Total Portfolio Allocation and Withdrawal (TPAW)

[Ben Mathew]

FINANCIAL PLANNING USING THE LIFECYCLE MODEL

Total Portfolio Allocation and Withdrawal (TPAW) is a financial planner that implements the lifecycle model of investing and spending from economics.

The key concepts of personal financial planning such as risk, return, consumption smoothing, and portfolio construction come from economics. The model that studies how an investor should allocate and consume out of their portfolio over their lifetime (i.e. the optimal asset allocation and withdrawal strategy) is known as the lifecycle model. A number of prominent economists, including two Nobel laureates (Paul Samuelson and Robert Merton), have contributed to its development.

Institutions like Vanguard use the lifecycle model to calculate the glide path of their target date funds. But personal financial planners and software have been slow to adopt this model, instead relying on the problematic Safe Withdrawal Rate (SWR) methodology. SWR is an ad hoc method that assumes a simplistic framework of fixed withdrawals and pass/fail grading that leads to poor guidance about asset allocation and withdrawals.

FEEDBACK FROM EXPERTS AND USE IN THE CLASSROOM

I’ve gotten feedback on TPAW Planner from two of the leading experts in the field of lifecycle finance, Professor John Y. Campbell in the economics department at Harvard University and Professor Luis Viceira in the Finance Unit at Harvard Business School. They have taken a look at the planner and approve of the rigorous approach that it takes. They see it as a welcome improvement over SWR modeling. Professor Campbell has gone on to use TPAW Planner in the personal finance class that he teaches at Harvard.

PLANNER

Online Planner (recommended for most users): tpawplanner.com

Spreadsheet Planner: "Planner with Monte Carlo Simulation" located in the TPAW wiki.

RECENT UPDATES:

8/14/2024: CAPE earnings and historical return data updated with the latest data from Shiller. post

8/4/2024: How to distinguish between the extra spending tilt and preference for the future. post

5/2/2024: Long links replaced with files. post

4/26/2024: "Dateless" plans (stable plans for examples) added to the online planner. post

4/17/2024: Expected return options "Fixed Equity Premium" and "Custom" added to the online planner. post

4/4/2024: CAPE earnings and historical return data updated with the latest data from Shiller. post

3/9/2024: How to extend variable spending/saving to the accumulation phase. post

3/5/2024: Personal finance education in college and high school

2/28/2024: Thread on VPW vs TPAW. post

2/22/2024: Return data and CAPE regressions updated in the online planner. post

1/20/2024: The Missing Billionaires: A Guide to Better Financial Decisions by Victor Haghani and James White is an excellent book on financial planning using the lifecycle model (which is what TPAW is based on). post

1/11/2024: PDF report improvements in the online planner. post

11/18/2023: Graph with retirement funding sources added to the online planner. post

11/12/2023: Why adding a ceiling doesn't improve the lower percentile outcomes much. Posts here and here

11/04/2023: Why does the recommended asset allocation change so much?

• The optimal asset allocation changes when the equity premium changes. post

• But don't rebalance too frequently. post

• Is this market timing? post

10/13/2023: Calculating the Funded Ratio using the online planner. post

9/26/2023: Turning off bond volatility + TPAW's spending tilt in the online planner. post

9/15/2023: Modeling the VPW amortization in the online planner. post

9/9/2023: Modeling the 1/N withdrawal strategy in the online planner. post

8/23/2023: Multiple plans, autosave, viewing links, plan history, and undo/redo features added to the online planner. post

6/20/2023: Balance sheet (wealth = spending) accounting added to the online planner. post

6/15/2023: Feedback from Professors John Y. Campbell and Luis Viceira. post

Summary: I’ve gotten feedback on TPAW Planner from two of the leading experts in the field of lifecycle finance, Professor John Y. Campbell at the economics department at Harvard University and Professor Luis Viceira in the Finance Unit at Harvard Business School. They have taken a look at the planner and approve of the rigorous approach that it takes. They see it as a welcome improvement over Safe Withdrawal Rate (SWR) modeling. Professor Campbell teaches a course in personal finance at Harvard and is considering offering TPAW Planner as a resource for his students.

6/13/2023: Generate a printable report in the online planner. post

4/2/2023: Calendar inputs + automatic rolling forward in the online planner. post

2/24/2023: Monthly planning + block sampling in the online planner. post

1/5/2023: New risk inputs in the online planner. post

11/5/2022: Ways to save a plan in the online planner. post

10/14/2022: Making the online planner easier to use. post

8/20/2022: TPAW vs SWR with the same expected return assumption. post

7/21/2022: Option to reduce risk at older ages in TPAW. post

7/16/2022: Safe Withdrawal Rate (SWR) strategy added to tpawplanner.com. post

7/7/2022: Simulation option using only historical sequences added to tpawplanner.com. post

7/2/2022: Reward/risk ratio added to tpawplanner.com. post

6/26/2022: Expected stock return estimates from CAPE regressions. post

6/11/2022: Savings portfolio vs total portfolio: risk as a function of market performance. post

6/1/2022: Savings portfolio vs total portfolio: risk as a function of age. post

5/28/2022: Savings portfolio strategy added to tpawplanner.com

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

12/7/2021: TPAW now has an online planner: tpawplanner.com.

More features and easier to use than the spreadsheet planners. post

10/8/2021: The withdrawal strategy derived in Merton (1969) is ABW. post

Summary: The seminal academic papers on optimal allocation and withdrawal are Samuelson (1969) and Merton (1969). They have similar models and were published as companion papers in the August 1969 issue of The Review of Economics and Statistics. I show that the optimal allocation and withdrawal strategy derived in Merton (1969) aligns with the allocation and withdrawal strategy in TPAW.

9/28/2021: Updated "Planner with Monte Carlo Simulation" and "Simulator" spreadsheets. The update fixes an error in how entries in the "extra withdrawals" column were handled. post

9/4/2021: Why calculate the present value of the pension? post

8/23/2021: Instructions on how to customize "TPAW Planner with Monte Carlo Simulation." For accumulators. For retirees.

8/20/2021: "TPAW Planner with Monte Carlo Simulation" added to the wiki. post

Summary: 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.

7/3/2021 The problem with safe withdrawal rates (SWR). post

6/16/2021: How to make retirement income more stable. post

6/12/2021: Asset allocation on the savings portfolio. post

Summary: The glidepath on the savings portfolio gets adjusted quite a bit over a lifetime. Setting a glidepath at age 25 and sticking to it would be suboptimal. The glidepath needs 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.

6/10/2021: Managing gap years without a bridge to Social Security. post

6/8/2021: Time diversification of stock risk. post

6/6/2021: Why retirement income recovers fully after a poor sequence of returns (temporary crash). post

6/4/2021: How retirement income responds to a poor sequence of returns (temporary crash). post

Summary: 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. I 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.

6/1/2021: Results of historical simulations covering 1881-2021. post

HOW IT WORKS

Following the lifecycle model, TPAW combines a "total portfolio" perspective with amortization based withdrawal (ABW) to arrive at a strategy with attractive risk/return characteristics.

The "total portfolio" refers to the fact that the present value of future savings and retirement income is counted as bonds in the portfolio. As indicated by the lifecycle model, a fixed asset allocation is maintained on this total portfolio. This translates to a downward sloping glidepath on the savings portfolio during working years. Retirement withdrawals are calculated by amortizing the total portfolio across retirement years.

