If the long-term average real return from the stock market is 7%, does that mean one can safely use a 7% withdrawal rate from a 100% stocks portfolio without worrying about running out of wealth or even dipping into the original principal? The answer is No. But answering yes is a common mistake; one which William Bengen set out to dispel.

Stocks do not earn their average real return each year. Some years they go up, and some years they go down. For a retiree who is withdrawing from their savings, the sequence of returns matters. If the market value of one’s assets falls in the early retirement period, then withdrawals will dig a further hole. Climbing out of this hole becomes increasingly difficult even if a subsequent recovery arrives. This is the sequence of returns risk. 

William Bengen’s seminal study in the October 1994 Journal of Financial Planning, “Determining Withdrawal Rates Using Historical Data,” helped usher in the modern area of retirement withdrawal rate research by codifying the importance of sequence of returns risk. The problem he set up is simple: a new retiree makes plans for withdrawing some inflation-adjusted amount from their savings at the end of each year for a 30-year retirement period. What is the highest withdrawal amount as a percentage of retirement date assets that with inflation adjustments will be sustainable for the full 30 years?

To answer this question, he obtained a copy of Ibbotson Associates’  Stocks, Bonds, Bills, and Inflation yearbook, which provides monthly data for a variety of U.S. asset classes and inflation since January 1926. He decided to investigate using the S&P 500 index to represent the stock market and intermediate-term government bonds to represent the bond market.

His exceedingly clever trick was to construct rolling 30-year periods from this data. He could consider a retirement lasting from 1926 through 1955, then 1927 through 1956, and so on. This technique is called ‘historical simulations.’  For each rolling historical period, he could calculate the maximum sustainable withdrawal rate. Though he did not produce the following illustration for his article, what he would have been looking at in his spreadsheet is something like this:


To bring greater realism to the discussion of safe withdrawal rates in retirement, he then focused his attention on what he called the SAFEMAX. It is simply the highest sustainable withdrawal rate for the worst-case retirement scenario in the historical period. With a 50/50 allocation for stocks and bonds, the SAFEMAX was 4.15%, and it occurred in 1966. That is the impact of sequence of returns risk. 4% turned out to be a much more realistic number than 7%. It was from these humble origins that the world of financial planning received the 4% rule.

[Note: I am following the same assumptions as in Mr. Bengen’s original research, except that I deduct withdrawals at the start of each year rather than the end of each year. I do think this is more realistic, and since it results in less time for assets to grow, withdrawal rates are slightly less with this assumption. My SAFEMAX is 4.04%.]

One other important issue coming out of William Bengen’s original study is asset allocation. In particular, Mr. Bengen recommended that retirees maintain a stock allocation of 50-75%. More specifically, he wrote, “I think it is appropriate to advise the client to accept a stock allocation as close to 75 percent as possible, and in no cases less than 50 percent.”

I will have a lot more to say about asset allocation (as well as about the 4% rule), and this stock allocation does sound rather high with respect to what we usually hear is reasonable for retirees. It is particularly poisonous to the ears of advocates of a safety-first retirement planning approach such as Zvi Bodie. But for now, let’s understand from where the 50-75% stock allocation recommendation comes.

One starting point to think about this is to consider Figure 2.2, which shows the time path of maximum sustainable withdrawal rates for different asset allocations. It’s hard to see exactly what is going on in the 1960s, but the general idea is that higher stock allocations tended to support higher withdrawal rates with little in the way of downside risk. I mean, the SAFEMAX does not appear to be that much lower with higher stock allocations.


This point can be seen more clearly in Figure 2.3, which shows the SAFEMAX across the range of stock allocations. Low stock allocations resulted in lower SAFEMAXs, with an all-bonds portfolio even falling below a 2.5% SAFEMAX, but there appears to be a sweet spot between about 35% stocks and 80% stocks in which higher stock allocations have no discernable impact on the SAFEMAX. A 4% withdrawal rate tended to work no matter what stock allocation is chosen in this range.  On the downside, retirees would have been just as well off with 80% stocks as with 35% stocks.


