Total Portfolio Allocation and Withdrawal (TPAW)

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Ben Mathew
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Ben Mathew »

TPAWPLANNER.COM UPDATES 12/7/2021 - 5/13/2022

A summary of the main updates to tpawplanner.com since the first version in December:

1. Spending floor + fixed spending

A spending floor can now be set. Fixed withdrawals can be modeled by setting spending floor = spending ceiling.

2. Discretionary goal scaling
Ben Mathew wrote: Wed Dec 08, 2021 2:19 pm The modeling behind legacy and extra discretionary withdrawals is bit tricky because they have to scale with the market (i.e. if markets do well, the target should increase, and if markets do badly, the target should decrease.) The scaling I'm doing isn't quite perfect and it's possible that it's sometimes allocating too much to legacy and too little to retirement spending.

[...] at some point I'll try to improve the scaling algorithm. That's a tough problem, and probably a long term goal.
This has been done. Discretionary goals are now updated on the basis of wealth rather than the performance of a hypothetical portfolio. This will result in better scaling of discretionary goals in the simulations.

3. Additional output graphs
longratio wrote: Wed Dec 15, 2021 1:57 pm Can you maybe add the output tables of the portfolio, withdrawal and equity / bond splits for the 25th label of the simulation runs for each year. Personally I think it is helpful if I see this over time (that's what I like about the excel also).
Additional output graphs are now available for spending subcategories, portfolio balance, asset allocation, and withdrawal rate. Use the drop down menu next to the graph title to select these graphs. Restricting a graph to a specific percentile has not yet been implemented.

4. Separate inputs for couples

Age, retirement and max age can now be entered separately for partners. Click on "Add a Partner" in the "Age and Retirement" section to enter partner's info.
Total Portfolio Allocation and Withdrawal (TPAW)
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Ben Mathew
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Re: Total portfolio allocation and withdrawal (TPAW)

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SAVINGS PORTFOLIO STRATEGY ADDED TO TPAWPLANNER.COM

The online TPAW Planner now supports a "savings portfolio" strategy in addition to the default "total portfolio" strategy.

The savings portfolio approach is simpler and more familiar. The present value of future savings and retirement income is not counted as a bond. You directly specify the asset allocation of the savings portfolio. Income during retirement such as Social Security and pensions simply reduce the withdrawals required from the savings portfolio during the years in which you receive the income. Conversely, an extra expense in any year increases the withdrawal required from the savings portfolio for that year. The savings portfolio is amortized to meet the net withdrawal requirements.

You can toggle between "total portfolio approach" and "savings portfolio approach" in the "Strategy" section. The impact of the strategy can be seen in the retirement spending graph.
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gerontius
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by gerontius »

Awesome! It's a very valuable and easy-to-use tool. Thanks, Ben.

I prefer the default "total portfolio" approach, but this addition makes the tool usable for those who prefer not to consider the present value of future income streams as part of the asset allocation.
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Re: Total portfolio allocation and withdrawal (TPAW)

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gerontius wrote: Sun May 29, 2022 8:11 am Awesome! It's a very valuable and easy-to-use tool. Thanks, Ben.
Thanks for the feedback. Glad to hear you're finding it useful.
gerontius wrote: Sun May 29, 2022 8:11 am I prefer the default "total portfolio" approach, but this addition makes the tool usable for those who prefer not to consider the present value of future income streams as part of the asset allocation.
:thumbsup I figured that adding the savings portfolio strategy and making it easy to compare between that and the total portfolio method would help people figure out what works best for them. I also plan on generalizing the the total portfolio method to allow risk to be a function of income and age. That would bring in even more options.
Total Portfolio Allocation and Withdrawal (TPAW)
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Re: Total portfolio allocation and withdrawal (TPAW)

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SAVINGS PORTFOLIO VS TOTAL PORTFOLIO: RISK AS A FUNCTION OF AGE

Now that TPAW Planner supports a savings portfolio strategy, let's look at some of the differences between the total portfolio and saving portfolio strategies. The difference really is in the asset allocation (AA), not in the withdrawal calculation. In the total portfolio approach, AA is adjusted to maintain constant risk to spending. In the savings portfolio approach, risk becomes a function of age and past stock market performance. For example, if there is a gap before pension begins, a fixed allocation on the savings portfolio will be riskier at the start of retirement and less risky when you get closer to the start of the pension. The following example illustrates why:

Take a 55 year old retiree with a savings portfolio of $1 million. Planning till age 100. The retiree will receive a pension of $30,000 per year starting age 70. If the expected return of stocks is 3.5% and bonds is 0.5%, a total portfolio strategy with a fixed AA of 35/65 on the total portfolio will support expected spending of $54,221 per year. A savings portfolio strategy with a fixed AA of 80/20 will generate the same expected spending of $54,221 per year. Both strategies plan to draw $54,221 from the savings portfolio during the gap and $54,221-$30,000 = $24,221 after the pension starts.

The following graph illustrates how this $54,221 per year is funded:

Image

At the start of the retirement (age 55), the savings portfolio funds a bigger share of total spending. So a 10% rise or fall in the portfolio will have a bigger impact on spending per year. Towards the end of the gap (age 65), the savings portfolio is funding a smaller share. So a 10% rise or fall in the savings portfolio has a smaller impact on spending per year. And once the pension begins (age 70), the share is even smaller and the impact is even smaller.

A fixed asset allocation maintains constant risk on the savings portfolio. But because the impact of the savings portfolio on spending is itself decreasing, the risk being applied to spending decreases during the gap years. If this is not what the investor wants, they would have to specify an increasing glide path on the savings portfolio to counter this and level out the risk. We can look to the total portfolio approach to see what AA constant risk would have entailed: rather than a fixed 80/20 allocation, the total portfolio approach would have glided up from 65/35 to 99/1 on the savings portfolio over the course of the gap.

If the retiree actually wants to reduce risk in this way as they grow older, the savings portfolio strategy may be a reasonable option. The cost to doing this is that the non-constant risk reduces time diversification and increases risk for the same expected consumption. But if the retiree still wants to reduce risk to spending as they age, maybe because spending adjustments are harder to make at older ages, then this savings portfolio approach may be preferable to the constant risk applied by the total portfolio method. Eventually, I plan to generalize the total portfolio strategy to allow the option to reduce risk with age.
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bridge2benefits
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by bridge2benefits »

Ben, this is a really great tool, thanks so much for creating it and continuing to enhance it!

How would you recommend modeling a TIPS ladder in the planner? Does it make sense to add the rungs as extra income and reduce the size of the portfolio accordingly?
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Re: Total portfolio allocation and withdrawal (TPAW)

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bridge2benefits wrote: Thu Jun 02, 2022 1:27 am Ben, this is a really great tool, thanks so much for creating it and continuing to enhance it!
Glad to hear you're finding it useful.
bridge2benefits wrote: Thu Jun 02, 2022 1:27 am How would you recommend modeling a TIPS ladder in the planner? Does it make sense to add the rungs as extra income and reduce the size of the portfolio accordingly?
I'm assuming that the intent of the ladder is to create a guaranteed spending floor for retirement, either on its own or in combination with Social Security or pensions (a bond bridge). If so, you can enter the desired spending floor as an essential expense for all of retirement in the "Extra Spending" section. You don't have to have the full ladder in place already. The planner will simply set aside enough bonds to cover the spending floor and will not include it in the rebalancing of the risk portfolio. The full or partial bond ladder you currently hold will count towards the bond allocation target given in "Tasks for this year."

Note that the simulation currently assumes that all bonds, including the ones set aside for the guaranteed spending floor, are rolled over. So it does not capture the risk reduction you get from using a duration matched bond ladder. I plan to add the option to duration match bonds at some point.

Also, the guaranteed spending floor input will eventually get its own section. That will provide a better way to enter it than the current "Extra Expenses" hack.
Last edited by Ben Mathew on Fri Jun 03, 2022 3:42 pm, edited 2 times in total.
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Re: Total portfolio allocation and withdrawal (TPAW)

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Ben, I just wanted to check back into this thread and say thank you, again. Your TPAW model is so simple and powerful.

I have a giant spreadsheet with a historical model like firecalc using Simbas back testing data, a monte carlo model, a deterministic model and your TPAW model. I use TPAW as my primary measure of effectiveness (MOE). Such a simple calculation, but very powerful.
Consistently sets low goals and fails to achieve them.
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Re: Total portfolio allocation and withdrawal (TPAW)

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corn18 wrote: Fri Jun 03, 2022 6:37 am Ben, I just wanted to check back into this thread and say thank you, again. Your TPAW model is so simple and powerful.

I have a giant spreadsheet with a historical model like firecalc using Simbas back testing data, a monte carlo model, a deterministic model and your TPAW model. I use TPAW as my primary measure of effectiveness (MOE). Such a simple calculation, but very powerful.
Glad to hear this, corn! Thanks for letting me know.
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Zeno
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Zeno »

Ben:

I'm also just weighing in (again) to say how much I love TPAW. It has taken me some time to appreciate the difference between "total portfolio" and "saving portfolio," but I think I know understand how most of this works.

May I impose upon you to ask the following additional questions?

1. "Spending During Retirement" graph. I understand that this is the key visual output. If we wish to be further additionally conservative (beyond the inputs) I understand that we should follow the 5th percentile line. Correct?

2. "Portfolio" graph. Is this showing the "total portfolio" or the "spending portfolio"? If the latter -- and again we want to be as conservative as possible -- year by year can we look at the 5th percentile line and judge whether our remaining "saving portfolio" is, in aggregate, above that amount? I'm trying to understand if there is a practical way we can use the "Portfolio" graph to judge how we are doing, year by year, in retirement.

