-tricare-back-pay-issues-early-reserve-guard-retirement/ Mixed plate: Tricare, “back pay” issues, early Reserve & Guard retirement] (scroll down to Free PowerPoint presentation for basic financial management training), June 27, 2013.<br />
||Nords<br />
|- valign="top"<br />
|| Military Saves Week 2015 Investing for the future<br />
PowerPoint presentation available from:<br />
*[https://drive.google.com/file/d/0B8VSNcUR-B6IZnFLbHdjM19tc3M/view?usp=sharing Google Drive]<br />
||<br />
*When can I retire?<br />
**Pay scale examples supplied.<br />
*Thinking about getting out? Plan for it.<br />
*How much do I need?<br />
*How do I invest?<br />
**Keep costs low<br />
*What about Social Security?<br />
*Just tell me what to do.<br />
||<br />
A PowerPoint presentation for Military Saves Week (part of America Saves). It applies to all of the military services and all ranks, and has been used in military training seminars.<br />
<br />
Each slide contains a Notes section for the instructor. <br />
||<br />
Nords<br>(Created by aaronmagan1)<br />
|}<br />
<br />
==Website resources==<br />
*[http://personalfinance.byu.edu/ Brigham Young University’s Marriott School of Management]: Complete courses in financial literacy. Supplied materials include course video, PowerPoint files, and PDF guides. See: [http://www.bogleheads.org/forum/viewtopic.php?f=2&t=117735#p1724745 this forum post]. For non-commercial use only.<br />
*[http://financinglife.org/ FinancingLife.org], by forum member Stickman (Rick Van Ness). Stickman created the [[Video:Bogleheads® investment philosophy | Bogleheads® investment philosophy videos]]. Additional videos are on his website.<br />
*[http://www.financialworkshopkits.org/getting-started.aspx National Endowment for Financial Education®] (NEFE®): All-inclusive workshops which include PowerPoint presentations, scripts, handouts, other resources, and a FAQ. See: [http://www.bogleheads.org/forum/viewtopic.php?p=1724745#p1724745 this forum post]. For non-profit non-commercial use only.<br />
<br />
==See also==<br />
*[[Video:Bogleheads® investment philosophy | Bogleheads® investment philosophy videos]]<br />
<br />
==References==<br />
<references /><br />
<br />
==External links==<br />
*{{Forum post|t=117735|title=Help create a Financial Presentation: Calling all Bogleheads}}<br />
<br />
{{Bogleheads}}<br />
[[Category:The Bogleheads]]</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Bond_basics&diff=70135
Bond basics
2020-09-13T15:17:38Z
<p>Siamond: /* Role in a portfolio */ removed faulty sentence about correlation with equities</p>
<hr />
<div>A '''bond''' is a debt investment. Investors loan money to corporations or governments for a set term and interest rate. After issuance bonds trade on the over-the-counter market where their principal value fluctuates according to changes in interest rates and any changes in the bond's credit quality. <ref>Securities Industry and Financial Markets Association [http://www.investinginbonds.com/learnmore.asp?catid=3&id=383 Risks of Investing in Bonds]</ref> Newly issued [[Corporate bonds | corporate bonds]] are syndicated by consortiums of investment banks who initially buy an offering for resale to investors. Government bonds are offered by auction, where investors tender bids for the issue<ref>[[Wikipedia:Bond (finance)| Bond (finance)]], wikipedia</ref> Bonds are typically used by investors to stabilize the value of a portfolio and/or produce a stream of income.<br />
<br />
''Note:'' Those looking for a "very basic" introduction to bonds should start with the [[#Tutorial | tutorial]] at the bottom of this page.<br />
<br />
==Features==<br />
<br />
[[File:Bonddiagram.gif|frame|400px|right| Advanced Bond Concepts:Bond Type Specifics, investopedia<ref>[http://www.investopedia.com/university/advancedbond/advancedbond1.asp Advanced Bond Concepts: Bond Type Specifics]</ref>]]<br />
<br />
Bonds possess a number of distinctive features. Common features include:<br />
*'''Coupon rate''': the interest rate paid by the bond. The rate may be fixed, floating, or inflation indexed, depending on the specific issue. The coupon date spells out the frequency of interest payments, usually biannually for US bonds. Bonds which pay a fixed coupon rate based upon the principal (face amount) are called [[:Nominal bond |''nominal'' bonds]].<br />
*'''Maturity date''': the date at which the bond principal will be repaid. Bonds are usually issued with maturities [[Money_Markets | ranging from 1 year]] to thirty years.<br />
*'''[[Options]]''': the most common option involving bonds is the existence of a '''call feature'''. This feature gives the issuer the right to repay the bond before the maturity date. Since an issuer will call bonds when the interest rate is lower than the coupon rate, this feature is not advantageous to the buyer of the bond, who is then faced with reinvesting the proceeds of the redeemed bond in a lower interest rate environment. Thus it is usual for a callable bond to offer a higher coupon than an uncallable bond as compensation for the risk of early redemption. Some callable bonds also provide for a small sum to be added to the par value of a redeemed bond. Alternately, some bonds are issued with a '''put feature ''' which gives the bond holder the right to force the issuer to repay the bond before the maturity date, usually on prescribed put dates <br />
*'''Sinking funds''' provide a means of repaying a bond issue. The issuer makes periodic payments to a trustee who retires part of the issue by purchasing the bonds in the open market. Sinking funds tend to reduce the risk of default, and thus allow the issuer of a bond to pay a lower interest rate on the bond. <br />
*'''Senior''' vs. '''Subordinated debt''': Senior debt<ref>[[Wikipedia:Senior debt|Senior debt]], wikipedia</ref> is given priority over other debt in case of default; Subordinated debt<ref>[[Wikipedia:Subordinated debt|Subordinated debt]], wikipedia</ref> is unsecured and, in a default, is repayable after other debts have been paid.<ref>[[Wikipedia:Bond (finance)| Bond (finance)]], wikipedia</ref><br />
<br />
==Types of bonds==<br />
<br />
There are three main issuers of bonds in the U.S.<ref>Thau, Annette, ''The Bond Book,'' McGraw-Hill, (2001), pp. 29-36. ISBN 0-07-135862-5</ref><br />
<br />
'''[[Treasury Bonds]]''' are issued by the US treasury in groups of three maturity ranges<br />
*Bills have a range up to one year;<br />
*Notes have a range between one year and ten years;<br />
*Bonds have a range greater than ten years. <br />
<br />
Treasury bonds are usually not callable. Treasuries also carry the full faith and credit backing of the US government. The interest income is exempt from state tax. Treasuries can be purchased through brokerages and banks as well as through an individual account at Treasury Direct<ref>[http://www.treasurydirect.gov/indiv/products/prod_tbills_glance.htm Treasury Direct]</ref>. Government agencies also issue debt, some of which is backed by the full faith and credit of the government and some which is not.<br />
<br />
'''[[Treasury Inflation Protected Securities]]''' provide for inflation indexed income and inflation protection for the bond's principal. The bond pays a fixed real interest rate based on a principal value indexed to the CPI-U inflation measure. Like all treasury bonds, inflation indexed treasuries have the "full faith and credit" backing of the Treasury and interest income and inflation adjusted accruals are exempt from state taxation. The inflation adjusted accruals, however, are taxable to the federal government as they accrue. This "phantom income" taxation makes the bonds candidates for placement in tax-advantaged accounts.<br />
<br />
'''[[Corporate bonds]]''' are issued by corporations and are often callable. Since a corporation can default on it's debts, corporate bonds are subject to credit risk and usually pay higher coupon interest rates over comparable term treasury maturities as compensation for this risk.<ref> Refer to [http://www.moodys.com/cust/content/content.ashx?source=StaticContent/Free+pages/Credit+Policy+Research/documents/current/2006400000429618.pdf Corporate Bond Defaults and Recovery Rates 1920-2006] and [http://www.moodyskmv.com/research/files/wp/21727.pdf Historical Default Rates of Corporate Bond Issuers, 1920 – 1996] for data on defaults.</ref><br />
Corporate bonds are subject to federal and state income tax. <br />
<br />
'''[[Municipal bonds]]''' are issued by states and localities. These bonds are subject to credit risk.<ref>Refer to [http://www.moodys.com/cust/content/content.ashx?source=StaticContent/Free+pages/Credit+Policy+Research/documents/current/2001700000407258.pdf Moody's US Municipal Bond Rating Scale 1970-2000] for default and recovery data on municipal bonds.</ref> Many municipal bonds are also callable. The bonds are generally exempt from federal tax, although some private revenue municipal bonds are subject to the federal alternative minimum tax. A tax exempt bond is also usually state tax exempt for residents of the state issuing the bond. Due to these tax preferences, municipal bonds generally offer lower coupon interest rates than do comparable term treasuries and corporates. <br />
<br />
Other types of bonds:<br />
<br />
'''[[Zero-coupon bond |Zero Coupon bonds]]''' are accrual bonds and do not pay current coupon interest. They are issued at a deep discount from par value and compound continuously at the coupon rate. The bond holder receives the full principal amount as well as the value that has accrued from interest on the redemption date. Zero coupon bonds may be created from fixed rate bonds by financial institutions by "stripping off" the coupons. In other words, the coupons are separated from the final principal payment of the bond and traded independently. Individuals are taxed on the annual accrual of income, although the investor receives no current interest payment.<br />
<br />
'''[[Asset-backed securities]]''' are bonds whose interest and principal payments are backed by underlying cash flows from other assets. Examples of asset-backed securities are [[Mortgage-backed security|mortgage-backed securities]] (MBS's), which include GNMA securities backed by the full faith and credit of the US treasury, collateralized mortgage obligations (CMOs) and collateralized debt obligations (CDOs).whose underlying securities are often such assets as auto loans or credit card receivables.<br />
<br />
'''[[High yield bonds]]''' are corporate bonds with lower credit quality than top credits. These companies are at much greater risk of default than higher quality credits and, as a result, pay higher coupon interest rates than comparable high quality corporate bonds.<br />
<br />
==Sources of return==<br />
<br />
There are three sources of return for a bond:<br />
# Return of principal<br />
# Interest (coupon payments)<br />
# Interest-on-interest (reinvested coupon payments)<br />
<br />
According to [[Frank J. Fabozzi|Fabozzi]] in the ''Handbook of Fixed Income Securities'', 1991, p97:<br />
"In high interest rate environments, the interest-on-interest component for long-term bonds may be as high as 70 percent of the bond's potential total dollar return." In low interest rate environments, the principal is likely the largest source of value of all but the longest bonds.<br />
<br />
Illustration of the three sources of bond return:<br />
<br />
<center>[[File:Sources_of_bond_return.png|800px]]</center><br />
<br />
==Risks==<br />
<br />
Each of the following risks of bonds carries some premium as compensation for bearing these risks. The amount of that premium varies according to the market's assessment of the likelihood of the adverse event occurring.<br />
<br />
===Interest rate risk===<br />
<br />
Interest rate risk, also called price risk, is that the value of a bond fluctuates depending on the interest rate. Also known as "market risk." The amount of interest rate risk assumed is measured primarily by the [[Bonds: advanced topics#Duration | duration]] (and secondarily by [[Bonds: advanced topics#Convexity | convexity]]). See [[Bond basics#Bonds on the secondary_market | below]] for more information on how bond prices react to interest rate changes.<br />
<br />
Interest rate risk is in some sense an artifact of the traditional framework which looks at short-term returns. Over longer periods, longer duration bonds will have a more certain return than short-term bonds, as a quote from John Campbell and Luis Viceira's academic text, ''Strategic Asset Allocation'' (pp86-87), makes clear:<br />
<br />
"If one uses conventional mean-variance analysis, it is hard to explain why any investors hold large positions in bonds. Mean-variance analysis treats cash as the riskless asset and bonds as merely another risky asset like stocks. Bonds are valued only for their potential contribution to the short-run excess return, relative to risk, of a diversified risky portfolio. ... A long-horizon analysis treats bonds very differently, and assigns them a much more important role in the optimal portfolio. For long-term investors, money market investments are not riskless because they must be rolled over at uncertain future interest rates."<br />
<br />
Because unexpected inflation changes that picture somewhat, the reduced risk of longer-term bonds is primarily true when discussing inflation-protected bonds in real dollars (or nominal bonds with nominal liabilities).<br />
<br />
===Credit risk===<br />
<br />
Credit risk is a risk that the issuer of a bond may default. Also known as "default risk." <br />
<br />
Credit risk is assessed by the major ratings agencies (Moody's, S&P, and Fitch).<ref group="note">Moody's Investors Service, Fitch, and Standard & Poor's Ratings Services are 3 of several credit rating agencies categorized as a [http://www.sec.gov/answers/nrsro.htm Nationally Recognized Statistical Rating Organization (NRSRO)] by the SEC. The SEC's Office of Credit Ratings maintains a list here: [http://www.sec.gov/ocr/ratingagency.html Nationally Recognized Statistical Rating Organizations ("NRSROs")]</ref> Each [[Bond basics#Credit ratings | credit rating]] has an expected rate of default, which increases substantially in lower tiers. For a given credit rating, the default rate has historically been lower for municipal bonds than for corporate bonds. Wikipedia has [http://en.wikipedia.org/wiki/Bond_credit_rating tables] of how the ratings compare between ratings firms and of historical default rates.<br />
<br />
===Call risk===<br />
<br />
Call risk is a risk that the issuer may call the bond, terminating a stream of income for the investor. This risk is often called prepayment risk for [[Mortgage Backed Securities | mortgage backed securities]]. Call options embedded in a bond lead to negative [[convexity]].<br />
<br />
===Reinvestment risk===<br />
<br />
Reinvestment risk is a risk that when a bond matures or is called, an investor may have to reinvest the proceeds in a bond yielding a lower interest.<br />
<br />
===Inflation risk===<br />
<br />
Inflation risk is a risk that the interest from a bond may not keep up with inflation. [[Treasury_Inflation_Protected_Securities|TIPS]] are inflation-adjusted and therefore largely immune to inflation risk. Also known as "purchasing power risk."<br />
<br />
===Liquidity risk===<br />
<br />
Liquidity risk is the risk that you may not be able to extract the remaining value from your bond in the timeframe needed without losing a disproportionate amount of value. Thinly-traded issues (such as most corporate, municipal, and TIPS issues) have liquidity risk. The liquidity premium is expected to rise in times of crisis. Also known as "marketability risk."<br />
<br />
The presence of liquidity risk can be seen most clearly in "off-the-run" Treasury bonds, where an older but otherwise identical bond trades at a reduced price/higher yield simply because it is less liquid.<br />
<br />
=== Other risks ===<br />
<br />
These risks are either not important for individual investors or are generally wrapped into the risks above (e.g. credit risk commonly encompasses event risk). They are included for completeness.<br />
<br />
==== Yield curve or maturity risk ====<br />
Generally only important in hedging situations.<br />
<br />
==== Exchange rate or currency risk ====<br />
Only relevant for non-dollar-denominated bonds, which are not recommended by Mr. Bogle.<br />
<br />
==== Volatility risk ====<br />
Bonds with embedded options (commonly a corporate bond with a call option) are affected by volatility, because the value of an option depends on volatility. If the price of an issue is highly volatile, the likelihood of a random fluctuation straying above the strike price is much greater.<br />
<br />
==== Political or legal risk ====<br />
Tax-code changes and regulatory decisions can all affect the value of a bond. <br />
<br />
==== Event risk ====<br />
A type of credit risk which affects many firms due to a single event (and therefore event risk cannot be fully diversified away).<br />
<br />
==== Sector risk ====<br />
A type of credit risk which affects all or many firms in a single sector.<br />
<br />
==Credit ratings==<br />
<br />
Three major ratings agencies assess the likelihood of a bond defaulting and assign that bond ratings according to a standardized scale.<br />
<br />
<center><br />
{| class=wikitable style="text-align:center" width=400px<br />
|+ Bond Ratings <ref>Investopedia [http://www.investopedia.com/articles/03/102203.asp What Is A Corporate Credit Rating?]</ref><br />
! style="background:#f0f0f0;"|'''Grade'''<br />
! style="background:#f0f0f0;"|'''Risk'''<br />
! style="background:#f0f0f0;"|'''Moody’s'''<br />
! style="background:#f0f0f0;"|'''S&P/Fitch'''<br />
|-<br />
| Investment||Quality Highest||Aaa||AAA<br />
|-<br />
| Investment||High Quality||AA||Aa<br />
|-<br />
| Investment||Strong||A||A<br />
|-<br />
| Investment||Medium Grade||Baa||BBB<br />
|-<br />
| Junk||Speculative||Ba.B||BB,B<br />
|-<br />
| Junk||Highly Speculative||Caa/Ca/C||CCC/CC/C<br />
|-<br />
| Junk||In Default||C||D<br />
|}<br />
</center><br />
<br />
For a given credit rating, the default rate has historically been lower for municipal bonds than for corporate bonds.<br />
<br />
==Factors affecting bond prices==<br />
''See [[Bond pricing]] for definitions of bond pricing terminology. (This is an advanced topic.)''<br />
<br />
===New issues===<br />
The coupon of a newly issued bond is primarily set by two major factors: the credit quality of the bond and the maturity of the bond. It is axiomatic in the investment markets that if investors are to invest in risky securities higher risk must be compensated by higher expected return. Thus the US Treasury pays a lower coupon on its debt than do corporate borrowers subject to default risk, Non treasury debt is graded for credit quality by three rating agencies. The above table describes the ratings.<br />
<br />
The longer the maturity of a bond the greater the risk to the bondholder. Longer time horizons increase the likelihood that a bond issuer will become a greater credit risk through bad management decisions, the deterioration of economic conditions, or the company engaging in future merger and acquisition activity which changes the leverage of a company's balance sheet. Longer horizons also increase the likelihood that a bond's coupon income will be eroded by higher than expected inflation. Finance economics defines a bond's expected return to be comprised of three basic building blocks: first, the risk-free rate as defined by the current yield of a treasury bill; a time horizon premium to compensate investors for the risks of longer maturities; and a default risk premium to compensate investors for bearing credit risk. <ref>[[Dimson, Elroy]], Marsh, Paul R., and Staunton, Mike, ''Triumph of the Optimists:101 Years of Global Investment Return,'' Princeton, NJ; Princeton University Press, (2002), pp. 89-90. ISBN 0-691-09194-3</ref> These building blocks can be visualized in the following table:<br />
<br />
<br />
<center><br />
{| style="background:blue; color:white"<br />
|- <br />
| Default Risk Premium<br />
|- style="background:dodgerblue; color:black"<br />
| Time Horizon Premium<br />
|- style="background: lightblue; color:black"<br />
| T-bill Rate<br />
|}<br />
</center><br />
<br />
<br />
===Bonds on the secondary market===<br />
<br />
Once a bond has been issued, it trades on the secondary market, and fluctuates in price until it matures. A bond will change in price for two main reasons:<br />
<br />
1. The bond's credit rating has changed (either upgraded or downgraded).<br />
<br />
2. Interest rates have changed.<br />
<br />
Unless a bond is falling into or out of default, price movements associated with changes in credit rating tend to be infrequent, although during periods of economic distress and economic recovery credit rating changes can be significant price factors. The ever present driver of changes in a bond's market value comes from fluctuations in current market interest rates. We can understand this law of bond pricing by considering the following scenario. Let us assume that we purchase at issue a $1,000 ten year bond yielding a 5% coupon. This entitles us to $50 of annual income. Assume that one year later, interest rates have risen to 6% and we wish to liquidate the bond. No rational investor will pay $1,000 for $50 of income, when he can receive $60 per annum for the same $1,000 dollar investment. In this interest rate scenario, our 5% bond will have to decrease in market value until its current yield approximately produces a 6% return. A similar, yet opposite price movement occurs if interest rates fall. Suppose, in our scenario above, interest rates fall to 4 percent during the year after our purchase. Our $1,000 bond produces $50 of annual income in an environment where investors can only receive $40 of annual income from a newly issued bond. Our bond will therefore rise in price until it provides a purchaser with a 4% return. Thus we come to the basic rule of bond price movements in the open market.<ref>Thau, Annette, ''The Bond Book,'' McGraw-Hill, (2001), p. 30. ISBN 0-07-135862-5</ref><br />
<br />
<br />
<center><br />
{| class=wikitable style="text-align:center" width=400px<br />
| align="center" style="background:#f0f0f0;"|'''when'''<br />
| align="center" style="background:#f0f0f0;"|'''then'''<br />
|-<br />
| interest rates rise||bond prices fall<br />
|-<br />
| interest rates fall||bond prices rise<br />
|}<br />
</center> <br />
<br />
To calculate how much prices will rise or fall, please see [[Bonds:_Advanced_Topics#Duration | Duration]].<br />
<br />
<br />
A corollary principle to this price movement is the fact that, all things being equal, fluctuations in price are greater for long maturities than for shorter maturities. <ref>Thau, Annette, ''The Bond Book,'' McGraw-Hill, (2001), p. 73. ISBN 0-07-135862-5</ref> At any given time in the secondary market one is likely to find any number of bonds selling at a discount over par value, or at a premium to par value.<br />
<br />
==Role in a portfolio==<br />
''See [[Asking bond questions]] for tips on how to ask about bonds on the [http://www.bogleheads.org/forum/index.php Forum].''<br />
<br />
Bonds are typically used to stabilize the value of a portfolio and/or produce a stream of income.<br />
<br />
===Long- vs. short-term===<br />
<br />
Boglehead and financial expert [[William Bernstein]] recommends<ref>{{cite web|author=William Bernstein|date=December 30, 2009|url=http://bucks.blogs.nytimes.com/2009/12/30/pascal-and-the-long-term-bond-dilemma/|title=Pascal and the long-term bond dilemma|publisher=New York Times}}</ref> limiting bond holdings to short-term funds, on the basis of their relative immunity to the risk of unexpected inflation. An article by Vanguard<ref>[https://personal.vanguard.com/us/insights/article/duration-diversification-052015 The long and short of finding bond balance], (June 12, 2015) Vanguard, Retrieved 21 March 2016</ref> however, argues that when the yield curve is particularly steep, running to short-term bonds for safety can result in losses if the yield curve flattens. A common recommendation of other experts is intermediate-term funds. Long-term bonds have historically returned no more than intermediate-term bonds, but with far greater volatility--in other words, their risk has not been rewarded. Yale endowment manager David Swensen recommends long-term Treasuries, however, as part of a portfolio dominated by equities, as they will provide the biggest counterweight to the collapse of other asset classes during a deflationary crisis.<br />
<br />
Even proponents of short-term bonds such as Dr. Bernstein are comfortable with longer-term holdings in inflation-protected securities such as [[Treasury_Inflation_Protected_Securities | TIPS]], as they no longer carry any risk of unexpected inflation, leaving them vulnerable only to a real rate rise (which if held to the duration incurs only an opportunity cost).<br />
<br />
While you should always keep the [[Bonds:_Advanced_Topics#Duration | duration]] less than or equal to your investment horizon, unless you have a specific funding need to be met at a specific date (in which case a [[Zero-coupon bond]] is the risk-free solution), you should choose between short-term and intermediate-term funds. The former is lower risk but the latter has historically been rewarded with higher overall returns.<br />
<br />
===Credit quality===<br />
<br />
The ''Bogleheads' Guide'' authors recommend the use of Vanguard's Total Bond Market, which contains investment-grade [[Corporate bonds |corporate bonds]]. Mr. Bogle also recommends Total Bond Market, although he seems to prefer Vanguard's Intermediate-Term Index Fund for its lack of [[MBS]]'s.<ref>{[cite web|date=June 15, 2007|url=http://johncbogle.com/wordpress/?s=intermediate|title=John Bogle reponds to "Ask Jack" questions|publisher= The Bogle Eblog]</ref> By contrast, Boglehead and bond expert Larry Swedroe recommends only the very highest quality investments for bonds (and specifically recommends against Total Bond Market because of its negative [[Bonds:_Advanced_Topics#Convexity | convexity]]), citing evidence in which the risk of corporate bonds has not been historically rewarded. Yale endowment manager David Swensen also recommends only Treasuries. Finally, Boglehead and financial expert Rick Ferri advocates for not only the inclusion of investment-grade corporate bonds but also [[High yield bonds | high yield bonds]], on the basis of their diversification benefits.<br />
<br />
Perhaps the best conclusion that can be drawn from the predominance of highly respected and conflicting advice is to:<br />
* Ensure that your bond holdings are built around a core of Treasuries.<br />
* If you choose to include corporate bonds, understand the risks you are taking (moderate in relation to stock investing but nevertheless quite real), and do not include too high a proportion. A good benchmark would be the market portfolio represented by Vanguard's Total Bond Market fund.<br />
* If you choose to include high-yield bonds which incorporate considerable default and call risk, prudence suggests that you take the funds from the equity portion of your asset allocation rather than the bond portion.<br />
<br />
===Taxes===<br />
<br />
Almost all of the return on a bond or bond fund comes from the dividend yield, which is fully taxed; in contrast, stocks get most of their return from price appreciation, which is not taxed until the stocks are sold and is taxed at the capital-gains tax rate. Therefore, when bond interest rates are relatively high, bonds are widely regarded as being [[Principles_of_Tax-Efficient_Fund_Placement | less tax-efficient than stock index funds]] (which rarely sell stock) and should be held in tax-deferred accounts when possible. For investors in high tax brackets without sufficient taxable space, [[Municipal bonds]] are likely the preferred solution; these bonds are not taxed but there is a cost in lower yield. Investors in low tax brackets should calculate their after-tax return on taxable bonds in taxable accounts to determine whether or not to use municipal bonds.<br />
<br />
==Style boxes==<br />
“Style boxes” are 3 x 3 grids used to categorize securities. Different investment styles have various levels of risk which leads to differences in returns. This visualization allows investors to perform informed comparisons using an easy-to-understand standardized format.<br />
<br />
Fixed income funds (bonds) classify risk as levels of [[:#Credit risk | credit risk]] (credit quality) on the vertical axis, and [[:#Interest rate risk | interest rate risk]] (term risk) on the horizontal axis.<br />
