Friday, April 1, 2011

Trinity Study Updates

In October, I wrote a blog post providing updated numbers for the Trinity Study, which is the nickname of Cooley, Hubbard, and Walz's 1998 paper, "Retirement Savings: Choosing a Withdrawal Rate That is Sustainable," published in the AAII Journal.  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, in my opinion, the most important part of the paper. Their original study used data through 1995.

In the April 2011 issue of the Journal of Financial Planning, the Trinity authors provide these updates as well, making my original blog post obsolete. 
 Along with William Bengen's research, the Trinity study helped to motivate what has become known at the 4% rule for retirement withdrawals.  In the U.S. historical data, the 4% rule has worked quite successfully.  But more generally, William Bengen's research and the Trinity study were originally meant to dispel the notion that withdrawal rates like 6% or 7% (which matches the historical inflation-adjusted returns for stocks) are safe.

The studies have since taken on a life of their own, and many prospective retirees now use the Trinity study tables to guide their own retiree withdrawal decisions.  The natural conclusion from doing this is that 4% should be a safe withdrawal rate.

In this blog post, I would mostly just like to include a list of issues that I think prospective retirees should also consider as they plan their retirements using the Trinity study tables.  In conducting my own research about retirement planning, I have come to be concerned about the safety of the 4% rule for recent retirees since the mid-1990s.  Of course no one can predict the future, and I don't wish to be alarmist.  Most importantly, as the Trinity authors suggest, you must maintain flexibility with your retirement expenditures. I'm just worried that retirees who think of 4% as working in the worst-case scenario will be ill-prepared for the spending cuts that this flexibility may potentially entail.

In conducting your own due diligence with regard to your retirement planning, I humbly request that you also consider the following points:

1. Trinity study does not incorporate mutual fund fees. Anyone investing in actively managed funds may be paying 1 or 2% a year in fees. If the fund manager is not providing large enough risk-adjusted returns (alpha) to offset the fees, then the sustainability of the 4% rule will slip stealthily away. Another interpretation of this point could be that real-world investors may be unlucky in that their portfolio returns do not precisely match returns for the historical indices. For an example of this, the 50-50 portfolio over 30 years with 4% inflation-adjusted withdrawals had a 96% success rate without fees, 84% success rate with 1% fees, and 65% success rate with 2% fees.

2. The Trinity study considers retirement lengths of up to 30 years.  Please keep in mind that for a married couple both retiring at age 65, there is a good chance for at least one of the spouses living longer than 30 years. For an example of this, the 50-50 portfolio over 30 years with 4% inflation-adjusted withdrawals had a 96% success rate over 30 years, an 88% success rate over 35 years, and an 82% success rate over 40 years. Combined with a 1% fee, the success rate over 40 years falls to 60%.

3. The Trinity study is based on U.S. data, 1926-2009. For 30-year retirement lengths, this allows for an analysis of retirements beginning between 1926 and 1980. Despite the Great Depression and Great Stagflation, this was a remarkable period in U.S. history:

3a: The 4% rule has not held up nearly as well in most other developed market countries as it has in the U.S.  [Pfau, 2010a]

3b: In recent years, stock market valuations have been high (reaching an extreme historical peak in 2000), dividend yields have fallen to historical lows, and bond yields are also rather low. These three variables together have explained maximum sustainable withdrawal rates quite well for a variety of asset allocations in the U.S. historical data, and the recent values for these variables suggest that 4 percent withdrawals may not be sustainable [Pfau, 2010c]

3c: There may be some confusion about the implications that the success rates did not decrease after the Trinity authors incorporated data for 1996-2009 to their analysis. Retirement success is more dependent on what happens early in retirement than late in retirement. In fact, the wealth remaining 10 years after retirement combined with the cumulative inflation during those 10 years can explain 80 percent of the variation in a retiree's maximum sustainable withdrawal rate after 30 years.  So the fact that success probabilities did not decrease after adding data for 1996-2009, which is only incorporated into the ends of retirements for retirees up to 1980 in the updated study, does not have any meaningful implications, either good or bad. [Pfau, 2010b]

4. There may be some confusion that the Trinity study seemingly implies that a high stock allocation (such as 75% stocks) is needed for the best chance of success in retirement.  However, with U.S. data, the choice of stock allocations between 30% and 80% had very little impact on the worst-case sustainable withdrawal rates. [Pfau, 2010a]. As well, as this discussion starting with this post at the Boglehead's Forum makes clear, the Trinity study over-represents a portion of the historical record that shows bonds in a bad light. With an alternative Monte Carlo simulation methodology, lower stock allocations appear much more attractive than suggested by the Trinity study's success rate tables.

5. The Trinity study was conducted under the assumption that retirees do not specifically plan to bequeath an estate.

6. On the other hand, there is some good news. Retirees who diversify their portfolios with international assets and TIPS many very well find an edge to keep the 4% rule alive.
7. UPDATE - MORE GOOD NEWS: I am hearing more and more that actual retirees do not necessarily need to adjust their spending for inflation each year, and that actual retirees may voluntarily reduce their spending as they get older.  For both of these cases, a higher initial withdrawal rate can be supported.  The combination of these factors may mean that the no-inflation adjustments case (which is shown in Table 1 of the updated Trinity study) may be more representative of what actual retirees will experience. I hadn't realized this.  The traditional 4% rule only applies when taking annual inflation adjustments. I have not done research about how my other concerns listed above impact withdrawal rates for the no-inflation adjustments case, but I hope to do this later.