So why then did William Bengen recommend 50-75% stocks?  The answer lies in Figure 2.4, which shows the median remaining real wealth after 30 years as a multiple of retirement date wealth. In this figure, we can see a general upward trajectory in remaining wealth as the stock allocation increases. In the average case, retirees using at least 45% stocks would have found that their entire initial principal had remained intact, even after adjusting with inflation! And with higher stock allocations, wealth tended to continue to grow more and more in the average case. So while Figure 2.3 showed that there was little in the way of downside with higher stock allocations, Figure 2.4 shows that there was a whole lot of upside available with higher stock allocations. This is the source of Mr. Bengen’s recommendation.


Finally, one other way to look at this is found in Figure 2.5.  For different stock allocations, I plot not only the SAFEMAX, but also the median sustainable withdrawal rate and the best-case scenario sustainable withdrawal rate. This is another way to see the same point: with higher stock allocations, sustainable withdrawal rates tended to rise, but even the worst-case scenario held their ground even with a more volatile stock allocation.



  1. Avatar Brad Nichol on February 7, 2012 at 10:19 am

    It is unclear whether the withdrawal rate is X% of your beginning principal or your annual balance. I would assume the discussion is based on a fixed withdrawal amount (or indexed for inflation), but if not, an important part of the discussion is the total amount withdrawn as well as sustainability of a minimum or the bequest.

    • Avatar Wade Pfau on February 7, 2012 at 3:03 pm


      This can be a confusing point. Your assumption is correct. The 4% part just refers to the percentage of initial retirement assets withdrawn in the first year. In subsequent years, that dollar amount is adjusted for inflation. The actual withdrawal percentage in subsequent years will fluctuate based on market returns and withdrawals.

      This is not a constant annual 4% of remaining balance. That is another viable approach, but it will leave spending rather volatile and unpredictable. People generally prefer smoother spending. Though clearly real people will adjust their spending partly based on market performance. That is a modification incorporated into later research which I will eventually get around to describing.

  2. Avatar Anonymous on February 7, 2012 at 9:40 pm

    Dr. Pfau,
    Another fascinating and crucial piece of analysis. This is extremely valuable information for those planning to retire (practically everyone, right?). I am intrigued that the SAFEMAX is so similar along the equity spectrup of 35-90%.

    this article makes me think of the ‘bucket approach’ (I follow Frank Armstrong @ investor solutions) and how your non-equity allocation can be drawn down in a down market until equities recover.
    Similarly, you can be withdrawaling from the asset class that has increased and deviated the most from your target Asset Allocation. I imagine this would also help raise the SAFEMAX tremendously. Do you know of any research on this as well?

    Your articles are always throught-provoking and I want to encourage you as you continue your research.

    • Avatar Wade Pfau on February 8, 2012 at 12:44 am


      Thank you. I’m interested to investigate the bucket approach some more, but I haven’t gotten to it yet. I did write about it once here:


      I finished reading Zvi Bodie’s new book “Risk Less and Prosper” and he really does tear into the concept. One thing that does concern me is that the bucket approach has mostly only been tested with US data since 1926. It was really hard to go wrong with stocks during this time period (when stocks went down, they usually came back up fairly quickly), but that may not always be true in the future.

      I would like to look more at what you are suggesting in the future using Monte Carlo simulations.

      Thanks, Wade

    • Avatar Anonymous on February 8, 2012 at 7:01 pm

      Though I haven’t read it yet, the approach in “Risk Less and Prosper” seems to be short on the ‘Prosper’ aspect of it, and also seems to ignore other risks that I find crucial to be aware of. He does mention that it is specific to the individuals real desired risk, so is always going to be specific to the individual.

      I’d also like to see this SAFEMAX applied to your other research related to the valuations – specifically regarding your PE10 market timing paper published in March. I imagine the variable asset allocation would make the analysis more complex, but these two seem to be complementary studies that could prove very valuable.
      I thuroughly enjoy reading about what you’re doing, keep it up.


    • Avatar Wade Pfau on February 9, 2012 at 2:01 pm


      I too was thinking that the purpose of his book wasn’t about how to “prosper,” but rather how to make sure one’s basic needs are met. I suppose you could prosper in a relative sense if everyone else’s stock portfolio crashes. But then I heard from someone that authors have very little say in what the final title of their book is, and so perhaps it wasn’t his fault about that being the title. Maybe “prosper” helps to sell more copies. Which may be a good thing, as the book is worth reading for anyone thinking about whether their plans to become prosperous are actually riskier than they may have imagined.