<br />
There are a number of ways to characterize interest rate risk, such as [[:Bonds: Advanced Topics#Duration | Duration]] (sensitivity to changes in interest rates) and various maturity measures. In either case, the objective is to categorize interest rate risk into short-term, intermediate-term, and long-term periods of time.<br />
<br />
Morningstar (interest rate sensitivity) and Vanguard (maturity) provide fixed income fund ''style boxes''. Either format can be used to compare funds, but compare using the same methodology. When comparing ''only'' Vanguard funds, Vanguard's style box is valid. Otherwise, if no Vanguard style box is available, use Morningstar's style box for all funds. Vanguard funds will be shown on Morningstar's site using the Morningstar style box.<ref>{{Forum post|t= |p=948589 |title=9-style box - Vanguard vs M*t}}</ref><br />
<br />
{|border="0" cellspacing="0" cellpadding="4"<br />
|+'''Bond Fund Style Box Comparison'''<br />
|<br />
{|border="1" cellspacing="0" cellpadding="4"<br />
|+'''Morningstar Style Box(tm)'''<ref>[http://www.morningstar.com/InvGlossary/morningstar_style_box.aspx Morningstar Style Box]</ref><br />
|-<br />
|align = "center" colspan = "3"|'''Interest Rate Sensitivity'''<br>'''(Duration)'''<br />
|rowspan = "2"|'''Credit Quality'''<br>'''(Rating)'''<br />
|-<br />
|align = "center"|Limited<br />
|align = "center"|Moderate<br />
|align = "center"|Extensive<br />
|-<br />
|align = "center" bgcolor = "Gold"|&nbsp;<br />
|bgcolor = "Gold"|&nbsp;<br />
|align = "center" bgcolor = "Gold"|&nbsp;<br />
|High (AA- or higher)<br />
|-<br />
|align = "center" bgcolor = "Gold"|&nbsp;<br />
|bgcolor = "Gold"|&nbsp;<br />
|align = "center" bgcolor = "Gold"|&nbsp;<br />
|Medium (BBB- to less than AA-)<br />
|-<br />
|align = "center" bgcolor = "Gold"|&nbsp;<br />
|bgcolor = "Gold"|&nbsp;<br />
|align = "center" bgcolor = "Gold"|&nbsp;<br />
|Low (less than BBB-)<br />
|}<br />
|<br />
{|border="1" cellspacing="0" cellpadding="4"<br />
|+'''Vanguard Domestic Bond Fund Style Box'''<ref>[https://personal.vanguard.com/us/funds/tools/stylebox?View=Fund&Cat=vgibond Vanguard Funds by Style Box, Bond Funds]</ref><br />
|-<br />
|align = "center" colspan = "3"|<br>'''Average Weighted Maturity'''<br />
|rowspan = "2"|'''Credit Quality'''<br>'''(Grade)'''<br />
|-<br />
|align = "center"|Short<br />
|align = "center"|Intermediate<br />
|align = "center"|Long<br />
|-<br />
|align = "center" bgcolor = "Gold"|&nbsp;<br />
|align = "center" bgcolor = "Gold"|&nbsp;<br />
|align = "center" bgcolor = "Gold"|&nbsp;<br />
|Treasury / Agency<br />
|-<br />
|align = "center" bgcolor = "Gold"|&nbsp;<br />
|align = "center" bgcolor = "Gold"|&nbsp;<br />
|align = "center" bgcolor = "Gold"|&nbsp;<br />
|Investment Grade<br />
|-<br />
|align = "center" bgcolor = "Gold"|&nbsp;<br />
|align = "center" bgcolor = "Gold"|&nbsp;<br />
|align = "center" bgcolor = "Gold"|&nbsp;<br />
|Below Investment Grade<br />
|}<br />
|}<br />
<br />
[[:Stock Basics#Style Boxes | Equity style boxes]] (stock funds) and fixed income style boxes (bond funds) represent two-dimensional (horizontal and vertical axis) views of risk versus return. However, the background behind these boxes is based on very different concepts. '''Only compare stocks-to-stocks and bonds-to-bonds.'''<br />
<br />
Both equity and fixed income style boxes are a way to visualize how diversified your portfolio is with respect to the main characteristic of each asset class - size and value for equities; credit risk and term risk for fixed income.<ref>{{Forum post|t= |p=757434|title=Style boxes - Why the differences? Some questions}}</ref><br />
<br />
For example, suppose an investor is interested in Vanguard's balanced funds<ref>[https://personal.vanguard.com/us/funds/tools/stylebox?View=Fund&Cat=Domestic_Balanced_Balanced Vanguard balanced funds],Vanguard, style boxes</ref> which contain both stock and bond funds. The style boxes provide the investor with a simple collection of colored boxes, facilitating asset allocation decisions with a minimum of effort.<br />
<br />
==Notes==<br />
<references group="note" /><br />
<br />
==See also==<br />
* [[Video: Why bother with bonds?]]<br />
* [[Bond pricing]]<br />
* [[Bonds: advanced topics]]<br />
* [[Individual bonds vs a bond fund]]<br />
<br />
==References==<br />
{{Reflist|30em}}<br />
<br />
==External links==<br />
*[http://www.morningstar.com/InvGlossary/morningstar_style_box.aspx Morningstar Style Box]<br />
*[https://personal.vanguard.com/us/funds/tools/stylebox?View=Fund&Cat=vgibond Vanguard Funds by Style Box, Bond Funds]<br />
*{{Forum post|t=56339|title=Style boxes - Why the differences? Some question}}<br />
*{{Forum post|t=68058|title=9-style box - Vanguard vs M*}}<br />
* {{cite web|url=http://www2.investinginbonds.com/learnmore.asp?catid=2&id=62|title=Overview, Investinginbonds.com|publisher=The Securities Industry and Financial Markets Association}}<br />
* [https://www.investopedia.com/financial-edge/0312/the-basics-of-bonds.aspx The Basics Of Bonds], from Investopedia.<br />
{{Bogleheads investing start-up kit}}<br />
{{Bonds}}<br />
[[Category:Asset allocation]]<br />
[[Category:Bonds]]</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Simba%27s_backtesting_spreadsheet&diff=69665
Simba's backtesting spreadsheet
2020-07-20T17:51:38Z
<p>Siamond: /* Spreadsheet overview and download instructions */ v19d link</p>
<hr />
<div><br />
'''{{PAGENAME}}''' describes a spreadsheet originally developed by forum member ''Simba'' for the purpose of acting as a reference for historical returns, and analyzing a portfolio based on such historical data. The spreadsheet is no longer maintained by Simba, but other forum members continue to support it and to expand functionality, as a Bogleheads community project.<br />
<br />
{{Notice|This spreadsheet and the information it contains is intended for your personal, non-commercial, use only (e.g. for educational purposes). This is a learning, researching and teaching tool, nothing more.}}<br />
<br />
==Backtesting==<br />
Backtesting is a term used in oceanography, meteorology and the financial industry to refer to testing a predictive model using existing historic data.<ref name="Wiki">[[wikipedia:Backtesting|Backtesting]], on Wikipedia</ref> It is also often used to analyze the past for research purposes. It is notably useful to quantitatively assess the impact [[asset allocation]] had (in known history) on possible investment strategies.<br />
<br />
Backtesting seeks to estimate the performance of a strategy if it had been employed during a past period. This requires simulating past conditions with sufficient detail, making one limitation of backtesting the need for detailed historical data. A second limitation is the inability to model strategies that would affect historic prices.<br />
<br />
Finally, backtesting, like other modeling, is limited by potential overfitting. That is, it is often possible to find a strategy that would have worked well in the past, but will not work well in the future. <br />
<br />
Despite these limitations, backtesting provides valuable information not available when models and strategies are tested on synthetic data.<br />
<br />
==Spreadsheet overview and download instructions==<br />
The spreadsheet is discussed in this {{Forum post|t=2520|title=Simba's backtesting spreadsheet <nowiki>[a Bogleheads community project]</nowiki>}}.<br />
<br />
The latest version and download instructions are in '''[{{{url|https://www.bogleheads.org/forum/viewtopic.php?f=10&t=2520&p=5382859#p5382859}}} this post]'''.<br />
<br />
Detailed instructions, glossary and revision history can be found in the '''README''' tab. Here is a brief overview of the individual worksheets:<br />
<br />
*'''Analyze_Portfolio''' provides a simple way to customize the asset allocation of a single portfolio and study its historical performance over specific time periods. This worksheet compares a custom portfolio to a benchmark portfolio (e.g. 60/40) and provides charts and statistics to illustrate respective growth and drawdowns.<br />
*'''Compare_Portfolios''' allows to compare two sets of 5 different portfolios, with the ability to change the portfolios' composition, the time period being examined, and to check the impact on various metrics and charts.<br />
*'''Lazy_Portfolios''' compares 25 predefined portfolios and provides risk/return statistics and charts for all portfolios.<br />
*'''Portfolio_Math''' calculates portfolio returns for all combinations of interest and performs most of the 'under the hood' calculations. <br />
*'''Analyze_Series''' investigates annual returns for all selected data series. Various statistics are provided, as well as a correlation matrix and rolling returns over various time periods.<br />
*'''Data_Series''' provides a selection mechanism to choose the data series to be analyzed and combined in portfolios in the rest of the spreadsheet.<br />
*'''Raw_Data''' provides a dynamic splicing mechanism to combine raw data (e.g. funds, indices and synthetic models) into full data series, while applying expense ratio adjustments.<br />
*'''Data_Sources''' identifies the various data sources used in this spreadsheet. More details on a per data series basis can be found in Raw_Data.<br />
<br />
==Historical Returns==<br />
The spreadsheet provides an extensive set of historical returns for various types of passive index funds, plus a few active funds. Most funds are from Vanguard and all corresponding historical returns have been validated with Vanguard. All returns are expressed as total returns, i.e. including dividends. The perspective of a U.S. investor is assumed, with returns expressed in USD.<br />
<br />
When actual fund returns are not available (e.g. early years), attempts were made to provide credible numbers to extend the fund's history, using returns from corresponding indices, and in some cases, using a synthetic model. <br />
<br />
In general, fairly good quality data is available starting in 1927 for U.S. stocks and bonds. Most International returns are available starting in 1970. Most sector returns aren't available before 1985.<br />
<br />
The ''Raw_Data'' worksheet is the main repository for such historical data. The ''Data_Series'' worksheet assembles a synthetic list of data series returns and can be easily copied in another spreadsheet, allowing to perform other types of backtesting analysis than the tools provided by the Simba spreadsheet.<br />
<br />
==Telltale chart==<br />
{{Main article|Telltale chart}}<br />
<br />
<onlyinclude>John Bogle stated:<ref>[https://personal.vanguard.com/bogle_site/sp20020626.html The Telltale Chart], [[John C. Bogle]], Vanguard.com (Bogle_site), June 26, 2002.</ref><br />
<blockquote>''A telltale chart is devised simply by dividing the cumulative returns of one data series into another'' (the benchmark).</blockquote><br />
In the Simba spreadsheet, such a chart compares the trajectory of historical returns for the various portfolios of interest to a Telltale benchmark (itself a portfolio), in a relative manner.<br />
<br />
Using Telltale charts can be very informative, truly 'telling the tale' of what happened over time to portfolio trajectories, illustrating return to the mean properties, or lack thereof.<br />
<br />
It is interesting to observe that ''growth charts'' are actually a special form of ''telltale charts'', and can be generated by the same tool. <br />
<br />
A telltale/growth chart is provided in the ''Compare_Portfolios'' worksheet and can be used in multiple ways:<br />
<br />
* If the benchmark is defined as 100% cash, the telltale chart becomes a simple growth chart (i.e. showing the growth of an initial investment over time, in nominal terms).<br />
* If the benchmark is defined as 100% inflation, the telltale chart becomes an inflation-adjusted growth chart (i.e. showing the growth of an initial investment over time, in real terms).<br />
* If a more concrete benchmark is used (e.g. US Total Market, aka TSM), the telltale chart shows the relative growth over time of the portfolios of interest compared to the benchmark.<br />
<br />
Typical examples of Telltale charts generated with the Simba spreadsheet can be found here: [https://finpage.blog/2018/02/15/telling-tales-2017-update Telling Tales – 2017 update].<br />
</onlyinclude><br />
<br />
==Compatibility==<br />
The spreadsheet is maintained using Microsoft Excel 2011, and provided in XLSX format.<br />
<br />
It should work fairly well with recent versions of [https://www.libreoffice.org/discover/calc/ LibreOffice Calc], with some minor limitations (e.g. dynamic chart titles do not automatically update). Once the file has been downloaded from Google Drive, open the file and save it in the suggested "ODF" default format. Otherwise, the charts will not be preserved in the correct format.<br />
<br />
There is limited compatibility with Google Sheets. The calculations and statistics appear to work well, while the charts do not work properly.<br />
<br />
==Inner Workings==<br />
As any complex spreadsheet, the inner workings of the Simba spreadsheet may not be quite obvious by just looking at formulas. The following series of blog articles document various aspects of how it actually works.<br />
<br />
*[https://www.bogleheads.org/blog/2018/02/02/inner-workings-of-the-simba-backtesting-spreadsheet-a-layered-structure/ Simba backtesting spreadsheet: a layered structure], elaborating on how the spreadsheet is constructed, and providing an overview of its layered structure.<br />
*[https://www.bogleheads.org/blog/2018/02/04/simba-backtesting-spreadsheet-risk-metrics-risk-ratios Simba backtesting spreadsheet: risk metrics, risk ratios]: elaborating on how risk metrics (e.g. volatility, drawdowns, etc) and risk ratios (e.g. Sharpe, Sortino, etc) are computed.<br />
*[https://www.bogleheads.org/blog/2018/02/04/simba-backtesting-spreadsheet-advanced-topics Simba backtesting spreadsheet: advanced topics]: elaborating on more advanced topics (e.g. unbalancing, safe withdrawal rate).<br />
*[https://www.bogleheads.org/blog/2018/02/05/simba-backtesting-spreadsheet-miscellaneous-topics Simba backtesting spreadsheet: miscellaneous topics]: addressing a few miscellaneous topics (e.g. end label on charts, compatibility issues, spreadsheet analytics).<br />
<br />
==References==<br />
<references /><br />
<br />
==External links==<br />
*[http://www.bogleheads.org/forum/viewtopic.php?t=2520 Spreadsheet for backtesting (includes TrevH's data)], forum thread containing Simba's spreadsheet.<br />
*[[wikipedia:Backtesting|Backtesting]], on Wikipedia<br />
*[http://www.financialtrading.com/issues-related-to-back-testing/ Issues Related to Back Testing], from FinancialTrading.com<br />
*[http://www.investopedia.com/terms/b/backtesting.asp Backtesting], from Investopedia<br />
{{Resources and links}}<br />
{{Spreadsheets}}<br />
[[Category:Google Docs.spreadsheets]]<br />
[[Category:Resources and links]]</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Simba%27s_backtesting_spreadsheet&diff=69337
Simba's backtesting spreadsheet
2020-04-11T19:52:23Z
<p>Siamond: /* Spreadsheet overview and download instructions */ link to v19c post</p>
<hr />
<div><br />
'''{{PAGENAME}}''' describes a spreadsheet originally developed by forum member ''Simba'' for the purpose of acting as a reference for historical returns, and analyzing a portfolio based on such historical data. The spreadsheet is no longer maintained by Simba, but other forum members continue to support it and to expand functionality, as a Bogleheads community project.<br />
<br />
{{Notice|This spreadsheet and the information it contains is intended for your personal, non-commercial, use only (e.g. for educational purposes). This is a learning, researching and teaching tool, nothing more.}}<br />
<br />
==Backtesting==<br />
Backtesting is a term used in oceanography, meteorology and the financial industry to refer to testing a predictive model using existing historic data.<ref name="Wiki">[[wikipedia:Backtesting|Backtesting]], on Wikipedia</ref> It is also often used to analyze the past for research purposes. It is notably useful to quantitatively assess the impact [[asset allocation]] had (in known history) on possible investment strategies.<br />
<br />
Backtesting seeks to estimate the performance of a strategy if it had been employed during a past period. This requires simulating past conditions with sufficient detail, making one limitation of backtesting the need for detailed historical data. A second limitation is the inability to model strategies that would affect historic prices.<br />
<br />
Finally, backtesting, like other modeling, is limited by potential overfitting. That is, it is often possible to find a strategy that would have worked well in the past, but will not work well in the future. <br />
<br />
Despite these limitations, backtesting provides valuable information not available when models and strategies are tested on synthetic data.<br />
<br />
==Spreadsheet overview and download instructions==<br />
The spreadsheet is discussed in this {{Forum post|t=2520|title=Simba's backtesting spreadsheet <nowiki>[a Bogleheads community project]</nowiki>}}.<br />
<br />
The latest version and download instructions are in '''[{{{url|https://www.bogleheads.org/forum/viewtopic.php?f=10&t=2520&p=5178028#p5178028}}} this post]'''.<br />
<br />
Detailed instructions, glossary and revision history can be found in the '''README''' tab. Here is a brief overview of the individual worksheets:<br />
<br />
*'''Analyze_Portfolio''' provides a simple way to customize the asset allocation of a single portfolio and study its historical performance over specific time periods. This worksheet compares a custom portfolio to a benchmark portfolio (e.g. 60/40) and provides charts and statistics to illustrate respective growth and drawdowns.<br />
*'''Compare_Portfolios''' allows to compare two sets of 5 different portfolios, with the ability to change the portfolios' composition, the time period being examined, and to check the impact on various metrics and charts.<br />
*'''Lazy_Portfolios''' compares 25 predefined portfolios and provides risk/return statistics and charts for all portfolios.<br />
*'''Portfolio_Math''' calculates portfolio returns for all combinations of interest and performs most of the 'under the hood' calculations. <br />
*'''Analyze_Series''' investigates annual returns for all selected data series. Various statistics are provided, as well as a correlation matrix and rolling returns over various time periods.<br />
*'''Data_Series''' provides a selection mechanism to choose the data series to be analyzed and combined in portfolios in the rest of the spreadsheet.<br />
*'''Raw_Data''' provides a dynamic splicing mechanism to combine raw data (e.g. funds, indices and synthetic models) into full data series, while applying expense ratio adjustments.<br />
*'''Data_Sources''' identifies the various data sources used in this spreadsheet. More details on a per data series basis can be found in Raw_Data.<br />
<br />
==Historical Returns==<br />
The spreadsheet provides an extensive set of historical returns for various types of passive index funds, plus a few active funds. Most funds are from Vanguard and all corresponding historical returns have been validated with Vanguard. All returns are expressed as total returns, i.e. including dividends. The perspective of a U.S. investor is assumed, with returns expressed in USD.<br />
<br />
When actual fund returns are not available (e.g. early years), attempts were made to provide credible numbers to extend the fund's history, using returns from corresponding indices, and in some cases, using a synthetic model. <br />
<br />
In general, fairly good quality data is available starting in 1927 for U.S. stocks and bonds. Most International returns are available starting in 1970. Most sector returns aren't available before 1985.<br />
<br />
The ''Raw_Data'' worksheet is the main repository for such historical data. The ''Data_Series'' worksheet assembles a synthetic list of data series returns and can be easily copied in another spreadsheet, allowing to perform other types of backtesting analysis than the tools provided by the Simba spreadsheet.<br />
<br />
==Telltale chart==<br />
{{Main article|Telltale chart}}<br />
<br />
<onlyinclude>John Bogle stated:<ref>[https://personal.vanguard.com/bogle_site/sp20020626.html The Telltale Chart], [[John C. Bogle]], Vanguard.com (Bogle_site), June 26, 2002.</ref><br />
<blockquote>''A telltale chart is devised simply by dividing the cumulative returns of one data series into another'' (the benchmark).</blockquote><br />
In the Simba spreadsheet, such a chart compares the trajectory of historical returns for the various portfolios of interest to a Telltale benchmark (itself a portfolio), in a relative manner.<br />
<br />
Using Telltale charts can be very informative, truly 'telling the tale' of what happened over time to portfolio trajectories, illustrating return to the mean properties, or lack thereof.<br />
<br />
It is interesting to observe that ''growth charts'' are actually a special form of ''telltale charts'', and can be generated by the same tool. <br />
<br />
A telltale/growth chart is provided in the ''Compare_Portfolios'' worksheet and can be used in multiple ways:<br />
<br />
* If the benchmark is defined as 100% cash, the telltale chart becomes a simple growth chart (i.e. showing the growth of an initial investment over time, in nominal terms).<br />
* If the benchmark is defined as 100% inflation, the telltale chart becomes an inflation-adjusted growth chart (i.e. showing the growth of an initial investment over time, in real terms).<br />
* If a more concrete benchmark is used (e.g. US Total Market, aka TSM), the telltale chart shows the relative growth over time of the portfolios of interest compared to the benchmark.<br />
<br />
Typical examples of Telltale charts generated with the Simba spreadsheet can be found here: [https://finpage.blog/2018/02/15/telling-tales-2017-update Telling Tales – 2017 update].<br />
</onlyinclude><br />
<br />
==Compatibility==<br />
The spreadsheet is maintained using Microsoft Excel 2011, and provided in XLSX format.<br />
<br />
It should work fairly well with recent versions of [https://www.libreoffice.org/discover/calc/ LibreOffice Calc], with some minor limitations (e.g. dynamic chart titles do not automatically update). Once the file has been downloaded from Google Drive, open the file and save it in the suggested "ODF" default format. Otherwise, the charts will not be preserved in the correct format.<br />
<br />
There is limited compatibility with Google Sheets. The calculations and statistics appear to work well, while the charts do not work properly.<br />
<br />
==Inner Workings==<br />
As any complex spreadsheet, the inner workings of the Simba spreadsheet may not be quite obvious by just looking at formulas. The following series of blog articles documents various aspects of how it actually works.<br />
<br />
*[https://finpage.blog/2018/02/02/inner-workings-of-the-simba-backtesting-spreadsheet-a-layered-structure Simba backtesting spreadsheet: a layered structure], elaborating on how the spreadsheet is constructed, and providing an overview of its layered structure.<br />
*[https://finpage.blog/2018/02/04/simba-backtesting-spreadsheet-risk-metrics-risk-ratios Simba backtesting spreadsheet: risk metrics, risk ratios]: elaborating on how risk metrics (e.g. volatility, drawdowns, etc) and risk ratios (e.g. Sharpe, Sortino, etc) are computed.<br />
*[https://finpage.blog/2018/02/04/simba-backtesting-spreadsheet-advanced-topics Simba backtesting spreadsheet: advanced topics]: elaborating on more advanced topics (e.g. unbalancing, safe withdrawal rate).<br />
*[https://finpage.blog/2018/02/05/simba-backtesting-spreadsheet-miscellaneous-topics Simba backtesting spreadsheet: miscellaneous topics]: addressing a few miscellaneous topics (e.g. end label on charts, compatibility issues, spreadsheet analytics).<br />
<br />
==References==<br />
<references /><br />
<br />
==External links==<br />
*[http://www.bogleheads.org/forum/viewtopic.php?t=2520 Spreadsheet for backtesting (includes TrevH's data)], forum thread containing Simba's spreadsheet.<br />
*[[wikipedia:Backtesting|Backtesting]], on Wikipedia<br />
*[http://www.financialtrading.com/issues-related-to-back-testing/ Issues Related to Back Testing], from FinancialTrading.com<br />
*[http://www.investopedia.com/terms/b/backtesting.asp Backtesting], from Investopedia<br />
{{Resources and links}}<br />
{{Spreadsheets}}<br />
[[Category:Google Docs.spreadsheets]]<br />
[[Category:Resources and links]]</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Rebalancing&diff=69271
Rebalancing
2020-03-19T22:14:04Z
<p>Siamond: /* External links */ fixed a dead link, removed another one (Vanguard/Tokat article isn't available any more), minor clean-up</p>
<hr />
<div>'''{{PAGENAME}}''' is the action of bringing a [[portfolio]] that has deviated away from one's target [[asset allocation]] back into line. The objective is to maintain a consistent mix of [[asset class]]es (most commonly [[equities]] vs. [[fixed income]]) in order to control risk at the level desired by the investor. This is accomplished by transferring funds from higher-performing classes to lower-performing classes. While potentially counterintuitive, rebalancing ensures that investors "Buy Low" and "Sell High".<br />
<br />
==Example==<br />
* You own two funds (Fund A and Fund B). The funds could be either [[mutual fund]]s, [[index fund]]s or [[exchange-traded fund]]s (ETFs).<br />
* You have a $10,000 portfolio and have selected an asset allocation such that each fund represents 50% of the total ($5000 each)<br />
* Over time, Fund A rises in value to $6000 while Fund B declines in value to $4000 - you now have a 60/40 split instead of 50/50<br />
* To maintain your asset allocation, you would rebalance your portfolio by taking $1000 from Fund A and transferring it to Fund B<br />
* After doing so, your asset allocation is once again 50/50<br />
<br />
==Different rebalancing approaches==<br />
There are a variety of ways in which investors determine it is time to rebalance:<br />
* When a certain calendar event is reached (e.g. beginning of the year, specific day of the year, every other year, etc). For example, you might systematically rebalance your portfolio once a year, on your birthday.<br />
* When asset classes deviate from their target by a certain ''absolute percentage''. For example, if your target asset allocation is 60% equities and 40% fixed income and your (absolute) rebalancing threshold is +/- 5%, you would rebalance your portfolio when your portfolio reaches (65% equities / 35% fixed income) or (55% equities / 45% fixed income).<ref group="note" name="5/25">Larry Swedroe uses a "5/25 rule" which can be restated:<br />
*'''Absolute percentage of 5% for allocations 20% or greater:''' When asset classes deviate from their target by an ''absolute'' percentage of 5%. For example, if your target asset allocation is 60% equities and 40% fixed income, you would rebalance your portfolio when your portfolio reaches (65% equities / 35% fixed income) or (55% equities / 45% fixed income).<br />
*'''Relative percentage of 25% for allocations less than 20%:''' When asset classes deviate from their target by a ''relative'' percentage of 25%. For example, if your target equities asset allocation is 60%, composed of 45% Total Stock Market and 15% Total International, you would rebalance Total International if it changes by more than +/- 3.75% (25% of 15%).<br />
See: [http://seekingalpha.com/article/2130243-portfolio-rebalancing-the-whys-and-the-hows Portfolio Rebalancing: The Whys And The Hows], Larry Swedroe. ''Disable'' cookies to view article on single page, no subscription required.</ref><br />
* When asset classes deviate from their target by a certain ''relative percentage''. For example, if your target equities asset allocation is 60%, composed of 40% Total Stock Market and 20% Total International, and your (relative) rebalancing threshold is +/- 25%, you would rebalance International if it changes by more than +/- 5% (25% of 20%).<ref group="note" name="5/25" /><br />
* When asset classes deviate from their target by a certain dollar amount. For example, if you hold $6000 in equities and $4000 in fixed income and your rebalancing threshold is +/- $1000, you would rebalance your portfolio when either of your holdings deviates from their target asset allocation of 60% equities / 40% fixed income by at least $1000.<br />