The advantage of this approach is that total risk is kept consistent from year to year. This more even spreading of risk across time reduces the total risk that the retiree would need to take to achieve a given expected return (due to time diversification).

To calculate withdrawals, TPAW amortizes the portfolio as indicated by the lifecycle model. This is a variable withdrawal method that adjusts to portfolio performance, so there is no risk of running out of money before the end of retirement. The risk instead is that spending drops too low during retirement. This can be addressed by reducing portfolio risk (choosing a safer asset allocation) and/or increasing precautionary savings (reducing spending in early retirement).

USING THE ONLINE PLANNER

The planner uses simulations to show the impact of your planning choices. You can select Monte Carlo or historical simulations.

You enter a set of inputs, and the simulation results corresponding to those inputs are displayed in the graph. You then adjust the inputs until you are satisfied with the simulation results.



USING THE SPREADSHEET PLANNER

The basic process is the same as the online planner. You enter your inputs using a table like this (inputs in yellow):



And the results of the simulation are displayed in a graph like this:



Like with the online planner, you adjust your inputs until you arrive at the simulation results that you most prefer.

[Uncorrelated]

Could you explain how the withdrawal rate is calculated?

It looks like the withdrawal rate is based on maximum sustainable withdrawal, given the withdrawal growth rate and total portfolio return. This ignores the (quite important) effects of uncertainty in realized returns. I feel this calculation is based on gut feeling instead of rational utility maximization.


Additionally, it is very probable that users around age 60 to 70 will see higher certainty equivalent consumption if they annuitize most of their portfolio. With the default settings, the portfolio suggests that 44% of the liquid savings should be invested into stocks. But I feel it's more appropriate to invest all but 44% of liquid savings in annuities and hold the remainder (100% of liquid savings left after purchasing annuity) in stocks. See Floor and Upside Investing in Retirement with Nominal SPIAs for calculation details. Was this considered or is that outside the scope of this calculator?

[Rajsx]

I am following this informative & very helpful thread now & also in the coming years to refer back to.

Thanks

[Ben Mathew]

Could you explain how the withdrawal rate is calculated?

It looks like the withdrawal rate is based on maximum sustainable withdrawal, given the withdrawal growth rate and total portfolio return. This ignores the (quite important) effects of uncertainty in realized returns. I feel this calculation is based on gut feeling instead of rational utility maximization.

This strategy is consistent with rational utility maximization. To see why, it's helpful to break it down and see what's going on at a simpler level.

Suppose you had $10,000 today meant to fund consumption for when you are 75. Don't think about any other age. This money is only for age 75. And this is the only money for age 75. How would you allocate and withdraw? A good answer (consistent with utility theory) would be to invest the $10,000 at a fixed asset allocation. An advantage of the fixed allocation is that it spreads risk evenly across time. This leads to lower total risk compared to rising or falling glide paths which concentrate risk into early or later years. A more risk averse person can choose a safer fixed allocation like 20/80 and a less risk averse person can choose a risker fixed allocation like 60/40. So that's the allocation part. The withdrawal part is easy: withdraw 100% of the funds at age 75.

What is going on in the TPAW method boils down to what I described in the above paragraph. Just with a more complicated portfolio and more years that need to be funded. Let's bring in another year and see what happens:

Suppose you had $10,000 but two years to fund: age 75 and age 83. You now have an extra decision to make. How much to allocate to age 75 consumption and how much to age 83? The more you want for age 75, then less you have for age 83, and vice versa. Depending on your preferences and return expectations, let's say you decide to allocate $5,500 to age 75 and $4,500 for age 83. Same fixed allocation for both years (because same risk aversion applies to both years in simple models, but we can generalize this later.) Let's say it's 40/60. Now our portfolio has been divided into two buckets both invested at 40/60 fixed. Bucketing is bad if it leads to behavioral errors. But in this case, it's a helpful mental model to understand and build a good strategy and we'll take care not to make behavioral errors. Look at what happens to the buckets over time. Suppose the market rises 10%. Both buckets rise by the same percentage. So, unless something else has changed (your life situation, your expectations about future returns, etc.) you will not want to move money between the buckets. The AA decision for each bucket determines how that bucket responds to market performance. You have already planned for this. So age 75 funds can stay in the age 75 bucket and age 83 funds can stay in the age 83 bucket. This is a result, not a constraint. And it simplifies the problem a lot.

This means that when you're planning today for retirement from age 65 to age 100, you can actually think of it as subdividing your portfolio into different buckets for different years (and more generally, different consumption needs), picking a fixed asset allocation for each year, and letting it ride until it's consumed at the appropriate year. Of course, life situations and expectations about future returns will change and you will adjust your plans. This strategy is meant to be updated every year with new information and forward looking assumptions. But this year, we plan with the information and expectations we have this year.

To summarize: when you run this spreadsheet, you are implicitly subdividing your portfolio into separate buckets for each year of withdrawal, picking a fixed AA for each bucket, and planning to let it ride at that AA until the bucket is consumed--all of which is consistent with utility theory. Market fluctuations by themselves won't require a course correction because it's already accounted for in the plan. But changes in life situations and expected returns will require a course correction. Which is why it's important to re-run the spreadsheet and update the plan regularly.

Additionally, it is very probable that users around age 60 to 70 will see higher certainty equivalent consumption if they annuitize most of their portfolio. With the default settings, the portfolio suggests that 44% of the liquid savings should be invested into stocks. But I feel it's more appropriate to invest all but 44% of liquid savings in annuities and hold the remainder (100% of liquid savings left after purchasing annuity) in stocks. See Floor and Upside Investing in Retirement with Nominal SPIAs for calculation details. Was this considered or is that outside the scope of this calculator?

How much to annuitize remains outside the scope of this calculator.

It's important to note that I don't intend any of the inputs in the calculator to be a default settings. All inputs should come from the user. The numbers I put in are just for illustration, to help understand the spreadsheet.

[Ben Mathew]

I am following this informative & very helpful thread now & also in the coming years to refer back to.

Thanks

Thanks. Hope you find it useful!

[Steve Reading]

Very cool Ben thanks! Bookmarked.

Note that if your target stock allocation on your savings portfolio exceeds 100% and you are not able to achieve the target, the expected rate of return of the total portfolio calculated in cell C29 will not be accurate. You can either
(1) create a custom spreadsheet to handle this, or
(2) choose a lower target stock allocation for the total portfolio (cell C19) so you can achieve your target stock allocation in the savings portfolio."

Haha me thinks there’s a 3rd potential solution...

[Ben Mathew]

Very cool Ben thanks! Bookmarked.

Note that if your target stock allocation on your savings portfolio exceeds 100% and you are not able to achieve the target, the expected rate of return of the total portfolio calculated in cell C29 will not be accurate. You can either
(1) create a custom spreadsheet to handle this, or
(2) choose a lower target stock allocation for the total portfolio (cell C19) so you can achieve your target stock allocation in the savings portfolio."

Haha me thinks there’s a 3rd potential solution...

You troublemaker, you...

[Uncorrelated]

Could you explain how the withdrawal rate is calculated?

It looks like the withdrawal rate is based on maximum sustainable withdrawal, given the withdrawal growth rate and total portfolio return. This ignores the (quite important) effects of uncertainty in realized returns. I feel this calculation is based on gut feeling instead of rational utility maximization.