3. "Asset Allocation" graph. I understand that this is showing the AA for the "total portfolio," correct? In the "Tasks for This Year" I'm advised to set a AA that is currently higher than our AA in our "saving portfolio" but the explanation in the "Tasks for This Year" section of the output is terrific, so that makes sense. As with question #2 above, however, I'm just trying to understand if there is some practical use to which I can put the "Asset Allocation" graph -- and again, in the most conservative way --- i.e., should I be looking at the 5th percentile line?

4. "Withdrawal Rate" graph. It took me awhile to understand this. I used to assume it was a SWR, but I think I now understand that is the actual percentage withdrawal (although I am unclear if that is the actual percentage withdrawal from the "total portfolio" or "saving portfolio"). I also think I now understand that the 95th percentile is the "worst case" in that it shows the percentage withdrawal from a greatly diminished portfolio. As with questions ## 2 and 3 above, is this output merely informative as well, or is there some use to which I should/could be using it? We are hyper conservative and currently intend to use a Perpetual Withdrawal Rate (~2%). I'm trying to understand if I can look at the TPAW output on this graph to ascertain (with respect to a specific percentile line) if we are actually in line with a PWR.

Again, TPAW is wonderful. Thank you.

Z

Edit: Corrected typos
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Re: Total portfolio allocation and withdrawal (TPAW)

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Zeno wrote: Sat Jun 04, 2022 8:06 am I'm also just weighing in (again) to say how much I love TPAW. It has taken me some time to appreciate the difference between "total portfolio" and "saving portfolio," but I think I know understand how most of this works.

May I impose upon you to ask the following additional questions?
Thanks for the feedback! I'm happy to answer questions. Feel free to ask if anything is not clear.
Zeno wrote: Sat Jun 04, 2022 8:06 am 1. "Spending During Retirement" graph. I understand that this is the key visual output. If we wish to be further additionally conservative (beyond the inputs) I understand that we should follow the 5th percentile line. Correct?
Yes. Spending is the main graph to base decisions on because it's spending (broadly defined to include legacy) that matters. Portfolio balance, asset allocation, and withdrawal rates are all just tools to generate the spending. You could do all of your planning by looking at just the spending graphs. The other graphs are there to help see what's going on under the hood, and are not strictly necessary for developing a good plan.

Making sure the 5th percentile of spending is acceptable should be a reasonably conservative strategy. Saving more, retiring later, choosing a safer asset allocation, and increasing spending tilt should all result in higher 5th percentile spending outcomes.
Zeno wrote: Sat Jun 04, 2022 8:06 am 2. "Portfolio" graph. Is this showing the "total portfolio" or the "spending portfolio"? If the latter -- and again we want to be as conservative as possible -- year by year can we look at the 5th percentile line and judge whether our remaining "saving portfolio" is, in aggregate, above that amount? I'm trying to understand if there is a practical way we can use the "Portfolio" graph to judge how we are doing, year by year, in retirement.
The portfolio graph is showing the savings portfolio balance, not the total portfolio balance. Picking more conservative inputs will generally result in higher portfolio balances at the 5th percentile level. But I would encourage focus on the spending graph while picking the strategy. That is the more meaningful metric to assess safety. It's hard to know if a particular savings portfolio balance is safe or not without looking at the spending it generates, and that information is in the spending graph. One place the portfolio graph may carry some useful information is if you look at the balance just before pension begins. This tells you how close you got to runnning out of funds before pension begins. i.e. The spending graph may show that, at the 5th percentile, you didn't run out of money before the pension began. You can then look at the savings portfolio graph to see how low the balance got before the pension kicked in. I don't think this is essential to do, but it may be of some interest.

Zeno wrote: Sat Jun 04, 2022 8:06 am 3. "Asset Allocation" graph. I understand that this is showing the AA for the "total portfolio," correct? In the "Tasks for This Year" I'm advised to set a AA that is currently higher than our AA in our "saving portfolio" but the explanation in the "Tasks for This Year" section of the output is terrific, so that makes sense. As with question #2 above, however, I'm just trying to understand if there is some practical use to which I can put the "Asset Allocation" graph -- and again, in the most conservative way --- i.e., should I be looking at the 5th percentile line?
The asset allocation (AA) graph is showing the allocation of the savings portfolio. The allocation of the total portfolio will remain fixed at the value you set in the "Risk and Time Preference" section, except in situations like in early career where the target allocation isn't achieved because the savings portfolio is too small and even 100% stocks is not enough. The latter would be interesting to see, but I have not added that in yet.

There is no reason to base decisions directly on the AA of the saving portfolio displayed in the graph. The spending graph is much more relevant. This is more of an under the hood perspective of how AA on the savings portfolio changes to maintain constant risk to spending. For people who don't want to use a total portfolio approach and would prefer a predetermined glidepath on the savings portfolio, the 50th percentile might be a good recommendation for a static glidepath.

Better market performance would usually result in lower AA because the pension "bonds" becomes a smaller fraction of the total portfolio and you need to buy more bonds in the savings portfolio to get to target asset allocation of the total portfolio. So the 5th percentile corresponds to the "good" outcome and the 95th percentile to the "bad" outcome. If you want to see what happens to your AA when things go badly, you'll likely want to look at the 95th percentile outcomes. But again, there is no practical benefit from doing this.
Zeno wrote: Sat Jun 04, 2022 8:06 am 4. "Withdrawal Rate" graph. It took me awhile to understand this. I used to assume it was a SWR, but I think I now understand that is the actual percentage withdrawal (although I am unclear if that is the actual percentage withdrawal from the "total portfolio" or "saving portfolio"). I also think I now understand that the 95th percentile is the "worst case" in that it shows the percentage withdrawal from a greatly diminished portfolio. As with questions ## 2 and 3 above, is this output merely informative as well, or is there some use to which I should/could be using it? We are hyper conservative and currently intend to use a Perpetual Withdrawal Rate (~2%). I'm trying to understand if I can look at the TPAW output on this graph to ascertain (with respect to a specific percentile line) if we are actually in line with a PWR.
Yes, this is the actual percentage withdrawn from the "savings portfolio". You're right that the 95th percentile is the "bad" outcome and the 5th percentile is the "good" outcome. Good market performance increases both the numerator (withdrawal amount) and the denominator (savings portfolio balance). But the withdrawal amount in the numerator will typically increase by a smaller percentage than the savings portfolio balance in the denominator. So the withdrawal rate will typically decline if the market does well. Again, there is no practical use for this in planning. But it helps us understand how it works.

I will eventually add a safe withdrawal rate (SWR) option to the planner. That will make it easy to compare the 2% perpetual withdrawal rate (PWR) strategy against other strategies.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Zeno »

Ben:

Thank you once again for the thoughtful and thorough response above ^^^.

One more question, if I may. Everything below deals with TPAW's AA feature. (And if we should take this to PM, just let me know that, too, and I will stop pestering you publicly like this.)

As background, I'm 58 and DW is 62. I anticipate retiring anytime over the next 18 months. She is already retired. Our portfolio is 45x (down from 50x). Our target AA is 65/32/3, which for TPAW purposes I gather should just be expressed as 65/35. We rebalance only when we are out-of-whack by 5%. Our actual AA (per PersonalCapital) is currently 62/38, so despite all of the recent festivities in the market we have not yet been required to rebalance per our IPS.

In TPAW, I set the stock allocation for the total portfolio at 50%. I assume that 50% is reasonable given our ages and my imminent retirement horizon, but I'm not actually certain. I also told TPAW that I would retire when I turn 59.

When I look at the Asset Allocation graph from the drop down menu, I get a common AA at the beginning (age 58 for me; stock allocation of 69% for all percentiles, from 5th through 95th) and at the end (age 95 for me; stock allocation of 50% for all percentiles, from 5th through 95th). From ages 59 through 94, however, the stock percentage for the AA vary greatly as a function of both age and percentile. I understand from your commentary above that the 5th percentile is "good" and the 95th percentile is "things aren't going well." This tells me for AA purposes I want to be looking at the 5th percentile line.

When I click on "Tasks for this Year," it tells me to rebalance my current portfolio to 69/31. And again as background, we are currently at 62/38. That makes sense to me, as 69% is the starting point for all percentiles on the Asset Allocation graph per above.

I interpret all of the above to mean that we should actually do that rebalancing this year, right?

And going forward each year -- and again being conservative -- should we follow the 5th percentile glide path AA in the Asset Allocation graph? That line (5th percentile) generally drops nicely, year by year, from age 58 (69%) through 95 (50%). I assume it ends at 50% because if I expire magically at that finish line (age 95) the AA for the investment portfolio (50%) should match the AA we set for the target portfolio originally in TPAW (50%).

It seems to me that the Asset Allocation graph is actionable for year-by-year rebalancing.

Again, sorry to pester you.

Z
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Re: Total portfolio allocation and withdrawal (TPAW)

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Zeno wrote: Sat Jun 04, 2022 5:44 pm One more question, if I may. Everything below deals with TPAW's AA feature. (And if we should take this to PM, just let me know that, too, and I will stop pestering you publicly like this.)
Not at all. Working through real-world scenarios is always helpful.
Zeno wrote: Sat Jun 04, 2022 5:44 pm As background, I'm 58 and DW is 62. I anticipate retiring anytime over the next 18 months. She is already retired. Our portfolio is 45x (down from 50x). Our target AA is 65/32/3, which for TPAW purposes I gather should just be expressed as 65/35. We rebalance only when we are out-of-whack by 5%. Our actual AA (per PersonalCapital) is currently 62/38, so despite all of the recent festivities in the market we have not yet been required to rebalance per our IPS.

In TPAW, I set the stock allocation for the total portfolio at 50%. I assume that 50% is reasonable given our ages and my imminent retirement horizon, but I'm not actually certain. I also told TPAW that I would retire when I turn 59.

