Trinity Study Updates

Wade Pfau, Ph.D., CFA

by Wade Pfau, Ph.D., CFA

April 1, 2011

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. 

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

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.

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. . 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

a) Pfau, W. D., “An International Perspective on Safe Withdrawal Rates from Retirement Savings: The Demise of the 4 Percent Rule?” Journal of Financial Planning. Vol. 23, No. 12 (December 2010), 52-61.

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.

Trinity Study Updates

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:

Trinity Study Updates——————–

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

 

100% Stocks

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

3% 4% 5% 6% 7% 8% 9% 10% 11% 12%
15 Years 100 100 100 93 8 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 69 49 36 20 7 2 0 0

 

50% Stocks

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

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

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

100% Stocks

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

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

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

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

3% 4% 5% 6% 7% 8% 9% 10% 11% 12%
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.

100% Stocks

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

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

3% 4% 5% 6% 7% 8% 9% 10% 11% 12%
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 64 12 0 0 0 0 0
40 Years 100 82 51 20 9 0 0 0 0 0

 

25% Stocks

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

3% 4% 5% 6% 7% 8% 9% 10% 11% 12%
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.


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