This strategy is consistent with rational utility maximization. To see why, it's helpful to break it down and see what's going on at a simpler level.

Thanks for the clear explanation, that was quite helpful.

But I can't help but think there is a slight error calculation error in the excel sheet. Let's use the following parameters:

n = 2
savings portfolio = 1
expected stock return = μ = 5%
expected bond return = 0%
expected stock volatility = σ = 10%
constant relative risk aversion = γ = 10
This brings us to an stock allocation of 50% = μ / (γ * σ²) = (5% / (10 * 10%²)). The portfolio expected return is 2.5%, and the certainty equivalent return of the portfolio is 1.25% = μ - .5 * γ * σ² = (2.5% - .5 * 10 * 5%²).

In the first year, the expected withdrawal according to the workbook is $0.50617, in the second year, the certainty equivalent withdrawal is (1 - $0.50617) multiplied by the certainty equivalent return, which is $0.50000. The total utility (isoelastic utility) is -107.607.

But, if we withdrawal $0.50311 the first year, then the certainty equivalent withdrawal in the second year will be (1 - $0.50311) multiplied by the certainty equivalent return, which is $0.50310, almost the same as in the first year! The total utility is slightly higher at -107.388. This withdrawal amount was calculated by substituting the rate of return (r) by the certainty equivalent return of the portfolio. It looks like this is still not the optimal withdrawal amount, but it's fairly close. This may be because I'm using an approximation of the certainty equivalent return, or because of rounding errors.


I'm not 100% sure on the math, but I'm fairly sure using the portfolio expected return in the sheet is an error. Substituting the portfolio expected return (r) by the certainty equivalent return seems to result in something that agrees with utility theory (to the extent that the retiree has a CRRA utility function).

[Ben Mathew]

In the first year, the expected withdrawal according to the workbook is $0.50617
...
But, if we withdrawal $0.50311 the first year ... The total utility is slightly higher at -107.388.

I haven't fully worked through the example you gave. But based on what you said the above, I think the issue might be that you are not adjusting the input "g" (growth rate of withdrawal, cell C14) to get to the optimal withdrawal.

The calculator does not know how much to allocate between year 1 and year 2. That depends on the user's preferences, so that's an input. The way you control that in the spreadsheet is through g, the growth rate of withdrawals. Increasing g will allocate less to early years and more to later years. So based on the numbers you gave above, it looks like you will need to increase g (withdraw less in the first year and more in the second year) to get to the optimal consumption.

I don't expect that most users will use the spreadsheet in quite this way--i.e. find the analytical solution and then find the g that matches that. The goal is to have them pick g directly. Eventually I plan to introduce confidence intervals for expected consumption, so people can choose g based on the distribution of consumption that it implies. i.e. Input different values for g and choose the one they like the best.

[AlohaJoe]

Nice work Ben. I always love seeing more retirement solutions that include the reality of things like eventually receiving Social Security, downsizing a family home from a 5-bedroom place with a 2-acre lawn, and so on. I've always felt that part of the big appeal for Bernstein's "Liability Matching Portfolio" with its TIPS ladder is that it is basically the only actual explanation of how to handle the eventual arrival of Social Security income that most Bogleheads have ever seen.

It's hard not to feel that the Bogleheads answer of how to deal with things like home equity and pensions is to just be rich enough that it doesn't matter what choices you make so it is nice to see more efforts that directly tackle the problems instead of handwaving them.

[Ben Mathew]

Nice work Ben. I always love seeing more retirement solutions that include the reality of things like eventually receiving Social Security, downsizing a family home from a 5-bedroom place with a 2-acre lawn, and so on. I've always felt that part of the big appeal for Bernstein's "Liability Matching Portfolio" with its TIPS ladder is that it is basically the only actual explanation of how to handle the eventual arrival of Social Security income that most Bogleheads have ever seen.

It's hard not to feel that the Bogleheads answer of how to deal with things like home equity and pensions is to just be rich enough that it doesn't matter what choices you make so it is nice to see more efforts that directly tackle the problems instead of handwaving them.

Thanks, AlohaJoe. Yes, I feel it's important to have options when it comes to dealing with lumpy income/expense cash flows. Those who want an LMP can still do so. They can enter the LMP in the "extra expenses" column if they want to manage it within the spreadsheet. But those who don't need that level of foolproof consumption can forgo it. They can still manage their risk with the total portfolio approach without having to even out all the gaps in the income/expense flows with bonds.

More options are also possible. You could have different categories of expenses invested at different AA reflecting its own risk/reward considerations. For example, funds for food and housing could be invested at a safer AA--need that regardless of how well stocks do. But the vacation fund could go in at a risky AA--plan to go on a big vacation if stocks to well and stay home if it does badly. The current spreadsheet doesn't support this this. It's a single AA for general expenses and 100/0 for the extra expenses. But this can be changed to allow for multiple categories of consumption with different AA.

[gordoni2]

For most retirees guaranteed income in the form of Social Security is their largest retirement asset. It is thus vitally important to consider the total portfolio (not just retirement savings) in making asset allocation and consumption decisions. TPAW thus sounds like a step in the right direction.

However it is only a step:

This strategy is consistent with rational utility maximization.

...

I think the issue might be that you are not adjusting the input "g" (growth rate of withdrawal, cell C14) to get to the optimal withdrawal.

The first problem I see is that the optimal growth rate to use might vary from one year to the next depending on the number of years remaining, and the relative size of the portfolio components.

To compute the correct values of g to use at each point to maximize utility you would have to resort to dynamic programming. But then TPAW wouldn't be adding any value as dynamic programming is already known to be capable of solving the portfolio problem.

The second problem is life expectancy is a stochastic variable. Rational utility maximization would treat it as such. If there is a 80% chance of living to age 80, and a 10% chance of living to age 100, the outcomes for the different ages should be weighted accordingly when constructing the utility maximization problem.

Don't take these criticisms too harshly. VPW, ABW, TPAW, and so on, are all rough attempts at solving the portfolio problem, and TPAW sounds like a one of the better attempts. What is missed though is the portfolio problem was solved exactly by Merton 50 years ago in a restricted form, using dynamic programming just as long ago in a slightly less restrictive form, and the fully general problem can now be solved somewhat approximately using reinforcement learning.

[Uncorrelated]

In the first year, the expected withdrawal according to the workbook is $0.50617
...
But, if we withdrawal $0.50311 the first year ... The total utility is slightly higher at -107.388.

I haven't fully worked through the example you gave. But based on what you said the above, I think the issue might be that you are not adjusting the input "g" (growth rate of withdrawal, cell C14) to get to the optimal withdrawal.

I set the withdrawal growth (g) to zero. But the problem is that the sheet doesn't succeed in calculating the correct withdrawal amount that would result in the withdrawal amount being exactly (certainty-equivalent) equal in the first two years. With the withdrawal growth rate set to zero, the (certainty equivalent) withdrawal in the first year is ~1.25% greater than the withdrawal in the second year.

The rate of return (r) should not be an input to the calculation, the certainty equivalent return should be used instead. I'm not sure if doing so will result in the actual optimal solution for longer time horizons, but it will be closer to the optimal solution.

[dknightd]

Not sure if I should post this here or in the ABW thread.

