Total Portfolio Allocation and Withdrawal (TPAW)

[Ben Mathew]

Hi Ben. I've been enjoying playing around with TPAW. This is probably too complex to code, but I think the most useful enhancement for me might be a "ceiling bonus" - adjusting spending floors for prior year ceilings. I think most folks have ceilings - few people double their retirement spending during the "no go" years, regardless of market returns. But setting that ceiling in one year should (somehow!) give you a floor boost in future years for the set of results that exceed it. I know that's hard, since the ceiling bonus is probabilistic, but there should be some way to account for it. Thanks.

There is a ceiling bonus already: The excess that you don't spend stays in the portfolio and increases the portfolio balance, which in turn helps with future spending. It reduces the probability of spending declines from that point on, which in turn reduces the probability of hitting the spending floor. But typically this effect will be concentrated at the percentiles close to the ceiling. At the median and lower percentiles, the impact will be small—often indistinguishable from zero. This is because if you hit a ceiling, it means that you're already on a very good sequence of returns. At that point, it's unlikely that you will drop back down to the median or the 5th percentile or the floor. So the fact that you save the excess above the ceiling doesn't help much with the median and lower outcomes.

Example:
...

Thanks, Ben, for the clear and illuminating reply to TipsQuestions. I had played around with ceilings and floors, and saw that lowering the ceiling often increased the legacy amount but rarely changed the worst outcomes. I was a bit disappointed because I thought it should help in both directions, but you explained so well why it hardly affects the worst outcomes, since hitting the ceiling vs approaching the worse outcomes is largely a reflection of a good vs bad sequence of returns.

Yes, it can be surprising because it's easy to forget that the two ends of the distribution represent opposite extremes of possible sequences, and in a sense occupy different universes. The 95th percentile requires a good draw followed by a good draw followed by more good draws. The 5th percentile is usually bad draws followed by bad draws followed by even more bad draws. So once you have some good draws, it becomes unlikely that the sequence will drop all the way down to the 5th percentile. And once you have some bad draws, it becomes unlikely that the sequence can climb all the way back up to the 95th percentile. So a sequence that has climbed up to the ceiling will almost certainly never get back down to the floor. So saving above the ceiling won't reduce the risk of breaching the floor, because the floor was already safe in that sequence.

[Ben Mathew]

There is a ceiling bonus already: The excess that you don't spend stays in the portfolio and increases the portfolio balance, which in turn helps with future spending. It reduces the probability of spending declines from that point onwards, which in turn reduces the probability of hitting the spending floor. But typically this effect will be concentrated at the percentiles close to the ceiling. At the median and lower percentiles, the impact will typically be small—often indistinguishable from zero. This is because if you hit a ceiling, it means that you're already on a very good sequence of returns. At that point, it's unlikely that you will drop back down to the median or the 5th percentile or the floor. So the fact that you save the excess above the ceiling doesn't help much with the median and lower outcomes.

Thanks from me also, Ben. That's very helpful. For me the most eye opening thing about TPAW for the early retiree is that it suggests you can spend more in early retirement with a higher bond allocation. Of course, eventually the higher stock allocation catches up, but most folks want to spend more in their active years. This seems true whether or not you add a spending tilt, and even though I bumped up the stock return %. Food for thought!

Yes, a higher allocation to bonds can increase starting withdrawals even though the expected return of the portfolio falls. This is because you are taking less risk and so need less precautionary savings, which makes the base spending tilt lower. This logic becomes clear if you turn off bond volatility (Expected Returns and Volatility -> Bond Volatility). This removes interest rate risk, which is partially attainable in practice by duration matching.

This implies that the main benefit of an aggressive asset allocation is not increased spending in early retirement, but a high probability of very high spending in late retirement or a large legacy. Spending in early retirement is circumscribed by the need for precautionary savings.

To increase spending in early retirement, you also have some other controls you can use: You can adjust the time preference (Risk -> Advanced -> Time Preference), increase the extra spending tilt (Risk -> Spending Tilt), or schedule extra expenses in early retirement (Adjustments to Spending -> Add Extra Expenses). Each of these options increases spending in early retirement and reduces it in late retirement, but in different ways resulting in different spending distributions.

[Horton]

Ben - the expected returns for stocks are based on the S&P 500. Most people own international stocks and some may also favor various factors like small value. I’m compensating for this by using the “regression prediction for stocks” rather than the “suggested” expected returns since the former is a bit higher (currently about 0.8%). I’d prefer not to use the “manual” setting. What do you think?

[Ben Mathew]

Ben - the expected returns for stocks are based on the S&P 500. Most people own international stocks and some may also favor various factors like small value. I’m compensating for this by using the “regression prediction for stocks” rather than the “suggested” expected returns since the former is a bit higher (currently about 0.8%). I’d prefer not to use the “manual” setting. What do you think?

There is no good solution to this at the moment. I hope to eventually add a full blown menu where assumptions about the expected returns, volatility and correlations of various asset classes can be set and automatically updated. But that will take some time and is pretty far down the list. For now, I can add an option to set the expected return of stocks to one of the current automatically updated options (suggested, 1/CAPE, regression prediction) plus a constant that you input. That will provide a few more options. The main issue of course is that the expected returns of the different asset classes can change relative to each other, and these options won't capture that. That will have to wait for the full menu to be implemented.

