Total Portfolio Allocation and Withdrawal (TPAW)

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Gufomel
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Gufomel »

Ben Mathew wrote: Thu Feb 18, 2021 5:40 pm TPAW: ACCUMULATION PHASE

I have added a spreadsheet to the TPAW wiki that covers the accumulation phase.

The accumulation spreadsheet is similar to the withdrawal one, with only a few tweaks necessary to the wording and interpretation. That's because the underlying model covers saving and investing over a lifetime and there isn't really a conceptual difference between what's happening during accumulation vs withdrawal. In both phases, the goal is to maintain a fixed allocation on the total portfolio.

A conservative estimate of future savings during working years is now added to the retirement income column. The model will typically assume high levels of leverage when young because the savings portfolio is small relative to future savings. It's up to the user to decide what their maximum acceptable AA is going to be and whether it will involve leverage. If they don't achieve the target AA, the withdrawal calculations will be off. By mid to late career, it's more likely that the savings portfolio is large enough that the target AA can be maintained without requiring leverage. So the withdrawal distribution displayed will become more accurate at that stage. In early career, even though the withdrawal numbers won't be accurate because the assumed AA is not achieved, the calculations can still serve as a guide to AA. For example, if the spreadsheet says that you should leverage 300%, and you are not willing or able to leverage that much, you can instead just go up to the top of your acceptable AA range.

The example below shows a 25 year old with $30,000 in current savings. They expect to save $10,000 per year till retirement at age 65, and to draw $20,000 from social security starting age 70. They select an AA of 30/70 on the total portfolio, and withdrawal growth rate (g) of .30%. This gives them the following withdrawal distribution, with withdrawals scheduled to grow from $51,140 at age 65 to $56,793 by age 100:

Image

The projected glidepath for the savings portfolio is shown in the table below, in red on the right. The 30/70 fixed AA on the total portfolio translates to a savings portfolio glidepath that starts at 1300% stocks (i.e. 1200% leverage) at age 25, gliding down to 100% stocks at age 41, and stabilizing around 50% stocks around age 65. If the user is not willing or able to take on the leverage indicated in any given year (likely to be the case in the early stages), then they would simply go up to the top of their acceptable AA range that year.

Image

Q&A

How is this related to lifecycle investing?

The underlying model behind TPAW is a lifecycle model, which is a broad term for a model that optimizes consumption over a lifetime. Lifecycle models are the basic models of saving and investing in economics. The strategy that emerges from these models involves spreading consumption and investment risk as much as possible. Spreading investment risk across time means taking enough risk in early years, which will usually require leverage because the savings portfolio is too small to take on enough risk even with 100% stocks. High borrowing costs, call risk, psychological distress, and other such considerations may limit the amount of leverage you want to take on. TPAW leaves it to the user to decide what their personal max AA is, and whether or not it involves leverage. It takes no position on whether you should leverage. If you don't want to leverage, just go up to 100% stocks when the calculator calls for leverage.
It looks like if you try to put an extra withdrawal (column O) in a year after retirement date, it doesn’t adjust the regular withdrawal (column Q) going forward because because the PMT formula is only in the row for the retirement year. This causes the final balance to be negative in cell W132.

Shouldn’t the PMT formula go in every row, and use column C as the nper each year? The PMT formula would need absolute references instead of relative for the expected real return (cell I35) and the growth rate (cell Q51) before doing a drag and drop.

Let me know if I’m missing something as to why it’s set up the way that it is currently.

Edit: I guess the problem with my solution is it only changes the regular withdrawals from the point of the extra withdrawal and going forward, when really it should impact the regular withdrawal for every year. Maybe you have a better solution than me, if you do in fact see the same issue that I’m seeing with post-retirement extra withdrawals.
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Steve Reading
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Steve Reading »

Ben Mathew wrote: Mon Nov 30, 2020 8:39 pm
In the "extra withdrawals" column, one should not put any after the "regular withdrawal retirement" period has started right? Ex: If you knew you wanted to spend an extra 50K when you're 75 to buy a car, there's no way to put that into the spreadsheet and have it adjust the annuitized yearly withdrawals (column Q) to account for that.

I fixed it on mine by changing the first equation of column Q from:
=PMT((1+$I$35)/(1+$Q$51)-1,$I$13,-U97+SUM(,0,1)

To:
=PMT((1+I35)/(1+Q51)-1,I13,-U97+NPV($I$35,O97:O132)*(1+$I$35),0,1)

Now I can put extra withdrawals on any year for the risk portfolio, and it always depletes exactly to zero.
Thoughts?

EDIT: Lmao I literally just noticed the poster above said this exact same thing hahaha. Whoah that's spooky. Quoting them so they see my (temporary?) solution.
Gufomel wrote: Thu Feb 25, 2021 7:55 pm
EDIT 2: The graph will look hella funky though haha. One would have to make sure the graph graphs the current column, minus the risk withdrawals perhaps. Just a thought.
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson
Gufomel
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Gufomel »

Steve Reading wrote: Thu Feb 25, 2021 11:09 pm
Ben Mathew wrote: Mon Nov 30, 2020 8:39 pm
In the "extra withdrawals" column, one should not put any after the "regular withdrawal retirement" period has started right? Ex: If you knew you wanted to spend an extra 50K when you're 75 to buy a car, there's no way to put that into the spreadsheet and have it adjust the annuitized yearly withdrawals (column Q) to account for that.

I fixed it on mine by changing the first equation of column Q from:
=PMT((1+$I$35)/(1+$Q$51)-1,$I$13,-U97+SUM(,0,1)

To:
=PMT((1+I35)/(1+Q51)-1,I13,-U97+NPV($I$35,O97:O132)*(1+$I$35),0,1)

Now I can put extra withdrawals on any year for the risk portfolio, and it always depletes exactly to zero.
Thoughts?

EDIT: Lmao I literally just noticed the poster above said this exact same thing hahaha. Whoah that's spooky. Quoting them so they see my (temporary?) solution.
Gufomel wrote: Thu Feb 25, 2021 7:55 pm
EDIT 2: The graph will look hella funky though haha. One would have to make sure the graph graphs the current column, minus the risk withdrawals perhaps. Just a thought.
Yes that’s incredibly spooky. I’ll have to check out your solution when I have a chance. I get the basic idea and formulas here, but some of this is a bit above my head. So I’m interested to see you and Ben hash it out before I make any changes myself :D
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Ben Mathew
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Ben Mathew »

Gufomel wrote: Thu Feb 25, 2021 7:55 pm It looks like if you try to put an extra withdrawal (column O) in a year after retirement date, it doesn’t adjust the regular withdrawal (column Q) going forward because because the PMT formula is only in the row for the retirement year. This causes the final balance to be negative in cell W132.
Steve Reading wrote: Thu Feb 25, 2021 11:09 pm I fixed it on mine by changing the first equation of column Q from:
=PMT((1+$I$35)/(1+$Q$51)-1,$I$13,-U97+SUM(,0,1)

To:
=PMT((1+I35)/(1+Q51)-1,I13,-U97+NPV($I$35,O97:O132)*(1+$I$35),0,1)

Now I can put extra withdrawals on any year for the risk portfolio, and it always depletes exactly to zero.
Thoughts?
Thanks for catching this mistake. It appears on the accumulation spreadsheet because of a careless shortcut I took. The withdrawal spreadsheet is not affected.

Steve, your solution works. But to keep it more consistent with the withdrawal spreadsheet which takes the PV from the accounting at the top of the table, I decided to take the value from the same cell (Q47) and then convert it to age 65 value. So the formula is now

=PMT((1+$I$35)/(1+$Q$51)-1,I13,-$Q$47*(1+$I$35)^($B$97-$B$57),0,1)

I think that should fix it. I have uploaded the corrected version. Let me know if there are problems.
Total Portfolio Allocation and Withdrawal (TPAW)
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Steve Reading
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Steve Reading »

Ben Mathew wrote: Fri Feb 26, 2021 10:45 am
Gufomel wrote: Thu Feb 25, 2021 7:55 pm It looks like if you try to put an extra withdrawal (column O) in a year after retirement date, it doesn’t adjust the regular withdrawal (column Q) going forward because because the PMT formula is only in the row for the retirement year. This causes the final balance to be negative in cell W132.
Steve Reading wrote: Thu Feb 25, 2021 11:09 pm I fixed it on mine by changing the first equation of column Q from:
=PMT((1+$I$35)/(1+$Q$51)-1,$I$13,-U97+SUM(,0,1)

To:
=PMT((1+I35)/(1+Q51)-1,I13,-U97+NPV($I$35,O97:O132)*(1+$I$35),0,1)

Now I can put extra withdrawals on any year for the risk portfolio, and it always depletes exactly to zero.
Thoughts?
Thanks for catching this mistake. It appears on the accumulation spreadsheet because of a careless shortcut I took. The withdrawal spreadsheet is not affected.

Steve, your solution works. But to keep it more consistent with the withdrawal spreadsheet which takes the PV from the accounting at the top of the table, I decided to take the value from the same cell (Q47) and then convert it to age 65 value. So the formula is now

=PMT((1+$I$35)/(1+$Q$51)-1,I13,-$Q$47*(1+$I$35)^($B$97-$B$57),0,1)

I think that should fix it. I have uploaded the corrected version. Let me know if there are problems.
Yeah, that works. Also, don't want to sound pedantic, but perhaps put dollars signs on the second term (I13), I see you're good about that stuff.

Also, FWIW, here's some things that would be cool if the sheet had. I'm not asking you to do it (you've already done so much, like others, I'm amazed with it and already using it along with my personal one), but if you're ever like "hey I want to add things to it, what would be cool to add?" here's my humble recommendation:
1) A way to change the nature of future savings contributions as somewhere between stocks and bonds? Currently it assumes it is purely bonds which will produce more aggressive AAs. FWIW, I use a 5-10% correlation to future employment savings with stocks (but not for SS).
2) I would find it super, super, super cool if there was a way to change g() such that each year's withdrawal did have the same certainty equivalent as Uncorrelated mentioned. I already picked a g() I liked (0.5% seemed about right) but I just think it'd be so neat if the spreadsheet calculated what utility theory would say is optimal for me.

Also, why recommend 20Y TIPs seems a strange recommendation for the accumulating spreadsheet. Shouldn't it be 30Y TIPs? Using the 20Y will make the portfolio a little more aggressive as the rate is lower.

Also, "portfoliio" has a typo on G53 of 3. Planner. And "savingns" has a typo on B19.

Again, pedantic, I just figured this is the sort of random s@'t you're hoping some of us pick up on.
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson
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Ben Mathew
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Ben Mathew »

Steve Reading wrote: Fri Feb 26, 2021 1:42 pm perhaps put dollars signs on the second term (I13)
Thanks. I'll fix that.
Steve Reading wrote: Fri Feb 26, 2021 1:42 pm Also, FWIW, here's some things that would be cool if the sheet had. I'm not asking you to do it (you've already done so much, like others, I'm amazed with it and already using it along with my personal one), but if you're ever like "hey I want to add things to it, what would be cool to add?" here's my humble recommendation:
Great, I'm looking for feedback and suggestions.
Steve Reading wrote: Fri Feb 26, 2021 1:42 pm 1) A way to change the nature of future savings contributions as somewhere between stocks and bonds? Currently it assumes it is purely bonds which will produce more aggressive AAs. FWIW, I use a 5-10% correlation to future employment savings with stocks (but not for SS).
Yes, the spreadsheet is assuming that the future savings is safe and using the safe bond rate to discount. So this would have to be a very conservative estimate. For example, if $15,000 per year is the expected savings, maybe $10,000 per year or something like that may be a safe estimate. That way, the allocation doesn't get too aggressive.

To explicitly model savings risk, one option would be to rerun the spreadsheet with low, medium, and high estimates of future savings, and see if the withdrawal distribution is acceptable across all three scenarios. You could have three separate tabs for the low, medium and high estimates and aggregate them in a summary tab. You can also introduce correlations through different weighting schemes: high correlation means more weight on the high savings+high return and low savings + low return outcomes. This may be a bit cumbersome, but I think this may be easier to actually understand and interpret than a more elegant/formal model that assumes that savings is a random walk and so on.
Steve Reading wrote: Fri Feb 26, 2021 1:42 pm 2) I would find it super, super, super cool if there was a way to change g() such that each year's withdrawal did have the same certainty equivalent as Uncorrelated mentioned. I already picked a g() I liked (0.5% seemed about right) but I just think it'd be so neat if the spreadsheet calculated what utility theory would say is optimal for me.
The expected utility calculation involves integrating u(x)*p(x) where u() is the CRRA utility function and p() is the lognormal distribution. Excel can't do that integration. We would need an explicit solution. I googled a bit and found this. See equation (1) on page 6. I wonder if that's the formula we would need. If so, then calculating utility given risk and time preferences is straightforward. You could adjust AA and g and see what the utility for each year and total utility would be for different combinations. Wouldn't maximize it for you, but you can at least see the utility impact.
Steve Reading wrote: Fri Feb 26, 2021 1:42 pm Also, why recommend 20Y TIPs seems a strange recommendation for the accumulating spreadsheet. Shouldn't it be 30Y TIPs? Using the 20Y will make the portfolio a little more aggressive as the rate is lower.
The 20 year suggestion was just a carryover from the withdrawal spreadsheet. You're right that 30 year would be better for most accumulators. I'll update that in the next round.
Steve Reading wrote: Fri Feb 26, 2021 1:42 pm Also, "portfoliio" has a typo on G53 of 3. Planner. And "savingns" has a typo on B19.
Thanks. Fixed. Will go through in the next update.
Total Portfolio Allocation and Withdrawal (TPAW)
Gufomel
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Gufomel »

I use 1/CAPE for expected stock returns, but I’ve wondered if it really makes sense to use that as the projection for a lifetime, especially for an early accumulator. Would it make sense to only use that for, let’s say, 10 years but then have it revert toward the historical mean going forward? Probably the same for bonds, but it’s not as clear to me what mean it should revert toward.

