Trinity Study 2019 Edition

When you come to retire, how much of your nest egg will you spend each year? 4%? Right, I get it, you’ve done your homework on the ‘Trinity Study’ that originated the ‘4% Rule’. But have you looked at the Trinity Study from another dimension? What would the answer be in that case? Join me as I take this cornerstone study for FIRE enthusiasts to another dimension and see how the results change in surprising ways. (oooh! Things are gonna get all actuary-like. You betcha!)

The Trinity Study

There has been so much written on the Trinity Study in the personal finance blogosphere that I’m going to pass on a detailed introduction to this famous piece of work. But very briefly - the researchers looked back at what would have happened to your retirement nest egg under different spending amounts and different historical periods. The parameters of the study were;

  • Historical data from 1926-2009
  • Portfolios composed of US large cap stocks and long term corporate bonds
  • 30 year retirement duration

This produced 54 separate time periods (most of them overlapping) and the researchers looked at the maximum amount that could be withdrawn per year without exhausting your funds. The punchline of the study was that all the withdrawal rates were at least 4% a year with a portfolio composed of 75% stocks and 25% bonds. This then coined the term that 4% was a “safe withdrawal rate”. Said another way; as long as you don’t withdraw more than 4% a year then according to the Trinity Study your funds should be safe from running out.

Obvious Questions

At this point the obvious questions you should ask are:

  • What about testing this further back in time?
  • Tell me what happens with different investment strategies?
  • What about different time periods?

Other writers (for example Big ERN) have addressed these issues comprehensively and this is a pretty well trodden path. And honestly, you really didn’t want me to answer the obvious questions, did you? So we’re going to break through the Matrix and look at the problem in a different way.

Another Dimension

Let’s break some rules. One of the issues with the Trinity Study is that it is based on very little data and the time periods are overlapping, so we don’t even have 54 independent observations. We therefore need a way to extend the data. So… I’m going to construct new 30 year retirement periods. Uh, what? I’m going to take stock and bond data stretching back to 1802 and randomly take 30 of those returns to make a new retirement period. Hang on, what? This new retirement period will be composed of actual historical data but in a random order. And get this bit; I’m going to allow replacement, so that any particular return could be chosen twice or more! Oh man, this is crazy actuary sh!t. Stay with it, this is a completely respectable method suggested by one of the most important economists of the modern age.

Paul Samuelson

Paul Samuelson was the first American to win the Nobel prize for economics and generally reckoned to be the most influential economist of the later 20th Century. He proposed a thought experiment;

What if you wrote down the annual historical stock returns from the last 150 years on 150 separate pieces of paper and put them in a hat. Then randomly pull out of the hat 30 pieces of paper to represent a new thirty year historical period, but crucially replace each piece of paper in the hat after you make each draw.

At this point you enter a different dimension where an important hypothesis of the market is killed.

Mean-Reversion of Stocks

Most people believe that stocks will mean revert over time. In other words after an extended down market, the market will somehow bounce-back, and over the long term the return on stocks will stay healthy. There is no doubt that we have a huge amount of compelling historical evidence that stocks exhibit this kind of behavior. In every 20 year period stocks have outperformed bonds, and they always come back after a crash. The resilience of the US equity market is quite extraordinary, and this is one reason that makes lump sum investing preferable to dollar cost averaging. But think of this; since 1802 there have only been 12 non-overlapping 20 year periods. Moreover the stock market between 1802 and the 1870’s was extremely under-developed and basically consisted of only a few railroad stocks, so consider that there has only been 8 non-overlapping 20 year periods since the 1870’s. That’s really not a lot of evidence for the bounce-backability of equities. If your surgeon proposed a very delicate life-saving procedure that could result in death, but happily announced that there had been eight previous successful operations, would you go for it? Or would you want to see more successful trials before subjecting yourself to it? So by creating new 30 year retirement sequences of returns we are creating market scenarios with historically accurate equity volatility and returns, but we are simply discarding the rainbow and unicorns assumption that the equity market always comes good in the end. If at this point you are becoming red-faced with disgust at my cavalier attitude to simulating retirement periods, then perhaps visit the technical notes to get some further background before making your judgement.