* When contributing to or withdrawing from your portfolio. For example, if your target allocation is 60% equities and 40% fixed income, you hold $7000 of equities and $3000 of fixed income, and you wish to contribute $1000 to your portfolio, you would simply buy $1000 worth of fixed income assets. This would bring you to an allocation of 64% equities / 36% fixed income. This approach minimizes transaction costs, effort, and taxes. This [http://optimalrebalancing.tk portfolio rebalancing calculator] can help in cases where it isn't obvious how much of a new contribution or withdrawal to allocate to each asset.<br />
<br />
==Other considerations==<br />
* Transaction costs should be noted when deciding whether or not to rebalance. Since many transactions have costs associated with them, many investors choose to wait for their portfolio to pass a significant threshold of deviation (whether defined by percentage or dollars) before rebalancing.<br />
* Many investors find it difficult "selling winners" to "buy losers". To help remove emotions from the decision, many choose a specific date to rebalance (e.g. Birthday, Tax Day, etc.). Note: Investors who find the prospect daunting may want to consider [[Vanguard Target Retirement Funds|Target Retirement Funds]], which automatically rebalance as necessary to maintain a consistent asset allocation.<br />
* The frequency at which the portfolio is monitored for deviations from its target has some influence on the returns gains (or losses) that may be obtained by rebalancing.<ref group="note" name="frequency">Research seems to indicate that monitoring on a weekly basis (while actually rebalancing very infrequently, e.g. by using large deviation thresholds) could provide the best rebalancing bonus. Conversely, rebalancing too frequently and using low thresholds would be detrimental. See: [http://www.tdainstitutional.com/pdf/Opportunistic_Rebalancing_JFP2007_Daryanani.pdf Opportunistic Rebalancing: A New Paradigm For Wealth Managers], Gobind Daryanani.</ref><br />
<br />
==Modified Approaches==<br />
For those fearful of rebalancing into a sustained bear market, one of the following modifications to standard rebalancing methods could be employed:<br />
* Keep a floor level of bonds, i.e. once the total amount of bonds has dropped to a fixed amount, stop rebalancing into stocks.<br />
* Only rebalance out of stocks, never into stocks.<br />
<br />
==Estimating changes in asset allocation==<br />
Normal market fluctuations do not frequently trigger rebalancing.<br />
* Shifting the balance of a 50/50 portfolio by 1% requires a 4% change in the price of stocks relative to bonds. All other portfolios are less sensitive, with 70/30 or 30/70 requiring a 5% change, 80/20 or 20/80 a 6% change, and 90/10 or 10/90 an 11% change. For example, a $10,000 60/40 portfolio will, after a 10% stock market drop, have $6,000 * 0.9 = $5,400 in stocks and $4,000 in bonds, for a stock allocation of $5,400 / ($5,400 + $4,000) = 57.45%, a 2.55% shift.<br />
<br />
==Notes==<br />
<references group="note" /><br />
<br />
==Further reading==<br />
*[https://www.stanford.edu/class/msande348/papers/PeroldSharpe.pdf Dynamic Strategies for Asset Allocation], Andre F. Perold, [[William F. Sharpe]], Financial Analysts Journal, (January/February 1988):16-27.<br />
*[http://resource.fpanet.org/resource/09BBF2F9-D5B3-9B76-B02E27EB8731C337/daryanani.pdf Opportunistic Rebalancing: A New Paradigm For Wealth Managers], Gobind Daryanani, ''Journal of Financial Planning'', (January 2008).<br />
<br />
==External links==<br />
*[http://optimalrebalancing.tk Optimal lazy portfolio rebalancing calculator]: rebalance optimally without making any "backwards" transactions - from forum member [http://optimalrebalancing.tk/about.html Albert Mao] (the_one_smiley)<br />
*[https://www.vanguard.com/pdf/ISGPORE.pdf Best Practices for Portfolio Rebalancing] by Vanguard Institutional Research, November 2015.<br />
*[http://seekingalpha.com/article/2130243-portfolio-rebalancing-the-whys-and-the-hows Portfolio Rebalancing: The Whys And The Hows] by [[Larry Swedroe]], April 2014.<br />
*{{forum post|t=150267|title=How to use Vanguard Portfolio Watch for rebalancing}}.<br />
*[http://www.able2pay.com/rebalancing.html Rebalancing]: a tutorial which discusses several methods of rebalancing, by [http://www.able2pay.com/about.html Able to Pay], discussed in this {{Forum post|t=182926|title=Rebalancing, another study}}.<br />
*{{forum post|t=186203|title=Rebalancing: adaptive bands}}, discussion about idiosyncrasies of absolute percentage and relative percentage approaches, suggesting a more 'adaptive' way to define rebalancing bands.<br />
<br />
===Spreadsheets===<br />
* [https://docs.google.com/spreadsheets/d/18HKaSlRFVlNhB1AG_npZO_aHh9mu_6QY5zKrKzZioKY/edit?usp=sharing Rebalancing Bands Spreadsheet] illustrating how to define 5/25 absolute/relative rebalancing bands across asset classes, on Google Docs from wiki contributor [[User:Hoppy08520 |Hoppy08520]], October 2014.<br />
*[https://docs.google.com/spreadsheet/ccc?key=0AsVSNcUR-B6IdE4tZm0yVk9ObkxsZ2xvNmJpRTB0b0E Rebalancing spreadsheet], free download from Google Docs. Supplies three example approaches to rebalance a portfolio by allocation percentage, transfer amount, or final value; by forum member LadyGeek. To download, select File --> Download As --> Excel or OpenOffice.<br />
*[https://drive.google.com/file/d/1bg9c7kxDEvHXDzEvCni7ethZ8uHwMJyd/view?usp=sharing Boglehead rebalance.xls] on Google Drive, by forum member LeeMKE. Rebalance your portfolio across multiple accounts. Includes space to keep notes.<br />
*[https://kissmoneyblog.blogspot.com/2020/02/simple-portfolio-allocation-and.html Simple Portfolio Allocation and Rebalancing spreadsheet] by forum member kiss, [https://docs.google.com/spreadsheets/d/1VxGYuQSnTqkAnE2LPuYAhwJY1Tv_CCFYLUPjpDoMAVQ/edit?usp=sharing Google Sheets]. Allocate across taxable and tax-deferred accounts.<br />
<br />
{{Bogleheads investing start-up kit}}<br />
{{Portfolios}}<br />
[[Category:Asset allocation]]<br />
[[Category:Portfolios]]</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Rebalancing&diff=69270
Rebalancing
2020-03-19T21:04:40Z
<p>Siamond: /* Further reading */ Dead link replaced by working link</p>
<hr />
<div>'''{{PAGENAME}}''' is the action of bringing a [[portfolio]] that has deviated away from one's target [[asset allocation]] back into line. The objective is to maintain a consistent mix of [[asset class]]es (most commonly [[equities]] vs. [[fixed income]]) in order to control risk at the level desired by the investor. This is accomplished by transferring funds from higher-performing classes to lower-performing classes. While potentially counterintuitive, rebalancing ensures that investors "Buy Low" and "Sell High".<br />
<br />
==Example==<br />
* You own two funds (Fund A and Fund B). The funds could be either [[mutual fund]]s, [[index fund]]s or [[exchange-traded fund]]s (ETFs).<br />
* You have a $10,000 portfolio and have selected an asset allocation such that each fund represents 50% of the total ($5000 each)<br />
* Over time, Fund A rises in value to $6000 while Fund B declines in value to $4000 - you now have a 60/40 split instead of 50/50<br />
* To maintain your asset allocation, you would rebalance your portfolio by taking $1000 from Fund A and transferring it to Fund B<br />
* After doing so, your asset allocation is once again 50/50<br />
<br />
==Different rebalancing approaches==<br />
There are a variety of ways in which investors determine it is time to rebalance:<br />
* When a certain calendar event is reached (e.g. beginning of the year, specific day of the year, every other year, etc). For example, you might systematically rebalance your portfolio once a year, on your birthday.<br />
* When asset classes deviate from their target by a certain ''absolute percentage''. For example, if your target asset allocation is 60% equities and 40% fixed income and your (absolute) rebalancing threshold is +/- 5%, you would rebalance your portfolio when your portfolio reaches (65% equities / 35% fixed income) or (55% equities / 45% fixed income).<ref group="note" name="5/25">Larry Swedroe uses a "5/25 rule" which can be restated:<br />
*'''Absolute percentage of 5% for allocations 20% or greater:''' When asset classes deviate from their target by an ''absolute'' percentage of 5%. For example, if your target asset allocation is 60% equities and 40% fixed income, you would rebalance your portfolio when your portfolio reaches (65% equities / 35% fixed income) or (55% equities / 45% fixed income).<br />
*'''Relative percentage of 25% for allocations less than 20%:''' When asset classes deviate from their target by a ''relative'' percentage of 25%. For example, if your target equities asset allocation is 60%, composed of 45% Total Stock Market and 15% Total International, you would rebalance Total International if it changes by more than +/- 3.75% (25% of 15%).<br />
See: [http://seekingalpha.com/article/2130243-portfolio-rebalancing-the-whys-and-the-hows Portfolio Rebalancing: The Whys And The Hows], Larry Swedroe. ''Disable'' cookies to view article on single page, no subscription required.</ref><br />
* When asset classes deviate from their target by a certain ''relative percentage''. For example, if your target equities asset allocation is 60%, composed of 40% Total Stock Market and 20% Total International, and your (relative) rebalancing threshold is +/- 25%, you would rebalance International if it changes by more than +/- 5% (25% of 20%).<ref group="note" name="5/25" /><br />
* When asset classes deviate from their target by a certain dollar amount. For example, if you hold $6000 in equities and $4000 in fixed income and your rebalancing threshold is +/- $1000, you would rebalance your portfolio when either of your holdings deviates from their target asset allocation of 60% equities / 40% fixed income by at least $1000.<br />
* When contributing to or withdrawing from your portfolio. For example, if your target allocation is 60% equities and 40% fixed income, you hold $7000 of equities and $3000 of fixed income, and you wish to contribute $1000 to your portfolio, you would simply buy $1000 worth of fixed income assets. This would bring you to an allocation of 64% equities / 36% fixed income. This approach minimizes transaction costs, effort, and taxes. This [http://optimalrebalancing.tk portfolio rebalancing calculator] can help in cases where it isn't obvious how much of a new contribution or withdrawal to allocate to each asset.<br />
<br />
==Other considerations==<br />
* Transaction costs should be noted when deciding whether or not to rebalance. Since many transactions have costs associated with them, many investors choose to wait for their portfolio to pass a significant threshold of deviation (whether defined by percentage or dollars) before rebalancing.<br />
* Many investors find it difficult "selling winners" to "buy losers". To help remove emotions from the decision, many choose a specific date to rebalance (e.g. Birthday, Tax Day, etc.). Note: Investors who find the prospect daunting may want to consider [[Vanguard Target Retirement Funds|Target Retirement Funds]], which automatically rebalance as necessary to maintain a consistent asset allocation.<br />
* The frequency at which the portfolio is monitored for deviations from its target has some influence on the returns gains (or losses) that may be obtained by rebalancing.<ref group="note" name="frequency">Research seems to indicate that monitoring on a weekly basis (while actually rebalancing very infrequently, e.g. by using large deviation thresholds) could provide the best rebalancing bonus. Conversely, rebalancing too frequently and using low thresholds would be detrimental. See: [http://www.tdainstitutional.com/pdf/Opportunistic_Rebalancing_JFP2007_Daryanani.pdf Opportunistic Rebalancing: A New Paradigm For Wealth Managers], Gobind Daryanani.</ref><br />
<br />
==Modified Approaches==<br />
For those fearful of rebalancing into a sustained bear market, one of the following modifications to standard rebalancing methods could be employed:<br />
* Keep a floor level of bonds, i.e. once the total amount of bonds has dropped to a fixed amount, stop rebalancing into stocks.<br />
* Only rebalance out of stocks, never into stocks.<br />
<br />
==Estimating changes in asset allocation==<br />
Normal market fluctuations do not frequently trigger rebalancing.<br />
* Shifting the balance of a 50/50 portfolio by 1% requires a 4% change in the price of stocks relative to bonds. All other portfolios are less sensitive, with 70/30 or 30/70 requiring a 5% change, 80/20 or 20/80 a 6% change, and 90/10 or 10/90 an 11% change. For example, a $10,000 60/40 portfolio will, after a 10% stock market drop, have $6,000 * 0.9 = $5,400 in stocks and $4,000 in bonds, for a stock allocation of $5,400 / ($5,400 + $4,000) = 57.45%, a 2.55% shift.<br />
<br />
==Notes==<br />
<references group="note" /><br />
<br />
==Further reading==<br />
*[https://www.stanford.edu/class/msande348/papers/PeroldSharpe.pdf Dynamic Strategies for Asset Allocation], Andre F. Perold, [[William F. Sharpe]], Financial Analysts Journal, (January/February 1988):16-27.<br />
*[http://resource.fpanet.org/resource/09BBF2F9-D5B3-9B76-B02E27EB8731C337/daryanani.pdf Opportunistic Rebalancing: A New Paradigm For Wealth Managers], Gobind Daryanani, ''Journal of Financial Planning'', (January 2008).<br />
<br />
==External links==<br />
*[http://optimalrebalancing.tk Optimal lazy portfolio rebalancing calculator]: rebalance optimally without making any "backwards" transactions - from forum member [http://optimalrebalancing.tk/about.html Albert Mao] (the_one_smiley)<br />
*[http://www.vanguard.com/pdf/icrpr.pdf Best Practices for Portfolio Rebalancing] by Vanguard Institutional Research, (7/21/2010)<br />
* [https://personal.vanguard.com/pdf/flgprtp.pdf Portfolio Rebalancing in Theory and Practice] by Vanguard Institutional Research, 2007, Viewed August 25, 2015.<br />
* [http://seekingalpha.com/article/2130243-portfolio-rebalancing-the-whys-and-the-hows Portfolio Rebalancing: The Whys And The Hows] by [[Larry Swedroe]], April 8, 2014 (Disable cookies to view on a single page. Otherwise, a subscription will be required to view.)<br />
*{{forum post|t=150267|title=How to use Vanguard Portfolio Watch for rebalancing}}<br />
*[http://www.able2pay.com/rebalancing.html Rebalancing] A tutorial which discusses several methods of rebalancing, by [http://www.able2pay.com/about.html Able to Pay], discussed in this {{Forum post|t=182926|title=Rebalancing, another study}}.<br />
*{{forum post|t=186203|title=Rebalancing: adaptive bands}}, discussion about some idiosyncrasies of the absolute percentage and relative percentage approaches, and suggesting a more 'adaptive' way to define rebalancing bands.<br />
<br />
===Spreadsheets===<br />
* [https://docs.google.com/spreadsheets/d/18HKaSlRFVlNhB1AG_npZO_aHh9mu_6QY5zKrKzZioKY/edit?usp=sharing Rebalancing Bands Spreadsheet] illustrating how to define 5/25 absolute/relative rebalancing bands across asset classes, on Google Docs from wiki contributor [[User:Hoppy08520 |Hoppy08520]], 11 October 2014<br />
*[https://docs.google.com/spreadsheet/ccc?key=0AsVSNcUR-B6IdE4tZm0yVk9ObkxsZ2xvNmJpRTB0b0E Rebalancing spreadsheet], free download from Google Docs. Supplies three example approaches to rebalance a portfolio by allocation percentage, transfer amount, or final value; by forum member LadyGeek. To download, select File --> Download As --> Excel or OpenOffice.<br />
*[https://drive.google.com/file/d/1bg9c7kxDEvHXDzEvCni7ethZ8uHwMJyd/view?usp=sharing Boglehead rebalance.xls] on Google Drive, by forum member LeeMKE. Rebalance your portfolio across multiple accounts. Includes space to keep notes.<br />
*[https://kissmoneyblog.blogspot.com/2020/02/simple-portfolio-allocation-and.html Simple Portfolio Allocation and Rebalancing spreadsheet] by forum member kiss, [https://docs.google.com/spreadsheets/d/1VxGYuQSnTqkAnE2LPuYAhwJY1Tv_CCFYLUPjpDoMAVQ/edit?usp=sharing Google Sheets]. Allocate across taxable and tax-deferred accounts.<br />
<br />
{{Bogleheads investing start-up kit}}<br />
{{Portfolios}}<br />
[[Category:Asset allocation]]<br />
[[Category:Portfolios]]</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Simba%27s_backtesting_spreadsheet&diff=68988
Simba's backtesting spreadsheet
2020-02-03T22:44:27Z
<p>Siamond: /* Spreadsheet overview and download instructions */ v19b post</p>
<hr />
<div><br />
'''{{PAGENAME}}''' describes a spreadsheet originally developed by forum member ''Simba'' for the purpose of acting as a reference for historical returns, and analyzing a portfolio based on such historical data. The spreadsheet is no longer maintained by Simba, but other forum members continue to support it and to expand functionality, as a Bogleheads community project.<br />
<br />
{{Notice|This spreadsheet and the information it contains is intended for your personal, non-commercial, use only (e.g. for educational purposes). This is a learning, researching and teaching tool, nothing more.}}<br />
<br />
==Backtesting==<br />
Backtesting is a term used in oceanography, meteorology and the financial industry to refer to testing a predictive model using existing historic data.<ref name="Wiki">[[wikipedia:Backtesting|Backtesting]], on Wikipedia</ref> It is also often used to analyze the past for research purposes. It is notably useful to quantitatively assess the impact [[asset allocation]] had (in known history) on possible investment strategies.<br />
<br />
Backtesting seeks to estimate the performance of a strategy if it had been employed during a past period. This requires simulating past conditions with sufficient detail, making one limitation of backtesting the need for detailed historical data. A second limitation is the inability to model strategies that would affect historic prices.<br />
<br />
Finally, backtesting, like other modeling, is limited by potential overfitting. That is, it is often possible to find a strategy that would have worked well in the past, but will not work well in the future. <br />
<br />
Despite these limitations, backtesting provides valuable information not available when models and strategies are tested on synthetic data.<br />
<br />
==Spreadsheet overview and download instructions==<br />
The spreadsheet is discussed in this {{Forum post|t=2520|title=Simba's backtesting spreadsheet <nowiki>[a Bogleheads community project]</nowiki>}}.<br />
<br />
The latest version and download instructions are in '''[{{{url|https://www.bogleheads.org/forum/viewtopic.php?f=10&t=2520&p=4997466#p4997466}}} this post]'''.<br />
<br />
Detailed instructions, glossary and revision history can be found in the '''README''' tab. Here is a brief overview of the individual worksheets:<br />
<br />
*'''Analyze_Portfolio''' provides a simple way to customize the asset allocation of a single portfolio and study its historical performance over specific time periods. This worksheet compares a custom portfolio to a benchmark portfolio (e.g. 60/40) and provides charts and statistics to illustrate respective growth and drawdowns.<br />
*'''Compare_Portfolios''' allows to compare two sets of 5 different portfolios, with the ability to change the portfolios' composition, the time period being examined, and to check the impact on various metrics and charts.<br />
*'''Lazy_Portfolios''' compares 25 predefined portfolios and provides risk/return statistics and charts for all portfolios.<br />
*'''Portfolio_Math''' calculates portfolio returns for all combinations of interest and performs most of the 'under the hood' calculations. <br />
*'''Analyze_Series''' investigates annual returns for all selected data series. Various statistics are provided, as well as a correlation matrix and rolling returns over various time periods.<br />
*'''Data_Series''' provides a selection mechanism to choose the data series to be analyzed and combined in portfolios in the rest of the spreadsheet.<br />
*'''Raw_Data''' provides a dynamic splicing mechanism to combine raw data (e.g. funds, indices and synthetic models) into full data series, while applying expense ratio adjustments.<br />
*'''Data_Sources''' identifies the various data sources used in this spreadsheet. More details on a per data series basis can be found in Raw_Data.<br />
<br />
==Historical Returns==<br />
The spreadsheet provides an extensive set of historical returns for various types of passive index funds, plus a few active funds. Most funds are from Vanguard and all corresponding historical returns have been validated with Vanguard. All returns are expressed as total returns, i.e. including dividends. The perspective of a U.S. investor is assumed, with returns expressed in USD.<br />
<br />
When actual fund returns are not available (e.g. early years), attempts were made to provide credible numbers to extend the fund's history, using returns from corresponding indices, and in some cases, using a synthetic model. <br />
<br />
In general, fairly good quality data is available starting in 1927 for U.S. stocks and bonds. Most International returns are available starting in 1970. Most sector returns aren't available before 1985.<br />
<br />
The ''Raw_Data'' worksheet is the main repository for such historical data. The ''Data_Series'' worksheet assembles a synthetic list of data series returns and can be easily copied in another spreadsheet, allowing to perform other types of backtesting analysis than the tools provided by the Simba spreadsheet.<br />
<br />
==Telltale chart==<br />
{{Main article|Telltale chart}}<br />
<br />
<onlyinclude>John Bogle stated:<ref>[https://personal.vanguard.com/bogle_site/sp20020626.html The Telltale Chart], [[John C. Bogle]], Vanguard.com (Bogle_site), June 26, 2002.</ref><br />
<blockquote>''A telltale chart is devised simply by dividing the cumulative returns of one data series into another'' (the benchmark).</blockquote><br />
In the Simba spreadsheet, such a chart compares the trajectory of historical returns for the various portfolios of interest to a Telltale benchmark (itself a portfolio), in a relative manner.<br />
<br />
Using Telltale charts can be very informative, truly 'telling the tale' of what happened over time to portfolio trajectories, illustrating return to the mean properties, or lack thereof.<br />
<br />
It is interesting to observe that ''growth charts'' are actually a special form of ''telltale charts'', and can be generated by the same tool. <br />
<br />
A telltale/growth chart is provided in the ''Compare_Portfolios'' worksheet and can be used in multiple ways:<br />
<br />
* If the benchmark is defined as 100% cash, the telltale chart becomes a simple growth chart (i.e. showing the growth of an initial investment over time, in nominal terms).<br />
* If the benchmark is defined as 100% inflation, the telltale chart becomes an inflation-adjusted growth chart (i.e. showing the growth of an initial investment over time, in real terms).<br />
* If a more concrete benchmark is used (e.g. US Total Market, aka TSM), the telltale chart shows the relative growth over time of the portfolios of interest compared to the benchmark.<br />
<br />
Typical examples of Telltale charts generated with the Simba spreadsheet can be found here: [https://finpage.blog/2018/02/15/telling-tales-2017-update Telling Tales – 2017 update].<br />
</onlyinclude><br />
<br />
==Compatibility==<br />
The spreadsheet is maintained using Microsoft Excel 2011, and provided in XLSX format.<br />
<br />
It should work fairly well with recent versions of [https://www.libreoffice.org/discover/calc/ LibreOffice Calc], with some minor limitations (e.g. dynamic chart titles do not automatically update). Once the file has been downloaded from Google Drive, open the file and save it in the suggested "ODF" default format. Otherwise, the charts will not be preserved in the correct format.<br />
<br />
There is limited compatibility with Google Sheets. The calculations and statistics appear to work well, while the charts do not work properly.<br />
<br />
==Inner Workings==<br />
As any complex spreadsheet, the inner workings of the Simba spreadsheet may not be quite obvious by just looking at formulas. The following series of blog articles documents various aspects of how it actually works.<br />
<br />
*[https://finpage.blog/2018/02/02/inner-workings-of-the-simba-backtesting-spreadsheet-a-layered-structure Simba backtesting spreadsheet: a layered structure], elaborating on how the spreadsheet is constructed, and providing an overview of its layered structure.<br />
*[https://finpage.blog/2018/02/04/simba-backtesting-spreadsheet-risk-metrics-risk-ratios Simba backtesting spreadsheet: risk metrics, risk ratios]: elaborating on how risk metrics (e.g. volatility, drawdowns, etc) and risk ratios (e.g. Sharpe, Sortino, etc) are computed.<br />
*[https://finpage.blog/2018/02/04/simba-backtesting-spreadsheet-advanced-topics Simba backtesting spreadsheet: advanced topics]: elaborating on more advanced topics (e.g. unbalancing, safe withdrawal rate).<br />
*[https://finpage.blog/2018/02/05/simba-backtesting-spreadsheet-miscellaneous-topics Simba backtesting spreadsheet: miscellaneous topics]: addressing a few miscellaneous topics (e.g. end label on charts, compatibility issues, spreadsheet analytics).<br />
<br />
==References==<br />
<references /><br />
<br />
==External links==<br />
*[http://www.bogleheads.org/forum/viewtopic.php?t=2520 Spreadsheet for backtesting (includes TrevH's data)], forum thread containing Simba's spreadsheet.<br />
*[[wikipedia:Backtesting|Backtesting]], on Wikipedia<br />
*[http://www.financialtrading.com/issues-related-to-back-testing/ Issues Related to Back Testing], from FinancialTrading.com<br />
*[http://www.investopedia.com/terms/b/backtesting.asp Backtesting], from Investopedia<br />
{{Resources and links}}<br />
{{Spreadsheets}}<br />
[[Category:Google Docs.spreadsheets]]<br />
[[Category:Resources and links]]</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Leveraged_and_inverse_ETFs&diff=68863
Leveraged and inverse ETFs
2020-01-29T03:54:47Z
<p>Siamond: /* Risks and rewards */ Switched VFINX to VFIAX</p>
<hr />
<div>'''{{PAGENAME}}''' ([[Exchange-traded funds]])<ref group="note">''Leveraging'' is also called ''gearing''. ''Leveraged'' ETFs and ''Geared'' ETFs mean the same thing.</ref> are ETF structures intended to provide returns that are positive or negative multiples of an equivalent ETF benchmark. The purpose of this article is to explain why these ETFs present significant risks as long-term investments.<br />
{{Warning|The SEC and FINRA has issued a joint alert, "Leveraged and Inverse ETFs: Specialized Products with Extra Risks for Buy-and-Hold Investors." It states:<ref name="SEC">{{cite web| publisher=Financial Industry Regulator Authority| url=http://www.finra.org/investors/alerts/leveraged-and-inverse-etfs-specialized-products-extra-risks-buy-and-hold-investors| title=Leveraged and Inverse ETFs: Specialized Products with Extra Risks for Buy-and-Hold Investors| date=August 18, 2009}}</ref><blockquote>The SEC staff and FINRA are issuing this Alert because we believe individual investors may be confused about the performance objectives of leveraged and inverse exchange-traded funds (ETFs). Leveraged and inverse ETFs typically are designed to achieve their stated performance objectives on a daily basis. Some investors might invest in these ETFs with the expectation that the ETFs may meet their stated daily performance objectives over the long term as well. [...] Only invest if you are confident the product can help you meet your investment objectives and you are knowledgeable and comfortable with the risks associated with these specialized ETFs.</blockquote>}}<br />
<br />
==Overview==<br />
There are 3 structures:<ref name="SEC" /><br />
<br />
*'''Leveraged ETFs''' seek to deliver multiples of the performance of the index or benchmark they track.<br />
*'''Inverse ETFs''' (also called "short" funds) seek to deliver the ''opposite'' of the performance of the index or benchmark they track.<br />
*'''Leveraged inverse ETFs''' (also known as "ultra short" funds) seek to achieve a return that is a multiple of the inverse performance of the underlying index.<br />
<br />
Here are several example ETF descriptions:<br />
*'''ProShares UltraPro S&P500 (UPRO)''' seeks daily investment results, before fees and expenses, that correspond to three times (3x) the daily performance of the S&P 500<sup>®</sup>.<ref>[http://www.proshares.com/funds/upro.html ProShares ETFs: UltraPro S&P500]</ref><br />