I know there’s a lot of argument whether 1/CAPE is even appropriate to begin with. I’m not wanting to get into that. But assuming 1/CAPE is appropriate as the expectation for the next 10 years, is it appropriate to use for decades into the future? Based on where 1/CAPE is relative to historical averages, it’s definitely the more conservative approach. I’m just not sure if too conservative.

I will say that using 1/CAPE in conjunction with a lifecycle investing model like this TPAW spreadsheet really helps put your current savings portfolio in perspective with your lifetime wealth and projected retirement withdrawal. Stocks fell this week, but my projected retirement withdrawal went up fairly significantly because of the increase in 1/CAPE. This really helps an accumulator conceptualize how a decline in stocks can be a good thing and help you not spooked by market crashes when taking into account your entire lifetime projection.

So with that said, even though 1/CAPE is the more conservative approach compared to historical averages, I’m wondering if using that (or any other conservative fixed return estimate) as the expected stock returns for decades ends up actually making a decline in stocks look like it has *too rosy* of an impact on retirement projections. Whereas if you have expected returns revert to the mean over time in your projection, the amount of impact that a change in 1/CAPE has would be dampened (perhaps appropriately?).

1) would that approach make sense?

2) if yes, do you think it would ever be possible to implement it in this spreadsheet?

Edit: I guess the assumption is that in order for 1/CAPE to rise (even after 10 years), stocks would have had to return less than expected in the first 10 years, so it all balances out. Therefore 1/CAPE would be used for the whole lifetime projection. If that’s how it’s best to think about it, then I think that makes sense.

Edit2: Ok after thinking about it more, I bet the reason I saw my retirement withdrawal increase when stocks fell & 1/CAPE rose is because my actual current savings portfolio is more conservative than what the spreadsheet says I should be. If I was leveraged according to what the spreadsheet says I should be, my portfolio would have declined enough to offset the rise in future expectations. So if that’s case, I guess it is correct to use the same return expectations for every year in the future and not revert to the mean. But the fact still remains that this spreadsheet helps an accumulator (who is not yet at their desired stock allocation according to lifecycle investing) see that declining stocks is a good thing for them.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Steve Reading »

Gufomel wrote: Sat Feb 27, 2021 7:19 am I use 1/CAPE for expected stock returns, but I’ve wondered if it really makes sense to use that as the projection for a lifetime, especially for an early accumulator.
FWIW, AQR mentions that for 5-10 year expectations, valuations are reasonable. But for longer-term, generally best to rely on intuition about risk-return. Source:
https://www.aqr.com/Insights/Research/A ... et-Classes
As usual, we present local real (inflationadjusted) annual compound rates of return for a horizon of 5 to 10 years. Over such intermediate horizons, initial market yields and valuations tend to be useful inputs. For multi-decade forecast horizons, the impact of starting yields is diluted, so theory and long-term historical average returns (or yields) may matter more in judging expected returns.
In other words, to estimate stock returns over 30 years, a better estimate might be the 30Y TIPs + the historical equity risk premium of stocks over 30Y real bond returns.

Personally, I use an average between the two. YMMV
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson
Gufomel
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Gufomel »

Steve Reading wrote: Sat Feb 27, 2021 8:08 am
Gufomel wrote: Sat Feb 27, 2021 7:19 am I use 1/CAPE for expected stock returns, but I’ve wondered if it really makes sense to use that as the projection for a lifetime, especially for an early accumulator.
FWIW, AQR mentions that for 5-10 year expectations, valuations are reasonable. But for longer-term, generally best to rely on intuition about risk-return. Source:
https://www.aqr.com/Insights/Research/A ... et-Classes
As usual, we present local real (inflationadjusted) annual compound rates of return for a horizon of 5 to 10 years. Over such intermediate horizons, initial market yields and valuations tend to be useful inputs. For multi-decade forecast horizons, the impact of starting yields is diluted, so theory and long-term historical average returns (or yields) may matter more in judging expected returns.
In other words, to estimate stock returns over 30 years, a better estimate might be the 30Y TIPs + the historical equity risk premium of stocks over 30Y real bond returns.

Personally, I use an average between the two. YMMV
Interesting. When you say “average between the two” you mean the average of 1) 1/CAPE and 2) 30Y TIPs + the historical equity risk premium of stocks over 30Y real bond returns?

And that’s what you’d use for every year starting today?

Do you mind providing the equity risk premium number you use and your source?
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Steve Reading »

Gufomel wrote: Sat Feb 27, 2021 8:25 am
Steve Reading wrote: Sat Feb 27, 2021 8:08 am
Gufomel wrote: Sat Feb 27, 2021 7:19 am I use 1/CAPE for expected stock returns, but I’ve wondered if it really makes sense to use that as the projection for a lifetime, especially for an early accumulator.
FWIW, AQR mentions that for 5-10 year expectations, valuations are reasonable. But for longer-term, generally best to rely on intuition about risk-return. Source:
https://www.aqr.com/Insights/Research/A ... et-Classes
As usual, we present local real (inflationadjusted) annual compound rates of return for a horizon of 5 to 10 years. Over such intermediate horizons, initial market yields and valuations tend to be useful inputs. For multi-decade forecast horizons, the impact of starting yields is diluted, so theory and long-term historical average returns (or yields) may matter more in judging expected returns.
In other words, to estimate stock returns over 30 years, a better estimate might be the 30Y TIPs + the historical equity risk premium of stocks over 30Y real bond returns.

Personally, I use an average between the two. YMMV
Interesting. When you say “average between the two” you mean the average of 1) 1/CAPE and 2) 30Y TIPs + the historical equity risk premium of stocks over 30Y real bond returns?

And that’s what you’d use for every year starting today?

Do you mind providing the equity risk premium number you use and your source?
Yes to your 1st question. For the second, you're asking the right questions haha.

For stock returns and volatility, I used yearly USA returns from Fama French from 1952-1970. And used yearly MSCI World returns from 1970 onwards. That gives me 10.2% CAGR (nominal) with yearly volatility of 17.7%.
For LT bond, I used the Simba return calculator, from 1952 to today. That's a 6.17% nominal (and includes roll yield). Something interesting happened in 1952 for LT bonds that is besides the point but it means the best measure should be from 1952 onwards.

So you could get the equity risk premium by converting stock's annualized returns to mean returns (annualized returns + volatility^2/2) and subtract bond returns. I get 5.6%.

You can then add that 5.6% to current 30Y TIPs (ideally plus an extra 0.1-0.2% to represent the roll yield for accumulators who have more than a 15 year time horizon like you and I) to get the average real return for USA stocks today. And then re-convert back to annualized returns by subtracting volatility^2.
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson
Gufomel
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Gufomel »

Steve Reading wrote: Sat Feb 27, 2021 8:34 am
Gufomel wrote: Sat Feb 27, 2021 8:25 am
Steve Reading wrote: Sat Feb 27, 2021 8:08 am
Gufomel wrote: Sat Feb 27, 2021 7:19 am I use 1/CAPE for expected stock returns, but I’ve wondered if it really makes sense to use that as the projection for a lifetime, especially for an early accumulator.
FWIW, AQR mentions that for 5-10 year expectations, valuations are reasonable. But for longer-term, generally best to rely on intuition about risk-return. Source:
https://www.aqr.com/Insights/Research/A ... et-Classes
As usual, we present local real (inflationadjusted) annual compound rates of return for a horizon of 5 to 10 years. Over such intermediate horizons, initial market yields and valuations tend to be useful inputs. For multi-decade forecast horizons, the impact of starting yields is diluted, so theory and long-term historical average returns (or yields) may matter more in judging expected returns.
In other words, to estimate stock returns over 30 years, a better estimate might be the 30Y TIPs + the historical equity risk premium of stocks over 30Y real bond returns.

Personally, I use an average between the two. YMMV
Interesting. When you say “average between the two” you mean the average of 1) 1/CAPE and 2) 30Y TIPs + the historical equity risk premium of stocks over 30Y real bond returns?

And that’s what you’d use for every year starting today?

Do you mind providing the equity risk premium number you use and your source?
Yes to your 1st question. For the second, you're asking the right questions haha.

For stock returns and volatility, I used yearly USA returns from Fama French from 1952-1970. And used yearly MSCI World returns from 1970 onwards. That gives me 10.2% CAGR (nominal) with yearly volatility of 17.7%.
For LT bond, I used the Simba return calculator, from 1952 to today. That's a 6.17% nominal (and includes roll yield). Something interesting happened in 1952 for LT bonds that is besides the point but it means the best measure should be from 1952 onwards.

So you could get the equity risk premium by converting stock's annualized returns to mean returns (annualized returns + volatility^2/2) and subtract bond returns. I get 5.6%.

You can then add that 5.6% to current 30Y TIPs (ideally plus an extra 0.1-0.2% to represent the roll yield for accumulators who have more than a 15 year time horizon like you and I) to get the average real return for USA stocks today. And then re-convert back to annualized returns by subtracting volatility^2.
Thanks for walking through it. That’s probably a little past me, but helpful to see how you approach it.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Steve Reading »

Gufomel wrote: Sat Feb 27, 2021 8:42 am
Steve Reading wrote: Sat Feb 27, 2021 8:34 am
Gufomel wrote: Sat Feb 27, 2021 8:25 am
Steve Reading wrote: Sat Feb 27, 2021 8:08 am
Gufomel wrote: Sat Feb 27, 2021 7:19 am I use 1/CAPE for expected stock returns, but I’ve wondered if it really makes sense to use that as the projection for a lifetime, especially for an early accumulator.
FWIW, AQR mentions that for 5-10 year expectations, valuations are reasonable. But for longer-term, generally best to rely on intuition about risk-return. Source:
https://www.aqr.com/Insights/Research/A ... et-Classes
As usual, we present local real (inflationadjusted) annual compound rates of return for a horizon of 5 to 10 years. Over such intermediate horizons, initial market yields and valuations tend to be useful inputs. For multi-decade forecast horizons, the impact of starting yields is diluted, so theory and long-term historical average returns (or yields) may matter more in judging expected returns.
In other words, to estimate stock returns over 30 years, a better estimate might be the 30Y TIPs + the historical equity risk premium of stocks over 30Y real bond returns.

Personally, I use an average between the two. YMMV
Interesting. When you say “average between the two” you mean the average of 1) 1/CAPE and 2) 30Y TIPs + the historical equity risk premium of stocks over 30Y real bond returns?

And that’s what you’d use for every year starting today?

Do you mind providing the equity risk premium number you use and your source?
Yes to your 1st question. For the second, you're asking the right questions haha.

For stock returns and volatility, I used yearly USA returns from Fama French from 1952-1970. And used yearly MSCI World returns from 1970 onwards. That gives me 10.2% CAGR (nominal) with yearly volatility of 17.7%.
For LT bond, I used the Simba return calculator, from 1952 to today. That's a 6.17% nominal (and includes roll yield). Something interesting happened in 1952 for LT bonds that is besides the point but it means the best measure should be from 1952 onwards.

So you could get the equity risk premium by converting stock's annualized returns to mean returns (annualized returns + volatility^2/2) and subtract bond returns. I get 5.6%.

You can then add that 5.6% to current 30Y TIPs (ideally plus an extra 0.1-0.2% to represent the roll yield for accumulators who have more than a 15 year time horizon like you and I) to get the average real return for USA stocks today. And then re-convert back to annualized returns by subtracting volatility^2.
Thanks for walking through it. That’s probably a little past me, but helpful to see how you approach it.
If it makes you feel any better, I currently get basically the same results whether I use historical or current valuations. Riveting, I know.
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Gufomel »

Steve Reading wrote: Sat Feb 27, 2021 8:58 am
Gufomel wrote: Sat Feb 27, 2021 8:42 am
Steve Reading wrote: Sat Feb 27, 2021 8:34 am
Gufomel wrote: Sat Feb 27, 2021 8:25 am
Steve Reading wrote: Sat Feb 27, 2021 8:08 am

FWIW, AQR mentions that for 5-10 year expectations, valuations are reasonable. But for longer-term, generally best to rely on intuition about risk-return. Source:
https://www.aqr.com/Insights/Research/A ... et-Classes


In other words, to estimate stock returns over 30 years, a better estimate might be the 30Y TIPs + the historical equity risk premium of stocks over 30Y real bond returns.

Personally, I use an average between the two. YMMV
Interesting. When you say “average between the two” you mean the average of 1) 1/CAPE and 2) 30Y TIPs + the historical equity risk premium of stocks over 30Y real bond returns?

And that’s what you’d use for every year starting today?

Do you mind providing the equity risk premium number you use and your source?
Yes to your 1st question. For the second, you're asking the right questions haha.

For stock returns and volatility, I used yearly USA returns from Fama French from 1952-1970. And used yearly MSCI World returns from 1970 onwards. That gives me 10.2% CAGR (nominal) with yearly volatility of 17.7%.
For LT bond, I used the Simba return calculator, from 1952 to today. That's a 6.17% nominal (and includes roll yield). Something interesting happened in 1952 for LT bonds that is besides the point but it means the best measure should be from 1952 onwards.

So you could get the equity risk premium by converting stock's annualized returns to mean returns (annualized returns + volatility^2/2) and subtract bond returns. I get 5.6%.

