improving the 4% rule and solving the starting point paradox
improving the 4% rule and solving the starting point paradox
Michael Kitces introduced the starting point paradox back in 2008, where, under Bengen's "4% Rule", two people with nearly identical retirement savings can have dramatically different "safe" withdrawals due to market movement between their retirement dates even if they retire only a year apart. This issue seems highly problematic and the existing approaches for resolving it seem insufficient.
We think we have a solution based on thinking about the "drawdown path" of every retiree, i.e. the sequence of withdrawals and account values over their full retirement. We argue that a new retiree can follow the drawdown path of a previous retiree so long as they plan for the same final withdrawal date. So if you planned for a 40 year retirement 10 years ago, I can start following your drawdown path today (in terms of withdrawal percent, not absolute dollar amounts) so long as I'm ok with a 30 year retirement. Then we simply argue that new retirees can follow the *best* drawdown path over all previous (hypothetical) retirees. Doing so is exactly as safe, in the Bengen sense, as it is for the original retiree.
We call our approach the DMSWR, which is a play off our initials (we're both D.M.) and safe withdrawal rate (SWR). The DMSWR has some really nice effects: you can often use a much higher SWR than Bengen predicts, the precise retirement date doesn't matter too much, and retiring right after a market correction isn't as harmful as it seems.
We wrote a paper describing the idea in detail, which was published this month in the Journal of Financial Planning:
Safely Boosting Retirement Income by Harmonizing Drawdown Paths (pdf version)
We don't get into full financial planning in the paper, and we generally do *not* think that retirees should only use the DMSWR. Instead, we see it as an extension and improvement on Bengen's work and the considerable literature that followed it. In practice, we'd argue for a mix of annuities, DMSWR, and VPW to try to capture the benefits of each approach, though we may be more sensitive to income reductions during retirement compared to typical VPW proponents.
Of course there's no magic here, and the tradeoff is that if you take the full DMSWR (i.e. literally follow the best drawdown path), you increase your risk of outofsample failure. This issue exists with Bengen's work  "safe" means that a method never fails (or, in some formulations, only fails with very low probability) for all *historical* periods  which is why we're careful to say things like "safe in the Bengen sense". We include a walkforward analysis of Bengen's method but need to do more analysis to understand how to best adjust the DMSWR and monitor for potential failures before it's too late. In practice, you probably want to use a withdrawal rate between Bengen's number and the DMSWR, overestimate your projected retirement duration, and use "reretire" opportunities to extend your final withdrawal date to further reduce risk. Regardless, we think this is an understudied problem in the literature, though some methods (like VPW) avoid it by construction.
We hope this way of thinking about "harmonizing drawdown paths" sparks a useful discussion, and we’re very interested in your thoughts, questions, and suggestions for improvement!

p.s. The mods had a few concerns so: (1) they approved linking to our paper, (2) we have explicit permission from JFP to distribute the paper, (3) we've posted the data underlying the analysis, (4) you can find code for generating the data and basic graphs here, and (5) we enjoy discussing financial planning and FIRE issues as a hobby and this work is wholly unrelated to our day jobs or any other commercial venture.
We think we have a solution based on thinking about the "drawdown path" of every retiree, i.e. the sequence of withdrawals and account values over their full retirement. We argue that a new retiree can follow the drawdown path of a previous retiree so long as they plan for the same final withdrawal date. So if you planned for a 40 year retirement 10 years ago, I can start following your drawdown path today (in terms of withdrawal percent, not absolute dollar amounts) so long as I'm ok with a 30 year retirement. Then we simply argue that new retirees can follow the *best* drawdown path over all previous (hypothetical) retirees. Doing so is exactly as safe, in the Bengen sense, as it is for the original retiree.
We call our approach the DMSWR, which is a play off our initials (we're both D.M.) and safe withdrawal rate (SWR). The DMSWR has some really nice effects: you can often use a much higher SWR than Bengen predicts, the precise retirement date doesn't matter too much, and retiring right after a market correction isn't as harmful as it seems.
We wrote a paper describing the idea in detail, which was published this month in the Journal of Financial Planning:
Safely Boosting Retirement Income by Harmonizing Drawdown Paths (pdf version)
We don't get into full financial planning in the paper, and we generally do *not* think that retirees should only use the DMSWR. Instead, we see it as an extension and improvement on Bengen's work and the considerable literature that followed it. In practice, we'd argue for a mix of annuities, DMSWR, and VPW to try to capture the benefits of each approach, though we may be more sensitive to income reductions during retirement compared to typical VPW proponents.
Of course there's no magic here, and the tradeoff is that if you take the full DMSWR (i.e. literally follow the best drawdown path), you increase your risk of outofsample failure. This issue exists with Bengen's work  "safe" means that a method never fails (or, in some formulations, only fails with very low probability) for all *historical* periods  which is why we're careful to say things like "safe in the Bengen sense". We include a walkforward analysis of Bengen's method but need to do more analysis to understand how to best adjust the DMSWR and monitor for potential failures before it's too late. In practice, you probably want to use a withdrawal rate between Bengen's number and the DMSWR, overestimate your projected retirement duration, and use "reretire" opportunities to extend your final withdrawal date to further reduce risk. Regardless, we think this is an understudied problem in the literature, though some methods (like VPW) avoid it by construction.
We hope this way of thinking about "harmonizing drawdown paths" sparks a useful discussion, and we’re very interested in your thoughts, questions, and suggestions for improvement!

p.s. The mods had a few concerns so: (1) they approved linking to our paper, (2) we have explicit permission from JFP to distribute the paper, (3) we've posted the data underlying the analysis, (4) you can find code for generating the data and basic graphs here, and (5) we enjoy discussing financial planning and FIRE issues as a hobby and this work is wholly unrelated to our day jobs or any other commercial venture.
Re: improving the 4% rule and solving the starting point paradox
Welcome! I confirm that minnend has received permission from the Advisory Board to link to his paper and websites. See: No Solicitation
VPW = Variable percentage withdrawal
Acronym decoder:Please do not solicit business or website traffic on this forum. Forum officers will determine what constitutes solicitation on a case by case basis, but we offer the following guidelines about commonly encountered issues:
 Authors, software developers, or others looking for feedback should contact bhadmin@bogleheads.org for approval before posting.
VPW = Variable percentage withdrawal
 geerhardusvos
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Re: improving the 4% rule and solving the starting point paradox
Something looks familiar... copy catting is a form of flattery I suppose... then again, I don’t know if ERN came up with the format (maybe the Trinity study did?). Anyone know?minnend wrote: ↑Sat Nov 07, 2020 4:07 pm
We wrote a paper describing the idea in detail, which was published this month in the Journal of Financial Planning:
Safely Boosting Retirement Income by Harmonizing Drawdown Paths (pdf version)
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 willthrill81
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Re: improving the 4% rule and solving the starting point paradox
To be honest, I think that this is a well intentioned move to correct a problem that doesn't actually exist. Virtually no one is actually using the '4% rule' to make their withdrawals for reasons I outline below.
Also, I've never seen what was so paradoxical and the starting point of the '4% rule'. It's a mere byproduct of the inherently flawed notion that retirees can and should determine at the beginning of their retirement how much they will withdraw in inflationadjusted dollars for the next three decades with nary a glance at their portfolio value. Calling such a notion flawed is probably being generous. Close to insanity is probably nearer the mark.
That doesn't mean that the '4% rule' is of no use whatsoever for a potential retiree. At the time it was put forth by Bengen back in 1994, many viewed 7% as a good withdrawal rate; 4% was probably viewed as being crazy conservative at the time, so it is very ironic that these days many are proclaiming the '4% rule' to be wildly optimistic, a position I do not agree with.
The '4% rule' provides a reasonably safe starting point for the withdrawals of a retiree planning for a 30 year retirement. The amount withdrawn can and in most cases should be adjusted in a manner at least partly dependent on portfolio performance; Bengen himself said so in his famous paper. There are literally an infinite number of ways that such adjustments can be made. The GuytonKlinger guardrails are one such approach. Further, there are other withdrawal methods that completely remove the risk of premature portfolio depletion, such as the already mentioned VPW, the fixed percentage of portfolio method, and the amortization based withdrawal method (ABW).
