Difference between revisions of "User:LadyGeek/Diversification"

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(→‎Introduction: Include asset classes in broad diversification.)
(→‎Sector diversification: a) picking stocks in different sectors b) equal-weighting sectors)
 
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{{Under construction|comment= Comments are solicited in this {{Forum post|t=285269|title=De-Risking and Diversification aren't the same thing.}}}}
 
{{Under construction|comment= Comments are solicited in this {{Forum post|t=285269|title=De-Risking and Diversification aren't the same thing.}}}}
==Introduction==
+
 
Generally speaking, ''diversification'' is about not putting all of one's eggs into a single basket. The U.S. Securities and Exchange Commission writes:
+
Generally speaking, '''diversification''' is about not putting all of one's eggs into a single basket. The U.S. Securities and Exchange Commission writes:
  
 
<blockquote>Diversification can be neatly summed up as, “Don’t put all your eggs in one basket.” The idea is that if one investment loses money, the other investments will make up for those losses. Diversification can’t guarantee that your investments won’t suffer if the market drops. But it can improve the chances that you won’t lose money, or that if you do, it won’t be as much as if you weren’t diversified.<ref>The Securities and Exchange Commission[https://www.investor.gov/introduction-investing/basics/save-invest/diversify-your-investments]</ref></blockquote>
 
<blockquote>Diversification can be neatly summed up as, “Don’t put all your eggs in one basket.” The idea is that if one investment loses money, the other investments will make up for those losses. Diversification can’t guarantee that your investments won’t suffer if the market drops. But it can improve the chances that you won’t lose money, or that if you do, it won’t be as much as if you weren’t diversified.<ref>The Securities and Exchange Commission[https://www.investor.gov/introduction-investing/basics/save-invest/diversify-your-investments]</ref></blockquote>
  
Unfortunately, there is no single universally accepted ''precise'' definition for "diversification". Different authors use the word "diversification" to mean different things. This is much like the word "risk" which, for example, is used by some authors to mean "volatility" and by other authors to mean "possibility of loss". Yet, we can identify two main meanings for the word diversification in an investment context.
+
Unfortunately, there is no single universally accepted ''precise'' definition for "diversification". Different authors use the word "diversification" to mean different things. This is much like the word "[[Risk and return: an introduction|risk]]" which, for example, is used by some authors to mean "possibility of loss" and by other authors to mean "volatility". Two main meanings for the word diversification in an investment context follow:
  
The first meaning appears in the text of authors who often combine the word "broad" (or a similar one) with the word "diversification" to mean "spreading one's money broadly across a market" (using capitalisation-weighting for obvious arithmetic reasons<ref>Equal-weighting can't be applied to the total market: {{forum post|p=120430|title=What's wrong with this critique of indexing?}}.</ref>) and across stocks, bonds, and (sometimes) cash. For example, when discussing the creation of the Vanguard S&P 500 index fund and of the Vanguard Total Stock Market index fund, Jack Bogle wrote:
+
The first meaning appears in the text of authors who often combine the word "broad" (or a similar one) with the word "diversification" to mean "spreading one's money broadly across a market" (using capitalization-weighting for obvious arithmetic reasons<ref>Equal-weighting can't be applied to the total market: {{forum post|p=120430|title=What's wrong with this critique of indexing?}}.</ref>) and across [[Stock basics|stocks]], [[Bond basics|bonds]], and (sometimes) cash. For example, when discussing the creation of the Vanguard S&P 500 [[index fund]] and of the Vanguard Total Stock Market index fund, [[John C. Bogle|Jack Bogle]] wrote:
  
 
<blockquote>In 1975, I created the first index mutual fund, now known as Vanguard 500 Index Fund. Then, as now, I considered it the very paradigm of long-term investing, '''a fully diversified''' portfolio of U.S. stocks operated at high tax efficiency and rock-bottom costs, and designed to be held, well, “forever.” It is now the world’s largest equity mutual fund.<ref>The Clash of the Cultures, John C. Bogle, 2012.</ref></blockquote>
 
<blockquote>In 1975, I created the first index mutual fund, now known as Vanguard 500 Index Fund. Then, as now, I considered it the very paradigm of long-term investing, '''a fully diversified''' portfolio of U.S. stocks operated at high tax efficiency and rock-bottom costs, and designed to be held, well, “forever.” It is now the world’s largest equity mutual fund.<ref>The Clash of the Cultures, John C. Bogle, 2012.</ref></blockquote>
  
The second meaning stems from economic theory, where economists, like Markowitz, define "diversification" as a technique to combine securities to reduce "risk" (defined as "volatility") without sacrificing "expected return".
+
The second meaning stems from economic theory, where economists, like [[Harry M. Markowitz|Markowitz]], define "diversification" as a technique to combine securities to reduce "risk" (defined as "volatility") without sacrificing "expected return".
  