Will do it here since one comment is specific to the example spreadsheet.
I think there is an error in the way C39, "Net withdrawal from savings portfolio", is calculated.
This is easily fixed by subtracting "Extra income", and adding "Extra expenses", to "Withdrawal for general expenses". (just a matter of moving minus sign from expenses to income)

The more general comment is about how risk management is handled by the Total portfolio approach. For a retiree like me, which I'll attempt to explain below, this approach front loads my risk too much.
For me, my "Savings portfolio" does two things. 1) carries me over till "Extra income" kicks in (in my case mostly SS), and 2) provides discretionary spending for life. I have arranged things so that once I claim SS at 70 all our base expenses (including a small amount of what could be considered discretionary) are covered by SS, small pension, and SPIA. If I followed the Total portfolio method, and rebalanced as suggested, my savings portfolio would be about 100% in stocks. I consider that WAY too risky. A very bad sequence of return might mean I could not wait till 70 to claim SS. That would throw all my planning off.

Apparently my "utility function of money" (which I've yet to be able to express as a simple function) does not match what is used by the "total portfolio" approach. Which is fine. I've taken the suggestion and have a spreadsheet that I think will work for me. Based on similar NPV/PMT calculations.

One good thing about all these methods is you have to revisit and recalculate occasionally. So if my estimates about returns, or inflation, are wrong, they will slowly correct.

I just can't bring myself to be 100% in stocks in my actual savings portfolio. It might help protect against risk in the long term, but in the short term it could ruin me.

[siamond]

I considered a similar approach in the past, but then ruled it out as the prospect of a variable AA for the regular (savings) portfolio didn't appeal to me. Notably when such variability is a function of future and somewhat uncertain events.

Also other future cash flows come with more uncertainties than Social Security (e.g. house downsizing, inheritance) and I was looking for a fully general-purpose solution. Even SS future benefits can actually vary depending on life events (I ended up retiring earlier than planned, completely stopped working, then a surprise opportunity actually led me to work part-time in a lucrative manner for some of my early retirement).

I do understand the intellectual appeal of such approach though and am genuinely curious to see discussions about it. John Bogle himself was a proponent of taking SS/Pensions in account when establishing one's (regular) AA, although he clearly didn't mean it in the same mathematical way as TPAW.

[Ben Mathew]

The first problem I see is that the optimal growth rate to use might vary from one year to the next depending on the number of years remaining, and the relative size of the portfolio components.

Are you saying that g might need to be updated in future years based on new information?

Or are you saying that in the current year, a user might want to use a varying g to achieve the optimal solution (given current information and expectations)?

If the former, I agree. If the latter, then know there will be another version of the spreadsheet that allows for a more flexible withdrawal profile using consumption weights instead of a constant g. A spreadsheet showing such an amortization is here: ABW calculator with custom withdrawal profile.

Either way, I think you'll agree that introducing the option of a non-zero g is an improvement over methods that assume that g=0.

To compute the correct values of g to use at each point to maximize utility you would have to resort to dynamic programming.

I don't think of this spreadsheet as trying to compute g from other inputs such as time preference and risk aversion. While that is a common approach, my problem with it is that most people don't know what their number is for risk aversion and time preference or have a good feel for what it means. Instead, why not ask them something further downstream, something they can understand a little more easily -- AA and g? By varying AA and g and seeing the impact on the distribution of consumption (eventually I'll add confidence intervals so they can see this properly), they settle on something they like. No unreliable surveys like how do you feel about crossing the road and so on. They just get right down to planning and pick a plan they like by varying AA and g. They are implicitly stating risk and time preferences by doing that, but through planning concepts that are easier to wrap one's head around.

The second problem is life expectancy is a stochastic variable. Rational utility maximization would treat it as such. If there is a 80% chance of living to age 80, and a 10% chance of living to age 100, the outcomes for the different ages should be weighted accordingly when constructing the utility maximization problem.

I haven't done anything with life expectancy yet. Would like to at some point.

Don't take these criticisms too harshly. VPW, ABW, TPAW, and so on, are all rough attempts at solving the portfolio problem, and TPAW sounds like a one of the better attempts. What is missed though is the portfolio problem was solved exactly by Merton 50 years ago in a restricted form, using dynamic programming just as long ago in a slightly less restrictive form, and the fully general problem can now be solved somewhat approximately using reinforcement learning.

There will always be more sophisticated approaches. My goal is to try to help a few people improve on their current practice, not find the perfect solution.

[Ben Mathew]

In the first year, the expected withdrawal according to the workbook is $0.50617
...
But, if we withdrawal $0.50311 the first year ... The total utility is slightly higher at -107.388.

I haven't fully worked through the example you gave. But based on what you said the above, I think the issue might be that you are not adjusting the input "g" (growth rate of withdrawal, cell C14) to get to the optimal withdrawal.

I set the withdrawal growth (g) to zero. But the problem is that the sheet doesn't succeed in calculating the correct withdrawal amount that would result in the withdrawal amount being exactly (certainty-equivalent) equal in the first two years. With the withdrawal growth rate set to zero, the (certainty equivalent) withdrawal in the first year is ~1.25% greater than the withdrawal in the second year.

If you set g=0, you're scheduling a flat withdrawal schedule. That means that if realized return equals expected return, then second year withdrawal will equal the first year withdrawal. First year consumption is risk-free. Second year consumption is risky. So utility of second year consumption will be lower than utility of first year consumption, so its certainty equivalent is lower.

You will need to set g>0 if you want to set utility of second year=utility of first year.

[Ben Mathew]

I think there is an error in the way C39, "Net withdrawal from savings portfolio", is calculated.
This is easily fixed by subtracting "Extra income", and adding "Extra expenses", to "Withdrawal for general expenses". (just a matter of moving minus sign from expenses to income)

Fixed. Thanks!

The more general comment is about how risk management is handled by the Total portfolio approach. For a retiree like me, which I'll attempt to explain below, this approach front loads my risk too much.
For me, my "Savings portfolio" does two things. 1) carries me over till "Extra income" kicks in (in my case mostly SS), and 2) provides discretionary spending for life. I have arranged things so that once I claim SS at 70 all our base expenses (including a small amount of what could be considered discretionary) are covered by SS, small pension, and SPIA. If I followed the Total portfolio method, and rebalanced as suggested, my savings portfolio would be about 100% in stocks. I consider that WAY too risky. A very bad sequence of return might mean I could not wait till 70 to claim SS. That would throw all my planning off.

Apparently my "utility function of money" (which I've yet to be able to express as a simple function) does not match what is used by the "total portfolio" approach. Which is fine. I've taken the suggestion and have a spreadsheet that I think will work for me. Based on similar NPV/PMT calculations.

One good thing about all these methods is you have to revisit and recalculate occasionally. So if my estimates about returns, or inflation, are wrong, they will slowly correct.

I just can't bring myself to be 100% in stocks in my actual savings portfolio. It might help protect against risk in the long term, but in the short term it could ruin me.

There is a simple solution to this: Enter a safer AA for the total portfolio (cell C21).

The total portfolio approach does not make any assumptions about your risk tolerance. You control that completely via your input in cell C21. What it does is keep your chosen risk level consistent from year to year. That will effectively reduce the total risk you face over the course of your retirement (for any given expected return).