Also, I've never seen what was so paradoxical and the starting point of the '4% rule'. It's a mere byproduct of the inherently flawed notion that retirees can and should determine at the beginning of their retirement how much they will withdraw in inflationadjusted dollars for the next three decades with nary a glance at their portfolio value. Calling such a notion flawed is probably being generous. Close to insanity is probably nearer the mark.
That doesn't mean that the '4% rule' is of no use whatsoever for a potential retiree. At the time it was put forth by Bengen back in 1994, many viewed 7% as a good withdrawal rate; 4% was probably viewed as being crazy conservative at the time, so it is very ironic that these days many are proclaiming the '4% rule' to be wildly optimistic, a position I do not agree with.
The '4% rule' provides a reasonably safe starting point for the withdrawals of a retiree planning for a 30 year retirement. The amount withdrawn can and in most cases should be adjusted in a manner at least partly dependent on portfolio performance; Bengen himself said so in his famous paper. There are literally an infinite number of ways that such adjustments can be made. The GuytonKlinger guardrails are one such approach. Further, there are other withdrawal methods that completely remove the risk of premature portfolio depletion, such as the already mentioned VPW, the fixed percentage of portfolio method, and the amortization based withdrawal method (ABW).
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

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Re: improving the 4% rule and solving the starting point paradox
I'm a bit puzzled that they mention VPW and yet state "existing approaches for resolving it seem insufficient." VPW resolves the original issue they're discussing just fine, because it adjusts your withdrawal amount based on age / retirement time horizon.minnend wrote: ↑Sat Nov 07, 2020 4:07 pm Michael Kitces introduced the starting point paradox back in 2008, where, under Bengen's "4% Rule", two people with nearly identical retirement savings can have dramatically different "safe" withdrawals due to market movement between their retirement dates even if they retire only a year apart. This issue seems highly problematic and the existing approaches for resolving it seem insufficient.
We think we have a solution based on thinking about the "drawdown path" of every retiree, i.e. the sequence of withdrawals and account values over their full retirement. We argue that a new retiree can follow the drawdown path of a previous retiree so long as they plan for the same final withdrawal date. So if you planned for a 40 year retirement 10 years ago, I can start following your drawdown path today (in terms of withdrawal percent, not absolute dollar amounts) so long as I'm ok with a 30 year retirement. Then we simply argue that new retirees can follow the *best* drawdown path over all previous (hypothetical) retirees. Doing so is exactly as safe, in the Bengen sense, as it is for the original retiree.
We call our approach the DMSWR, which is a play off our initials (we're both D.M.) and safe withdrawal rate (SWR). The DMSWR has some really nice effects: you can often use a much higher SWR than Bengen predicts, the precise retirement date doesn't matter too much, and retiring right after a market correction isn't as harmful as it seems.
We wrote a paper describing the idea in detail, which was published this month in the Journal of Financial Planning:
Safely Boosting Retirement Income by Harmonizing Drawdown Paths (pdf version)
We don't get into full financial planning in the paper, and we generally do *not* think that retirees should only use the DMSWR. Instead, we see it as an extension and improvement on Bengen's work and the considerable literature that followed it. In practice, we'd argue for a mix of annuities, DMSWR, and VPW to try to capture the benefits of each approach, though we may be more sensitive to income reductions during retirement compared to typical VPW proponents.
Of course there's no magic here, and the tradeoff is that if you take the full DMSWR (i.e. literally follow the best drawdown path), you increase your risk of outofsample failure. This issue exists with Bengen's work  "safe" means that a method never fails (or, in some formulations, only fails with very low probability) for all *historical* periods  which is why we're careful to say things like "safe in the Bengen sense". We include a walkforward analysis of Bengen's method but need to do more analysis to understand how to best adjust the DMSWR and monitor for potential failures before it's too late. In practice, you probably want to use a withdrawal rate between Bengen's number and the DMSWR, overestimate your projected retirement duration, and use "reretire" opportunities to extend your final withdrawal date to further reduce risk. Regardless, we think this is an understudied problem in the literature, though some methods (like VPW) avoid it by construction.
We hope this way of thinking about "harmonizing drawdown paths" sparks a useful discussion, and we’re very interested in your thoughts, questions, and suggestions for improvement!

p.s. The mods had a few concerns so: (1) they approved linking to our paper, (2) we have explicit permission from JFP to distribute the paper, (3) we've posted the data underlying the analysis, (4) you can find code for generating the data and basic graphs here, and (5) we enjoy discussing financial planning and FIRE issues as a hobby and this work is wholly unrelated to our day jobs or any other commercial venture.
Re: improving the 4% rule and solving the starting point paradox
There's no "copy catting". That is a standard color gradient that every spreadsheet on the planet has done for 20+ years. I saw it when I was in university in 1997 and I doubt it was new then. It's not even "new" to retirement research. A quick glance at my archive shows Blanchett doing the same thing in a 2009 paper, many years before ERN had started his website (2016).geerhardusvos wrote: ↑Sat Nov 07, 2020 5:57 pm Something looks familiar... copy catting is a form of flattery I suppose... then again, I don’t know if ERN came up with the format (maybe the Trinity study did?). Anyone know?
Re: improving the 4% rule and solving the starting point paradox
We love ERN and cite the blog in our paper!geerhardusvos wrote: ↑Sat Nov 07, 2020 5:57 pm
Something looks familiar... copy catting is a form of flattery I suppose... then again, I don’t know if ERN came up with the format (maybe the Trinity study did?). Anyone know?
Regarding your question, I don't know who first designed a table with this style. It's a pretty straightforward table, and as AlohaJoe said, it's a standard color gradient.
Expanding a bit, this figure really isn't vital to our analysis, but it does serve a few purposes. First, we calculated all the percentages using Shiller's data for consistency with the rest of our analysis, and we were careful to use the YTM bond data properly (details in the paper, though it may be a review for boglehead folks since I think there was a long thread about bond modeling in relation to simba's spreadsheet). Do note that many of the numbers in our figure are different than the table you posted. We're pretty deep in the weeds at this point, but the exact data you use matters (source, timeframe, and various idiosyncrasies), the granularity (monthly vs. yearly) matters, the bond model matters, etc. Importantly, the numbers can also change over time.
Second, we only consider SWRs with a 100% (historical) success rate. This makes the DMSWR analysis much simpler, and we think that retirees should focus on outofsample risk without compounding the problem with additional insample risk. Of course, ultimately everyone should plan relative to their personal risk tolerance and specific situation.
Re: improving the 4% rule and solving the starting point paradox
Great point, and I should have been more precise. Different withdrawal strategies have different tradeoffs. For example, VPW trades the possibility of income reduction for a structural solution to account depletion. This is beautiful, but it's still a tradeoff that may not make sense for all retirees.Marseille07 wrote: ↑Sat Nov 07, 2020 10:46 pm I'm a bit puzzled that they mention VPW and yet state "existing approaches for resolving it seem insufficient." VPW resolves the original issue they're discussing just fine, because it adjusts your withdrawal amount based on age / retirement time horizon.
Our work is focused on improving "constant dollar" methods, which describes Bengen's method and the various approaches built on it. In these methods, the model seeks constant (inflationadjusted) income and accepts a nonzero risk of account depletion to get it. So my comment that "existing approaches for resolving [the starting point paradox] seem insufficient" was referring to approaches that build on Bengen's work like Klinger's guard rails, Guyton's decision rules, Kitces' ratcheting rules, etc. (see the paper for a more complete review with citations).
Re: improving the 4% rule and solving the starting point paradox
I think that this is an interesting line of argument so I'm glad to see your paper get published and explore it more. I've been a bit disappointed with the retirement research in the Journal of Financial Planning for the past few years so it is nice to see some fresh work there, especially one that emphasizes retirement is a process of continual monitoring, adjustment, and refinement.
I would suggest, however, that this can be viewed the other way around, too. When Carol uses a higher number than Dave, her remaining retirement is "unsafe", meaning her original withdrawal rate was also unsafe. I'm not sure that it is really decidable which interpretation is correct within the confines of SWR logic, is it?We know Carol’s withdrawals are safe and so Dave’s must be equally safe
I explored this take  similar logic to yours but essentially the polar opposite interpretation  a few years ago in a (admittedly somewhat tongue in cheek) blog post showing that the "real" SWR (for a 5% failure rate) was 2.01%.
https://medium.com/@justusjp/themyopia ... 6f35a1c8ebIf I started out with something that was “safe” but end up withdrawing something that isn’t safe…was my initial rate really safe after all?