*'''ProShares Ultra S&P500 (SSO)''' seeks daily investment results, before fees and expenses, that correspond to two times (2x) the daily performance of the S&P 500<sup>®</sup>.<ref>[http://www.proshares.com/funds/sso.html ProShares ETFs: Ultra S&P500]</ref><br />
*'''ProShares UltraShort S&P500 (SDS)''' seeks daily investment results, before fees and expenses, that correspond to two times the inverse (-2x) of the daily performance of the S&P 500<sup>®</sup>.<ref>[http://www.proshares.com/funds/sds.html ProShares ETFs: UltraShort S&P500]</ref><br />
*'''Direxion Emerging Markets Bear 3X ETF (EDZ)''' seeks daily investment results, before fees and expenses, of 300% of the inverse (or opposite) of the performance of the MSCI Emerging Markets Index.<ref>[http://www.direxionfunds.com/products/direxion-daily-emerging-markets-bear-3x-etf Direxion Daily Emerging Markets Bear 3x Shares]</ref><br />
<br />
Let's look at the 4th example fund provider, Direxion. Notice that Direxion itself<ref>[http://www.direxionfunds.com/signs Leveraged ETF List | Direxion]</ref> says these funds are for "short-term trading." This is not a detail or a pro forma disclaimer - it is explicitly displayed in the figure below.<br />
<br />
{|style="border-collapse: collapse;" border="1" <!-- set border="1" to see table boundaries, outer table draws outside border. --><br />
|+'''Direxion ETF Fund Categories'''<br />
||<br />
[[image:Direxionsayshorterm.png]]<br />
|}<br />
<br />
The first category, "Long Term Investment" contains 3 ETFs which match a benchmark. The second category contains 2 leveraged ETFs ("3X") and is titled "Short Term Trading" which is a warning sign that these ETFs will perform differently than those intended for long-term investments. The link "Are Direxion Shares ETFs for you?" is an additional warning sign, as there would be no reason to ask this question if these ETFs performed similarly to ETFs intended for long-term investments.<br />
<br />
Brokerages typically require customers to sign a special disclaimer in order to open a margin account. Everyone understands that using leverage in the form of a margin account is taking on a big risk, the risk of losing more than your total investment. It is a mistake to think you can get essentially similar results, more conveniently and without the risk of losing more than your investment, simply by using an inverse or leveraged ETF.<br />
<br />
Anyone thinking of using an inverse or leveraged ETF needs to read and understand the fund company's factsheets and prospectus, which disclose the issues in language varying from veiled to clear.<br />
<br />
==How does a daily leveraged ETF work?==<br />
A daily leveraged ETF holds a combination of derivatives and actual securities to track a multiple of the underlying index's daily performance.<br />
<br />
Let's examine ProShares UltraPro S&P500 (UPRO), which promises to deliver 3x the daily performance of the S&P 500. It does this by holding 77% individual S&P 500 stocks, nominal exposure to 215% of the S&P 500 through total return swaps, and 8% S&P futures. Add it all up, and you get exposure to 300% of the S&P 500’s daily performance.<ref>[https://www.proshares.com/resources/prospectus_reports.html ProShares Geared Funds Annual] 5/31/2019, market exposure on printed page LIX.</ref><br />
<br />
Total return swaps are contracts between the ETF and major investment banks. For UPRO, every day the banks pay the ETF the value of the S&P 500’s total return for that day, and in return the ETF pays the banks a pre-negotiated rate of interest, which is close to the short term treasury rate. As of May 2019, the borrowing rate of some UPRO's swap agreements was 3.01%.<ref>[https://www.proshares.com/resources/prospectus_reports.html ProShares Geared Funds Annual] 5/31/2019, swap agreements on printed page 138, e.g. BNP Paribas rate as of May 31, 2019.</ref> The corresponding cost is NOT included in UPRO's 0.92% expense ratio.<br />
<br />
==Daily results are significantly different than long-term==<br />
It is critical to understand that a movement in one direction followed by an equal movement in the opposite direction will '''not''' get you back to the starting value. For example, a gain of 10% followed by a loss of 10% will end up with a loss of 1.0%.<ref name="ReturnCalc">Details are in this {{Forum post| p=4882043|title = Re: <nowiki>[Wiki article update - Inverse and leveraged ETFs]</nowiki> |author = LadyGeek | date = December 09, 2019}}</ref> This is nothing but math at work. The math works the same for any investment – regardless if it’s a single stock or a fund. See [[Percentage gain and loss]] for the details.<br />
<br />
This math will be very evident as a fund performs over time. If the market has equal gains and losses over a period of time, the fund’s value will always be lower. For example, 6 consecutive days which alternate as +10% then -10% will result in a loss of 3.0%.<ref name="ReturnCalc" /> The change in loss from 1.0% to 3.0% is known as ''volatility decay''.<ref group="note">Also known as [[volatility drag]], but ''volatility decay'' is the term used for leveraged funds.</ref><br />
<br />
Over the course of a single day, the fund will generate a return as advertised. For example, a 3X leveraged fund will generate three times the gain (and loss) of an unleveraged fund.<br />
<br />
However, that’s not the entire story. Leveraged funds [[rebalance]] their exposure to their underlying benchmarks on a daily basis by trimming or adding to their positions. Over time, a longer-term investor is unlikely to continue to receive the fund's multiple of the benchmark's returns.<ref name="ProShares">{{cite web| publisher=ProShares| url=https://www.proshares.com/funds/performance/the_universal_effects_of_compounding.html| title=Effects Of Daily Rebalancing and Compounding on Geared Investing| accessdate=December 09, 2019}}</ref><br />
<br />
Investment returns compound over time. The effects of compounding will also cause the fund to deviate from the fund's stated objective, e.g. 2X or 3X of the index's return. In trending periods, compounding can enhance returns, but in volatile periods, compounding may hurt returns. Generally speaking, the greater the multiple or more volatile a fund's benchmark, the more pronounced the effects can be.<ref name="ProShares" /><br />
<br />
It is why the fund’s fact sheets have disclaimers stating that performance is only guaranteed on a daily basis.<br />
<br />
==A comprehensive example==<br />
<br />
Now, let's illustrate how big the difference is between "daily" and long-term results.<br />
<br />
Some investors think they see interesting theoretical possibilities for using [[leverage]] in long-term investing. If so, they should '''not''' think that over long periods of time they can get double the return of the S&P 500 simply by investing in a 2X leveraged S&P 500 ETF. <br />
<br />
The word "daily" has a very precise meaning. These products double or triple the long or short index for a single day, so '''if you are someone who trades in and out of positions on a daily basis''', they actually do pretty much what you'd expect. Not so over long periods, '''and the difference can be large'''.<br />
<br />
The ETF companies disclose this point fairly clearly in the factsheets, such as:<br />
<br />
<blockquote>'''Direxion:''' "This leveraged ETF seeks a return that is -300% the return of its benchmark index for a single day. The fund should not be expected to provide three times the return of the benchmark’s cumulative return for periods greater than a day.", and<br><br><br />
<br />
'''ProShares:''' "Due to the compounding of daily returns, ProShares' returns over periods other than one day will likely '''differ in amount''' and possibly '''<nowiki>[differ in]</nowiki> direction''' from the target return for the same period."</blockquote><br />
<br />
In order to illustrate the potential impact, let's ask: "'''How much is that in dollars?'''" which is quantified in the following sections.<br />
<br />
==="differ in amount"===<br />
"Differ in amount" means that the "2X" fund might not deliver twice the return of the index. For example, ProShares Ultra S&P 500 ETF, SSO began in 6/2007. $10,000 invested in the Vanguard 500 Index fund would have gained a total of $6,966 in total return since that time (6/20/2006 to 12/31/2013). Did the Ultra fund earn twice that ($13,932)?<br />
<br />
{|style="border-collapse: collapse;" border="1" <!-- set border="1" to see table boundaries, outer table draws outside border. --><br />
|+'''Comparison of ProShares Ultra S&P 500 (SSO) to Vanguard 500 Index (VFINX)'''<br />
||[[image:Vfinx-beats-sso.png]]<br />
|}<br />
<br />
It did not. It earned $6,097, which is less than the Vanguard 500 Index fund earnings. ''The 2X ETF earned less than the straight, unleveraged, direct investment.''<br />
<br />
==="differ in direction"===<br />
This is a way of saying that over periods of more than a day, your ETF could go down even when the inverse or leveraged index it is tied to goes up. This is why ProShares says "Investors should monitor their holdings consistent with their strategies, as frequently as daily."<br />
<br />
We will illustrate with a deliberately-picked and unusual period of time (12/31/2007 to 12/31/2010), but it is a valid illustration of the effect of volatility decay on a leveraged ETF. Before showing the results, here is a question. <br />
<br />
Over this time period, an investment of $10,000 in Vanguard 500 Index fund lost $846. Knowing this, which of these three investments do you think did the best over that time period?<br />
<br />
:a) Vanguard 500 Index Fund (VFINX)<br />
:b) ProShares Ultra S&P (SSO), "two times (2x) the daily performance of the S&P 500"<br />
:c) ProShares UltraShort S&P (SDS), "two times the inverse (-2x) of the daily performance of the S&P 500."<br />
<br />
'''The answer is (a)'''. If you reasoned that since the S&P 500 lost money, an ETF that shorts the S&P ought to have made money, you were mistaken.<br />
<br />
*The Vanguard 500 index fund lost $846. <br />
*ProShares Ultra S&P (SSO), the 2X ETF for the same index lost. But it didn't lose just twice as much as VFINX, it lost over four times as much-- $4,050.<br />
*ProShares UltraShort S&P (SDS), the 2X short ETF (-2X, gains if benchmark drops) which should have earned a profit, lost even more -- $4,595.<br />
<br />
Over this time period, you could have been right about the ''direction'' of the S&P but still lost money. And this isn't just a matter of a few percent or an expense ratio difference, ''the loss is more than 4.8 times the amount of an unleveraged direct investment''.<ref group="note">The loss is 4.8 times = 4050/846 for the 2X ETF, 5.4 times = 4,595/846 for the short -2X ETF.</ref><br />
<br />
{|style="border-collapse: collapse;" border="1" <!-- set border="1" to see table boundaries, outer table draws outside border. --><br />
|+'''Comparison of ProShares Ultra S&P (SSO), ProShares Ultra S&P 500 (SDS) and Vanguard 500 Index (VFINX)'''<br />
||[[image:Vfinx-sso-ssd-heads-you-lose-tails-you-lose.png]]<br />
|}<br />
<br />
==Historical drawdowns==<br />
A major risk presented by leveraged funds is how the impact of stock market crises can get magnified. Drawdowns (sudden loss of value) will get amplified in both depth and duration. The following chart (1955-2019) presents a simulation of a regular index fund, a 2x leverage fund and a 3x leverage, all tracking the S&P 500 index. As you can see, the oil crisis in the 70s would have been magnified with dizzying drops and drawdowns lasting more than a decade. The more recent Internet and financial crises would have led to nearly two decades of misery, finally followed by a steep recovery. Staying the course with a long term investment in leveraged funds during such a crisis would seem extremely challenging.<ref name="blog">[https://finpage.blog/2019/12/12/leveraging-sp-500-quantitative-analysis/ Bogleheads blog (2019): Leveraging S&P 500 – Quantitative Analysis]</ref><br />
<br />
{|<br />
[[File:S&P 500 LETF Drawdowns.jpg|960px]]<br />
|}<br />
<br />
==Risks and rewards==<br />
As clearly illustrated by the charts in previous sections, leveraged (and inverse) ETFs are much more volatile than corresponding indices (and index funds). Between Jan-10 and Dec-19, the standard deviation of monthly returns was amplified by approximately the amount of leverage:<ref name="blog"/><br />
* VFIAX (regular S&P 500 passive index fund from Vanguard): 12.5%<br />
* SSO (ProShares Ultra S&P500, 2x leverage): 25.3%<br />
* UPRO (ProShares UltraPro S&P500, 3x leverage): 38.4%<br />
<br />
A historical simulation of leveraged funds over the 1955 to 2019 time period showed similar characteristics:<ref name="blog"/><br />
* Regular S&P 500 passive fund: 14.4%<br />
* S&P 500 2x leverage: 29.0%<br />
* S&P 500 3x leverage: 43.6%<br />
<br />
The question becomes the following. If a steely investor had been able to cope with such increased volatility (including dizzying drawdowns), what would have been the rewards for staying the course? Real-life funds would have provided attractive annualized growth from 2010 to 2019 (VFIAX 13.5%, SSO 23.6%, UPRO 32.8%), but this isn't a terribly representative time period, since it was essentially a long bull market. <br />
<br />
Using the historical simulation, we can study rolling (annualized) returns over a much longer time frame, including three major crises of the US stock market.<ref name="blog"/><br />
<br />
{|<br />
[[File:Rolling_Periods_CAGR_Stats_Leveraging_2x_3x.jpg|960px]]<br />
|}<br />
<br />
As the table indicates, over short periods of time, leveraging can deliver stronger returns, albeit with a lot of risk. Over longer periods, the return premium disappears on average while the risk (dispersion of outcomes) remains very acute. Overall, the case for rewards (i.e. improved annualized returns) seems remarkably weak for long-term buy and hold investments, compared to the volatility and drawdown risks previously quantified.<br />
<br />
==Summary==<br />
Regardless of what you might or might not think about the possible usefulness of a long-term [[leverage|leveraged]] position achieved by using margin, leveraged and inverse ETFs are completely different products and do not give remotely comparable results. <br />
<br />
In short, leveraged and inverse ETFs are specialized products, which present major risks as long-term buy and hold investments and little rewards in return for such risks. The use of such products as part of a regular asset allocation should be discouraged.<br />
<br />
==Other points of view==<br />
Long-term risks associated with a specific asset can sometimes be mitigated by the use of another asset (e.g. using rebalancing and risk parity strategies<ref>Investopedia: [https://www.investopedia.com/terms/r/risk-parity.asp Risk Parity]</ref>). These are sophisticated portfolios, constructed by investors who fully understand all the risks described above; they accept the irreducible potential risk of any portfolio, no matter how carefully constructed, that contains high-risk assets.<br />
<br />
An article in the ''Journal of Indexes,'' authored by Joanne Hill and George Foster, both of ProShares, note that "it is likely that leveraged and inverse ETFs are commonly being utilized as short-term tactical trading tools" but state that, nevertheless, by applying certain rebalancing strategies, "leveraged and inverse funds have been and can be used successfully for periods longer than one day." The article, "Understanding Returns of Leveraged and Inverse Funds",<ref>Hill, Joanne, and George Foster (2009), [http://www.indexuniverse.com/publications/journalofindexes/joi-articles/6414-understanding-returns-of-leveraged-and-inverse-funds.html?showall=&fullart=1&start=7 Understanding Returns of Leveraged and Inverse Funds]. Dr. Hill is Head of Investment Strategy at ProShares; George Foster is Chief Investment Officer.</ref> gives a detailed analysis of how volatility affects leveraged and inverse ETFs.<br />
<br />
Another article authored by Cliff Asness, from AQR Capital Management, "Risk Parity: Why We Lever",<ref>Click Asness (2014), [https://www.aqr.com/Insights/Perspectives/Risk-Parity-Why-We-Fight-Lever Risk Parity: Why We Lever].</ref> advocates that "willingness to use modest leverage allows a risk parity investor to build a more diversified, more balanced, higher-return-for-the-risk-taken portfolio."<br />
<br />
==See also==<br />
*[[Exchange-traded funds]]<br />
*[[Leverage]]<br />
<br />
==Notes==<br />
<references group="note" /><br />
<br />
==References==<br />
<references /><br />
<br />
==External links==<br />
*[http://www.proshares.com/considerations_geared_investing.html Considerations for Geared Investing], by [http://www.proshares.com/about/index.html ProShares]. A brief overview of Geared ETFs.<br />
*[http://www.proshares.com/media/documents/geared_fund_performance.pdf What You Should Know about Geared Fund Performance], by [http://www.proshares.com/about/index.html ProShares]. A guide that covers several key concepts about geared fund performance.<br />
*{{Forum post|title = <nowiki>[Wiki article update - Inverse and leveraged ETFs]</nowiki>|t= 296428| date = Nov 30, 2019}}<br />
{{Mutual funds}}<br />
[[Category:ETFs]]</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Leveraged_and_inverse_ETFs&diff=68857
Leveraged and inverse ETFs
2020-01-28T23:35:21Z
<p>Siamond: /* Risks and rewards */ Stats, text and table to fully account for 2019</p>
<hr />
<div>'''{{PAGENAME}}''' ([[Exchange-traded funds]])<ref group="note">''Leveraging'' is also called ''gearing''. ''Leveraged'' ETFs and ''Geared'' ETFs mean the same thing.</ref> are ETF structures intended to provide returns that are positive or negative multiples of an equivalent ETF benchmark. The purpose of this article is to explain why these ETFs present significant risks as long-term investments.<br />
{{Warning|The SEC and FINRA has issued a joint alert, "Leveraged and Inverse ETFs: Specialized Products with Extra Risks for Buy-and-Hold Investors." It states:<ref name="SEC">{{cite web| publisher=Financial Industry Regulator Authority| url=http://www.finra.org/investors/alerts/leveraged-and-inverse-etfs-specialized-products-extra-risks-buy-and-hold-investors| title=Leveraged and Inverse ETFs: Specialized Products with Extra Risks for Buy-and-Hold Investors| date=August 18, 2009}}</ref><blockquote>The SEC staff and FINRA are issuing this Alert because we believe individual investors may be confused about the performance objectives of leveraged and inverse exchange-traded funds (ETFs). Leveraged and inverse ETFs typically are designed to achieve their stated performance objectives on a daily basis. Some investors might invest in these ETFs with the expectation that the ETFs may meet their stated daily performance objectives over the long term as well. [...] Only invest if you are confident the product can help you meet your investment objectives and you are knowledgeable and comfortable with the risks associated with these specialized ETFs.</blockquote>}}<br />
<br />
==Overview==<br />
There are 3 structures:<ref name="SEC" /><br />
<br />
*'''Leveraged ETFs''' seek to deliver multiples of the performance of the index or benchmark they track.<br />
*'''Inverse ETFs''' (also called "short" funds) seek to deliver the ''opposite'' of the performance of the index or benchmark they track.<br />
*'''Leveraged inverse ETFs''' (also known as "ultra short" funds) seek to achieve a return that is a multiple of the inverse performance of the underlying index.<br />
<br />
Here are several example ETF descriptions:<br />
*'''ProShares UltraPro S&P500 (UPRO)''' seeks daily investment results, before fees and expenses, that correspond to three times (3x) the daily performance of the S&P 500<sup>®</sup>.<ref>[http://www.proshares.com/funds/upro.html ProShares ETFs: UltraPro S&P500]</ref><br />
*'''ProShares Ultra S&P500 (SSO)''' seeks daily investment results, before fees and expenses, that correspond to two times (2x) the daily performance of the S&P 500<sup>®</sup>.<ref>[http://www.proshares.com/funds/sso.html ProShares ETFs: Ultra S&P500]</ref><br />
*'''ProShares UltraShort S&P500 (SDS)''' seeks daily investment results, before fees and expenses, that correspond to two times the inverse (-2x) of the daily performance of the S&P 500<sup>®</sup>.<ref>[http://www.proshares.com/funds/sds.html ProShares ETFs: UltraShort S&P500]</ref><br />
*'''Direxion Emerging Markets Bear 3X ETF (EDZ)''' seeks daily investment results, before fees and expenses, of 300% of the inverse (or opposite) of the performance of the MSCI Emerging Markets Index.<ref>[http://www.direxionfunds.com/products/direxion-daily-emerging-markets-bear-3x-etf Direxion Daily Emerging Markets Bear 3x Shares]</ref><br />
<br />
Let's look at the 4th example fund provider, Direxion. Notice that Direxion itself<ref>[http://www.direxionfunds.com/signs Leveraged ETF List | Direxion]</ref> says these funds are for "short-term trading." This is not a detail or a pro forma disclaimer - it is explicitly displayed in the figure below.<br />
<br />
{|style="border-collapse: collapse;" border="1" <!-- set border="1" to see table boundaries, outer table draws outside border. --><br />
|+'''Direxion ETF Fund Categories'''<br />
||<br />
[[image:Direxionsayshorterm.png]]<br />
|}<br />
<br />
The first category, "Long Term Investment" contains 3 ETFs which match a benchmark. The second category contains 2 leveraged ETFs ("3X") and is titled "Short Term Trading" which is a warning sign that these ETFs will perform differently than those intended for long-term investments. The link "Are Direxion Shares ETFs for you?" is an additional warning sign, as there would be no reason to ask this question if these ETFs performed similarly to ETFs intended for long-term investments.<br />
<br />
Brokerages typically require customers to sign a special disclaimer in order to open a margin account. Everyone understands that using leverage in the form of a margin account is taking on a big risk, the risk of losing more than your total investment. It is a mistake to think you can get essentially similar results, more conveniently and without the risk of losing more than your investment, simply by using an inverse or leveraged ETF.<br />
<br />
Anyone thinking of using an inverse or leveraged ETF needs to read and understand the fund company's factsheets and prospectus, which disclose the issues in language varying from veiled to clear.<br />
<br />
==How does a daily leveraged ETF work?==<br />
A daily leveraged ETF holds a combination of derivatives and actual securities to track a multiple of the underlying index's daily performance.<br />
<br />
Let's examine ProShares UltraPro S&P500 (UPRO), which promises to deliver 3x the daily performance of the S&P 500. It does this by holding 77% individual S&P 500 stocks, nominal exposure to 215% of the S&P 500 through total return swaps, and 8% S&P futures. Add it all up, and you get exposure to 300% of the S&P 500’s daily performance.<ref>[https://www.proshares.com/resources/prospectus_reports.html ProShares Geared Funds Annual] 5/31/2019, market exposure on printed page LIX.</ref><br />
<br />
Total return swaps are contracts between the ETF and major investment banks. For UPRO, every day the banks pay the ETF the value of the S&P 500’s total return for that day, and in return the ETF pays the banks a pre-negotiated rate of interest, which is close to the short term treasury rate. As of May 2019, the borrowing rate of some UPRO's swap agreements was 3.01%.<ref>[https://www.proshares.com/resources/prospectus_reports.html ProShares Geared Funds Annual] 5/31/2019, swap agreements on printed page 138, e.g. BNP Paribas rate as of May 31, 2019.</ref> The corresponding cost is NOT included in UPRO's 0.92% expense ratio.<br />
<br />
==Daily results are significantly different than long-term==<br />
It is critical to understand that a movement in one direction followed by an equal movement in the opposite direction will '''not''' get you back to the starting value. For example, a gain of 10% followed by a loss of 10% will end up with a loss of 1.0%.<ref name="ReturnCalc">Details are in this {{Forum post| p=4882043|title = Re: <nowiki>[Wiki article update - Inverse and leveraged ETFs]</nowiki> |author = LadyGeek | date = December 09, 2019}}</ref> This is nothing but math at work. The math works the same for any investment – regardless if it’s a single stock or a fund. See [[Percentage gain and loss]] for the details.<br />
<br />
This math will be very evident as a fund performs over time. If the market has equal gains and losses over a period of time, the fund’s value will always be lower. For example, 6 consecutive days which alternate as +10% then -10% will result in a loss of 3.0%.<ref name="ReturnCalc" /> The change in loss from 1.0% to 3.0% is known as ''volatility decay''.<ref group="note">Also known as [[volatility drag]], but ''volatility decay'' is the term used for leveraged funds.</ref><br />
<br />
Over the course of a single day, the fund will generate a return as advertised. For example, a 3X leveraged fund will generate three times the gain (and loss) of an unleveraged fund.<br />
<br />
However, that’s not the entire story. Leveraged funds [[rebalance]] their exposure to their underlying benchmarks on a daily basis by trimming or adding to their positions. Over time, a longer-term investor is unlikely to continue to receive the fund's multiple of the benchmark's returns.<ref name="ProShares">{{cite web| publisher=ProShares| url=https://www.proshares.com/funds/performance/the_universal_effects_of_compounding.html| title=Effects Of Daily Rebalancing and Compounding on Geared Investing| accessdate=December 09, 2019}}</ref><br />
<br />
Investment returns compound over time. The effects of compounding will also cause the fund to deviate from the fund's stated objective, e.g. 2X or 3X of the index's return. In trending periods, compounding can enhance returns, but in volatile periods, compounding may hurt returns. Generally speaking, the greater the multiple or more volatile a fund's benchmark, the more pronounced the effects can be.<ref name="ProShares" /><br />
<br />
It is why the fund’s fact sheets have disclaimers stating that performance is only guaranteed on a daily basis.<br />
<br />
==A comprehensive example==<br />
<br />
Now, let's illustrate how big the difference is between "daily" and long-term results.<br />
<br />
Some investors think they see interesting theoretical possibilities for using [[leverage]] in long-term investing. If so, they should '''not''' think that over long periods of time they can get double the return of the S&P 500 simply by investing in a 2X leveraged S&P 500 ETF. <br />
<br />
The word "daily" has a very precise meaning. These products double or triple the long or short index for a single day, so '''if you are someone who trades in and out of positions on a daily basis''', they actually do pretty much what you'd expect. Not so over long periods, '''and the difference can be large'''.<br />
<br />
The ETF companies disclose this point fairly clearly in the factsheets, such as:<br />
<br />
<blockquote>'''Direxion:''' "This leveraged ETF seeks a return that is -300% the return of its benchmark index for a single day. The fund should not be expected to provide three times the return of the benchmark’s cumulative return for periods greater than a day.", and<br><br><br />
<br />
'''ProShares:''' "Due to the compounding of daily returns, ProShares' returns over periods other than one day will likely '''differ in amount''' and possibly '''<nowiki>[differ in]</nowiki> direction''' from the target return for the same period."</blockquote><br />
<br />
In order to illustrate the potential impact, let's ask: "'''How much is that in dollars?'''" which is quantified in the following sections.<br />
<br />
==="differ in amount"===<br />
"Differ in amount" means that the "2X" fund might not deliver twice the return of the index. For example, ProShares Ultra S&P 500 ETF, SSO began in 6/2007. $10,000 invested in the Vanguard 500 Index fund would have gained a total of $6,966 in total return since that time (6/20/2006 to 12/31/2013). Did the Ultra fund earn twice that ($13,932)?<br />
<br />
{|style="border-collapse: collapse;" border="1" <!-- set border="1" to see table boundaries, outer table draws outside border. --><br />
|+'''Comparison of ProShares Ultra S&P 500 (SSO) to Vanguard 500 Index (VFINX)'''<br />
||[[image:Vfinx-beats-sso.png]]<br />
|}<br />
<br />
It did not. It earned $6,097, which is less than the Vanguard 500 Index fund earnings. ''The 2X ETF earned less than the straight, unleveraged, direct investment.''<br />
<br />
==="differ in direction"===<br />