Finding the right AA will become easier once I add confidence intervals to the scheduled withdrawals. Then you can directly see the implications for consumption risk as you try to find an AA that works for you.

[dknightd]

I'm starting to think I should enter 0 for everything. Except current balance, and future income. Then adjust as needed if investments do better than inflation. Thoughts.

[Ben Mathew]

I'm starting to think I should enter 0 for everything. Except current balance, and future income. Then adjust as needed if investments do better than inflation. Thoughts.

That would be a mix of conservative and not-so-conservative assumptions. Entering 0% would be conservative for stock returns, but not for bond returns and withdrawal growth rate (g).

To be consistently conservative, you can enter

- higher years of withdrawals (n)
- higher terminal balance (B)
- higher withdrawal growth rate (g)
- lower expected stock return
- lower expected bond return
- lower target AA for total portfolio
- lower extra income (column H)
- higher extra expenses (column I)

Tilt conservative along all these dimensions. Combine with regular course corrections from annual updates, and you should be in good shape.

[retiringwhen]

The Google Sheets link in the OP appears to be broken (it says the file is in the owner's trash). Can others see the file? TIA.

Fixed, thanks! (and its an Excel file not Google Sheets )

[Ben Mathew]

The Google Sheets link in the OP appears to be broken (it says the file is in the owner's trash). Can others see the file? TIA.

Fixed. Thanks.

[Uncorrelated]

In the first year, the expected withdrawal according to the workbook is $0.50617
...
But, if we withdrawal $0.50311 the first year ... The total utility is slightly higher at -107.388.

I haven't fully worked through the example you gave. But based on what you said the above, I think the issue might be that you are not adjusting the input "g" (growth rate of withdrawal, cell C14) to get to the optimal withdrawal.

I set the withdrawal growth (g) to zero. But the problem is that the sheet doesn't succeed in calculating the correct withdrawal amount that would result in the withdrawal amount being exactly (certainty-equivalent) equal in the first two years. With the withdrawal growth rate set to zero, the (certainty equivalent) withdrawal in the first year is ~1.25% greater than the withdrawal in the second year.

If you set g=0, you're scheduling a flat withdrawal schedule. That means that if realized return equals expected return, then second year withdrawal will equal the first year withdrawal. First year consumption is risk-free. Second year consumption is risky. So utility of second year consumption will be lower than utility of first year consumption, so its certainty equivalent is lower.

You will need to set g>0 if you want to set utility of second year=utility of first year.

So, to summarize:
If the user selects a withdrawal growth rate of 0%, this does not correspond to a merton's portfolio model discount rate of 0%.
If the user changes the asset allocation to something else with the same certainty equivalent return, but a different expected return, this implicitly changes the discount rate.
Can you confirm that this is the intended behavior? I would describe this behavior as quite surprising and not exactly consistent with utility theory.

[Ben Mathew]

In the first year, the expected withdrawal according to the workbook is $0.50617
...
But, if we withdrawal $0.50311 the first year ... The total utility is slightly higher at -107.388.

I haven't fully worked through the example you gave. But based on what you said the above, I think the issue might be that you are not adjusting the input "g" (growth rate of withdrawal, cell C14) to get to the optimal withdrawal.

I set the withdrawal growth (g) to zero. But the problem is that the sheet doesn't succeed in calculating the correct withdrawal amount that would result in the withdrawal amount being exactly (certainty-equivalent) equal in the first two years. With the withdrawal growth rate set to zero, the (certainty equivalent) withdrawal in the first year is ~1.25% greater than the withdrawal in the second year.

If you set g=0, you're scheduling a flat withdrawal schedule. That means that if realized return equals expected return, then second year withdrawal will equal the first year withdrawal. First year consumption is risk-free. Second year consumption is risky. So utility of second year consumption will be lower than utility of first year consumption, so its certainty equivalent is lower.

You will need to set g>0 if you want to set utility of second year=utility of first year.

So, to summarize:
If the user selects a withdrawal growth rate of 0%, this does not correspond to a merton's portfolio model discount rate of 0%.
If the user changes the asset allocation to something else with the same certainty equivalent return, but a different expected return, this implicitly changes the discount rate.
Can you confirm that this is the intended behavior? I would describe this behavior as quite surprising and not exactly consistent with utility theory.

That is correct. But it is consistent with utility theory. Think of this as a slider which the user can move up and down. What you are talking about is what units should be marked on the slider. The slider is still the same. As you move the slider up, it allocates more to the future and less to the present.

It looks like you want the units on the slider to be such that when the slider is set to 0, you get equal "certainty equivalent" consumption across years.

I instead used units of scheduled consumption (consumption if realized return equals expected return). So when the slider is set to 0, you get equal scheduled consumption across years.

But the unit used on the slider does not matter. Either way, as you move the slider up, it allocates more to the future and less to the present. What matters is that you see the implications of the position of the slider on the distribution of consumption (eventually I'll add confidence intervals so this can be seen), and then pick the position on the slider that you like (that match your preferences).

Think of this spreadsheet as helping people find their spot on the slider. They don't come to the spreadsheet knowing it. They move the slider up and down and find it. The units on the slider don't matter except as a way to communicate to the user that up means more tomorrow and less today. I chose scheduled consumption as the unit because it's what people are used to and I think they can understand it more easily. I will also include a version eventually which uses consumption weights instead of g to allocate consumption across years. Just another way for people to say I want more here and less there and feel their way towards a plan that works for them (i.e. matches their preferences).

[Horton]

I ask this question in sincerity: who is this approach for? The beauty of VPW is that it’s “so easy a caveman can do it.” In addition, longinvest spends most of his time focusing on the practical aspects of VPW. Seems like this discussion is more theoretical than practical. Perhaps this is “development” and the “production” thread will be more practical?

Edit: I retract my original critique. The online planner is very intuitive and informative. Job well done!

[Ben Mathew]

I ask this question in sincerity: who is this approach for? The beauty of VPW is that it’s “so easy a caveman can do it.” In addition, longinvest spends most of his time focusing on the practical aspects of VPW. Seems like this discussion is more theoretical than practical. Perhaps this is “development” and the “production” thread will be more practical?

The spreadsheet itself should be pretty easy to use. The theoretical discussion we are having at the moment is not really necessary for someone who trusts that it all works and just wants to use it. The problem of course is how can someone trust whether this approach or any other is sensible? Ideally, they would spend some time and effort figuring out whether the approach they are taking--whether it's the 4% rule, VPW, TPAW, or anything else--makes sense. And that can be difficult. People often rely on backtesting to evaluate a strategy. Backtesting is useful as part of the process. But relying on it alone leads to overfitted strategies. So it's always useful to check whether an approach also makes sense from a theoretical perspective.

I'm also happy to discuss any practical issues that come up.

[2pedals]

Thank you Ben, nicely done I love it. I especially love the ability to add annual lumpy expenses.

[Ben Mathew]

Thank you Ben, nicely done I love it. I especially love the ability to add annual lumpy expenses.

Thanks for the feedback, 2pedals. Glad to hear you liked it.

[Ben Mathew]

I have added two new functionalities to the spreadsheet:

1. EXTRA DISCRETIONARY WITHDRAWALS FUNDED BY RISKY PORTFOLIO

In the original spreadsheet, lumpy expenses were financed solely by 100% bonds. But lumpy expenses need not always be essential, requiring the safety of 100% bonds. It could be discretionary, like travel expenses in early retirement. You can plan to travel more if stocks do well, and less if they do badly. In return for taking that risk, you get a higher expected travel budget.