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Re: improving the 4% rule and solving the starting point paradox
Sorry, what's DMSWR?
The finest, albeit the most difficult, of all human achievements is being reasonable.
Re: improving the 4% rule and solving the starting point paradox
Thanks for taking the time respond!willthrill81 wrote: ↑Sat Nov 07, 2020 6:40 pm To be honest, I think that this is a well intentioned move to correct a problem that doesn't actually exist. Virtually no one is actually using the '4% rule' to make their withdrawals for reasons I outline below.
Also, I've never seen what was so paradoxical and the starting point of the '4% rule'. It's a mere byproduct of the inherently flawed notion that retirees can and should determine at the beginning of their retirement how much they will withdraw in inflationadjusted dollars for the next three decades with nary a glance at their portfolio value. Calling such a notion flawed is probably being generous. Close to insanity is probably nearer the mark.
That doesn't mean that the '4% rule' is of no use whatsoever for a potential retiree. At the time it was put forth by Bengen back in 1994, many viewed 7% as a good withdrawal rate; 4% was probably viewed as being crazy conservative at the time, so it is very ironic that these days many are proclaiming the '4% rule' to be wildly optimistic, a position I do not agree with.
The '4% rule' provides a reasonably safe starting point for the withdrawals of a retiree planning for a 30 year retirement. The amount withdrawn can and in most cases should be adjusted in a manner at least partly dependent on portfolio performance; Bengen himself said so in his famous paper. There are literally an infinite number of ways that such adjustments can be made. The GuytonKlinger guardrails are one such approach. Further, there are other withdrawal methods that completely remove the risk of premature portfolio depletion, such as the already mentioned VPW, the fixed percentage of portfolio method, and the amortization based withdrawal method (ABW).
I largely agree with the points you're making. From our point of view, there are different categories of withdrawal strategies and each has their own set of tradeoffs. A potential retiree should consider their specific situation (risk tolerance, health, income streams, etc.), weigh the tradeoffs of each approach and select one (or, more realistically, blend several) to suit their needs. In this framing, we took the "constant dollar" approach and made it much, much better. This gives planners a better tool for their toolbox, though it still may not be the right tool for some retirees.
Regarding methods like the GuytonKlinger guardrails (and others mentioned in my previous post and in the Lit Review section of the paper), we think the use of heuristics and various thresholds tuned for the historical data is excessively dangerous due to overfitting risk. Bengen's approach is already fairly optimistic in that it's only really safe relative to historical data (see our walkforward analysis for details). Our method doesn't solve this problem, but at least it doesn't exacerbate the problem as the heuristic approaches do (again, relative to overfitting risk, which we take to be quite serious).
I assume this is obvious, but the primary drawback of VPW (and similar methods) is the potential for income reductions. I think accepting small reductions is quite reasonable (I'd go so far as to say that it's *unreasonable* to expect no reductions at all, even though that's how Bengen's method is constructed). Larger reductions may be quite painful, though, and some retirees will want to avoid this situation. I don't know the exact history of VPW, but my understanding is that longevity risk and the need for an income floor is why "VPW is best used in conjunction with guaranteed base income from Social Security, a pension (if any), and (if necessary) an inflationindexed Single Premium Immediate Annuity (SPIA)." (source)
VPW (with SS/pension/SPIA) may be sufficient. A comparison of DMSWR with other popular withdrawal strategies is "future work" relative to this paper, but I'm excited to look into it. I know other researchers have tackled this problem (we cite Wade Pfau in the paper), but we haven't gotten there yet with DMSWR. My intuition is that our approach is complementary, but we'll need to do the analysis to confirm this hunch.
Finally, regarding the need to be adaptive, I completely agree. We didn't include that in this work because we had to draw the line somewhere. Our core idea for improving Bengen's approach stands on its own, but it's hardly the final word in retirement planning even if you accept the constraints of "constant dollar" methods.
Re: improving the 4% rule and solving the starting point paradox
It's just the name we use for our withdrawal strategy: DM = both of our initials and SWR = safe withdrawal rate.
Re: improving the 4% rule and solving the starting point paradox
One key variable within any discussion on Safe Withdrawal Rates is the beginning point of the withdrawals and what market conditions (as measured by P/E ratio) exist at the time.
Ed Easterling’s mid2000s essay on this is worth considering.
“When we dig further to understand the success rate for a retir(ees)... we can dissect the past history into four sets, socalled quartiles. These sets are ranked from the highest to the lowest starting P/E ratios. The result is that the highest quartile (i.e. the top 25%) includes all thirtyyear periods since 1900 that started with P/Es of 18.5 and higher. The second set (i.e. the second 25%) cutsoff at a P/E of 13.9; the third at 11.2; and the last at 5.3.
“Why does this matter? Although the success rate for the entire group was 95%, today’s retiree starts with P/Es over 18.5 and has an expected success rate of less than 80%...
“When P/Es started at relatively high levels, it had a major impact on future success. When P/Es started at relatively lower levels, returns always were sufficient for 4% withdrawals.”
https://www.crestmontresearch.com/docs/ ... ntSWR.pdf
Ed Easterling’s mid2000s essay on this is worth considering.
“When we dig further to understand the success rate for a retir(ees)... we can dissect the past history into four sets, socalled quartiles. These sets are ranked from the highest to the lowest starting P/E ratios. The result is that the highest quartile (i.e. the top 25%) includes all thirtyyear periods since 1900 that started with P/Es of 18.5 and higher. The second set (i.e. the second 25%) cutsoff at a P/E of 13.9; the third at 11.2; and the last at 5.3.
“Why does this matter? Although the success rate for the entire group was 95%, today’s retiree starts with P/Es over 18.5 and has an expected success rate of less than 80%...
“When P/Es started at relatively high levels, it had a major impact on future success. When P/Es started at relatively lower levels, returns always were sufficient for 4% withdrawals.”
https://www.crestmontresearch.com/docs/ ... ntSWR.pdf
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 willthrill81
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Re: improving the 4% rule and solving the starting point paradox
I agree that making one's withdrawals as volatile as one's portfolio, which VPW does, seems unnecessarily painful and conservative.minnend wrote: ↑Sun Nov 08, 2020 12:38 am I assume this is obvious, but the primary drawback of VPW (and similar methods) is the potential for income reductions. I think accepting small reductions is quite reasonable (I'd go so far as to say that it's *unreasonable* to expect no reductions at all, even though that's how Bengen's method is constructed). Larger reductions may be quite painful, though, and some retirees will want to avoid this situation. I don't know the exact history of VPW, but my understanding is that longevity risk and the need for an income floor is why "VPW is best used in conjunction with guaranteed base income from Social Security, a pension (if any), and (if necessary) an inflationindexed Single Premium Immediate Annuity (SPIA)." (source)
You might be really interested in the amortization based withdrawal (ABW) method several of us have worked on and promoted in this thread. At its core is the time value of money formula, and VPW is only one specific application of it. While not strictly necessary, most of us who favor the ABW method also favor the use of dynamic return assumptions (unlike VPW, which incorporates static return assumptions from historic data), which can result in significant smoothing of withdrawals. Another advantage of this method is that it can incorporate multiple income streams and/or expenses at different points in time (e.g. SS benefits beginning in X years, paying for a lump sum expense in Y years).
“It's a dangerous business, Frodo, going out your door. You step onto the road, and if you don't keep your feet, there's no knowing where you might be swept off to.” J.R.R. Tolkien,The Lord of the Rings

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Re: improving the 4% rule and solving the starting point paradox
It's not a true paradox. It is the result of looking at a probabilistic model through a deterministic lens.
If someone uses the SWR model to retire, and faces the unlucky outcome of a steep drop in value in year 1, that is an unlucky outcome. Were they not retired, they may well have chosen not to do so based in year 2 based on the status in year 2. That does not mean they will fail moving forward.
The conditional probability of success moving forward from year 2 conditioned on the event of the year 1 outcome may indeed be lower than the probability of success at the start of year 1.