You can then add that 5.6% to current 30Y TIPs (ideally plus an extra 0.1-0.2% to represent the roll yield for accumulators who have more than a 15 year time horizon like you and I) to get the average real return for USA stocks today. And then re-convert back to annualized returns by subtracting volatility^2.
Thanks for walking through it. That’s probably a little past me, but helpful to see how you approach it.
If it makes you feel any better, I currently get basically the same results whether I use historical or current valuations. Riveting, I know.
Good to know. So after you “re-convert back to annualized returns by subtracting volatility^2” it comes out roughly close to the current 1/CAPE (about 2.9% real). I know we’re talking rough estimate here, so that’s fine if it’s just in the ballpark. So essentially a 3% risk premium over 30Y TIPs, which basically means terrible expected real returns for both short and long-term no matter how you slice it. If I’m in the ballpark there then that’s good enough for me.
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Re: Total portfolio allocation and withdrawal (TPAW)

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Gufomel wrote: Sat Feb 27, 2021 10:03 am
Steve Reading wrote: Sat Feb 27, 2021 8:58 am
Gufomel wrote: Sat Feb 27, 2021 8:42 am
Steve Reading wrote: Sat Feb 27, 2021 8:34 am
Gufomel wrote: Sat Feb 27, 2021 8:25 am

Interesting. When you say “average between the two” you mean the average of 1) 1/CAPE and 2) 30Y TIPs + the historical equity risk premium of stocks over 30Y real bond returns?

And that’s what you’d use for every year starting today?

Do you mind providing the equity risk premium number you use and your source?
Yes to your 1st question. For the second, you're asking the right questions haha.

For stock returns and volatility, I used yearly USA returns from Fama French from 1952-1970. And used yearly MSCI World returns from 1970 onwards. That gives me 10.2% CAGR (nominal) with yearly volatility of 17.7%.
For LT bond, I used the Simba return calculator, from 1952 to today. That's a 6.17% nominal (and includes roll yield). Something interesting happened in 1952 for LT bonds that is besides the point but it means the best measure should be from 1952 onwards.

So you could get the equity risk premium by converting stock's annualized returns to mean returns (annualized returns + volatility^2/2) and subtract bond returns. I get 5.6%.

You can then add that 5.6% to current 30Y TIPs (ideally plus an extra 0.1-0.2% to represent the roll yield for accumulators who have more than a 15 year time horizon like you and I) to get the average real return for USA stocks today. And then re-convert back to annualized returns by subtracting volatility^2.
Thanks for walking through it. That’s probably a little past me, but helpful to see how you approach it.
If it makes you feel any better, I currently get basically the same results whether I use historical or current valuations. Riveting, I know.
Good to know. So after you “re-convert back to annualized returns by subtracting volatility^2” it comes out roughly close to the current 1/CAPE (about 2.9% real). I know we’re talking rough estimate here, so that’s fine if it’s just in the ballpark. So essentially a 3% risk premium over 30Y TIPs, which basically means terrible expected real returns for both short and long-term no matter how you slice it. If I’m in the ballpark there then that’s good enough for me.
Comes out to 4.09% real for me which is roughly what I get when I use current estimates from Vanguard, AQR, and other places for a global stock portfolio.

1/CAPE is decent for USA stock but almost half of my portfolio is global and the valuations are more attractive out there so I don't use CAPE personally. If I was 100% USA stocks, I probably would.

I don't know if these are "terrible" or "great". They just are *shrugs*.
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Re: Total portfolio allocation and withdrawal (TPAW)

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Gufomel wrote: Sat Feb 27, 2021 7:19 am I use 1/CAPE for expected stock returns, but I’ve wondered if it really makes sense to use that as the projection for a lifetime, especially for an early accumulator. Would it make sense to only use that for, let’s say, 10 years but then have it revert toward the historical mean going forward? Probably the same for bonds, but it’s not as clear to me what mean it should revert toward.

I know there’s a lot of argument whether 1/CAPE is even appropriate to begin with. I’m not wanting to get into that. But assuming 1/CAPE is appropriate as the expectation for the next 10 years, is it appropriate to use for decades into the future? Based on where 1/CAPE is relative to historical averages, it’s definitely the more conservative approach. I’m just not sure if too conservative.
The 1/CAPE assumption is assuming no mean reversion in valuations. So it's saying that valuations are equally likely to go up or down from where we are now.

If you want to assume mean reversion in valuation, the story gets more complicated. Since we are in a period of high valuations, reverting to the lower historical valuations will involve a crash (if it happens fast) or a long period of abnormally low returns (if it happens slowly). That would be the price we would have to pay to get to the lower valuations. So assuming 1/CAPE for the short term, and then higher returns based on lower valuations, without including the "price" of abnormally low returns during the transition, seems too optimistic.

Note also that the optimal strategy can change in response to mean reversion in valuations. If a correction in valuation is expected, then it may make sense to avoid stocks until the correction is over because returns are expected to be abnormally low in the near future. So it calls for market timing based on valuation levels.

The 1/CAPE assumption assumes no mean reversion, and that makes everything simple. Even if it's not exactly right, because your re-run the spreadsheet every year and update the return assumptions, you will be slowly correcting the assumption over time as the valuation changes unfold. That minimizes the impact of the error in expected return. TPAW (and ABW strategies in general) are very good at adjusting and correcting, so the impact of a bad assumption early on is mitigated. If expected return is always 1% lower than actual return, then withdrawals will grow at a rate 1% faster than expected. That compounds to 22% extra for withdrawals 20 years in the future, 49% extra for withdrawals 40 years in the future, and 82% extra for withdrawals 60 years away. Correcting expected return along the way should about halve the impact.
Gufomel wrote: Sat Feb 27, 2021 7:19 am I will say that using 1/CAPE in conjunction with a lifecycle investing model like this TPAW spreadsheet really helps put your current savings portfolio in perspective with your lifetime wealth and projected retirement withdrawal. Stocks fell this week, but my projected retirement withdrawal went up fairly significantly because of the increase in 1/CAPE. This really helps an accumulator conceptualize how a decline in stocks can be a good thing and help you not spooked by market crashes when taking into account your entire lifetime projection.
Yes, using 1/CAPE in TPAW rightfully moves the attention from stock market price fluctuations to the expected impact on retirement withdrawals, which is ultimately what we care about. Early in life, a reduction in valuations is more than worth the price of a crash. That's because the higher expected return acting over a long time horizon will more than make up for the loss in portfolio value. Later in life, you'd prefer high valuations over high expected returns because the time horizon remaining is too short to make up for the loss. Young people will benefit a stock market crash stemming from a valuation correction. Just like they would benefit from higher bond rates.

Ideally you'd have low valuations early and high valuations later. This has been the experience of the current generation of retirees. But this was very good luck. Using raw historical returns for the expected return estimate is assuming that the next generation will be as lucky, and that IMO is a very optimistic assumption.
Gufomel wrote: Sat Feb 27, 2021 7:19 am Edit: I guess the assumption is that in order for 1/CAPE to rise (even after 10 years), stocks would have had to return less than expected in the first 10 years, so it all balances out. Therefore 1/CAPE would be used for the whole lifetime projection. If that’s how it’s best to think about it, then I think that makes sense.
That's right. It won't exactly balance out, but those are the opposing forces at work.
Gufomel wrote: Sat Feb 27, 2021 7:19 am Edit2: Ok after thinking about it more, I bet the reason I saw my retirement withdrawal increase when stocks fell & 1/CAPE rose is because my actual current savings portfolio is more conservative than what the spreadsheet says I should be. If I was leveraged according to what the spreadsheet says I should be, my portfolio would have declined enough to offset the rise in future expectations.
Not quite. A fixed allocation on the total portfolio means that risk is spread evenly and so an exceptionally high or low return in one year has the same impact as a it would in any other year. So it doesn't matter if good fortune in the form of good returns comes early or late. But a change in valuations affect all future returns, not just the current return. So you'd still want a reduction in valuation to happen early (because there's more years left), and an increase in valuation to happen late.
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Re: Total portfolio allocation and withdrawal (TPAW)

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Thanks for the response above.

As far as a mortgage, in the future savings column I have income minus non-mortgage expenses, then in the essential expenses column I have my remaining mortgage payments for each year (discounted by inflation). So I think I’m handling the mortgage correctly. Let me know if I’m off on that.

But another thread got me thinking, if we’re accounting for a mortgage in the calculation, should house value also be accounted for and if so how would you do it on the accumulator spreadsheet? I have a harder time wrapping my head around counting imputed rent for a house than I do treating a mortgage as a negative bond.

My goal is to have a paid for house by retirement, and continue to own a house through retirement. So I can understand how paying down my mortgage factors into my retirement plan, but I have a hard time conceptualizing how my house value is factored in (if it should be at all). Basically I’m just expecting to need a lower withdrawal in retirement than I would if I was renting. Technically I could sell the house and invest the proceeds, and then have higher withdrawal to pay the higher monthly expenses in retirement. But I feel like that’s essentially a wash so should just be ignored for all practical purposes.

Am I correct to account for the mortgage but not the house value? Or if house value should be counted, any thoughts on how to do it in the spreadsheet and why?

Edit: sorry, I realized my previous questions about the mortgage were in Steve’s thread about Lifecycle Investing https://www.bogleheads.org/forum/viewt ... start=1250. But I’ll go ahead and leave my new question regarding house value here since it does relate to your spreadsheet.
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Re: Total portfolio allocation and withdrawal (TPAW)

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Gufomel wrote: Sat Feb 27, 2021 1:52 pm As far as a mortgage, in the future savings column I have income minus non-mortgage expenses, then in the essential expenses column I have my remaining mortgage payments for each year (discounted by inflation). So I think I’m handling the mortgage correctly. Let me know if I’m off on that.
Yes, this is a good way to enter it. Another way would be to subtract the mortgage from the savings and enter the reduced savings in the future savings column. Both are equivalent, and will lead to the same $ in the risk portfolio. Whichever seems more intuitive/clearer is fine. I think your way of doing it (entering into the essential income column) maybe cleaner, because the payments can just be continued into retirement if need be. Otherwise it's in savings column as a negative entry before retirement and in the essential expense column as a positive entry after retirement. Keeping it in one column seems cleaner.
Gufomel wrote: Sat Feb 27, 2021 1:52 pm But another thread got me thinking, if we’re accounting for a mortgage in the calculation, should house value also be accounted for and if so how would you do it on the accumulator spreadsheet? I have a harder time wrapping my head around counting imputed rent for a house than I do treating a mortgage as a negative bond.

My goal is to have a paid for house by retirement, and continue to own a house through retirement. So I can understand how paying down my mortgage factors into my retirement plan, but I have a hard time conceptualizing how my house value is factored in (if it should be at all). Basically I’m just expecting to need a lower withdrawal in retirement than I would if I was renting. Technically I could sell the house and invest the proceeds, and then have higher withdrawal to pay the higher monthly expenses in retirement. But I feel like that’s essentially a wash so should just be ignored for all practical purposes.

Am I correct to account for the mortgage but not the house value? Or if house value should be counted, any thoughts on how to do it in the spreadsheet and why?
Yes, all of this is correct. The ownership of the house shows up as higher essential expenses or lower savings during the mortgage payment years, and then lower expenses in retirement years because you don't have to cover rent. This lower expense is not explicitly seen in the spreadsheet. You just know that your withdrawals won't have to cover rent because you own the house.

You could compare this against renting. This would mean higher savings earlier, but higher rental expenses during retirement, and no house at the end of life.

If you don't plan to downsize or otherwise withdraw funds from the house, you don't have to explicitly enter the value of the house in the spreadsheet. But if you are planning to withdraw funds from the house, that can go into the future income column.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Gufomel »

Ben Mathew wrote: Sat Feb 27, 2021 4:07 pm
Gufomel wrote: Sat Feb 27, 2021 1:52 pm As far as a mortgage, in the future savings column I have income minus non-mortgage expenses, then in the essential expenses column I have my remaining mortgage payments for each year (discounted by inflation). So I think I’m handling the mortgage correctly. Let me know if I’m off on that.
Yes, this is a good way to enter it. Another way would be to subtract the mortgage from the savings and enter the reduced savings in the future savings column. Both are equivalent, and will lead to the same $ in the risk portfolio. Whichever seems more intuitive/clearer is fine. I think your way of doing it (entering into the essential income column) maybe cleaner, because the payments can just be continued into retirement if need be. Otherwise it's in savings column as a negative entry before retirement and in the essential expense column as a positive entry after retirement. Keeping it in one column seems cleaner.
Gufomel wrote: Sat Feb 27, 2021 1:52 pm But another thread got me thinking, if we’re accounting for a mortgage in the calculation, should house value also be accounted for and if so how would you do it on the accumulator spreadsheet? I have a harder time wrapping my head around counting imputed rent for a house than I do treating a mortgage as a negative bond.

My goal is to have a paid for house by retirement, and continue to own a house through retirement. So I can understand how paying down my mortgage factors into my retirement plan, but I have a hard time conceptualizing how my house value is factored in (if it should be at all). Basically I’m just expecting to need a lower withdrawal in retirement than I would if I was renting. Technically I could sell the house and invest the proceeds, and then have higher withdrawal to pay the higher monthly expenses in retirement. But I feel like that’s essentially a wash so should just be ignored for all practical purposes.

Am I correct to account for the mortgage but not the house value? Or if house value should be counted, any thoughts on how to do it in the spreadsheet and why?
Yes, all of this is correct. The ownership of the house shows up as higher essential expenses or lower savings during the mortgage payment years, and then lower expenses in retirement years because you don't have to cover rent. This lower expense is not explicitly seen in the spreadsheet. You just know that your withdrawals won't have to cover rent because you own the house.

You could compare this against renting. This would mean higher savings earlier, but higher rental expenses during retirement, and no house at the end of life.

If you don't plan to downsize or otherwise withdraw funds from the house, you don't have to explicitly enter the value of the house in the spreadsheet. But if you are planning to withdraw funds from the house, that can go into the future income column.
Ok good! Yes I settled on handling the mortgage that way because it made it clearer to me, especially since in my case I’m assuming income and non-mortgage expenses are already in real dollars but the mortgage needs to be discounted by inflation. It helped to see it separated in its own column. And as you said it makes it cleaner if you want to take the mortgage into retirement.

