Variable Percentage Withdrawal (VPW)

[L84SUPR]

Does VPW assume decreasing, constant, or increasing expenses? I recently read distributions from VPW are "front loaded". I understand the percentages increase but assumed they were balanced by a decreasing portfolio, in theory. Is there an intentional tilt toward real increasing or decreasing expenses/distributions?

I agree that reading through his posts will help understand this better, but I would start with understanding all withdrawal methods. For me, the VPW explanation here is quite sufficient: https://www.bogleheads.org/wiki/Withdrawal_methods

ABW withdrawal methods include a variable g which is used to model the intended slope of the expenses. All of the comments on this thread about "front loading" got me wondering if VPW assumed spending decreased with age and therefore incorporated a negative value of g. Based on longinvest's response the answer is no.

The comments about front loading appear to be based on comparison to other methods which tend to start around 4% for a typical retirement age as compared to VPW which can start higher depending upon AA.

[4nursebee]

Does VPW assume decreasing, constant, or increasing expenses? I recently read distributions from VPW are "front loaded". I understand the percentages increase but assumed they were balanced by a decreasing portfolio, in theory. Is there an intentional tilt toward real increasing or decreasing expenses/distributions?

I agree that reading through his posts will help understand this better, but I would start with understanding all withdrawal methods. For me, the VPW explanation here is quite sufficient: https://www.bogleheads.org/wiki/Withdrawal_methods

ABW withdrawal methods include a variable g which is used to model the intended slope of the expenses. All of the comments on this thread about "front loading" got me wondering if VPW assumed spending decreased with age and therefore incorporated a negative value of g. Based on longinvest's response the answer is no.

The comments about front loading appear to be based on comparison to other methods which tend to start around 4% for a typical retirement age as compared to VPW which can start higher depending upon AA.

I am confused as to what ABW means.
I am confused about discussing expenses, expense variables, slopes of expenses in a topic dedicated to a withdrawal method.
I am confused calling this a front loading thing when the withdrawal percentages get larger over time.
I am confused adhering to something as typical.

The nice thing about all of this, if someone wanted to be concerned about some large end of life expense, they can weight the risks and benefits of withdrawal strategies and adjust spending.

[Marseille07]

The comments about front loading appear to be based on comparison to other methods which tend to start around 4% for a typical retirement age as compared to VPW which can start higher depending upon AA.

Yes, it's all relative. Obviously front-loading doesn't mean you spend 50% of your portfolio on Day 1. But some methods draw more earlier than later.

[exodusing]

.

I'd be interested in your take on viewtopic.php?p=7390508#p7390508 about using RMD plus interest and dividends as a withdrawal strategy. bobcat2 believes it's superior to VPW. If you're so inclined, please reply in that thread.

[longinvest]

I'd be interested in your take on [..] using RMD plus interest and dividends as a withdrawal strategy. [Someone] believes it's superior to VPW. If you're so inclined, please reply in that thread.

Exodusing, there will always be someone who thinks that there's a better accumulation and retirement method than VPW. I've provided ample information in the current thread along with a realistic and detailed example in the ongoing forward test thread to help readers form their own opinion about VPW.

To address the specific subject of your post, I'll simply say that going into high-dividend stocks and "high-yield" bonds (more appropriately call junk bonds) to increase retirement income looks like a bad idea to me.

[exodusing]

I'd be interested in your take on [..] using RMD plus interest and dividends as a withdrawal strategy. [Someone] believes it's superior to VPW. If you're so inclined, please reply in that thread.

Exodusing, there will always be someone who thinks that there's a better accumulation and retirement method than VPW. I've provided ample information in the current thread along with a realistic and detailed example in the ongoing forward test thread to help readers form their own opinion about VPW.

To address the specific subject of your post, I'll simply say that going into high-dividend stocks and "high-yield" bonds (more appropriately call junk bonds) to increase retirement income looks like a bad idea to me.

I don't believe Bob (an economist who frequently posts on retirement issues) was suggesting high dividend stocks or junk. Neither were the Boston College researchers who suggested the approach in a paper linked in the thread. I thought Ben Mathew's posts were a good illustration of issues. Bob's specific critiques of VPW at viewtopic.php?p=7390508#p7390508 seem misguided, but you obviously have a better feel than I do.

Would you agree with Ben's conclusion: "I would agree with the authors that RMD is fine as a rule of thumb, and better than the 4% rule. However, RMD + 1.5% seems pretty aggressive to me and I'd caution people about the high risk of low spending in late retirement." Note that 1.5% is based on a market portfolio rather than high dividend and junk.

[Roque]

I am not partial to the RMD calculation, as it cannot be globally applied.

Longinvest, thank you for the VPW spreadsheet and the very entertaining VPW Forward Test. I have found both immensely helpful and appreciate your hard work and dedication to maintaining them.

[longinvest]

I am not partial to the RMD calculation, as it cannot be globally applied.

Longinvest, thank you for the VPW spreadsheet and the very entertaining VPW Forward Test. I have found both immensely helpful and appreciate your hard work and dedication to maintaining them.

Roque, thanks for the nice comments.

[longinvest]

On the forward test thread, forum member Yuba asked:

Thank you longinvest for all your work on this. Have you ever considered moving the Excel file into a web based input tool for greater reach and easier to use?

Thanks again
Rick dba Yuba

Rick dba Yuba, thanks for the nice comments.

The worksheet already works online (Google Sheets version).

There are significant advantages, for users, to a simple-to-use macro-less spreadsheet when compared to a server-based web tool:

• Downloadable versions (.xls and .ods) avoid privacy issues.
• The online version is stored privately within one's Google account which can be secured using 2-step verification.
• The spreadsheet contains no code. It simply cannot communicate any data to any server.
• The worksheet provides complete transparency. It only contains data and formulas and is unlocked. (Protected sheets, in the .ods version, require no password to disable the protection).
• The worksheet is persistent. Once downloaded to a computer, it stays there, even if the hosting server goes down. Similarly, once copied into one's Google account, the worksheet won't disappear even if the original source was to somehow disappear.

The worksheet is a very powerful tool for do-it-yourself investors. As explained in this post, a worse than Great Depression test can easily be performed by simply feeding the initial "Portfolio Balance After Loss" (red cell) as "Portfolio Balance" (yellow input cell), and looking at the resulting Required Flexibility projection. Detailed calculations which can easily be verified without using a spreadsheet are provided in the lower parts of the Accumulation and Retirement sheets. That's a very high level of transparency.

I see more drawbacks than advantages, for users, with a server-based tool.

[SnowBog]

On the forward test thread, forum member Yuba asked:

Thank you longinvest for all your work on this. Have you ever considered moving the Excel file into a web based input tool for greater reach and easier to use?

Thanks again
Rick dba Yuba

Rick dba Yuba, thanks for the nice comments.

The worksheet already works online (Google Sheet version).

You can also create a free Microsoft OneDrive account, where you can store the Excel version, and likewise have web, mobile, desktop access.

No need to reinvent the wheel!

[longinvest]

You can also create a free Microsoft OneDrive account, where you can store the Excel version, and likewise have web, mobile, desktop access.

Effectively! Thanks SnowBog.

[Yuba]

Thanks for the reply.

Rick dba Yuba

[count damoney]

Forgive me if this has been covered in the 41 page thread or elsewhere, but:

I noticed that the spreadsheet can be unlocked without a password.
Doing this, you can change the "age" input (I'm talking about the retirement tab) from a drop down to an input.

If I decided or choose to do quarterly withdrawals, has anyone used the spreadsheet to recalc the quarterly withdrawal amount based on current portfolio balance? This would seem to me to get ahead or react appropriately to any significant market fluctuations (both up and down) before deciding on an amount to take annually.

For instance, based on my inputs, if I put in a portfolio balance of $3M at age 62 with a 70/30 allocation, my quarterly withdrawal would be $50,938.
However, if my portfolio dropped by 15% by the start of the next quarter, my new portfolio balance would be $2.55M and my age 62.25, which would result in a quarterly withdrawal of $45,563.

[longinvest]

Forgive me if this has been covered in the 41 page thread or elsewhere, but:

I noticed that the spreadsheet can be unlocked without a password.

Count damoney, the worksheet isn't locked. I'm guessing that you're using the online Google Sheets version, so you probably had to first make a private copy of the worksheet before entering your data into it. That's normal. The shared public copy is protected against changes so that everyone who copies it (like you did) gets a fresh unmodified copy.

Doing this, you can change the "age" input (I'm talking about the retirement tab) from a drop down to an input.

If I decided or choose to do quarterly withdrawals, has anyone used the spreadsheet to recalc the quarterly withdrawal amount based on current portfolio balance? This would seem to me to get ahead or react appropriately to any significant market fluctuations (both up and down) before deciding on an amount to take annually.

I suggest reading the forward test thread. It illustrates how the worksheet can be used for monthly withdrawals. Worksheet inputs are updated every month before withdrawal. Quartely withdrawals would work similarly.

Personally, I'm a big fan of monthly withdrawals along with an income cushion containing approximately 5 months of retirement income* to dampen the impact of short-term portfolio fluctuations, as illustrated in this post.

* Retirement income = portfolio withdrawal + pension payments.

The idea of an income cushion could be replicated with quarterly withdrawals. It would contain 6 months of retirement income. Every quarter, all pension payments and the quarterly withdrawal would be added into it, then 1/3 of the resulting cushion would be taken out to cover the taxes and expenses for the upcoming quarter. (See this post and this post for a suggestion of how to operate on an after-tax basis).

For instance, based on my inputs, if I put in a portfolio balance of $3M at age 62 with a 70/30 allocation, my quarterly withdrawal would be $50,938.
However, if my portfolio dropped by 15% by the start of the next quarter, my new portfolio balance would be $2.55M and my age 62.25, which would result in a quarterly withdrawal of $45,563.

This would work. Note that the Age cell would remain 62 until the retiree's 63rd birthday as it has an annual granularity.

[count damoney]

Forgive me if this has been covered in the 41 page thread or elsewhere, but:

I noticed that the spreadsheet can be unlocked without a password.

Count damoney, the worksheet isn't locked. I'm guessing that you're using the online Google Sheets version, so you probably had to first make a private copy of the worksheet before entering your data into it. That's normal. The shared public copy is protected against changes so that everyone who copies it (like you did) gets a fresh unmodified copy.

Doing this, you can change the "age" input (I'm talking about the retirement tab) from a drop down to an input.

If I decided or choose to do quarterly withdrawals, has anyone used the spreadsheet to recalc the quarterly withdrawal amount based on current portfolio balance? This would seem to me to get ahead or react appropriately to any significant market fluctuations (both up and down) before deciding on an amount to take annually.

I suggest reading the forward test thread. It illustrates how the worksheet can be used for monthly withdrawals. Worksheet inputs are updated every month before withdrawal. Quartely withdrawals would work similarly.

Personally, I'm a big fan of monthly withdrawals along with an income cushion containing approximately 5 months of retirement income* to dampen the impact of short-term portfolio fluctuations, as illustrated in this post.

* Retirement income = portfolio withdrawal + pension payments.