SWR is a probabilistic model, and the probability of success normally will vary as outcomes materialize.
If someone uses the SWR model to retire, and faces the unlucky outcome of a steep drop in value in year 1, that is an unlucky outcome. Were they not retired, they may well have chosen not to do so based in year 2 based on the status in year 2. That does not mean they will fail moving forward.
The conditional probability of success moving forward from year 2 conditioned on the event of the year 1 outcome may indeed be lower than the probability of success at the start of year 1.
SWR is a probabilistic model, and the probability of success normally will vary as outcomes materialize.
Risk is not a guarantor of return.
Re: improving the 4% rule and solving the starting point paradox
Can somone do an "explain like I'm 5" summary for each of the withdrawal strategy variants?
Re: improving the 4% rule and solving the starting point paradox
Apologies for the misleading language. Yes, the starting P/E is mentioned with reference to Michael Kitce’s work and discussed in paragraph #10 of the posted essay by the OP. I wanted to add the Easterling essay to the discussion, as it points to greater validity and applicability of the beginning P/E point than the present essay concludes.AlohaJoe wrote,
This is already discussed in the paper. I'm not sure why you imply it isn't?cinghiale wrote:
One key variable within any discussion on Safe Withdrawal Rates is the beginning point of the withdrawals and what market conditions (as measured by P/E ratio) exist at the time.
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Re: improving the 4% rule and solving the starting point paradox
In my view the "4% rule" should be renamed the 25x rule. Decide what level of withdrawal you need in retirement to support a comfortable lifestyle. Then once your portfolio reaches 25 times that value, you are in a position to safely retire.
Mathematically the 4% and 25x rule are the same, but renaming the rule helps focus attention on what it is actually useful for  deciding when to retire. In my view the rule is not useful for deciding how much to actually spend each year in retirement, because that would require the retiree to ignore any new information received in the years after retirement. In real life, people will (and should) adjust their retirement spending based on how well their portfolio is actually doing postretirement.
Mathematically the 4% and 25x rule are the same, but renaming the rule helps focus attention on what it is actually useful for  deciding when to retire. In my view the rule is not useful for deciding how much to actually spend each year in retirement, because that would require the retiree to ignore any new information received in the years after retirement. In real life, people will (and should) adjust their retirement spending based on how well their portfolio is actually doing postretirement.
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Re: improving the 4% rule and solving the starting point paradox
Have you seen my topic Optimal asset allocation strategies for retirement & saving? I made this a while ago when I reached the same conclusion as you: most "SWR" calculations suffer from path dependence problems which guarantees their suboptimality. But rather than calculating a better SWR, I solve the asset allocation directly with optimization techniques that yield the optimal asset (timevarying) allocation based on some simple market assumptions. Once the optimal asset allocation is determined (needs to be done once), each retirement duration and withdrawal rate has a success probability. For reference the data with return assumptions ERP = 5%, bonds = 0% real is shown below:
Color indicates the asset allocation (percentage allocated to stocks). To maximize the survival chance, the retiree should change his asset allocation each year to the asset allocation indicated by this graph and keep the inflation adjusted spending constant.
If I understand it correctly, the DWSWR for a retiree looking to retire in 1970 is the maximum SWR of (30 year retirement ending 2000, 31 year retirement ending 2000, 32 year retirement engine 2000, ...). Surely I must be misunderstanding something here, because I can't imagine a situation where this knowledge would be useful.
Color indicates the asset allocation (percentage allocated to stocks). To maximize the survival chance, the retiree should change his asset allocation each year to the asset allocation indicated by this graph and keep the inflation adjusted spending constant.
If I understand it correctly, the DWSWR for a retiree looking to retire in 1970 is the maximum SWR of (30 year retirement ending 2000, 31 year retirement ending 2000, 32 year retirement engine 2000, ...). Surely I must be misunderstanding something here, because I can't imagine a situation where this knowledge would be useful.

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Re: improving the 4% rule and solving the starting point paradox
Interesting contribution and article. I found the worked examples early in the article helpful in driving home the point that the standard "4% rule" seems to be illdefined, in that it can produce a wildly different withdrawal policy based upon things that should not be relevant (the historical date you declared you retired and previous market trajectory) rather than defining the policy based on current state that would have a causal impact: the size and allocation of the portfolio right now now, expected future expenses, expected returns given current market conditions, etc.
I believe that it is possible to approximately estimate the returns of stocks and bonds in complete ignorance of their current market prices, based on fundamental valuation, and therefore expectations of future returns and safe withdrawals should take these fundamental valuations into account. A withdrawal policy that incorporates some reasonable model of expected returns based on current asset valuations seems more likely to be robust and able to produce sensible guidance when faced with novel conditions. Purely empirical policies that don't attempt to crudely model the underlying reality and "mechanics" of the situation are unlikely to be robust and make sensible decisions when faced with novel conditions. We're quite likely to see novel conditions during the next few decades given the longterm trend of falling bond yields along with the consequences of other neverbeforeobserved events such as climate change, new technological developments, etc.
For example, an extreme thought experiment: if the quoted market prices of my investments were to increase by a factor of 100 tomorrow without any new information about the underlying businesses / bond issuers, if I blindly applied the "4% rule" I would conclude that I can sustainably withdraw at least 100x more than I plan today. Sounds great! But this would of course be ludicrous: we'd clearly be in "out of sample" territory. In reality I would assume that such an inexplicable price rise was due to mispricing by an irrationally exuberant "mr market" and that my long term prospects for returns had plummeted accordingly.
For me the comment about out of sample risk is the main downside and needs to be emphasised: there's no guarantee that the returns from asset classes over the next few decades will resemble historical returns from those asset classes. There is always a risk that history will turn out to be a poor approximation of the future, and withdrawal policies cleverly tuned to maximise withdrawals on periods of observed historical data (such as DMSWR) may overfit to transient conditions, and fare poorly when attempting to generalise to the period we care about  the future.minnend wrote: ↑Sat Nov 07, 2020 4:07 pm Of course there's no magic here, and the tradeoff is that if you take the full DMSWR (i.e. literally follow the best drawdown path), you increase your risk of outofsample failure. This issue exists with Bengen's work  "safe" means that a method never fails (or, in some formulations, only fails with very low probability) for all *historical* periods [...]
I believe that it is possible to approximately estimate the returns of stocks and bonds in complete ignorance of their current market prices, based on fundamental valuation, and therefore expectations of future returns and safe withdrawals should take these fundamental valuations into account. A withdrawal policy that incorporates some reasonable model of expected returns based on current asset valuations seems more likely to be robust and able to produce sensible guidance when faced with novel conditions. Purely empirical policies that don't attempt to crudely model the underlying reality and "mechanics" of the situation are unlikely to be robust and make sensible decisions when faced with novel conditions. We're quite likely to see novel conditions during the next few decades given the longterm trend of falling bond yields along with the consequences of other neverbeforeobserved events such as climate change, new technological developments, etc.
For example, an extreme thought experiment: if the quoted market prices of my investments were to increase by a factor of 100 tomorrow without any new information about the underlying businesses / bond issuers, if I blindly applied the "4% rule" I would conclude that I can sustainably withdraw at least 100x more than I plan today. Sounds great! But this would of course be ludicrous: we'd clearly be in "out of sample" territory. In reality I would assume that such an inexplicable price rise was due to mispricing by an irrationally exuberant "mr market" and that my long term prospects for returns had plummeted accordingly.

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Re: improving the 4% rule and solving the starting point paradox
I did not make it through the paper. Is the withdrawal method proposed ("reretiring") as simple as using SWR but increasing withdrawals if you get favorable returns?

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Re: improving the 4% rule and solving the starting point paradox
I think these analyses, going back to the Trinity Study and others, are interesting and useful in deciding what one is comfortable with. That comfort level is different for different people. Before I retired, I estimated what level of withdrawal I would be comfortable with as I aged. For me that was less than 4%. I did not want to reduce my withdrawals in retirement due to market changes, but that's just me, not suggesting what anyone else is comfortable with. Then I took not a worst case scenario, but a scenario where equities dropped 50% just after I retired. I was comfortable with my withdrawal percentage, indexed for inflation each year, based on my portfolio after equities dropped 50%, so I decided to retire. Of course that does not work for everyone but it was what worked for me.