When I look at the Asset Allocation graph from the drop down menu, I get a common AA at the beginning (age 58 for me; stock allocation of 69% for all percentiles, from 5th through 95th) and at the end (age 95 for me; stock allocation of 50% for all percentiles, from 5th through 95th). From ages 59 through 94, however, the stock percentage for the AA vary greatly as a function of both age and percentile. I understand from your commentary above that the 5th percentile is "good" and the 95th percentile is "things aren't going well." This tells me for AA purposes I want to be looking at the 5th percentile line.

When I click on "Tasks for this Year," it tells me to rebalance my current portfolio to 69/31. And again as background, we are currently at 62/38. That makes sense to me, as 69% is the starting point for all percentiles on the Asset Allocation graph per above.

I interpret all of the above to mean that we should actually do that rebalancing this year, right?

And going forward each year -- and again being conservative -- should we follow the 5th percentile glide path AA in the Asset Allocation graph? That line (5th percentile) generally drops nicely, year by year, from age 58 (69%) through 95 (50%). I assume it ends at 50% because if I expire magically at that finish line (age 95) the AA for the investment portfolio (50%) should match the AA we set for the target portfolio originally in TPAW (50%).

It seems to me that the Asset Allocation graph is actionable for year-by-year rebalancing.
To illustrate this, I made up some inputs that produce an AA graph similar to what you describe.

Image

Let's look at why you might get an AA graph like this when you use the total portfolio strategy:

Your current asset allocation for age 58 is certain. It is 69/31 because you set the AA on the total portfolio to 50/50. You likely have Social Security and/or pensions that are being counted as bonds, so you need to hold only 31% bonds in your savings portfolio for the total portfolio to reach the 50/50 target you set.

However, your future AA on the savings portfolio is not known for sure today. It will depend on how the market does. That's why you're seeing a distribution for the AA rather than a precise number. But you don't need to decide today what AA percentile trajectory you'll follow over tme. When you enter your inputs next year, you will find out how you should rebalance next year. Each year, you'll enter your inputs and rebalance to whatever it says in "Tasks for this year." You just don't know in advance what it will say. And that's okay--you know that whatever it is, it will be calculated in accordance with your preferred risk target (which is captured by your total portfolio AA.)

You may be wondering why after a while the AA starts getting more tightly distributed and eventually converges to 50/50 at age 95. This happens when you enter a legacy goal with a target AA of 50/50 on the legacy portfolio. In late retirement, most of your remaining portfolio is the legacy portfolio. So the asset allocation of the portfolio becomes dominated by the legacy AA. That's why it's getting closer to the legacy AA of 50/50. At age 95, only the legacy portfolio remains and the AA becomes exactly equal to the legacy AA of 50/50.

But to return to your question, to be conservative, all you have to do is adjust your inputs till you get a spending graph that does not drop too low even at the 5th percentile in any year. Adjust the total portfolio AA and spending tilt to achieve that. 50/50 on the total portfolio is IMO somewhat aggressive. Try dropping to 40/60 or 30/70 and see if that generates a spending graph that looks more attractive to you. Total portfolio AA and spending tilt are the fundamental parameters that determine how conservative your plan is. The spending graph is what shows you how conservative your plan is.

So you don't need to directly consider the AA on the savings portfolio. That is just a means to an end. It is automatically calculated and displayed in "Tasks for this year". All you have to do is run the planner with updated inputs each year, and rebalance to the savings portfolio AA displayed in "Tasks for this year." You don't have to pick the savings portfolio AA in advance--leave it free to adjust as needed. That is the strength of the total portfolio method.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Zeno »

Ben, thank you so very much. Following your advice, I've spent more time with TPAW this morning and now have a spending model with which I'm happy. Your explanations above, coupled with the clear written guidance that accompanies the model, also has armed me with the information I need to understand what is going on under the hood. Again, thank you; I'm indebted to you.

Edit: Corrected typos.
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Ben Mathew
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Ben Mathew »

Zeno wrote: Sun Jun 05, 2022 8:07 am Ben, thank you so very much. Following your advice, I've spent more time with TPAW this morning and now have a spending model with which I'm happy.
That's great! Don't hesitate to ask if you have any more questions.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by jjj_22 »

I've been kind of half-interestedly following this thread for a while but just got around to reading through and using the online planner today. It is really impressive and super, super helpful. Huge thanks to you for doing all this work and just giving it away.

A couple things I wanted to share.

First, it seems more pessimistic than other tools I've tried, or other guidance I've heard. It is hard to compare because it's not apples to apples, but e.g. adjusting the stock/bond mix and setting the maximum 3% positive spending tilt for precautionary savings to start with something like a 2.5% withdrawal rate for 50 year retirement, TPAW's fifth percentile outcomes lead to what I thought were surprising large consumption cuts in the fifth percentile outcomes, while most other modelers and like, historical empirical results suggest it would be fine, even a FA I talked to. Even compared to when you describe what you call a conservative ABW strategy in the post here viewtopic.php?p=6099527#p6099527 with a lower g (which I think is the same as TPAW's tilt?) and higher initial withdrawal rate.

For example, in the simulation I'm looking at, at the fifth percentile, a first-year portfolio decline of 25% led to an initial spending decline of about 20%, and withdrawals starting from the next year never climbed above 75% of the first year's withdrawal, which is a pretty harsh outcome if you're planning your retirement that first year with that level of spending in mind.

I wonder why that is? (ETA: "that is" meaning "why it seems more pessimistic")

Second, it gives different presentation of risk that kind of surprised me. I am used to thinking of myself as having a high risk tolerance because portfolio value swings have never bothered me while accumulating, so I carry a high stock allocation, have never had trouble sleeping at night (which is the mantra that gets kicked around this forum a lot) and was planning to do that into retirement. But when I see the risk of having significantly reduced future consumption for a long period of time under the bad outcomes (like the one mentioned above), that is much more scary, while the upside on the good ones gets a reaction like "well, I'll never need that much money" so maybe I need to think more about my allocation for retirement.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Ben Mathew »

jjj_22 wrote: Sun Jun 05, 2022 1:44 pm I've been kind of half-interestedly following this thread for a while but just got around to reading through and using the online planner today. It is really impressive and super, super helpful. Huge thanks to you for doing all this work and just giving it away.
Thanks for the feedback. Glad to hear you're finding it helpful.
jjj_22 wrote: Sun Jun 05, 2022 1:44 pm First, it seems more pessimistic than other tools I've tried, or other guidance I've heard. It is hard to compare because it's not apples to apples, but e.g. adjusting the stock/bond mix and setting the maximum 3% positive spending tilt for precautionary savings to start with something like a 2.5% withdrawal rate for 50 year retirement, TPAW's fifth percentile outcomes lead to what I thought were surprising large consumption cuts in the fifth percentile outcomes, while most other modelers and like, historical empirical results suggest it would be fine, even a FA I talked to. Even compared to when you describe what you call a conservative ABW strategy in the post here viewtopic.php?p=6099527#p6099527 with a lower g (which I think is the same as TPAW's tilt?) and higher initial withdrawal rate.

For example, in the simulation I'm looking at, at the fifth percentile, a first-year portfolio decline of 25% led to an initial spending decline of about 20%, and withdrawals starting from the next year never climbed above 75% of the first year's withdrawal, which is a pretty harsh outcome if you're planning your retirement that first year with that level of spending in mind.

I wonder why that is? (ETA: "that is" meaning "why it seems more pessimistic")
This is primarily because the default expected returns used in TPAW Planner is much lower than historical averages. Simulations based on raw historical averages will look a lot better. Unadjusted raw historical averages for the data used in TPAW are 8.5% real for stocks and 3.1% real for bonds. The default expected return in TPAW Planner is adjusted to 3.7% real for stocks and 0.4% for bonds--so much lower than historical average. This is based on current yields of stocks and bonds which are a lot lower than historical (1/CAPE based estimates for stocks and TIPS yields for bonds).

These defaults are just the estimates that I think make sense. You can easily change it to reflect your expectations in the "Expected Returns" section. To use the raw historical simulation without any adjustments, enter 8.5% real for stocks and 3.1% real for bonds. I think that's too high for planning purposes and I say so in the guide, but ultimately that is for the user to decide. I don't think planners should hard code return assumptions.

A secondary reason (much less of a factor than the above expected return assumption) is that TPAW Planner's simulation does not assume mean reversion. Returns for each year are independently drawn for the Monte Carlo simulation, so one year's draw being higher than average does not make the next year more likely to be below average. I personally think that the mean reversion results in the annual data are not robust enough to rely on for planning purposes. My instinct is to err on the conservative side of this assumption, and that is no mean reversion. But eventually I do plan to add the option of mean reversion in the simulation for those who want to assume it.

So basically TPAW as an allocation and withdrawal strategy is not inherently aggressive or conservative. The return assumptions in TPAW Planner are conservative, but that can be easily changed to match the user's expectations.
jjj_22 wrote: Sun Jun 05, 2022 1:44 pm
Second, it gives different presentation of risk that kind of surprised me. I am used to thinking of myself as having a high risk tolerance because portfolio value swings have never bothered me while accumulating, so I carry a high stock allocation, have never had trouble sleeping at night (which is the mantra that gets kicked around this forum a lot) and was planning to do that into retirement. But when I see the risk of having significantly reduced future consumption for a long period of time under the bad outcomes (like the one mentioned above), that is much more scary, while the upside on the good ones gets a reaction like "well, I'll never need that much money" so maybe I need to think more about my allocation for retirement.
Yes, stock risk is often presented as short term fluctuations that if we have the stomach to handle it, will definitely work out in the long run. This is supported by the observation that at least in the data that we tend to look at, stocks have always beaten bonds over long enough horizons. This I think is a dangerous conclusion, and it leads people to hold too much stocks. Even 150 years of historical returns are just 5 independent 30 year periods and should not assure us that over 30 year horizons stocks will always beat bonds. Stocks must be risky even in the long run. If they weren't, then there would be a riskless arbitrage opportunity from issuing 30 year non-callable bonds and investing it all in stocks. Infinite leverage, infinite profits. The market doesn't seem to think that such an opportunity exists. So I don't think that we should make that assumption in our financial planning. We should recognize that there is a non-negligible chance that stocks will underperform bonds over the long run. Yes, it's a low probability event. But if it happens the impact will be severe. That's the reason to hold bonds over 30 year + horizons.

