In the retirement planning literature, a landmark study is Cooley, Hubbard, and Walz’s 1998 paper, “Retirement Savings: Choosing a Withdrawal Rate That is Sustainable,” published in the AAII Journal.  The paper is often called “The Trinity Study” because the 3 authors were all professors at Trinity University.  The study looked at historical data for the United States to determine the chances for success for different withdrawal rates from one’s retirement savings for different time horizons and for different asset allocations.  Most of the study concerned withdrawals that are not adjusted over time for inflation, but their Table 3 assumed inflation-adjusted withdrawals and is therefore the most important part of the paper.  For the annual data between 1926 and 1995, they found that a portfolio consisting of 50% large-capitalization stocks and 50% high-grade long-term corporate bonds would have provided a 95% chance for success in supporting inflation-adjusted annual withdrawals starting with an initial withdrawal of 4% of the portfolio value at the time of retirement.

I think people are sometimes curious if this result may have changed if the study were repeated today, especially in light of the recent financial crisis.  The simple answer is: no.  Though financial markets have provided bad returns in recent years, those would have only shown up in the final years of retirement, and sustainable withdrawal rates are much more sensitive to the returns experienced at the beginning of retirement instead of the end of retirement.

To see more clearly, let’s dissect that 95% chance of success number a bit more.  The Trinity Study had data from 1926 to 1995.  To consider retirements lasting 30 years, this means they could only consider retirement dates from 1926 to 1966.  For anyone retiring after 1966, they couldn’t calculate the withdrawal rate sustainable over 30 years because they didn’t have the data.  1926 to 1966 represents 41 beginning retirement dates.  Of those 41 dates, the 4% inflation-adjusted withdrawal rate failed 2 times, in 1965 and 1966.  Thus, it’s success rate was 39/41 = 95.12%, or 95% when rounded down.

Now complete annual data is available through the end of 2009, giving us now the chance to look at 55 retirement periods of 30 years, as we can now consider retirement dates between 1926 and 1980.  When we want to discuss a 30 year retirement duration, we still don’t know what happens for retirees after 1980, because their story has not been finished. Of the 55 periods now available, there are still only 2 failures, 1965 and 1966.  There hasn’t been any failures since then.  Now we have a success rate of 53/55 = 96.36% or 96%. 

I’m sorry for not formatting it real nicely, but here are the numbers updated with data through 2009 that you can directly compare to Table 3 in the Trinity Study, and the link for that study is provided above.

               3%   4%   5%    6%   7%   8%   9%   10%  11%  12%
100% Stocks

15 Years       100  100  100   93   83   76   70   64   54   47
20 Years       100  100   91   80   71   63   54   46   40   31
25 Years       100  100   87   73   63   52   42   37   28   20
30 Years       100   96   78   62   55   42   33   29   20   11
75% Stocks
15 Years       100  100  100   96   86   74   71   57   49   41
20 Years       100  100   92   80   69   60   49   40   29   15
25 Years       100  100   85   68   57   43   35   27   12    7
30 Years       100   98   76   62   45   36   20    5    2    0
50% Stocks
15 Years       100  100  100   94   83   71   61   46   39   23
20 Years       100  100   92   80   63   46   35   22    9    6
25 Years       100  100   82   62   45   27   15    8    7    2
30 Years       100   96   69   49   20   11    2    0    0    0
25% Stocks
15 Years       100  100  100   91   76   60   46   34   26   14
20 Years       100  100   86   58   45   31   23   15    8    2
25 Years       100   95   58   35   23   13   10    8    2    2
30 Years       100   75   33   22    7    2    0    0    0    0
0% Stocks
15 Years       100  100  100   77   51   37   34   29   19   13
20 Years       100   92   58   35   29   26   20    9    5    2
25 Years       100   58   32   23   18   12    8    5    2    2
30 Years        85   35   22   11    2    0    0    0    0    0

April 2011 Update: The authors of the Trinity study published updated figures using this same data in the April 2011 Journal of Financial Planning. I provided more thoughts about this in my “Trinity Study Updates” blog entry.


  1. Avatar Anonymous on December 4, 2010 at 2:41 am

    It is worth noting that you can get 12 times as many data points if you use monthly data. About 52 times as many if you use weekly. Or about 250 times if you use daily.

    But you would learn almost nothing new.

    The reality is there was one period of a couple of years where this would not have worked.

    But it is further worth noting that using overlapping periods gives an illusion that you have lots of data, but this is false. Fifty five overlapping periods of 30 samples is less than two independent data points.

    There is no way to generate statistically meaningful results from two data points.

    One can report out results to four figures (95.12%) or round to two figure (95%), but with less than two independent data points both are rather overly precise.

    We do not know the long term returns well enough to say they will be about 7%, but not 8% and not 6%. That is we don’t even have one significant figure.

    In a world were we have no guarantee of future results estimating a fixed and safe 30 years withdrawal rate is at best unwise.

    The world is far too uncertain for that.

    The original paper was written largely to show that the then popular notion you could withdraw 10% was unwise. People then picked it up and grabbed it as if the 4% figure and approach of fixing a withdrawal rate was an actual plan. This was not in accord with the beliefs of the authors.

    Rod Cole

  2. Avatar Wade Pfau on December 18, 2010 at 1:22 pm

    Dear Rod, Thank you for the comments and I due consider them a lot. I hope to write something about this one of these days.

    For now, there is another matter. I’m quite thankful that a couple nice people have provided links to this blog entry, but in the ensuing discussions about it, I’ve seen quotes of the first part of one of these paragraphs:

    I think people are sometimes curious if this result may have changed if the study were repeated today, especially in light of the recent financial crisis. The simple answer is: no.

    But leave out the VERY IMPORTANT second part of the paragraph:

    Though financial markets have provided bad returns in recent years, those would have only shown up in the final years of retirement, and sustainable withdrawal rates are much more sensitive to the returns experienced at the beginning of retirement instead of the end of retirement.

    Though that last sentence can qualify as a good example of a run-on sentence, it is very important and needs to be left with the first part of the paragraph. In the context of how the Trinity Study works, we don’t know yet how things will turn out for recent retirees.

  3. Avatar Anonymous on August 15, 2011 at 10:12 pm

    There is something wrong with financial planning when everyone- even Jack Bogle- uses rolling period analysis and acts as though it is valid statistically. It is not and it doesn’t matter who the author’s names are on the study. Example: the DOW was up 44% in 1954 and by using rolling periods you are counting that over and over again.
    One wonders what is afoot? Fred

  4. Avatar Wade Pfau on August 16, 2011 at 7:03 am

    Thanks for writing. Perhaps the best mix is to look at both Monte Carlo simulations and historical simulations, as they each have advantages and disadvantages.

  5. Avatar Anonymous on October 30, 2013 at 1:36 pm

    You dhould have your work proff-read prior to publishing. by an adult.

  6. Trinity Study Updates - Retirement Researcher on January 25, 2015 at 10:53 pm

    […] Studies, Fees, Sustainable Spending, The 4% Rule 2 Comments In October, I wrote a blog post providing updated numbers for the Trinity Study, which is the nickname of Cooley, Hubbard, and […]

  7. […] lot of people like to quote the Trinity Study indicating something along these […]

  8. Your Guide to Happiness on March 20, 2017 at 10:19 am

    […] by multiplying your annual expenses by 25.  The number you calculate will allow you to withdraw 4% per year indefinitely.  But their is no formula to calculate your FU number.  All you can do is guess, […]

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