The idea of an income cushion could be replicated with quarterly withdrawals. It would contain 6 months of retirement income. Every quarter, all pension payments and the quarterly withdrawal would be added into it, then 1/3 of the resulting cushion would be taken out to cover the taxes and expenses for the upcoming quarter. (See this post and this post for a suggestion of how to operate on an after-tax basis).

For instance, based on my inputs, if I put in a portfolio balance of $3M at age 62 with a 70/30 allocation, my quarterly withdrawal would be $50,938.
However, if my portfolio dropped by 15% by the start of the next quarter, my new portfolio balance would be $2.55M and my age 62.25, which would result in a quarterly withdrawal of $45,563.

This would work. Note that the Age cell would remain 62 until the retiree's 63rd birthday as it has an annual granularity.

Sorry, used the wrong term. Worksheet was protected (and needed to be unprotected) vs unlocked.

I'm unfamiliar with your term "annual granularity", but there must be some calculation based precisely on age.
If I use the exact same inputs and only changing age from 62 to 62.5, the suggested withdrawal changes, so some calculation is based on exact age.

Wouldn't this be easier and accomplish 95% of what you were trying to accomplish with the monkeying around with the 6 month Ally savings account?

[longinvest]

Sorry, used the wrong term. Worksheet was protected (and needed to be unprotected) vs unlocked.

Count damoney, none of the three versions (Google Sheets, Microsoft Excel, and LibreOffice Calc) needs to be unprotected to be used.

Only the LibreOffice Calc version "needs" to be unprotected to tamper with it. In other words, it's only to modify things the shouldn't be modified by users that a sheet must first be unprotected.

I'm unfamiliar with your term "annual granularity", but there must be some calculation based precisely on age.
If I use the exact same inputs and only changing age from 62 to 62.5, the suggested withdrawal changes, so some calculation is based on exact age.

I think that I understand what you did, now. I think that you unprotected the Retirement sheet of the LibreOffice Calc (.ods) version, and then you tampered with the validation rules of the Age cell to force it to accept a fractional number. This isn't supported.

Wouldn't this be easier and accomplish 95% of what you were trying to accomplish with the monkeying around with the 6 month Ally savings account?

Count damoney, did you really mean that? The term "monkeying" is pejorative.

I suggest reading this very detailed post. The small cushion significantly dampens the impact of short-term market fluctuations. (Cushion management was simplified in a later post).

In summary:
1- Tampering with the VPW Accumulation and Retirement Worksheet to make it do things it wasn't designed to do isn't recommended.
2- Contrary to intuition, using a small cushion is very effective at dampening the impact of short-term portfolio fluctuations. Using slightly more precise percentages doesn't change this.

[count damoney]

Got it. Thanks for the reply.
Appreciate all the hard work and responses that go into this.

[Ben Mathew]

The following post goes over Monte Carlo and historical simulations of the VPW amortization:

viewtopic.php?p=7463768#p7463768

I think it highlights the need to build in more precautionary savings (i.e. amortize at a lower rate than VPW's built-in "WAG" returns) if

1. expected returns are lower than historical, and
2. you don't want spending to drop a lot lower than the starting withdrawal

[longinvest]

The "V" in VPW stands for "Variable". The VPW model assumes that stock and bond markets fluctuate. While not frequent, it isn't unusual for stocks to lose -50% of their value and for bonds to fluctuate too, but significantly less than stocks. The worksheet calculates the impact of stocks immediately losing -50% while restricting asset allocation to include at least 30% in stocks, thus testing at least a -15% portfolio loss for a bond-heavy portfolio. This isn't a prediction that stocks will lose exactly -50% and bonds will remain perfectly stable. It's just a simple calculation that can easily be replicated without using a spreadsheet to help the retiree plan for the possibility of bad future returns. These bad returns could be due to stocks, to bonds, or both. Losses could be immediate, later, or spread over time. Losses could be worse, forcing the retiree to adapt. Losses might never happen. We simply don't know. Note that proper use of VPW requires accompanying it with (current or future) stable lifelong income like Social Security (possibly delayed to age 70 to increase its monthly inflation-indexed payments), a pension (if any), and (if necessary) a SPIA*, dampening the impact of portfolio losses on total retirement income, because no withdrawal method can create returns that markets don't deliver.

* Single Premium Immediate Annuity.

Every month in the forward test thread, like I did earlier today in this post, I take the time to explain the calculations of the VPW Worksheet in details.

I wrote, above, that a -50% loss is a normal thing for stocks, even if it's infrequent. As a consequence, such a loss shouldn't affect the retiree's comfort when the retiree has adequately planned retirement with the help of the VPW worksheet. This implies that required flexibility amounts, at the start of retirement, should be sufficient for the retiree to live in ample comfort.

A simple yet very harsh stress test for the plan, using the VPW worksheet, is to feed the initial "Portfolio Balance After Loss" (red cell) as "Portfolio Balance" (yellow input cell), and look at the resulting required flexibility estimate. This represents two consecutive -50% losses for stocks, or cumulative -75% losses (with rebalancing in between losses) at the worst of times, at the start of retirement immediately before first withdrawal. These are Great Depression types of losses without any quick recovery after losses. In such a situation, the retiree's comfort is most probably affected, yet, assuming that retirement was properly planned, the retiree is likely to be doing better financially than many others in society.

[RyeBourbon]

If I decided or choose to do quarterly withdrawals, has anyone used the spreadsheet to recalc the quarterly withdrawal amount based on current portfolio balance? This would seem to me to get ahead or react appropriately to any significant market fluctuations (both up and down) before deciding on an amount to take annually.

I have built my own excel spreadsheet for withdrawals (I'm recently retired). The methodology is based on longinvest's VPW spreadsheet, but I do the calculations monthly based on the portfolio value at the start of the month and recompute the bridge amount (based on # of months until SS) and % withdrawal each month (based on # of months until age 100). Each month is a row in the spreadsheet, so I have a history of each calculation. I have been computing the "VPW" advised withdrawal amount and the "Safety" amount (based on a 50% equity haircut). My actual withdrawal has been in between those values. I keep track of the portfolio withdrawals and compare to the cumulative recommended amount for the year (which allows me to make a larger withdrawal if needed for lumpy expenses). I am also using a more conservative return expectation (4% real for equity, 1.6% real for bonds).

[longinvest]

It's easy to attack VPW by (1) failing to combine it with lifelong income and (2) making doomsday future return predictions. Fortunately, the simplicity of VPW allows us to expose hidden doomsday predictions for what they really are.

An example attack is to use VPW withdrawals from a portfolio without combining it with current or future stable income, and to fail to follow wiki instructions (like considering buying a SPIA after age 80 to dampen financial risks related to living beyond age 100). In this attack, the withdrawal percentage at age 99 increases to 100%, leaving the retiree without a portfolio at age 100, if still alive. Of course, this isn't how VPW works, but to attack it, things have to look bad, right? Anyway, let's continue with the attack setup. The retiree's age is 65 with a $1,000,000 50/50 stocks/bonds portfolio.

The above setup hasn't been picked randomly. I'm just using the setup proposed by a proponent of prediction-driven withdrawals in a recent attack against VPW. The attacker fed this setup into his prediction-driven withdrawal tool which uses pseudo-random number sequences to project that VPW could leave the retiree with a tiny ($996 X 12) = $11,952 (inflation-adjusted) last withdrawal or less at age 99, while depleting the portfolio, with a probability of 1 out of every 20 projected retirements. In case you're wondering, your intuition is right: that wasn't even the worse projection of the tool; it was the 5th percentile projection. That's scary, isn't it?

But, here's the fun part, for those who like mathematics. Even if the prediction-driven withdrawal tool doesn't provide the detailed returns which lead to a $11,952 withdrawal at age 99, we can use the fact that VPW is immune to sequence of returns risk to recover the cumulative portfolio return that lead to that doomsday projection.

For a 50/50 stocks/bonds allocation, the VPW worksheet uses a 3.45% growth trend. In a hypothetical world where real portfolio returns would be constant and exactly 3.45% every year, the annual portfolio withdrawal amount would precisely be $47,991 every year. As ((1 + 3.45%)^34) = 3.16837684, we know that ($47,991 / 3.16837684) = $15,147 of the initial $1,000,000 portfolio was the source money for the last withdrawal (VPW's immunity to sequence of returns risk allows us to make this calculation). In the attack, this initial $15,147 shrank to $11,952 over 34 years. That's a cumulative (($11,952 / $15,147) - 1) = -21% loss, in real terms, for a 50/50 stocks/bonds portfolio over 34 years. That's a really awful cumulative return for such a balanced portfolio over the next 34 years, isn't it?

Note that the harsh stress test of my previous post is much milder and reasonable despite its harshness. It projects a ((3.16837684 X 75% X 75%) - 1) = 78% cumulative portfolio growth over 34 years.

Let's investigate this further. The attacker assumes that bonds will deliver more or less 2% real per year over the next 34 years, as this is slightly below the current yield of 30-year Treasury Inflation Protected Securities (TIPS). So, if bonds are to return 2% per year, over 34 years, how badly should stocks perform for the cumulative 34-year portfolio return to be as low as -21%?

Code: Select all

Annual portfolio return: ((1 + -21%)^(1/34)) - 1 = -0.69%
Annual return of stocks: (((1 + -0.69%) - (50% X (1 + 2%))) / 50%) - 1 = -3.39%
Cumulative returns of stocks over 34 years: ((1 + -3.39%)^34) - 1 = -69%

Here we are. Remember, this wasn't the worst case; it was the 5th percentile projection of the prediction-driven withdrawal tool! To attack VPW, the attacker is projecting that stocks will possibly cumulatively lose almost -70% in real terms, with dividends reinvested, over the next 34 years. If one is to plan for such end-of-the-world-as-we-know-it scenarios, one should also consider the possibility that the government might stop raising enough taxes to avoid defaulting on TIPS, if companies are to do so badly.

It's amazing to see how confident some proponents of prediction-driven withdrawals are in their future return predictions. Yet, the track record of those who made future return predictions in the past is pitiful. Even firms with countless PhDs among their staff get their predictions awfully wrong.


When used with a sensible asset allocation and accompanying (current or future) stable lifelong income, VPW is an easy-to-use and very robust retirement method which provides complete transparency about its calculations. As it isn't a server-hosted tool, it doesn't collect the private data of its users.

[Ben Mathew]

In this attack, the withdrawal percentage at age 99 increases to 100%, leaving the retiree without a portfolio at age 100, if still alive. Of course, this isn't how VPW works, but to attack it, things have to look bad, right?

Not sure where you're getting this. The simulations I did does not say anything about how there's nothing left in the portfolio after age 100. I did not show that spending past age 100 is $0. The graph stops at age 100, the presumed max age for retirement and the amortization. Nothing I showed suggested that this was a bad idea.

That's a really awful cumulative return for such a balanced portfolio over the next 34 years, isn't it?

A dollar in stocks used to produce more profits and a dollar in bonds used to pay out more interest. They yield less now. Every investor should confront this fact. It's not apparent if you focus only on historical returns. But it is apparent if you pay attention to the profit that a dollar's worth of stock generates and how it has changed over time.