This is why I strongly favor Monte Carlo simulations over raw historical simulations for financial planning. With or without mean reversion, it surfaces low probability bad sequences that may not have happened historically. I think sound financial planning involves taking these possibilities into account.

Here's a post I wrote about this.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Zeno »

Ben Mathew wrote: Sun Jun 05, 2022 5:54 pm ... This is primarily because the default expected returns used in TPAW Planner is much lower than historical averages ... These defaults are just the estimates that I think make sense. You can easily change it to reflect your expectations in the "Expected Returns" section. To use the raw historical simulation without any adjustments, enter 8.5% real for stocks and 3.1% real for bonds. I think that's too high for planning purposes and I say so in the guide, but ultimately that is for the user to decide. I don't think planners should hard code return assumptions ... My instinct is to err on the conservative side of this assumption, and that is no mean reversion. ... Yes, stock risk is often presented as short term fluctuations that if we have the stomach to handle it, will definitely work out in the long run. This is supported by the observation that at least in the data that we tend to look at, stocks have always beaten bonds over long enough horizons. This I think is a dangerous conclusion, and it leads people to hold too much stocks ... We should recognize that there is a non-negligible chance that stocks will underperform bonds over the long run. Yes, it's a low probability event. But if it happens the impact will be severe. That's the reason to hold bonds over 30 year + horizons ... With or without mean reversion, it surfaces low probability bad sequences that may not have happened historically. I think sound financial planning involves taking these possibilities into account.
I'm neither a modeler nor a statistician, Ben, but I suspect that Nassim Taleb would agree with you.

I learned today -- at least I think I did -- that if I followed VPW in Year 1 I could withdraw 56% more (in the "Required Flexibility" scenario) than what TPAW recommends. Expressed differently, VPW recommends a WR of 4% in Year 1 (in the "Required Flexibility" scenario; the default WR, however, starts at 4.6%). VPAW, in contrast, generates an effective 2.5% WR for me over all percentiles (5th through 95th).

And it really isn’t fair to say that VPAW “generated” a 2.5% WR for me. I got that by adjusting the AA and tilt to match my conservative tendencies. It is more accurate to say that I steered TPAW toward an outcome with which I was comfortable.

I have a lot to learn about withdrawal methods, and very much appreciate your guidance and input above.
Last edited by Zeno on Mon Jun 06, 2022 12:36 pm, edited 1 time in total.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by jjj_22 »

Ben Mathew wrote: Sun Jun 05, 2022 5:54 pm This is primarily because the default expected returns used in TPAW Planner is much lower than historical averages. Simulations based on raw historical averages will look a lot better. Unadjusted raw historical averages for the data used in TPAW are 8.5% real for stocks and 3.1% real for bonds.
Got it, thanks. I don't really know enough about this stuff to have my own expectations for returns, so was just using the defaults because they seemed not unreasonable. I agree the historical average seems a little out of whack with the current environment, but I guess I didn't realize the implications could be quite as severe as they might be. And the simulations seem extremely sensitive to these inputs so I gather that this is one of the things that matters most, and is also one we have no control over, and very poor ability to predict to boot. Oh well.
Ben Mathew wrote: Sun Jun 05, 2022 5:54 pm We should recognize that there is a non-negligible chance that stocks will underperform bonds over the long run. Yes, it's a low probability event. But if it happens the impact will be severe. That's the reason to hold bonds over 30 year + horizons.

This is why I strongly favor Monte Carlo simulations over raw historical simulations for financial planning. With or without mean reversion, it surfaces low probability bad sequences that may not have happened historically. I think sound financial planning involves taking these possibilities into account.

Here's a post I wrote about this.
Interesting. Running the TPAW simulator with the default expected 3.7% stock returns and a 100% stock portfolio, with a $1 fixed yearly spending to basically let it ride, seems to suggest almost a 25% chance of negative 30 year returns (a 25th percentile outcome portfolio balance at 30 years of a little over the initial amount). Is the outlook really that bad? That is a rhetorical question, kind of?
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Re: Total portfolio allocation and withdrawal (TPAW)

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Zeno wrote: Sun Jun 05, 2022 7:30 pm And it really isn’t fair to say that VPAW “generated” a 2.5% WR for me. I got that by adjusting the AA and tilt to match my conservative tendencies. It is more accurate to say that I steered TPAW toward an outcome with which I was comfortable.
Yes, as you recognize, the withdrawal rate will be very dependent on the inputs. To provide some context, here are the starting withdrawal rates for a 30 year retirement with an AA of 35/65 fixed and no legacy goals:

Image

In your case, I am guessing that a longer retirement and legacy goals are driving the withdrawal rate lower than the numbers above. This is highly individual, and I'm glad to hear you were able to find a plan that works for you.
Last edited by Ben Mathew on Mon Jun 06, 2022 11:18 pm, edited 1 time in total.
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Re: Total portfolio allocation and withdrawal (TPAW)

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jjj_22 wrote: Sun Jun 05, 2022 9:19 pm Running the TPAW simulator with the default expected 3.7% stock returns and a 100% stock portfolio, with a $1 fixed yearly spending to basically let it ride, seems to suggest almost a 25% chance of negative 30 year returns (a 25th percentile outcome portfolio balance at 30 years of a little over the initial amount).
Nice analysis. :beer

(BTW you can set fixed spending to $0 instead of $1)

In comparison, using unadjusted historical returns by setting expected return to 8.5% gives a 25th percentile of about 4x starting balance and a 5th percentile of about 1.5x starting balance.

So decreasing expected return from historical 8.5% to the default 3.7% certainly makes a big difference. (Though less so than what is suggested by this calculation because retirement spending horizons will be typically shorter and so expected returns will have a smaller impact on spending.)
jjj_22 wrote: Sun Jun 05, 2022 9:19 pm Is the outlook really that bad? That is a rhetorical question, kind of?
The honest answer is I don't know. I do feel strongly that because of the higher valuations prevailing now, raw historical returns are too high for financial planning. Historical returns had two things going for it. First, valuations were low starting out. So each dollar invested bought more return from profits alone. And second, increasing valuations goosed the returns even more. It was the best of both worlds. In contrast, investors now have one strike against them already: high valuations starting out, so returns from profits alone are likely to be lower. If valuations now stay the same, then returns will be from profits alone which are anemic already. The worst case scenario is if valuations decline thirty years from now. Then this generation of investors will get the worst of both worlds: starting out with high valuations and ending with low valuations: they will collect anemic profits and then sell at a lower price. The exact opposite of what previous generations had going for them. Will it happen? I don't know. Can it happen? Sure. And if it does happen, then real stock returns over the next thirty years might well turn out to be negative. It is easier for this to happen now at high valuations than was the case historically at lower valuations.

But these are just my thoughts and musings. I don't want to impose these expectations on users of the planner. Still I do feel the default setting should be on the conservative side of the spectrum. I got the 3.7% default by averaging the two lowest values of the 1/CAPE based estimates shown in the guide:

Estimates as of May 27, 2022:
  • CAPE = 32.52
  • 1/CAPE = 3.2%
  • Regression of future log returns on log 1/CAPE yields 4.3% for the 10 year expected return and 6.8% for the 30 year expected return.
  • Restricting the regression to data from 1950 onwards yields 4.2% for the 10 year expected return and 6.5% for the 30 year expected return.
A more optimistic estimate might be obtained by taking the average or median of the estimates above.

While it's hard to guess the expected return, the good news is that an amortization based variable withdrawal strategy involves constant course-corrections of withdrawals, which reduces the damage done by a bad guess.
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Re: Total portfolio allocation and withdrawal (TPAW)

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Ben Mathew wrote: Mon Jun 06, 2022 10:40 pm Will it happen? I don't know. Can it happen? Sure. And if it does happen, then real stock returns over the next thirty years might well turn out to be negative. It is easier for this to happen now at high valuations than was the case historically at lower valuations.

But these are just my thoughts and musings. I don't want to impose these expectations on users of the planner. Still I do feel the default setting should be on the conservative side of the spectrum.
All makes sense to me. I don't intellectually disagree, but since it leads to some unfortunate outcomes it really lights up my brain, like "hey! what's going on?!"

Let me ask this, are the same "expected return" values used for the full period of the simulations? I am wondering, in the event of a bad initial sequence for stocks, that would seem to mean that either valuations decreased, or earnings went down and valuations stayed the same (or some combination of lower earnings and lower valuations). If valuations go down, then wouldn't the estimation of future returns rise, improving expected outcomes? I guess if earnings start declining, and keep doing so, we'll be in for a rough ride no matter what. Maybe this is the mean reversion you talked about before as not including. I have heard that phrase kicked around but don't really know what it refers to.
Ben Mathew wrote: Mon Jun 06, 2022 10:40 pm While it's hard to guess the expected return, the good news is that an amortization based variable withdrawal strategy involves constant course-corrections of withdrawals, which reduces the damage done by a bad guess.
Yeah, this is the part I really like. I was a big fan of the initial ABW thread. The math of including future income in the allocation loses me a little, but also seems like a cool idea.
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Re: Total portfolio allocation and withdrawal (TPAW)

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jjj_22 wrote: Wed Jun 08, 2022 9:41 am Let me ask this, are the same "expected return" values used for the full period of the simulations? I am wondering, in the event of a bad initial sequence for stocks, that would seem to mean that either valuations decreased, or earnings went down and valuations stayed the same (or some combination of lower earnings and lower valuations). If valuations go down, then wouldn't the estimation of future returns rise, improving expected outcomes? I guess if earnings start declining, and keep doing so, we'll be in for a rough ride no matter what. Maybe this is the mean reversion you talked about before as not including. I have heard that phrase kicked around but don't really know what it refers to.
Yes, the expected return is assumed to be constant in the simulation. In reality, if returns are low due to a valuation decline, then this will be compensated for by a higher expected return going forward. This would be mean reversion--worse than average returns are followed by better than average returns and vice versa. The implication is that the variance of long term (say 30 year) returns should be less than what we would expect if annual returns were independent. There seems to be a decent amount of evidence for it, but I'm not sure how robust it is. For example, here is a quick analysis I did where I found no mean reversion. A large part of stock market volatility is of the random walk permanent type rather than mean reverting valuation changes. There is a lot of uncertainty about the future earnings of a company. The volatility that comes from this is not mean reverting.