 
The above two distinct definitions of "diversification" can be conflictual in the context of portfolio construction (much like the two definitions of "risk" mentioned above).
 
The above two distinct definitions of "diversification" can be conflictual in the context of portfolio construction (much like the two definitions of "risk" mentioned above).
  
 
=="Diversified" versus "non-diversified" funds==
 
=="Diversified" versus "non-diversified" funds==
By regulation, every mutual fund is classified as "diversified" or "not diversified." Most are officially diversified, and those that are not must say so. A summary of the requirements, known as the 75-5-10 rule, is:
+
By regulation, every [[Mutual fund|mutual fund]] is classified as "diversified" or "non-diversified." Most are officially diversified, and those that are not must say so. A summary of the requirements, known as the 75-5-10 rule, is:
  
*75% of the fund's assets must be invested in securities of other issuers. Cash and cash equivalents are included.
+
*75% of the fund's assets must be invested in securities of other issuers. Cash and [[Cash equivalent|cash equivalents]] are included.
 
*5% - The investment company may not invest more than 5% of its assets in any one company.
 
*5% - The investment company may not invest more than 5% of its assets in any one company.
 
*10% - The investment company may not own more than 10% of any company’s outstanding voting stock.<ref>[https://www.law.cornell.edu/uscode/text/15/80a–5 15 U.S. Code § 80a–5 - Subclassification of management companies]. Based on forum discussions, it is does not seem to be clear exactly what is or is not allowed outside the 75%</ref>
 