If you think that the lower yields mean that stocks and bonds are expected to pay out less in the future (and many people do!), then you have to model the future with lower expected returns. But expected returns are just the middle of the distribution. Things can get lower than expected. This can happen if profits end up being lower than expected, or if stock valuations fall. So starting with lower expected returns means that the 5th percentile is even lower than that and so can look pretty bad.

On the plus side, I'll allow that modeling more mean reversion over longer horizons can help make the 5th percentile look better than they do in my analysis. I have allowed for some mean reversion through block sampling. The Monte Carlo analyses I shared used the default block of five years. But I hope to incorporate more comprehensive mean reversion at some point. That can tighten the distribution and raise the 5th percentile.

Duration matching bonds is another option that can tighten the long term distribution by reducing interest rate risk.

So, yes, the 5th percentile can be made better by these things. But still, the main driver of why it's so low—lower than what you're willing to countenance—is that (1) the expected returns are lower than historical, and (2) the 5th percentile is lower even than that. Lower than the low expected return is pretty darn low. It may seem impossibly low and not worth considering if you look solely at US historical returns. But it's not impossibly low if you think of stocks as the share of a company that produces profits, and you believe that these profits are the ultimate source of long term stock returns, and you recognize that these profits are now much lower than what prevailed historically. This state of affairs is not going to change unless yields go back up. And that's not going to happen unless valuations correct. And that's not going to happen unless the market declines. There's no good way to back down out of high valuations.

So, if bonds are to return 2% per year, over 34 years, how badly should stocks perform for the cumulative 34-year portfolio return to be as low as -21%?

This analysis is flawed because bonds are not duration matched and so are not risk-free.

It's amazing to see how confident some proponents of prediction-driven withdrawals are in their future return predictions. Yet, the track record of those who made future return predictions in the past is pitiful. Even firms with countless PhDs among their staff get their predictions awfully wrong.

First, the Monte Carlo and historical simulations I shared don't update expected returns over time. They're fixed at the starting expected return. So it's not the "predication-driven withdrawals" that you're so against.

Second, you have this exactly backwards. I have little confidence in my ability to predict realized returns over the next 35 years. That is why I use Monte Carlo simulations to examine a wide range of possible portfolio returns and spending scenarios. Considering a wide range of possible portfolio returns and spending outcomes is the natural result of humility when it comes to predicting returns. The wider the range, the humbler you are!

And—the more willing you are to update your already humble assumptions when new information comes in, the humbler you are!

[Alpha4]

So, if bonds are to return 2% per year, over 34 years, how badly should stocks perform for the cumulative 34-year portfolio return to be as low as -21%?

This analysis is flawed because bonds are not duration matched and so are not risk-free.

OK, fair enough....so how badly did stocks perform in your 5% worst case simulated analysis, then?

I ask because even if they (assuming without withdrawals, taxes, or fees) "only" ended up down 40 or 50 or 55 or 60% in total return real terms (i.e. inflation adjusted returns with dividends reinvested) rather than 69 or 70% that boggles belief unless one is predicting that the US will be invaded and lose a war or something of that nature (in which case the withdrawal rates on portfolios won't be anywhere near our biggest worry).

Put it this way: Had you invested in Japanese stocks at the Japanese equity bubble bull market peak in late 1989 or very early 1990 your dividend reinvested real total return would as of mid-September 2023 be around 12 or 13% in total (i.e. for every one yen you invested on 1-1-1990 you would now have exactly 1.12 or 1.13 yen in real terms) which stinks but at least it's a positive number rather than being down 50 or 69% or the like...granted this is only 33.75 years and not 34 but you get my drift.

For another example, had you invested a sum in US stocks at exactly 34 years before the late May/very early June 1932 Depression market bottom and then (at the exact worst possible time) liquidated it on 5-31 or 6-1 of 1932 (very close to the exact bottom and quite likely at the bottom) you would've earned a real total return of around 167% which comes out to a roughly 2.95% CAGR. Not great at all but it easily beats actually ending up down 40 or 50 or 60 or 69% in real terms.

The only thing I can thin of that might make these horrible assumptions more plausible was that if those returns also included the effects of withdrawals (i.e. one would have only 30 or 40% of the stock portfolio left after having made thirty years or thirty-five years of withdrawals)....was this the case or was your assumption of the 5% worst case having stocks down so much one made even before the effect of withdrawals was considered?

[Ben Mathew]

So, if bonds are to return 2% per year, over 34 years, how badly should stocks perform for the cumulative 34-year portfolio return to be as low as -21%?

This analysis is flawed because bonds are not duration matched and so are not risk-free.

OK, fair enough....so how badly did stocks perform in your 5% worst case simulated analysis, then?

We can see the underlying stock returns by following these steps:

1. Change asset allocation to 100% stocks
2. Turn off spending by setting a spending ceiling of $0.
3. Switch to the "Portfolio Balance" graph.

This shows the growth of stocks without any withdrawals. So this is the cumulative return of stocks.

For the first Monte Carlo simulation that I shared, where expected stock return was set to 4.0%, we get the following graph:



So, over 35 years, $1 million in stocks grows to

95th percentile: $10.8 million
50th percentile: $2.2 million
5th percentile: $446K

This translates to gross returns of 975%, 117% and -55% respectively, and annualized returns of 7.0%, 2.2% and -2.3% respectively.

For the second Monte Carlo simulation that I shared, where expected stock return was set to 5.0% to match the WAG return, we get the following graph:



Over 35 years, $1 million in stocks grows to

95th percentile: $15.0 million
50th percentile: $3.0 million
5th percentile: $623K

This translates to gross returns of 1403%, 204% and -38% respectively, and annualized returns of 8.1%, 3.2% and -1.3% respectively.

I ask because even if they (assuming without withdrawals, taxes, or fees) "only" ended up down 40 or 50 or 55 or 60% in total return real terms (i.e. inflation adjusted returns with dividends reinvested) rather than 69 or 70% that boggles belief unless one is predicting that the US will be invaded and lose a war or something of that nature (in which case the withdrawal rates on portfolios won't be anywhere near our biggest worry).

Put it this way: Had you invested in Japanese stocks at the Japanese equity bubble bull market peak in late 1989 or very early 1990 your dividend reinvested real total return would as of mid-September 2023 be around 12 or 13% in total (i.e. for every one yen you invested on 1-1-1990 you would now have exactly 1.12 or 1.13 yen in real terms) which stinks but at least it's a positive number rather than being down 50 or 69% or the like...granted this is only 33.75 years and not 34 but you get my drift.

For another example, had you invested a sum in US stocks at exactly 34 years before the late May/very early June 1932 Depression market bottom and then (at the exact worst possible time) liquidated it on 5-31 or 6-1 of 1932 (very close to the exact bottom and quite likely at the bottom) you would've earned a real total return of around 167% which comes out to a roughly 2.95% CAGR. Not great at all but it easily beats actually ending up down 40 or 50 or 60 or 69% in real terms.

Keep in mind that the 5th percentile is unlikely. 1 in 20 is unlikely. I would be very surprised if we get such a bad draw, but feel that I should consider those outcomes in my planning.

We don't need apocalyptic type scenarios to get stocks to have negative real return over the course of 35 years. The key is that we are starting at a point where the earnings yield is down to 3.1%. A series of unlikely but not impossible events can get us there. If profits continue at the same pace, $1 million will become $1 million*(1+3.1%)^35 = $2.9 million in 35 years. If profits end up being half that, we are already down to $1 million*(1+1.6%)^35 = $1.7 million. If, on top of that, valuations halve (earnings yield rises from 3.1% to 6.2%), we are down to $856K. That's already -14% in the negative.

There's nothing special about 0% real returns for stocks. It's not a natural lower bound for planning purposes when you're starting at high stock valuations.

More pessimistic assumptions about profits and valuation changes can take us down towards -30% and below. I'm not sure if the 5th percentile should be -20% or -40% or -60%. As I said before, mean reversion in stocks can improve 5th percentile outcomes. My preference is to try to make things work without assuming mean reversion in long term stock returns. That's the conservative assumption. But I can understand the argument for incorporating mean reversion in planning.

Note that if you disagree with the expected return assumptions, you can increase it and see what that simulation looks like. If you increase the expected return to 6.5%, the 5th percentile cumulative return turns positive.

But to some extent, the focus on the 5th percentile is a red herring. Even the 50th percentile outcomes showed significant drop in spending, under both 4% and 5% expected stock return assumptions. The 50th percentile cumulative returns were 117% and 204% respectively. i.e. Even when the $1 million would have otherwise grown to $2.2 million over 35 years, spending would have dropped from $4,039 per month at the start to $2,735 per month by the end of retirement—a drop of 32%. And even when the $1 million would have otherwise grown to $3.0 million over 35 years, spending would have dropped from $4,056 per month at the start to $3,158 per month by the end of retirement—a drop of 22%.

The reason why even the 50th percentile outcomes have significant decline in spending is because VPW does not build in any precautionary savings (g>0%) in the amortization. I showed in this post that the amortization fomulas derived by Merton have significant precautionary savings (i.e. amortizes with g>0%) unless the subjective discount rate is quite high. So amortizing the portfolio with g=0% and WAG return assumptions like VPW does is quite aggressive, and is only appropriate if you care a lot less about future consumption than about current consumption.

People should be aware that VPW's aggressive portfolio amortization, even under WAG expected return assumptions of 5.0% and 2.0%, is likely to produce declining withdrawals—at the 50th percentile, not just the 5th percentile.

[longinvest]

In a previous post, I revealed how doomsday portfolio returns are being used to attack VPW.

Here's a formal proof that the cumulative time-weighted total portfolio return over 34 years, for a 50/50 stocks/bonds portfolio, must have been -21% (or very close to it) for VPW to end up delivering a ridiculously tiny $11,952 last withdrawal at age 99 from an initial $1,000,000 at age 65.

The proof is very easy to understand (and verify). It only involves arithmetic operations and some very basic algebra.

PROOF

All amounts and returns are expressed in inflation-adjusted terms.

The VPW Table percentage (in our wiki) for a 50/50 stocks/bonds allocation at age 65 is 4.8%. (Note that the VPW Worksheet, in its calculations, uses a more precise 4.7991255% percentage, but to keep this post readable, I'll use the rounded percentages found in our wiki.)

So, at age 65, the retiree withdraws 4.8% of $1,000,000. After withdrawal, ($1,000,000 X (1 - 4.8%)) remains in the portfolio. During the retiree's 65th year, the portfolio experiences an R1 total return (with dividends and coupons reinvested).

When reaching age 66, just before withdrawal, the portfolio balance is equal to ($1,000,000 X (1 - 4.8%) X (1 + R1)). At age 66 the VPW Table percentage is 4.9%. After withdrawal, ($1,000,000 X (1 - 4.8%) X (1 + R1) X (1 - 4.9%)) remains in the portfolio. During the retiree's 66th year, the portfolio experiences an R2 total return (with dividends and coupons reinvested).