Note also that if we take mean reversion seriously, the optimal strategy may mean market timing on the basis of past returns. Assuming no mean reversion leads to simpler strategies.

No mean reversion is also conservative. I would rather overestimate the volatility of 30 year returns by incorrectly assuming no mean reversion than underestimate it by incorrectly assuming mean reversion.

That said, I do plan to include mean reversion as an option in the simulation at some point.
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Re: Total portfolio allocation and withdrawal (TPAW)

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Ben Mathew wrote: Thu Jun 09, 2022 1:43 amNo mean reversion is also conservative. I would rather overestimate the volatility of 30 year returns by incorrectly assuming no mean reversion than underestimate it by incorrectly assuming mean reversion.
In my own musings on mean reversion I've come to realise that even if people assume mean reversion they want to do so in such an ad hoc way that it is hard to build it into a modelling tool.

For instance, a lot of people use 1/PE type expected returns in an ABW framework. But are any of them really going to keep using that if PE hits 7 again and the 30 year expected return is calculated at over 12%?

My guess is they'll suddenly find a reason not to believe in mean reversion. Or, rather, to change their definition of what mean reversion they believe.

In practice I think it ends up being just another lever to ratchet down, become more conservative, but without any actual consistent belief in mean reversion per se. When it gives the answer they want, they like it. But when it doesn't, they throw it away.

Case in point: my spreadsheet updates with 1/PE expected returns on a weekly basis. At the beginning of the year, that generated at expected return of 2.8%. Now the calculated expected return is 4.0%. That means that despite the stock market crash, war in Ukraine, and high inflation, the ABW calculated withdrawal has actually gone up by over 10%.

Is that the kind of mean reversion people really want? Or do they actually want... something else? Something that they'll only know when they see it?
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by jjj_22 »

Ben Mathew wrote: Thu Jun 09, 2022 1:43 am A large part of stock market volatility is of the random walk permanent type rather than mean reverting valuation changes. ... The volatility that comes from this is not mean reverting.
If this is true, then wouldn't regressions against historical 1/CAPE be kind of questionable? It seems like when you use that regression to estimate future returns as of now, you kind of have to assume that those data were mean reverting, unless I'm misunderstanding what you're saying. Otherwise you'd just be estimating based on actually random historical averages?

So why is there less or less robust evidence for using that same method to estimate future returns in a simulation? Because in the real world you will, when you run the worksheet again next year. Maybe it's that the relationship between prices and valuations is not mean reverting, so a hypothetical decline in portfolio value doesn't predict a valuation change with any useful degree of certainty? Or maybe the fact that you'd be estimating based on simulated data based on estimates means there'd be such huge error margins it would generate nothing but noise.
AlohaJoe wrote: Thu Jun 09, 2022 3:20 am In my own musings on mean reversion I've come to realise that even if people assume mean reversion they want to do so in such an ad hoc way that it is hard to build it into a modelling tool.

...

Or do they actually want... something else? Something that they'll only know when they see it?
I think you are probably right. It is kind of a way for people to express a desire that the future will be as rosy as the past has been, while trying to justify it with some quantitative reasoning even if the evidence does not fully support it, which it may not be, as Ben points out.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by GAAP »

I prefer to plan based upon what I know today. For mean reversion to be useful to me, I would need to know the mean for my planning interval -- not the historical mean (which may be outlying data).

To a degree 1/CAPE or 1/PE sort of assume mean reversion -- but they also express a meaningful relationship between cost and returns. They certainly aren't perfect. Periodic readjustment of the plan using the latest portfolio value and return estimate will bumble along the actual performance path to a sufficiently accurate level.

In reality, unexpected withdrawals are likely to have a bigger impact on the plan than minor variances in estimate accuracy. Choosing a conservative estimate means that the errors are more likely to be in your favor than not.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Lastrun »

I was struck listening to a Rational Reminder podcast with John Cochrane. What struck me was that historical return is not a crazy basis on which to run these calculations-albeit you need to define the period you pull from. Exchange and link below.

[RATIONAL REMINDER]: So something that we've been thinking about a lot recently is related to this. What should you use for an expected return for financial planning purposes? Should it be related to valuation ratios or should it be the long run average?

[COCHRANE]: You should use risk management. I think there is a tendency to survey the expected return forecast and say, "Aha, the expected return forecast is 4.23%." So we will plan on for the next 50 years, we'll lock in. We can spend 4.23% of our portfolio. That's probably not such a wise idea. This is a number that is subject to great uncertainty. The historical average is pretty darn good. Now it depends when you take your beginning and end sample, but your numbers in the 5%, 6%, 7%, 8%. Now, one way I like to think about this is did your grandfather or great-grandfather know in 1945, that stocks were going to earn on average 8% more than bonds, and he put it all into bonds, which is what my grandfather did even though he was a stockbroker, wonderful man.

https://rationalreminder.ca/podcast/169

One great thing about these TPAW, ABW, VPW approaches is the self-correction-very elegant.
Ben Mathew wrote: Mon Jun 06, 2022 10:40 pm [While it's hard to guess the expected return, the good news is that an amortization based variable withdrawal strategy involves constant course-corrections of withdrawals, which reduces the damage done by a bad guess.
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Re: Total portfolio allocation and withdrawal (TPAW)

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AlohaJoe wrote: Thu Jun 09, 2022 3:20 am Case in point: my spreadsheet updates with 1/PE expected returns on a weekly basis. At the beginning of the year, that generated at expected return of 2.8%. Now the calculated expected return is 4.0%. That means that despite the stock market crash, war in Ukraine, and high inflation, the ABW calculated withdrawal has actually gone up by over 10%.
This is an important point. People should know going in that 1/PE will vary quite a bit and can take on some really high and really low values. Using longer term earnings averages like CAPE helps, but even then the variation can be eye popping. My preference is to rely at least partly on regression estimates (from the regression of subsequent returns on starting ln(1/CAPE)). These are much less variable. Here's a graph comparing 1/CAPE to regression based 30 year expected return:

Image

1/CAPE (blue line) ranged from a high of 19.5% in 1921 to a low of 2.3% in 2000. The regression estimates (red line) ranged from a high of 9.6% in 1921 to a low of 5% in 2000.

The default estimates I'm currently using for the planner uses the average of the lowest two estimates, which is currently 1/CAPE and the 10 year regression estimate. So there is a significant conservative tilt to it, and it also won't fluctuate as much as 1/CAPE. That may be a feature for some and a bug for others.

Data is from the "Return Data" spreadsheet in this post.
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Re: Total portfolio allocation and withdrawal (TPAW)

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jjj_22 wrote: Thu Jun 09, 2022 10:57 am
Ben Mathew wrote: Thu Jun 09, 2022 1:43 am A large part of stock market volatility is of the random walk permanent type rather than mean reverting valuation changes. ... The volatility that comes from this is not mean reverting.
If this is true, then wouldn't regressions against historical 1/CAPE be kind of questionable? It seems like when you use that regression to estimate future returns as of now, you kind of have to assume that those data were mean reverting, unless I'm misunderstanding what you're saying. Otherwise you'd just be estimating based on actually random historical averages?
If 1/CAPE was not a useful predictor of future stock returns, then the regression of starting 1/CAPE on future stock returns would have a slope of zero. But regressions do show a positive slope, so let me interpret your question as "If there's not a lot of mean reversion in stock returns, then how can 1/CAPE be correlated with future returns?"

Let's talk about valuation generally first and then circle back to 1/CAPE as an imperfect proxy for valuations:

It is possible for valuations to have a big impact on expected returns and still not result in much mean reversion in stock returns. Imagine that in any given period, valuations change very little. Over time, these tiny changes add up and you can get a large change in valuations. So you still have substantial and meaningful variation in valuations over time. But in any given year, it's still a small portion of the return of that year. So we can still have that a "large part of stock market volatility is of the random walk permanent type rather than mean reverting valuation changes."

1/CAPE is just a rough proxy for valuation. Much of the variation in 1/CAPE is probably not variation in actual valuations. It's just measurement error. But even though 1/CAPE is an imperfect proxy, it seems to capture enough information about stock market valuations that the regressions show a positive and meaningful slope. It's not as strong of a predictor as the true stock market valuation would have been. But it's better than nothing. And it's possible for this to coexist with modest mean reversion because it's possible for valuations to have a big impact on expected returns without resulting in a whole lot of mean reversion.
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Re: Total portfolio allocation and withdrawal (TPAW)

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GAAP wrote: Thu Jun 09, 2022 12:44 pm Periodic readjustment of the plan using the latest portfolio value and return estimate will bumble along the actual performance path to a sufficiently accurate level.

In reality, unexpected withdrawals are likely to have a bigger impact on the plan than minor variances in estimate accuracy. Choosing a conservative estimate means that the errors are more likely to be in your favor than not.
Agree.