This is a way of saying that over periods of more than a day, your ETF could go down even when the inverse or leveraged index it is tied to goes up. This is why ProShares says "Investors should monitor their holdings consistent with their strategies, as frequently as daily."<br />
<br />
We will illustrate with a deliberately-picked and unusual period of time (12/31/2007 to 12/31/2010), but it is a valid illustration of the effect of volatility decay on a leveraged ETF. Before showing the results, here is a question. <br />
<br />
Over this time period, an investment of $10,000 in Vanguard 500 Index fund lost $846. Knowing this, which of these three investments do you think did the best over that time period?<br />
<br />
:a) Vanguard 500 Index Fund (VFINX)<br />
:b) ProShares Ultra S&P (SSO), "two times (2x) the daily performance of the S&P 500"<br />
:c) ProShares UltraShort S&P (SDS), "two times the inverse (-2x) of the daily performance of the S&P 500."<br />
<br />
'''The answer is (a)'''. If you reasoned that since the S&P 500 lost money, an ETF that shorts the S&P ought to have made money, you were mistaken.<br />
<br />
*The Vanguard 500 index fund lost $846. <br />
*ProShares Ultra S&P (SSO), the 2X ETF for the same index lost. But it didn't lose just twice as much as VFINX, it lost over four times as much-- $4,050.<br />
*ProShares UltraShort S&P (SDS), the 2X short ETF (-2X, gains if benchmark drops) which should have earned a profit, lost even more -- $4,595.<br />
<br />
Over this time period, you could have been right about the ''direction'' of the S&P but still lost money. And this isn't just a matter of a few percent or an expense ratio difference, ''the loss is more than 4.8 times the amount of an unleveraged direct investment''.<ref group="note">The loss is 4.8 times = 4050/846 for the 2X ETF, 5.4 times = 4,595/846 for the short -2X ETF.</ref><br />
<br />
{|style="border-collapse: collapse;" border="1" <!-- set border="1" to see table boundaries, outer table draws outside border. --><br />
|+'''Comparison of ProShares Ultra S&P (SSO), ProShares Ultra S&P 500 (SDS) and Vanguard 500 Index (VFINX)'''<br />
||[[image:Vfinx-sso-ssd-heads-you-lose-tails-you-lose.png]]<br />
|}<br />
<br />
==Historical drawdowns==<br />
A major risk presented by leveraged funds is how the impact of stock market crises can get magnified. Drawdowns (sudden loss of value) will get amplified in both depth and duration. The following chart (1955-2019) presents a simulation of a regular index fund, a 2x leverage fund and a 3x leverage, all tracking the S&P 500 index. As you can see, the oil crisis in the 70s would have been magnified with dizzying drops and drawdowns lasting more than a decade. The more recent Internet and financial crises would have led to nearly two decades of misery, finally followed by a steep recovery. Staying the course with a long term investment in leveraged funds during such a crisis would seem extremely challenging.<ref name="blog">[https://finpage.blog/2019/12/12/leveraging-sp-500-quantitative-analysis/ Bogleheads blog (2019): Leveraging S&P 500 – Quantitative Analysis]</ref><br />
<br />
{|<br />
[[File:S&P 500 LETF Drawdowns.jpg|960px]]<br />
|}<br />
<br />
==Risks and rewards==<br />
As clearly illustrated by the charts in previous sections, leveraged (and inverse) ETFs are much more volatile than corresponding indices (and index funds). Between Jan-10 and Dec-19, the standard deviation of monthly returns was amplified by approximately the amount of leverage:<ref name="blog"/><br />
* VFINX (regular S&P 500 passive index fund from Vanguard): 12.5%<br />
* SSO (ProShares Ultra S&P500, 2x leverage): 25.3%<br />
* UPRO (ProShares UltraPro S&P500, 3x leverage): 38.4%<br />
<br />
A historical simulation of leveraged funds over the 1955 to 2019 time period showed similar characteristics:<ref name="blog"/><br />
* Regular S&P 500 passive fund: 14.4%<br />
* S&P 500 2x leverage: 29.0%<br />
* S&P 500 3x leverage: 43.6%<br />
<br />
The question becomes the following. If a steely investor had been able to cope with such increased volatility (including dizzying drawdowns), what would have been the rewards for staying the course? Real-life funds would have provided attractive annualized growth from 2010 to 2019 (VFINX 13.4%, SSO 23.6%, UPRO 32.8%), but this isn't a terribly representative time period, since it was essentially a long bull market. <br />
<br />
Using the historical simulation, we can study rolling (annualized) returns over a much longer time frame, including three major crises of the US stock market.<ref name="blog"/><br />
<br />
{|<br />
[[File:Rolling_Periods_CAGR_Stats_Leveraging_2x_3x.jpg|960px]]<br />
|}<br />
<br />
As the table indicates, over short periods of time, leveraging can deliver stronger returns, albeit with a lot of risk. Over longer periods, the return premium disappears on average while the risk (dispersion of outcomes) remains very acute. Overall, the case for rewards (i.e. improved annualized returns) seems remarkably weak for long-term buy and hold investments, compared to the volatility and drawdown risks previously quantified.<br />
<br />
==Summary==<br />
Regardless of what you might or might not think about the possible usefulness of a long-term [[leverage|leveraged]] position achieved by using margin, leveraged and inverse ETFs are completely different products and do not give remotely comparable results. <br />
<br />
In short, leveraged and inverse ETFs are specialized products, which present major risks as long-term buy and hold investments and little rewards in return for such risks. The use of such products as part of a regular asset allocation should be discouraged.<br />
<br />
==Other points of view==<br />
Long-term risks associated with a specific asset can sometimes be mitigated by the use of another asset (e.g. using rebalancing and risk parity strategies<ref>Investopedia: [https://www.investopedia.com/terms/r/risk-parity.asp Risk Parity]</ref>). These are sophisticated portfolios, constructed by investors who fully understand all the risks described above; they accept the irreducible potential risk of any portfolio, no matter how carefully constructed, that contains high-risk assets.<br />
<br />
An article in the ''Journal of Indexes,'' authored by Joanne Hill and George Foster, both of ProShares, note that "it is likely that leveraged and inverse ETFs are commonly being utilized as short-term tactical trading tools" but state that, nevertheless, by applying certain rebalancing strategies, "leveraged and inverse funds have been and can be used successfully for periods longer than one day." The article, "Understanding Returns of Leveraged and Inverse Funds",<ref>Hill, Joanne, and George Foster (2009), [http://www.indexuniverse.com/publications/journalofindexes/joi-articles/6414-understanding-returns-of-leveraged-and-inverse-funds.html?showall=&fullart=1&start=7 Understanding Returns of Leveraged and Inverse Funds]. Dr. Hill is Head of Investment Strategy at ProShares; George Foster is Chief Investment Officer.</ref> gives a detailed analysis of how volatility affects leveraged and inverse ETFs.<br />
<br />
Another article authored by Cliff Asness, from AQR Capital Management, "Risk Parity: Why We Lever",<ref>Click Asness (2014), [https://www.aqr.com/Insights/Perspectives/Risk-Parity-Why-We-Fight-Lever Risk Parity: Why We Lever].</ref> advocates that "willingness to use modest leverage allows a risk parity investor to build a more diversified, more balanced, higher-return-for-the-risk-taken portfolio."<br />
<br />
==See also==<br />
*[[Exchange-traded funds]]<br />
*[[Leverage]]<br />
<br />
==Notes==<br />
<references group="note" /><br />
<br />
==References==<br />
<references /><br />
<br />
==External links==<br />
*[http://www.proshares.com/considerations_geared_investing.html Considerations for Geared Investing], by [http://www.proshares.com/about/index.html ProShares]. A brief overview of Geared ETFs.<br />
*[http://www.proshares.com/media/documents/geared_fund_performance.pdf What You Should Know about Geared Fund Performance], by [http://www.proshares.com/about/index.html ProShares]. A guide that covers several key concepts about geared fund performance.<br />
*{{Forum post|title = <nowiki>[Wiki article update - Inverse and leveraged ETFs]</nowiki>|t= 296428| date = Nov 30, 2019}}<br />
{{Mutual funds}}<br />
[[Category:ETFs]]</div>
Siamond
https://www.bogleheads.org/w/index.php?title=File:Rolling_Periods_CAGR_Stats_Leveraging_2x_3x.jpg&diff=68856
File:Rolling Periods CAGR Stats Leveraging 2x 3x.jpg
2020-01-28T23:20:59Z
<p>Siamond: Siamond uploaded a new version of File:Rolling Periods CAGR Stats Leveraging 2x 3x.jpg</p>
<hr />
<div>== Summary ==<br />
Stats about S&P 500 Leveraging over time</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Leveraged_and_inverse_ETFs&diff=68855
Leveraged and inverse ETFs
2020-01-28T23:19:36Z
<p>Siamond: /* Historical drawdowns */ chart now includes all of 2019</p>
<hr />
<div>'''{{PAGENAME}}''' ([[Exchange-traded funds]])<ref group="note">''Leveraging'' is also called ''gearing''. ''Leveraged'' ETFs and ''Geared'' ETFs mean the same thing.</ref> are ETF structures intended to provide returns that are positive or negative multiples of an equivalent ETF benchmark. The purpose of this article is to explain why these ETFs present significant risks as long-term investments.<br />
{{Warning|The SEC and FINRA has issued a joint alert, "Leveraged and Inverse ETFs: Specialized Products with Extra Risks for Buy-and-Hold Investors." It states:<ref name="SEC">{{cite web| publisher=Financial Industry Regulator Authority| url=http://www.finra.org/investors/alerts/leveraged-and-inverse-etfs-specialized-products-extra-risks-buy-and-hold-investors| title=Leveraged and Inverse ETFs: Specialized Products with Extra Risks for Buy-and-Hold Investors| date=August 18, 2009}}</ref><blockquote>The SEC staff and FINRA are issuing this Alert because we believe individual investors may be confused about the performance objectives of leveraged and inverse exchange-traded funds (ETFs). Leveraged and inverse ETFs typically are designed to achieve their stated performance objectives on a daily basis. Some investors might invest in these ETFs with the expectation that the ETFs may meet their stated daily performance objectives over the long term as well. [...] Only invest if you are confident the product can help you meet your investment objectives and you are knowledgeable and comfortable with the risks associated with these specialized ETFs.</blockquote>}}<br />
<br />
==Overview==<br />
There are 3 structures:<ref name="SEC" /><br />
<br />
*'''Leveraged ETFs''' seek to deliver multiples of the performance of the index or benchmark they track.<br />
*'''Inverse ETFs''' (also called "short" funds) seek to deliver the ''opposite'' of the performance of the index or benchmark they track.<br />
*'''Leveraged inverse ETFs''' (also known as "ultra short" funds) seek to achieve a return that is a multiple of the inverse performance of the underlying index.<br />
<br />
Here are several example ETF descriptions:<br />
*'''ProShares UltraPro S&P500 (UPRO)''' seeks daily investment results, before fees and expenses, that correspond to three times (3x) the daily performance of the S&P 500<sup>®</sup>.<ref>[http://www.proshares.com/funds/upro.html ProShares ETFs: UltraPro S&P500]</ref><br />
*'''ProShares Ultra S&P500 (SSO)''' seeks daily investment results, before fees and expenses, that correspond to two times (2x) the daily performance of the S&P 500<sup>®</sup>.<ref>[http://www.proshares.com/funds/sso.html ProShares ETFs: Ultra S&P500]</ref><br />
*'''ProShares UltraShort S&P500 (SDS)''' seeks daily investment results, before fees and expenses, that correspond to two times the inverse (-2x) of the daily performance of the S&P 500<sup>®</sup>.<ref>[http://www.proshares.com/funds/sds.html ProShares ETFs: UltraShort S&P500]</ref><br />
*'''Direxion Emerging Markets Bear 3X ETF (EDZ)''' seeks daily investment results, before fees and expenses, of 300% of the inverse (or opposite) of the performance of the MSCI Emerging Markets Index.<ref>[http://www.direxionfunds.com/products/direxion-daily-emerging-markets-bear-3x-etf Direxion Daily Emerging Markets Bear 3x Shares]</ref><br />
<br />
Let's look at the 4th example fund provider, Direxion. Notice that Direxion itself<ref>[http://www.direxionfunds.com/signs Leveraged ETF List | Direxion]</ref> says these funds are for "short-term trading." This is not a detail or a pro forma disclaimer - it is explicitly displayed in the figure below.<br />
<br />
{|style="border-collapse: collapse;" border="1" <!-- set border="1" to see table boundaries, outer table draws outside border. --><br />
|+'''Direxion ETF Fund Categories'''<br />
||<br />
[[image:Direxionsayshorterm.png]]<br />
|}<br />
<br />
The first category, "Long Term Investment" contains 3 ETFs which match a benchmark. The second category contains 2 leveraged ETFs ("3X") and is titled "Short Term Trading" which is a warning sign that these ETFs will perform differently than those intended for long-term investments. The link "Are Direxion Shares ETFs for you?" is an additional warning sign, as there would be no reason to ask this question if these ETFs performed similarly to ETFs intended for long-term investments.<br />
<br />
Brokerages typically require customers to sign a special disclaimer in order to open a margin account. Everyone understands that using leverage in the form of a margin account is taking on a big risk, the risk of losing more than your total investment. It is a mistake to think you can get essentially similar results, more conveniently and without the risk of losing more than your investment, simply by using an inverse or leveraged ETF.<br />
<br />
Anyone thinking of using an inverse or leveraged ETF needs to read and understand the fund company's factsheets and prospectus, which disclose the issues in language varying from veiled to clear.<br />
<br />
==How does a daily leveraged ETF work?==<br />
A daily leveraged ETF holds a combination of derivatives and actual securities to track a multiple of the underlying index's daily performance.<br />
<br />
Let's examine ProShares UltraPro S&P500 (UPRO), which promises to deliver 3x the daily performance of the S&P 500. It does this by holding 77% individual S&P 500 stocks, nominal exposure to 215% of the S&P 500 through total return swaps, and 8% S&P futures. Add it all up, and you get exposure to 300% of the S&P 500’s daily performance.<ref>[https://www.proshares.com/resources/prospectus_reports.html ProShares Geared Funds Annual] 5/31/2019, market exposure on printed page LIX.</ref><br />
<br />
Total return swaps are contracts between the ETF and major investment banks. For UPRO, every day the banks pay the ETF the value of the S&P 500’s total return for that day, and in return the ETF pays the banks a pre-negotiated rate of interest, which is close to the short term treasury rate. As of May 2019, the borrowing rate of some UPRO's swap agreements was 3.01%.<ref>[https://www.proshares.com/resources/prospectus_reports.html ProShares Geared Funds Annual] 5/31/2019, swap agreements on printed page 138, e.g. BNP Paribas rate as of May 31, 2019.</ref> The corresponding cost is NOT included in UPRO's 0.92% expense ratio.<br />
<br />
==Daily results are significantly different than long-term==<br />
It is critical to understand that a movement in one direction followed by an equal movement in the opposite direction will '''not''' get you back to the starting value. For example, a gain of 10% followed by a loss of 10% will end up with a loss of 1.0%.<ref name="ReturnCalc">Details are in this {{Forum post| p=4882043|title = Re: <nowiki>[Wiki article update - Inverse and leveraged ETFs]</nowiki> |author = LadyGeek | date = December 09, 2019}}</ref> This is nothing but math at work. The math works the same for any investment – regardless if it’s a single stock or a fund. See [[Percentage gain and loss]] for the details.<br />
<br />
This math will be very evident as a fund performs over time. If the market has equal gains and losses over a period of time, the fund’s value will always be lower. For example, 6 consecutive days which alternate as +10% then -10% will result in a loss of 3.0%.<ref name="ReturnCalc" /> The change in loss from 1.0% to 3.0% is known as ''volatility decay''.<ref group="note">Also known as [[volatility drag]], but ''volatility decay'' is the term used for leveraged funds.</ref><br />
<br />
Over the course of a single day, the fund will generate a return as advertised. For example, a 3X leveraged fund will generate three times the gain (and loss) of an unleveraged fund.<br />
<br />
However, that’s not the entire story. Leveraged funds [[rebalance]] their exposure to their underlying benchmarks on a daily basis by trimming or adding to their positions. Over time, a longer-term investor is unlikely to continue to receive the fund's multiple of the benchmark's returns.<ref name="ProShares">{{cite web| publisher=ProShares| url=https://www.proshares.com/funds/performance/the_universal_effects_of_compounding.html| title=Effects Of Daily Rebalancing and Compounding on Geared Investing| accessdate=December 09, 2019}}</ref><br />
<br />
Investment returns compound over time. The effects of compounding will also cause the fund to deviate from the fund's stated objective, e.g. 2X or 3X of the index's return. In trending periods, compounding can enhance returns, but in volatile periods, compounding may hurt returns. Generally speaking, the greater the multiple or more volatile a fund's benchmark, the more pronounced the effects can be.<ref name="ProShares" /><br />
<br />
It is why the fund’s fact sheets have disclaimers stating that performance is only guaranteed on a daily basis.<br />
<br />
==A comprehensive example==<br />
<br />
Now, let's illustrate how big the difference is between "daily" and long-term results.<br />
<br />
Some investors think they see interesting theoretical possibilities for using [[leverage]] in long-term investing. If so, they should '''not''' think that over long periods of time they can get double the return of the S&P 500 simply by investing in a 2X leveraged S&P 500 ETF. <br />
<br />
The word "daily" has a very precise meaning. These products double or triple the long or short index for a single day, so '''if you are someone who trades in and out of positions on a daily basis''', they actually do pretty much what you'd expect. Not so over long periods, '''and the difference can be large'''.<br />
<br />
The ETF companies disclose this point fairly clearly in the factsheets, such as:<br />
<br />
<blockquote>'''Direxion:''' "This leveraged ETF seeks a return that is -300% the return of its benchmark index for a single day. The fund should not be expected to provide three times the return of the benchmark’s cumulative return for periods greater than a day.", and<br><br><br />
<br />
'''ProShares:''' "Due to the compounding of daily returns, ProShares' returns over periods other than one day will likely '''differ in amount''' and possibly '''<nowiki>[differ in]</nowiki> direction''' from the target return for the same period."</blockquote><br />
<br />
In order to illustrate the potential impact, let's ask: "'''How much is that in dollars?'''" which is quantified in the following sections.<br />
<br />
==="differ in amount"===<br />
"Differ in amount" means that the "2X" fund might not deliver twice the return of the index. For example, ProShares Ultra S&P 500 ETF, SSO began in 6/2007. $10,000 invested in the Vanguard 500 Index fund would have gained a total of $6,966 in total return since that time (6/20/2006 to 12/31/2013). Did the Ultra fund earn twice that ($13,932)?<br />
<br />
{|style="border-collapse: collapse;" border="1" <!-- set border="1" to see table boundaries, outer table draws outside border. --><br />
|+'''Comparison of ProShares Ultra S&P 500 (SSO) to Vanguard 500 Index (VFINX)'''<br />
||[[image:Vfinx-beats-sso.png]]<br />
|}<br />
<br />
It did not. It earned $6,097, which is less than the Vanguard 500 Index fund earnings. ''The 2X ETF earned less than the straight, unleveraged, direct investment.''<br />
<br />
==="differ in direction"===<br />
This is a way of saying that over periods of more than a day, your ETF could go down even when the inverse or leveraged index it is tied to goes up. This is why ProShares says "Investors should monitor their holdings consistent with their strategies, as frequently as daily."<br />
<br />
We will illustrate with a deliberately-picked and unusual period of time (12/31/2007 to 12/31/2010), but it is a valid illustration of the effect of volatility decay on a leveraged ETF. Before showing the results, here is a question. <br />
<br />
Over this time period, an investment of $10,000 in Vanguard 500 Index fund lost $846. Knowing this, which of these three investments do you think did the best over that time period?<br />
<br />
:a) Vanguard 500 Index Fund (VFINX)<br />
:b) ProShares Ultra S&P (SSO), "two times (2x) the daily performance of the S&P 500"<br />
:c) ProShares UltraShort S&P (SDS), "two times the inverse (-2x) of the daily performance of the S&P 500."<br />
<br />
'''The answer is (a)'''. If you reasoned that since the S&P 500 lost money, an ETF that shorts the S&P ought to have made money, you were mistaken.<br />
<br />
*The Vanguard 500 index fund lost $846. <br />
*ProShares Ultra S&P (SSO), the 2X ETF for the same index lost. But it didn't lose just twice as much as VFINX, it lost over four times as much-- $4,050.<br />
*ProShares UltraShort S&P (SDS), the 2X short ETF (-2X, gains if benchmark drops) which should have earned a profit, lost even more -- $4,595.<br />
<br />
Over this time period, you could have been right about the ''direction'' of the S&P but still lost money. And this isn't just a matter of a few percent or an expense ratio difference, ''the loss is more than 4.8 times the amount of an unleveraged direct investment''.<ref group="note">The loss is 4.8 times = 4050/846 for the 2X ETF, 5.4 times = 4,595/846 for the short -2X ETF.</ref><br />
<br />
{|style="border-collapse: collapse;" border="1" <!-- set border="1" to see table boundaries, outer table draws outside border. --><br />
|+'''Comparison of ProShares Ultra S&P (SSO), ProShares Ultra S&P 500 (SDS) and Vanguard 500 Index (VFINX)'''<br />
||[[image:Vfinx-sso-ssd-heads-you-lose-tails-you-lose.png]]<br />
|}<br />
<br />
==Historical drawdowns==<br />
A major risk presented by leveraged funds is how the impact of stock market crises can get magnified. Drawdowns (sudden loss of value) will get amplified in both depth and duration. The following chart (1955-2019) presents a simulation of a regular index fund, a 2x leverage fund and a 3x leverage, all tracking the S&P 500 index. As you can see, the oil crisis in the 70s would have been magnified with dizzying drops and drawdowns lasting more than a decade. The more recent Internet and financial crises would have led to nearly two decades of misery, finally followed by a steep recovery. Staying the course with a long term investment in leveraged funds during such a crisis would seem extremely challenging.<ref name="blog">[https://finpage.blog/2019/12/12/leveraging-sp-500-quantitative-analysis/ Bogleheads blog (2019): Leveraging S&P 500 – Quantitative Analysis]</ref><br />
<br />
{|<br />
[[File:S&P 500 LETF Drawdowns.jpg|960px]]<br />
|}<br />
<br />
==Risks and rewards==<br />
As clearly illustrated by the charts in previous sections, leveraged (and inverse) ETFs are much more volatile than corresponding indices (and index funds). Between Jan-10 and Nov-19, the standard deviation of monthly returns was amplified by approximately the amount of leverage:<ref name="blog"/><br />
* VFINX (regular S&P 500 passive index fund from Vanguard): 12.5%<br />
* SSO (ProShares Ultra S&P500, 2x leverage): 25.4%<br />
* UPRO (ProShares UltraPro S&P500, 3x leverage): 38.5%<br />
<br />
A historical simulation of leveraged funds over the 1955 to 2018 time period showed similar characteristics:<ref name="blog"/><br />
* Regular S&P 500 passive fund: 14.5%<br />
* S&P 500 2x leverage: 29.1%<br />
* S&P 500 3x leverage: 43.7%<br />
<br />
The question becomes the following. If a steely investor had been able to cope with such increased volatility (including dizzying drawdowns), what would have been the rewards for staying the course? Real-life funds would have provided attractive annualized growth from Jan-10 to Nov-19 (VFINX 13%, SSO 23%, UPRO 32%), but this isn't a terribly representative time period, since it was essentially a long bull market. <br />
<br />
Using the historical simulation, we can study rolling (annualized) returns over a much longer time frame, including three major crises of the US stock market.<ref name="blog"/><br />
<br />
{|<br />
[[File:Rolling_Periods_CAGR_Stats_Leveraging_2x_3x.jpg|960px]]<br />
|}<br />
<br />
As the table indicates, over short periods of time, leveraging can deliver stronger returns, albeit with a lot of risk. Over longer periods, the return premium disappears on average while the risk (dispersion of outcomes) remains very acute. Overall, the case for rewards (i.e. improved annualized returns) seems remarkably weak for long-term buy and hold investments, compared to the volatility and drawdown risks previously quantified.<br />
<br />
==Summary==<br />
Regardless of what you might or might not think about the possible usefulness of a long-term [[leverage|leveraged]] position achieved by using margin, leveraged and inverse ETFs are completely different products and do not give remotely comparable results. <br />
<br />
In short, leveraged and inverse ETFs are specialized products, which present major risks as long-term buy and hold investments and little rewards in return for such risks. The use of such products as part of a regular asset allocation should be discouraged.<br />
<br />
==Other points of view==<br />
Long-term risks associated with a specific asset can sometimes be mitigated by the use of another asset (e.g. using rebalancing and risk parity strategies<ref>Investopedia: [https://www.investopedia.com/terms/r/risk-parity.asp Risk Parity]</ref>). These are sophisticated portfolios, constructed by investors who fully understand all the risks described above; they accept the irreducible potential risk of any portfolio, no matter how carefully constructed, that contains high-risk assets.<br />
<br />
An article in the ''Journal of Indexes,'' authored by Joanne Hill and George Foster, both of ProShares, note that "it is likely that leveraged and inverse ETFs are commonly being utilized as short-term tactical trading tools" but state that, nevertheless, by applying certain rebalancing strategies, "leveraged and inverse funds have been and can be used successfully for periods longer than one day." The article, "Understanding Returns of Leveraged and Inverse Funds",<ref>Hill, Joanne, and George Foster (2009), [http://www.indexuniverse.com/publications/journalofindexes/joi-articles/6414-understanding-returns-of-leveraged-and-inverse-funds.html?showall=&fullart=1&start=7 Understanding Returns of Leveraged and Inverse Funds]. Dr. Hill is Head of Investment Strategy at ProShares; George Foster is Chief Investment Officer.</ref> gives a detailed analysis of how volatility affects leveraged and inverse ETFs.<br />
<br />
Another article authored by Cliff Asness, from AQR Capital Management, "Risk Parity: Why We Lever",<ref>Click Asness (2014), [https://www.aqr.com/Insights/Perspectives/Risk-Parity-Why-We-Fight-Lever Risk Parity: Why We Lever].</ref> advocates that "willingness to use modest leverage allows a risk parity investor to build a more diversified, more balanced, higher-return-for-the-risk-taken portfolio."<br />
<br />
==See also==<br />
*[[Exchange-traded funds]]<br />
*[[Leverage]]<br />
<br />
==Notes==<br />
<references group="note" /><br />
<br />
==References==<br />
<references /><br />
<br />
==External links==<br />
*[http://www.proshares.com/considerations_geared_investing.html Considerations for Geared Investing], by [http://www.proshares.com/about/index.html ProShares]. A brief overview of Geared ETFs.<br />
*[http://www.proshares.com/media/documents/geared_fund_performance.pdf What You Should Know about Geared Fund Performance], by [http://www.proshares.com/about/index.html ProShares]. A guide that covers several key concepts about geared fund performance.<br />
*{{Forum post|title = <nowiki>[Wiki article update - Inverse and leveraged ETFs]</nowiki>|t= 296428| date = Nov 30, 2019}}<br />
{{Mutual funds}}<br />
[[Category:ETFs]]</div>
Siamond