Re: improving the 4% rule and solving the starting point paradox
Thanks for this new research.
Your finding seems to align with the link between CAPE (P/E Ratio) and SWR. If the P/E is lower, the SWR can be higher.
https://lab.madfientist.com/calculators/safe_withdrawal
TBH, I didn't understand everything. Maybe some simplified examples could be useful
Your finding seems to align with the link between CAPE (P/E Ratio) and SWR. If the P/E is lower, the SWR can be higher.
 https://www.madfientist.com/safewithdrawalrate/
https://www.kitces.com/wpcontent/uploa ... y2008.pdf
https://lab.madfientist.com/calculators/safe_withdrawal
TBH, I didn't understand everything. Maybe some simplified examples could be useful
Re: improving the 4% rule and solving the starting point paradox
It is Sequence of Returns risk (and reward). If the market fluctuates a lot during your first 510 years of retirement consider adjusting your glide slope.
Re: improving the 4% rule and solving the starting point paradox
I wonder if you're making the same mistake that is commonly done in the Monty Hall problem https://en.wikipedia.org/wiki/Monty_Hall_problem. In the Monty Hall problem, the paradox comes from not updating the probabilities with the information Monty Hall gives by opening one of the doors. When you say "We know Carol’s withdrawals are safe" I suspect you are not updating her probability of success with the information gained from her first five years of retirement.
This is similar to Northern Flicker's comment about conditional probabilities.
This is similar to Northern Flicker's comment about conditional probabilities.
Re: improving the 4% rule and solving the starting point paradox
ABW sounds very interesting so thanks for pointing it out and linking to the relevant thread! I'll check it out and share the link with my coauthor.willthrill81 wrote: ↑Sun Nov 08, 2020 1:34 amI agree that making one's withdrawals as volatile as one's portfolio, which VPW does, seems unnecessarily painful and conservative.minnend wrote: ↑Sun Nov 08, 2020 12:38 am I assume this is obvious, but the primary drawback of VPW (and similar methods) is the potential for income reductions. I think accepting small reductions is quite reasonable (I'd go so far as to say that it's *unreasonable* to expect no reductions at all, even though that's how Bengen's method is constructed). Larger reductions may be quite painful, though, and some retirees will want to avoid this situation. I don't know the exact history of VPW, but my understanding is that longevity risk and the need for an income floor is why "VPW is best used in conjunction with guaranteed base income from Social Security, a pension (if any), and (if necessary) an inflationindexed Single Premium Immediate Annuity (SPIA)." (source)
You might be really interested in the amortization based withdrawal (ABW) method several of us have worked on and promoted in this thread. At its core is the time value of money formula, and VPW is only one specific application of it. While not strictly necessary, most of us who favor the ABW method also favor the use of dynamic return assumptions (unlike VPW, which incorporates static return assumptions from historic data), which can result in significant smoothing of withdrawals. Another advantage of this method is that it can incorporate multiple income streams and/or expenses at different points in time (e.g. SS benefits beginning in X years, paying for a lump sum expense in Y years).
Re: improving the 4% rule and solving the starting point paradox
I read your medium article  it's a great take on thinking about the safety of intermediate years. I'll need to think more about this perspective. Effectively, you're arguing that unsafe intermediate years are bad (which is a quite reasonable position!), and we're using them almost as a good thing since it's exactly the high withdrawal rate in the middle of someone's retirement that allows a new retiree to "safely" (definitely using scare quotes here) boost their income.AlohaJoe wrote: ↑Sat Nov 07, 2020 11:50 pmI think that this is an interesting line of argument so I'm glad to see your paper get published and explore it more. I've been a bit disappointed with the retirement research in the Journal of Financial Planning for the past few years so it is nice to see some fresh work there, especially one that emphasizes retirement is a process of continual monitoring, adjustment, and refinement.
I would suggest, however, that this can be viewed the other way around, too. When Carol uses a higher number than Dave, her remaining retirement is "unsafe", meaning her original withdrawal rate was also unsafe. I'm not sure that it is really decidable which interpretation is correct within the confines of SWR logic, is it?We know Carol’s withdrawals are safe and so Dave’s must be equally safe
I explored this take  similar logic to yours but essentially the polar opposite interpretation  a few years ago in a (admittedly somewhat tongue in cheek) blog post showing that the "real" SWR (for a 5% failure rate) was 2.01%.
https://medium.com/@justusjp/themyopia ... 6f35a1c8ebIf I started out with something that was “safe” but end up withdrawing something that isn’t safe…was my initial rate really safe after all?
I'm not 100% sure how to resolve this apparent contradiction. Our formulation should be mathematically sound, but that's really only because we were careful to only claim "safety" in the Bengen sense (i.e. insample). This is fair, but not as useful as we'd like since the future is always out of sample.
The immediate questions I have based on your post are: what withdrawal rate leads to a 100% safe drawdown path (even in intermediate years), and what happens if you follow a plan that pulls `min(bengen_rate, safe_for_years_remaining)`. This approach will likely lead to income reductions so it also needs to be compared to VPW, ABW, etc.
Thanks for sharing a link to your post. It's highly relevant to the DMSWR and warrants more investigation.
Re: improving the 4% rule and solving the starting point paradox
Thanks for sharing the Easterling reference!cinghiale wrote: ↑Sun Nov 08, 2020 3:05 am Apologies for the misleading language. Yes, the starting P/E is mentioned with reference to Michael Kitce’s work and discussed in paragraph #10 of the posted essay by the OP. I wanted to add the Easterling essay to the discussion, as it points to greater validity and applicability of the beginning P/E point than the present essay concludes.
I haven't read it yet so can only repeat our very general position of trying to avoid giving the model more degrees of freedom since we're already quite worried about overfitting (i.e. designing a method that looks great on *historical* data but fails in the future). There's just so little uncorrelated data to work with that slicing it up further seems risky.
That said, I'd certainly entertain a more flexible method that used additional indicators (like P/E) to suggest *lower* withdrawal rates.
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Re: improving the 4% rule and solving the starting point paradox
In the medium article you mentioned that the “early retirement now 3.25% withdrawal rate over 40 years has around a 50% failure rate, and 50 years has a ~60% failure rate.” In that statement were you defining failure as “having unsafe years”? Because the success rate of those retirement horizons according to ERN were 100% with a 75/25 portfolio:AlohaJoe wrote: ↑Sat Nov 07, 2020 11:50 pm
I explored this take  similar logic to yours but essentially the polar opposite interpretation  a few years ago in a (admittedly somewhat tongue in cheek) blog post showing that the "real" SWR (for a 5% failure rate) was 2.01%.
https://medium.com/@justusjp/themyopia ... 6f35a1c8ebIf I started out with something that was “safe” but end up withdrawing something that isn’t safe…was my initial rate really safe after all?
VTSAX and chill
Re: improving the 4% rule and solving the starting point paradox
I largely agree with you. Our work follows the form: if you accept Bengen's assumptions, here's an alternative approach with the same assumptions and same safety (it succeeds and fails in exactly the same situations) that often predicts a much higher SWR. That seems interesting to us, and thinking about "drawdown paths" seems very important (AlohaJoe linked to a post exploring similar ideas with a different conclusion), but of course it's not a perfect model of a real retirement.Small Savanna wrote: ↑Sun Nov 08, 2020 3:13 am In my view the "4% rule" should be renamed the 25x rule. Decide what level of withdrawal you need in retirement to support a comfortable lifestyle. Then once your portfolio reaches 25 times that value, you are in a position to safely retire.
Mathematically the 4% and 25x rule are the same, but renaming the rule helps focus attention on what it is actually useful for  deciding when to retire. In my view the rule is not useful for deciding how much to actually spend each year in retirement, because that would require the retiree to ignore any new information received in the years after retirement. In real life, people will (and should) adjust their retirement spending based on how well their portfolio is actually doing postretirement.