[Horton]

Thanks, Ben. My approach is working well for now, I just wanted to make sure that I wasn’t missing any existing features of the tool. The broader menu of expected returns, volatilities, and correlations would be a nice enhancement, but I bet that would be a lot of work for only incremental value. Good to hear that it’s on the list though.

[TipsQuestions]

Yes, a higher allocation to bonds can increase starting withdrawals even though the expected return of the portfolio falls. This is because you are taking less risk and so need less precautionary savings, which makes the base spending tilt lower. This logic becomes clear if you turn off bond volatility (Expected Returns and Volatility -> Bond Volatility). This removes interest rate risk, which is partially attainable in practice by duration matching.

This implies that the main benefit of an aggressive asset allocation is not increased spending in early retirement, but a high probability of very high spending in late retirement or a large legacy. Spending in early retirement is circumscribed by the need for precautionary savings.

Good stuff, thanks again. Ending up with $10M I'll never spend at age 95 is just what I'm trying to avoid.

[ahc19081]

I have a very small interface issue on Mac OS Safari 17.1 (and prior versions): when viewed in a wide enough window that the two interface panels are side by side, the left panel (Age, Wealth, etc.) frequently "freezes" and stops scrolling until the window is resized (even a tiny resize solves the problem). Not a huge deal, just something to put on the punch list if you're able to replicate!

[Ben Mathew]

I have a very small interface issue on Mac OS Safari 17.1 (and prior versions): when viewed in a wide enough window that the two interface panels are side by side, the left panel (Age, Wealth, etc.) frequently "freezes" and stops scrolling until the window is resized (even a tiny resize solves the problem). Not a huge deal, just something to put on the punch list if you're able to replicate!

Thanks for reporting this bug. We tried it on a couple different Safari and Mac OS combinations but have not been able to reproduce it yet. If you (or anyone) can figure out how to reproduce the problem consistently, please let me know. That would be very helpful.

[TipsQuestions]

Hi Ben. Is there a way to increase risk tolerance (stock allocation) as you age?

[GaryA505]

Hi Ben. Is there a way to increase risk tolerance (stock allocation) as you age?

Oh, you asked what I was just thinking.

[Ben Mathew]

I have a very small interface issue on Mac OS Safari 17.1 (and prior versions): when viewed in a wide enough window that the two interface panels are side by side, the left panel (Age, Wealth, etc.) frequently "freezes" and stops scrolling until the window is resized (even a tiny resize solves the problem). Not a huge deal, just something to put on the punch list if you're able to replicate!

Thanks for reporting this bug. We tried it on a couple different Safari and Mac OS combinations but have not been able to reproduce it yet. If you (or anyone) can figure out how to reproduce the problem consistently, please let me know. That would be very helpful.

Thanks ahc19081 for PM'ing me the steps needed to replicate the issue. We are able to reproduce and will work on a fix.

[Ben Mathew]

Hi Ben. Is there a way to increase risk tolerance (stock allocation) as you age?

Oh, you asked what I was just thinking.

I assumed that people would only be interested in reducing risk with age, so I provided only the option to reduce risk. The idea was that it might be harder for older people to tolerate spending fluctuations. Change can be physically and cognitively challenging, so a 90 year old might value stability of retirement income more than a 70 year old.

I'm interested in learning more about the use case that you have in mind. Why increase risk—and so spending volatility—at older ages?

[GAAP]

Hi Ben. Is there a way to increase risk tolerance (stock allocation) as you age?

Oh, you asked what I was just thinking.

I assumed that people would only be interested in reducing risk with age, so I provided only the option to reduce risk. The idea was that it might be harder for older people to tolerate spending fluctuations. Change can be physically and cognitively challenging, so a 90 year old might value stability of retirement income more than a 70 year old.

I'm interested in learning more about the use case that you have in mind. Why increase risk—and so spending volatility—at older ages?

Maybe they like the increasing glidepath concept.

If their portfolio is big enough and performs well enough, maybe the variability doesn't matter.

Maybe they just want to see what happens/can happen.

FWIW, my mother was 95% equity at age 88, with no cognitive difficulties managing an old-school (individual stocks and bonds) portfolio.

[TipsQuestions]

Hi Ben. Is there a way to increase risk tolerance (stock allocation) as you age?

Oh, you asked what I was just thinking.

I assumed that people would only be interested in reducing risk with age, so I provided only the option to reduce risk. The idea was that it might be harder for older people to tolerate spending fluctuations. Change can be physically and cognitively challenging, so a 90 year old might value stability of retirement income more than a 70 year old.

I'm interested in learning more about the use case that you have in mind. Why increase risk—and so spending volatility—at older ages?

More info below...would be nice if we could model it in TPAW:

https://www.kitces.com/blog/should-equi ... ly-better/

https://www.forbes.com/sites/wadepfau/2 ... 6b4879343d

[GaryA505]

Hi Ben. Is there a way to increase risk tolerance (stock allocation) as you age?