      Regarding the SAFEMAX and PE10, I’ve got an answer for you. This article is scheduled to be in the April Journal of Financial Planning. You can read the working paper version here:

      I do find that, at least backtested in the U.S. historical data, valuation-based asset allocation does have the potential to noticeably raise the SAFEMAX.

      Thanks for reading, Wade

  3. Avatar Joe Tomlinson on February 7, 2012 at 9:50 pm

    This is a very interesting study–it adds a lot of valuable additional information to the original Bengen work. In particular, Figure 2.5 indicates that it might be very reasonable for someone with a significant bequest motivation (and/or lack of aversion to depleting savings) to invest heavily in stocks. (A cautionary note is that this does not take into account that the average magnitude of plan failures may increase as a function of the stock percentage–which we both take account of in other work we are doing on utility.) It’s interesting to note that Van Harlow is still in the press with his recommended low stock allocations–per this from last month’s Investment News:


    • Avatar Wade Pfau on February 8, 2012 at 12:53 am

      Thanks Joe!

      I was thinking about including the magnitude of failure vs. the probability of failure in that discussion, but thought it wasn’t relevant yet since I was talking about historical SAFEMAXs. But once shifting to Monte Carlo, or once dealing with higher than SAFEMAX withdrawal rates, then the magnitude of failure does become a more important consideration.

      Thanks for the link about Van Harlow’s article. I’m not opposed to low stock allocations, but I think you and I both do have some legitimate concerns about the methodology used in his research. I’m surprised it is still getting press coverage. I thought I sort of debunked it here:


      I’m glad to see your new column at AP:


      and also your research article in the new February JFP:


      I’d like to feature them both once I get caught up!

    • Avatar Wade Pfau on February 8, 2012 at 12:55 am


      Is the Investment News article worth reading? It looks like a lot of registration data entry is required first.

  4. Avatar Joe Tomlinson on February 8, 2012 at 9:46 am

    Wade, it’s not worth the registration hassle to get the article Harlow wrote–nothing new included. I was just noting that he’s still out there using his study to advocate for low stock allocations. Here’s the key section (via cut and paste):

    When the model used in the study sought to minimize the severity of depletion risk, it found that the optimal equity asset allocation for sustainable withdrawals is far lower than is typical in life cycle funds — ranging between just 5% and 25% for investors ages 65 to 85. These strikingly conservative equity allocations changed little even when the model’s assumptions on investment risk and market returns were altered.

    Further, for people willing to increase their depletion risk in hopes of improving their chances of leaving a larger bequest to heirs, the study suggests equity allocations of no more than 35% to 45%.

    • Avatar Wade Pfau on February 9, 2012 at 2:03 pm


      Thanks. I guess I should read the article again. I don’t really remember the section showing that the “equity allocations changed little even when the model’s assumptions on investment risk and market returns were altered.”


  5. Avatar Anonymous on February 10, 2012 at 7:49 pm

    Wade –
    I wonder if leaving a legacy was just a by product of Bengen’s work on withdrawal rates or something that he specifically set out to accomplish? Do you have any idea? It seems that all the discussion for years has been on the 4% withdrawal rate rule alone.

    As someone on the cusp of retiring we have no thoughts about leaving a legacy. And it has been a “concern” that safemax and other withdrawal strategies have, for the most part, large portfolios as legacies.

    I have come to the understanding that there will never ever be a way or means to forecast what is safe or reasonable in terms of withdrawal rates. It is always going to have to be something to look at annually at least.

    I personally find figure 2-5 very interesting. The median is much closer to the minimum than the maximum. I would have expected it to be more in the middle of the two.


  6. Avatar Wade Pfau on February 10, 2012 at 10:14 pm


    Thanks for writing. I don’t want to assume what Mr. Bengen was thinking, but I think that the legacy was a side product. I think he wanted to know the SAFEMAX, but then saw that the SAFEMAX was the same for so many different stock allocations, and then realized that one might as well use a higher stock allocation to get more legacy value.