Glad I was on the right track for the house value. The thing I’m still chewing on is that in my situation I do expect to have a house value at the end of life, and it seems like that should ideally be factored in some how. If I reach 80 years old and need extra money for monthly expenses, I could sell the house (or I may decide at 80 to sell anyways). I don’t have that advantage if I’ve rented up to that point. So it seems like the house should be factored in. But if I go throw several hundred thousand $ in the income column at 80 years old, it really throws off the stocks/bonds % in the savings portfolio trajectory.

I guess it’s best to just mentally note that owning a house does have value and could potentially be tapped, but in general I’m operating under the assumption that I’ll die with a house and all my savings, withdrawals, AA operate under that assumption. There’s no cash flow (other than requiring lower withdrawals in retirement) so there’s nothing that can be entered in the spreadsheet. Unless, as you said, I’m explicitly intending to downsize at a certain point in time then I could factor that in.
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Re: Total portfolio allocation and withdrawal (TPAW)

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Gufomel wrote: Sun Feb 28, 2021 7:13 am Glad I was on the right track for the house value. The thing I’m still chewing on is that in my situation I do expect to have a house value at the end of life, and it seems like that should ideally be factored in some how. If I reach 80 years old and need extra money for monthly expenses, I could sell the house (or I may decide at 80 to sell anyways). I don’t have that advantage if I’ve rented up to that point. So it seems like the house should be factored in. But if I go throw several hundred thousand $ in the income column at 80 years old, it really throws off the stocks/bonds % in the savings portfolio trajectory.

I guess it’s best to just mentally note that owning a house does have value and could potentially be tapped, but in general I’m operating under the assumption that I’ll die with a house and all my savings, withdrawals, AA operate under that assumption. There’s no cash flow (other than requiring lower withdrawals in retirement) so there’s nothing that can be entered in the spreadsheet. Unless, as you said, I’m explicitly intending to downsize at a certain point in time then I could factor that in.
Yes, that's our situation and how I handle it as well. The knowledge that you own the house will automatically make you more tolerant of risk in the portfolio, so it will show up in the asset allocation indirectly. You know your housing is prepaid, plus there is the equity that you can tap into if needed for an emergency. That will indirectly impact the choices you make with your portfolio and withdrawal planning.
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Re: Total portfolio allocation and withdrawal (TPAW)

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Ben Mathew wrote: Sun Feb 28, 2021 9:24 am
Gufomel wrote: Sun Feb 28, 2021 7:13 am Glad I was on the right track for the house value. The thing I’m still chewing on is that in my situation I do expect to have a house value at the end of life, and it seems like that should ideally be factored in some how. If I reach 80 years old and need extra money for monthly expenses, I could sell the house (or I may decide at 80 to sell anyways). I don’t have that advantage if I’ve rented up to that point. So it seems like the house should be factored in. But if I go throw several hundred thousand $ in the income column at 80 years old, it really throws off the stocks/bonds % in the savings portfolio trajectory.

I guess it’s best to just mentally note that owning a house does have value and could potentially be tapped, but in general I’m operating under the assumption that I’ll die with a house and all my savings, withdrawals, AA operate under that assumption. There’s no cash flow (other than requiring lower withdrawals in retirement) so there’s nothing that can be entered in the spreadsheet. Unless, as you said, I’m explicitly intending to downsize at a certain point in time then I could factor that in.
Yes, that's our situation and how I handle it as well. The knowledge that you own the house will automatically make you more tolerant of risk in the portfolio, so it will show up in the asset allocation indirectly. You know your housing is prepaid, plus there is the equity that you can tap into if needed for an emergency. That will indirectly impact the choices you make with your portfolio and withdrawal planning.
If you really want or need a number, you might be able to guestimate by using current HECM rates. However, at some point, you have to accept that you are still projecting numbers way out in the future, and that there is going to be a degree of unavailable precision.
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Re: Total portfolio allocation and withdrawal (TPAW)

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Ben Mathew wrote: Fri Feb 26, 2021 11:25 pm
Steve Reading wrote: Fri Feb 26, 2021 1:42 pm perhaps put dollars signs on the second term (I13)
Thanks. I'll fix that.
Steve Reading wrote: Fri Feb 26, 2021 1:42 pm Also, FWIW, here's some things that would be cool if the sheet had. I'm not asking you to do it (you've already done so much, like others, I'm amazed with it and already using it along with my personal one), but if you're ever like "hey I want to add things to it, what would be cool to add?" here's my humble recommendation:
Great, I'm looking for feedback and suggestions.
Steve Reading wrote: Fri Feb 26, 2021 1:42 pm 1) A way to change the nature of future savings contributions as somewhere between stocks and bonds? Currently it assumes it is purely bonds which will produce more aggressive AAs. FWIW, I use a 5-10% correlation to future employment savings with stocks (but not for SS).
Yes, the spreadsheet is assuming that the future savings is safe and using the safe bond rate to discount. So this would have to be a very conservative estimate. For example, if $15,000 per year is the expected savings, maybe $10,000 per year or something like that may be a safe estimate. That way, the allocation doesn't get too aggressive.

To explicitly model savings risk, one option would be to rerun the spreadsheet with low, medium, and high estimates of future savings, and see if the withdrawal distribution is acceptable across all three scenarios. You could have three separate tabs for the low, medium and high estimates and aggregate them in a summary tab. You can also introduce correlations through different weighting schemes: high correlation means more weight on the high savings+high return and low savings + low return outcomes. This may be a bit cumbersome, but I think this may be easier to actually understand and interpret than a more elegant/formal model that assumes that savings is a random walk and so on.
Steve Reading wrote: Fri Feb 26, 2021 1:42 pm 2) I would find it super, super, super cool if there was a way to change g() such that each year's withdrawal did have the same certainty equivalent as Uncorrelated mentioned. I already picked a g() I liked (0.5% seemed about right) but I just think it'd be so neat if the spreadsheet calculated what utility theory would say is optimal for me.
The expected utility calculation involves integrating u(x)*p(x) where u() is the CRRA utility function and p() is the lognormal distribution. Excel can't do that integration. We would need an explicit solution. I googled a bit and found this. See equation (1) on page 6. I wonder if that's the formula we would need. If so, then calculating utility given risk and time preferences is straightforward. You could adjust AA and g and see what the utility for each year and total utility would be for different combinations. Wouldn't maximize it for you, but you can at least see the utility impact.
Steve Reading wrote: Fri Feb 26, 2021 1:42 pm Also, why recommend 20Y TIPs seems a strange recommendation for the accumulating spreadsheet. Shouldn't it be 30Y TIPs? Using the 20Y will make the portfolio a little more aggressive as the rate is lower.
The 20 year suggestion was just a carryover from the withdrawal spreadsheet. You're right that 30 year would be better for most accumulators. I'll update that in the next round.
Steve Reading wrote: Fri Feb 26, 2021 1:42 pm Also, "portfoliio" has a typo on G53 of 3. Planner. And "savingns" has a typo on B19.
Thanks. Fixed. Will go through in the next update.
Been thinking about the comments above regarding using 20 vs 30 year rates. Wouldn’t using the 30 year rate actually be more aggressive in totality for accumulators? Yes, it discounts future savings more, but it also applies that rate to a lifetime of bond investments. I’m thinking the latter probably outweighs the former in most cases?

I guess ideally after retirement you would want the spreadsheet to be able to decrease the duration (and ultimately rate) of your bonds according the remaining investment horizon. But in lieu of that, which I’m sure would be complicated if even possible, picking a single duration that makes the most sense seems good enough. But I’m thinking maybe 20 year makes more sense than 30 year?
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Re: Total portfolio allocation and withdrawal (TPAW)

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Gufomel wrote: Tue Mar 02, 2021 7:27 am Been thinking about the comments above regarding using 20 vs 30 year rates. Wouldn’t using the 30 year rate actually be more aggressive in totality for accumulators? Yes, it discounts future savings more, but it also applies that rate to a lifetime of bond investments. I’m thinking the latter probably outweighs the former in most cases?

I guess ideally after retirement you would want the spreadsheet to be able to decrease the duration (and ultimately rate) of your bonds according the remaining investment horizon. But in lieu of that, which I’m sure would be complicated if even possible, picking a single duration that makes the most sense seems good enough. But I’m thinking maybe 20 year makes more sense than 30 year?
It comes down to matching bond duration with the investment horizon. This removes interest rate risk, which is uncompensated.

If you take a 40 year old in the accumulation phase, they would have a bond investment horizon ranging from 25 years for the bonds that will be consumed at age 65 to 60 years for the bonds that will be consumed at age 100. Averaging those gives us a duration of about 42.5 years. (Simple averaging horizons like this is not exactly right for a couple reasons, but let's call it close enough for this exercise.)

A 65 year old in the withdrawal phase will have an investment horizon ranging from 1 year for bonds to be consumed at age 66 to 35 years for bonds to be consumed at age 100. Averaging that comes to a duration of 18 years.

So that was the thought process behind 20 years for withdrawal and 30 years for accumulation. Though it looks like 20 years may be too long for the average person in the withdrawal phase. We could of course calculate it more carefully and create a table of target bond duration by year. So a 40 year old would use 30 year TIPS, a 65 year old would use 18 year TIPS, and a 75 year old would use 13 years TIPS, and so on (or the closest maturities available.)
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Re: Total portfolio allocation and withdrawal (TPAW)

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Ben Mathew wrote: Tue Mar 02, 2021 9:08 pm
Gufomel wrote: Tue Mar 02, 2021 7:27 am Been thinking about the comments above regarding using 20 vs 30 year rates. Wouldn’t using the 30 year rate actually be more aggressive in totality for accumulators? Yes, it discounts future savings more, but it also applies that rate to a lifetime of bond investments. I’m thinking the latter probably outweighs the former in most cases?

I guess ideally after retirement you would want the spreadsheet to be able to decrease the duration (and ultimately rate) of your bonds according the remaining investment horizon. But in lieu of that, which I’m sure would be complicated if even possible, picking a single duration that makes the most sense seems good enough. But I’m thinking maybe 20 year makes more sense than 30 year?
It comes down to matching bond duration with the investment horizon. This removes interest rate risk, which is uncompensated.

If you take a 40 year old in the accumulation phase, they would have a bond investment horizon ranging from 25 years for the bonds that will be consumed at age 65 to 60 years for the bonds that will be consumed at age 100. Averaging those gives us a duration of about 42.5 years. (Simple averaging horizons like this is not exactly right for a couple reasons, but let's call it close enough for this exercise.)

A 65 year old in the withdrawal phase will have an investment horizon ranging from 1 year for bonds to be consumed at age 66 to 35 years for bonds to be consumed at age 100. Averaging that comes to a duration of 18 years.

So that was the thought process behind 20 years for withdrawal and 30 years for accumulation. Though it looks like 20 years may be too long for the average person in the withdrawal phase. We could of course calculate it more carefully and create a table of target bond duration by year. So a 40 year old would use 30 year TIPS, a 65 year old would use 18 year TIPS, and a 75 year old would use 13 years TIPS, and so on (or the closest maturities available.)
Kind of interesting that this would entail a slight equity glide rise as retirement years go by since the lower the bond duration used, generally the lower the yield and the more attractive equities will appear in turn.
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Re: Total portfolio allocation and withdrawal (TPAW)

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Gufomel wrote: Tue Mar 02, 2021 7:27 am I guess ideally after retirement you would want the spreadsheet to be able to decrease the duration (and ultimately rate) of your bonds according the remaining investment horizon. But in lieu of that, which I’m sure would be complicated if even possible
It's not actually that complicated; my personal retirement spreadsheet does this. The US Treasury publishes real TIPS yields daily at

http://www.treasury.gov/resource-center ... _yield.xml

In includes 30, 20, 10, 7, 5 year TIPS, which is enough to make a "good enough" yield curve for retirement purposes. Especially in this age of pretty flat yield curves.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Ben Mathew »

Steve Reading wrote: Tue Mar 02, 2021 9:49 pm
Ben Mathew wrote: Tue Mar 02, 2021 9:08 pm
Gufomel wrote: Tue Mar 02, 2021 7:27 am Been thinking about the comments above regarding using 20 vs 30 year rates. Wouldn’t using the 30 year rate actually be more aggressive in totality for accumulators? Yes, it discounts future savings more, but it also applies that rate to a lifetime of bond investments. I’m thinking the latter probably outweighs the former in most cases?

I guess ideally after retirement you would want the spreadsheet to be able to decrease the duration (and ultimately rate) of your bonds according the remaining investment horizon. But in lieu of that, which I’m sure would be complicated if even possible, picking a single duration that makes the most sense seems good enough. But I’m thinking maybe 20 year makes more sense than 30 year?
It comes down to matching bond duration with the investment horizon. This removes interest rate risk, which is uncompensated.

If you take a 40 year old in the accumulation phase, they would have a bond investment horizon ranging from 25 years for the bonds that will be consumed at age 65 to 60 years for the bonds that will be consumed at age 100. Averaging those gives us a duration of about 42.5 years. (Simple averaging horizons like this is not exactly right for a couple reasons, but let's call it close enough for this exercise.)

A 65 year old in the withdrawal phase will have an investment horizon ranging from 1 year for bonds to be consumed at age 66 to 35 years for bonds to be consumed at age 100. Averaging that comes to a duration of 18 years.