Oh, you asked what I was just thinking.

I assumed that people would only be interested in reducing risk with age, so I provided only the option to reduce risk. The idea was that it might be harder for older people to tolerate spending fluctuations. Change can be physically and cognitively challenging, so a 90 year old might value stability of retirement income more than a 70 year old.

I'm interested in learning more about the use case that you have in mind. Why increase risk—and so spending volatility—at older ages?

I think the idea isn't so much that you may want to increase risk at later years retirement, rather it is to decrease it in the early retirement years to mitigate SORR.

Let's say you are comfortable with a 70/30 portfolio in retirement, except that you worry about SORR in the few years just before and after your retirement date. So, maybe you start with 30/70 and cause it to glide up to 70/30.

[Ben Mathew]

I have a very small interface issue on Mac OS Safari 17.1 (and prior versions): when viewed in a wide enough window that the two interface panels are side by side, the left panel (Age, Wealth, etc.) frequently "freezes" and stops scrolling until the window is resized (even a tiny resize solves the problem). Not a huge deal, just something to put on the punch list if you're able to replicate!

Thanks for reporting this bug. We tried it on a couple different Safari and Mac OS combinations but have not been able to reproduce it yet. If you (or anyone) can figure out how to reproduce the problem consistently, please let me know. That would be very helpful.

Thanks ahc19081 for PM'ing me the steps needed to replicate the issue. We are able to reproduce and will work on a fix.

This has been fixed. Let me know if there are any more issues.

Thanks for reporting the bug.

[GoWithTheCashFlow]

Guys...

The whole point is that TPAW already takes care of sequence of returns risk.

See this post from Ben as well as his next couple of posts after that one.

Any other attempts to mitigate sequence of returns risk are just imperfect versions of what TPAW does.

[Fairfox]

First, I want to say thank you for making the TPAW planner — I have learned a lot and gone deep as a result of digging into it. I was impressed that it effectively generated (algorithmically) the process of building up a TIPS ladder before early retirement and then spending it down before claiming SS.

A couple requests — one perhaps easier than the other:

1) I’d love to be able to see actual samples from the Monte Carlo. The median looks nice and smooth, but I know the actual experience would have ups and downs. The amortization process should mute those to some degree, but as it stands now I can’t actually see how much year-to-year variation might be expected. Does a trajectory that ends up in the 5th percentile stay low throughout? If you start off on a low trajectory, do you bounce out of it, or stay in the low band of the results throughout? (And vice versa with high samples) More equities/risk appetite should make individual trajectories noisier, too, in addition to broadening the overall cloud of possible outcomes. I’m imagining having ten sample trajectories (in distinct colors) that span the possible outcomes, and you can even see the same colors on different graphs so you can see how the asset allocation relates to the portfolio level, etc. Thanks for considering this!

2) Have you considered some kind of retirement date flexibility in the Monte Carlo? That is, I know that if the portfolio has generally underperformed I’d probably work longer, and vice versa. This has the effect of narrowing the range of potential outcomes. It also means that I am happy with a higher risk tolerance than otherwise, because if it doesn’t pan out I know I can wait a bit longer before retiring (thereby reducing the amount of assets required and giving the market time to recover). There are papers on this (including by Merton) that back up this way of thinking — having a flexible retirement date results in higher overall lifetime utility than having a fixed one, and higher risk portions in the lifetime allocation. How would you suggest exploring this in the Planner? Or is there some cool math you can do with a “how certain are you about your retirement date” slider to actually model this?

Thanks again!

[Ben Mathew]

It seems like some of the motivations for increasing risk over time might be:

1. Wealth increases over time, which might make you less risk averse over time

This can happen if you have decreasing relative risk aversion (DRRA). But it's important to keep in mind that with DRRA, risk is a function of wealth, not a function of age. Wealth may be correlated to age, but it's still wealth, not age, that determines how much risk you want to take. If the portfolio happens to do badly and you end up with low wealth and low spending in old age, you are not interested in taking more risk simply because you're older.

For more about decreasing (DRRA) vs constant (CRRA) vs increasing (IRRA) relative risk aversion, see "Wealth and Risk Aversion" in the Learn > Risk Aversion section of the planner.

You can model DRRA in the planner by creating a funded spending floor. (For now, you can do this by entering an essential expense for all of retirement. Eventually there will be a separate section for creating a funded floor where you can do this more easily.) When you insert a floor, you are effectively cutting risk when the portfolio does badly and spending drops towards the floor, and increasing risk as the portfolio does well and spending rises away from the floor. This relationship between the spending floor and DRRA is described under "Guaranteed spending level" in the Learn > Extra Spending section of the planner.

With precautionary savings (spending tilt > 0), wealth will tend to rise with age. So, if a spending floor is inserted, asset allocation will also tend to rise with age.

2. Wealth increases over time, so most of your wealth is destined for legacy and allocated aggressively for your heirs

If you have a legacy goal, then if the markets do well, an increasingly large fraction of your wealth may be headed for legacy. You may want to invest legacy assets at an asset allocation that's appropriate for your heirs, which will usually be more aggressive than your retirement spending. You can input this in Risk -> Increase Risk Tolerance for Legacy. If you choose to increase risk tolerance for legacy, and markets do well, you will get an asset allocation that tends to rise over time.