So I put in a new column where you can enter extra discretionary withdrawals (column L). These lumpy expenses are funded by the risky portfolio (i.e. total portfolio), just like the regular amortized withdrawals. With the addition of this extra withdrawal column, you have full flexibility over the shape of the withdrawal schedule.

I removed the terminal balance option because the same thing can be achieved by entering an extra withdrawal at age 100.

2. ADD RISKY BONDS

Previously, the AA was defined over stocks and safe bonds. Now it's defined over stocks, risky bonds, and safe bonds. This will allow people using risky bond funds to enter a separate expected return for risky bonds.

[corn18]

I really like TPAW. It makes sense to me and adds another layer of analysis. Thanks!

I just ran my data through the spreadsheet and it was interesting. If I put all of my base expenses in as essential and put in my current planned blow that dough money (travel) in the non essential column, the output exactly matches what firecalc says is a 99% probability of success. But if I only put my mortgage and taxes in the essential column and new car(s) and blow that dough in the non-essential column, it spits out a withdrawal rate that is much greater than the remaining planned expenses. I assume this is because the regular withdrawal assumes pulling that from the portfolio while maintaining the AA? If so, that more closely matches what I think the most likely scenario is for my plan. I would love to use the TPAW recommended withdrawal rate. It is much more generous.

[1210sda]

Is TPAW basically the same as ABW but with some enhancements?

[Ben Mathew]

I really like TPAW. It makes sense to me and adds another layer of analysis. Thanks!

I just ran my data through the spreadsheet and it was interesting. If I put all of my base expenses in as essential and put in my current planned blow that dough money (travel) in the non essential column, the output exactly matches what firecalc says is a 99% probability of success. But if I only put my mortgage and taxes in the essential column and new car(s) and blow that dough in the non-essential column, it spits out a withdrawal rate that is much greater than the remaining planned expenses. I assume this is because the regular withdrawal assumes pulling that from the portfolio while maintaining the AA? If so, that more closely matches what I think the most likely scenario is for my plan. I would love to use the TPAW recommended withdrawal rate. It is much more generous.

Yes, as you move planned expenses from the essential to the discretionary withdrawal category, you get more in expected terms because it's being funded by a faster growing (but riskier) risk portfolio. That of course also means that the future high withdrawals you are scheduling are subject to market performance. You'll get what you'lve scheduled if the market meets expectations. You'll get more if it does better, and less if it does worse. You can adjust how sensitive your withdrawals are to market performance by adjusting the AA in cells C24-26. You might also want to consider setting withdrawal growth rate g > 0. Because future withdrawals funded by the risky portfolio are not guaranteed, you might want a cushion for them. g>0 provides that cushion. Even if the market does poorly, you won't do too badly because you scheduled a generous withdrawal to begin with.

[Ben Mathew]

Is TPAW basically the same as ABW but with some enhancements?

Yes. It is ABW combined with a "total portfolio" approach to handling extra future income (like pensions and social security) and extra expenses (both "essential expenses" like remaining mortgage payments and "discretionary expenses" like additional travel in early retirement years).

[corn18]

I really like TPAW. It makes sense to me and adds another layer of analysis. Thanks!

I just ran my data through the spreadsheet and it was interesting. If I put all of my base expenses in as essential and put in my current planned blow that dough money (travel) in the non essential column, the output exactly matches what firecalc says is a 99% probability of success. But if I only put my mortgage and taxes in the essential column and new car(s) and blow that dough in the non-essential column, it spits out a withdrawal rate that is much greater than the remaining planned expenses. I assume this is because the regular withdrawal assumes pulling that from the portfolio while maintaining the AA? If so, that more closely matches what I think the most likely scenario is for my plan. I would love to use the TPAW recommended withdrawal rate. It is much more generous.

Yes, as you move planned expenses from the essential to the discretionary withdrawal category, you get more in expected terms because it's being funded by a faster growing (but riskier) risk portfolio. That of course also means that future high withdrawals that you are scheduling is subject to market performance. You can adjust how sensitive it is to market performance by adjusting the AA in cells C24-26. You might also want to consider setting withdrawal growth rate g > 0. Because future withdrawals funded by the risky portfolio are not guaranteed, you might want a cushion for them. g>0 provides that cushion. Even if the market does poorly, you won't do too badly because you scheduled a generous withdrawal to begin with.

Thanks Ben! Your model really resonates with how I think about spending. It is interesting to move expenses between essential and non essential. Really makes a difference in what you can withdraw. Your model really works well for my situation because I have a COLA military pension and SS. So I can model them perfectly by year. Since my base expenses are $118k and my pension + SS @ 70 is $110k, I'm feeling pretty safe after 70. I really want to be able to spend a lot of blow that dough money between 55 and 70 without going broke. I can't really use the 4% rule. Your model is really good for this.

TPAW rocks!

[Ben Mathew]

I really like TPAW. It makes sense to me and adds another layer of analysis. Thanks!

I just ran my data through the spreadsheet and it was interesting. If I put all of my base expenses in as essential and put in my current planned blow that dough money (travel) in the non essential column, the output exactly matches what firecalc says is a 99% probability of success. But if I only put my mortgage and taxes in the essential column and new car(s) and blow that dough in the non-essential column, it spits out a withdrawal rate that is much greater than the remaining planned expenses. I assume this is because the regular withdrawal assumes pulling that from the portfolio while maintaining the AA? If so, that more closely matches what I think the most likely scenario is for my plan. I would love to use the TPAW recommended withdrawal rate. It is much more generous.

Yes, as you move planned expenses from the essential to the discretionary withdrawal category, you get more in expected terms because it's being funded by a faster growing (but riskier) risk portfolio. That of course also means that future high withdrawals that you are scheduling is subject to market performance. You can adjust how sensitive it is to market performance by adjusting the AA in cells C24-26. You might also want to consider setting withdrawal growth rate g > 0. Because future withdrawals funded by the risky portfolio are not guaranteed, you might want a cushion for them. g>0 provides that cushion. Even if the market does poorly, you won't do too badly because you scheduled a generous withdrawal to begin with.

Thanks Ben! Your model really resonates with how I think about spending. It is interesting to move expenses between essential and non essential. Really makes a difference in what you can withdraw. Your model really works well for my situation because I have a COLA military pension and SS. So I can model them perfectly by year. Since my base expenses are $118k and my pension + SS @ 70 is $110k, I'm feeling pretty safe after 70. I really want to be able to spend a lot of blow that dough money between 55 and 70 without going broke. I can't really use the 4% rule. Your model is really good for this.

TPAW rocks!

Thanks, corn18! Glad to hear the spreadsheet is working well for you.

I will eventually add confidence intervals to the withdrawals so you can see the distribution around scheduled withdrawals. Withdrawals will look more like:

Age 65: $50,000
Age 66: $52,000 +- $3,000
Age 67: $54,000 +- $5,000
...
Age 100: $68,000 +- $25,000

That will enable the user to see the risk directly, and decide on an AA that suits their needs more easily.

[corn18]

I really like TPAW. It makes sense to me and adds another layer of analysis. Thanks!