    I will write more about this later, but if you have no interest to leave a legacy, then you may reasonably end up deciding to use a lower stock allocation. I don’t think the historical SAFEMAXs go far enough to tell us about the potential downsides. Well, there is a lot of factors to consider. I will try to lay them all out systematically in the coming months.

    Yes, the maximum is much higher than the median. The distribution of these withdrawal rates will not be symmetric. They are what’s called a lognormal distribution. The largest values can get very large. You can see a picture of a lognormal distribution here:


  7. Avatar John Caldeira on February 19, 2012 at 7:47 pm

    Mr. Wade,

    The analysis above uses a constant stock-bond mix throughout the 30 year period, as do most withdrawal rate studies. However, many investors actually reduce their allocation to stocks as their investing horizon shortens. I am curious to learn how sustainable withdrawal rates hold up in declining stock portfolios.

    I realize it’s a significant task, but think it would be a good service to investors if you, or someone, analyzed the typical “age in bonds”, “age-10 in bonds” and perhaps a popular target retirement fund glide path for stock allocations in a withdrawal study. Comparisons to a static stock mix withdrawal rate would be helpful.

    John Caldeira

  8. Avatar Wade Pfau on February 20, 2012 at 1:05 am

    Dear John,

    Thanks for the comment. Regarding William Bengen’s SAFEMAX concept, I think he already provided an answer for you in a 1996 article he wrote:


    I’ve also done some preliminary analysis of this which shares Bengen’s conclusions and finds the opposite of the usual advice: that one should actually consider increasing their stock allocation as they get older, past the retirement date. Basically, at around retirement your wealth is the highest, and that is when you want the lowest stock allocation. I describe some preliminary results here:


    Best wishes, Wade

  9. Avatar Anonymous on March 6, 2012 at 1:21 am

    Good Evening, Wade ~

    I would appreciate your views on the Comment I made in the WSJ today about liquidating a fixed number of shares, rather than a percentage.

    Thanks ~ Gil Chapman

    P.S. Richard Blumenthal is my next door neighbor, and allows me to use his name as my ‘pen name’ on WSJ postings.

  10. Avatar Wade Pfau on March 6, 2012 at 4:43 am

    Thanks for stopping by, Gil.

    It sounds like a reasonable approach if you can accept the inevitable volatility of the spending power. I made a comment at the WSJ.

    I’d also like to compare that with something like just withdrawing a fixed percentage of the remaining assets each year.


    • Avatar Anonymous on March 6, 2012 at 11:34 am

      Wade ~

      Thank you for your response.

      With respect to your volatility concern, I mentioned in one Comment that it would be wise to keep about 3 times 50% of the ‘norm’ in cash for periods like 2009-2012, to protect one’s needed cash flow.

      Actually, I’ve ‘tested’ your idea of of withdrawing a fixed percentage of the remaining assets each year, and it comes out pretty much the same as my fixed number of shares concept does, i.e 1970-2010, 1980-2010.

      My original premise was DOLLAR-Cost-Average in, SHARE Cost Average out (for lack of a better term).

      Also, by assuming the shares will appreciate by 6% (on average) during 30 or 40 years, ‘excess profits’ in good years could be reinvested in a second portfolio.

      Again . . . Thank you for your thoughtful response.

      ~ Gil

    • Avatar Wade Pfau on March 6, 2012 at 11:44 am


      That’s a good idea about if the share value gets higher than you can spend, then go ahead and save some for a rainy day. And keeping a separate emergency fund from the beginning.

      Have you only looked at selling a constant number of shares each year, or have you experimented with: sell more shares early on and less shares later on, since you are expecting on average for the value of shares to increase.


  11. Avatar Anonymous on March 6, 2012 at 1:33 pm

    Re: Your second paragraph

    No . . . But I will now. Never dawned on me to be honest . . . Thanks for the idea ! ! !

    (I’ll be back to you when I’ve re-worked the data I’ve spent 40 years collecting . . . It will take some time . . . But I promise “I shall return.”)

  12. Avatar Gilbert W. Chapman on March 6, 2012 at 4:55 pm

    Wade ~

    You mentioned using a ‘deeply deferred income annuity’ in your WSJ response.

    Here’s an alternative. If I ‘live too long’ I could always tap into the cash values.


    I don’t know how old you are, or whether you’ve seen the re-runs of “Leave It To Beaver”, but, in any case, I think you may still enjoy it.