*10% - The investment company may not own more than 10% of any company’s outstanding voting stock.<ref>[https://www.law.cornell.edu/uscode/text/15/80a–5 15 U.S. Code § 80a–5 - Subclassification of management companies]. Based on forum discussions, it is does not seem to be clear exactly what is or is not allowed outside the 75%</ref>
 +
 +
This corresponds well with one traditional understanding of diversification. Before buying any mutual fund, a buyer should take time to look at the official fund documents for a statement such as "the fund is considered non-diversified." Such a statement isn't necessarily reason for alarm, but it is a red flag that says the fund is ''unusual,'' and that you should look farther and make sure you know ''why'' it is "non-diversified" and whether it is a concern to you.
 +
 +
The definition results in some surprising categorizations. For example, the Vanguard REIT Index Fund, VGSIX, is considered diversified even though it is invested exclusively in a single narrow industry sector, constituting less than only 4% of the stock market: commercial real estate.
 +
 +
On the other hand, the Vanguard Growth Index Fund, VIGAX, holds stocks in ten different sectors. Yet, in April 2019, Vanguard noted that <blockquote>more than 25% of the Fund’s total assets are invested in issuers representing more than 5% of the Fund’s total assets. As a result, the Fund is nondiversified under the Investment Company Act of 1940, although it continues to hold more than 300 stocks across a number of sectors.</blockquote>
 +
 +
AQR says that its Style Premia Alternative Fund<ref>[https://funds.aqr.com/-/media/files/fund-documents/fact-sheets/spaf.pdf QSPIX, Style Premia Alternatives Fund] factsheet</ref> invests "in a broad spectrum of asset classes and markets" and "[seeks] to limit exposure to poor performance within any single style or asset class," while containing a fine-print disclosure that "This Fund is a non-diversified fund."
 +
 +
These seeming surprises simply underline the fact that there is more than one understanding of the term "diversification."
 +
 +
John C. Bogle and others have pointed out that as the assets in a mutual fund grow, the 10% requirement makes it harder and harder for a "diversified" fund to own smaller-cap stocks. For example, a diversified mutual fund with $100 billion in assets, that is actively managed, cannot have any meaningful investment in a microcap stock with $100 million in market cap, because it cannot invest more than $10 million = 0.1% of its portfolio in that stock without breaking the 10% rule. Therefore, as a diversified mutual funds grows, it is constrained to put a smaller and smaller percentage of its portfolio into poorly-known small-company stocks that might offer an opportunity for stockpicking skill, and more and more into the larger-cap stocks that everybody knows about. It becomes harder and harder for growing funds to depart much from the market. This is sometimes called "the curse of success."
 +
 +
==Sector diversification==
 +
Sectors are eleven broad categories of similar businesses. In 1999, MSCI and S&P developed the Global Industry Classification Standard (GICS), which is accepted as the standard definition. Companies that are in the same sector are subject to similar economic forces. The behavior of e.g. Cisco Systems stock depends to a large degree on how high-tech in general is doing, and only partly on what things Cisco itself is doing differently from other high-tech companies.
 +
 +
To illustrate this, consider three stocks in the information technology sector--Amazon, Apple, and Cisco System--and three in the financial sector--Citigroup, AIG, and Bank of America.
 +
 +
During 2000-2003, all of three of the information technology stocks imploded, Apple losing 70% of its value, Amazon losing ''more than 90%''. Meanwhile, the three financials were largely unaffected.
 +
 +
[[File:IT and financials in 2000.jpg|frameless|600px|IT and financials in 2000]]
 +
 +
The turn of financials came in 2008-2009, and this time it was the financials that imploded--a $10,000 investment in Citigroup losing more than 90% of its value, while AIG lost 99.5%, $10,000 becoming $20! Information technology was ''relativy'' unaffected. The value of Cisco was "only" cut in half, and Apple and Amazon made money.
 +
 +
[[File:IT and financials in 2008.jpeg|frameless|600px|IT and financials in 2008]]
 +
 +
 +
The stock market itself, total stock market indexes and index funds, and the S&P 500 which is an approximation to the total market, include stocks in every sector, but not with equal dollar weighting.
 +
 +
[[File:S&P 500 sector weightings 3-31-2019.png|frameless|600px]]
 +
 +
In the context of picking a portfolio of a small number of individual stocks--which is not what Bogleheads generally do with most of their portfolio--diversification can be simply a risk control measure; and intentionally choosing stocks from a variety of sectors is one way to achieve it.
 +
 +
In the context of portfolio construction, perhaps using ETFs and mutual funds, sectors can be viewed as a kind of asset class, and since they have imperfect correlation they can be viewed as uncorrelated asset classes that might produced a quantitative diversification benefit in the Markowitz sense. Thus, it is sometimes suggested that equal sector weighting--putting an equal number of dollars into each of the eleven sectors--might be superior to investing in an S&P 500 or total market index, allowing each sector to have its natural capitalization weight.
 +
 +
==Diversification to reduce idiosyncratic risk==
  
 
==Markowitz diversification==
 
==Markowitz diversification==
Within the framework of modern portfolio theory (MPT), the term ''Markowitz diversification'' can mean <blockquote>combining securities with less-than-perfect positive correlation in order to reduce risk in the portfolio without sacrificing any of the portfolio’s expected return.<ref>{{cite book |last1=Francis|first1=Jack Clark |last2=Kim |first2=Dongcheol |date=213 |title="Modern Portfolio Theory" |url= |location= |publisher="John Wiley & Sons, Inc." |page=120 |isbn=9781118417201 |author-link= }}</ref></blockquote>
+
Within the framework of modern portfolio theory (MPT), the term ''Markowitz diversification'' can mean: <blockquote>Combining securities with less-than-perfect positive correlation in order to reduce risk in the portfolio without sacrificing any of the portfolio’s expected return.<ref>{{cite book |last1=Francis|first1=Jack Clark |last2=Kim |first2=Dongcheol |date=213 |title="Modern Portfolio Theory" |url= |location= |publisher="John Wiley & Sons, Inc." |page=120 |isbn=9781118417201 |author-link= }}</ref></blockquote>
This approach to diversification was introduced by [[Harry M. Markowitz]] in his ground-breaking 1952 paper, ''Portfolio Selection''.<ref>{{cite web |author=Markowitz, H.M.|url=https://www.jstor.org/stable/2975974?seq=1#page_scan_tab_contents |title=Portfolio Selection |publication=[[The Journal of Finance]] |date=March 1952 |volume=7 |issue=1 |pages=77–91}}</ref>
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This approach to diversification was introduced by Harry M. Markowitz in his ground-breaking 1952 paper, ''Portfolio Selection''.<ref>{{cite web |author=Markowitz, H.M.|url=https://www.jstor.org/stable/2975974?seq=1#page_scan_tab_contents |title=Portfolio Selection |publication=[[The Journal of Finance]] |date=March 1952 |volume=7 |issue=1 |pages=77–91}}</ref>
  