I just ran my data through the spreadsheet and it was interesting. If I put all of my base expenses in as essential and put in my current planned blow that dough money (travel) in the non essential column, the output exactly matches what firecalc says is a 99% probability of success. But if I only put my mortgage and taxes in the essential column and new car(s) and blow that dough in the non-essential column, it spits out a withdrawal rate that is much greater than the remaining planned expenses. I assume this is because the regular withdrawal assumes pulling that from the portfolio while maintaining the AA? If so, that more closely matches what I think the most likely scenario is for my plan. I would love to use the TPAW recommended withdrawal rate. It is much more generous.

Yes, as you move planned expenses from the essential to the discretionary withdrawal category, you get more in expected terms because it's being funded by a faster growing (but riskier) risk portfolio. That of course also means that future high withdrawals that you are scheduling is subject to market performance. You can adjust how sensitive it is to market performance by adjusting the AA in cells C24-26. You might also want to consider setting withdrawal growth rate g > 0. Because future withdrawals funded by the risky portfolio are not guaranteed, you might want a cushion for them. g>0 provides that cushion. Even if the market does poorly, you won't do too badly because you scheduled a generous withdrawal to begin with.

Thanks Ben! Your model really resonates with how I think about spending. It is interesting to move expenses between essential and non essential. Really makes a difference in what you can withdraw. Your model really works well for my situation because I have a COLA military pension and SS. So I can model them perfectly by year. Since my base expenses are $118k and my pension + SS @ 70 is $110k, I'm feeling pretty safe after 70. I really want to be able to spend a lot of blow that dough money between 55 and 70 without going broke. I can't really use the 4% rule. Your model is really good for this.

TPAW rocks!

Thanks, corn18! Glad to hear the spreadsheet is working well for you.

I will eventually add confidence intervals to the withdrawals so you can see the distribution around scheduled withdrawals. Withdrawals will look more like:

Age 65: $50,000
Age 66: $52,000 +- $3,000
Age 67: $54,000 +- $5,000
...
Age 100: $68,000 +- $25,000

That will enable the user to see the risk directly, and decide on an AA that suits their needs more easily.

That would be a cool feature. Although it might scare me.

I just imported the calculation sheet into my mega spreadsheet and it still works! So many times I cannot do this due to weird functions or referencing. Now I am really happy.

[corn18]

Ben, been playing around a lot with the TPAW spreadsheet. Question: What would you define as Extra Essential Expenses vs. Extra Withdrawal? Right now, I am putting all of my base expenses into Extra Essential Withdrawals (this includes base budget + taxes + cars + mortgage). I leave the Extra Withdrawal blank. Then I use the Regular Withdrawal as the amount I can spend above the Extra Essential Expenses.

But this seems overly conservative because this results in nearly all my expenses coming out of safe bonds. That is not my intent during retirement. I plan to use my total portfolio to fund all my expenses. No buckets.

The reason I am asking is the difference in how I categorize expenses is quite large.

1. No extra essential expenses or extra withdrawals yields a regular withdrawal of $200k. Since my base expenses are $121k, that leaves $79k a year extra. Yeah!

2. If I put all my base expenses in the Extra Essential Expenses category ($121k) and nothing in extra withdrawal, the regular withdrawal is $22k. Much less than $79k.

Could you please help me understand the large variation in these numbers? And what should I be putting in each spending category?

[Ben Mathew]

Ben, been playing around a lot with the TPAW spreadsheet. Question: What would you define as Extra Essential Expenses vs. Extra Withdrawal? Right now, I am putting all of my base expenses into Extra Essential Withdrawals (this includes base budget + taxes + cars + mortgage). I leave the Extra Withdrawal blank. Then I use the Regular Withdrawal as the amount I can spend above the Extra Essential Expenses.

But this seems overly conservative because this results in nearly all my expenses coming out of safe bonds. That is not my intent during retirement. I plan to use my total portfolio to fund all my expenses. No buckets.

The reason I am asking is the difference in how I categorize expenses is quite large.

1. No extra essential expenses or extra withdrawals yields a regular withdrawal of $200k. Since my base expenses are $121k, that leaves $79k a year extra. Yeah!

2. If I put all my base expenses in the Extra Essential Expenses category ($121k) and nothing in extra withdrawal, the regular withdrawal is $22k. Much less than $79k.

Could you please help me understand the large variation in these numbers? And what should I be putting in each spending category?

The difference in withdrawals comes from the difference in expected returns between bonds and the risk portfolio. More essential expenses funded with 100% bonds will lead to lower withdrawals because of the low returns of bonds. Funding with the risk portfolio will get you higher expected withdrawals because the risk portfolio is expected to grow faster, but of course the actual withdrawal will depend on the performance of the market.

There are two ways to get a safer portfolio:

(1) Schedule more expenses as essential--so a larger safe portfolio.
(2) Choose a safer AA for the risk portfolio

The first type of safety (large safe portfolio) meets the needs of people who really need a certain amount, say $40,000 per year, and will be very unhappy with less. They are willing to give up the upside of stocks to protect this floor. But above that floor of $40,000, they are willing to take on risks. Formally, this is infinite risk aversion below the floor. i.e. They are not willing to take even attractive bets with high expected return if it risks landing them below the floor. But above the floor, the risk aversion turns finite and they become willing to gamble.

Funding the floor with 100% bonds will be very expensive, which is what you are seeing in the spreadsheet. For some people, it may be worth it. People following Bill Bernstein's liability matched portfolio (LMP) strategy are saying that the cost of creating a floor is worth it to them. To help you figure out if it is worth it to you, you can ask yourself the following question:

If you have just enough to fund $X per year for sure, would you invest it in 100% bonds to guarantee that you can withdraw $X per year? Or would you still invest 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 at $X per year. You can do this by entering $X per year in the extra expense column. On the other hand, if your preference is to continue investing in stocks even at low wealth levels, then the second form of safety (safer AA on the risk portfolio) may be more up your alley. Of course, you can do a combination. The goal is to finding the combination that feels right to you (matches your preferences).

If you think you'd like to make the same percentage bets (invest at the same AA) at low wealth levels, then it's perfectly fine to not have a safe portfolio at all--i.e. enter zeros in the essential expense column. In fact, the basic models in finance assume exactly this--that you keep making the same percentage bets (same AA) regardless of your wealth.

So I would start by asking whether the amount you're considering scheduling as essential expenses (base budget + taxes + cars + mortgage) is really "essential" to you. If you had just enough wealth to fund these essential expenses risk free with 100% bonds, would you go with 100% bonds in order to not jeopardize these funds? Or would you still invest something in stocks and take the risk in order to get higher expected withdrawals?

[corn18]

Ben, thanks for the great explanation. That makes sense.

For me, I am 60/40 and plan to stay that way forever. Since my COLA pension + SS @ 70 covers all my expenses, I don't mind taking some risk between 55 and 70. Funding a bridge from 55-70 with a SPIA (or 100% safe bonds) is certainly tempting, but not my style. I will use the TPAW output to bounce off my myriad other outputs.

[Ben Mathew]

UPDATE Jan 7, 2021:

Updated the spreadsheet as follows:

(1) The spreadsheet better shows the accounting:

WEALTH (savings portfolio + future income) = SPENDING (withdrawals from safe portfolio + withdrawals from risk portfolio).