This is discussed under under "Legacy" in the Learn > Extra Spending section of the planner.

3. Rising Equity Glidepath to Reduce Sequence of Return Risk (SORR)

The rising equity glidepath result is an artifact of the fixed withdrawal assumption and pass/fail grading of SWR. If you use SWR (Advanced -> Strategy -> SWR), you can specify any glidepath you want in the Risk section, including a rising glidepath.

The rising glidepath result does not apply to the TPAW strategy which uses variable amortization based withdrawals (ABW) as suggested by the lifecycle model. For ABW, a fixed asset allocation on the total portfolio produces the lowest spending risk, which is why the fixed asset allocation is optimal in the lifecycle model. This post explains why it's different:

The rising equity glidepath is an artifact of the fixed withdrawal assumption of SWR. For variable withdrawals, a fixed asset allocation (after accounting for future savings and retirement income) would be optimal. The lifecycle model explains the mechanism behind this:

With variable withdrawals, at any point in time, spending for all remaining retirement years moves up and down with portfolio gains and losses. So each year, it makes sense to take the same bet on the portfolio because it impacts retirement spending (of remaining years) the same way. If 40/60 was a good idea last year, it's a good idea this year because it has the same percentage impact on retirement spending for all remaining years.

Fixed withdrawals behave very differently. With fixed withdrawals, portfolio gains and losses does not impact all retirement years equally. It impacts only the final few retirement years, making them funded or unfunded, while spending in the early years of retirement remain unimpacted. If the portfolio balance is declining, a fixed asset allocation would have too much impact early on and too little later on, potentially making an upward sloping glidepath useful.

This is one of the problems of using SWR analysis with fixed withdrawals and pass/fail grading (success rates) to draw conclusions about asset allocation when you are actually planning to use variable withdrawals. It's best to explicitly model your intended plan—whether fixed or variable. That will help draw conclusions appropriate for that plan.

In TPAW, because of the constant risk and full spending adjustments, SORR is eliminated prior to retirement and confined to reduced spending during the temporary crash (poor sequence of returns). There is no permanent damage to the portfolio, regardless of when the crash occurs. This is because spending at any age depends only on the cumulative returns of the portfolio up to that age. So the order of returns till that age does not matter. The intuition for this is easy to see using the "bucket view" described in Learn > Asset Allocation > Multiple Goals.

This post shows that ABW withdrawals depend only on cumulative returns and are not sensitive to the order of past returns:

Here's the ABW simulator with four columns added at the end to show how sequence of returns plays out in ABW. The last two columns in red show that the withdrawal at any age matches the total cumulative excess return (i.e. excess over expected return) up to that point. So the withdrawal at any age is only a function of total return till that age. It does not depend on the order of returns till that age.



Spreadsheet here.

This spreadsheet assumes g=0, but the result is valid for any g. We would just need to compare against the scheduled withdrawal rather than the starting withdrawal.

Once we recognize that ABW withdrawals don't depend on the sequence of portfolio returns, it's easy to see why the optimal asset allocation for the funds in any given age bucket has to be fixed: If the asset allocation is higher in year X than in some other year Y, and year X has the same impact on spending as year Y (because they both contribute to the cumulative return the same way), then the return in year X will have a bigger impact on spending for that age than the return in year Y, which can't be optimal. So the asset allocation for the funds in an age bucket should be the same for all years. Apply the same logic for spending for all age buckets, and we get a fixed asset allocation for the entire retirement portfolio.

The posts that GoWithTheCashFlow referenced above go into more detail on how this works:

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

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

Time diversification of stock risk

[Ben Mathew]

First, I want to say thank you for making the TPAW planner — I have learned a lot and gone deep as a result of digging into it. I was impressed that it effectively generated (algorithmically) the process of building up a TIPS ladder before early retirement and then spending it down before claiming SS.

Glad to hear that!

A couple requests — one perhaps easier than the other:

1) I’d love to be able to see actual samples from the Monte Carlo. The median looks nice and smooth, but I know the actual experience would have ups and downs. The amortization process should mute those to some degree, but as it stands now I can’t actually see how much year-to-year variation might be expected. Does a trajectory that ends up in the 5th percentile stay low throughout? If you start off on a low trajectory, do you bounce out of it, or stay in the low band of the results throughout? (And vice versa with high samples) More equities/risk appetite should make individual trajectories noisier, too, in addition to broadening the overall cloud of possible outcomes. I’m imagining having ten sample trajectories (in distinct colors) that span the possible outcomes, and you can even see the same colors on different graphs so you can see how the asset allocation relates to the portfolio level, etc. Thanks for considering this!

Yes, I agree that getting a sense of the behavior of individual sequences would be useful. We'll play around with some possibilities for surfacing individual sequences. We had thought about surfacing specific sequences in historical simulations, so that you can select, for example, the July 1953 to March 1981 sequence and have it be highlighted inside the percentile range. We can extend that idea to random sequences in the Monte Carlo simulations as well.