So that was the thought process behind 20 years for withdrawal and 30 years for accumulation. Though it looks like 20 years may be too long for the average person in the withdrawal phase. We could of course calculate it more carefully and create a table of target bond duration by year. So a 40 year old would use 30 year TIPS, a 65 year old would use 18 year TIPS, and a 75 year old would use 13 years TIPS, and so on (or the closest maturities available.)
Kind of interesting that this would entail a slight equity glide rise as retirement years go by since the lower the bond duration used, generally the lower the yield and the more attractive equities will appear in turn.
Yes, that's interesting. Haven't thought about it much so far. The other option would be to take a longer term bond for the higher interest rate and accept the interest rate risk. Wonder whether taking on higher interest rate risk or higher stock risk provides a better risk/return opportunity for retirees?
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Re: Total portfolio allocation and withdrawal (TPAW)

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AlohaJoe wrote: Tue Mar 02, 2021 10:38 pm
Gufomel wrote: Tue Mar 02, 2021 7:27 am I guess ideally after retirement you would want the spreadsheet to be able to decrease the duration (and ultimately rate) of your bonds according the remaining investment horizon. But in lieu of that, which I’m sure would be complicated if even possible
It's not actually that complicated; my personal retirement spreadsheet does this. The US Treasury publishes real TIPS yields daily at

http://www.treasury.gov/resource-center ... _yield.xml

In includes 30, 20, 10, 7, 5 year TIPS, which is enough to make a "good enough" yield curve for retirement purposes. Especially in this age of pretty flat yield curves.
I think this might be something to add to the TPAW calculator eventually. Calculating bond duration weighted by present value I don't think will be too hard.
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Re: Total portfolio allocation and withdrawal (TPAW)

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I have added a new spreadsheet called "simulator" to the TPAW wiki that can be used for simulations. It calculates TPAW allocation and withdrawals given stock and bond returns. It can be used for backtesting the TPAW strategy using historical returns, or for forward looking analyses using simulated returns. Users can use the results of the backtests and simulations to adjust their asset allocation and withdrawal plan till they find their preferred strategy.

The simulation assumes no borrowing. If the unconstrained TPAW strategy calls for borrowing to invest (i.e. AA >100% stocks, likely in early career), the simulation uses an AA of 100% stocks instead. And if the unconstrained TPAW strategy calls for borrowing to consume (a possibility in early retirement before pensions begin), the simulation only withdraws whatever is available in the savings portfolio.

The spreadsheet is located in the TPAW wiki under Simulator.

EXAMPLE

Let's do a simulation using the "simulator" spreadsheet for an investor who began with $30,000 in savings at age 25 (year 1946), saved $10,000 per year during working years, retired at age 55 (year 1976), collected $20,000 per year in social security starting age 70, and just reached reached age 100 this year (year 2021).

Historical real returns during the period averaged 8.6% for stocks (S&P 500) and 2% for risky bonds (10 year T bonds). Safe bonds assumed to be 1.9%.

Suppose our investor guessed long term returns correctly and entered 8.6% for stocks and 2% for risky bonds. AA set to 30/10/60 on stocks/risky bonds/safe bonds.

Image

TPAW withdrawals for this investor would be the middle line in red in the graph above:
  • Starting withdrawal would have been $54,819 at age 55 (year 1976)
  • Lowest withdrawal would have been $46,755 at age 61 (year 1982)
  • Highest withdrawal would have been $70,349 at age 79 (year 2000)
  • Withdrawal during the recent financial crisis would have been $50,981 at age 88 (year 2009)
  • Final withdrawal would have been $60,187 at age 100 (year 2021)
If stock returns had been 2% lower (averaging 6.6% instead of 8.6%), withdrawals would be the lower line in gray:
  • Starting withdrawal would have been $46,814 at age 55 (year 1976)
  • Lowest withdrawal would have been $36,081 at age 88 during the recent financial crisis (year 2009)
  • Highest withdrawal would have been $52,167 at age 79 (year 2000)
  • Final withdrawal would have been $39,811 at age 100 (year 2021)
If stock returns had been 2% higher (averaging 10.6% instead of 8.6%), withdrawals would be the higher line in yellow:
  • Starting withdrawal would have been $64,522 at age 55 (year 1976)
  • Lowest withdrawal would have been $56,926 at age 61 (year 1982)
  • Highest withdrawal would have been $95,526 at age 79 (year 2000)
  • Withdrawal during the recent financial crisis would have been $72,648 at age 88 (year 2009)
  • Final withdrawal would have been $92,213 at age 100 (year 2021)
Spreadsheet with these simulations: Excel or Google Sheets
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Re: Total portfolio allocation and withdrawal (TPAW)

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HISTORICAL SIMULATIONS 1881-2021

I ran historical simulations showing how TPAW would have done from 1881-2021.

PDF describing the results:
- TPAW Simulation Results

Supporting Excel spreadsheets
- Results Summary
- Return Data
- Example simulation A (1941-2016)
- Example simulation B (1941-2016)

All dollars and rates are real (i.e. inflation adjusted.)

Data: I use Shiller's data, which gives S&P500 returns for stocks and 10 year US Treasury returns for bonds. More details on the data in this post.

Lifecycle: I simulate a person who starts working at age 25, retires early at age 55, and lives till age 100. This person saves $25,000 per year during their working years (ages 25 to 54) and gets social security of $30,000 per year starting age 70.

Asset allocation: A 35/65 fixed asset allocation is maintained on the total portfolio. While a 35/65 allocation may be considered conservative for a savings portfolio, it is not conservative for a total portfolio because the present value of future savings and social security is being counted in the 65% for bonds. The allocation on the savings portfolio is not fixed, but the pattern that emerges from the simulations is 100% stocks till about the mid-thirties, gliding down to about 50/50 by start of retirement (age 55) and holding roughly steady afterwards. A glidepath like this would usually be considered “moderate” rather than “conservative.”

Withdrawals: Withdrawals are calculated by amortizing the portfolio over the remaining retirement years. The portfolio is fully depleted by age 100. Withdrawals are recalculated each year, so they continually adjust to portfolio performance and changes in expected returns. If the markets do well or expected returns increase, withdrawal increases. If the markets do poorly or expected returns decrease, withdrawal decreases. Because withdrawals adjust, the portfolio never fails—meaning it never runs out of money. The consequence of poor portfolio performance is not failure but lower withdrawals. So rather than calculating failure rates as is often done in retirement studies, we would be looking at how low withdrawals got during bad times.

To put the simulation results in context, note that if the person knew for sure that stock and bond returns would be 0% every year, their retirement income would be a constant $36,522 per year. If instead they knew for sure that returns would be 7.0% for stocks and 2.7% for bonds every year (the averages in our data), retirement income would be a constant $110,097 per year. So we should expect average withdrawals across all of our simulations to be around $110,097 per year. The question for our simulations is how much lower did it get in the bad years?

Results of Simulation A: Fixed Expected Return

In this round of simulations, I assume the person has the same expected return every year: the average return for the whole period, 1871-2021, which is 7.0% for stocks and 2.7% for bonds. So expectations don’t change from year to year based on stock or bond valuations.

Individual simulations are shown in the attached graphs at the end of the pdf file. Following is an example which shows the results for period 1941-2016.

Image

This person started working at age 25 (1941). At that time, they expected to withdraw $110,097 in retirement based on their projections. The grey line shows how the projection evolved over the course of their working years. The orange line shows the actual income during retirement. Income in the first year of retirement at age 55 was $121,231. The lowest income was $70,629 at age 66. This was in 1982 after the bond crash of 1977-'81. Highest income was $144,725 at age 83 which came during the tech bubble in 1999. Income in the last year of retirement (age 100) was $122,148 in 2016.

The results of the simulations are summarized in Table 1.

Image

I start the first simulation in 1881. This is because in the next round of simulations (simulation B) I use CAPE valuations which look back ten years for earnings and so starts only in 1881.

In the first simulation, the individual starts working in 1881 (age 25), retires in 1911 (age 55), and lives till 1956 (age 100). I move this window forward 10 years for each new simulation. This gives me seven completed simulations and four ongoing ones, for a total of eleven simulations. The summary statistics described below is for the completed simulations only.

The average retirement income for the seven completed simulations was $103,141.

The lowest income was $60,394 at age 65 for the 1881-1956 simulation. This occurred in 1921, after the 1916-’20 WW1 crash.

The highest income was $144,725 at age 83 for the 1941-2016 simulation. This occurred in 1999, at the peak of the tech boom.

Withdrawal rates from the savings portfolio at the start of retirement (age 55) ranged from 5.6% to 7.1%. The average was 6.0%.

Relative to starting retirement income, the lowest income year was 49% of starting retirement income. The highest income year was 199% of starting retirement income.

Results of Simulation B: Update Expected Return

For this round of simulations, I update the expected return every year based on CAPE (for stocks) and estimated real yield (for bonds). Bond real yields are estimated as the stated nominal yield minus expected inflation, which in turn is estimated by regressing future ten years’ inflation on past ten years’ inflation. The expected return is obtained by regressing future thirty years’ return on CAPE (for stocks) and on estimated real yield (for bonds).

Individual simulations are shown in the attached graphs at the end. The results are summarized in Table 2.

Image

The average retirement income for the seven completed simulations was $120,542.

The lowest income was $71,252 at age 65 for the 1881-1956 simulation. This occurred in 1921, after the 1916-’20 World War I crash.

The highest retirement income was $175,331 at age 80 for the 1911-1986 simulation. This occurred in 1966, at the end of a long bull run for stocks from 1948-’66.

Withdrawal rates from the savings portfolio at the start of retirement (age 55) ranged from 4.7% to 8.0%. The average was 5.5%.

Relative to starting retirement income, the lowest income year was 68% of starting retirement income and the highest income year was 210% of starting retirement income.

What if we systematically overestimate or underestimate expected returns?

These simulations use expected returns that are not too wrong because they are derived from the historical returns over the period being simulated. The individual is not systematically overestimating or underestimating the returns that they will get over the long term. The consequence of overestimating returns by 1% each year would be retirement income that starts too high and declines by 1% per year. The consequence of underestimating returns by 1% each year would be retirement income that starts too low and rises by 1% per year.

Duration matching and inflation indexing bonds

These simulations use nominal bonds that are not duration matched. So bond returns in the simulations are subject to inflation risk, interest rate risk, and reinvestment risk. It may be possible to stabilize retirement income further by using inflation indexed bonds (like TIPS) and duration matching.
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Re: Total portfolio allocation and withdrawal (TPAW)

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HOW RETIREMENT INCOME RESPONDS TO A POOR SEQUENCE OF RETURNS (TEMPORARY CRASH)

This post examines how retirement income responds to a market decline, based on the simulations described in the previous post.

The table below shows how income responded to the oil crisis from 1973-'74. Over two years, stocks declined 46%, bonds declined 12%, and a 35/65 portfolio declined 25%.

Image

The table shows that regardless of when the oil crisis happened--eight years prior to retirement, right around retirement, or twelve years after retirement--the reduction in income remained roughly the same at about 26-28%. (Income prior to retirement refers to projected income.)

To examine why the income response remains the same regardless of the timing of the crash, let's run a simulation where we make expected returns and realized returns a constant equal to the average return for the period, which is 7.0% for stocks and 2.7% for bonds. Projected and actual income then becomes constant at $110,097 as shown in the figure below.

Image

Crash at Age 50 (Before Retirement)

Now, let’s introduce a stock market crash of 50% followed by a full recovery 3 years later. The recovery return will need to be 100% to make stocks whole again because (1-.50) (1+1)=1. Also, this drop and recovery are on top of the regular expected return of 7%. So total return in the drop year works out to (1+.07)(1-.50)=-47%. The total return in the recovery year works out to (1+.07)(1+1)=114%.

So realized stock returns are going to be
{ …7% ,7%, 7%, -47% (drop year), 7%, 7%, 114% (recovery year), 7%, 7%, 7%,… }

Bond returns are constant at 2.7% per year.

With this sequence of returns, a 100% stock portfolio will temporarily decline to 53% of the no-crash trajectory and then catch back up fully to 100% in the recovery year. A 35/65 portfolio will temporarily decline to 82% of the no-crash trajectory at the drop. But with the recovery it will bounce back higher to 112% of the no-crash trajectory. The extra 12% is from the rebalancing bonus that accrued during the crash.

If we insert this crash at age 50, we get the following retirement income:

Image

Mirroring a 35/65 portfolio, projected income drops to 82%, or $90,315 at the drop. With the recovery, it bounces back to 112%, or $122,770 because of the rebalancing bonus, just like the 35/65 portfolio. Since the recovery happened before withdrawals had begun, actual retirement income is not hurt. It is in fact helped because of the rebalancing bonus.

Crash at Age 55 (Just After Retirement)

Let us now insert the crash at age 55, just after retirement starts:

Image

Retirement income decreases to $90,315 or 82% of pre-crash income, mirroring the performance of a 35/65 portfolio. With the recovery, income bounces back higher to $122,770, or 112% of no-crash income because of the rebalancing bonus. Since the crash happened after withdrawals had begun, actual retirement income is reduced during the crash. But there is no long term damage. In fact, long term retirement income is permanently raised by the rebalancing bonus.

Crash at Age 85 (Late Retirement)

Let us now insert the crash at age 85, towards the end of retirement:

Image

The story remains the same: Income drops to $90,315 (82%) and then recovers back to $122,770 (112%), mirroring the performance of a 35/65 portfolio.

Conclusion

There is concern that a market crash right around retirement can permanently damage a retirement because portfolios are at their peak value and very sensitive to returns (sequence of return risk). TPAW manages this risk by maintaining a fixed asset allocation on the total portfolio and employing amortization based withdrawals. This results in a strategy that is well diversified across time, making the outcome less sensitive to the timing of returns. The above examples show that a crash and subsequent recovery would have no harmful effect on retirement even if it occurred just prior to retirement when the savings portfolio is at its peak. During retirement, no matter when the crash occurs, the loss would be limited to reduced income during the depressed years. The income will recover fully if and when the market recovers. There would be no permanent damage to the portfolio that persists after the market has recovered.
Last edited by Ben Mathew on Thu Jun 10, 2021 8:22 pm, edited 4 times in total.
Total Portfolio Allocation and Withdrawal (TPAW)
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Re: Total portfolio allocation and withdrawal (TPAW)

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WHY RETIREMENT INCOME RECOVERS FULLY AFTER A POOR SEQUENCE OF RETURNS (TEMPORARY CRASH)

The previous post showed that the concern that a poor sequence of returns at the start of retirement will permanently damage the retirement does not apply to TPAW. TPAW generates only a temporary reduction in income during the depressed years and will fully recover with the market. Retirement income tracks the performance of a 35/65 portfolio and will recover with it.