Consistently overestimating return by 1% will result in spending reductions of 1% per year if spending tilt is 0%. This compounds to a 26% reduction over 30 years. And if spending tilt is set to 1%, then there would be no reduction in spending per year.

Somewhat conservative assumptions and regular course-corrections makes for a good plan.
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Re: Total portfolio allocation and withdrawal (TPAW)

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Lastrun wrote: Thu Jun 09, 2022 2:23 pm I was struck listening to a Rational Reminder podcast with John Cochrane. What struck me was that historical return is not a crazy basis on which to run these calculations-albeit you need to define the period you pull from. Exchange and link below.

[RATIONAL REMINDER]: So something that we've been thinking about a lot recently is related to this. What should you use for an expected return for financial planning purposes? Should it be related to valuation ratios or should it be the long run average?

[COCHRANE]: You should use risk management. I think there is a tendency to survey the expected return forecast and say, "Aha, the expected return forecast is 4.23%." So we will plan on for the next 50 years, we'll lock in. We can spend 4.23% of our portfolio. That's probably not such a wise idea. This is a number that is subject to great uncertainty. The historical average is pretty darn good. Now it depends when you take your beginning and end sample, but your numbers in the 5%, 6%, 7%, 8%. Now, one way I like to think about this is did your grandfather or great-grandfather know in 1945, that stocks were going to earn on average 8% more than bonds, and he put it all into bonds, which is what my grandfather did even though he was a stockbroker, wonderful man.

https://rationalreminder.ca/podcast/169
Interesting. I have seen that segment before, and even linked to it in this post. But I interpreted Cochrane's comment that "historical returns were pretty darn good" in the underlined part above to mean that "historical returns were pretty darn high"--higher than expected--and not that the historical returns were a good estimate for expected returns.
Lastrun wrote: Thu Jun 09, 2022 2:23 pm One great thing about these TPAW, ABW, VPW approaches is the self-correction-very elegant.
+1
Last edited by Ben Mathew on Thu Jun 09, 2022 9:18 pm, edited 1 time in total.
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Re: Total portfolio allocation and withdrawal (TPAW)

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Ben Mathew wrote: Thu Jun 09, 2022 6:13 pm Using longer term earnings averages like CAPE helps,
Sure but using CAPE introduces its own set of issues unless you are 100% US TSM. I assume very few ABW users do that so now you've got another source of errors in your estimates. And not always in a conservative direction.

Don't get me wrong, I don't think retirees should let the perfect be the enemy of the good. I use 1/PE because it is easy for me to get the PE for the funds I actually own on; fund sponsors all update that on a monthly basis on their websites. So I use it despite the shortcomings because it is easy to get.

All this stuff should just be inputs to help a human make human powered judgements on a semi regular basis.

I guess I'm mostly just saying that the people asking for more and more complexity in the tools are probably pushing in the wrong direction. You should look for high frequency feedback rather than high complexity forward planning.
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Re: Total portfolio allocation and withdrawal (TPAW)

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AlohaJoe wrote: Thu Jun 09, 2022 9:18 pm
Ben Mathew wrote: Thu Jun 09, 2022 6:13 pm Using longer term earnings averages like CAPE helps,
Sure but using CAPE introduces its own set of issues unless you are 100% US TSM. I assume very few ABW users do that so now you've got another source of errors in your estimates. And not always in a conservative direction.
Yes, this is a problem. I personally do look at the published earnings yields, with all its flaws, for all of the funds I invest in. They've been higher than 1/CAPE, so I've been thinking of 1/CAPE as a conservative estimate. If that changes, I'd probably get nervous and knock the expected returns down a bit. :happy
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by dcabler »

AlohaJoe wrote: Thu Jun 09, 2022 9:18 pm
Ben Mathew wrote: Thu Jun 09, 2022 6:13 pm Using longer term earnings averages like CAPE helps,
Sure but using CAPE introduces its own set of issues unless you are 100% US TSM. I assume very few ABW users do that so now you've got another source of errors in your estimates. And not always in a conservative direction.

Don't get me wrong, I don't think retirees should let the perfect be the enemy of the good. I use 1/PE because it is easy for me to get the PE for the funds I actually own on; fund sponsors all update that on a monthly basis on their websites. So I use it despite the shortcomings because it is easy to get.

All this stuff should just be inputs to help a human make human powered judgements on a semi regular basis.

I guess I'm mostly just saying that the people asking for more and more complexity in the tools are probably pushing in the wrong direction. You should look for high frequency feedback rather than high complexity forward planning.
Also, there's always the issue of "will the real PE please stand up?"
Forward PE?
Trailing PE with losers removed from the calculation?
Trailing PE with everything included?

Good thread on this topic: viewtopic.php?t=199804

Last I checked, etf.com is the only source of PE ratio that measures trailing PE with all losers included.
https://www.etf.com/sections/blog/23121 ... nopaging=1

Cheers.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Ben Mathew »

dcabler wrote: Fri Jun 10, 2022 5:37 am Last I checked, etf.com is the only source of PE ratio that measures trailing PE with all losers included.
https://www.etf.com/sections/blog/23121 ... nopaging=1
Thanks for publicizing this. I have been using PE numbers from etf.com based on your prior posts about this. For the mutual funds I hold, there's usually a related etf for which I can get the data from etf.com.

The practice of dropping companies with losses from fund PE calculations is very troubling.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by GAAP »

Ben Mathew wrote: Thu Jun 09, 2022 6:13 pm
AlohaJoe wrote: Thu Jun 09, 2022 3:20 am Case in point: my spreadsheet updates with 1/PE expected returns on a weekly basis. At the beginning of the year, that generated at expected return of 2.8%. Now the calculated expected return is 4.0%. That means that despite the stock market crash, war in Ukraine, and high inflation, the ABW calculated withdrawal has actually gone up by over 10%.
This is an important point. People should know going in that 1/PE will vary quite a bit and can take on some really high and really low values. Using longer term earnings averages like CAPE helps, but even then the variation can be eye popping. My preference is to rely at least partly on regression estimates (from the regression of subsequent returns on starting ln(1/CAPE)). These are much less variable. Here's a graph comparing 1/CAPE to regression based 30 year expected return:

Image

1/CAPE (blue line) ranged from a high of 19.5% in 1921 to a low of 2.3% in 2000. The regression estimates (red line) ranged from a high of 9.6% in 1921 to a low of 5% in 2000.

The default estimates I'm currently using for the planner uses the average of the lowest two estimates, which is currently 1/CAPE and the 10 year regression estimate. So there is a significant conservative tilt to it, and it also won't fluctuate as much as 1/CAPE. That may be a feature for some and a bug for others.

Data is from the "Return Data" spreadsheet in this post.
Just visually, the correlation between the two methods seems to be fairly high -- have you actually calculated that?

What I find interesting is that a 1-year period (1/PE), a 10-year period (1/CAPE10), and a 30-year regression all show the same general relationship between prices and long-term performance. To me, that means that the concept of that general relationship is valid -- even though the error margin is also significant at times.

Using any PMT-based method (VPW, TPAW, home-grown) that recalculates each year based upon any of these estimates is a valid strategy in my opinion -- choosing the method comes down more to what you want to achieve than picking a single "right" method.
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Re: Total portfolio allocation and withdrawal (TPAW)

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GAAP wrote: Fri Jun 10, 2022 2:02 pm Just visually, the correlation between the two methods seems to be fairly high -- have you actually calculated that?
The log of the regression estimate of the expected return is a linear function of the log of 1/CAPE, and so is perfectly correlated to log of 1/CAPE. Specifically, the 30 year regression based expected return used in the graph above is

ln(1+30 year expected stock return) = 0.275*ln(1+1/CAPE)+.0428
Last edited by Ben Mathew on Fri Jun 10, 2022 8:44 pm, edited 1 time in total.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by GAAP »

Ben Mathew wrote: Fri Jun 10, 2022 6:12 pm
GAAP wrote: Fri Jun 10, 2022 2:02 pm Just visually, the correlation between the two methods seems to be fairly high -- have you actually calculated that?
The log of the regression estimate of the expected return is a linear function of the log of 1/CAPE, and so is perfectly correlated to log of 1/CAPE. Specifically, the 30 year regression based expected return used in the graph above is

ln(30 year expected stock return) = 0.275*ln(1/CAPE)+.0428
:oops: I guess I should have read what you wrote...

The regression estimate is essentially providing a smoothed 1/CAPE estimate. That smoothing may make the estimate changes more palatable to some. Assuming a 30-year regression is appropriate for a particular need, it would make sense to me to prefer the regression to the raw calculation. I'm not sure what averaging the two really gives you.

For my needs, I might play around with a 20-year regression since 1/CAPE correlation to actual results peaks at around 19 years. I get nervous about going too far back in time for this sort of thing. ERISA changed a lot of things in 1974 -- we still don't have two full 20-year cycles since then.
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Re: Total portfolio allocation and withdrawal (TPAW)

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SAVINGS PORTFOLIO VS TOTAL PORTFOLIO: RISK AS A FUNCTION OF MARKET PERFORMANCE

An earlier post looked at how risk is a function of age in the savings and total portfolio strategies. This post looks at how risk is a function of market performance.

Same setup as before: A 55 year old retiree with a savings portfolio of $1 million. Planning till age 100. The retiree will receive a pension of $30,000 per year starting age 70. If the expected return of stocks is 3.5% and bonds is 0.5%, a total portfolio strategy with a fixed AA of 35/65 on the total portfolio will support expected spending of $54,221 per year. A savings portfolio strategy with a fixed AA of 80/20 will generate the same expected spending of $54,221 per year. Both strategies plan to draw $54,221 from the savings portfolio during the gap and $54,221-$30,000 = $24,221 after the pension starts.

The first graph below shows how the $54,221 per year is funded.