When reaching age 67, just before withdrawal, the portfolio balance is equal to ($1,000,000 X (1 - 4.8%) X (1 + R1) X (1 - 4.9%) X (1 + R2)). At age 67 the VPW Table percentage is 4.9%. After withdrawal, ($1,000,000 X (1 - 4.8%) X (1 + R1) X (1 - 4.9%) X (1 + R2) X (1 - 4.9%)) remains in the portfolio. During the retiree's 67th year, the portfolio experiences an R3 total return (with dividends and coupons reinvested).

When reaching age 68, just before withdrawal, the portfolio balance is equal to ($1,000,000 X (1 - 4.8%) X (1 + R1) X (1 - 4.9%) X (1 + R2) X (1 - 4.9%) X (1 + R3)). At age 68 the VPW Table percentage is 5.0%. After withdrawal, ($1,000,000 X (1 - 4.8%) X (1 + R1) X (1 - 4.9%) X (1 + R2) X (1 - 4.9%) X (1 + R3) X (1 - 5.0%)) remains in the portfolio. During the retiree's 68th year, the portfolio experiences an R4 total return (with dividends and coupons reinvested).

You see the pattern. This continues until age 99.

Assuming a pure VPW Table depletion model, without the 10% cap on withdrawal percentage, when reaching age 99, just before withdrawal, the portfolio balance is equal to:
($1,000,000 X
(1 - 4.8%) X (1 + R1) X (1 - 4.9%) X (1 + R2) X (1 - 4.9%) X (1 + R3) X (1 - 5.0%) X (1 + R4) X (1 - 5.1%) X (1 + R5) X
(1 - 5.2%) X (1 + R6) X (1 - 5.3%) X (1 + R7) X (1 - 5.4%) X (1 + R8) X (1 - 5.5%) X (1 + R9) X (1 - 5.7%) X (1 + R10) X
(1 - 5.8%) X (1 + R11) X (1 - 6.0%) X (1 + R12) X (1 - 6.1%) X (1 + R13) X (1 - 6.3%) X (1 + R14) X (1 - 6.5%) X (1 + R15) X
(1 - 6.8%) X (1 + R16) X (1 - 7.0%) X (1 + R17) X (1 - 7.3%) X (1 + R18) X (1 - 7.6%) X (1 + R19) X (1 - 7.9%) X (1 + R20) X
(1 - 8.3%) X (1 + R21) X (1 - 8.8%) X (1 + R22) X (1 - 9.3%) X (1 + R23) X (1 - 10.0%) X (1 + R24) X (1 - 10.7%) X (1 + R25) X
(1 - 11.6%) X (1 + R26) X (1 - 12.7%) X (1 + R27) X (1 - 14.0%) X (1 + R28) X (1 - 15.8%) X (1 + R29) X (1 - 18.1%) X (1 + R30) X
(1 - 21.4%) X (1 + R31) X (1 - 26.3%) X (1 + R32) X (1 - 34.5%) X (1 + R33) X (1 - 50.8%) X (1 + R34))

In the above formula, we replace (1 - 4.8%) with 95.2%, (1 - 4.9%) with 95.1%, and so on :

($1,000,000 X
95.2% X (1 + R1) X 95.1% X (1 + R2) X 95.1% X (1 + R3) X 95.0% X (1 + R4) X 94.9% X (1 + R5) X
94.8% X (1 + R6) X 94.7% X (1 + R7) X 94.6% X (1 + R8) X 94.5% X (1 + R9) X 94.3% X (1 + R10) X
94.2% X (1 + R11) X 94.0% X (1 + R12) X 93.9% X (1 + R13) X 93.7% X (1 + R14) X 93.5% X (1 + R15) X
93.2% X (1 + R16) X 93.0% X (1 + R17) X 92.7% X (1 + R18) X 92.4% X (1 + R19) X 92.1% X (1 + R20) X
91.7% X (1 + R21) X 91.2% X (1 + R22) X 90.7% X (1 + R23) X 90.0% X (1 + R24) X 89.3% X (1 + R25) X
88.4% X (1 + R26) X 87.3% X (1 + R27) X 86.0% X (1 + R28) X 84.2% X (1 + R29) X 81.9% X (1 + R30) X
78.6% X (1 + R31) X 73.7% X (1 + R32) X 65.5% X (1 + R33) X 49.2% X (1 + R34))

As multiplication is commutative (A X B = B X A), we can reorganise the terms as follows:

(($1,000,000 X
95.2% X 95.1% X 95.1% X 95.0% X 94.9% X 94.8% X 94.7% X 94.6% X 94.5% X 94.3% X
94.2% X 94.0% X 93.9% X 93.7% X 93.5% X 93.2% X 93.0% X 92.7% X 92.4% X 92.1% X
91.7% X 91.2% X 90.7% X 90.0% X 89.3% X 88.4% X 87.3% X 86.0% X 84.2% X 81.9% X
78.6% X 73.7% X 65.5% X 49.2%) X
((1 + R1) X (1 + R2) X (1 + R3) X (1 + R4) X (1 + R5) X (1 + R6) X (1 + R7) X (1 + R8) X (1 + R9) X (1 + R10) X
(1 + R11) X (1 + R12) X (1 + R13) X (1 + R14) X (1 + R15) X (1 + R16) X (1 + R17) X (1 + R18) X (1 + R19) X (1 + R20) X
(1 + R21) X (1 + R22) X (1 + R23) X (1 + R24) X (1 + R25) X (1 + R26) X (1 + R27) X (1 + R28) X (1 + R29) X (1 + R30) X
(1 + R31) X (1 + R32) X (1 + R33) X (1 + R34)))

Using a calculator or a spreadsheet, it's easy to calculate that ($1,000,000 X 95.2% X ... X 49.2%) is equal to $15,241. Note that the small difference with the $15,147 calculated in my previous post is due to using rounded percentages in this post for calculations (to allow readers to easily replicate my calculations).

As a consequence, the portfolio balance, at age 99, before withdrawal is equal to:

($15,241 X
((1 + R1) X (1 + R2) X (1 + R3) X (1 + R4) X (1 + R5) X (1 + R6) X (1 + R7) X (1 + R8) X (1 + R9) X (1 + R10) X
(1 + R11) X (1 + R12) X (1 + R13) X (1 + R14) X (1 + R15) X (1 + R16) X (1 + R17) X (1 + R18) X (1 + R19) X (1 + R20) X
(1 + R21) X (1 + R22) X (1 + R23) X (1 + R24) X (1 + R25) X (1 + R26) X (1 + R27) X (1 + R28) X (1 + R29) X (1 + R30) X
(1 + R31) X (1 + R32) X (1 + R33) X (1 + R34)))

The last withdrawal, at age 99, depletes the portfolio and, obviously, the VPW Table percentage is 100%. As a consequence, the withdrawal amount, at age 99 is necessarily equal to the above formula.

The attack against VPW claimed that, at age 99, the withdrawal amount could be $11,952 (or less) for every 1 out of every 20 projections of the attackers's prediction-driven withdrawal tool. This gives use the following equation:

($15,241 X
((1 + R1) X (1 + R2) X (1 + R3) X (1 + R4) X (1 + R5) X (1 + R6) X (1 + R7) X (1 + R8) X (1 + R9) X (1 + R10) X
(1 + R11) X (1 + R12) X (1 + R13) X (1 + R14) X (1 + R15) X (1 + R16) X (1 + R17) X (1 + R18) X (1 + R19) X (1 + R20) X
(1 + R21) X (1 + R22) X (1 + R23) X (1 + R24) X (1 + R25) X (1 + R26) X (1 + R27) X (1 + R28) X (1 + R29) X (1 + R30) X
(1 + R31) X (1 + R32) X (1 + R33) X (1 + R34)))
= $11,952

Dividing both sides of the equation by $15,241 give us:

((1 + R1) X (1 + R2) X (1 + R3) X (1 + R4) X (1 + R5) X (1 + R6) X (1 + R7) X (1 + R8) X (1 + R9) X (1 + R10) X
(1 + R11) X (1 + R12) X (1 + R13) X (1 + R14) X (1 + R15) X (1 + R16) X (1 + R17) X (1 + R18) X (1 + R19) X (1 + R20) X
(1 + R21) X (1 + R22) X (1 + R23) X (1 + R24) X (1 + R25) X (1 + R26) X (1 + R27) X (1 + R28) X (1 + R29) X (1 + R30) X
(1 + R31) X (1 + R32) X (1 + R33) X (1 + R34))
= ($11,952 / $15,241)

My calculator tells me that ($11,952 / $15,241) is equal to 0.7842. Replacing this and subtracting 1 from both sides of the equation gives us:

((1 + R1) X (1 + R2) X (1 + R3) X (1 + R4) X (1 + R5) X (1 + R6) X (1 + R7) X (1 + R8) X (1 + R9) X (1 + R10) X
(1 + R11) X (1 + R12) X (1 + R13) X (1 + R14) X (1 + R15) X (1 + R16) X (1 + R17) X (1 + R18) X (1 + R19) X (1 + R20) X
(1 + R21) X (1 + R22) X (1 + R23) X (1 + R24) X (1 + R25) X (1 + R26) X (1 + R27) X (1 + R28) X (1 + R29) X (1 + R30) X
(1 + R31) X (1 + R32) X (1 + R33) X (1 + R34)) - 1
= 0.7842 - 1

The left part is equal to the cumulative portfolio growth, over 34 years. As for (.7842 - 1), it's equal to -21.58%.

Q.E.D.

[Wrench]

My hats off to both Longinvest and Ben Mathew for their detailed and adversarial but friendly back and forth on the risks/benefits of VPW! This is a fine example of the power and beauty of Bogleheads. Thank you both for enriching our community!

As for me, the debate has reconfirmed my belief and plan to stick with a more conservative and (arguably) much safer approach of generating inflation adjusted income to cover all my expenses using social security (@ age 70) and a TIPS ladder (even if there is a >20% SS reduction). The balance of my portfolio can then be invested in stocks without concern about their effect on my income. Should stocks fall over 30 years by 21%, 34% or even 50% I will only have less for discretionary spending and/or to leave to my heirs.

Wrench

[Ben Mathew]

My hats off to both Longinvest and Ben Mathew for their detailed and adversarial but friendly back and forth on the risks/benefits of VPW! This is a fine example of the power and beauty of Bogleheads. Thank you both for enriching our community!

Thank you for your kind words, Wrench. I appreciate it!

As for me, the debate has reconfirmed my belief and plan to stick with a more conservative and (arguably) much safer approach of generating inflation adjusted income to cover all my expenses using social security (@ age 70) and a TIPS ladder (even if there is a >20% SS reduction). The balance of my portfolio can then be invested in stocks without concern about their effect on my income. Should stocks fall over 30 years by 21%, 34% or even 50% I will only have less for discretionary spending and/or to leave to my heirs.

Wrench

That's a fine plan. There's a lot of security in having a floor.

[GaryA505]

My hats off to both Longinvest and Ben Mathew for their detailed and adversarial but friendly back and forth on the risks/benefits of VPW! This is a fine example of the power and beauty of Bogleheads. Thank you both for enriching our community!