To see why it works this way in TPAW, it's helpful to look at it from the bucket point of view. The bucket view was described in more detail in this post, but total portfolio + amortizated withdrawals is equivalent to separating the funds for each age into different age buckets and applying a fixed asset allocation on each bucket. So the funds that are earmarked for age 55 is in bucket 55, the funds for age 56 is in bucket 56, and so on. The same fixed asset allocation is applied to each bucket--35/65 in our example. So a poor sequence of returns between ages 55 and 58 affects only income between ages 55 and 58. Age 59 is not impacted because the 35/65 mini-portfolio in that bucket has fully recovered.
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Re: Total portfolio allocation and withdrawal (TPAW)

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TIME DIVERSIFICATION OF STOCK RISK

To show how TPAW diversifies stock risk over time, I rerun the above simulations removing bond risk leaving behind only stock risk. Realized returns for stocks are the actual historical returns. Realized returns for bonds are held constant at 2.7%. Expected returns are held constant at 7.0% for stocks and 2.7% for bonds.

So now changes in retirement income are driven solely by stock market performance. (Retirement income during working years refers to projected retirement income.) At age 25, retirement income is projected to be $110,097 per year. Each year, depending on how the stock market does, retirement income adjusts up or down. If the stock market does better than expected, retirement income adjusts up. If the stock market does worse than expected, retirement income adjusts down. So think of retirement income as a random walk, stepping up or down each year depending on the excess performance of the stock market.

Time diversification means taking medium sized steps up or down every year, rather than rather than giant steps in some years and tiny steps in others. This even spreading of risk-taking across time reduces the total risk required to achieve a given expected return. It's similar to how diversifying across assets reduces risk without sacrificing return.

The following graph shows the size of the steps taken at each age in the simulations. The X axis shows the age and the Y axis shows the percentage change in retirement income at that age:

Image

Early on, in the 20s and early 30s, the steps are too small. This is because the investor is underexposed to stocks at those ages--even the 100% stock allocation in early years is not enough stocks because there's not much savings. But from about the mid 30s onwards when the investor has reached full stock exposure, the steps become evenly dispersed all the way up to age 100. No age stands out as being more important than other ages. This is time diversification.

Let's look at the lowest points on the graph, which show a 15.1% reduction in income. This occurred after the worst year of the Great Depression--1931--when stocks lost 38%. This caused the 35/65 portfolio to underperform expectations by 15.1%. In response, retirement income also declined by 15.1% for all the cohorts who experienced it, regardless of age. On the far left, we have the young cohort (1921-1966) who experienced the 15.1% reduction at age 36. On the far right, we have the old cohort (1881-1956) who experienced the same 15.1% reduction at age 76. If we had even older cohorts in our simulations, we would have seen the same 15.1% reduction for them at ages 86 and 96 as well. So no matter how old you are, TPAW has retirement income responding in the same way to the same events. This means that the risk being taken at different ages is the same. Risk is constant across time.

The only exception in our simulation is the youngest cohort to experience this event. The 1931-2006 cohort experienced the crash during their first year working. Their projected retirement income dropped by only 1.5% in response because they had not accumulated much savings. Even a 100% stock allocation on their savings did not give them the same stock exposure that the older cohorts had.
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Re: Total portfolio allocation and withdrawal (TPAW)

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MANAGING GAP YEARS WITHOUT A BRIDGE TO SOCIAL SECURITY

Separating Social Security from the LMP decision

A problem faced by many retirees is how to manage the gap years before Social Security starts. One option is to build a bridge to Social Security--something like a TIPS ladder that pays out till Social Security kicks in. But a bridge is expensive and should be used only if necessary. The simulations above show that it is possible to manage risk in the gap years without a bridge. In the simulations, after the investor reached full stock exposure in their 30s, the same amount of risk was applied to their retirement income every year--their working years, the gap years after retirement and before social security, and after social security started. Gap year risk was no greater than risk in other years, even though a bridge was not used. This was because the asset allocation took Social Security into account and continually adjusted for it.

So it makes sense to build a bridge only if your preferences call for it. A simple test is: would you build a liability matched portfolio (LMP) if you didn't have Social Security?

- If your answer is "yes", then an LMP is right for you. You can create an LMP in TPAW by entering your desired bridge in the "essential expenses" column. Note that the size of the LMP need not match Social Security or pension payouts. It could be higher or lower. You get to decide.

- If "no", then building a bridge to Social Security is unlikely to be the right solution for your needs.

TPAW allows you to decouple the LMP decision from whether or not you have Social Security. It does this by rebalancing as if Social Security were bonds, thereby maintaining the same risk to retirement income every year regardless of the timing of Social Security (and other pensions.)

Liquidity risk during the gap years

If you choose not to create a bridge to Social Security, you will need to pay special attention to liquidity during the gap years. You can't sell Social Security like you can sell regular bonds. So it's possible that after a prolonged stretch of poor market performance, you'll run out of savings and TPAW will ask you to sell some of your future Social Security "bonds" to live on. Since you can't, you'll be left high and dry till Social Security starts.

This is unlikely to happen if

(1) your savings is large compared to Social Security and
(2) you have chosen a conservative asset allocation.

Under these conditions, poor market returns are unlikely to drive your savings portfolio down to zero during the gap years. So the issue of having to sell Social Security to live on is less likely to come up.

But if your savings is small relative to Social Security and you have chosen an aggressive asset allocation, then you can run out of savings during the gap. TPAW simulations can warn you ahead of time if this is likely to be a problem. Enter a series of poor returns in the simulator and see if your projected retirement income becomes zero during the gap years. If it does, then you have a liquidity problem. You can address it by choosing a more conservative asset allocation or setting aside funds for the problem years in the LMP (i.e. adding funds in the "essential expenses" column for those years.)

Let's see how the historical simulations above did when it comes to liquidity. During the gap years (ages 55-69), the highest percentage withdrawal from the savings portfolio was (among completed simulations):

- In simulation A, the 1881-1956 retiree had to withdraw $69,880 (10.3%) from a savings portfolio balance of $678,189 at age 68.
- In simulation B, the 1881-1956 retiree had to withdraw $71,252 (11.0%) from a savings portfolio balance of $645,966 at age 65.

So in these simulations, the retiree did not come close to running out of savings during the gap. Liquidity was not a problem.
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Re: Total portfolio allocation and withdrawal (TPAW)

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ASSET ALLOCATION ON THE SAVINGS PORTFOLIO

TPAW continually adjusts the asset allocation on the savings portfolio to maintain a fixed allocation on the total portfolio. This keeps risk constant, resulting in time diversification and risk reduction.

Let's look at the asset allocation on the savings portfolio in these simulations. How did the asset allocation adjust to keep risk constant through the three distinct phases:

1. working years
2. retirement years before Social Security begans (gap years), and
3. retirement years after Social Security began

The grey line in the graph below shows the projected glidepath at the start--age 25--in simulation A.

Image

The plan is to stay 100/0 till age 33, gliding down to 43/57 by the start of retirement, gliding up slightly to 52/48 by the time Social Security begins, and then gliding down very slightly to 49/51 by age 100. Note that if there had been no Social Security, the glidepath would have gone down to 35/65 by the start of retirement and then stayed flat. So the extra 15% or so of stocks during retirement is due to the presence of Social Security. So is the slight glide up at the start of retirement during the gap years till Social Security begins. Extra bonds are needed for the gap, leading to the rising glide path as the gap shortens and less bonds are needed.

But that's just the plan at age 25. The actual glide path will constantly adjust based on how the market does. So each simulation will trace its own path. The blue line in the graph above shows the average glidepath for simulation A and the orange line shows the average for simulation B. The averages came in close to the starting plan at age 25. But that hides a lot of variation between individual simulations. The graph below shows the separate paths taken by the completed A simulations.

Image

This shows that there was a good bit of adjusting needed along the way to maintain constant risk. Setting a glidepath at age 25 and sticking to it would not have been ideal. The glidepath needs to be flexible, adpating to new circumstances to keep risk constant. However, if you prefer the more familiar approach of a predetermined glidepath on the savings portfolio, designing one customized to your personal circumstances--risk preference, pension start dates, and pension amount as a percentage of retirement income--would still be better than going with a generic target date fund glidepath that does not take these factors into consideration.
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Re: Total portfolio allocation and withdrawal (TPAW)

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HOW TO MAKE RETIREMENT INCOME MORE STABLE

Simulation A showed retirement incomes that ranged from from 49% to 199% of starting (age 55) retirement income. What options do we have if we want income to be more stable?

1. Choose a more conservative allocation for the portfolio

Suppose your portfolio drops 10%. Suppose also that it's not because of a valuation change, so expected returns has not changed. Then it's as if someone stole 10% of your portfolio. Yes, your portfolio will likely grow and eventually exceed what was in there before the drop. But that doesn't change the fact that you will always have 10% less than you would have had otherwise. So in response, your planned retirement income has to drop by 10% on average. If you reduce it by less than 10% today, then you have to plan to reduce it by more than 10% in the future. So trying to dampen income volatility by not fully responding to this shock today only increases income volatility later on. Anything less than the full hit today gets added on to the hit you will have to take tomorrow.

So the main way to get a smoother retirement income is to simply choose a safer asset allocation for the portfolio. The more stable your portfolio, the more stable your retirement income.

2. Use valuation based models to calculate expected return.

Now suppose that your portfolio drops 10%, but this time it's because of a valuation drop. Because of the valuation drop, the expected return of the portfolio increases. Retirement income will now drop by less than 10% because the the increased expected return offsets some of the 10% drop. In fact, for younger investors, retirement income can actually rise because they over a long enough horizon the higher expected return can more than offset the portfolio drop. Simulation B showed what happens when we used CAPE and bond yields to calculate expected return. Compared to simulation A, average income rose from $103,141 to $120,542. It's not clear why this happened. It might just be luck. But more to the point here, the distribution of retirement income tightened a bit, ranging now from 68% to 210% of starting income.

3. Reduce bond risk by duration matching and inflation adjusting

You may be able to reduce bond risk by holding duration matched inflation indexed bonds (like TIPS). Duration matching reduces interest rate risk. Inflation indexing removes inflation risk. To see how much bond risk contributed to retirement income uncertainty, I reran simulation B by fixing bond returns to the starting (age 25) yields. You can think of this as duration matching and inflation adjusting all bonds at the start of their investing career. Compared to simulation B, average incomes remained practically the same at $120,220. But retirement income range tightened to 81% to 178% of starting (age 55) income. This level of risk reduction is not achievable because even if all bonds are duration matched, interest rate risk still shows up when rebalancing. But it should help, particularly in conservative portfolios. (An LMP does not require rebalancing, so it is possible to remove all bond risk in an LMP.)

4. Have low withdrawal rates

If you have a low enough withdrawal rate, then you can keep retirement income stable regardless of what happens. Even a 50% drop in the portfolio does not require an income adjustment if you are withdrawing very little to begin with. This works for those who don't care for higher retirement incomes during their lifetimes and are happy to leave a large inheritance to their heirs. Note that the full risk of portfolio performance is now borne by the heirs. If the portfolio drops 10% and expected returns don't change, your income does not change but the inheritance will drop by a lot more than 10%. That math still holds. If that's what you want, this system is fine. But if you want to do divide things up differently--maybe apply some of the portfolio gain/loss on your own retirement income and some to your heirs' inheritance--it is possible to explicitly do that in TPAW.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Ben Mathew »

THE PROBLEM WITH SAFE WITHDRAWAL RATES (SWR)

TPAW uses amortization based withdrawal (ABW) rather than safe withdrawal rates (SWR) to calculate withdrawals. This post shows why.

SWR asks the question: if you don't adjust your withdrawals over the course of your retirement, how much can you take out every year to ensure a high probability (usually 95%) of not running out of money?

Suppose the answer we get at the start of retirement is $40,000 per year. There are two ways to use this information.

The first way is to actually stick to taking out $40,000 per year over the entire course of your retirement regardless of how your portfolio does. This means that even if the market does well and you can easily take out much more, you still take out only $40,000 because that's what you calculated back at the start of retirement. Conversely, if the market does much worse than expected and it looks like you'll run out of money soon, you still continue to take out $40,000. This obviously is not a good strategy. Realistically, you will have to adjust. The question is when and how?

You can use SWR to create a flexible strategy by recalculating the safe withdrawal amount periodically. So each year you ask, what's the new safe withdrawal amount based on my new portfolio value and my new horizon? This strategy adjusts every year to market performance and shortening horizons. The SWR at age 100 will be 100% of the portfolio, so you will fully draw down the portfolio by the end.

Let's take a look at what such a strategy will look like. The following table shows SWR for 95% success rates for a 35/65 portfolio using Shiller's data described earlier. The rates were calculated using 105 retirement cohorts for retirements starting 1871 through 1975. For comparison, I include ABW withdrawal rates for a flat (g=0%) amortization schedule and a much more conservative growing (g=2.4%) amortization schedule.

Image

As expected, the SWR schedule is very conservative. It starts out at 3.1% withdrawal rate at age 55 compared to 4.8% using ABW with zero growth. It has to be very conservative because it's designed not to fail even if you don't adjust. But you are adjusting. So it probably doesn't need to be so conservative. But let's suppose that you do want to be quite conservative. ABW can be made as conservative as you like by selecting a growing withdrawal schedule. By setting g=2.4%, we get a conservative ABW schedule that matches the SWR age 55 withdrawal rate of 3.1%.

