Tuesday, February 7, 2012

The Trinity Study and Portfolio Success Rates

The other main retirement planning study from the 1990s to enter the retirement research canon came four years after William Bengen’s initial work. The Trinity Study, a nickname for the article, “Retirement Spending: Choosing a Sustainable Withdrawal Rate,” by Philip L. Cooley, Carl M. Hubbard, and Daniel T. Walz (all professors at Trinity University in Texas), appeared in the February 1998 issue of the Journal of the American Association of Individual Investors. The innovation introduced in the Trinity study is ‘portfolio success rates.’ The authors updated their findings from time to time, most recently in the article, “Portfolio Success Rates: Where to Draw the Line” from the April 2011 Journal of Financial Planning.
Before proceeding any further, something must be clear. I will be discussing many different studies, each of which tends to come up with slightly different numbers. This is simply because they use different data sources or make different assumptions.
The only difference in assumptions between William Bengen’s work and the Trinity study regards the choice of bond indices. While Mr. Bengen’s original research combined the S&P 500 index with 5-year intermediate term government bond returns, the Trinity Study used long-term high-grade corporate bond returns instead. The different choice for bonds explains why the worst-case scenario for Mr. Bengen (his SAFEMAX) was a withdrawal rate of 4.15%, but why the original Trinity Study found that a 4% withdrawal rate only had a 95% success rate (with more volatile corporate bonds, the sustainable withdrawal rate dipped below 4% in 1965 and 1966).
Since keeping volatility low is just as important as obtaining high returns, I do think it makes more sense to use intermediate term government bonds than to use corporate bonds. So my re-creation here will follow Mr. Bengen’s choice and will also include 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 rolling periods of the historical data. The Trinity Study went a step further by tallying up the percentage of times that withdrawal rates fell below or above certain lines.
They calculated these portfolio success rates for different withdrawal rates (between 3 and 12 percent, both on a fixed and inflation-adjusted basis) and for different time horizons (15, 20, 25, and 30 years) and for different asset allocations (stock allocations of 100, 75, 50, 25, and 0 percent large-capitalization stocks, with the remainder in high-grade long-term corporate bonds).
To understand what they did, again consider Figure 2.1:

What is the success rate for a 5% inflation-adjusted withdrawal rate over a 30-year period with a 50/50 asset allocation?  Well, there are 56 rolling 30-year periods starting between 1926 and 2010.  These rolling 30-year periods begin in the years 1926 through 1981. Nothing is known yet for the 30-year results of more recent starting periods.  Of these 56 rolling periods, we can count up in Figure 2.1 the number of times that the withdrawal rate is above 5%. It is 37 times. That means the portfolio success rate is 100 x 37 / 56 = 66%. I’ve highlighted that number in yellow in the following Table 2.1, which shows the results for many other cases as well. And that is the Trinity Study. I’m not sure how particularly useful this table is for planning future retirements (more on that later), but enjoy looking at Table 2.1 nonetheless:


  1. Wade –

    This table of yours makes me shout both “YES!” and “NO!”

    YES, because it reinforces a conclusion that I’m getting from similar testing with Monte Carlo. So thanks for preparing and showing it.

    NO, because it has such a depressing message for the population whose options I’m looking at, folks whose wealth is not sufficient for decent retirement years at 4%. There are tens of millions who are or will be in that position, many despite trying to plan prudently based on reasonable job and home-equity assumptions which recent economic events have shattered . . .

    The numbers say that as you raise the withdrawal rate above 4%, success probabilities drop FAST. Arrghh.

    For many folks, it will be desirable to consider the kind of information in your table or a Monte Carlo equivalent, and also look at mortality tables – and then maybe choose something like all-stocks with 7% withdrawal rate, taking some risk of a povertous end in order to have a decent retirement life all or most of the way.

    I think we have responsibility to show them these options.

    Dick Purcell

    1. Dick,

      Thank you. You and I have talked a lot about concerns with the Trinity study. I will be getting to those. But I'm trying to start again from first principles.

      But what you are writing, about how the success rates drop rapidly as the withdrawal rate rises above 4%, is quite scary. Even for someone who places their faith in the study, there isn't much margin for error. Then again, if it wasn't for that pesky 1959-1974 period (see Figure 2.1), 5% wouldn't have been hit so hard.

      Next Tuesday my review of "Risk Less and Prosper" will be coming out at Advisor Perspectives. Zvi Bodie would VEHEMENTLY disagree with your solution for many folks. I'm still working through this all myself and haven't developed an opinion yet. But certainly I can agree that people should be aware of all the options, and what you are suggesting is one extreme option. The opposite extreme option would be to take whatever you've got and build a TIPS ladder or buy an inflation-adjusted single premium fixed annuity. And then there are various possibilities in between.

      Thanks as always for commenting! Wade

  2. Great presentation. What if you considered a bucket approach your portfolio mix. Instead of setting 25% bonds, you set X years of living in bonds and the rest in stocks. What would be the optimum X. The percentage would migrate from say 10% Bonds to up to 100% bonds when I'm 85 or 90. My simple study showed that the probability of making a profit increased with time to a critical point (or knee) at about 100 months (S&P 500) to about 95% based upon historical data. Where the slope of the curve changed from a more vertical to almost horizontal.

  3. Excellent Work. The great gamble of course are the black swans that can occur throughout the retirement period. Ebola, Civil Unrest, Personal tragedies to name a few. The risks we will face in 20 years are impossible to imagine now.

    Time, however is a currency that cannot be earned it can only be spent. The risk in retiring early and spending time doing the things you love is priceless. Money cannot replace the joys of free time.

    Your post, offers hope to those like me working hard towards financial independence. Thanks for your work! - ResilientMan.com