Re: improving the 4% rule and solving the starting point paradox
Yeah, I'm also not sure either. On the one hand it seems like you want to have a consistent story about risk. If you are only willing to tolerate a 5% risk of ruin in year 1, then why are you willing to tolerate a higher risk of ruin in year 2 after the market crashed and your portfolio is down? On the other hand, part of it is some poorly surfaced story about belief in reversion to mean  but a belief in reversion to the mean doesn't seem complete indefensible to me.minnend wrote: ↑Mon Nov 09, 2020 12:57 am I'm not 100% sure how to resolve this apparent contradiction. Our formulation should be mathematically sound, but that's really only because we were careful to only claim "safety" in the Bengen sense (i.e. insample). This is fair, but not as useful as we'd like since the future is always out of sample.
I can't seem to immediately locate the python jupyter book I used for that post so I can't give a precise number but it would be quite low. Probably 1.5% and possibly less. The problem is several of the worst retirement cohorts have such steep drawdowns that any percentage of the original portfolio ends up being quite a large percent of the new (smaller) portfolio. For example, the 19291931 drawdown was something like 8090% for equities. If you had $1,000,000 to start with and used a 1% withdrawal rate ($10,000 a year), then after 3 years your portfolio is down to just $200,000 or so ignoring withdrawals. Suddenly that $10,000 a year is over 5% of the remaining portfolio and you've still got 25+ years of retirement ahead of you. Admittedly that's assuming 100% equities but it illustrates how low it can get if you're looking for absolute safety.The immediate questions I have based on your post are: what withdrawal rate leads to a 100% safe drawdown path (even in intermediate years)
Absolutely! One paper I saw taking this approach is "The Perfect Withdrawal Amount" by Suarez et al[1] where they do essentially what you suggest. And it does lead to varying withdrawal amounts. I liked their paper but came away feeling that the PMT based approach in things like VPW or actuarial based methods gave similarish results but felt sounder, since it wasn't as reliant on backtesting or monte carlo.and what happens if you follow a plan that pulls `min(bengen_rate, safe_for_years_remaining)`. This approach will likely lead to income reductions so it also needs to be compared to VPW, ABW, etc.
Here's a chart from the Suarez paper showing the idea charted. Not "safe" but "50% chance of failure" and "25% chance of failure".
[1]: https://papers.ssrn.com/sol3/papers.cfm ... id=2551370
Re: improving the 4% rule and solving the starting point paradox
I did see your thread before  your approach seems really interesting!Uncorrelated wrote: ↑Sun Nov 08, 2020 4:38 am Have you seen my topic Optimal asset allocation strategies for retirement & saving? I made this a while ago when I reached the same conclusion as you: most "SWR" calculations suffer from path dependence problems which guarantees their suboptimality. But rather than calculating a better SWR, I solve the asset allocation directly with optimization techniques that yield the optimal asset (timevarying) allocation based on some simple market assumptions. Once the optimal asset allocation is determined (needs to be done once), each retirement duration and withdrawal rate has a success probability.
We almost entirely avoided the asset allocation question and just stuck with very standard stock/bond splits. Speaking broadly, my concern with tweaking asset allocations based on historical data comes back to overfitting. You can actually see this somewhat frequently (e.g. Merriman does this, and Bengen even had a paper on it though he was upfront about the dangers).
In your case, it looks like you're assuming a fixed return and then optimizing relative to account depletion. That's an interesting take that I hadn't considered before seeing your thread. I'm not sure how to select the return percentages though, and I'm (vaguely?) worried about sequence risk. Apologies if these are basic issues already covered in your thread; I bookmarked it but haven't reread it yet.
I think the missing component is that the DMSWR is based on the "effective" (or "current") withdrawal rate of a previous retiree, not just the SWR for a longer duration. So in the 1970 example, say I retired in 1969 and withdrew $40k out of $1M. Then the market moves down and there's some inflation so in 1970 I withdraw $41k out of $950k, which is 4.3%. So if you retire in 1970, you can take the 30 year SWR (call it 4%) or 4.3% if you want to follow my drawdown path. We argue that taking 4.3% in this case is safe relative to the historical data, which is how "safe" is defined in this line of work.If I understand it correctly, the DWSWR for a retiree looking to retire in 1970 is the maximum SWR of (30 year retirement ending 2000, 31 year retirement ending 2000, 32 year retirement engine 2000, ...). Surely I must be misunderstanding something here, because I can't imagine a situation where this knowledge would be useful.
Re: improving the 4% rule and solving the starting point paradox
This is an interesting connection, and I'm certainly familiar with and appreciate the Monty Hall problem.jj45 wrote: ↑Sun Nov 08, 2020 11:08 am I wonder if you're making the same mistake that is commonly done in the Monty Hall problem https://en.wikipedia.org/wiki/Monty_Hall_problem. In the Monty Hall problem, the paradox comes from not updating the probabilities with the information Monty Hall gives by opening one of the doors. When you say "We know Carol’s withdrawals are safe" I suspect you are not updating her probability of success with the information gained from her first five years of retirement.
This is similar to Northern Flicker's comment about conditional probabilities.
We're taking "safe" to mean something very specific: a safe withdrawal rate will have a 100% success rate on all historical retirement durations. This is how "safe" was used in Bengen's 1994 paper (he might have also considered the case where there was a small chance of failure  I can't remember if that was the '94 paper or if it came later). In this sense, "we know that Carol's withdrawals are safe" is true.
If you go beyond the assumptions of the original formulation (which you should since we live in the real world and not a historical dataset!), then you need to deal with generalization to new data. There is no guarantee that what's safe for historical data will be safe in the future, and we're not making that claim. We offer some analysis (the walkforward part) but for now I can only say that I'm excited to investigate methods for monitoring and adapting withdrawals, especially when the solution is "structural" rather than heuristic.
p.s If you enjoyed thinking through the Monty Hall problem, check out the Sleeping Beauty Problem and this page on nuances of probability theory, where I find the "query sensitivity" section to be particularly interesting.
Re: improving the 4% rule and solving the starting point paradox
I agree, if you base your withdrawal rate on 100% success then the only possible failure in your method is out of sample data. Most of the discussion of SWR I have seen looks at 95% or similar success rate. Relying on 100% safe withdrawals for a finite, and as you say, relatively small, sample, increases the importance of outofsample failure. Choosing a more reasonable 95% safety brings some previously outofsample failures into the sample where they can be analyzed.minnend wrote: ↑Mon Nov 09, 2020 3:18 am [We're taking "safe" to mean something very specific: a safe withdrawal rate will have a 100% success rate on all historical retirement durations. This is how "safe" was used in Bengen's 1994 paper (he might have also considered the case where there was a small chance of failure  I can't remember if that was the '94 paper or if it came later). In this sense, "we know that Carol's withdrawals are safe" is true.
If you go beyond the assumptions of the original formulation (which you should since we live in the real world and not a historical dataset!), then you need to deal with generalization to new data. There is no guarantee that what's safe for historical data will be safe in the future, and we're not making that claim. We offer some analysis (the walkforward part) but for now I can only say that I'm excited to investigate methods for monitoring and adapting withdrawals, especially when the solution is "structural" rather than heuristic.
p.s If you enjoyed thinking through the Monty Hall problem, check out the Sleeping Beauty Problem and this page on nuances of probability theory, where I find the "query sensitivity" section to be particularly interesting.
Here's a worst case example using data from http://www.cfiresim.com/. Their 95% inflationadjusted 30 year SWR is 4.17%. Suppose I want an 8 year retirement. Following your method, I look at all past start dates and am free to pick the one with the highest withdrawal in year 22. One of the failures starts in 1966 with $1M. In 1988, right before failure, the portfolio has a value of $84K and the inflationadjusted withdrawal is $152K. I like this start date, I get to withdraw 181% of my portfolio, so I pick the 1966 drawdown path, withdraw $152K and the check bounces.
I think If you include any nonzero failure rate in the sample then your method, if I understand it right, amplifies the failure rate.
Re: improving the 4% rule and solving the starting point paradox
Yes, great example. Our method fails whenever you follow an earlier drawdown path that will fail. I highly recommend you don't do that.jj45 wrote: ↑Mon Nov 09, 2020 10:25 amI agree, if you base your withdrawal rate on 100% success then the only possible failure in your method is out of sample data. Most of the discussion of SWR I have seen looks at 95% or similar success rate. Relying on 100% safe withdrawals for a finite, and as you say, relatively small, sample, increases the importance of outofsample failure. Choosing a more reasonable 95% safety brings some previously outofsample failures into the sample where they can be analyzed.minnend wrote: ↑Mon Nov 09, 2020 3:18 am [We're taking "safe" to mean something very specific: a safe withdrawal rate will have a 100% success rate on all historical retirement durations. This is how "safe" was used in Bengen's 1994 paper (he might have also considered the case where there was a small chance of failure  I can't remember if that was the '94 paper or if it came later). In this sense, "we know that Carol's withdrawals are safe" is true.