As for me, the debate has reconfirmed my belief and plan to stick with a more conservative and (arguably) much safer approach of generating inflation adjusted income to cover all my expenses using social security (@ age 70) and a TIPS ladder (even if there is a >20% SS reduction). The balance of my portfolio can then be invested in stocks without concern about their effect on my income. Should stocks fall over 30 years by 21%, 34% or even 50% I will only have less for discretionary spending and/or to leave to my heirs.

Wrench

If only the TIPS ladder was easy to do for the average person!

[longinvest]

People should be aware that VPW's aggressive portfolio amortization, even under WAG expected return assumptions of 5.0% and 2.0%, is likely to produce declining withdrawals—at the 50th percentile, not just the 5th percentile.

The poster's tool uses arithmetic average returns to calibrate the generation of its pseudo-random sequence of returns. As the geometric average is necessarily smaller than the arithmetic average in presence of volatility (this article on Wikipedia provides a proof of the inequality), the tool projects a declining average when compounding returns. What's most frightening, about it, is that the tool's author didn't realize this [Unnecessary comment removed by admin LadyGeek] about VPW with a broken example.

The selected growth trends for stocks and bonds, in the VPW worksheet, are based on the long-term geometric average (or annualized) real returns of world stocks and bonds from 1900 to 2018 according the Summary Edition of the Credit Suisse Global Investment Returns Yearbook 2019. These returns include the disappointing real returns of nominal bond returns across the world caused by dropping off the gold standard (among other things), as well as the returns of markets which totally collapsed (Russia and China) during the 20th century.

We don't know the distribution of future stock and bond returns, but the Central limit theorem exists. By using long-term geometric averages as growth trends for both asset classes (which are necessarily smaller than the arithmetic averages), and by calculating a weighted average to derive an allocation-specific growth trend, without adding any bonus for the reduction in volatility due to imperfect correlation, VPW's choice of growth trend is conservative.

VPW's growth trend must necessarily be a geometric average return to properly discriminate between high and low returns and achieve its objective of causing withdrawal amounts to go up or down accordingly, because the Nth withdrawal amount is determined by the geometric average portfolio return between retirement and the withdrawal. As a quick example, I've just provided a formal proof that showed (among its calculations) that the 35th withdrawal at age 99, from an initial $1,000,000 portfolio at age 65, is equal to ($15,241 X (1 + cumulative return during the 34 years from 65 to 99)), regardless of what each individual annual return was. This is equal to ($15,241 X ( 1 + geometric average return from 65 to 99)^34).

In other words, with a 3.45% growth trend, the Nth withdrawal amount will be higher than the initial withdrawal amount if the annualized portfolio return since retirement is higher than 3.45%, and it will be lower than the initial withdrawal amount if the annualized portfolio return is lower than 3.45%. Note that VPW doesn't promise that a 50/50 stocks/bonds portfolio will have higher, equal, or lower returns than 3.45% over the long run. On the contrary, the VPW Worksheet specifically contains a Required Flexibility section which I've repeatedly explained in posts like this very recent one.

Contrary to the poster's claims, VPW is quite conservative when properly used. This means combining portfolio withdrawals with (current or future) stable lifelong income and making sure the retiree has ample comfort at the start of retirement based on the required flexibilty estimate. But, more importantly, VPW accepts and advertises through its name (variable percentage withdrawal) that withdrawal amounts will fluctuate during retirement. Whether fluctuations will eventually trend up or down can't be know in advance, as predicting the future returns of a portfolio, over the next 30, 40, 50, 60 or more years, is simply impossible.

Unlike the so-called "safe" withdrawal rate (SWR) method or prediction-driven withdrawal methods, VPW doesn't try to estimate current valuations to futilely try to calibrate an initial withdrawal in the hope that future withdrawals won't get lower. There are countless threads, in this forum, about reducing the initial withdrawal amount to 2% (sometimes less) just in fear of ever getting a smaller withdrawal amount, during retirement, than the first year's amount. VPW is different. VPW accepts that withdrawal amounts will fluctuate, possibly up or down of the initial withdrawal amount.

One of the primary objectives of VPW is to safely spend most (but not all) the portfolio while alive, instead of dying with a huge unspent portfolio. VPW and the VPW worksheet have been very carefully and prudently designed, based on mathematics, to achieve this objective with simplicity.

[SevenBridgesRoad]

That's a fine plan. There's a lot of security in having a floor.

I agree. The VPW Plan calls for a floor. My floor of SS and SPIA provides a ton of security.

[SnowBog]

That's a fine plan. There's a lot of security in having a floor.

I agree. The VPW Plan calls for a floor. My floor of SS and SPIA provides a ton of security.

+1

Seems people keep forgetting this part of VPW. It's not intended to be used "on its own", but in combination with a "lifelong income" source.

In our case, we are also planning on a DIY Annuity of sorts using primarily I & EE Bonds to bridge the years from "retirement" to delayed pensions & social security. If the plan holds, we'll have our "floor" covered for our entire life.

VPW will provide our upper limit on spending (mostly discretionary as our "floor" covers essentials). VPW is both surprisingly simple yet very powerful.

And my personal favorite part, no "predictions required". I have no clue what the future returns will be, and I don't want to pull a bunch of levers and tweak a bunch of variables that I have no clue if they'll be right or wrong. And no way my non-financially inclined spouse would be interested in - or want to deal with that IMHO unnecessary complexity. This was a big reason I was drawn to VPW, and a big reason I'll stay - is a simple, easy to follow, potentially one-update a year (change portfolio value).

No withdrawal method is "perfect". But VPW is about as perfect as I expect we'll find for our needs. My continued thanks to longinvest (and the others who have contributed) for bringing us VPW.

[Ben Mathew]

People should be aware that VPW's aggressive portfolio amortization, even under WAG expected return assumptions of 5.0% and 2.0%, is likely to produce declining withdrawals—at the 50th percentile, not just the 5th percentile.

The poster's tool uses arithmetic average returns to calibrate the generation of its pseudo-random sequence of returns. As the geometric average is necessarily smaller than the arithmetic average in presence of volatility (this article on Wikipedia provides a proof of the inequality), the tool projects a declining average when compounding returns. What's most frightening, about it, is that the tool's author didn't realize this [Unnecessary comment removed by admin LadyGeek] about VPW with a broken example.

The portfolio balance will be right tailed after compounding, making the median less than the average. Even if you work with log returns (which is what I do), once you convert the log returns into dollars for the portfolio balance and spending, you are back with a right tailed distribution.

Here's an example that shows why the median portfolio balance and spending are less than what you would expect from average returns:

Suppose returns are equally likely to be 10% or 20%. So expected return is 15%.

Let's compound this over two periods:

There are four possible outcomes, each equally likely:

20% followed by 20%
20% followed by 10%
10% followed by 20%
10% followed by 10%

In each of these scenarios, $100 becomes:

$100(1.20)(1.20) = $144.00
$100(1.20)(1.10) = $132.00
$100(1.10)(1.20) = $132.00
$100(1.10)(1.10) = $121.00

The average balance is $132.25. Note that this corresponds to the balance determined using the expected return of 15%:

$100(1.15)(1.15) = $132.25

But the median balance is a bit lower at $132.00.

The more variance there is in returns and the longer it compounds, the more the difference there is between the median payout and the average payout.

You can see this effect in the raw historical simulation as well. It's not specific to the Monte Carlo methodology.

[Ben Mathew]

VPW will provide our upper limit on spending (mostly discretionary as our "floor" covers essentials).

That's fine. But longinvest has insisted that people should spend the VPW withdrawal amount, not use it as a ceiling.

[TimeRunner]

That's fine. But longinvest has insisted that people should spend the VPW withdrawal amount, not use it as a ceiling.

I don't think "insisted" is correct, but I'm not going to go back through hundreds of posts to confirm that. I've certainly been using it as a ceiling and am comfortable with that approach. I'm pretty sure longinvest isn't going to scold me.

[SnowBog]

VPW will provide our upper limit on spending (mostly discretionary as our "floor" covers essentials).

That's fine. But longinvest has insisted that people should spend the VPW withdrawal amount, not use it as a ceiling.

For my two cents, yes - and no... And I personally feel like this is another area often taken out of context.

In the most literal sense, yes I've seen comments to that effect. And IMHO rightfully so, the whole point is to provide a simple withdrawal method, not a set of "guardrails". Besides, the underlying principal is the "variable" aspect - which in a way becomes "sell correcting" (within reason). So if you don't use the full withdrawal, you aren't really following the "intent" of VPW, and you'll likely end up with a large unspent pile of money (which goes against one of the goals of VPW over SWR as I understand it).

However, "spend" isn't what I've seen/understood. I've not seen recommendations that one should "inflate their expenses" such as to use up 100% of the amount. More that one can feel free to use up 100% in the way they'd like, which could be a mix of spending, acceleration of gifting to heirs/charity, etc. Again, one does not need to "reserve" or "limit" their withdrawal (other than retaining "required flexibility" to scale back if/when needed).

I've also seen references related to VPW being an intuitive transition from ones working years into retirement. Perhaps this is more for people with "variable" income (like me), where the amount "available" to spend/gift/save/etc. may vary from year to year. I've had many years of looking at our "variable" income (while working) and figuring out where it's going to go. My perspective is "nothing changes" going to VPW. As an example, whether while working or when retired, let's say we have an "extra" $10k of "net income" in a given year - we will ultimately still spend/gift/"save" that amount. Yes, I understand "literally" VPW would say "save" isn't an option, but again I don't believe it's intending for us to artificially increase our expenses either - and at some point we may just not have anything at the moment we want to spend/gift/etc. on. IMHO that's perfectly fine - we aren't "depriving" ourselves, or attempting to defer "income" to later years thinking it's going to have a material impact on a better retirement result - we just don't have anything at that moment we'd spend money on. But maybe the following year, we'd consider replacing our car - if/when we had an "extra" $10k ($20k total - and purely an example). IIRC longinvest has supported this "carryover" in other posts, although IIRC they recommend "withdrawing"/"removing" the amount(s) from the portfolio to keep "outside" VPW. Again, this how we currently operate - we might "set aside" some excess towards a future planned expense, and once fully funded, we pull the trigger.

[dcabler]

VPW will provide our upper limit on spending (mostly discretionary as our "floor" covers essentials).

That's fine. But longinvest has insisted that people should spend the VPW withdrawal amount, not use it as a ceiling.

For my two cents, yes - and no... And I personally feel like this is another area often taken out of context.

In the most literal sense, yes I've seen comments to that effect. And IMHO rightfully so, the whole point is to provide a simple withdrawal method, not a set of "guardrails". Besides, the underlying principal is the "variable" aspect - which in a way becomes "sell correcting" (within reason). So if you don't use the full withdrawal, you aren't really following the "intent" of VPW, and you'll likely end up with a large unspent pile of money (which goes against one of the goals of VPW over SWR as I understand it).

However, "spend" isn't what I've seen/understood. I've not seen recommendations that one should "inflate their expenses" such as to use up 100% of the amount. More that one can feel free to use up 100% in the way they'd like, which could be a mix of spending, acceleration of gifting to heirs/charity, etc. Again, one does not need to "reserve" or "limit" their withdrawal (other than retaining "required flexibility" to scale back if/when needed).