https://www.bogleheads.org/w/index.php?title=File:S%26P_500_LETF_Drawdowns.jpg&diff=68854
File:S&P 500 LETF Drawdowns.jpg
2020-01-28T23:18:09Z
<p>Siamond: Siamond uploaded a new version of File:S&P 500 LETF Drawdowns.jpg</p>
<hr />
<div>== Summary ==<br />
S&P 500 Leveraged Funds - Historical drawdowns</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Simba%27s_backtesting_spreadsheet&diff=68799
Simba's backtesting spreadsheet
2020-01-11T05:35:10Z
<p>Siamond: /* Spreadsheet overview and download instructions */ link to v19a download post</p>
<hr />
<div><br />
'''{{PAGENAME}}''' describes a spreadsheet originally developed by forum member ''Simba'' for the purpose of acting as a reference for historical returns, and analyzing a portfolio based on such historical data. The spreadsheet is no longer maintained by Simba, but other forum members continue to support it and to expand functionality, as a Bogleheads community project.<br />
<br />
{{Notice|This spreadsheet and the information it contains is intended for your personal, non-commercial, use only (e.g. for educational purposes). This is a learning, researching and teaching tool, nothing more.}}<br />
<br />
==Backtesting==<br />
Backtesting is a term used in oceanography, meteorology and the financial industry to refer to testing a predictive model using existing historic data.<ref name="Wiki">[[wikipedia:Backtesting|Backtesting]], on Wikipedia</ref> It is also often used to analyze the past for research purposes. It is notably useful to quantitatively assess the impact [[asset allocation]] had (in known history) on possible investment strategies.<br />
<br />
Backtesting seeks to estimate the performance of a strategy if it had been employed during a past period. This requires simulating past conditions with sufficient detail, making one limitation of backtesting the need for detailed historical data. A second limitation is the inability to model strategies that would affect historic prices.<br />
<br />
Finally, backtesting, like other modeling, is limited by potential overfitting. That is, it is often possible to find a strategy that would have worked well in the past, but will not work well in the future. <br />
<br />
Despite these limitations, backtesting provides valuable information not available when models and strategies are tested on synthetic data.<br />
<br />
==Spreadsheet overview and download instructions==<br />
The spreadsheet is discussed in this {{Forum post|t=2520|title=Simba's backtesting spreadsheet <nowiki>[a Bogleheads community project]</nowiki>}}.<br />
<br />
The latest version and download instructions are in '''[{{{url|https://www.bogleheads.org/forum/viewtopic.php?f=10&t=2520&p=4946413#p4946413}}} this post]'''.<br />
<br />
Detailed instructions, glossary and revision history can be found in the '''README''' tab. Here is a brief overview of the individual worksheets:<br />
<br />
*'''Analyze_Portfolio''' provides a simple way to customize the asset allocation of a single portfolio and study its historical performance over specific time periods. This worksheet compares a custom portfolio to a benchmark portfolio (e.g. 60/40) and provides charts and statistics to illustrate respective growth and drawdowns.<br />
*'''Compare_Portfolios''' allows to compare two sets of 5 different portfolios, with the ability to change the portfolios' composition, the time period being examined, and to check the impact on various metrics and charts.<br />
*'''Lazy_Portfolios''' compares 25 predefined portfolios and provides risk/return statistics and charts for all portfolios.<br />
*'''Portfolio_Math''' calculates portfolio returns for all combinations of interest and performs most of the 'under the hood' calculations. <br />
*'''Analyze_Series''' investigates annual returns for all selected data series. Various statistics are provided, as well as a correlation matrix and rolling returns over various time periods.<br />
*'''Data_Series''' provides a selection mechanism to choose the data series to be analyzed and combined in portfolios in the rest of the spreadsheet.<br />
*'''Raw_Data''' provides a dynamic splicing mechanism to combine raw data (e.g. funds, indices and synthetic models) into full data series, while applying expense ratio adjustments.<br />
*'''Data_Sources''' identifies the various data sources used in this spreadsheet. More details on a per data series basis can be found in Raw_Data.<br />
<br />
==Historical Returns==<br />
The spreadsheet provides an extensive set of historical returns for various types of passive index funds, plus a few active funds. Most funds are from Vanguard and all corresponding historical returns have been validated with Vanguard. All returns are expressed as total returns, i.e. including dividends. The perspective of a U.S. investor is assumed, with returns expressed in USD.<br />
<br />
When actual fund returns are not available (e.g. early years), attempts were made to provide credible numbers to extend the fund's history, using returns from corresponding indices, and in some cases, using a synthetic model. <br />
<br />
In general, fairly good quality data is available starting in 1927 for U.S. stocks and bonds. Most International returns are available starting in 1970. Most sector returns aren't available before 1985.<br />
<br />
The ''Raw_Data'' worksheet is the main repository for such historical data. The ''Data_Series'' worksheet assembles a synthetic list of data series returns and can be easily copied in another spreadsheet, allowing to perform other types of backtesting analysis than the tools provided by the Simba spreadsheet.<br />
<br />
==Telltale chart==<br />
{{Main article|Telltale chart}}<br />
<br />
<onlyinclude>John Bogle stated:<ref>[https://personal.vanguard.com/bogle_site/sp20020626.html The Telltale Chart], [[John C. Bogle]], Vanguard.com (Bogle_site), June 26, 2002.</ref><br />
<blockquote>''A telltale chart is devised simply by dividing the cumulative returns of one data series into another'' (the benchmark).</blockquote><br />
In the Simba spreadsheet, such a chart compares the trajectory of historical returns for the various portfolios of interest to a Telltale benchmark (itself a portfolio), in a relative manner.<br />
<br />
Using Telltale charts can be very informative, truly 'telling the tale' of what happened over time to portfolio trajectories, illustrating return to the mean properties, or lack thereof.<br />
<br />
It is interesting to observe that ''growth charts'' are actually a special form of ''telltale charts'', and can be generated by the same tool. <br />
<br />
A telltale/growth chart is provided in the ''Compare_Portfolios'' worksheet and can be used in multiple ways:<br />
<br />
* If the benchmark is defined as 100% cash, the telltale chart becomes a simple growth chart (i.e. showing the growth of an initial investment over time, in nominal terms).<br />
* If the benchmark is defined as 100% inflation, the telltale chart becomes an inflation-adjusted growth chart (i.e. showing the growth of an initial investment over time, in real terms).<br />
* If a more concrete benchmark is used (e.g. US Total Market, aka TSM), the telltale chart shows the relative growth over time of the portfolios of interest compared to the benchmark.<br />
<br />
Typical examples of Telltale charts generated with the Simba spreadsheet can be found here: [https://finpage.blog/2018/02/15/telling-tales-2017-update Telling Tales – 2017 update].<br />
</onlyinclude><br />
<br />
==Compatibility==<br />
The spreadsheet is maintained using Microsoft Excel 2011, and provided in XLSX format.<br />
<br />
It should work fairly well with recent versions of [https://www.libreoffice.org/discover/calc/ LibreOffice Calc], with some minor limitations (e.g. dynamic chart titles do not automatically update). Once the file has been downloaded from Google Drive, open the file and save it in the suggested "ODF" default format. Otherwise, the charts will not be preserved in the correct format.<br />
<br />
There is limited compatibility with Google Sheets. The calculations and statistics appear to work well, while the charts do not work properly.<br />
<br />
==Inner Workings==<br />
As any complex spreadsheet, the inner workings of the Simba spreadsheet may not be quite obvious by just looking at formulas. The following series of blog articles documents various aspects of how it actually works.<br />
<br />
*[https://finpage.blog/2018/02/02/inner-workings-of-the-simba-backtesting-spreadsheet-a-layered-structure Simba backtesting spreadsheet: a layered structure], elaborating on how the spreadsheet is constructed, and providing an overview of its layered structure.<br />
*[https://finpage.blog/2018/02/04/simba-backtesting-spreadsheet-risk-metrics-risk-ratios Simba backtesting spreadsheet: risk metrics, risk ratios]: elaborating on how risk metrics (e.g. volatility, drawdowns, etc) and risk ratios (e.g. Sharpe, Sortino, etc) are computed.<br />
*[https://finpage.blog/2018/02/04/simba-backtesting-spreadsheet-advanced-topics Simba backtesting spreadsheet: advanced topics]: elaborating on more advanced topics (e.g. unbalancing, safe withdrawal rate).<br />
*[https://finpage.blog/2018/02/05/simba-backtesting-spreadsheet-miscellaneous-topics Simba backtesting spreadsheet: miscellaneous topics]: addressing a few miscellaneous topics (e.g. end label on charts, compatibility issues, spreadsheet analytics).<br />
<br />
==References==<br />
<references /><br />
<br />
==External links==<br />
*[http://www.bogleheads.org/forum/viewtopic.php?t=2520 Spreadsheet for backtesting (includes TrevH's data)], forum thread containing Simba's spreadsheet.<br />
*[[wikipedia:Backtesting|Backtesting]], on Wikipedia<br />
*[http://www.financialtrading.com/issues-related-to-back-testing/ Issues Related to Back Testing], from FinancialTrading.com<br />
*[http://www.investopedia.com/terms/b/backtesting.asp Backtesting], from Investopedia<br />
{{Resources and links}}<br />
{{Spreadsheets}}<br />
[[Category:Google Docs.spreadsheets]]<br />
[[Category:Resources and links]]</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Simba%27s_backtesting_spreadsheet&diff=68798
Simba's backtesting spreadsheet
2020-01-11T05:26:21Z
<p>Siamond: /* Compatibility */ Added warning about dynamic titles</p>
<hr />
<div><br />
'''{{PAGENAME}}''' describes a spreadsheet originally developed by forum member ''Simba'' for the purpose of acting as a reference for historical returns, and analyzing a portfolio based on such historical data. The spreadsheet is no longer maintained by Simba, but other forum members continue to support it and to expand functionality, as a Bogleheads community project.<br />
<br />
{{Notice|This spreadsheet and the information it contains is intended for your personal, non-commercial, use only (e.g. for educational purposes). This is a learning, researching and teaching tool, nothing more.}}<br />
<br />
==Backtesting==<br />
Backtesting is a term used in oceanography, meteorology and the financial industry to refer to testing a predictive model using existing historic data.<ref name="Wiki">[[wikipedia:Backtesting|Backtesting]], on Wikipedia</ref> It is also often used to analyze the past for research purposes. It is notably useful to quantitatively assess the impact [[asset allocation]] had (in known history) on possible investment strategies.<br />
<br />
Backtesting seeks to estimate the performance of a strategy if it had been employed during a past period. This requires simulating past conditions with sufficient detail, making one limitation of backtesting the need for detailed historical data. A second limitation is the inability to model strategies that would affect historic prices.<br />
<br />
Finally, backtesting, like other modeling, is limited by potential overfitting. That is, it is often possible to find a strategy that would have worked well in the past, but will not work well in the future. <br />
<br />
Despite these limitations, backtesting provides valuable information not available when models and strategies are tested on synthetic data.<br />
<br />
==Spreadsheet overview and download instructions==<br />
The spreadsheet is discussed in this {{Forum post|t=2520|title=Simba's backtesting spreadsheet <nowiki>[a Bogleheads community project]</nowiki>}}.<br />
<br />
The latest version and download instructions are in '''[{{{url|https://www.bogleheads.org/forum/viewtopic.php?f=10&t=2520&p=4379369#p4379369}}} this post]''', which links to Google Drive.<br />
<br />
Detailed instructions, glossary and revision history can be found in the "README" tab. Here is a brief overview of the individual worksheets:<br />
<br />
*'''Analyze_Portfolio''' provides a simple way to customize the asset allocation of a single portfolio and study its historical performance over specific time periods. This worksheet compares a custom portfolio to a benchmark portfolio (e.g. 60/40) and provides charts and statistics to illustrate respective growth and drawdowns.<br />
*'''Compare_Portfolios''' allows to compare two sets of 5 different portfolios, with the ability to change the portfolios' composition, the time period being examined, and to check the impact on various metrics and charts.<br />
*'''Lazy_Portfolios''' compares 25 predefined portfolios and provides risk/return statistics and charts for all portfolios.<br />
*'''Portfolio_Math''' calculates portfolio returns for all combinations of interest and performs most of the 'under the hood' calculations. <br />
*'''Analyze_Series''' investigates annual returns for all selected data series. Various statistics are provided, as well as a correlation matrix and rolling returns over various time periods.<br />
*'''Data_Series''' provides a selection mechanism to choose the data series to be analyzed and combined in portfolios in the rest of the spreadsheet.<br />
*'''Raw_Data''' provides a dynamic splicing mechanism to combine raw data (e.g. funds, indices and synthetic models) into full data series, while applying expense ratio adjustments.<br />
*'''Data_Sources''' identifies the various data sources used in this spreadsheet. More details on a per data series basis can be found in Raw_Data.<br />
<br />
==Historical Returns==<br />
The spreadsheet provides an extensive set of historical returns for various types of passive index funds, plus a few active funds. Most funds are from Vanguard and all corresponding historical returns have been validated with Vanguard. All returns are expressed as total returns, i.e. including dividends. The perspective of a U.S. investor is assumed, with returns expressed in USD.<br />
<br />
When actual fund returns are not available (e.g. early years), attempts were made to provide credible numbers to extend the fund's history, using returns from corresponding indices, and in some cases, using a synthetic model. <br />
<br />
In general, fairly good quality data is available starting in 1927 for U.S. stocks and bonds. Most International returns are available starting in 1970. Most sector returns aren't available before 1985.<br />
<br />
The ''Raw_Data'' worksheet is the main repository for such historical data. The ''Data_Series'' worksheet assembles a synthetic list of data series returns and can be easily copied in another spreadsheet, allowing to perform other types of backtesting analysis than the tools provided by the Simba spreadsheet.<br />
<br />
==Telltale chart==<br />
{{Main article|Telltale chart}}<br />
<br />
<onlyinclude>John Bogle stated:<ref>[https://personal.vanguard.com/bogle_site/sp20020626.html The Telltale Chart], [[John C. Bogle]], Vanguard.com (Bogle_site), June 26, 2002.</ref><br />
<blockquote>''A telltale chart is devised simply by dividing the cumulative returns of one data series into another'' (the benchmark).</blockquote><br />
In the Simba spreadsheet, such a chart compares the trajectory of historical returns for the various portfolios of interest to a Telltale benchmark (itself a portfolio), in a relative manner.<br />
<br />
Using Telltale charts can be very informative, truly 'telling the tale' of what happened over time to portfolio trajectories, illustrating return to the mean properties, or lack thereof.<br />
<br />
It is interesting to observe that ''growth charts'' are actually a special form of ''telltale charts'', and can be generated by the same tool. <br />
<br />
A telltale/growth chart is provided in the ''Compare_Portfolios'' worksheet and can be used in multiple ways:<br />
<br />
* If the benchmark is defined as 100% cash, the telltale chart becomes a simple growth chart (i.e. showing the growth of an initial investment over time, in nominal terms).<br />
* If the benchmark is defined as 100% inflation, the telltale chart becomes an inflation-adjusted growth chart (i.e. showing the growth of an initial investment over time, in real terms).<br />
* If a more concrete benchmark is used (e.g. US Total Market, aka TSM), the telltale chart shows the relative growth over time of the portfolios of interest compared to the benchmark.<br />
<br />
Typical examples of Telltale charts generated with the Simba spreadsheet can be found here: [https://finpage.blog/2018/02/15/telling-tales-2017-update Telling Tales – 2017 update].<br />
</onlyinclude><br />
<br />
==Compatibility==<br />
The spreadsheet is maintained using Microsoft Excel 2011, and provided in XLSX format.<br />
<br />
It should work fairly well with recent versions of [https://www.libreoffice.org/discover/calc/ LibreOffice Calc], with some minor limitations (e.g. dynamic chart titles do not automatically update). Once the file has been downloaded from Google Drive, open the file and save it in the suggested "ODF" default format. Otherwise, the charts will not be preserved in the correct format.<br />
<br />
There is limited compatibility with Google Sheets. The calculations and statistics appear to work well, while the charts do not work properly.<br />
<br />
==Inner Workings==<br />
As any complex spreadsheet, the inner workings of the Simba spreadsheet may not be quite obvious by just looking at formulas. The following series of blog articles documents various aspects of how it actually works.<br />
<br />
*[https://finpage.blog/2018/02/02/inner-workings-of-the-simba-backtesting-spreadsheet-a-layered-structure Simba backtesting spreadsheet: a layered structure], elaborating on how the spreadsheet is constructed, and providing an overview of its layered structure.<br />
*[https://finpage.blog/2018/02/04/simba-backtesting-spreadsheet-risk-metrics-risk-ratios Simba backtesting spreadsheet: risk metrics, risk ratios]: elaborating on how risk metrics (e.g. volatility, drawdowns, etc) and risk ratios (e.g. Sharpe, Sortino, etc) are computed.<br />
*[https://finpage.blog/2018/02/04/simba-backtesting-spreadsheet-advanced-topics Simba backtesting spreadsheet: advanced topics]: elaborating on more advanced topics (e.g. unbalancing, safe withdrawal rate).<br />
*[https://finpage.blog/2018/02/05/simba-backtesting-spreadsheet-miscellaneous-topics Simba backtesting spreadsheet: miscellaneous topics]: addressing a few miscellaneous topics (e.g. end label on charts, compatibility issues, spreadsheet analytics).<br />
<br />
==References==<br />
<references /><br />
<br />
==External links==<br />
*[http://www.bogleheads.org/forum/viewtopic.php?t=2520 Spreadsheet for backtesting (includes TrevH's data)], forum thread containing Simba's spreadsheet.<br />
*[[wikipedia:Backtesting|Backtesting]], on Wikipedia<br />
*[http://www.financialtrading.com/issues-related-to-back-testing/ Issues Related to Back Testing], from FinancialTrading.com<br />
*[http://www.investopedia.com/terms/b/backtesting.asp Backtesting], from Investopedia<br />
{{Resources and links}}<br />
{{Spreadsheets}}<br />
[[Category:Google Docs.spreadsheets]]<br />
[[Category:Resources and links]]</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Simba%27s_backtesting_spreadsheet&diff=68797
Simba's backtesting spreadsheet
2020-01-11T05:24:30Z
<p>Siamond: /* Historical Returns */ Added italics for worksheet names, like in the next section</p>
<hr />
<div><br />
'''{{PAGENAME}}''' describes a spreadsheet originally developed by forum member ''Simba'' for the purpose of acting as a reference for historical returns, and analyzing a portfolio based on such historical data. The spreadsheet is no longer maintained by Simba, but other forum members continue to support it and to expand functionality, as a Bogleheads community project.<br />
<br />
{{Notice|This spreadsheet and the information it contains is intended for your personal, non-commercial, use only (e.g. for educational purposes). This is a learning, researching and teaching tool, nothing more.}}<br />
<br />
==Backtesting==<br />
Backtesting is a term used in oceanography, meteorology and the financial industry to refer to testing a predictive model using existing historic data.<ref name="Wiki">[[wikipedia:Backtesting|Backtesting]], on Wikipedia</ref> It is also often used to analyze the past for research purposes. It is notably useful to quantitatively assess the impact [[asset allocation]] had (in known history) on possible investment strategies.<br />
<br />
Backtesting seeks to estimate the performance of a strategy if it had been employed during a past period. This requires simulating past conditions with sufficient detail, making one limitation of backtesting the need for detailed historical data. A second limitation is the inability to model strategies that would affect historic prices.<br />
<br />
Finally, backtesting, like other modeling, is limited by potential overfitting. That is, it is often possible to find a strategy that would have worked well in the past, but will not work well in the future. <br />
<br />
Despite these limitations, backtesting provides valuable information not available when models and strategies are tested on synthetic data.<br />
<br />
==Spreadsheet overview and download instructions==<br />
The spreadsheet is discussed in this {{Forum post|t=2520|title=Simba's backtesting spreadsheet <nowiki>[a Bogleheads community project]</nowiki>}}.<br />
<br />
The latest version and download instructions are in '''[{{{url|https://www.bogleheads.org/forum/viewtopic.php?f=10&t=2520&p=4379369#p4379369}}} this post]''', which links to Google Drive.<br />
<br />
Detailed instructions, glossary and revision history can be found in the "README" tab. Here is a brief overview of the individual worksheets:<br />
<br />
*'''Analyze_Portfolio''' provides a simple way to customize the asset allocation of a single portfolio and study its historical performance over specific time periods. This worksheet compares a custom portfolio to a benchmark portfolio (e.g. 60/40) and provides charts and statistics to illustrate respective growth and drawdowns.<br />
*'''Compare_Portfolios''' allows to compare two sets of 5 different portfolios, with the ability to change the portfolios' composition, the time period being examined, and to check the impact on various metrics and charts.<br />
*'''Lazy_Portfolios''' compares 25 predefined portfolios and provides risk/return statistics and charts for all portfolios.<br />
*'''Portfolio_Math''' calculates portfolio returns for all combinations of interest and performs most of the 'under the hood' calculations. <br />
*'''Analyze_Series''' investigates annual returns for all selected data series. Various statistics are provided, as well as a correlation matrix and rolling returns over various time periods.<br />
*'''Data_Series''' provides a selection mechanism to choose the data series to be analyzed and combined in portfolios in the rest of the spreadsheet.<br />
*'''Raw_Data''' provides a dynamic splicing mechanism to combine raw data (e.g. funds, indices and synthetic models) into full data series, while applying expense ratio adjustments.<br />
*'''Data_Sources''' identifies the various data sources used in this spreadsheet. More details on a per data series basis can be found in Raw_Data.<br />
<br />
==Historical Returns==<br />
The spreadsheet provides an extensive set of historical returns for various types of passive index funds, plus a few active funds. Most funds are from Vanguard and all corresponding historical returns have been validated with Vanguard. All returns are expressed as total returns, i.e. including dividends. The perspective of a U.S. investor is assumed, with returns expressed in USD.<br />
<br />
When actual fund returns are not available (e.g. early years), attempts were made to provide credible numbers to extend the fund's history, using returns from corresponding indices, and in some cases, using a synthetic model. <br />
<br />
In general, fairly good quality data is available starting in 1927 for U.S. stocks and bonds. Most International returns are available starting in 1970. Most sector returns aren't available before 1985.<br />
<br />
The ''Raw_Data'' worksheet is the main repository for such historical data. The ''Data_Series'' worksheet assembles a synthetic list of data series returns and can be easily copied in another spreadsheet, allowing to perform other types of backtesting analysis than the tools provided by the Simba spreadsheet.<br />
<br />
==Telltale chart==<br />
{{Main article|Telltale chart}}<br />
<br />
<onlyinclude>John Bogle stated:<ref>[https://personal.vanguard.com/bogle_site/sp20020626.html The Telltale Chart], [[John C. Bogle]], Vanguard.com (Bogle_site), June 26, 2002.</ref><br />
<blockquote>''A telltale chart is devised simply by dividing the cumulative returns of one data series into another'' (the benchmark).</blockquote><br />
In the Simba spreadsheet, such a chart compares the trajectory of historical returns for the various portfolios of interest to a Telltale benchmark (itself a portfolio), in a relative manner.<br />
<br />
Using Telltale charts can be very informative, truly 'telling the tale' of what happened over time to portfolio trajectories, illustrating return to the mean properties, or lack thereof.<br />
<br />
It is interesting to observe that ''growth charts'' are actually a special form of ''telltale charts'', and can be generated by the same tool. <br />
<br />
A telltale/growth chart is provided in the ''Compare_Portfolios'' worksheet and can be used in multiple ways:<br />
<br />
* If the benchmark is defined as 100% cash, the telltale chart becomes a simple growth chart (i.e. showing the growth of an initial investment over time, in nominal terms).<br />
* If the benchmark is defined as 100% inflation, the telltale chart becomes an inflation-adjusted growth chart (i.e. showing the growth of an initial investment over time, in real terms).<br />
* If a more concrete benchmark is used (e.g. US Total Market, aka TSM), the telltale chart shows the relative growth over time of the portfolios of interest compared to the benchmark.<br />
<br />
Typical examples of Telltale charts generated with the Simba spreadsheet can be found here: [https://finpage.blog/2018/02/15/telling-tales-2017-update Telling Tales – 2017 update].<br />
</onlyinclude><br />
<br />
==Compatibility==<br />
The spreadsheet is maintained using Microsoft Excel 2011, and provided in XLSX format.<br />
<br />
It should work fairly well with recent versions of [https://www.libreoffice.org/discover/calc/ LibreOffice Calc], with some minor limitations. Once the file has been downloaded from Google Drive, open the file and save it in the suggested "ODF" default format. Otherwise, the charts will not be preserved in the correct format.<br />
<br />
There is some level of incompatibility with Google Sheets. The calculations and statistics appear to work well, while the charts do not. <br />
<br />
==Inner Workings==<br />
As any complex spreadsheet, the inner workings of the Simba spreadsheet may not be quite obvious by just looking at formulas. The following series of blog articles documents various aspects of how it actually works.<br />
<br />
*[https://finpage.blog/2018/02/02/inner-workings-of-the-simba-backtesting-spreadsheet-a-layered-structure Simba backtesting spreadsheet: a layered structure], elaborating on how the spreadsheet is constructed, and providing an overview of its layered structure.<br />
*[https://finpage.blog/2018/02/04/simba-backtesting-spreadsheet-risk-metrics-risk-ratios Simba backtesting spreadsheet: risk metrics, risk ratios]: elaborating on how risk metrics (e.g. volatility, drawdowns, etc) and risk ratios (e.g. Sharpe, Sortino, etc) are computed.<br />
*[https://finpage.blog/2018/02/04/simba-backtesting-spreadsheet-advanced-topics Simba backtesting spreadsheet: advanced topics]: elaborating on more advanced topics (e.g. unbalancing, safe withdrawal rate).<br />