If you go beyond the assumptions of the original formulation (which you should since we live in the real world and not a historical dataset!), then you need to deal with generalization to new data. There is no guarantee that what's safe for historical data will be safe in the future, and we're not making that claim. We offer some analysis (the walkforward part) but for now I can only say that I'm excited to investigate methods for monitoring and adapting withdrawals, especially when the solution is "structural" rather than heuristic.
p.s If you enjoyed thinking through the Monty Hall problem, check out the Sleeping Beauty Problem and this page on nuances of probability theory, where I find the "query sensitivity" section to be particularly interesting.
Here's a worst case example using data from http://www.cfiresim.com/. Their 95% inflationadjusted 30 year SWR is 4.17%. Suppose I want an 8 year retirement. Following your method, I look at all past start dates and am free to pick the one with the highest withdrawal in year 22. One of the failures starts in 1966 with $1M. In 1988, right before failure, the portfolio has a value of $84K and the inflationadjusted withdrawal is $152K. I like this start date, I get to withdraw 181% of my portfolio, so I pick the 1966 drawdown path, withdraw $152K and the check bounces.
I think If you include any nonzero failure rate in the sample then your method, if I understand it right, amplifies the failure rate.
In reality, of course, you don't know yet which midretirement drawdown paths will fail. This is a key source of risk, and it's why we're very interested in methods for monitoring and adapting. There's nothing unique here  if you calculate an SWR with a 95% chance of success, you really should be monitoring to see if you're on one of the unlucky 5% paths so that you can adapt as early as possible.
Re: improving the 4% rule and solving the starting point paradox
OP,
Hopefully you were prepared for the discussion and critiques! I just wanted to make sure someone said congrats for getting your work published and thanks for sharing it with us.
The fact that doing this isn't a commercial / day job venture for you makes it even cooler. This means it was a labor of love, not something that helps drive views to your blog or signups for your advisory service (not that anything is wrong with that!)
Hopefully you were prepared for the discussion and critiques! I just wanted to make sure someone said congrats for getting your work published and thanks for sharing it with us.
The fact that doing this isn't a commercial / day job venture for you makes it even cooler. This means it was a labor of love, not something that helps drive views to your blog or signups for your advisory service (not that anything is wrong with that!)

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Re: improving the 4% rule and solving the starting point paradox
I agree. Another thing is why would I spend more money that doesn't need to be spent because a formula tells me I can? Likewise I might have an unexpected emergency expense and have to spend more than a formula tells me some years (the idea of an EF doesn't make sense to me in retirement).willthrill81 wrote: ↑Sat Nov 07, 2020 6:40 pm To be honest, I think that this is a well intentioned move to correct a problem that doesn't actually exist. Virtually no one is actually using the '4% rule' to make their withdrawals for reasons I outline below.
Also, I've never seen what was so paradoxical and the starting point of the '4% rule'. It's a mere byproduct of the inherently flawed notion that retirees can and should determine at the beginning of their retirement how much they will withdraw in inflationadjusted dollars for the next three decades with nary a glance at their portfolio value. Calling such a notion flawed is probably being generous. Close to insanity is probably nearer the mark.
That doesn't mean that the '4% rule' is of no use whatsoever for a potential retiree. At the time it was put forth by Bengen back in 1994, many viewed 7% as a good withdrawal rate; 4% was probably viewed as being crazy conservative at the time, so it is very ironic that these days many are proclaiming the '4% rule' to be wildly optimistic, a position I do not agree with.
The '4% rule' provides a reasonably safe starting point for the withdrawals of a retiree planning for a 30 year retirement. The amount withdrawn can and in most cases should be adjusted in a manner at least partly dependent on portfolio performance; Bengen himself said so in his famous paper. There are literally an infinite number of ways that such adjustments can be made. The GuytonKlinger guardrails are one such approach. Further, there are other withdrawal methods that completely remove the risk of premature portfolio depletion, such as the already mentioned VPW, the fixed percentage of portfolio method, and the amortization based withdrawal method (ABW).
Personally, I used the Trinity study as a starting point for my first year of retirement. I am not going to make withdrawal amounts more complicated than it needs to be. My expenses are what they are. If my portfolio balance is trending down for a number of years I will tighten my belt and spend less. If it trends up for a number of years I might spend more.
Re: improving the 4% rule and solving the starting point paradox
Ha! Thanks for the kind words!
We welcome the discussion and critiques. Random people are thinking hard about our work and sharing ideas to improve it  all for free! And the bogleheads community skews toward constructive conversation and directbutnotrude comments, at least by internet standards.
Thanks again! I really enjoy the DIY financial planning communities. There's a ton of helpful discussion here, in various FIRE forums, and on accessible blogs (ERN, MMM, A Wealth of Common Sense, Reformed Broker, pragcap, Kitces' blog, etc.). We did briefly discuss ways to monetize our work but never came up with anything compelling. We both publish professionally (in machine learning and computer vision, not finance) so it felt natural to go that route here.
Re: improving the 4% rule and solving the starting point paradox
Why not replace VPW in the above and go instead with (SS/pension/SPIA) and additional safe income by duration matching income from either a TIPS bond ladder or duration matched TIPS bond funds. This does away completely with needing to compute 'safe' withdrawal rates.
The above is Robert Merton's solution to the retirement income problem. Perhaps you have heard of him.
Michael Kitces did not introduce the starting point paradox of swr rules. This was well known by economists long before Kitces brought it up. In particular, in the early 2000s Bill Sharpe wrote several articles pounding home this point. I wrote about it here at Bogleheads back in 2007 using the example of identical twins with one retiring one year earlier than the other, but once they are both retired they have identical portfolios but drastically different 'safe' withdrawal rates.minnend wrote: ↑Sat Nov 07, 2020 4:07 pm Michael Kitces introduced the starting point paradox back in 2008, where, under Bengen's "4% Rule", two people with nearly identical retirement savings can have dramatically different "safe" withdrawals due to market movement between their retirement dates even if they retire only a year apart. This issue seems highly problematic and the existing approaches for resolving it seem insufficient.
BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). 
The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
Re: improving the 4% rule and solving the starting point paradox
On that note, you guys should consider perceptually uniform, colorblindfriendly colormaps in the future. They're a lot easier to interpret and look better to boot.
Here's a helpful writeup: https://bids.github.io/colormap/
And more examples: https://cran.rproject.org/web/packages ... ridis.html

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Re: improving the 4% rule and solving the starting point paradox
So, as long as I don't mind dying ten years sooner, this should work?minnend wrote: ↑Sat Nov 07, 2020 4:07 pm Michael Kitces introduced the starting point paradox back in 2008, where, under Bengen's "4% Rule", two people with nearly identical retirement savings can have dramatically different "safe" withdrawals due to market movement between their retirement dates even if they retire only a year apart. This issue seems highly problematic and the existing approaches for resolving it seem insufficient.
We think we have a solution based on thinking about the "drawdown path" of every retiree, i.e. the sequence of withdrawals and account values over their full retirement. We argue that a new retiree can follow the drawdown path of a previous retiree so long as they plan for the same final withdrawal date. So if you planned for a 40 year retirement 10 years ago, I can start following your drawdown path today (in terms of withdrawal percent, not absolute dollar amounts) so long as I'm ok with a 30 year retirement. Then we simply argue that new retirees can follow the *best* drawdown path over all previous (hypothetical) retirees. Doing so is exactly as safe, in the Bengen sense, as it is for the original retiree.

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Re: improving the 4% rule and solving the starting point paradox
There are so many future unknowns. Trying to come up with a simple formula and following it blindly is like ramming a square peg into a round hole. Use 25x as a planning guide and use common sense as it unfolds. It is a fool's errand.