The planning is done by scheduling income and withdrawals in the following table:



(2) The balance and AA trajectory of both the risk portfolio and the savings portfolio is now shown in full detail.

[corn18]

Oh goody! A new spreadsheet to play with! Will report back on findings.

Reporting back: It does not like it when my real income exceeds my real expenses (when SS kicks in with my COLA pension). The safe bond portfolio gets all wonky and spits out silly rates.

Everything else is fantastic! Love the additional details.

[Ben Mathew]

Oh goody! A new spreadsheet to play with! Will report back on findings.

Reporting back: It does not like it when my real income exceeds my real expenses (when SS kicks in with my COLA pension). The safe bond portfolio gets all wonky and spits out silly rates.

Everything else is fantastic! Love the additional details.

Thanks for the feedback, corn18. Is the safe bond allocation in the savings portfolio in column AB negative? If so, does the following comment in cell U87 help?

Column AB shows the target safe bond allocation for the savings portfolio for each year. If this is negative in any year, it means that you have more safe bonds in the form of net future income than the total safe bonds required by your target asset allocation. The calculator is telling you to sell some of your safe bonds and rebalance towards stocks or risky bonds. But you can't do this because all of your safe bonds are in the form of net future income and can't be sold. Since you can't achieve your target asset allocation, the expected return of the risk portfolio calculated in cell I25 will be wrong and so the withdrawal calculations will also be wrong. To address this, you can:

(1) Enter more "essential extra expenses" in column M. Since these are funded by safe bonds, it will remove some safe bonds from the risk portfolio.

(2) Choose a higher safe bond allocation for your risk portfolio (cells I21:23).

These adjustments mean lower risk and lower return. If you have a strong preference for higher risk and higher return and don't want to settle for a safer portfolio just to get a constant expected return for planning purposes, you can create a custom spreadsheet that incorporates non-constant expected returns.

[corn18]

Ben, wanted to stop back in this thread and give you a shout out. I think TPAW is the most elegant tool out there for deciding whether you can retire. I liken it the F=ma or E=mc2. It takes a complex problem and makes it simple:

Total Income - Total Expenses + Savings

If this is positive, you are good to go. If it is negative, then you need to explore some options.

I didn't complicate things with any returns at all. If you want to add some bling, then your spreadsheet allows you to do that. But it's not necessary.

I love it!

Corn

[Ben Mathew]

Ben, wanted to stop back in this thread and give you a shout out. I think TPAW is the most elegant tool out there for deciding whether you can retire.

Thanks, corn18. I will put out a new version soon showing the probability distribution of withdrawals. It will provide a simple and sensible way of picking AA and g.

[corn18]

Ben,

I have modified your TPAW to fit my model. The basics are the same, I just simplified things because I don't need TPAW to tell me my withdrawals, I just need it to cross check my historical returns and Monte Carlo model. Here's what I did:

Total Expenses:

Essential expenses: I just add up all the essential expenses. I use a 0% discount rate because I keep most of my cash in my 401k stable value fund and it keeps up with inflation very well. I may take a look at a negative discount rate, but haven't yet.

Extra withdrawals: This is my fun money. I discount it @ 2% because that is what I have chosen to use as my forecast for average real total return on my 60/40 portfolio.

Total Income: This is easy. My COLA pension + SS

Savings: This one is easy

Then I just do the simple math prescribed by TPAW:

Total Income - Total Expenses + Savings

If this is positive, I am good to go.

You might be interested to know that your approach matches a 100% probability of success (Ps) in firecalc/historical returns. It's amazing how close the two are. When I am right on the cusp of going less than 100% in my historical model, my TPAW balance is very close to zero (but still positive). When my historical model goes less than 100%, the TPAW balance goes negative. What I concluded from this is a positive TPAW balance = 100% in firecalc. This only works for my particular plan. I can make it not work, but I always trust TPAW.

The Monte Carlo sim is a bit weird because of the huge tails it produces. 100% in firecalc = 97% in my Monte Carlo sim (validated with the Flexible Retirement Planner Monte Carlo sim).

The reason I like TPAW the best is its simplicity. I don't have to make complex calculations in giant arrays where I could make myriad errors. Just some simple addition and subtraction of actual numbers. Really a fantastic tool and my favorite.

[Ben Mathew]

I have modified your TPAW to fit my model. The basics are the same, I just simplified things because I don't need TPAW to tell me my withdrawals, I just need it to cross check my historical returns and Monte Carlo model. Here's what I did:

Total Expenses:

Essential expenses: I just add up all the essential expenses. I use a 0% discount rate because I keep most of my cash in my 401k stable value fund and it keeps up with inflation very well. I may take a look at a negative discount rate, but haven't yet.

Extra withdrawals: This is my fun money. I discount it @ 2% because that is what I have chosen to use as my forecast for average real total return on my 60/40 portfolio.

Total Income: This is easy. My COLA pension + SS

Savings: This one is easy

Then I just do the simple math prescribed by TPAW:

Total Income - Total Expenses + Savings

If this is positive, I am good to go.

You can definitely use the TPAW calculator in this way to check the withdrawals you have in mind by plugging it into the "essential expenses" and "extra withdrawals" and see if its feasible given your wealth (savings + future income). Indeed, the spreadsheet is intended to provide the flexibility to play around with different withdrawal schedules and see if it's feasible. It doesn't have to fit the straitjacket of constant withdrawals and so on.

But one thing that you will still need to be careful about is to make sure you can actually maintain the 60/40 for the risk portfolio. Look at the trajectory of the savings portfolio on the right and make sure that the savings portfolio does not turn negative. If it does, then you're assuming that you will sell your pension and SS "bonds" and rebalance to stocks to maintain the 60/40 allocation on the risk portfolio. There should be an error message and related directions in the spreadsheet. If this is fine, then you should be good to go. If not, you'll definitely want to address the issue.

[corn18]

Ben, how hard would it be to set up your spreadsheet so that I can enter actual portfolio balances as the years go by and the spreadsheet updates the withdrawal?

[Ben Mathew]

Ben, how hard would it be to set up your spreadsheet so that I can enter actual portfolio balances as the years go by and the spreadsheet updates the withdrawal?

As it stands now, you'd have to manually delete a row each year (to reflect one less year of withdrawals remaining), and then enter updated numbers. I can't think of a simple way to automate this.

[Ben Mathew]

I have added a graph showing the probability distribution of withdrawals. This helps the user choose asset allocation and withdrawal growth rate (g) by directly showing its impact on withdrawals. The user reviews the graph and adjusts AA and g till they find the distribution they like the most.



Current year withdrawal is certain. Future years' withdrawals are uncertain because they depend on the returns of the risk portfolio. Withdrawals farther away in the future are more uncertain because they depend on the returns of a greater number of years. So the distribution becomes more dispersed for later ages:

OP shows an example of how the decision process works.

From the Q&A in the OP:

Why not use failure probabilities instead of the probability distribution of withdrawals to help guide decision-making?

Since TPAW adjusts withdrawals in response to portfolio performance, it does not fail (run out of money). So failure probabilities don't convey meaningful information. The situation facing the retiree is that if returns are poor, then future withdrawals will be low, and if returns are good, then future withdrawals will be high. The probability distribution of withdrawals directly communicates this range of withdrawals, and so clearly captures the actual situation faced by the retiree.

[Ben Mathew]

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:



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.



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.