2) Have you considered some kind of retirement date flexibility in the Monte Carlo? That is, I know that if the portfolio has generally underperformed I’d probably work longer, and vice versa. This has the effect of narrowing the range of potential outcomes. It also means that I am happy with a higher risk tolerance than otherwise, because if it doesn’t pan out I know I can wait a bit longer before retiring (thereby reducing the amount of assets required and giving the market time to recover). There are papers on this (including by Merton) that back up this way of thinking — having a flexible retirement date results in higher overall lifetime utility than having a fixed one, and higher risk portions in the lifetime allocation. How would you suggest exploring this in the Planner? Or is there some cool math you can do with a “how certain are you about your retirement date” slider to actually model this?

Thanks again!

It has been on the back of my mind. Retirement date flexibility does seem important and I'd like to model it eventually. I don't think it would be too hard to allow retirement to be a range—like ages 50 to 70—rather than a fixed number and then specify a (presumably decreasing) retirement threshold by age. So something like:

- retire at age 50 if predicted retirement spending >= $50,000 per year
- retire at age 60 if predicted retirement spending >= $40,000 per year
- retire at age 70 no matter what

Thanks for these suggestions. I'll add them to the list.

[TipsQuestions]

It seems like some of the motivations for increasing risk over time might be:

Hi Ben. Thanks for your detailed reply. What you're saying is, you hold risk constant and vary withdrawals with TPAW. I get that. However some studies have shown that (given the right assumptions) an upwards glide path can be optimal: https://papers.ssrn.com/sol3/papers.cfm ... id=2324930 . Might be nice to counter or validate those ideas. Since you've already got the Decrease Risk With Age slider, it might not be too hard to make it bidirectional.

More generally, I might humbly suggest you make this tool a more general platform for retirement analysis, not one with any specific "point". Might allow for a broader user base, monetization opps...

[GoWithTheCashFlow]

However some studies have shown that (given the right assumptions) an upwards glide path can be optimal: https://papers.ssrn.com/sol3/papers.cfm ... id=2324930 . Might be nice to counter or validate those ideas. Since you've already got the Decrease Risk With Age slider, it might not be too hard to make it bidirectional.

The paper says if you're using the safe withdrawal rate method, then using a rising equity glidepath reduces the risk of ruin. So, for a given constant level of risk aversion (as expressed in the acceptable chance of ruin under this strategy), if you pre-commit to using the safe withdrawal rate method, then a rising equity glidepath allows for a higher withdrawal rate. It says nothing about a changing level of risk aversion, i.e. changing the acceptable level of the risk of ruin over time.

The important point here is that risk aversion does not equal asset allocation, particularly when using a suboptimal strategy like safe withdrawal rates.

More generally, I might humbly suggest you make this tool a more general platform for retirement analysis, not one with any specific "point". Might allow for a broader user base, monetization opps...

I'd like to offer the counter voice. On the one hand, flexibility is important to capture a wide variety of circumstances. However, I see two potential downsides to being completely general. First, simplicity, in both the ability to use and understand the tool and its outputs, will often be sacrificed for added flexibility. Second, guardrails on the options available can help me make a financial plan which is right for me, and help me avoid making one with little economic rationale. Just my two cents.

[Ben Mathew]

It seems like some of the motivations for increasing risk over time might be:

Hi Ben. Thanks for your detailed reply. What you're saying is, you hold risk constant and vary withdrawals with TPAW. I get that. However some studies have shown that (given the right assumptions) an upwards glide path can be optimal: https://papers.ssrn.com/sol3/papers.cfm ... id=2324930 . Might be nice to counter or validate those ideas. Since you've already got the Decrease Risk With Age slider, it might not be too hard to make it bidirectional.

More generally, I might humbly suggest you make this tool a more general platform for retirement analysis, not one with any specific "point". Might allow for a broader user base, monetization opps...

That study was based on fixed SWR withdrawals. The planner lets you model SWR with rising equity glidepath, after choosing Advanced -> Strategy -> SWR. It just doesn't let you enter rising risk aversion for the TPAW strategy.

A rising equity glidepath and rising risk aversion are conceptually different. A rising equity glidepath is a result. You can get rising equity in TPAW in some situations, like the examples I described earlier. But risk aversion itself is about your fundamental preferences. Risk aversion defines your preferences over spending risk, not portfolio risk. The portfolio itself is just a tool for creating spending (broadly defined to include legacy). So unless there is a case for saying that you can tolerate spending risk better as you age (holding constant wealth and other variables, as described earlier), rising risk aversion will be an option that is likely to be misinterpreted and lead people to make mistakes in their planning.

I would also broadly caution against relying on results based on SWR analysis. The lifecycle model starts with well-defined preferences and derives the optimal asset allocation and withdrawal strategy. That puts it on solid ground where the assumptions and mechanisms are clear. From there, you can consider all sorts of changes and extensions as many have done (non CRRA preferences, spending floors, retirement flexibility, longevity risk, etc.). By contrast, SWR starts with a poorly conceived strategy with no grounding in preferences, and it's hard to wrangle it conceptually onto some sort of solid ground where it's clear what's driving the results—whether it's something sensible or something reliant on assumptions like fixed withdrawals and pass/fail grading. The rising equity glidepath is driven by fixed withdrawals and pass/fail grading, and does not apply without those assumptions.