 
The basic idea of the math behind Markowitz diversification looks like this:
 
The basic idea of the math behind Markowitz diversification looks like this:
  
[[File:Markowitz-risk-reduction.jpg||Risk reduction in a 50/50 portfolio of uncorrelated assets]]
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{|
 +
|+'''Risk reduction in a 50/50 portfolio of uncorrelated assets'''
 +
|-
 +
||[[File:Markowitz-risk-reduction.jpg|600px]]
 +
:Note: Axis units are in percent.
 +
|-
 +
|}
  
The vertical axis represents return; we want it to be as high as possible. The horizontal axis represents risk; we want to be as far to the left as possible. The green and red dots represent bonds and stocks, respectively. The values shown are very close to the actual historical value for intermediate-term government bonds and large-company stocks from 1926 to the present, but I've rounded them for ease in doing mental arithmetic.
+
The vertical axis represents return; investors want it to be as high as possible. The horizontal axis represents risk; investors want to be as far to the left as possible. The green and red dots represent bonds and stocks, respectively. The values shown are very close to the actual historical value for US intermediate-term [[United States Treasury security|government bonds]] and US large-company stocks from 1926 to the present, but rounded for ease in doing mental arithmetic.
  
Each lines joining the red and green dots show all combinations of returns and standard deviations, for every possible portfolio mixes ranging from all bonds to all stocks. A purple dot marks the return and standard deviation of a 50/50 portfolio.  
+
Each line joining the red and green dots show all combinations of returns and standard deviations, for every possible portfolio mix ranging from all bonds to all stocks. A purple dot marks the return and standard deviation of a 50/50 portfolio.  
  
 
The straight line shows what the results would be if stocks and bonds had moved perfectly together, a correlation of ρ = 1.0.  
 
The straight line shows what the results would be if stocks and bonds had moved perfectly together, a correlation of ρ = 1.0.  
  
 
In reality, the correlation of stocks and bonds was almost exactly zero. Their movements have been perfectly independent. (Not perfectly '''opposed''', just perfectly '''independent''') The curved line shows all of the portfolio returns and standard deviations assuming a correlation of zero.
 
In reality, the correlation of stocks and bonds was almost exactly zero. Their movements have been perfectly independent. (Not perfectly '''opposed''', just perfectly '''independent''') The curved line shows all of the portfolio returns and standard deviations assuming a correlation of zero.
 +
One might expect that in a 50/50 portfolio of stocks and bonds, the (arithmetic average) annual return of the portfolio would be exactly halfway in between stocks and bonds, and this is true. It always is. It has to be. In this example, stocks averaged 12%, bonds averaged 5%, and the portfolio will average exactly in between, 8.5%. It was exactly the same regardless of whether the correlation, ρ, was 0.0 or 1.0.
  
You might expect that in a 50/50 portfolio of stocks and bonds, the (arithmetic average) annual return of the portfolio would be exactly halfway in between stocks and bonds, and you would be right. It always is. It has to be. In this example, stocks averaged 12%, bonds averaged 5%, and the portfolio will averaged exactly in between, 8.5%. It was exactly the same regardless of whether the correlation, ρ, was 0.0 or 1.0.
+
One might expect that the risk of the portfolio, measured by 𝛔, sigma, the [[standard deviation]], would also be exactly halfway in between stocks and bonds, but it turns out that this is not true. If stocks and bonds were perfectly correlated--correlation coefficient ρ = 1.0--then it would be true, as indicated by the straight line and the midpoint. When the correlation is 1.0, the risk of the 50/50 portfolio exactly splits the difference between that of stocks, 𝛔 = 20, and bonds, 𝛔 = 6. For the 50/50 portfolio, 𝛔 = 13.
 