    ~ Gil

  13. Avatar Wade Pfau on March 7, 2012 at 2:36 am

    “Leave It To Beaver” was a fixture of 1980s syndicated television, and so an important part of my childhood too.

    Thanks for sharing your article. I need to learn more about those avenues for retirement planning.

  14. Avatar Gilbert W. Chapman on March 7, 2012 at 4:40 am

    I’ll ‘leave you alone’ for awhile after offering one final ‘thought’ for consideration.

    Appearing in the February 1, 1993 edition of Forbes Magazine was an article by the legendary Peter L. Bernstein, entitled, “Who Needs Bonds?”, and it interfaces nicely with the conversation above relative to the stock/bond mix appropriate for retirees.

    The conclusion I drew from it (not necessarily the only one worthy of consideration) was that one could have a portfolio with 100% equities, and no bonds, and not be at a higher risk level over the long run. It was from this article that I developed the idea of using the cash values from whole life insurance, interfaced with the share liquidation idea (rather than percentage)to ‘insure’ liquidity in down markets.

    In other words, I looked at those cash values as a low yield bond fund of sorts. The ‘mix’ I came up with as extremely safe was 80%-85% in equities and 15%-20% in cash values.

    I must admit, however, I could never conceive of a ‘plan’ that could accommodate a “Black Swan” event; and decided that if the DJIA did ever drop by more than 60% (and stayed there for more than 4 years) that it was ‘all over’ for all of us.

    So long for awhile . . . I’m going to see whether it is possible to liquidate more and more SHARES during retirement (as mentioned in an earlier Comment above).

    Cordially ~ Gil

    P.S. If you lay your hands on the Bernstein article, let me know, and I’ll Fax it to you.

    • Avatar Wade Pfau on March 7, 2012 at 11:52 am


      Thanks. I will have a look for that article. And in the mean time, please see this blog entry:


      Though it is showing how a dollar invested in the stock market might grow (or shrink) over 30 years, it could just as easily be interpreted as the price of a share with an initial value of $1. Then, multipled by the number of shares, this speaks to your issue of selling a constant fraction of shares over time.

  15. Avatar g on March 7, 2012 at 4:42 am

    Typo in the P.S. ~ If you CAN’T lay your . . .

  16. Avatar Terry Reitan on April 22, 2013 at 7:34 pm

    As someone who has followed Mr. Bengen since the original article, I appreciate your update and blog. I have recommended the 4% withdrawal rate for years.

    However, one of Mr. Bengen’s early articles recommended an equity percentage equal to a constant minus your age at retirement–the constant for the 30 year retirement case being 128 (+/- 12 for aggressive/conservative investors) for taxable accounts and 135 (+/-13) for non-taxable. For example, the equity percentages for a 65 year old would be 63 and 70, respectively. (It is worth noting here that these are much higher percentages than most life-cycle or target retirement mutual funds.) This approach had the advantage of being easily understood and didn’t require modeling software.

    However, Mr Bengen later dropped the rule-of-thumb approach and went to financial planning software applied on an individual basis. (As one who used sophisticated Monte Carlo software for many years to model the behavior of complicated mortgage-backed security derivatives, I am mistrustful of the assumptions that are made by the financial planning models, particularly in the area of stable correlation coefficients among asset classes and the use of normal frequency distributions of returns.) I am concerned that such software understates the true risk of black swan events.

    I would be interested in your comments on the equity percentages over retirement.

  17. The Trinity Study and Portfolio Success Rates on January 25, 2015 at 9:56 pm

    […] the assumption that withdrawals are made at the start of the year rather than the end of the year. William Bengen’s research gave us the SAFEMAX, which he defined as the highest sustainable withdrawal rate in the worst-case scenario from […]

  18. […] natural starting point for discussions about retirement spending is the 4% rule. William Bengen look at all the different 30 year periods in US history and found that withdrawing […]

  19. Ten Reasons Why the 4% Rule is Too Simplistic on September 3, 2015 at 11:47 am

    […] withdrawn 4.15% at most. This is where the 4% rule comes from, and you can read more about it at William Bengen’s SAFEMAX. This doesn’t necessarily mean that 4% is an appropriate withdrawal rate for every new […]

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