Something worth noting here is that the rising equity glidepath is actually not the optimal strategy for SWR. That would be a more complicated strategy that looks something like this:

- bet big when you are likely to fail in the hope of a small chance of success
- bet smaller when you get closer to success
- stop betting as soon as you succeed

This results in failing big when you fail, because small failures are as bad as big failures. Clearly, this is not optimal. Nobody should be doing this. And yet, that's what SWR taken seriously will lead you to. And it all starts with the fact that the objective was poorly specified at the start: "success" vs "failure"—effectively a binary utility function—instead of a continuous utility function with decreasing marginal utility of spending.

This type of optimization is described by Haghani and White under "goal-based investing" (page 98):

We'll define the [goals-based approach to wealth management] as determining an investment plan that maximizes the probability of reaching a pre-set wealth goal over a chosen horizon. [...]

We'll use a Monte Carlo simulation to figure out the optimal betting strategy for an investor who is trying to maximize the probability of reaching a modest goal of increasing wealth by 50%. The general form of the optimal betting rule is to bet more aggressively the further away the goal is from the current level of wealth, adjusted for the number of flips remaining.



In Exhibit 6.6, we show what the distribution of outcomes looks like for the goal-based strategy with a goal of growing wealth by 50%, and for the strategy of risking a constant 10% on each flip. Notice that the goal-based strategy doesn't generate any outcomes above the goal, because once you reach it, you don't take any more risk, as such risk would only serve to decrease the profitability of very bad outcomes—about a 7% chance of losing more than 50% of starting wealth. The constant fractional sizing strategy entails only about a 1% probability of such large losses.

[…] It is noteworthy that your Certainty-equivalent Wealth from the constant fractional sizing strategy is about 75% higher than that from the goal-based approach.

Within the financial planning industry, a lot of focus is on maximizing or minimizing the probabilities of various investor outcomes. We hope this brief exploration of goal-based investing will make you skeptical of any approach that is effectively concerned with just one or a few outcomes to the exclusion of all others. To reach the best decisions, we need to use an approach that assesses the whole range of possible outcomes and how likely they are to occur, which in a nutshell is exactly what Expected Utility is designed to do. As MIT economist Paul Samuelson put it: “No slave can serve two independent masters. If one is an Expected Utility maximizer, he cannot generally be a maximizer of the probability of some gain.”

SWR is presented as simple, but in reality the optimal asset allocation for SWR is far more complicated (not to mention inappropriate) than the fixed asset allocation of the lifecycle model.

[Ben Mathew]

On the one hand, flexibility is important to capture a wide variety of circumstances. However, I see two potential downsides to being completely general. First, simplicity, in both the ability to use and understand the tool and its outputs, will often be sacrificed for added flexibility. Second, guardrails on the options available can help me make a financial plan which is right for me, and help me avoid making one with little economic rationale. Just my two cents.

Yes, there is a tradeoff to be made between a general tool that can model everything and a focused tool that is easy to use correctly. My approach has been to try to provide a wider set of options while using defaults and warnings to steer people towards what I think is reasonable. SWR and historical expected returns are two examples of options that I don't think lead to good planning. I've provided them because they are widely used. But I also try to steer people towards other more reasonable settings using defaults and warnings.

For example, here are the disadvantages of SWR listed in the guide:



And on basing expected returns on historical returns vs current yields:

[Ben Mathew]

GRAPH WITH RETIREMENT FUNDING SOURCES

What about adding a fifth graph to your pulldown (currently 4 graph selections) called "Monthly Spending In Retirement, By Source" or something, and the little floating window contains individual amounts from the income sources as entered, as opposed to the full monthly spend?
In the case of the scenario I inputted, I have 5 income sources: his pension, her pension, his SS, her SS, shared portfolio. Since four of them are (mostly) known, and we are mostly solving for portfolio withdrawals, it would be nice to see that number broken out. Maybe just include the 50th percentile calculation to keep it simple.
One reason it might be nice to have the sources broken down is because, for example, his pension starts a 64, her pension starts at 60, both want to take SS at 67, and they are different ages... but maybe they are retiring at 56 or 60. Seeing how withdrawals play into the sequence might add further insight for the user.

Cool. Yeah when I use retirement software for my relatives a lot of them have different sources of guaranteed income. So it's reassuring for them to see what they have coming in and that their portfolio only has to make up the difference or they can choose to spend more.

This has been implemented. In the Monthly Spending During Retirement graph, click on the "Show funding sources" button. The breakdown of funding sources for the 50th percentile of spending outcomes is displayed on the graph. You can also switch to the 5th or 95th percentiles to see the breakdown for those outcomes.

Example:

- 65 year old retiree planning to age 95
- $1 million portfolio
- Pension of $1,500 per month starting now
- Social Security of $3,000 per month starting at age 70

Turn on the "Show funding sources" button to see the breakdown:



The pink bars show the pension, the purple bars show Social Security, and the gray bars show portfolio withdrawals.