 
You might expect that the risk of the portfolio, measured by 𝛔, sigma, the standard deviation, would also be exactly halfway in between stocks and bonds, but it turns out that this is not true. If stocks and bonds were perfectly correlated--correlation coefficient ρ = 1.0--then it would be true, as indicated by the straight line and the midpoint. When the correlation is 1.0, the risk of the 50/50 portfolio exactly splits the difference between that of stocks, 𝛔 = 20, and bonds, 𝛔 = 6. For the 50/50 portfolio, 𝛔 = 13.
 
  
 
However, with a correlation coefficient of zero, the return of the portfolio is not changed, but the risk of the portfolio is somewhat reduced. This is shown by the fact that the ρ = 0 line is curved, and that it is always on the left of the ρ = 1.0 curve.
 
However, with a correlation coefficient of zero, the return of the portfolio is not changed, but the risk of the portfolio is somewhat reduced. This is shown by the fact that the ρ = 0 line is curved, and that it is always on the left of the ρ = 1.0 curve.
Line 50: Line 91:
 
This, then, is the diversification effect in portfolios, from the point of view of modern portfolio theory. Portfolios of uncorrelated assets have an efficient frontier that bows toward the left. The ''return'' is just the weighted average of the returns of the holdings, but if they are uncorrelated, the ''standard deviation is less'' than the weighted average of the standard deviations of the holdings.
 
This, then, is the diversification effect in portfolios, from the point of view of modern portfolio theory. Portfolios of uncorrelated assets have an efficient frontier that bows toward the left. The ''return'' is just the weighted average of the returns of the holdings, but if they are uncorrelated, the ''standard deviation is less'' than the weighted average of the standard deviations of the holdings.
  
Two points should be noted. First, this doesn't imply that diversified portfolios are crashproof. The effect is there, but for realistic asset characteristics it is fine tuning. It is an edge, not armor plate. Whenever I have read official fund documents, if "diversification" is mentioned as a benefit, I have always seen a boilerplate disclaimer, "Diversification does not ensure a profit or protect against a loss in a declining market,"
+
Two points should be noted. First, this doesn't imply that diversified portfolios are crashproof. The effect is there, but for realistic asset characteristics it is fine tuning. It is an edge, not armor plate. In official fund documents, if "diversification" is mentioned as a benefit,it includes a boilerplate disclaimer, "Diversification does not ensure a profit or protect against a loss in a declining market."
  
Second, the effect as I've illustrated is just math. It applies in the real world if the assumptions behind the model apply. It doesn't if they don't. If we knew for sure that over the next ten years stocks and bonds would duplicate their historic values--returns of 12% and 5% respectively, standard deviations of 20% and 6% respectively, and correlation of 0.0--then of course we would know that a 50/50 portfolio would have a return of 8.5% and a standard deviation of 10.44%. But past returns are not a sure predictor of future returns, and the same is true of standard deviations or correlations. In fact, correlations seem to be even less stable than return itself.
+
Second, the illustrated effect is just math. It applies in the real world if the assumptions behind the model apply. It doesn't if they don't. If we knew for sure that over the next ten years stocks and bonds would duplicate their historic values--returns of 12% and 5% respectively, standard deviations of 20% and 6% respectively, and correlation of 0.0--then of course we would know that a 50/50 portfolio would have a return of 8.5% and a standard deviation of 10.44%. But past returns are not a sure predictor of future returns, and the same is true of standard deviations or correlations. In fact, correlations seem to be even less stable than return itself.
  
==Jack Bogle on Diversification==
+
==Jack Bogle on diversification==
  
John C. Bogle has written "Diversify, diversify, diversify!"<ref>[https://www.vanguard.com/bogle_site/april272001.html, "The Twelve Pillars of Wisdom"], point #5</ref>. His views that investors should prefer to invest using broadly diversified stock and bond mutual funds is a core element of the [[Bogleheads® investment philosophy]].
+
John C. Bogle has written "Diversify, diversify, diversify!"<ref>[http://johncbogle.com/wordpress/wp-content/uploads/2019/08/AZRepublic-4-27-01.pdf, "The Twelve Pillars of Wisdom"], Pillar #5</ref>. His views that investors should prefer to invest using broadly diversified stock and bond mutual funds is a core element of the [[Bogleheads® investment philosophy]].
  