Reference List

b) Pfau, Wade D. "Will 2000-Era Retirees Experience the Worst Retirement Outcomes in U.S. History? A Progress Report after 10 Years." Munich Personal RePEc Archive Paper #27107. November 2010. 

c) Pfau, Wade D. "Predicting Sustainable Retirement Withdrawal Rates Using Valuation and Yield Measures." Munich Personal RePEc Archive Paper #27487. December 2010. 


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Update: Trinity Study visualizations


I think it is helpful to see time series plots of the maximum sustainable withdrawal rates. This figure shows the 30-year results for the 50/50 and 75/25 stock/bond allocation cases for the Trinity study with inflation adjustments.  To get the probabilities shown in the updated Trinity study's Table 2, you add the number of circles above the withdrawal rate of interest and divide it by 55. This gives you the portfolio success rate.



As well, the main reason I made these graphs now is related to the point #7 about not needing inflation adjustments.  I wanted to see the graph for maximum sustainable withdrawal rates for the case when inflation-adjustments are used, compared to the case with no inflation adjustments.  Here it is for the 50/50 allocation:


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Appendix

I am using annual data, rather than monthly data like their updated study (this explains small differences in results). But let me show their original Table 3 / revised Table 2 (it is the table with inflation adjustments) after incorporating some administrative fees. 
 
If retirees pay a 1% account fee at the end of the year, the table looks like this:

1% Administrative Fee
               3%   4%   5%   6%   7%   8%   9%  10%  11%  12%
100% Stocks
15 Years       100  100  100   87   81   73   69   57   49   41
20 Years       100  100   88   75   66   60   46   40   31   22
25 Years       100   93   77   65   55   47   37   30   20    8
30 Years       100   89   69   56   45   35   29   20    9    5
75% Stocks
15 Years       100  100  100   93   81   71   60   51   46   27
20 Years       100  100   88   75   63   51   42   32   17    9
25 Years       100   93   77   62   48   38   28   12    7    2
30 Years       100   89   65   49   36   20    7    2    0    0
50% Stocks
15 Years       100  100  100   90   79   69   50   39   34   14
20 Years       100  100   86   71   58   37   28   12    6    2
25 Years       100   92   70   52   32   18   10    7    2    2
30 Years       100   84   53   31   13    2    0    0    0    0
25% Stocks
15 Years       100  100  100   86   66   49   34   33   19    9
20 Years       100   97   75   49   31   25   17    8    5    2
25 Years       100   80   45   28   13   12    8    2    2    0
30 Years       100   51   24   11    4    0    0    0    0    0
0% Stocks
15 Years       100  100   94   67   37   34   31   24   14    6
20 Years       100   80   40   29   28   23   11    6    2    2
25 Years        88   38   28   18   13    8    5    2    2    0
30 Years        42   25   13    4    0    0    0    0    0    0


Whereas 2% fees lead to:

2% Administrative Fee
               3%   4%   5%   6%   7%   8%   9%  10%  11%  12%
100% Stocks
15 Years       100  100   94   83   76   70   63   51   46   34
20 Years       100   94   78   71   62   52   43   34   22   15
25 Years       100   88   72   60   48   38   32   23   10    5
30 Years       100   78   58   53   38   31   16    9    5    2
75% Stocks
15 Years       100  100   97   86   74   71   54   49   37   23
20 Years       100   95   80   69   57   45   34   18   11    3
25 Years       100   87   68   55   40   30   15    7    2    0
30 Years       100   76   58   42   24    7    0    0    0    0
50% Stocks
15 Years       100  100   99   84   71   60   46   39   20    6
20 Years       100   95   80   63   43   32   17    6    3    2
25 Years       100   83   57   40   20   10    7    2    2    0
30 Years        96   65   42   16    2    0    0    0    0    0
25% Stocks
15 Years       100  100   99   76   59   43   34   20   10    4
20 Years       100   89   60   42   29   17    9    6    2    2
25 Years        97   57   33   18   12    8    2    2    0    0
30 Years        76   31   15    4    0    0    0    0    0    0
0% Stocks
15 Years       100  100   81   51   37   33   27   16    9    1
20 Years       100   65   35   29   25   11    8    2    2    0
25 Years        60   32   22   13    8    5    2    2    0    0
30 Years        36   18    4    2    0    0    0    0    0    0


The 50-50 portfolio over 30 years with 4% withdrawals had a 96% success rate without fees, 84% success rate with 1% fees, and 65% success rate with 2% fees. 


Also, for what it's worth.  Here is a table of the inflation-adjusted success rates when adding 35 and 40 year retirements as well. 

With 35 Years and 40 Years too

               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
35 Years       100   92   72   56   50   36   30   24   12    6
40 Years       100   91   76   58   51   38   31   24   11    7
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
35 Years       100   92   68   52   38   28   10    2    0    0
40 Years       100   91   67   49   38   18    7    0    0    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
35 Years       100   88   54   34   12    0    0    0    0    0
40 Years       100   82   51   20    9    0    0    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
35 Years       100   50   18   10    2    0    0    0    0    0
40 Years       100   33   18    4    0    0    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
35 Years        46   22   12    2    0    0    0    0    0    0
40 Years        29   16    4    0    0    0    0    0    0    0 

That 96% for 30 years becomes 88% for 35 years and 82% for 40 years.

Note, in a couple cases the probabilities increase as the time length increases. This is because for 40 years, we can only consider retirements beginning up to 1970. Any retirements between 1971-1980 that failed with 30 years will not show up in the 40 year calculations. This explains it.