For age 80 yr 0 mo, the graph shows that at the 50th percentile, the retiree gets $1,500 from the pension, $3,000 in Social Security, and $3,429 from portfolio withdrawals, for a total of $7,929 in spending that month.

Thanks for suggesting this feature. I think this is a really useful graph. It clarifies what's going on quite a bit!

Relocation of PDF Report

The button to generate the PDF report (for printing or saving) has been moved to the results panel inside "More" at the bottom right.

[Harry Livermore]

Looks great, Ben. Many thanks. I will try it out this afternoon!
Cheers

ETA: I had a half hour and loaded up my most recent iteration. The new features perform flawlessly on my Mac, in Chrome. I played around a bit and it's a very useful feature to visualize the effects of claiming earlier/ later, and also how effective the other income sources are in providing a "floor".
I think I'd even be happy at the fifth percentile outcome!
Anyway, thanks again for implementing this.

[Horton]

Well done, this is a nice feature!

[GP813]

Ran everything in the browser and like the changes. I think it's nice to see that big block of guaranteed income sources.

[ahc19081]

Really nice additional features!

A small bug in the PDF generation from my plan: Under "Monthly Spending in Retirement," there is a sub-heading "Funding Sources for the 5th Percentile," which is indeed what the graph below shows. However, right below the sub-heading is an explainer caption that reads, "The graph shows the 5th to 95th percentile range with the 50th percentile in bold." That is incorrect — the bold line on the graph is in fact, as the sub-heading reads, the 5th percentile.

That said, I wonder if this section really should be the 50th percentile, not the 5th, since the rest of the report consistently uses the 50th percentile.

[Ben Mathew]

Really nice additional features!

A small bug in the PDF generation from my plan: Under "Monthly Spending in Retirement," there is a sub-heading "Funding Sources for the 5th Percentile," which is indeed what the graph below shows. However, right below the sub-heading is an explainer caption that reads, "The graph shows the 5th to 95th percentile range with the 50th percentile in bold." That is incorrect — the bold line on the graph is in fact, as the sub-heading reads, the 5th percentile.

Fixed. Thanks for reporting this bug.

That said, I wonder if this section really should be the 50th percentile, not the 5th, since the rest of the report consistently uses the 50th percentile.

We thought we'd show the 5th percentile in this graph because it allows the 50th and 95th percentiles to be displayed in the background. Showing the 50th percentile would cover up the 5th. And the income streams are the same anyway for all percentiles.

[ahc19081]

Great! Yes, after posting that I realized that it makes more sense, in this case, to show the 5% scenario.

[Fairfox]

2) Have you considered some kind of retirement date flexibility in the Monte Carlo? That is, I know that if the portfolio has generally underperformed I’d probably work longer, and vice versa. This has the effect of narrowing the range of potential outcomes. It also means that I am happy with a higher risk tolerance than otherwise, because if it doesn’t pan out I know I can wait a bit longer before retiring (thereby reducing the amount of assets required and giving the market time to recover). There are papers on this (including by Merton) that back up this way of thinking — having a flexible retirement date results in higher overall lifetime utility than having a fixed one, and higher risk portions in the lifetime allocation. How would you suggest exploring this in the Planner? Or is there some cool math you can do with a “how certain are you about your retirement date” slider to actually model this?

Thanks again!

It has been on the back of my mind. Retirement date flexibility does seem important and I'd like to model it eventually. I don't think it would be too hard to allow retirement to be a range—like ages 50 to 70—rather than a fixed number and then specify a (presumably decreasing) retirement threshold by age. So something like:

- retire at age 50 if predicted retirement spending >= $50,000 per year
- retire at age 60 if predicted retirement spending >= $40,000 per year
- retire at age 70 no matter what

Thanks for these suggestions. I'll add them to the list.

I'm glad this strikes your fancy; I look forward to what you can do on this front. While some kind of decision-rule base structure sounds like a good initial step, that doesn't necessarily allow you to fully implement the lifecycle investing implications of retirement flexibility. Bodie, Merton, and Samuelson showed (https://www.nber.org/system/files/worki ... /w3954.pdf) that having a flexible retirement date allows a greater equity share for a given level of overall risk aversion. This, in turn, allows the overall lifetime utility to be higher. I definitely see this in my use of the TPAW Planner: the asset allocation that seems to make sense to me, given that I know (or think) I can work longer if I want to corresponds to an RRA value that is distinctly lower than I would have anticipated from basic "what is my RRA?"-type questions/tools. Anyway, thanks for considering this!

[Ben Mathew]

2) Have you considered some kind of retirement date flexibility in the Monte Carlo? That is, I know that if the portfolio has generally underperformed I’d probably work longer, and vice versa. This has the effect of narrowing the range of potential outcomes. It also means that I am happy with a higher risk tolerance than otherwise, because if it doesn’t pan out I know I can wait a bit longer before retiring (thereby reducing the amount of assets required and giving the market time to recover). There are papers on this (including by Merton) that back up this way of thinking — having a flexible retirement date results in higher overall lifetime utility than having a fixed one, and higher risk portions in the lifetime allocation. How would you suggest exploring this in the Planner? Or is there some cool math you can do with a “how certain are you about your retirement date” slider to actually model this?