So… are you still with me? Are we gonna head into another dimension on this one? We will look at 30 year periods, since that was the period of the original Trinity Study. The proprietary AoF model cranked out 1,000 new 30 year simulations and I tested what the safe withdrawal rate would have been. Here’s my results on the top with the actual Trinity Study results below for comparison. I’ve ordered the scenarios from lowest to highest withdrawal rate and showed the number of simulations in each 1% bucket. [caption id="attachment_39280" align="aligncenter" width="475"] Original Results from Trinity Study[/caption] What’s the first thing you notice? The Trinity Study has laughably few results. It’s perhaps amazing that the most important question for wannabe retirees: how much can I spend in retirement? Is being based on a study with so few data points. I know that there have been extensions to this study, but the lack of non-overlapping historical periods reduces the effectiveness of the results. What’s the second thing you notice? There is a much greater spread of results, from the very high, to the disturbingly low. In the alternative dimensions there are scenarios with a SWR in excess of 20% and some scenarios with a SWR of less than 2%! In these alternative dimensions stocks can genuinely result in a sustained period of great returns, or a sustained bear market. Without an automatic reversion to the mean the market can stay down for a long time. Let’s summarize the results so we can compare them.

Alternative Dimension (75% Stocks)

Trinity Study (75% stocks)

Number of simulations



Median swr



Minimum swr



What’s a Safe Withdrawal Rate in an Alternative Dimension?

Did you see in the table above that over all 1,000 simulations the minimum SWR was a buttock-clenchingly low 1.8%? It’s tempting to dismiss that as too low and resulting from a crazily harsh sequence of returns that could only happen in another dimension. But let’s look at this single scenario a bit more closely. In the chart below I have taken the single simulation that generated the SWR of 1.8% and shown the annual equity returns. [caption id="attachment_39283" align="aligncenter" width="543"] Stock Returns in Bad Scenario[/caption] You’ll see that there is a brutal 6 year bear market from years 6 to 12, but on the other hand there are plenty of years with returns in excess of 10%. And remember that is 10% real returns – not bad! But what I think is the real nail in the coffin for this retiree cohort is the big drawdown of over 20% in the first year of retirement. As we know from sequence of returns risk, a big drawdown early in your retirement can be deadly without remedial action. I’m going to guess that if those first two years had higher returns then the SWR would improve from 1.8% to around 2.5%.

What Else Have We Learned?

I was expecting some pretty bad scenarios to be honest, and correspondingly I expected some pretty high SWR scenarios. That’s just my actuarial spidey-sense tingling. But I did not expect the SWR values to be so high in general. In the chart I showed earlier you can see a big clump of results in the 5%-8% range. Over half the scenarios produced SWR values in the range 5.5% to 8.8%. In addition, 950 out of the 1,000 scenarios produced a SWR in excess of 3.8%! This is saying that if you live in another dimension (and by this point you might think that I do) then to be 95% certain that you will have sufficient retirement funds then a 3.8% SWR is sufficient. You might want to be 100% certain on this important issue, but I think most of us believe in some mean reversion of equities and so this 95% level of certainty could be acceptable.

Final Thoughts

What’s my final thoughts on this? I think the 4% rule from the Trinity Study is simply an accident that resulted from analyzing too few scenarios. Had the Trinity Study been done in another dimension the lowest safe withdrawal rate would likely have been lower and this might have changed the course of hundreds of early retirements. It also seems that the results point the way to higher withdrawal rates being acceptable. Even a withdrawal rate north of 5% would have been successful most of the time in the alternative dimension. When you combine this relatively high withdrawal rate with some additional income in retirement (e,g, from a part-time job) and the ability to tighten your belt on spending if the market crashes then I would be comfortable with a withdrawal rate in excess of 4%. What did you think of the Trinity Study in another dimension? Did you think that removing the mean reversion of stock returns provided an interesting insight into this? Does the very low SWR worry you, or were you cheered up by the number of scenarios that resulted in a relatively high SWR? Comment below! I’ve written some more technical notes on this subject here. The following is a guest post from the Actuary on Fire.