I've also seen references related to VPW being an intuitive transition from ones working years into retirement. Perhaps this is more for people with "variable" income (like me), where the amount "available" to spend/gift/save/etc. may vary from year to year. I've had many years of looking at our "variable" income (while working) and figuring out where it's going to go. My perspective is "nothing changes" going to VPW. As an example, whether while working or when retired, let's say we have an "extra" $10k of "net income" in a given year - we will ultimately still spend/gift/"save" that amount. Yes, I understand "literally" VPW would say "save" isn't an option, but again I don't believe it's intending for us to artificially increase our expenses either - and at some point we may just not have anything at the moment we want to spend/gift/etc. on. IMHO that's perfectly fine - we aren't "depriving" ourselves, or attempting to defer "income" to later years thinking it's going to have a material impact on a better retirement result - we just don't have anything at that moment we'd spend money on. But maybe the following year, we'd consider replacing our car - if/when we had an "extra" $10k ($20k total - and purely an example). IIRC longinvest has supported this "carryover" in other posts, although IIRC they recommend "withdrawing"/"removing" the amount(s) from the portfolio to keep "outside" VPW. Again, this how we currently operate - we might "set aside" some excess towards a future planned expense, and once fully funded, we pull the trigger.

Reminds me of the discussions that happen regarding RMD's where the RMD amount is more than the retiree can spend, with the responses usually being along the lines of "you must withdraw it, but you don't have to spend it"

Yes, I think an argument can be made for keeping it "outside" of the amortized portfolio or "inside". Outside can serve a useful purpose such as unplanned expense or even that rainy day where the calculated withdrawal is less than your basic living expenses. Yeah, that's all mitigatable other ways, but rainy days can still happen even with mitigation. Keeping it inside can do the same thing, though it's spread across the remaining years, but the more years you underspend, the larger your margin will be.

In our case, we're using an amortization method and we have a $0 terminal value. A lot of people don't know that Amortization isn't required to have a $0 terminal value by the way. Anyway, we don't plan to be a slave to a spreadsheet but to use it as a guide with a number of checkpoints along the way during our retirement to consider things such as SPIAs. And if things are going particularly well, we may consider just pushing the terminal date out some. We'll see. We have only one kiddo and we're not targeting a particular inheritance for her - whatever is left, she gets...

Cheers.

[longinvest]

People should be aware that VPW's aggressive portfolio amortization, even under WAG expected return assumptions of 5.0% and 2.0%, is likely to produce declining withdrawals—at the 50th percentile, not just the 5th percentile.

The poster's tool uses arithmetic average returns to calibrate the generation of its pseudo-random sequence of returns. As the geometric average is necessarily smaller than the arithmetic average in presence of volatility (this article on Wikipedia provides a proof of the inequality), the tool projects a declining average when compounding returns. What's most frightening, about it, is that the tool's author didn't realize this [Unnecessary comment removed by admin LadyGeek] about VPW with a broken example.

The portfolio balance will be right tailed after compounding, making the median less than the average. Even if you work with log returns (which is what I do), once you convert the log returns into dollars for the portfolio balance and spending, you are back with a right tailed distribution.

Here's an example that shows why the median portfolio balance and spending are less than what you would expect from average returns:

Suppose returns are equally likely to be 10% or 20%. So expected return is 15%.

Let's compound this over two periods:

There are four possible outcomes, each equally likely:

20% followed by 20%
20% followed by 10%
10% followed by 20%
10% followed by 10%

In each of these scenarios, $100 becomes:

$100(1.20)(1.20) = $144.00
$100(1.20)(1.10) = $132.00
$100(1.10)(1.20) = $132.00
$100(1.10)(1.10) = $121.00

The average balance is $132.25. Note that this corresponds to the balance determined using the expected return of 15%:

$100(1.15)(1.15) = $132.25

But the median balance is a bit lower at $132.00.

The more variance there is in returns and the longer it compounds, the more the difference there is between the median payout and the average payout.

You can see this effect in the raw historical simulation as well. It's not specific to the Monte Carlo methodology.

It's quite unfortunate that forum member Ben Mathew cut the next four paragraphs of my post, when quoting it. So, I'll do it:

The selected growth trends for stocks and bonds, in the VPW worksheet, are based on the long-term geometric average (or annualized) real returns of world stocks and bonds from 1900 to 2018 according the Summary Edition of the Credit Suisse Global Investment Returns Yearbook 2019. These returns include the disappointing real returns of nominal bond returns across the world caused by dropping off the gold standard (among other things), as well as the returns of markets which totally collapsed (Russia and China) during the 20th century.

We don't know the distribution of future stock and bond returns, but the Central limit theorem exists. By using long-term geometric averages as growth trends for both asset classes (which are necessarily smaller than the arithmetic averages), and by calculating a weighted average to derive an allocation-specific growth trend, without adding any bonus for the reduction in volatility due to imperfect correlation, VPW's choice of growth trend is conservative.

VPW's growth trend must necessarily be a geometric average return to properly discriminate between high and low returns and achieve its objective of causing withdrawal amounts to go up or down accordingly, because the Nth withdrawal amount is determined by the geometric average portfolio return between retirement and the withdrawal. As a quick example, I've just provided a formal proof that showed (among its calculations) that the 35th withdrawal at age 99, from an initial $1,000,000 portfolio at age 65, is equal to ($15,241 X (1 + cumulative return during the 34 years from 65 to 99)), regardless of what each individual annual return was. This is equal to ($15,241 X ( 1 + geometric average return from 65 to 99)^34).

In other words, with a 3.45% growth trend, the Nth withdrawal amount will be higher than the initial withdrawal amount if the annualized portfolio return since retirement is higher than 3.45%, and it will be lower than the initial withdrawal amount if the annualized portfolio return is lower than 3.45%. Note that VPW doesn't promise that a 50/50 stocks/bonds portfolio will have higher, equal, or lower returns than 3.45% over the long run. On the contrary, the VPW Worksheet specifically contains a Required Flexibility section which I've repeatedly explained in posts like this very recent one.

VPW is calibrated using a growth trend representing a geometric average return, or more precisely, a compound annual growth rate (CAGR). Let's express this using an example similar to that of forum member Ben Mathew's post.

The system can only generate two returns: 10% and 20%. Both are equally likely.

The CAGR, assuming both returns happen an equal number of times, is:

• CAGR: (((1 + 10%) X (1 + 20%))^(1 / 2) - 1) = 14.89125293%
  • because multiplication is commutative and (X^N)^(1/N) = X
    • Example:
      ((1 + 10%) X (1 + 20%) X (1 + 20%) X (1 X 10%))^(1/4) - 1
      = (((1 + 10%) X (1 + 20%)) X ((1 + 10%) X (1 X 20%)))^(1/4) - 1
      = (((1 + 10%) X (1 + 20%))^2)^(1/4) - 1
      = (1.32^2)^(1/2 X 1/2) - 1
      = ((1.32^2)^(1/2))^(1/2) - 1
      = 1.32^(1/2) - 1
      = 1.1489125293 - 1
      = 14.89125293%

Let's check this with a few examples.

1) Sequence of 2 returns: 10%, 20%

An initial $100 grows to ($100 X (1 + 10%) X (1 + 20%)) = $132
CAGR: ($132 / $100)^(1 / 2) - 1 = 14.89125293%

2) Sequence of 4 returns: 10%, 20%, 20%, 10%

An initial $100 grows to ($100 X (1 + 10%) X (1 + 20%) X (1 + 20%) X (1 + 10%)) = $174.24
CAGR: ($174.24 / $100)^(1 / 4) - 1 = 14.89125293%

3) Sequence of 6 returns: 20%, 10%, 20%, 20%, 10%, 10%
An initial $100 grows to ($100 X (1 + 20%) X (1 + 10%) X (1 + 20%) X (1 + 20%) X (1 + 10%) X (1 + 10%)) = $229.9968
CAGR: ($229.9968 / $100)^(1 / 6) - 1 = 14.89125293%

No matter how many times the 10% and 20% returns are repeated, as long as their counts are equal, the CAGR will necessarily be 14.89125293%.

So, over a simulation where 10% and 20% are equally likely to happen, the CAGR at the 50% percentile will tend towards 14.89125293%.

The fair VPW schedule to use for such a simulation has a 14.89125293% growth trend and would result into a relatively stable withdrawal amount (not declining nor increasing) at the 50% percentile.

The simulation used by forum member Ben Mathew in the first quote, at the top of this post, was calibrated to deliver an approximate 2.7% CAGR at the 50% percentile based on arithmetic average 5.0% and 2.0% returns for stocks and bonds (and undisclosed volatility for both assets). He used this simulation to claim that a VPW schedule for a 50/50 stocks/bonds portfolio (calibrated with a 3.45% growth trend, based on the 5.0% and 1.9% historical CAGRs of world stocks and bonds) results into a declining average withdrawal. This is unfair. Knowingly or not, the simulation was setup to make VPW look bad.

[smectym]

VPW will provide our upper limit on spending (mostly discretionary as our "floor" covers essentials).

That's fine. But longinvest has insisted that people should spend the VPW withdrawal amount, not use it as a ceiling.

Ben, pretty sure longinvest has never stated that VPW adherents are violating any protocol if they elect to withdraw less than the full portfolio percentage amount proposed on the VPW grid (vertical axis retiree age, horizontal axis stock/bond portfolio allocation).

Nor has longinvest, or any other serious VPW proponent I’m aware of, argued that any withdrawals under the VPW rubric somehow must be *spent*, as in used for consumption, as opposed to saved or invested.

In my view the chief problem with retirement savings withdrawals in excess of consumption needs, even if green-lighted by VPW, arises in the case of higher-income households that might incur unwelcome and avoidable additional tax liability. But that’s really more an issue to be settled between the retiree and his accountant: This is a “nice problem to have” that may not be that material for most withdrawal scenarios; and VPW has never purported to solve for any household’s idiosyncratic tax situation.

VPW on its face, by inherent design, simply and transparently protects against unexpected or unpredictable late-stage withdrawal strategy failures—even in the case of baroquely uncooperative market environments. Therefore, while any withdrawal protocol can in principle always be tweaked at the margin, it’s unlikely that attacks on the fundamental methodology of VPW will gain much traction. We owe longinvest and his colleagues a reiterated vote of thanks.

[ResearchMed]

VPW will provide our upper limit on spending (mostly discretionary as our "floor" covers essentials).

That's fine. But longinvest has insisted that people should spend the VPW withdrawal amount, not use it as a ceiling.

What longinvest actually wrote, including the bit above, is:

One of the primary objectives of VPW is to safely spend most (but not all) the portfolio while alive, instead of dying with a huge unspent portfolio. VPW and the VPW worksheet have been very carefully and prudently designed, based on mathematics, to achieve this objective with simplicity.

[emphasis added]

That is, spend most of it "while alive", NOT spending "all" of each year's withdrawal amount within that particular year.
That's very different from what you have claimed.

Save some of the withdrawal (or several) for that extra trip, or for a newer car before originally planned, or whatever one wants whenever one wants it... "this year" OR in a future year when one wants a bit of a splurge (relatively speaking, since the model includes this spending at some point).