The second graph shows how, after a 30% gain in the savings portfolio, spending would increase to $65,777. A higher fraction of annual spending would be funded by the savings portfolio. So a 10% rise or fall in the portfolio will have a bigger percentage impact on spending per year.

The third graph shows how, after a 30% loss in the savings portfolio, spending would decrease to $42,665. A smaller fraction of annual spending would be funded by the savings portfolio. So a 10% rise or fall in the saving portfolio will have a smaller impact on spending per year.

Image

If we maintain a fixed AA on the savings portfolio, we are keeping risk on the savings portfolio constant. But because the impact of the savings portfolio on spending is itself smaller when the market does poorly, risk to spending is reduced when the market does poorly. This is consistent with decreasing relative risk aversion (DRRA), A person with DDRA will want to reduce risk as wealth declines--effectively protecting the little that's left.

In the total portfolio strategy, if we maintain a fixed AA on the total portfolio, risk to spending would be held constant. A 10% rise or fall in the portfolio will have the same percentage impact on spending per year. This is consistent with constant relative risk aversion (CRRA). If you have decreasing relative risk aversion (DRRA) and want to cut risk as wealth declines, you can do so by creating a guaranteed spending floor. This would work like a self-constructed pension and reduce risk in the same way. The difference would be that the guaranteed spending floor covers all of retirement, whereas the pension may not. So though both methods would cut risk as markets do badly, the precise trajectory of the cuts may be different.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by dcabler »

Ben Mathew wrote: Fri Jun 10, 2022 6:12 pm
GAAP wrote: Fri Jun 10, 2022 2:02 pm Just visually, the correlation between the two methods seems to be fairly high -- have you actually calculated that?
The log of the regression estimate of the expected return is a linear function of the log of 1/CAPE, and so is perfectly correlated to log of 1/CAPE. Specifically, the 30 year regression based expected return used in the graph above is

ln(1+30 year expected stock return) = 0.275*ln(1+1/CAPE)+.0428
If you're comparing, shouldn't you be comparing the 30 year regression to a 30 year based CAPE instead of a 10 year based one?

Cheers.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Ben Mathew »

dcabler wrote: Mon Jun 13, 2022 5:32 am
Ben Mathew wrote: Fri Jun 10, 2022 6:12 pm
GAAP wrote: Fri Jun 10, 2022 2:02 pm Just visually, the correlation between the two methods seems to be fairly high -- have you actually calculated that?
The log of the regression estimate of the expected return is a linear function of the log of 1/CAPE, and so is perfectly correlated to log of 1/CAPE. Specifically, the 30 year regression based expected return used in the graph above is

ln(1+30 year expected stock return) = 0.275*ln(1+1/CAPE)+.0428
If you're comparing, shouldn't you be comparing the 30 year regression to a 30 year based CAPE instead of a 10 year based one?

Cheers.
Since CAPE30 isn't widely used/available, I was restricting myself to CAPE10 as the signal. The question I had in mind is should we use the 1/CAPE10 signal directly, or should we run a regression and then use the predicted expected return over the relevant planning horizon (which may be different from 10 years). I will do a more detailed post about these regressions which will include the 10 year predicted returns as well, if you want to compare that to 1/CAPE10.

A separate question is whether CAPE30 would be a better signal for certain horizons than CAPE10. I haven't looked at that.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by dcabler »

Ben Mathew wrote: Mon Jun 13, 2022 3:34 pm
dcabler wrote: Mon Jun 13, 2022 5:32 am
Ben Mathew wrote: Fri Jun 10, 2022 6:12 pm
GAAP wrote: Fri Jun 10, 2022 2:02 pm Just visually, the correlation between the two methods seems to be fairly high -- have you actually calculated that?
The log of the regression estimate of the expected return is a linear function of the log of 1/CAPE, and so is perfectly correlated to log of 1/CAPE. Specifically, the 30 year regression based expected return used in the graph above is

ln(1+30 year expected stock return) = 0.275*ln(1+1/CAPE)+.0428
If you're comparing, shouldn't you be comparing the 30 year regression to a 30 year based CAPE instead of a 10 year based one?

Cheers.
Since CAPE30 isn't widely used/available, I was restricting myself to CAPE10 as the signal. The question I had in mind is should we use the 1/CAPE10 signal directly, or should we run a regression and then use the predicted expected return over the relevant planning horizon (which may be different from 10 years). I will do a more detailed post about these regressions which will include the 10 year predicted returns as well, if you want to compare that to 1/CAPE10.

A separate question is whether CAPE30 would be a better signal for certain horizons than CAPE10. I haven't looked at that.
From a pure correlation (R2) standpoint CAPE10 has maxed out beyond 10 years - exactly where depends on the timeframe you're using. Siamond did some work on this a few years back: https://www.bogleheads.org/blog/2018/02 ... wal-rates/

Anyway, CAPE30 (or any arbitrary length CAPE besides CAPE10) isn't readily available, but it wouldn't take much work to extract it from Prof Shiller's spreadsheet.

And it goes without saying that regression based approaches often suffer from using only in-sample data to create the regression formula. Heck, there is at least one person here who likes to state pretty often that the "1" in 1/CAPE is a curve fit. :D

Keen on seeing further thoughts on regressions, but would also like to see either the predictability of future returns vs. those regressions or, more importantly for this topic, the trajectories of withdrawals using an amortization approach with various approaches to predicting future stock returns.

Cheers.
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Re: Total portfolio allocation and withdrawal (TPAW)

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EXPECTED STOCK RETURN ESTIMATES FROM CAPE REGRESSIONS

I obtain expected stock return estimates from regressions of future log stock returns on log (1+1/CAPE). For those not familiar with regressions, a regression of Y on X is simply the average of Y as a function of X. So here the regression is giving us an equation that tells us what the average future log stock returns was when log (1+1/CAPE) took on different values.

I run regressions for 5 year, 10 year, 20 year and 30 year future return horizons using all available data (1881-2021). I run a second set of regressions restricting the data to recent years (1950-2021).

Image


CAPE=30.22 (as of Fri Jun 24, from multpl.com)
1/CAPE = 1/30.22 = 3.31%
ln(1+1/CAPE) = ln (1+1/.0331) = 3.26%

Enter x = 3.26% in the regression estimates (in yellow in the graphs above) to obtain the following estimates of expected future log stock returns:

Next 5 years: 2.9% (all years) and 4.4% (recent years)
Next 10 years: 3.0% (all years) and 3.1% (recent years)
Next 20 years: 3.9% (all years) and 3.0% (recent years)
Next 30 years: 5.2% (all years) and 5.0% (recent years)

Since log of expected returns is not equal to expected log returns, we have to add an adjustment factor to expected log return before converting to expected return. For a normal distribution, the adjustment factor is variance/2, which would be 1.48% in our data. The actual adjustment we need as estimated directly from our data is fairly close to this: 1.41%. So we have:

Expected return = exp(expected log return+1.41%) - 1

This gives us the following estimates of expected future stock returns:

Next 5 years: 4.5% (all years) and 6.0% (recent years)
Next 10 years: 4.5% (all years) and 4.6% (recent years)
Next 20 years: 5.4% (all years) and 4.5% (recent years)
Next 30 years: 6.9% (all years) and 6.7% (recent years)

The raw 1/CAPE estimate of expected future return is 3.3%

The lowest two of the nine expected return estimates above are 3.3% and 4.5%. Averaging these, we get 3.9%. This is the default expected stock return currently used in tpawplanner.com.

The following graph shows the expected return estimates over time (regression based estimates are "all years"):

Image

The 1/CAPE, 5 year predicted return, and 10 year predicted returns vary quite a bit over time. The 30 year predicted return is more stable.

Excel spreadsheet with data and calculations: Return Data - Expected Return Regressions
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by dcabler »

Ben Mathew wrote: Sun Jun 26, 2022 1:22 am EXPECTED STOCK RETURN ESTIMATES FROM CAPE REGRESSIONS

I obtain expected stock return estimates from regressions of future log stock returns on log (1+1/CAPE). For those not familiar with regressions, a regression of Y on X is simply the average of Y as a function of X. So here the regression is giving us an equation that tells us what the average future log stock returns was when log (1+1/CAPE) took on different values.

I run regressions for 5 year, 10 year, 20 year and 30 year future return horizons using all available data (1881-2021). I run a second set of regressions restricting the data to recent years (1950-2021).

Image


CAPE=30.22 (as of Fri Jun 24, from multpl.com)
1/CAPE = 1/30.22 = 3.31%
ln(1+1/CAPE) = ln (1+1/.0331) = 3.26%

Enter x = 3.26% in the regression estimates (in yellow in the graphs above) to obtain the following estimates of expected future log stock returns:

Next 5 years: 2.9% (all years) and 4.4% (recent years)
Next 10 years: 3.0% (all years) and 3.1% (recent years)
Next 20 years: 3.9% (all years) and 3.0% (recent years)
Next 30 years: 5.2% (all years) and 5.0% (recent years)

Since log of expected returns is not equal to expected log returns, we have to add an adjustment factor to expected log return before converting to expected return. For a normal distribution, the adjustment factor is variance/2, which would be 1.48% in our data. The actual adjustment we need as estimated directly from our data is fairly close to this: 1.41%. So we have:

Expected return = exp(expected log return+1.41%) - 1

This gives us the following estimates of expected future stock returns:

Next 5 years: 4.5% (all years) and 6.0% (recent years)
Next 10 years: 4.5% (all years) and 4.6% (recent years)
Next 20 years: 5.4% (all years) and 4.5% (recent years)
Next 30 years: 6.9% (all years) and 6.7% (recent years)

The raw 1/CAPE estimate of expected future return is 3.3%

The lowest two of the nine expected return estimates above are 3.3% and 4.5%. Averaging these, we get 3.9%. This is the default expected stock return currently used in tpawplanner.com.