 
Bogle also cautioned against succumbing to salesmanship under the guise of diversification: "And let me say this about a better diversifier: Better diversification is the last refuge of the scoundrel."<ref>''The Man in the Arena: Vanguard Founder John C. Bogle and His Lifelong Battle to Serve Investors First,'' Knut A. Rostad, John Wiley & Sons, 2013</ref>
 
Bogle also cautioned against succumbing to salesmanship under the guise of diversification: "And let me say this about a better diversifier: Better diversification is the last refuge of the scoundrel."<ref>''The Man in the Arena: Vanguard Founder John C. Bogle and His Lifelong Battle to Serve Investors First,'' Knut A. Rostad, John Wiley & Sons, 2013</ref>

Latest revision as of 20:58, 13 September 2019


Generally speaking, diversification is about not putting all of one's eggs into a single basket. The U.S. Securities and Exchange Commission writes:

Diversification can be neatly summed up as, “Don’t put all your eggs in one basket.” The idea is that if one investment loses money, the other investments will make up for those losses. Diversification can’t guarantee that your investments won’t suffer if the market drops. But it can improve the chances that you won’t lose money, or that if you do, it won’t be as much as if you weren’t diversified.[1]

Unfortunately, there is no single universally accepted precise definition for "diversification". Different authors use the word "diversification" to mean different things. This is much like the word "risk" which, for example, is used by some authors to mean "possibility of loss" and by other authors to mean "volatility". Two main meanings for the word diversification in an investment context follow:

The first meaning appears in the text of authors who often combine the word "broad" (or a similar one) with the word "diversification" to mean "spreading one's money broadly across a market" (using capitalization-weighting for obvious arithmetic reasons[2]) and across stocks, bonds, and (sometimes) cash. For example, when discussing the creation of the Vanguard S&P 500 index fund and of the Vanguard Total Stock Market index fund, Jack Bogle wrote:

In 1975, I created the first index mutual fund, now known as Vanguard 500 Index Fund. Then, as now, I considered it the very paradigm of long-term investing, a fully diversified portfolio of U.S. stocks operated at high tax efficiency and rock-bottom costs, and designed to be held, well, “forever.” It is now the world’s largest equity mutual fund.[3]

The second meaning stems from economic theory, where economists, like Markowitz, define "diversification" as a technique to combine securities to reduce "risk" (defined as "volatility") without sacrificing "expected return".

The above two distinct definitions of "diversification" can be conflictual in the context of portfolio construction (much like the two definitions of "risk" mentioned above).

"Diversified" versus "non-diversified" funds

By regulation, every mutual fund is classified as "diversified" or "non-diversified." Most are officially diversified, and those that are not must say so. A summary of the requirements, known as the 75-5-10 rule, is:

  • 75% of the fund's assets must be invested in securities of other issuers. Cash and cash equivalents are included.
  • 5% - The investment company may not invest more than 5% of its assets in any one company.
  • 10% - The investment company may not own more than 10% of any company’s outstanding voting stock.[4]

This corresponds well with one traditional understanding of diversification. Before buying any mutual fund, a buyer should take time to look at the official fund documents for a statement such as "the fund is considered non-diversified." Such a statement isn't necessarily reason for alarm, but it is a red flag that says the fund is unusual, and that you should look farther and make sure you know why it is "non-diversified" and whether it is a concern to you.

The definition results in some surprising categorizations. For example, the Vanguard REIT Index Fund, VGSIX, is considered diversified even though it is invested exclusively in a single narrow industry sector, constituting less than only 4% of the stock market: commercial real estate.

On the other hand, the Vanguard Growth Index Fund, VIGAX, holds stocks in ten different sectors. Yet, in April 2019, Vanguard noted that

more than 25% of the Fund’s total assets are invested in issuers representing more than 5% of the Fund’s total assets. As a result, the Fund is nondiversified under the Investment Company Act of 1940, although it continues to hold more than 300 stocks across a number of sectors.

AQR says that its Style Premia Alternative Fund[5] invests "in a broad spectrum of asset classes and markets" and "[seeks] to limit exposure to poor performance within any single style or asset class," while containing a fine-print disclosure that "This Fund is a non-diversified fund."