It's very much like the confusion about RMDs, where some people mistakenly believe that they must SPEND what is required to be withdrawn from the pre-tax account within each year. Nope. It can be put into taxable account for later spending (e.g., that special vacation) or it can be invested for longer in the future, etc.). Or it can be gifted/donated that year OR in a future year.

A main goal of the VPW strategy is not to spend "too little" during retirement, when one could have afforded - and enjoyed - more of whichever pleasures one was planning during retirement.

That does NOT mean that one is "supposed" to spend some current money on something one isn't ready to buy.
As with pre-retirement, perhaps save some for various lumpy expenses, be they "needed" or discretionary.

RM

[Ben Mathew]

VPW is calibrated using a growth trend representing a geometric average return, or more precisely, a compound annual growth rate (CAGR). Let's express this using an example similar to that of forum member Ben Mathew's post.

The system can only generate two returns: 10% and 20%. Both are equally likely.

The average CAGR, assuming both returns happen an equal number of times, is:

• Average CAGR: (((1 + 10%) X (1 + 20%))^(1 / 2) - 1) = 14.89125293%

OK, I think I understand what you're saying.

But first, let me go over a simplified version of how the Monte Carlo simulation I shared works:

Continuing with the example above: We observe a historical sequence with equal proportions of 10% and 20%. So the distribution of annual returns is 10% and 20% with equal probability. The mean of this annual return distribution ("the expected annual return") is 15%. Importantly, it is not 14.89%, which is the CAGR of the historical sequence.

Monte Carlo sequences are then constructed by drawing randomly from this annual return distribution. In a sequence of length two years, we have four possible combinations that I listed earlier, each with equal probability:

$100(1.20)(1.20) = $144.00 [CAGR: 20.00%]
$100(1.20)(1.10) = $132.00 [CAGR: 14.89%]
$100(1.10)(1.20) = $132.00 [CAGR: 14.89%]
$100(1.10)(1.10) = $121.00 [CAGR: 10.00%]

As I showed earlier, the expected payout is $132.25. This corresponds to the expected return of 15%:

$100(1.15)(1.15) = $132.25

The 14.89% CAGR of the observed historical sequence corresponds to the median payout:

$100(1.1489)(1.1489) = $132.00

So I believe what you are saying is that the 5.0% and 1.9% WAG returns corresponds to the CAGR of the historical sequence (14.89% in this example) and not to the expected annual return (15% in this example). In other words, you are amortizing so that the median payout will be constant, not so that the expected payout will be constant.

In that case, yes, you are correct. The median spending will be flat under your return assumptions. The expected annual return will need to be higher than 5.0% and 1.9% to simulate this.

I tried some combinations of expected returns that will make the median flat. I find that bumping up the WAG returns by 0.6% will produce the desired result. So we have

Expected real stock return = 5.0% + 0.6% = 5.6%
Expected real bond return = 1.9% + 0.6% = 2.5%

So

r = .50 * 5.6% + .50 * 2.5% = 4.05%
r_wag = .50 * 5.0% + .50 * 1.9% = 3.45%
g = (1+r)/(1+r_wag) - 1 = (1+4.05%)/(1+3.5%) - 1 = 0.6%

Entering these inputs into the simulation, I get the following monthly spending outcomes:



Median withdrawal holds steady from $4,045 per month at the start to $4,081 per month by the end of retirement. If markets do badly, at the 5th percentile level, spending declines to $1,303 per month by the end of retirement.

I hope that this is a more accurate representation of your assumptions about future returns.

[Ben Mathew]

That's fine. But longinvest has insisted that people should spend the VPW withdrawal amount, not use it as a ceiling.

I don't think "insisted" is correct, but I'm not going to go back through hundreds of posts to confirm that. I've certainly been using it as a ceiling and am comfortable with that approach. I'm pretty sure longinvest isn't going to scold me.

Ben, pretty sure longinvest has never stated that VPW adherents are violating any protocol if they elect to withdraw less than the full portfolio percentage amount proposed on the VPW grid (vertical axis retiree age, horizontal axis stock/bond portfolio allocation).

Nor has longinvest, or any other serious VPW proponent I’m aware of, argued that any withdrawals under the VPW rubric somehow must be *spent*, as in used for consumption, as opposed to saved or invested.

What longinvest actually wrote, including the bit above, is:

One of the primary objectives of VPW is to safely spend most (but not all) the portfolio while alive, instead of dying with a huge unspent portfolio. VPW and the VPW worksheet have been very carefully and prudently designed, based on mathematics, to achieve this objective with simplicity.

[emphasis added]
That is, spend most of it "while alive", NOT spending "all" of each year's withdrawal amount within that particular year.
That's very different from what you have claimed.

"Insist" may be too strong a word for it, but below is what I'm referring to:

2. VPW is calculating a withdrawal value higher than I currently need to meet my expenses.

Which is better, to withdraw what VPW suggests, or to take out what I need and leave the rest invested?

One of the goals of VPW is to allow deferred spending to actually happen! When I save money, today, it isn't with the objective of dying with the biggest possible portfolio; it's because I am deferring spending I could do today to later.

The thing is this. When assets prices are higher, the portfolio is larger and VPW withdrawal amounts are likely bigger than what the retiree needs for great comfort. Let's say that the excess amount represents 1% of the retiree's portfolio. If the retiree leaves this money in the portfolio, this will only increase future withdrawal amounts by 1%. If, for example, next year's withdrawal amount drops by -20%, this might result in a drop of -19.2% instead. The retiree won't notice the difference.

If the retiree thinks of putting the money aside, just in case future withdrawals drop, this means that the retiree hasn't appropriately planned for using the variable percentage withdrawal method. The retiree is supposed to already have ample flexibility to reduce expenses in bad markets, taking into account stable lifelong income and asset allocation.

So, we're back to square one: what to do with the money? I say: either spend it, gift it, or earmark it for future specific near-term spending (leaving it appropriately in a savings account).

Here are ideas from previous posts:

• Provide gifts to children, grandchildren, and favorite charities while alive, taken from excess money that VPW withdrawals provide and that the retiree doesn't need. Take the opportunity to check that the money is properly used or managed before giving additional gifts.
• For major donations, build a separate portfolio (possibly managed by the receiving charity organization) and regularly add to it when VPW provides excess money over the retiree's needs.

Every year of retirement, my wife and I plan to give money we don't need and enjoy the process (hopefully making a difference in the lives of others).

In summary, I suggest to withdraw the money as suggested by the VPW worksheet and use it for something fun or meaningful which will increase the retiree's happiness. Isn't it for exactly this that the money was saved and invested decades earlier?

[Ben Mathew]

Therefore, while any withdrawal protocol can in principle always be tweaked at the margin, it’s unlikely that attacks on the fundamental methodology of VPW will gain much traction.

If by the fundamental methodology of VPW, you mean amortizing the portfolio to calculate withdrawals, then I'm a strong proponent. I think it's the best withdrawal strategy. It's flexible, commonsensical, and the only withdrawal strategy that has any basis in economics. I like it so much that I've helped write the wiki article on it: Amortization Based Withdrawal (ABW).

All I'm saying is to consider using numbers smaller than 5.0% and 1.9% to do the amortization. Surely that's not fundamental to the methodology?

[smectym]

That's fine. But longinvest has insisted that people should spend the VPW withdrawal amount, not use it as a ceiling.

I don't think "insisted" is correct, but I'm not going to go back through hundreds of posts to confirm that. I've certainly been using it as a ceiling and am comfortable with that approach. I'm pretty sure longinvest isn't going to scold me.

Ben, pretty sure longinvest has never stated that VPW adherents are violating any protocol if they elect to withdraw less than the full portfolio percentage amount proposed on the VPW grid (vertical axis retiree age, horizontal axis stock/bond portfolio allocation).

Nor has longinvest, or any other serious VPW proponent I’m aware of, argued that any withdrawals under the VPW rubric somehow must be *spent*, as in used for consumption, as opposed to saved or invested.

What longinvest actually wrote, including the bit above, is:

One of the primary objectives of VPW is to safely spend most (but not all) the portfolio while alive, instead of dying with a huge unspent portfolio. VPW and the VPW worksheet have been very carefully and prudently designed, based on mathematics, to achieve this objective with simplicity.

[emphasis added]
That is, spend most of it "while alive", NOT spending "all" of each year's withdrawal amount within that particular year.
That's very different from what you have claimed.

"Insist" may be too strong a word for it, but below is what I'm referring to:

2. VPW is calculating a withdrawal value higher than I currently need to meet my expenses.

Which is better, to withdraw what VPW suggests, or to take out what I need and leave the rest invested?

One of the goals of VPW is to allow deferred spending to actually happen! When I save money, today, it isn't with the objective of dying with the biggest possible portfolio; it's because I am deferring spending I could do today to later.

The thing is this. When assets prices are higher, the portfolio is larger and VPW withdrawal amounts are likely bigger than what the retiree needs for great comfort. Let's say that the excess amount represents 1% of the retiree's portfolio. If the retiree leaves this money in the portfolio, this will only increase future withdrawal amounts by 1%. If, for example, next year's withdrawal amount drops by -20%, this might result in a drop of -19.2% instead. The retiree won't notice the difference.

If the retiree thinks of putting the money aside, just in case future withdrawals drop, this means that the retiree hasn't appropriately planned for using the variable percentage withdrawal method. The retiree is supposed to already have ample flexibility to reduce expenses in bad markets, taking into account stable lifelong income and asset allocation.

So, we're back to square one: what to do with the money? I say: either spend it, gift it, or earmark it for future specific near-term spending (leaving it appropriately in a savings account).

Here are ideas from previous posts:

• Provide gifts to children, grandchildren, and favorite charities while alive, taken from excess money that VPW withdrawals provide and that the retiree doesn't need. Take the opportunity to check that the money is properly used or managed before giving additional gifts.
• For major donations, build a separate portfolio (possibly managed by the receiving charity organization) and regularly add to it when VPW provides excess money over the retiree's needs.

Every year of retirement, my wife and I plan to give money we don't need and enjoy the process (hopefully making a difference in the lives of others).

In summary, I suggest to withdraw the money as suggested by the VPW worksheet and use it for something fun or meaningful which will increase the retiree's happiness. Isn't it for exactly this that the money was saved and invested decades earlier?

Ben, Of course, VPW does propose withdrawal percentages for different age and asset allocation cohorts. And yes: an explicit objective of VPW is to inform the retiree withdrawal process, as it were, ambidextrously, i.e., not just to ensure the retiree withdraw only an amount that will not exhaust the portfolio; but also to ensure the retiree not needlessly impoverish himself or his dependents by an unduly overcautious withdrawal protocol. This is not just an abstract matter of the dead guy leaving money “on the table“ that he won’t need in the afterlife in any event. This affects the QOL of the retiree household, their peace of mind, and the amount of support available to other dependents, adult children, and charities. So sort of a big deal. VPW goes some way toward addressing such problems. In that context, it’s not surprising that longinvest might point out several productive uses for retiree withdrawal amounts in excess of the minimum withdrawal required to sustain life. But none of that amounts to some sort of mandate or stricture that failure to withdraw the sum specified in the VPW grid amounts to a violation, a mistake, or any other pejorative.