Thanks again!

It has been on the back of my mind. Retirement date flexibility does seem important and I'd like to model it eventually. I don't think it would be too hard to allow retirement to be a range—like ages 50 to 70—rather than a fixed number and then specify a (presumably decreasing) retirement threshold by age. So something like:

- retire at age 50 if predicted retirement spending >= $50,000 per year
- retire at age 60 if predicted retirement spending >= $40,000 per year
- retire at age 70 no matter what

Thanks for these suggestions. I'll add them to the list.

I'm glad this strikes your fancy; I look forward to what you can do on this front. While some kind of decision-rule base structure sounds like a good initial step, that doesn't necessarily allow you to fully implement the lifecycle investing implications of retirement flexibility. Bodie, Merton, and Samuelson showed (https://www.nber.org/system/files/worki ... /w3954.pdf) that having a flexible retirement date allows a greater equity share for a given level of overall risk aversion. This, in turn, allows the overall lifetime utility to be higher. I definitely see this in my use of the TPAW Planner: the asset allocation that seems to make sense to me, given that I know (or think) I can work longer if I want to corresponds to an RRA value that is distinctly lower than I would have anticipated from basic "what is my RRA?"-type questions/tools. Anyway, thanks for considering this!

It won't capture the full implications of retirement flexibility, but it might be a pretty good approximation. In particular, once this is implemented, it will naturally cause you to increase your stock allocation. That's because you're choosing your risk tolerance by looking at the distribution of monthly spending displayed in the graph. Once we make retirement date a range instead of a fixed number, that spending distribution will tighten because some of the risk will be absorbed by the option to work longer. This will cause you to increase risk tolerance on the slider, and so your stock allocation will go up.

In other words, it will help you execute what you described above—increase your risk tolerance because of retirement flexibility. Without the simulation, you have to compute yourself what that flexibility will translate to for spending outcomes. Explicitly simulating the flexibility in the planner will show the impact directly in the spending graph. So that can help you decide how much more risk you can take in response.

[iim7V7IM7]

Ben, In TPAW planner is there a way to assign a fixed annual adjustment (e.g. 2, 3 or 4%) to an income stream like a SPIA? I only see nominal or adjust by CPI. I suspect that there is a way but I have missed it.

[Ben Mathew]

Ben, In TPAW planner is there a way to assign a fixed annual adjustment (e.g. 2, 3 or 4%) to an income stream like a SPIA? I only see nominal or adjust by CPI. I suspect that there is a way but I have missed it.

This is on the list, but hasn't happened yet. Likely in the next few weeks.

For now you might want to enter the income stream as constant in real dollars. If you want to be more accurate, you can split up the income stream into smaller segments and adjust the amount in each segment for the difference between the annual adjustment and the expected inflation rate.

[iim7V7IM7]

Thank you.

Ben, In TPAW planner is there a way to assign a fixed annual adjustment (e.g. 2, 3 or 4%) to an income stream like a SPIA? I only see nominal or adjust by CPI. I suspect that there is a way but I have missed it.

This is on the list, but hasn't happened yet. Likely in the next few weeks.

For now you might want to enter the income stream as constant in real dollars. If you want to be more accurate, you can split up the income stream into smaller segments and adjust the amount in each segment for the difference between the annual adjustment and the expected inflation rate.

[ivgrivchuck]

I'm playing around with the TPAW planner.

I can see that I can enter my expected future annual savings to account for my human capital.

However since all those future earnings are far from certain shouldn't they be discounted at a certain rate to the present value? Is the Planner already doing something like this? Why/why not?

Some discussion online for example here: https://www.analystforum.com/t/how-to-c ... l/116483/6

[Gufomel]

I'm playing around with the TPAW planner.

I can see that I can enter my expected future annual savings to account for my human capital.

However since all those future earnings are far from certain shouldn't they be discounted at a certain rate to the present value? Is the Planner already doing something like this? Why/why not?

Some discussion online for example here: https://www.analystforum.com/t/how-to-c ... l/116483/6

Ben will have to confirm, but I think it’s using the same bond rate that you select for investment earnings as the discount rate for human capital. Again Ben needs to confirm that, but that’s my understanding.

If that’s true, is there a way to use a higher discount rate for human capital? And if so how should we determine what that discount rate is? The link you posted factors in income volatility of 3%. How is that number determined?

[Ben Mathew]

I'm playing around with the TPAW planner.

I can see that I can enter my expected future annual savings to account for my human capital.

However since all those future earnings are far from certain shouldn't they be discounted at a certain rate to the present value? Is the Planner already doing something like this? Why/why not?

Ben will have to confirm, but I think it’s using the same bond rate that you select for investment earnings as the discount rate for human capital.

Yes, future savings are assumed to be like bonds and discounted using the bond rate.

I haven't modeled labor income risk yet, but hope to do it at some point. It's pretty far down the list though.

Risky income can be handled to some extent by entering a relatively conservative estimate of future savings.