These seeming surprises simply underline the fact that there is more than one understanding of the term "diversification."

John C. Bogle and others have pointed out that as the assets in a mutual fund grow, the 10% requirement makes it harder and harder for a "diversified" fund to own smaller-cap stocks. For example, a diversified mutual fund with $100 billion in assets, that is actively managed, cannot have any meaningful investment in a microcap stock with $100 million in market cap, because it cannot invest more than $10 million = 0.1% of its portfolio in that stock without breaking the 10% rule. Therefore, as a diversified mutual funds grows, it is constrained to put a smaller and smaller percentage of its portfolio into poorly-known small-company stocks that might offer an opportunity for stockpicking skill, and more and more into the larger-cap stocks that everybody knows about. It becomes harder and harder for growing funds to depart much from the market. This is sometimes called "the curse of success."

Sector diversification

Sectors are eleven broad categories of similar businesses. In 1999, MSCI and S&P developed the Global Industry Classification Standard (GICS), which is accepted as the standard definition. Companies that are in the same sector are subject to similar economic forces. The behavior of e.g. Cisco Systems stock depends to a large degree on how high-tech in general is doing, and only partly on what things Cisco itself is doing differently from other high-tech companies.

To illustrate this, consider three stocks in the information technology sector--Amazon, Apple, and Cisco System--and three in the financial sector--Citigroup, AIG, and Bank of America.

During 2000-2003, all of three of the information technology stocks imploded, Apple losing 70% of its value, Amazon losing more than 90%. Meanwhile, the three financials were largely unaffected.

IT and financials in 2000

The turn of financials came in 2008-2009, and this time it was the financials that imploded--a $10,000 investment in Citigroup losing more than 90% of its value, while AIG lost 99.5%, $10,000 becoming $20! Information technology was relativy unaffected. The value of Cisco was "only" cut in half, and Apple and Amazon made money.

IT and financials in 2008


The stock market itself, total stock market indexes and index funds, and the S&P 500 which is an approximation to the total market, include stocks in every sector, but not with equal dollar weighting.

S&P 500 sector weightings 3-31-2019.png

In the context of picking a portfolio of a small number of individual stocks--which is not what Bogleheads generally do with most of their portfolio--diversification can be simply a risk control measure; and intentionally choosing stocks from a variety of sectors is one way to achieve it.

In the context of portfolio construction, perhaps using ETFs and mutual funds, sectors can be viewed as a kind of asset class, and since they have imperfect correlation they can be viewed as uncorrelated asset classes that might produced a quantitative diversification benefit in the Markowitz sense. Thus, it is sometimes suggested that equal sector weighting--putting an equal number of dollars into each of the eleven sectors--might be superior to investing in an S&P 500 or total market index, allowing each sector to have its natural capitalization weight.

Diversification to reduce idiosyncratic risk

Markowitz diversification

Within the framework of modern portfolio theory (MPT), the term Markowitz diversification can mean:

Combining securities with less-than-perfect positive correlation in order to reduce risk in the portfolio without sacrificing any of the portfolio’s expected return.[6]

This approach to diversification was introduced by Harry M. Markowitz in his ground-breaking 1952 paper, Portfolio Selection.[7]

The basic idea of the math behind Markowitz diversification looks like this:

Risk reduction in a 50/50 portfolio of uncorrelated assets
Markowitz-risk-reduction.jpg
Note: Axis units are in percent.

The vertical axis represents return; investors want it to be as high as possible. The horizontal axis represents risk; investors want to be as far to the left as possible. The green and red dots represent bonds and stocks, respectively. The values shown are very close to the actual historical value for US intermediate-term government bonds and US large-company stocks from 1926 to the present, but rounded for ease in doing mental arithmetic.

Each line joining the red and green dots show all combinations of returns and standard deviations, for every possible portfolio mix ranging from all bonds to all stocks. A purple dot marks the return and standard deviation of a 50/50 portfolio.

The straight line shows what the results would be if stocks and bonds had moved perfectly together, a correlation of ρ = 1.0.