The following graph shows the expected return estimates over time (regression based estimates are "all years"):

Image

The 1/CAPE, 5 year predicted return, and 10 year predicted returns vary quite a bit over time. The 30 year predicted return is more stable.

Excel spreadsheet with data and calculations: Return Data - Expected Return Regressions
Why does the stability of the predicted return itself matter in the context of an amortization based withdrawal method? Isn't the goal more about how well predicted returns end up matching reality so as to provide smoother withdrawals over time, assuming you're updating predicted returns periodically over the course of a retirement?

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Re: Total portfolio allocation and withdrawal (TPAW)

Post by GAAP »

dcabler wrote: Sun Jun 26, 2022 3:13 pm Why does the stability of the predicted return itself matter in the context of an amortization based withdrawal method? Isn't the goal more about how well predicted returns end up matching reality so as to provide smoother withdrawals over time, assuming you're updating predicted returns periodically over the course of a retirement?
Stability of predicted return leads to the use of a more stable interest rate in the amortization formula which leads to more stability in the outputs of the amortization. Effectively, that means that predicted return stability is a smoothing agent itself -- the calculation closes on to the "correct" value more quickly and with less variability.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by dcabler »

GAAP wrote: Sun Jun 26, 2022 3:21 pm
dcabler wrote: Sun Jun 26, 2022 3:13 pm Why does the stability of the predicted return itself matter in the context of an amortization based withdrawal method? Isn't the goal more about how well predicted returns end up matching reality so as to provide smoother withdrawals over time, assuming you're updating predicted returns periodically over the course of a retirement?
Stability of predicted return leads to the use of a more stable interest rate in the amortization formula which leads to more stability in the outputs of the amortization. Effectively, that means that predicted return stability is a smoothing agent itself -- the calculation closes on to the "correct" value more quickly and with less variability.
That's not been the case when I've backtested something more VPW-like with its use of a fixed expected return (nothing more stable than that) vs. one that is dynamically adjusted based on predicted returns using something like 1/CAPE. Not for every sequence of withdrawals for sure, but what I and others have seen is reduced variation of withdrawals (in real terms) over time with something that's more dynamic. If actual returns over time are moving around and the expected returns aren't so much, I don't see how that's going to result in smoother withdrawals vs. actual & predicted returns moving more in sync.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Ben Mathew »

dcabler wrote: Sun Jun 26, 2022 3:13 pm Why does the stability of the predicted return itself matter in the context of an amortization based withdrawal method? Isn't the goal more about how well predicted returns end up matching reality so as to provide smoother withdrawals over time, assuming you're updating predicted returns periodically over the course of a retirement?

Cheers
I am not advocating the use of one predicted return series over the other. Just pointing out that there is a lot of variability in some signals so people using it won't be surprised when it happens. The countercyclical variability of some of these signals may be attractive to some investors who like the consumption smoothing generated by it. But my inclination is to make a somewhat conservative guess about the expected return over my remaining investing horizon. So if my investing horizon was 30 years, and 5 year returns are predicted to be 15% and 30 year returns are predicted to be 5%, I would enter 5% as my expected return for planning purposes. Even if historically it was the case that highly variable countercyclical short term signals worked well too smooth amortization based withdrawals, I would worry about whether I'm overfitting and relying too much on a pattern that may not repeat.

Conversely, if the 5 year predicted return is 5% and the 30 year predicted return is 10%, I would enter maybe 6% or 7% in the planner. I'm more comfortable with somewhat conservative return estimates. I know that I would not have entered 15% real expected returns for stocks in 1982. So for me it's best to recognize that and not plan to do that.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by dcabler »

Ben Mathew wrote: Sun Jun 26, 2022 3:47 pm
dcabler wrote: Sun Jun 26, 2022 3:13 pm Why does the stability of the predicted return itself matter in the context of an amortization based withdrawal method? Isn't the goal more about how well predicted returns end up matching reality so as to provide smoother withdrawals over time, assuming you're updating predicted returns periodically over the course of a retirement?

Cheers
I am not advocating the use of one predicted return series over the other. Just pointing out that there is a lot of variability in some signals so people using it won't be surprised when it happens. The countercyclical variability of some of these signals may be attractive to some investors who like the consumption smoothing generated by it. But my inclination is to make a somewhat conservative guess about the expected return over my remaining investing horizon. So if my investing horizon was 30 years, and 5 year returns are predicted to be 15% and 30 year returns are predicted to be 5%, I would enter 5% as my expected return for planning purposes. Even if historically it was the case that highly variable countercyclical short term signals worked well too smooth amortization based withdrawals, I would worry about whether I'm overfitting and relying too much on a pattern that may not repeat.

Conversely, if the 5 year predicted return is 5% and the 30 year predicted return is 10%, I would enter maybe 6% or 7% in the planner. I'm more comfortable with somewhat conservative return estimates. I know that I would not have entered 15% real expected returns for stocks in 1982. So for me it's best to recognize that and not plan to do that.
I didn't assume you were making a recommendation as there are as many possible ways to calculate future returns as there are people who come up with them, including various versions of CAPE of different lengths with different equations for the regression, "Greatest Predictor", and momentum based predictions. All have their flaws. And that's actually a good thing because we'd probably lose the stock return premium otherwise. :D

It just appeared that smoothness of the predicted returns was more important than the accuracy of the predicted returns. But I do understand your point above and, of course, everybody has different goals, etc. In fact, one of my backup plans for my DW who has little interest in this is to do a pre-calculation of something VPW-ish should I predecease.

Yep, overfitting can definitely be a problem, especially when one doesn't at least test a method out-of-sample.

As you note above, withdrawals can get pretty noisy if the expected time remaining in retirement is less than the number of years out where the prediction is most accurate. I first noticed this when looking at stock and bond withdrawals separately and was studying bonds. It was kind of a "duh" moment for me. If you have 5 years left until you think you're done but you're holding a bond fund with 10 years duration you have a mismatch in your duration vs. horizon. And it was pretty obvious in my backtests. Since bonds are quite a bit more deterministic than stocks are, this can be remedied by either reducing your duration over time as described by vineviz and BobK or even just stepping down duration in a few discrete steps along the way from Long-to-intermediate-to-short-to-ultrashort/cash-to-worm food.

On my to-do list is to go back to the stock side and play around with something like what you mention above with different methods/equations/techniques based on an ever shortening horizon. All, of course, including out-of-sample testing.

cheers.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by dcabler »

Ben Mathew wrote: Sun Jun 26, 2022 1:22 am EXPECTED STOCK RETURN ESTIMATES FROM CAPE REGRESSIONS

I obtain expected stock return estimates from regressions of future log stock returns on log (1+1/CAPE). For those not familiar with regressions, a regression of Y on X is simply the average of Y as a function of X. So here the regression is giving us an equation that tells us what the average future log stock returns was when log (1+1/CAPE) took on different values.

I run regressions for 5 year, 10 year, 20 year and 30 year future return horizons using all available data (1881-2021). I run a second set of regressions restricting the data to recent years (1950-2021).

Image


CAPE=30.22 (as of Fri Jun 24, from multpl.com)
1/CAPE = 1/30.22 = 3.31%
ln(1+1/CAPE) = ln (1+1/.0331) = 3.26%

Enter x = 3.26% in the regression estimates (in yellow in the graphs above) to obtain the following estimates of expected future log stock returns:

Next 5 years: 2.9% (all years) and 4.4% (recent years)
Next 10 years: 3.0% (all years) and 3.1% (recent years)
Next 20 years: 3.9% (all years) and 3.0% (recent years)
Next 30 years: 5.2% (all years) and 5.0% (recent years)

Since log of expected returns is not equal to expected log returns, we have to add an adjustment factor to expected log return before converting to expected return. For a normal distribution, the adjustment factor is variance/2, which would be 1.48% in our data. The actual adjustment we need as estimated directly from our data is fairly close to this: 1.41%. So we have:

Expected return = exp(expected log return+1.41%) - 1

This gives us the following estimates of expected future stock returns:

Next 5 years: 4.5% (all years) and 6.0% (recent years)
Next 10 years: 4.5% (all years) and 4.6% (recent years)
Next 20 years: 5.4% (all years) and 4.5% (recent years)
Next 30 years: 6.9% (all years) and 6.7% (recent years)

The raw 1/CAPE estimate of expected future return is 3.3%

The lowest two of the nine expected return estimates above are 3.3% and 4.5%. Averaging these, we get 3.9%. This is the default expected stock return currently used in tpawplanner.com.

The following graph shows the expected return estimates over time (regression based estimates are "all years"):

Image

The 1/CAPE, 5 year predicted return, and 10 year predicted returns vary quite a bit over time. The 30 year predicted return is more stable.

Excel spreadsheet with data and calculations: Return Data - Expected Return Regressions
I know I mentioned this upstream but I still wonder about using CAPE (based on 10 year price / earnings) to predict 5, 10, 20, and 30 year forward returns. CAPE is going to have maximum predictability of future returns only over a narrow range of years, though it could well be that it's "good enough" I'm still curious, though, what a full matrix of, say, 1, 5, 10, 20 year CAPE (aka PE, PE5, PE10, PE20) would look like. It's on my own "to do someday" list since it's going to require some tedium to extract that from the Shiller data. :D
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Ben Mathew
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Ben Mathew »

dcabler wrote: Sun Jun 26, 2022 4:14 pm Since bonds are quite a bit more deterministic than stocks are, this can be remedied by either reducing your duration over time as described by vineviz and BobK or even just stepping down duration in a few discrete steps along the way from Long-to-intermediate-to-short-to-ultrashort/cash-to-worm food.
Duration matching can significantly reduce bond risk and generally help people think more clearly about their bond investments. I will eventually include the option to duration match in tpawplanner.
Total Portfolio Allocation and Withdrawal (TPAW)
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