To translate these withdrawal rates to dollars, here's a graph showing scheduled withdrawals using the three plans:

Image

- The flat ABW plan (orange line) schedules a constant withdrawal of $47,616 per year.
- The conservative ABW plan (blue line) starts out at $31,459 at age 55 and grows at a constant 2.4% per year and ends with $91,462 at age 100.
- The SWR plan (grey line) starts out at $31,000 at age 55, grows slowly in the early years and faster in the later years and ends with $160,396 at age 100.

Here's how these plans would have worked out in the latest retirement cohort in the data. These would be the withdrawals of a person who retired with $1 million in 1976 aged 55 and took the final withdrawal at age 100 in 2021:

Image

- The flat ABW plan (orange line) started out at $47,616 and went up to $83,860 by age 100.
- The conservative ABW plan (blue line) started out at $31,459 and went up to $$161,081 by age 100.
- The SWR plan (grey line) started out at $31,000, similar to the conservative ABW plan, but stayed conservative longer and ended with $282,487 by age 100.

So the problems with SWR are:

1. It's overly conservative because it assumes you won't adjust. In reality you will adjust and so you probably don't need to be that conservative.

2. Even if you want to be conservative, ABW can be made as conservative as you want by selecting a sufficiently high growth amortization schedule. ABW has the advantage of providing a constant growth schedule whereas SWR growth is variable. It's not clear why you would want growth to be slow between some years and fast between others. But even if you did have a good reason, you can model that directly in ABW. SWR is delivering variable growth without a good reason based on retiree preferences.

3. SWR planning does not clearly communicate the impact of your choices on your retirement income. It tells you what will happen if you don't adjust. But the reality is that you will adjust. So what's useful to know is what will happen when you do adjust. What is income expected to be at age 80? At age 90? What are the chances that income will fall below $40,000? Below $30,000? You don't see any of this if all you're asking is what happens if you never adjust. You are going to adjust and your planning should tell you what's going to happen as you adjust and how your choices impact it.
Last edited by Ben Mathew on Mon Jul 05, 2021 1:32 pm, edited 2 times in total.
Total Portfolio Allocation and Withdrawal (TPAW)
AlohaJoe
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by AlohaJoe »

Ben Mathew wrote: Sat Jul 03, 2021 12:19 pm 2. Even if you want to be conservative, ABW can be made as conservative as you want by selecting a sufficiently high growth amortization schedule. ABW has the advantage of providing a constant growth schedule whereas SWR growth is variable. It's not clear why you would want growth to be slow between some years and fast between others. But even if you did have a good reason, you can model that directly in ABW. SWR is delivering variable growth without a good reason based on retiree preferences.
I realize I am in the minority of people in enjoying these more complex withdrawal schemes. But this passage (perhaps inadvertently) shows why I feel the way I do. All of the complexity is actually still there in the typical SWR scheme (or in the "bury your head in the sand and follow Taylor's withdraw whatever you feel like" scheme). It is just hidden under the covers with lots of implicit answers to questions you didn't even know were being asked. But just because someone else (implicitly, by accident) provided answers doesn't mean they are the right answers (or the right answers for you). And forcing oneself to work through the questions and come up with personalized answers doesn't seem like a huge ask when we're talking about 30+ years of retirement income. Most people probably spend more effort on planning a 10-day holiday than they do on their 30-year retirement.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Ben Mathew »

AlohaJoe wrote: Sun Jul 04, 2021 12:01 am
Ben Mathew wrote: Sat Jul 03, 2021 12:19 pm 2. Even if you want to be conservative, ABW can be made as conservative as you want by selecting a sufficiently high growth amortization schedule. ABW has the advantage of providing a constant growth schedule whereas SWR growth is variable. It's not clear why you would want growth to be slow between some years and fast between others. But even if you did have a good reason, you can model that directly in ABW. SWR is delivering variable growth without a good reason based on retiree preferences.
I realize I am in the minority of people in enjoying these more complex withdrawal schemes. But this passage (perhaps inadvertently) shows why I feel the way I do. All of the complexity is actually still there in the typical SWR scheme (or in the "bury your head in the sand and follow Taylor's withdraw whatever you feel like" scheme). It is just hidden under the covers with lots of implicit answers to questions you didn't even know were being asked. But just because someone else (implicitly, by accident) provided answers doesn't mean they are the right answers (or the right answers for you). And forcing oneself to work through the questions and come up with personalized answers doesn't seem like a huge ask when we're talking about 30+ years of retirement income. Most people probably spend more effort on planning a 10-day holiday than they do on their 30-year retirement.
Yes, absolutely. Strategies that may seem simple on the surface become complex once you open the hood and start asking questions. Every withdrawal strategy has a probability distribution of expected withdrawals--it's only a question of knowing what it is and whether it's the way it is for a good reason. A strategy that looks simpler may be the more complex one in terms of what it's actually doing.

TPAW sounds complex, but under the hood, it's elegantly simple and easy to understand what is happening and why it's happening. That's because it's based on the solution to a formal utility maximization problem. The formal utility approach is not popular in the Bogleheads community, but it actually means that there is an overall logic to how it works and everything is there for a reason. It also makes it easy to modify in a sensible way because you can see why something is the way it is and how to modify it if that's not what you want. Formal utility maximization makes its assumptions explicit. Ad hoc methods hide the assumptions and it's hard to understand what's going on.

Under the hood, TPAW is about as simple as it can get. It places the funds for each goal--whether it's college expenses or retirement funding for age 87--into its own bucket and applies a fixed AA on that bucket based on risk preferences for that goal. The complexity comes from the fact that there are many goals and many buckets. It's the aggregation--the adding up of all the buckets--that can make things look complex from up top. But the mechanism operating on each bucket is extremely simple. I can't imagine a simpler solution that is so naturally and directly linked to goals and preferences.
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AlohaJoe
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by AlohaJoe »

Ben Mathew wrote: Sat Jun 12, 2021 1:06 pm ASSET ALLOCATION ON THE SAVINGS PORTFOLIO

TPAW continually adjusts the asset allocation on the savings portfolio to maintain a fixed allocation on the total portfolio. This keeps risk constant, resulting in time diversification and risk reduction.

Let's look at the asset allocation on the savings portfolio in these simulations. How did the asset allocation adjust to keep risk constant through the three distinct phases:
These simulations don't include housing, right? It seems like both the negative bond of the mortgage early on and the equity in the house later on would dramatically change these results. Any thoughts on what it would look like if the total portfolio included the housing asset & liability?
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Ben Mathew »

AlohaJoe wrote: Sun Jul 04, 2021 3:47 pm
Ben Mathew wrote: Sat Jun 12, 2021 1:06 pm ASSET ALLOCATION ON THE SAVINGS PORTFOLIO

TPAW continually adjusts the asset allocation on the savings portfolio to maintain a fixed allocation on the total portfolio. This keeps risk constant, resulting in time diversification and risk reduction.

Let's look at the asset allocation on the savings portfolio in these simulations. How did the asset allocation adjust to keep risk constant through the three distinct phases:
These simulations don't include housing, right? It seems like both the negative bond of the mortgage early on and the equity in the house later on would dramatically change these results. Any thoughts on what it would look like if the total portfolio included the housing asset & liability?
The total portfolio needs only to include all the assets that fund retirement withdrawals. So unless the retiree is planning to sell the house at some point and use those funds to live on, the value of the house can be left out of the total portfolio. The ownership of the house would show up as a smaller total portfolio (current savings reduced by home equity and future savings reduced by remaining mortgage payments) and lower retirement expenses (no rent). Owning a house may increase the willingness to take risk on the remaining portfolio because it now only needs to fund less essential non-housing expenses and the home equity is there as a cushion. So someone who would have been 35/65 without a house may choose to be say 45/55 with a house. So you can think of the simulation results of a 35/65 total portfolio as either that of a less risk averse renter (35/65 without a house) or a more risk averse homeowner (35/65 in spite of a house).
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Taylor Larimore »

Aloha Joe wrote:
"bury your head in the sand and follow Taylor's withdraw whatever you feel like scheme."
Aloha Joe:

I never wrote anything like your quote. Please give your source -- or a retraction.

Thank you.
Taylor
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dbr
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by dbr »

Ben Mathew wrote: Sun Jul 04, 2021 2:14 pm [
TPAW sounds complex, but under the hood, it's elegantly simple and easy to understand what is happening and why it's happening. That's because it's based on the solution to a formal utility maximization problem. The formal utility approach is not popular in the Bogleheads community, but it actually means that there is an overall logic to how it works and everything is there for a reason. It also makes it easy to modify in a sensible way because you can see why something is the way it is and how to modify it if that's not what you want. Formal utility maximization makes its assumptions explicit. Ad hoc methods hide the assumptions and it's hard to understand what's going on.
Do you have a presentation somewhere for how that problem is formulated and solved resulting in the TPAW methodology?

I agree it is very important to see explicit assumptions and also the motivation.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Ben Mathew »

dbr wrote: Wed Aug 11, 2021 12:37 pm
Ben Mathew wrote: Sun Jul 04, 2021 2:14 pm [
TPAW sounds complex, but under the hood, it's elegantly simple and easy to understand what is happening and why it's happening. That's because it's based on the solution to a formal utility maximization problem. The formal utility approach is not popular in the Bogleheads community, but it actually means that there is an overall logic to how it works and everything is there for a reason. It also makes it easy to modify in a sensible way because you can see why something is the way it is and how to modify it if that's not what you want. Formal utility maximization makes its assumptions explicit. Ad hoc methods hide the assumptions and it's hard to understand what's going on.
Do you have a presentation somewhere for how that problem is formulated and solved resulting in the TPAW methodology?

I agree it is very important to see explicit assumptions and also the motivation.
The "fixed allocation on the total portfolio" portion of TPAW is explained in Ayres and Nalebuff's Lifecycle Investing. TPAW follows the same strategy as Ayres and Nalebuff, except stock allocation is capped at 100% to avoid leverage. (Ayres and Nalebuff caps stock allocation at 200%.)

Ayres and Nalebuff don't really go into the withdrawal side of the strategy. They sidestep it by assuming that the entire portfolio will be annuitized at the start of retirement. This post describes how TPAW utilizes the lifecycle model in the withdrawal phase as well to get the withdrawal strategy. The following posts illustrate how stock risk becomes perfectly diversified across both the accumulation and the retirement years:

- How retirement income responds to a poor sequence of returns (temporary crash). post

- Why retirement income recovers fully after a poor sequence of returns (temporary crash). post

- Time diversification of stock risk. post

TPAW does have an option that is not technically supported by standard utility maximization models--the ability to add essential expenses. These expenses are 100% funded by bonds and are fully insulated from market performance. This requires infinite risk aversion for the essential expenses. If the user enters $5,000 as essential expenses for some year, then they are saying they have infinite risk aversion below that threshold. That is unlikely to be literally true. But I've included the option because it can serve as an approximation for decreasing relative risk aversion. The TPAW calculator has instructions to get the user to think hard about whether their expenses really are essential:
ESSENTIAL EXPENSES (funded by safe bonds): In column M, enter a conservatively high estimate of extra future expenses that you consider essential and would like to fund with a safe portfolio of 100% safe bonds rather than with the risk portfolio. This is a floor below which you don't want your consumption to fall. Not everyone needs a floor. To see if it's right for you, ask yourself the following question: If you have just enough in your portfolio to fund a consumption floor with safe bonds, would you invest it all in safe bonds to create the floor and eliminate the risk of falling below the floor? Or would you still invest some in stocks for the higher expected withdrawal? If the former, then that means you're willing to pay the cost of low returns and low withdrawals to create a floor. If the latter, then you may not need a safe portfolio--you can still reduce risk by entering a safer AA for the risk portfolio in cells I24:25.
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dbr
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by dbr »

Ben Mathew wrote: Wed Aug 11, 2021 2:10 pm
dbr wrote: Wed Aug 11, 2021 12:37 pm
Ben Mathew wrote: Sun Jul 04, 2021 2:14 pm [
TPAW sounds complex, but under the hood, it's elegantly simple and easy to understand what is happening and why it's happening. That's because it's based on the solution to a formal utility maximization problem. The formal utility approach is not popular in the Bogleheads community, but it actually means that there is an overall logic to how it works and everything is there for a reason. It also makes it easy to modify in a sensible way because you can see why something is the way it is and how to modify it if that's not what you want. Formal utility maximization makes its assumptions explicit. Ad hoc methods hide the assumptions and it's hard to understand what's going on.
Do you have a presentation somewhere for how that problem is formulated and solved resulting in the TPAW methodology?

I agree it is very important to see explicit assumptions and also the motivation.
The "fixed allocation on the total portfolio" portion of TPAW is explained in Ayres and Nalebuff's Lifecycle Investing. TPAW follows the same strategy as Ayres and Nalebuff, except stock allocation is capped at 100% to avoid leverage. (Ayres and Nalebuff caps stock allocation at 200%.)