[Ben Mathew]

[...] But none of that amounts to some sort of mandate or stricture that failure to withdraw the sum specified in the VPW grid amounts to a violation, a mistake, or any other pejorative.

I read the following as a "mistake":

If the retiree thinks of putting the money aside, just in case future withdrawals drop, this means that the retiree hasn't appropriately planned for using the variable percentage withdrawal method. The retiree is supposed to already have ample flexibility to reduce expenses in bad markets, taking into account stable lifelong income and asset allocation.

[longinvest]

I tried some combinations of expected returns that will make the median flat. I find that bumping up the WAG returns by 0.6% will produce the desired result. So we have

[...] real stock return = 5.0% + 0.6% = 5.6%
[...] real bond return = 1.9% + 0.6% = 2.5%

According to the Credit Suisse Global Investment Returns Yearbook 2019, the real CAGR of world stocks was 5.0% and the real CAGR of world bonds was 1.9% from 1900 to 2018. A simulation of pseudo-historical random returns should therefore be set up such that a 100% stocks $1,000,00 portfolio grows to approximately ($1,000,000 X (1 + 5.0%)^34) = $5,516,015 over 34 years, and that a 100% bonds $1,000,00 portfolio grows to approximately ($1,000,000 X (1 + 1.9%)^34) = $1,932,397 over 34 years at the 50% percentile.

In a previous post, forum member Ben Mathew wrote:

For the second Monte Carlo simulation that I shared, where expected stock return was set to 5.0% to match the WAG return, we get the following graph:
[...]
Over 35 years, $1 million in stocks grows to
[...]
50th percentile: $3.0 million

This tells us that his tool is probably configured with a 19% Std Dev for stocks.

Code: Select all

arithmetic return ≈ CAGR + (variance / 2)
5.0% ≈ (($3,000,000 / $1,000,000)^(1 / 35) - 1)+ (variance / 2)
5.0% ≈ 3.19% + (variance / 2)
variance ≈ (5.0% - 3.19%) X 2
variance ≈ 1.81% X 2
variance ≈ 3.62%

Std Dev ≈ (0.0362)^(1 / 2)
Std Dev ≈ 19%

Instead, forum member Ben Mathew is proposing to simulate pseudo-random returns such that the real CAGR of stocks will approximately be (5.6% - 1.81%) = 3.79%, growing a 100% stocks $1,000,00 portfolio to approximately ($1,000,000 X (1 + 3.79%)^34) = $3,542,317 over 34 years at the 50% percentile. That's significantly less than the $5,516,015 that a proper pseudo-historical simulation should deliver.

I think that I've spent enough time on this off-topic discussion. I created this thread in July 2013, a little over 10 years ago, to discuss VPW.

Other threads can be created to discuss topics like the difference between arithmetic and geometric average returns, or how to properly model pseudo-historical returns in a Monte Carlo simulator, as well as the deep flaws of Monte Carlo simulators. I think that it would be best for me to stop paying attention, in this thread, to posts about an unrelated prediction-driven withdrawal tool that projects, when using the parameters proposed by its author, that there's a 1 in 20 chances that, over the next 34 years, stocks will decline by at least -55%:

So, over 35 years, $1 million in stocks grows to
[...]
5th percentile: $446K

This translates to gross returns of [...] -55% [...]

If there was a 1 in 20 chances that I'd be killed by a car every time I crossed a street, I would never cross a street. But, this isn't the thread to discuss the simulator or give opinions about it. It has its own thread.

[longinvest]

Ben, Of course, VPW does propose withdrawal percentages for different age and asset allocation cohorts. And yes: an explicit objective of VPW is to inform the retiree withdrawal process, as it were, ambidextrously, i.e., not just to ensure the retiree withdraw only an amount that will not exhaust the portfolio; but also to ensure the retiree not needlessly impoverish himself or his dependents by an unduly overcautious withdrawal protocol. This is not just an abstract matter of the dead guy leaving money “on the table“ that he won’t need in the afterlife in any event. This affects the QOL of the retiree household, their peace of mind, and the amount of support available to other dependents, adult children, and charities. So sort of a big deal. VPW goes some way toward addressing such problems. In that context, it’s not surprising that longinvest might point out several productive uses for retiree withdrawal amounts in excess of the minimum withdrawal required to sustain life. But none of that amounts to some sort of mandate or stricture that failure to withdraw the sum specified in the VPW grid amounts to a violation, a mistake, or any other pejorative.

Smectym and the few other posters before you, thank you for explaining my previous posts and statements so elegantly.

When I'm asked questions about VPW, in this thread, I try to explain how it's designed and how it works. In particular, I think that it would be a mistake, for me, not to warn about the "Sell less high! Sell more low!" behavior that would result from making smaller withdrawals when markets are up in the hope of making bigger ones when markets are down. But, I also explained in other posts that taking a slightly smaller or bigger withdrawal amount than suggested by VPW, once in a while, isn't a problem as VPW will automatically adjust future withdrawal amounts accordingly.

This thread is in the theory forum, not in one of the personal investments or finance forums. In our personal lives, it's up to each of us to decide how to manage our own money and investments. It's fine for someone to use VPW for only part of one's wealth, if this matches one's personal objectives. Some users might even decide to only use VPW as a ceiling while fully understanding that this is likely to defeat one of its main objectives, that of spending most of the portfolio while alive. But, I don't think that this is the best thread to discuss the various ways of using VPW in a way that defeats one or more of its objectives. I'll continue to focus my posts on how to use VPW to achieve its objectives.

Thanks again, Smectym, SevenBridgesRoad, SnowBog, TimeRunner, Dcabler, and ResearchMed for explaining various aspects of VPW in your own words.

[Ben Mathew]

According to the Credit Suisse Global Investment Returns Yearbook 2019, the real CAGR of world stocks was 5.0% and the real CAGR of world bonds was 1.9% from 1900 to 2018. A simulation of pseudo-historical random returns should therefore be set up such that a 100% stocks $1,000,00 portfolio grows to approximately ($1,000,000 X (1 + 5.0%)^34) = $5,516,015 over 34 years, and that a 100% bonds $1,000,00 portfolio grows to approximately ($1,000,000 X (1 + 1.9%)^34) = $1,932,397 over 34 years at the 50% percentile.

To be clear, a simulation of the VPW strategy does not need to assume that the returns you assumed when you constructed the strategy will in fact happen. It can be simulated with any distribution of returns that someone else finds plausible. There's nothing special about your assumption. What you can specify in the strategy is the rate at which you will amortize the portfolio, which you have said is 5.0% and 1.9%. What you can't specify is what the distribution of future returns will be. It does not need to have 5.0% and 1.9% as either the mean or the median or the 5th percentile or the 95th percentile.

What I've done is shared a range of simulations with different expected returns and simulation methods. I have shared Monte Carlo simulations where the expected real returns were {4.0%, 2.0%}, {5.0%, 1.9%}, and {5.6%, 2.5%}, and a raw historical simulation where it was {8.3%, 3.1%}.

None of these are right or wrong, because none of us know the true distribution of future returns, which is what matters. The best we can do is try to guess. You have tried to guess it by looking at historical world stock and bond returns. Others can try to guess it by looking at US historical returns. Still others can try to guess it by looking at the earnings yields of stocks and interest rates of bonds. I have shown how to change the expected return assumptions and create your own simulation.

I personally think that it makes sense to consider what stocks and bonds actually produce in terms of profits and interest. With bonds especially, it's quite strange that you would amortize the portfolio based on a 1.9% historical real return when the bonds in your portfolio are yielding a lot less. You were doing this for quite some time until the recent increase in interest rates eliminated the difference. Even if interest rates rise (which is not guaranteed), the bond market will have to fall to accomodate that. So if you have $500,000 in bonds yielding -0.5%, it does not make sense to consume out of it as if they are yielding 1.9%. Even if yields became 1.9% overnight, you wouldn't have the full $500,000 after the crash.

This is if bonds are not duration matched. If bonds are duration matched, then what you're doing is even more strange. Duration matching in some sense locks in the current balance and interest rate combination so that you get a more predicatable payout. So you should clearly use the current rate combined with your current balance to amortize the bond portfolio, not the historical 1.9% combined with your current balance. You can call this "prediction driven withdrawals" if you want, but it's simply reflecting the reality of the interest rates and bond portfolio balance combination that you are locked into (fully locked into if the bonds are separate and not rebalanced, and partially locked into if they are being rebalanced).

Though I have my own beliefs and guesses about the return distribution, I have not hard coded those into the simulator. Expected returns are easy to change. If anyone thinks my guesses are too low, it's easy to move the expected return slider to the right to increase it, recalculate the implied g using the formula I gave, move the spending tilt slider to the new g, and see the resulting simulation.

[sandramjet]

It's fine for someone to use VPW for only part of one's wealth, if this matches one's personal objectives.

You have frequently insisted that VPW implementation relies on having a "floor" amount that is stable to cover your needs. So it seems to me that it is a requirement, not an option based on personal objectives, to use VPW for only a part of of ones wealth. Whatever funds that base amount is in fact part of your wealth, isn't it?

[longinvest]

You have frequently insisted that VPW implementation relies on having a "floor" amount that is stable to cover your needs.

Sandramjet, this is incorrect. I wrote that VPW is meant to be combined with (current or future) stable lifelong income. It's only around age 80, not before, that I suggest making sure there's a sufficient lifelong income floor to live comfortably independently of future portfolio withdrawals.

Every month, in the forward test thread, I explain how the VPW worksheet replaces missing payments between retirement and the start of a future pension with portfolio withdrawals, keeping the plan ultra simple to execute with a single undivided portfolio.

So it seems to me that it is a requirement, not an option based on personal objectives, to use VPW for only a part of of ones wealth. Whatever funds that base amount is in fact part of your wealth, isn't it?

Here's what I wrote:

It's fine for someone to use VPW for only part of one's wealth, if this matches one's personal objectives.

Here are two examples to clarify what I meant:

- A very wealthy retiree possesses a collection of managed rental buildings and keeps them apart from the VPW plan. The collection of managed rental buildings is a part of the retiree's wealth that isn't included into the VPW plan.

- The forward test retiree has a retirement portfolio, a work pension, and will get lifelong Social Security payments starting next year. The portfolio and two pensions are all included into the VPW plan.

Note that, in the second example, whether the retiree owns a home or rents isn't mentioned, so we don't know. If the retiree owns a home, it's obviously not included into the VPW plan (but it has an impact on the retiree's personal finances, as might the income from the collection of managed rental buildings in the first example).

[dogagility]

IIRC longinvest has supported this "carryover" in other posts, although IIRC they recommend "withdrawing"/"removing" the amount(s) from the portfolio to keep "outside" VPW. Again, this how we currently operate - we might "set aside" some excess towards a future planned expense, and once fully funded, we pull the trigger.

Thanks for this practical insight in how you're using VPW, SnowBog. I handn't considered having a distinct balance set aside. Need to cogitate on this...