*[https://finpage.blog/2018/02/05/simba-backtesting-spreadsheet-miscellaneous-topics Simba backtesting spreadsheet: miscellaneous topics]: addressing a few miscellaneous topics (e.g. end label on charts, compatibility issues, spreadsheet analytics).<br />
<br />
==References==<br />
<references /><br />
<br />
==External links==<br />
*[http://www.bogleheads.org/forum/viewtopic.php?t=2520 Spreadsheet for backtesting (includes TrevH's data)], forum thread containing Simba's spreadsheet.<br />
*[[wikipedia:Backtesting|Backtesting]], on Wikipedia<br />
*[http://www.financialtrading.com/issues-related-to-back-testing/ Issues Related to Back Testing], from FinancialTrading.com<br />
*[http://www.investopedia.com/terms/b/backtesting.asp Backtesting], from Investopedia<br />
{{Resources and links}}<br />
{{Spreadsheets}}<br />
[[Category:Google Docs.spreadsheets]]<br />
[[Category:Resources and links]]</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Simba%27s_backtesting_spreadsheet&diff=68796
Simba's backtesting spreadsheet
2020-01-11T05:22:55Z
<p>Siamond: /* Historical Returns */ Updated for v19a</p>
<hr />
<div><br />
'''{{PAGENAME}}''' describes a spreadsheet originally developed by forum member ''Simba'' for the purpose of acting as a reference for historical returns, and analyzing a portfolio based on such historical data. The spreadsheet is no longer maintained by Simba, but other forum members continue to support it and to expand functionality, as a Bogleheads community project.<br />
<br />
{{Notice|This spreadsheet and the information it contains is intended for your personal, non-commercial, use only (e.g. for educational purposes). This is a learning, researching and teaching tool, nothing more.}}<br />
<br />
==Backtesting==<br />
Backtesting is a term used in oceanography, meteorology and the financial industry to refer to testing a predictive model using existing historic data.<ref name="Wiki">[[wikipedia:Backtesting|Backtesting]], on Wikipedia</ref> It is also often used to analyze the past for research purposes. It is notably useful to quantitatively assess the impact [[asset allocation]] had (in known history) on possible investment strategies.<br />
<br />
Backtesting seeks to estimate the performance of a strategy if it had been employed during a past period. This requires simulating past conditions with sufficient detail, making one limitation of backtesting the need for detailed historical data. A second limitation is the inability to model strategies that would affect historic prices.<br />
<br />
Finally, backtesting, like other modeling, is limited by potential overfitting. That is, it is often possible to find a strategy that would have worked well in the past, but will not work well in the future. <br />
<br />
Despite these limitations, backtesting provides valuable information not available when models and strategies are tested on synthetic data.<br />
<br />
==Spreadsheet overview and download instructions==<br />
The spreadsheet is discussed in this {{Forum post|t=2520|title=Simba's backtesting spreadsheet <nowiki>[a Bogleheads community project]</nowiki>}}.<br />
<br />
The latest version and download instructions are in '''[{{{url|https://www.bogleheads.org/forum/viewtopic.php?f=10&t=2520&p=4379369#p4379369}}} this post]''', which links to Google Drive.<br />
<br />
Detailed instructions, glossary and revision history can be found in the "README" tab. Here is a brief overview of the individual worksheets:<br />
<br />
*'''Analyze_Portfolio''' provides a simple way to customize the asset allocation of a single portfolio and study its historical performance over specific time periods. This worksheet compares a custom portfolio to a benchmark portfolio (e.g. 60/40) and provides charts and statistics to illustrate respective growth and drawdowns.<br />
*'''Compare_Portfolios''' allows to compare two sets of 5 different portfolios, with the ability to change the portfolios' composition, the time period being examined, and to check the impact on various metrics and charts.<br />
*'''Lazy_Portfolios''' compares 25 predefined portfolios and provides risk/return statistics and charts for all portfolios.<br />
*'''Portfolio_Math''' calculates portfolio returns for all combinations of interest and performs most of the 'under the hood' calculations. <br />
*'''Analyze_Series''' investigates annual returns for all selected data series. Various statistics are provided, as well as a correlation matrix and rolling returns over various time periods.<br />
*'''Data_Series''' provides a selection mechanism to choose the data series to be analyzed and combined in portfolios in the rest of the spreadsheet.<br />
*'''Raw_Data''' provides a dynamic splicing mechanism to combine raw data (e.g. funds, indices and synthetic models) into full data series, while applying expense ratio adjustments.<br />
*'''Data_Sources''' identifies the various data sources used in this spreadsheet. More details on a per data series basis can be found in Raw_Data.<br />
<br />
==Historical Returns==<br />
The spreadsheet provides an extensive set of historical returns for various types of passive index funds, plus a few active funds. Most funds are from Vanguard and all corresponding historical returns have been validated with Vanguard. All returns are expressed as total returns, i.e. including dividends. The perspective of a U.S. investor is assumed, with returns expressed in USD.<br />
<br />
When actual fund returns are not available (e.g. early years), attempts were made to provide credible numbers to extend the fund's history, using returns from corresponding indices, and in some cases, using a synthetic model. <br />
<br />
In general, fairly good quality data is available starting in 1927 for U.S. stocks and bonds. Most International returns are available starting in 1970. Most sector returns aren't available before 1985.<br />
<br />
The Raw_Data worksheet is the main repository for such historical data. The Data_Series worksheet assembles a synthetic list of data series returns and can be easily copied in another spreadsheet, allowing to perform other types of backtesting analysis than the tools provided by the Simba spreadsheet.<br />
<br />
==Telltale chart==<br />
{{Main article|Telltale chart}}<br />
<br />
<onlyinclude>John Bogle stated:<ref>[https://personal.vanguard.com/bogle_site/sp20020626.html The Telltale Chart], [[John C. Bogle]], Vanguard.com (Bogle_site), June 26, 2002.</ref><br />
<blockquote>''A telltale chart is devised simply by dividing the cumulative returns of one data series into another'' (the benchmark).</blockquote><br />
In the Simba spreadsheet, such a chart compares the trajectory of historical returns for the various portfolios of interest to a Telltale benchmark (itself a portfolio), in a relative manner.<br />
<br />
Using Telltale charts can be very informative, truly 'telling the tale' of what happened over time to portfolio trajectories, illustrating return to the mean properties, or lack thereof.<br />
<br />
It is interesting to observe that ''growth charts'' are actually a special form of ''telltale charts'', and can be generated by the same tool. <br />
<br />
A telltale/growth chart is provided in the ''Compare_Portfolios'' worksheet and can be used in multiple ways:<br />
<br />
* If the benchmark is defined as 100% cash, the telltale chart becomes a simple growth chart (i.e. showing the growth of an initial investment over time, in nominal terms).<br />
* If the benchmark is defined as 100% inflation, the telltale chart becomes an inflation-adjusted growth chart (i.e. showing the growth of an initial investment over time, in real terms).<br />
* If a more concrete benchmark is used (e.g. US Total Market, aka TSM), the telltale chart shows the relative growth over time of the portfolios of interest compared to the benchmark.<br />
<br />
Typical examples of Telltale charts generated with the Simba spreadsheet can be found here: [https://finpage.blog/2018/02/15/telling-tales-2017-update Telling Tales – 2017 update].<br />
</onlyinclude><br />
<br />
==Compatibility==<br />
The spreadsheet is maintained using Microsoft Excel 2011, and provided in XLSX format.<br />
<br />
It should work fairly well with recent versions of [https://www.libreoffice.org/discover/calc/ LibreOffice Calc], with some minor limitations. Once the file has been downloaded from Google Drive, open the file and save it in the suggested "ODF" default format. Otherwise, the charts will not be preserved in the correct format.<br />
<br />
There is some level of incompatibility with Google Sheets. The calculations and statistics appear to work well, while the charts do not. <br />
<br />
==Inner Workings==<br />
As any complex spreadsheet, the inner workings of the Simba spreadsheet may not be quite obvious by just looking at formulas. The following series of blog articles documents various aspects of how it actually works.<br />
<br />
*[https://finpage.blog/2018/02/02/inner-workings-of-the-simba-backtesting-spreadsheet-a-layered-structure Simba backtesting spreadsheet: a layered structure], elaborating on how the spreadsheet is constructed, and providing an overview of its layered structure.<br />
*[https://finpage.blog/2018/02/04/simba-backtesting-spreadsheet-risk-metrics-risk-ratios Simba backtesting spreadsheet: risk metrics, risk ratios]: elaborating on how risk metrics (e.g. volatility, drawdowns, etc) and risk ratios (e.g. Sharpe, Sortino, etc) are computed.<br />
*[https://finpage.blog/2018/02/04/simba-backtesting-spreadsheet-advanced-topics Simba backtesting spreadsheet: advanced topics]: elaborating on more advanced topics (e.g. unbalancing, safe withdrawal rate).<br />
*[https://finpage.blog/2018/02/05/simba-backtesting-spreadsheet-miscellaneous-topics Simba backtesting spreadsheet: miscellaneous topics]: addressing a few miscellaneous topics (e.g. end label on charts, compatibility issues, spreadsheet analytics).<br />
<br />
==References==<br />
<references /><br />
<br />
==External links==<br />
*[http://www.bogleheads.org/forum/viewtopic.php?t=2520 Spreadsheet for backtesting (includes TrevH's data)], forum thread containing Simba's spreadsheet.<br />
*[[wikipedia:Backtesting|Backtesting]], on Wikipedia<br />
*[http://www.financialtrading.com/issues-related-to-back-testing/ Issues Related to Back Testing], from FinancialTrading.com<br />
*[http://www.investopedia.com/terms/b/backtesting.asp Backtesting], from Investopedia<br />
{{Resources and links}}<br />
{{Spreadsheets}}<br />
[[Category:Google Docs.spreadsheets]]<br />
[[Category:Resources and links]]</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Simba%27s_backtesting_spreadsheet&diff=68795
Simba's backtesting spreadsheet
2020-01-11T05:18:09Z
<p>Siamond: /* Spreadsheet overview and download instructions */ Updated for v19a</p>
<hr />
<div><br />
'''{{PAGENAME}}''' describes a spreadsheet originally developed by forum member ''Simba'' for the purpose of acting as a reference for historical returns, and analyzing a portfolio based on such historical data. The spreadsheet is no longer maintained by Simba, but other forum members continue to support it and to expand functionality, as a Bogleheads community project.<br />
<br />
{{Notice|This spreadsheet and the information it contains is intended for your personal, non-commercial, use only (e.g. for educational purposes). This is a learning, researching and teaching tool, nothing more.}}<br />
<br />
==Backtesting==<br />
Backtesting is a term used in oceanography, meteorology and the financial industry to refer to testing a predictive model using existing historic data.<ref name="Wiki">[[wikipedia:Backtesting|Backtesting]], on Wikipedia</ref> It is also often used to analyze the past for research purposes. It is notably useful to quantitatively assess the impact [[asset allocation]] had (in known history) on possible investment strategies.<br />
<br />
Backtesting seeks to estimate the performance of a strategy if it had been employed during a past period. This requires simulating past conditions with sufficient detail, making one limitation of backtesting the need for detailed historical data. A second limitation is the inability to model strategies that would affect historic prices.<br />
<br />
Finally, backtesting, like other modeling, is limited by potential overfitting. That is, it is often possible to find a strategy that would have worked well in the past, but will not work well in the future. <br />
<br />
Despite these limitations, backtesting provides valuable information not available when models and strategies are tested on synthetic data.<br />
<br />
==Spreadsheet overview and download instructions==<br />
The spreadsheet is discussed in this {{Forum post|t=2520|title=Simba's backtesting spreadsheet <nowiki>[a Bogleheads community project]</nowiki>}}.<br />
<br />
The latest version and download instructions are in '''[{{{url|https://www.bogleheads.org/forum/viewtopic.php?f=10&t=2520&p=4379369#p4379369}}} this post]''', which links to Google Drive.<br />
<br />
Detailed instructions, glossary and revision history can be found in the "README" tab. Here is a brief overview of the individual worksheets:<br />
<br />
*'''Analyze_Portfolio''' provides a simple way to customize the asset allocation of a single portfolio and study its historical performance over specific time periods. This worksheet compares a custom portfolio to a benchmark portfolio (e.g. 60/40) and provides charts and statistics to illustrate respective growth and drawdowns.<br />
*'''Compare_Portfolios''' allows to compare two sets of 5 different portfolios, with the ability to change the portfolios' composition, the time period being examined, and to check the impact on various metrics and charts.<br />
*'''Lazy_Portfolios''' compares 25 predefined portfolios and provides risk/return statistics and charts for all portfolios.<br />
*'''Portfolio_Math''' calculates portfolio returns for all combinations of interest and performs most of the 'under the hood' calculations. <br />
*'''Analyze_Series''' investigates annual returns for all selected data series. Various statistics are provided, as well as a correlation matrix and rolling returns over various time periods.<br />
*'''Data_Series''' provides a selection mechanism to choose the data series to be analyzed and combined in portfolios in the rest of the spreadsheet.<br />
*'''Raw_Data''' provides a dynamic splicing mechanism to combine raw data (e.g. funds, indices and synthetic models) into full data series, while applying expense ratio adjustments.<br />
*'''Data_Sources''' identifies the various data sources used in this spreadsheet. More details on a per data series basis can be found in Raw_Data.<br />
<br />
==Historical Returns==<br />
The spreadsheet provides an extensive set of historical returns for various types of index (and non-index) funds. Most funds are from Vanguard, and all corresponding historical returns have been validated with Vanguard. All returns are expressed as total returns, i.e. including dividends. The perspective of a U.S. investor is assumed, with returns expressed in USD.<br />
<br />
When actual fund returns are not available (e.g. early years), attempts were made to provide credible numbers to extend the fund's history, using returns from corresponding indices, and in some cases, using a synthetic model. <br />
<br />
In general, fairly good quality data is available starting in 1927 for U.S. stocks and bonds. Most International returns are available starting in 1970. Most sector returns aren't available before 1985.<br />
<br />
The Data_TR_USD worksheet is the main repository for such historical data, and can be easily copied in another spreadsheet, allowing to perform other types of backtesting analysis than the fairly basic tools provided by the Simba spreadsheet.<br />
<br />
==Telltale chart==<br />
{{Main article|Telltale chart}}<br />
<br />
<onlyinclude>John Bogle stated:<ref>[https://personal.vanguard.com/bogle_site/sp20020626.html The Telltale Chart], [[John C. Bogle]], Vanguard.com (Bogle_site), June 26, 2002.</ref><br />
<blockquote>''A telltale chart is devised simply by dividing the cumulative returns of one data series into another'' (the benchmark).</blockquote><br />
In the Simba spreadsheet, such a chart compares the trajectory of historical returns for the various portfolios of interest to a Telltale benchmark (itself a portfolio), in a relative manner.<br />
<br />
Using Telltale charts can be very informative, truly 'telling the tale' of what happened over time to portfolio trajectories, illustrating return to the mean properties, or lack thereof.<br />
<br />
It is interesting to observe that ''growth charts'' are actually a special form of ''telltale charts'', and can be generated by the same tool. <br />
<br />
A telltale/growth chart is provided in the ''Compare_Portfolios'' worksheet and can be used in multiple ways:<br />
<br />
* If the benchmark is defined as 100% cash, the telltale chart becomes a simple growth chart (i.e. showing the growth of an initial investment over time, in nominal terms).<br />
* If the benchmark is defined as 100% inflation, the telltale chart becomes an inflation-adjusted growth chart (i.e. showing the growth of an initial investment over time, in real terms).<br />
* If a more concrete benchmark is used (e.g. US Total Market, aka TSM), the telltale chart shows the relative growth over time of the portfolios of interest compared to the benchmark.<br />
<br />
Typical examples of Telltale charts generated with the Simba spreadsheet can be found here: [https://finpage.blog/2018/02/15/telling-tales-2017-update Telling Tales – 2017 update].<br />
</onlyinclude><br />
<br />
==Compatibility==<br />
The spreadsheet is maintained using Microsoft Excel 2011, and provided in XLSX format.<br />
<br />
It should work fairly well with recent versions of [https://www.libreoffice.org/discover/calc/ LibreOffice Calc], with some minor limitations. Once the file has been downloaded from Google Drive, open the file and save it in the suggested "ODF" default format. Otherwise, the charts will not be preserved in the correct format.<br />
<br />
There is some level of incompatibility with Google Sheets. The calculations and statistics appear to work well, while the charts do not. <br />
<br />
==Inner Workings==<br />
As any complex spreadsheet, the inner workings of the Simba spreadsheet may not be quite obvious by just looking at formulas. The following series of blog articles documents various aspects of how it actually works.<br />
<br />
*[https://finpage.blog/2018/02/02/inner-workings-of-the-simba-backtesting-spreadsheet-a-layered-structure Simba backtesting spreadsheet: a layered structure], elaborating on how the spreadsheet is constructed, and providing an overview of its layered structure.<br />
*[https://finpage.blog/2018/02/04/simba-backtesting-spreadsheet-risk-metrics-risk-ratios Simba backtesting spreadsheet: risk metrics, risk ratios]: elaborating on how risk metrics (e.g. volatility, drawdowns, etc) and risk ratios (e.g. Sharpe, Sortino, etc) are computed.<br />
*[https://finpage.blog/2018/02/04/simba-backtesting-spreadsheet-advanced-topics Simba backtesting spreadsheet: advanced topics]: elaborating on more advanced topics (e.g. unbalancing, safe withdrawal rate).<br />
*[https://finpage.blog/2018/02/05/simba-backtesting-spreadsheet-miscellaneous-topics Simba backtesting spreadsheet: miscellaneous topics]: addressing a few miscellaneous topics (e.g. end label on charts, compatibility issues, spreadsheet analytics).<br />
<br />
==References==<br />
<references /><br />
<br />
==External links==<br />
*[http://www.bogleheads.org/forum/viewtopic.php?t=2520 Spreadsheet for backtesting (includes TrevH's data)], forum thread containing Simba's spreadsheet.<br />
*[[wikipedia:Backtesting|Backtesting]], on Wikipedia<br />
*[http://www.financialtrading.com/issues-related-to-back-testing/ Issues Related to Back Testing], from FinancialTrading.com<br />
*[http://www.investopedia.com/terms/b/backtesting.asp Backtesting], from Investopedia<br />
{{Resources and links}}<br />
{{Spreadsheets}}<br />
[[Category:Google Docs.spreadsheets]]<br />
[[Category:Resources and links]]</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Placing_cash_needs_in_a_tax-advantaged_account&diff=68668
Placing cash needs in a tax-advantaged account
2019-12-29T20:00:57Z
<p>Siamond: /* Fine points */ Another round of rewording, plus consolidated bullet points about capital gains</p>
<hr />
<div><br />
If you have a sizable taxable account, it is possible to '''place a cash needs requiremen'''t, such as an [[:Emergency fund | emergency fund]] or home down payment, '''in a tax-advantaged account''' and improve the overall tax efficiency of an investment portfolio.<br />
<br />
{{Notice|<br />
Placing emergency funds in volatile accounts can be risky. Consider that the stock market may drop 50% when you need the money the most, forcing you to withdraw from the tax-advantaged account.<ref>{{forum post|t=65387|title=Emergency funds}}, Dec 26, 2010</ref> Thus, the taxable account should be twice as large as your cash needs. If it's smaller, keep a proportional portion of your cash needs in cash.<br />
}}<br />
<br />
==How it works==<br />
<br />
Suppose you have $15,000 in your portfolio with additional $5,000 as emergency fund. Then you could have:<br />
<br />
* Taxable<br>$10,000 tax-efficient stock index funds<br />
<br />
* Tax-advantaged account, such as [[401(k)]]<br>$5,000 money market fund <- emergency fund<br>$5,000 bond fund<br />
<br />
Let's say you need $5,000 in emergency. Then you sell $5,000 from the stock index funds in your taxable account and exchange the money market fund for similar stock funds in the money market fund in your tax-advantaged account. You are left with:<br />
<br />
* Taxable<br>$5,000 tax-efficient stock index funds<br />
<br />
* Tax-advantaged account, such as 401(k)<br>$5,000 stock funds<br>$5,000 bond fund<br />
<br />
Notice that you have not changed the asset allocation at all.<ref group="note"><br />
''White Coat Investor'' commented in this {{Forum post|t=177528&p=2686420#p2686420|title=Buying a house in 2-4 years; what do I do with my mutual funds?}} on the transfer from an existing investment in equity to a safer option for a house down payment:<br />
<blockquote>"The main thing is to consider your options in the event of a huge bear market. If the market drops 50%, what will you do? Here are some choices:<br />
<br />
# Don't buy the house and just keep renting until the stocks recover and future savings gets you back to where you want to be.<br />
# Maybe houses will be cheaper in an economic downturn and you can still buy it with your decreased amount.<br />
# Maybe houses will be cheaper and you can use a mortgage with < 20% down, leaving your investments intact.<br />
# Maybe you won't buy a house at all.<br />
<br />
For some people, for whom these options aren't good choices, should sell their stocks now and put the money in CDs. But there are many people for whom these other options are very realistic alternatives. For them, keeping some or all of the money in stocks is probably okay. The expected return is higher, even if the actual return may not be."</blockquote></ref><br />
<br />
==Why it works==<br />
<br />
The tax efficiency of holding your cash needs in a tax-advantaged account comes in two forms.<br />
<br />
===While you do not need the cash===<br />
While you do not need the cash, tax-efficient stock index funds generally yield 2% or so, which are all or mostly qualified dividends; most of the return is from capital gains which are not taxed until you sell. Depending on the interest rate, a typical money market fund yields anywhere from 2% to 5%, and the dividends are all non-qualified dividends. In addition, you can do [[Tax loss harvesting | tax loss harvesting]] on the stock funds.<br />
<br />
===When you need the cash===<br />
When you sell a part of the tax-efficient stock index funds, you realize either losses or long-term capital gains. Losses can be deducted on your tax return after offsetting capital gains, if any. Long-term capital gains are taxed more favorably than non-qualified dividends.<br />
<br />
==Candidates for tax-efficient stock index funds==<br />
The following funds are good candidates to invest cash needs in, but there are others that are just as good.<br />
<br />
US Domestic:<br />
* Vanguard Total Stock Market Index Fund<br />
* Vanguard Large-Cap Index Fund<br />
<br />
International:<br />
* Vanguard Total International Stock Market Index Fund<br />
* Vanguard FTSE All-World ex-US Index Fund<br />
<br />
The ''[[Principles of tax-efficient fund placement]]'' article prefers placing international stocks in the taxable account. Each pair is suitable for [[Tax loss harvesting | tax loss harvesting]] and avoiding [[wash sale | wash sales]].<br />
<br />
==Fine points==<br />
<br />
* Use [[Specific identification of shares]]. Sell tax lots with losses or tax lots with the highest cost basis that have long-term capital gains. If you do not use [[Specific identification of shares]], it's difficult to minimize tax. Short-term capital gains are usually taxed more heavily than ordinary income, which negates the benefit of placing cash needs in a tax-advantaged account. For this reason, you may want to wait for 12 months before you place cash needs in a tax-advantaged account if you are starting a taxable account now.<br />
* Avoid a [[wash sale]]. If you sell shares of the tax-efficient stock index funds with losses and buy "substantially identical" securities in your the tax-advantaged account (within 30 days before or after the sale), that is a wash sale. Losses cannot be deducted at all in this case. Therefore, you need to find a fund which is not substantially identical to purchase in your tax-advantaged account; preferably, it should be similar, such as an active fund in the same asset class as the index, or a fund tracking a different index. If you prefer to hold the original fund in your tax-advantaged account, you may switch after 31 days.<br />
* Make sure your taxable account is large enough. Keep in mind that the stock market tanking by 50% is not uncommon. If your taxable account is not large enough, say twice as large as the cash needs, then you may not have enough money in your taxable account during a market downturn. The market could actually go down by '''more''' than 50%, and that is a risk of this technique if the taxable account doesn’t provide enough cushion. For this reason, you may be able to keep a small amount of cash needs (e.g. sized for emergency needs) in tax-efficient stock index funds, but you may not want to keep a large amount of cash needs (e.g. a home down payment fund) in such potentially volatile investments, unless you have a very large taxable retirement portfolio.<br />
<br />
==See also==<br />
*[[:Emergency fund]]<br />
*[[Principles of tax-efficient fund placement]]<br />
*[[Tax loss harvesting]]<br />
<br />
==Notes== <br />
<references group="note"/><br />
<br />
==References==<br />
{{Reflist|30em}}<br />
<br />
{{Tax considerations}}<br />
{{Money markets}}<br />
<br />
[[Category:Asset allocation]]<br />
[[Category:Tax considerations]]<br />
[[Category:Money markets]]</div>
Siamond
https://www.bogleheads.org/w/index.php?title=Placing_cash_needs_in_a_tax-advantaged_account&diff=68666
Placing cash needs in a tax-advantaged account
2019-12-29T18:55:19Z
<p>Siamond: /* Fine points */ Slightly reworded 50% drop commentary</p>
<hr />
<div><br />
If you have a sizable taxable account, it is possible to '''place a cash needs requiremen'''t, such as an [[:Emergency fund | emergency fund]] or home down payment, '''in a tax-advantaged account''' and improve the overall tax efficiency of an investment portfolio.<br />
<br />
{{Notice|<br />
Placing emergency funds in volatile accounts can be risky. Consider that the stock market may drop 50% when you need the money the most, forcing you to withdraw from the tax-advantaged account.<ref>{{forum post|t=65387|title=Emergency funds}}, Dec 26, 2010</ref> Thus, the taxable account should be twice as large as your cash needs. If it's smaller, keep a proportional portion of your cash needs in cash.<br />
}}<br />
<br />
==How it works==<br />
<br />
Suppose you have $15,000 in your portfolio with additional $5,000 as emergency fund. Then you could have:<br />
<br />
* Taxable<br>$10,000 tax-efficient stock index funds<br />
<br />
* Tax-advantaged account, such as [[401(k)]]<br>$5,000 money market fund <- emergency fund<br>$5,000 bond fund<br />
<br />
Let's say you need $5,000 in emergency. Then you sell $5,000 from the stock index funds in your taxable account and exchange the money market fund for similar stock funds in the money market fund in your tax-advantaged account. You are left with:<br />