Re: improving the 4% rule and solving the starting point paradox
Here is my post from nearly 13 years ago (1/8/2008) that explains the starting point paradox that Kitces supposedly 'discovered or introduced' 5 months later. But I certainly didn't discover or introduce it, and neither did Kitces. I was simply reiterating problems with a static withdrawal rule that economists had known for many years.
Link  viewtopic.php?f=10&t=9609
BobK
Here's a link to the entire discussion where my above post appeared. The discussion began in midDecember 2007 and this was about by third stab at getting people to understand why retirement decumulation plans need to be dynamic, rather than static such as the 4% rule.bobcat2 wrote: ↑Tue Jan 08, 2008 9:59 am Here’s one more way of seeing how the SWR rule is a bad rule. I retire at age 64 with a million dollar portfolio. Using the SWR 4% rule I will withdraw and spend $40,000 real (in terms of today’s dollars) per year from my portfolio for the rest of my life.
The stock market has three bad years over the first three years of my retirement. At age 67 after those three years of stock market losses, moderate inflation, and $120,000 in real withdrawals I have a portfolio that has seen its real value reduced to only $700,000 but, following the SWR rule, I will continue to withdraw and spend $40,000 real per year.
My twin brother retires in that third year when both he and I are both 67 years old. In that year he also has a portfolio worth $700,000 real. The SWR 4% rule says he should withdraw and spend $28,000 real per year. Adjusting for a retirement period expected to be three years shorter than mine, the SWR 4% rule advises a slight upward adjustment. This results in the rule having him withdrawing and spending about $29,000 real per year.
So here we have two 67 year old male retirees with identical $700,000 portfolios, identical portfolio asset allocations, and identical life expectancies, and the SWR 4% rule advises the one guy to withdraw and spend $40,000 real per year for life and the other guy to withdraw and spend $29,000 real per year for life.
Question: What sense does such an inconsistent policy rule make? Any reasonable strategy would advise these two guys to withdraw and spend the same amount per year in retirement going forward since they are in the exact same situation. The SWR 4% rule fails this simple test.
Of course one could argue that in this situation the first retiree should now ignore the rule. But that’s just another way of saying the rule shouldn’t be used. The problem with the SWR rule is its inability to adapt to changing circumstances. However, during retirement it’s reasonable to expect such changing circumstances when relying on income from a portfolio containing some risky assets, therefore such a static rule simply shouldn’t be used in the first place.
This is a classic case where a “common sense” rule lacks “good sense”.
Bob K
Link  viewtopic.php?f=10&t=9609
BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). 
The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
Re: improving the 4% rule and solving the starting point paradox
Thank you, bobcat2 for reposting what you contributed in 2007 to this perennial topic. Your illustration is like a parable of old— a clear and straightforward story that captures an essential truth. This post belongs in one of the “best of” listings.
"We don't see things as they are; we see them as we are." Anais Nin 

"Sometimes the first duty of intelligent men is the restatement of the obvious." George Orwell
Re: improving the 4% rule and solving the starting point paradox
Indeed, I've heard of Merton  it's tough to miss someone who both wins a nobel prize for options pricing and is central to one of the great cautionary tales of investing.bobcat2 wrote: ↑Fri Nov 13, 2020 3:47 pmWhy not replace VPW in the above and go instead with (SS/pension/SPIA) and additional safe income by duration matching income from either a TIPS bond ladder or duration matched TIPS bond funds. This does away completely with needing to compute 'safe' withdrawal rates.
The above is Robert Merton's solution to the retirement income problem. Perhaps you have heard of him.
The pro/cons of annuitization and durationmatched bonds are outside the scope of our paper. I can repeat some of the standard arguments, but so far I haven't analyzed the tradeoffs in enough detail to add anything meaningful to the conversation. Merton's 2014 HBR article looks like a good starting point to understand his position so I'll start there.
Thanks for pointing out the earlier reference. I see you found the earlier thread and provided an excerpt and link below. Thank you! It's too late to revise the paper, but I'll be sure to reference Sharpe and your thread going forward.bobcat2 wrote: ↑Fri Nov 13, 2020 3:47 pmMichael Kitces did not introduce the starting point paradox of swr rules. This was well known by economists long before Kitces brought it up. In particular, in the early 2000s Bill Sharpe wrote several articles pounding home this point. I wrote about it here at Bogleheads back in 2007 using the example of identical twins with one retiring one year earlier than the other, but once they are both retired they have identical portfolios but drastically different 'safe' withdrawal rates.minnend wrote: ↑Sat Nov 07, 2020 4:07 pm Michael Kitces introduced the starting point paradox back in 2008, where, under Bengen's "4% Rule", two people with nearly identical retirement savings can have dramatically different "safe" withdrawals due to market movement between their retirement dates even if they retire only a year apart. This issue seems highly problematic and the existing approaches for resolving it seem insufficient.
BobK
Re: improving the 4% rule and solving the starting point paradox
Yes, good point, and thanks for the links! I also like Color Brewer 2 for discrete color palettes, and I've used some of the improved colormaps (viridis, magma, etc.) via matplotlib for other data visualization tasks at work.cos wrote: ↑Sat Nov 14, 2020 2:51 pmOn that note, you guys should consider perceptually uniform, colorblindfriendly colormaps in the future. They're a lot easier to interpret and look better to boot.
Here's a helpful writeup: https://bids.github.io/colormap/
And more examples: https://cran.rproject.org/web/packages ... ridis.html
Re: improving the 4% rule and solving the starting point paradox
Our focus is on the math, not the specific numbers in this example. So you can and should plan for whatever retirement duration makes sense for your situation. The core idea behind the DMSWR (following an earlier retiree's drawdown path) still applies.trueblueky wrote: ↑Sat Nov 14, 2020 3:58 pmSo, as long as I don't mind dying ten years sooner, this should work?minnend wrote: ↑Sat Nov 07, 2020 4:07 pm Michael Kitces introduced the starting point paradox back in 2008, where, under Bengen's "4% Rule", two people with nearly identical retirement savings can have dramatically different "safe" withdrawals due to market movement between their retirement dates even if they retire only a year apart. This issue seems highly problematic and the existing approaches for resolving it seem insufficient.
We think we have a solution based on thinking about the "drawdown path" of every retiree, i.e. the sequence of withdrawals and account values over their full retirement. We argue that a new retiree can follow the drawdown path of a previous retiree so long as they plan for the same final withdrawal date. So if you planned for a 40 year retirement 10 years ago, I can start following your drawdown path today (in terms of withdrawal percent, not absolute dollar amounts) so long as I'm ok with a 30 year retirement. Then we simply argue that new retirees can follow the *best* drawdown path over all previous (hypothetical) retirees. Doing so is exactly as safe, in the Bengen sense, as it is for the original retiree.
Many argue that should avoid strategies that require estimating your retirement duration up front. That's a very reasonable concern. If you're worried about it, the standard advise is to grossly overestimate your life expectancy, create an income floor with annuities, and/or use a percentagebased strategy that avoids account depletion by design (VPW, ABW, etc.).
Re: improving the 4% rule and solving the starting point paradox
Thanks again for linking to this 13 year old thread!bobcat2 wrote: ↑Sun Nov 15, 2020 12:45 am Here is my post from nearly 13 years ago (1/8/2008) that explains the starting point paradox that Kitces supposedly 'discovered or introduced' 5 months later. But I certainly didn't discover or introduce it, and neither did Kitces. I was simply reiterating problems with a static withdrawal rule that economists had known for many years.
<snip>
Here's a link to the entire discussion where my above post appeared. The discussion began in midDecember 2007 and this was about by third stab at getting people to understand why retirement decumulation plans need to be dynamic, rather than static such as the 4% rule.
Link  viewtopic.php?f=10&t=9609
BobK
From my point of view, within the assumptions of Bengenstyle withdrawal strategies there's a big problem (Kitces calls it the starting point paradox and Sharpe and probably others identified it years earlier). Our paper solves it.
I understand your point (and willthrill81 and others upthread) as saying that people shouldn't adopt the assumptions and structure of a Bengenstyle withdrawal strategy at all. This point is very well taken! From this perspective, our work has relatively low impact since it solves a problem that won't arise for retirees who stick to annuities, bonds, VPW, ABW, etc. for their withdrawal plan. This is a great point and will certainly influence the next step in my investigation of withdrawal strategies.