In reality, the correlation of stocks and bonds was almost exactly zero. Their movements have been perfectly independent. (Not perfectly opposed, just perfectly independent) The curved line shows all of the portfolio returns and standard deviations assuming a correlation of zero. One might expect that in a 50/50 portfolio of stocks and bonds, the (arithmetic average) annual return of the portfolio would be exactly halfway in between stocks and bonds, and this is true. It always is. It has to be. In this example, stocks averaged 12%, bonds averaged 5%, and the portfolio will average exactly in between, 8.5%. It was exactly the same regardless of whether the correlation, ρ, was 0.0 or 1.0.

One might expect that the risk of the portfolio, measured by 𝛔, sigma, the standard deviation, would also be exactly halfway in between stocks and bonds, but it turns out that this is not true. If stocks and bonds were perfectly correlated--correlation coefficient ρ = 1.0--then it would be true, as indicated by the straight line and the midpoint. When the correlation is 1.0, the risk of the 50/50 portfolio exactly splits the difference between that of stocks, 𝛔 = 20, and bonds, 𝛔 = 6. For the 50/50 portfolio, 𝛔 = 13.

However, with a correlation coefficient of zero, the return of the portfolio is not changed, but the risk of the portfolio is somewhat reduced. This is shown by the fact that the ρ = 0 line is curved, and that it is always on the left of the ρ = 1.0 curve.

When the correlation is imperfect, the returns from one asset may sometimes partially fill in gaps in the returns from another. The result is that the fluctuations in the portfolio as a whole are somewhat smoothed out. In this case, the smoothing is manifested as a reduction in 𝛔 from 13 to 10.44.

How important is this? Well, John C. Bogle wrote "An extra percentage point of long-term return is priceless, and [a] extra percentage point [reduction in] short-term standard deviation is meaningless." But in this case, we have a 2.56% reduction in standard deviation.

This, then, is the diversification effect in portfolios, from the point of view of modern portfolio theory. Portfolios of uncorrelated assets have an efficient frontier that bows toward the left. The return is just the weighted average of the returns of the holdings, but if they are uncorrelated, the standard deviation is less than the weighted average of the standard deviations of the holdings.

Two points should be noted. First, this doesn't imply that diversified portfolios are crashproof. The effect is there, but for realistic asset characteristics it is fine tuning. It is an edge, not armor plate. In official fund documents, if "diversification" is mentioned as a benefit,it includes a boilerplate disclaimer, "Diversification does not ensure a profit or protect against a loss in a declining market."

Second, the illustrated effect is just math. It applies in the real world if the assumptions behind the model apply. It doesn't if they don't. If we knew for sure that over the next ten years stocks and bonds would duplicate their historic values--returns of 12% and 5% respectively, standard deviations of 20% and 6% respectively, and correlation of 0.0--then of course we would know that a 50/50 portfolio would have a return of 8.5% and a standard deviation of 10.44%. But past returns are not a sure predictor of future returns, and the same is true of standard deviations or correlations. In fact, correlations seem to be even less stable than return itself.

Jack Bogle on diversification

John C. Bogle has written "Diversify, diversify, diversify!"[8]. His views that investors should prefer to invest using broadly diversified stock and bond mutual funds is a core element of the Bogleheads® investment philosophy.

Bogle also cautioned against succumbing to salesmanship under the guise of diversification: "And let me say this about a better diversifier: Better diversification is the last refuge of the scoundrel."[9]

References

  1. The Securities and Exchange Commission[1]
  2. Equal-weighting can't be applied to the total market: Bogleheads® forum post: What's wrong with this critique of indexing?.
  3. The Clash of the Cultures, John C. Bogle, 2012.
  4. 15 U.S. Code § 80a–5 - Subclassification of management companies. Based on forum discussions, it is does not seem to be clear exactly what is or is not allowed outside the 75%
  5. QSPIX, Style Premia Alternatives Fund factsheet
  6. Francis, Jack Clark; Kim, Dongcheol (213). "Modern Portfolio Theory". "John Wiley & Sons, Inc.". p. 120. ISBN 9781118417201.
  7. Markowitz, H.M. (March 1952). "Portfolio Selection". pp. 77–91. Unknown parameter |publication= ignored (help)
  8. "The Twelve Pillars of Wisdom", Pillar #5
  9. The Man in the Arena: Vanguard Founder John C. Bogle and His Lifelong Battle to Serve Investors First, Knut A. Rostad, John Wiley & Sons, 2013

Further reading

External links