<br />
* Taxable<br>$5,000 tax-efficient stock index funds<br />
<br />
* Tax-advantaged account, such as 401(k)<br>$5,000 stock funds<br>$5,000 bond fund<br />
<br />
Notice that you have not changed the asset allocation at all.<ref group="note"><br />
''White Coat Investor'' commented in this {{Forum post|t=177528&p=2686420#p2686420|title=Buying a house in 2-4 years; what do I do with my mutual funds?}} on the transfer from an existing investment in equity to a safer option for a house down payment:<br />
<blockquote>"The main thing is to consider your options in the event of a huge bear market. If the market drops 50%, what will you do? Here are some choices:<br />
<br />
# Don't buy the house and just keep renting until the stocks recover and future savings gets you back to where you want to be.<br />
# Maybe houses will be cheaper in an economic downturn and you can still buy it with your decreased amount.<br />
# Maybe houses will be cheaper and you can use a mortgage with < 20% down, leaving your investments intact.<br />
# Maybe you won't buy a house at all.<br />
<br />
For some people, for whom these options aren't good choices, should sell their stocks now and put the money in CDs. But there are many people for whom these other options are very realistic alternatives. For them, keeping some or all of the money in stocks is probably okay. The expected return is higher, even if the actual return may not be."</blockquote></ref><br />
<br />
==Why it works==<br />
<br />
The tax efficiency of holding your cash needs in a tax-advantaged account comes in two forms.<br />
<br />
===While you do not need the cash===<br />
While you do not need the cash, tax-efficient stock index funds generally yield 2% or so, which are all or mostly qualified dividends; most of the return is from capital gains which are not taxed until you sell. Depending on the interest rate, a typical money market fund yields anywhere from 2% to 5%, and the dividends are all non-qualified dividends. In addition, you can do [[Tax loss harvesting | tax loss harvesting]] on the stock funds.<br />
<br />
===When you need the cash===<br />
When you sell a part of the tax-efficient stock index funds, you realize either losses or long-term capital gains. Losses can be deducted on your tax return after offsetting capital gains, if any. Long-term capital gains are taxed more favorably than non-qualified dividends.<br />
<br />
==Candidates for tax-efficient stock index funds==<br />
The following funds are good candidates to invest cash needs in, but there are others that are just as good.<br />
<br />
US Domestic:<br />
* Vanguard Total Stock Market Index Fund<br />
* Vanguard Large-Cap Index Fund<br />
<br />
International:<br />
* Vanguard Total International Stock Market Index Fund<br />
* Vanguard FTSE All-World ex-US Index Fund<br />
<br />
The ''[[Principles of tax-efficient fund placement]]'' article prefers placing international stocks in the taxable account. Each pair is suitable for [[Tax loss harvesting | tax loss harvesting]] and avoiding [[wash sale | wash sales]].<br />
<br />
==Fine points==<br />
<br />
* Use [[Specific identification of shares]]. Sell tax lots with losses or tax lots with the highest cost basis that have long-term capital gains. If you do not use [[Specific identification of shares]], it's difficult to minimize tax.<br />
* Avoid a [[wash sale]]. If you sell shares of the tax-efficient stock index funds with losses and buy "substantially identical" securities in your the tax-advantaged account (within 30 days before or after the sale), that is a wash sale. Losses cannot be deducted at all in this case. Therefore, you need to find a fund which is not substantially identical to purchase in your tax-advantaged account; preferably, it should be similar, such as an active fund in the same asset class as the index, or a fund tracking a different index. If you prefer to hold the original fund in your tax-advantaged account, you may switch after 31 days.<br />
* Make sure your taxable account is large enough. Keep in mind that the stock market tanking by 50% is not uncommon. If your taxable account is not large enough, say twice as large as the cash needs, then you may not have enough money in your taxable account during a market downturn. For this reason, you may be able to keep a small amount of cash needs (e.g. sized for emergency needs) in tax-efficient stock index funds, but you may not want to keep a large amount of cash needs (e.g. a home down payment fund) in such potentially volatile investments, unless you have a very large taxable retirement portfolio. Keep in mind that the market could go down by more than 50%, and that is a risk of this technique if the taxable account doesn’t provide enough cushion.<br />
* Make sure you have shares that you can sell with long-term capital gains. Otherwise, you may have to sell shares with short-term capital gains. In some states, short-term capital gains are taxed more heavily than ordinary income, which negates the benefit of placing cash needs in a tax-advantaged account. For this reason, you may want to wait for 12 months before you place cash needs in a tax-advantaged account if you are starting a taxable account now.<br />
<br />
==See also==<br />
*[[:Emergency fund]]<br />
*[[Principles of tax-efficient fund placement]]<br />
*[[Tax loss harvesting]]<br />
<br />
==Notes== <br />
<references group="note"/><br />
<br />
==References==<br />
{{Reflist|30em}}<br />
<br />
{{Tax considerations}}<br />
{{Money markets}}<br />
<br />
[[Category:Asset allocation]]<br />
[[Category:Tax considerations]]<br />
[[Category:Money markets]]</div>
Siamond
https://www.bogleheads.org/w/index.php?title=User:Siamond/Inverse_and_leveraged_ETFs&diff=68560
User:Siamond/Inverse and leveraged ETFs
2019-12-13T04:27:47Z
<p>Siamond: Siamond moved page User:Siamond/Inverse and leveraged ETFs to User:Siamond/Leveraged and inverse ETFs: Same order of word as SEC/FINRA alert</p>
<hr />
<div>#REDIRECT [[User:Siamond/Leveraged and inverse ETFs]]</div>
Siamond
https://www.bogleheads.org/w/index.php?title=User:Siamond/Leveraged_and_inverse_ETFs&diff=68559
User:Siamond/Leveraged and inverse ETFs
2019-12-13T04:27:47Z
<p>Siamond: Siamond moved page User:Siamond/Inverse and leveraged ETFs to User:Siamond/Leveraged and inverse ETFs: Same order of word as SEC/FINRA alert</p>
<hr />
<div>{{Under construction|comment = Comments are solicited in this {{Forum post| t= 296428| title= <nowiki>[Wiki article update - Inverse and leveraged ETFs]</nowiki>}}}}<br />
'''Leveraged and Inverse ETFs''' ([[Exchange-traded funds]])<ref group="note">''Leveraging'' is also called ''gearing''. ''Leveraged'' ETFs and ''Geared'' ETFs mean the same thing.</ref> are ETF structures intended to provide returns that are positive or negative multiples of an equivalent ETF benchmark. The purpose of this article is to explain why these ETFs present significant risks as long-term investments.<br />
{{Warning|The SEC and FINRA has issued a joint alert, "Leveraged and Inverse ETFs: Specialized Products with Extra Risks for Buy-and-Hold Investors." It states:<ref name="SEC">{{cite web| publisher=Financial Industry Regulator Authority| url=http://www.finra.org/investors/alerts/leveraged-and-inverse-etfs-specialized-products-extra-risks-buy-and-hold-investors| title=Leveraged and Inverse ETFs: Specialized Products with Extra Risks for Buy-and-Hold Investors| date=August 18, 2009}}</ref><blockquote>The SEC staff and FINRA are issuing this Alert because we believe individual investors may be confused about the performance objectives of leveraged and inverse exchange-traded funds (ETFs). Leveraged and inverse ETFs typically are designed to achieve their stated performance objectives on a daily basis. Some investors might invest in these ETFs with the expectation that the ETFs may meet their stated daily performance objectives over the long term as well. [...] Only invest if you are confident the product can help you meet your investment objectives and you are knowledgeable and comfortable with the risks associated with these specialized ETFs.</blockquote>}}<br />
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==Overview==<br />
There are 3 structures:<ref name="SEC" /><br />
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*'''Leveraged ETFs''' seek to deliver multiples of the performance of the index or benchmark they track.<br />
*'''Inverse ETFs''' (also called "short" funds) seek to deliver the ''opposite'' of the performance of the index or benchmark they track.<br />
*'''Leveraged inverse ETFs''' (also known as "ultra short" funds) seek to achieve a return that is a multiple of the inverse performance of the underlying index.<br />
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Here are several example ETF descriptions:<br />
*'''ProShares UltraPro S&P500 (UPRO)''' seeks daily investment results, before fees and expenses, that correspond to three times (3x) the daily performance of the S&P 500<sup>®</sup>.<ref>[http://www.proshares.com/funds/upro.html ProShares ETFs: UltraPro S&P500]</ref><br />
*'''ProShares Ultra S&P500 (SSO)''' seeks daily investment results, before fees and expenses, that correspond to two times (2x) the daily performance of the S&P 500<sup>®</sup>.<ref>[http://www.proshares.com/funds/sso.html ProShares ETFs: Ultra S&P500]</ref><br />
*'''ProShares UltraShort S&P500 (SDS)''' seeks daily investment results, before fees and expenses, that correspond to two times the inverse (-2x) of the daily performance of the S&P 500<sup>®</sup>.<ref>[http://www.proshares.com/funds/sds.html ProShares ETFs: UltraShort S&P500]</ref><br />
*'''Direxion Emerging Markets Bear 3X ETF (EDZ)''' seeks daily investment results, before fees and expenses, of 300% of the inverse (or opposite) of the performance of the MSCI Emerging Markets Index.<ref>[http://www.direxionfunds.com/products/direxion-daily-emerging-markets-bear-3x-etf Direxion Daily Emerging Markets Bear 3x Shares]</ref><br />
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Let's look at the 4th example fund provider, Direxion. Notice that Direxion itself<ref>[http://www.direxionfunds.com/signs Leveraged ETF List | Direxion]</ref> says these funds are for "short-term trading." This is not a detail or a pro forma disclaimer - it is explicitly displayed in the figure below.<br />
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{|style="border-collapse: collapse;" border="1" <!-- set border="1" to see table boundaries, outer table draws outside border. --><br />
|+'''Direxion ETF Fund Categories'''<br />
||<br />
[[image:Direxionsayshorterm.png]]<br />
|}<br />
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The first category, "Long Term Investment" contains 3 ETFs which match a benchmark. The second category contains 2 leveraged ETFs ("3X") and is titled "Short Term Trading" which is a warning sign that these ETFs will perform differently than those intended for long-term investments. The link "Are Direxion Shares ETFs for you?" is an additional warning sign, as there would be no reason to ask this question if these ETFs performed similarly to ETFs intended for long-term investments.<br />
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Brokerages typically require customers to sign a special disclaimer in order to open a margin account. Everyone understands that using leverage in the form of a margin account is taking on a big risk, the risk of losing more than your total investment. It is a mistake to think you can get essentially similar results, more conveniently and without the risk of losing more than your investment, simply by using an inverse or leveraged ETF.<br />
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Anyone thinking of using an inverse or leveraged ETF needs to read and understand the fund company's factsheets and prospectus, which disclose the issues in language varying from veiled to clear.<br />
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==How does a daily leveraged ETF work?==<br />
A daily leveraged ETF holds a combination of derivatives and actual securities to track a multiple of the underlying index's daily performance.<br />
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Let's examine ProShares UltraPro S&P500 (UPRO), which promises to deliver 3x the daily performance of the S&P 500. It does this by holding 77% individual S&P 500 stocks, nominal exposure to 215% of the S&P 500 through total return swaps, and 8% S&P futures. Add it all up, and you get exposure to 300% of the S&P 500’s daily performance.<ref>[https://www.proshares.com/resources/prospectus_reports.html ProShares Geared Funds Annual] 5/31/2019, market exposure on printed page LIX.</ref><br />
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Total return swaps are contracts between the ETF and major investment banks. For UPRO, every day the banks pay the ETF the value of the S&P 500’s total return for that day, and in return the ETF pays the banks a pre-negotiated rate of interest, which is close to the short term treasury rate. As of May 2019, the borrowing rate of some UPRO's swap agreements was 3.01%.<ref>[https://www.proshares.com/resources/prospectus_reports.html ProShares Geared Funds Annual] 5/31/2019, swap agreements on printed page 138, e.g. BNP Paribas rate as of May 31, 2019.</ref> The corresponding cost is NOT included in UPRO's 0.92% expense ratio.<br />
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==Daily results are significantly different than long-term==<br />
It is critical to understand that a movement in one direction followed by an equal movement in the opposite direction will '''not''' get you back to the starting value. For example, a gain of 10% followed by a loss of 10% will end up with a loss of 1.0%.<ref name="ReturnCalc">Details are in this {{Forum post| p=4882043|title = Re: <nowiki>[Wiki article update - Inverse and leveraged ETFs]</nowiki> |author = LadyGeek | date = December 09, 2019}}</ref> This is nothing but math at work. The math works the same for any investment – regardless if it’s a single stock or a fund. See [[Percentage gain and loss]] for the details.<br />
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This math will be very evident as a fund performs over time. If the market has equal gains and losses over a period of time, the fund’s value will always be lower. For example, 6 consecutive days which alternate as +10% then -10% will result in a loss of 3.0%.<ref name="ReturnCalc" /> The change in loss from 1.0% to 3.0% is known as ''volatility decay''.<ref group="note">Also known as [[volatility drag]], but ''volatility decay'' is the term used for leveraged funds.</ref><br />
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Over the course of a single day, the fund will generate a return as advertised. For example, a 3X leveraged fund will generate three times the gain (and loss) of an unleveraged fund.<br />
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However, that’s not the entire story. Leveraged funds [[rebalance]] their exposure to their underlying benchmarks on a daily basis by trimming or adding to their positions. Over time, a longer-term investor is unlikely to continue to receive the fund's multiple of the benchmark's returns.<ref name="ProShares">{{cite web| publisher=ProShares| url=https://www.proshares.com/funds/performance/the_universal_effects_of_compounding.html| title=Effects Of Daily Rebalancing and Compounding on Geared Investing| accessdate=December 09, 2019}}</ref><br />
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Investment returns compound over time. The effects of compounding will also cause the fund to deviate from the fund's stated objective, e.g. 2X or 3X of the index's return. In trending periods, compounding can enhance returns, but in volatile periods, compounding may hurt returns. Generally speaking, the greater the multiple or more volatile a fund's benchmark, the more pronounced the effects can be.<ref name="ProShares" /><br />
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It is why the fund’s fact sheets have disclaimers stating that performance is only guaranteed on a daily basis.<br />
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==A comprehensive example==<br />
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Now, let's illustrate how big the difference is between "daily" and long-term results.<br />
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Some investors think they see interesting theoretical possibilities for using [[leverage]] in long-term investing. If so, they should '''not''' think that over long periods of time they can get double the return of the S&P 500 simply by investing in a 2X leveraged S&P 500 ETF. <br />
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The word "daily" has a very precise meaning. These products double or triple the long or short index for a single day, so '''if you are someone who trades in and out of positions on a daily basis''', they actually do pretty much what you'd expect. Not so over long periods, '''and the difference can be large'''.<br />
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The ETF companies disclose this point fairly clearly in the factsheets, such as:<br />
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<blockquote>'''Direxion:''' "This leveraged ETF seeks a return that is -300% the return of its benchmark index for a single day. The fund should not be expected to provide three times the return of the benchmark’s cumulative return for periods greater than a day.", and<br><br><br />
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'''ProShares:''' "Due to the compounding of daily returns, ProShares' returns over periods other than one day will likely '''differ in amount''' and possibly '''<nowiki>[differ in]</nowiki> direction''' from the target return for the same period."</blockquote><br />
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In order to illustrate the potential impact, let's ask: "'''How much is that in dollars?'''" which is quantified in the following sections.<br />
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==="differ in amount"===<br />
"Differ in amount" means that the "2X" fund might not deliver twice the return of the index. For example, ProShares Ultra S&P 500 ETF, SSO began in 6/2007. $10,000 invested in the Vanguard 500 Index fund would have gained a total of $6,966 in total return since that time (6/20/2006 to 12/31/2013). Did the Ultra fund earn twice that ($13,932)?<br />
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{|style="border-collapse: collapse;" border="1" <!-- set border="1" to see table boundaries, outer table draws outside border. --><br />
|+'''Comparison of ProShares Ultra S&P 500 (SSO) to Vanguard 500 Index (VFINX)'''<br />
||[[image:Vfinx-beats-sso.png]]<br />
|}<br />
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It did not. It earned $6,097, which is less than the Vanguard 500 Index fund earnings. ''The 2X ETF earned less than the straight, unleveraged, direct investment.''<br />
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==="differ in direction"===<br />
This is a way of saying that over periods of more than a day, your ETF could go down even when the inverse or leveraged index it is tied to goes up. This is why ProShares says "Investors should monitor their holdings consistent with their strategies, as frequently as daily."<br />
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We will illustrate with a deliberately-picked and unusual period of time (12/31/2007 to 12/31/2010), but it is a valid illustration of the effect of volatility decay on a leveraged ETF. Before showing the results, here is a question. <br />
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Over this time period, an investment of $10,000 in Vanguard 500 Index fund lost $846. Knowing this, which of these three investments do you think did the best over that time period?<br />
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:a) Vanguard 500 Index Fund (VFINX)<br />
:b) ProShares Ultra S&P (SSO), "two times (2x) the daily performance of the S&P 500"<br />
:c) ProShares UltraShort S&P (SDS), "two times the inverse (-2x) of the daily performance of the S&P 500."<br />
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'''The answer is (a)'''. If you reasoned that since the S&P 500 lost money, an ETF that shorts the S&P ought to have made money, you were mistaken.<br />
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*The Vanguard 500 index fund lost $846. <br />
*ProShares Ultra S&P (SSO), the 2X ETF for the same index lost. But it didn't lose just twice as much as VFINX, it lost over four times as much-- $4,050.<br />
*ProShares UltraShort S&P (SDS), the 2X short ETF (-2X, gains if benchmark drops) which should have earned a profit, lost even more -- $4,595.<br />
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Over this time period, you could have been right about the ''direction'' of the S&P but still lost money. And this isn't just a matter of a few percent or an expense ratio difference, ''the loss is more than 4.8 times the amount of an unleveraged direct investment''.<ref group="note">The loss is 4.8 times = 4050/846 for the 2X ETF, 5.4 times = 4,595/846 for the short -2X ETF.</ref><br />
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{|style="border-collapse: collapse;" border="1" <!-- set border="1" to see table boundaries, outer table draws outside border. --><br />
|+'''Comparison of ProShares Ultra S&P (SSO), ProShares Ultra S&P 500 (SDS) and Vanguard 500 Index (VFINX)'''<br />
||[[image:Vfinx-sso-ssd-heads-you-lose-tails-you-lose.png]]<br />
|}<br />
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==Historical drawdowns==<br />
A major risk presented by leveraged funds is how the impact of stock market crises can get magnified. Drawdowns (sudden loss of value) will get amplified in both depth and duration. The following chart presents a simulation of a regular index fund, a 2x leverage fund and a 3x leverage, all tracking the S&P 500 index. As you can see, the oil crisis in the 70s would have been magnified with dizzying drops and drawdowns lasting more than a decade. The more recent Internet and financial crises would have led to nearly two decades of misery, finally followed by a steep recovery. Staying the course with a long term investment in leveraged funds during such a crisis would seem extremely challenging.<ref name="blog">[https://finpage.blog/2019/12/12/leveraging-sp-500-quantitative-analysis/ Bogleheads blog (2019): Leveraging S&P 500 – Quantitative Analysis]</ref><br />
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{|<br />
[[File:S&P 500 LETF Drawdowns.jpg|960px]]<br />
|}<br />
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==Risks and rewards==<br />
As clearly illustrated by the charts in previous sections, leveraged (and inverse) ETFs are much more volatile than corresponding indices (and index funds). Between Jan-10 and Nov-19, the standard deviation of monthly returns was amplified by approximately the amount of leverage:<ref name="blog"/><br />
* VFINX (regular S&P 500 passive index fund from Vanguard): 12.5%<br />
* SSO (ProShares Ultra S&P500, 2x leverage): 25.4%<br />
* UPRO (ProShares UltraPro S&P500, 3x leverage): 38.5%<br />
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A historical simulation of leveraged funds over the 1955 to 2018 time period showed similar characteristics:<ref name="blog"/><br />
* Regular S&P 500 passive fund: 14.5%<br />
* S&P 500 2x leverage: 29.1%<br />
* S&P 500 3x leverage: 43.7%<br />
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The question becomes the following. If a steely investor had been able to cope with such increased volatility (including dizzying drawdowns), what would have been the rewards for staying the course? Real-life funds would have provided attractive annualized growth from Jan-10 to Nov-19 (VFINX 13%, SSO 23%, UPRO 32%), but this isn't a terribly representative time period, since it was essentially a long bull market. <br />
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Using the historical simulation, we can study rolling (annualized) returns over a much longer time frame, including three major crises of the US stock market.<ref name="blog"/><br />
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{|<br />
[[File:Rolling_Periods_CAGR_Stats_Leveraging_2x_3x.jpg|960px]]<br />
|}<br />
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As the table indicates, over short periods of time, leveraging can deliver stronger returns, albeit with a lot of risk. Over longer periods, the return premium disappears on average while the risk (dispersion of outcomes) remains very acute. Overall, the case for rewards (i.e. improved annualized returns) seems remarkably weak for long-term buy and hold investments, compared to the volatility and drawdown risks previously quantified.<br />
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==Summary==<br />
Regardless of what you might or might not think about the possible usefulness of a long-term [[leverage|leveraged]] position achieved by using margin, leveraged and inverse ETFs are completely different products and do not give remotely comparable results. <br />
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In short, leveraged and inverse ETFs are specialized products, which present major risks as long-term buy and hold investments and little rewards in return for such risks. The use of such products as part of a regular asset allocation should be discouraged.<br />
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==Other points of view==<br />
Long-term risks associated with a specific asset can sometimes be mitigated by the use of another asset (e.g. using rebalancing and risk parity strategies<ref>Investopedia: [https://www.investopedia.com/terms/r/risk-parity.asp Risk Parity]</ref>). These are sophisticated portfolios, constructed by investors who fully understand all the risks described above; they accept the irreducible potential risk of any portfolio, no matter how carefully constructed, that contains high-risk assets.<br />
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An article in the ''Journal of Indexes,'' authored by Joanne Hill and George Foster, both of ProShares, note that "it is likely that leveraged and inverse ETFs are commonly being utilized as short-term tactical trading tools" but state that, nevertheless, by applying certain rebalancing strategies, "leveraged and inverse funds have been and can be used successfully for periods longer than one day." The article, "Understanding Returns of Leveraged and Inverse Funds",<ref>Hill, Joanne, and George Foster (2009), [http://www.indexuniverse.com/publications/journalofindexes/joi-articles/6414-understanding-returns-of-leveraged-and-inverse-funds.html?showall=&fullart=1&start=7 Understanding Returns of Leveraged and Inverse Funds]. Dr. Hill is Head of Investment Strategy at ProShares; George Foster is Chief Investment Officer.</ref> gives a detailed analysis of how volatility affects leveraged and inverse ETFs.<br />
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Another article authored by Cliff Asness, from AQR Capital Management, "Risk Parity: Why We Lever",<ref>Click Asness (2014), [https://www.aqr.com/Insights/Perspectives/Risk-Parity-Why-We-Fight-Lever Risk Parity: Why We Lever].</ref> advocates that "willingness to use modest leverage allows a risk parity investor to build a more diversified, more balanced, higher-return-for-the-risk-taken portfolio."<br />
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==See also==<br />
*[[Exchange-traded funds]]<br />
*[[Leverage]]<br />
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==Notes==<br />
<references group="note" /><br />
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==References==<br />
<references /><br />
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==External links==<br />
*[http://www.proshares.com/considerations_geared_investing.html Considerations for Geared Investing], by [http://www.proshares.com/about/index.html ProShares]. A brief overview of Geared ETFs.<br />
*[http://www.proshares.com/media/documents/geared_fund_performance.pdf What You Should Know about Geared Fund Performance], by [http://www.proshares.com/about/index.html ProShares]. A guide that covers several key concepts about geared fund performance.<br />
*{{Forum post|title = <nowiki>[Wiki article update - Inverse and leveraged ETFs]</nowiki>|t= 296428| date = Nov 30, 2019}}<br />
{{Mutual funds}}</div>
Siamond