Ayres and Nalebuff don't really go into the withdrawal side of the strategy. They sidestep it by assuming that the entire portfolio will be annuitized at the start of retirement. This post describes how TPAW utilizes the lifecycle model in the withdrawal phase as well to get the withdrawal strategy. The following posts illustrate how stock risk becomes perfectly diversified across both the accumulation and the retirement years:

- How retirement income responds to a poor sequence of returns (temporary crash). post

- Why retirement income recovers fully after a poor sequence of returns (temporary crash). post

- Time diversification of stock risk. post

TPAW does have an option that is not technically supported by standard utility maximization models--the ability to add essential expenses. These expenses are 100% funded by bonds and are fully insulated from market performance. This requires infinite risk aversion for the essential expenses. If the user enters $5,000 as essential expenses for some year, then they are saying they have infinite risk aversion below that threshold. That is unlikely to be literally true. But I've included the option because it can serve as an approximation for decreasing relative risk aversion. The TPAW calculator has instructions to get the user to think hard about whether their expenses really are essential:
ESSENTIAL EXPENSES (funded by safe bonds): In column M, enter a conservatively high estimate of extra future expenses that you consider essential and would like to fund with a safe portfolio of 100% safe bonds rather than with the risk portfolio. This is a floor below which you don't want your consumption to fall. Not everyone needs a floor. To see if it's right for you, ask yourself the following question: If you have just enough in your portfolio to fund a consumption floor with safe bonds, would you invest it all in safe bonds to create the floor and eliminate the risk of falling below the floor? Or would you still invest some in stocks for the higher expected withdrawal? If the former, then that means you're willing to pay the cost of low returns and low withdrawals to create a floor. If the latter, then you may not need a safe portfolio--you can still reduce risk by entering a safer AA for the risk portfolio in cells I24:25.
Thanks I'll have a look. Might take awhile.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Ben Mathew »

TPAW PLANNER WITH MONTE CARLO SIMULATION

I have uploaded the TPAW Planner with Monte Carlo Simulation to the wiki. This is the full featured planner that I've had in mind for a while. It uses Monte Carlo simulations to show the impact of your planning choices. You adjust your plan until you're satisfied with the simulation results.

From instructions in the spreadsheet:
The graph below shows the results of the Monte Carlo simulation. 500 sequences of returns are randomly generated and the resulting retirement spending is summarized using percentiles. Adjust the asset allocation (cells I28:29) and the growth rate of scheduled withdrawals 'g' (cell Q49) till you arrive at your preferred spending profile. Raising the stock allocation will increase average spending but widen the dispersion (more risk, more return). Raising g will reduce spending in early retirement and increase it in late retirement, making the graph more upward sloping (higher saving). A higher g reduces the likelihood of bad outcomes in late retirement. So more risk averse people will want to choose a higher g (precautionary saving).

If you have a gap before social security and pensions start, pay special attention to the gap years to make sure that your savings portfolio does not run of out funds before social security and pensions begin. If the graph shows that the risk of running out of funds is unacceptably high, you can reduce the risk by (i) choosing a safer asset allocation in cells I28:29, (ii) increasing 'g' in cell Q49, or (iii) adding a fixed essential expense for all retirement years (not just the gap years) in column M. If using method (iii), add the same amount of essential expenses (e.g. $10,000) to all retirement years to keep risk consistent.
Let's look at an example for a user who is 25 years old, has $50,000 in savings, expects to save $25,000 per year till age 54, plans to retire early at age 55, and expects $30,000 in Social Security starting age 70. Planning till age 100. Expected stock return = 3.5% Expected bond return = 0%. All $ and rates are real.

By choosing an AA of 35/65 and scheduled withdrawal growth g = 1%, the user gets the retirement spending profile graphed below. Median (50th percentile) withdrawal starts at $49,006 at age 55 and climbs to $64,059 by age 100. Even the 10th percentile outcomes don't look too terrible. Note that the 10th percentile outcome did not run out of funds during the gap years before SS starts (age 55-69). So with 90%+ probability, the user will be okay during the gap years.

Figure 2: AA=35/65, g=1%
Image

If, instead, the user chooses a more aggressive AA of 60/40 and scheduled withdrawal growth g=0%, they get the spending profile below. The median starts out high at $73,173 but declines to $36,122 by age 100. The 10th percentile outcome runs out of funds towards the end of the gap year (ages 67-69) and then relies solely on Social Security of $30,000 from age 70. By age 97, even the 40th percentile outcome is down to Social Security alone. This is probably an unattractive scenario for most people. They can reduce AA, increase withdrawal growth 'g', or add essential expenses until they find their preferred spending profile.

Figure 3: AA = 60/40, g=0%
Image
Last edited by Ben Mathew on Fri Oct 08, 2021 10:50 pm, edited 3 times in total.
Total Portfolio Allocation and Withdrawal (TPAW)
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by KarenC »

Ben Mathew wrote: Sat Aug 21, 2021 1:08 am TPAW PLANNER WITH MONTE CARLO SIMULATION

I have uploaded the TPAW Planner with Monte Carlo Simulation to the wiki. This is the full featured planner that I've had in mind for a while. It uses Monte Carlo simulations to show the impact of your planning choices. You adjust your plan until you're satisfied with the simulation results. […]
Looks interesting! I found modifying the spreadsheet unwieldy, however. I needed to delete some rows for my situation, and I was attempting to follow the instructions in Planner!B36 by deleting BK54:UO99, but I ended up with a giant sea of unresolved references. I had to back out of that; perhaps the range in question is BJ54:UO99? (Also, in addition to "After fixing the rows, recreate the data table using Data -> What If -> Data table. The TPAW support thread shows how to do this.", is it possible to add a link to the specific thread?)
"The first principle is that you must not fool yourself—and you are the easiest person to fool." — Richard P. Feynman
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Ben Mathew »

KarenC wrote: Sat Aug 21, 2021 7:45 am
Ben Mathew wrote: Sat Aug 21, 2021 1:08 am TPAW PLANNER WITH MONTE CARLO SIMULATION

I have uploaded the TPAW Planner with Monte Carlo Simulation to the wiki. This is the full featured planner that I've had in mind for a while. It uses Monte Carlo simulations to show the impact of your planning choices. You adjust your plan until you're satisfied with the simulation results. […]
Looks interesting! I found modifying the spreadsheet unwieldy, however. I needed to delete some rows for my situation, and I was attempting to follow the instructions in Planner!B36 by deleting BK54:UO99, but I ended up with a giant sea of unresolved references. I had to back out of that; perhaps the range in question is BJ54:UO99? (Also, in addition to "After fixing the rows, recreate the data table using Data -> What If -> Data table. The TPAW support thread shows how to do this.", is it possible to add a link to the specific thread?)
The initial setup of adding or deleting rows to get the spreadsheet to match your situation can be a bit challenging, especially with the data table needed for the Monte Carlo simulation. But once you've gotten over the hump of setting up the spreadsheet, using it will be a lot easier.

The BK:UO referred to in the instructions is correct. The data in the first column (BK) should not be deleted. After doing only this step (before deleting any rows), I am not getting any unresolved references. The unresolved references only come after I delete rows. Is that what you're getting too?

I will add the instructions on how to remove and add back the data table soon.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by KarenC »

Ben Mathew wrote: Sat Aug 21, 2021 11:27 am
KarenC wrote: Sat Aug 21, 2021 7:45 am
Ben Mathew wrote: Sat Aug 21, 2021 1:08 am TPAW PLANNER WITH MONTE CARLO SIMULATION

I have uploaded the TPAW Planner with Monte Carlo Simulation to the wiki. This is the full featured planner that I've had in mind for a while. It uses Monte Carlo simulations to show the impact of your planning choices. You adjust your plan until you're satisfied with the simulation results. […]
Looks interesting! I found modifying the spreadsheet unwieldy, however. I needed to delete some rows for my situation, and I was attempting to follow the instructions in Planner!B36 by deleting BK54:UO99, but I ended up with a giant sea of unresolved references. I had to back out of that; perhaps the range in question is BJ54:UO99? (Also, in addition to "After fixing the rows, recreate the data table using Data -> What If -> Data table. The TPAW support thread shows how to do this.", is it possible to add a link to the specific thread?)
The initial setup of adding or deleting rows to get the spreadsheet to match your situation can be a bit challenging, especially with the data table needed for the Monte Carlo simulation. But once you've gotten over the hump of setting up the spreadsheet, using it will be a lot easier.

The BK:UO referred to in the instructions is correct. The data in the first column (BK) should not be deleted. After doing only this step (before deleting any rows), I am not getting any unresolved references. The unresolved references only come after I delete rows. Is that what you're getting too?

I will add the instructions on how to remove and add back the data table soon.
Yes; my apologies for not being clear about that. After I clear out the data and then try to delete a row, I get the all the unresolved references.
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Re: Total portfolio allocation and withdrawal (TPAW)

Post by Ben Mathew »

KarenC wrote: Sat Aug 21, 2021 11:51 am
Ben Mathew wrote: Sat Aug 21, 2021 11:27 am
KarenC wrote: Sat Aug 21, 2021 7:45 am
Ben Mathew wrote: Sat Aug 21, 2021 1:08 am TPAW PLANNER WITH MONTE CARLO SIMULATION

I have uploaded the TPAW Planner with Monte Carlo Simulation to the wiki. This is the full featured planner that I've had in mind for a while. It uses Monte Carlo simulations to show the impact of your planning choices. You adjust your plan until you're satisfied with the simulation results. […]
Looks interesting! I found modifying the spreadsheet unwieldy, however. I needed to delete some rows for my situation, and I was attempting to follow the instructions in Planner!B36 by deleting BK54:UO99, but I ended up with a giant sea of unresolved references. I had to back out of that; perhaps the range in question is BJ54:UO99? (Also, in addition to "After fixing the rows, recreate the data table using Data -> What If -> Data table. The TPAW support thread shows how to do this.", is it possible to add a link to the specific thread?)
The initial setup of adding or deleting rows to get the spreadsheet to match your situation can be a bit challenging, especially with the data table needed for the Monte Carlo simulation. But once you've gotten over the hump of setting up the spreadsheet, using it will be a lot easier.

The BK:UO referred to in the instructions is correct. The data in the first column (BK) should not be deleted. After doing only this step (before deleting any rows), I am not getting any unresolved references. The unresolved references only come after I delete rows. Is that what you're getting too?

I will add the instructions on how to remove and add back the data table soon.
Yes; my apologies for not being clear about that. After I clear out the data and then try to delete a row, I get the all the unresolved references.
No worries, the unresolved references will get resolved as you copy over the relevant formulas. Delete rows in the middle (not the first two or last two rows). Rows below the deleted rows will display #REF! in several columns. But you actually need to fix only three columns to resolve it: columns B, C and U. For these three columns, copy the formula from an unaffected row above and paste into the first #REF! row. That should resolve the #REF! in all columns. Let me know if it doesn't.
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Re: Total portfolio allocation and withdrawal (TPAW)

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INSTRUCTIONS FOR CUSTOMIZING "TPAW PLANNER WITH MONTE CARLO SIMULATION - FOR RETIREES"

The following example shows how to delete 5 rows in the retiree spreadsheet to get a spreadsheet appropriate for a 60 year old planning to age 100 (instead of the original 55 year old planning to age 100.)

1. Change current age in the inputs to 60 and years of withdrawals (n) to 41.

2. Excel won't let you delete part of a data table. So before deleting rows, delete the entire data table in cells BN55:UR100 (under run numbers 2 to 500).
Image

3. Select 5 rows in the middle (avoid first two and last two rows) and delete.
Image

4. This will generate #REF! errors in several columns in the rows below the deletion.
Image

5. You actually need to fix only five columns to resolve it: columns B, C, U, AY and BG. For these five columns, copy the formula from an unaffected cell above and paste into the first #REF! cell (shown in red in the figure below).
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6. All the #REF! errors should now be resolved.
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7. Recreate the data table by highlighting the deleted data table plus the bordering row above (containing the run numbers 1,...,500) and the bordering column to the left (under run number 1). Click on Data -> What If Analysis -> Data Table. A dialog window pops up. In the "Row input cell," enter any cell outside the data table, for example the cell immediately above ($BM$51). Leave the "Column input cell" blank. Click OK.
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8. The data table is generated and the spreadsheet is ready for use.
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Last edited by Ben Mathew on Tue Sep 28, 2021 7:30 pm, edited 2 times in total.
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 »

INSTRUCTIONS FOR CUSTOMIZING "TPAW PLANNER WITH MONTE CARLO SIMULATION - FOR ACCUMULATORS"

This example shows how an accumulator can modify the planner to match their situation.

The original spreadsheet is for a 25 year old, retiring at age 55, and planning to age 100. This means 30 years in the accumulation phase (ages 25-54) and 46 years in retirement (ages 55-100).

Suppose the user is 30 years old, retiring at age 65, and planning to age 100. This means 35 years in the accumulation phase (ages 30-64) and 36 years in retirement (ages 65-100). So the user has to :

(1) add 5 years to the accumulation phase
(2) subtract 10 years from the retirement phase

Here's how to do it:

1. In the inputs, change current age to 30, retirement age to 65, and years of withdrawals (n) to 36.

2. Excel won't let you delete part of a data table. So before deleting rows, delete the entire data table in cells BN55:UR130 (under run numbers 2 to 500).
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3. Insert 5 rows somewhere in the middle of the accumlation phase of the spreadsheet.
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4. Copy the formulas from a row above. Paste the formulas in the newly created empty rows and the first row of the pre-existing cells below (row 68 in the screenshot below).
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5. Delete 10 rows from the retirement phase (which is row 89 onwards in the screenshot below). Don't delete the first two and last two rows of the retirement phase--delete from somewhere in the middle.
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6. This will generate #REF! errors in several columns in the rows below the deletion.
Image

7. You actually need to fix only five columns to resolve it: columns B, C, U, AY and BG. For these five columns, copy the formula from an unaffected cell above and paste into the first #REF! cell (shown in red in the figure below).
Image

8. All the #REF! errors should now be resolved.
Image

9. Recreate the data table by highlighting the deleted data table plus the bordering row above (containing the run numbers 1,...,500) and the bordering column to the left (under run number 1). Click on Data -> What If Analysis -> Data Table. A dialog window pops up. In the "Row input cell," enter any cell outside the data table, for example the cell immediately above ($BM$51). Leave the "Column input cell" blank. Click OK.
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10. The data table is generated and the spreadsheet is ready for use.
Image
Last edited by Ben Mathew on Tue Sep 28, 2021 7:20 pm, edited 1 time in total.
Total Portfolio Allocation and Withdrawal (TPAW)
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