## Some Useful Charts And Thoughts About Personal Investing

I just finished a paper called “Managing Laurels: Liability-Driven Investment for Professional Athletes,” and I thought that one or two of the charts might be interesting for readers in this space.

An athlete’s investing challenge is actually much more like that of a pension fund than it is of a typical retiree, because of the extremely long planning horizon he or she faces. While a typical retiree at the age of 65 faces the need to plan for two or three decades, an athlete who finishes a career at 30 or 35 years of age may have to harvest investments for fifty or sixty years! This is, in some ways, closer to the endowment’s model of a perpetual life than it is to a normal retiree’s challenge, and it follows that by making investing decisions in the same way that a pension fund or endowment makes them (optimally, anyway) an athlete may be better served than by following the routine “withdrawal rules” approach.

In the paper, I demonstrate that an athlete can have *both* good downside protection *and* preserve upside tail performance if he or she follows certain LDI (liability-driven investing) principles. This is true to some extent for every investor, but what I really want to do here is to look at those “withdrawal rules” and where they break down. A withdrawal policy describes how the investor will draw on the portfolio over time. It is usually phrased as a proportion of the original portfolio value, and may be considered either a level nominal dollar amount or adjusted for inflation (a real amount).

For many years, the “four percent rule” said that an investor can take 4% of his original portfolio value, adjusted for inflation every year, and almost surely not run out of money. This analysis, based on a study by Bengen (1994) and treated more thoroughly by Cooley, Hubbard, and Walz in the famous “Trinity Study” in 1998, was to use historical sampling methods to determine the range of outcomes that would historically have resulted from a particular combination of asset allocation and withdrawal policies. For example, Cooley et. al. established that given a portfolio mix of 75% stocks and 25% bonds and a withdrawal rate of 6% of the initial portfolio value, for a thirty-year holding period (over the historical interval covered by the study) the portfolio would have failed 32% of the time for, conversely, a 68% success rate.

The Trinity Study produced a nice chart that is replicated below, showing the success rates for various investment allocations for various investing periods and various withdrawal rates.

Now, the problem with this method is that the period studied by the authors ended in 1995, and started in 1926, meaning that it started from a period of low valuations and ended in a period of high valuations. The simple, uncompounded average nominal return to equities over that period was 12.5%, or roughly 9% over inflation for the same period. Guess what: that’s **far** above any sustainable return for a developed economy’s stock market, and is an artifact of the measurement period.

I replicated the Trinity Study’s success rates (roughly) using a Monte Carlo simulation, but then replaced the return estimates with something more rational: a 4.5% long-term real return for equities (but see yesterday’s article for whether the market is *currently* priced for that), and 2% real for nominal bonds (later I added 2% for inflation-indexed bonds…again, these are long-term, in equilibrium numbers, not what’s available now which is a different investing question). I re-ran the simulations, and took the horizons out to 50 years, and the chart below is the result.

Especially with respect to equity-heavy portfolios, the realistic portfolio success rates are **dramatically** lower than those based on the “historical record” (when that historical record happened to be during a very cheerful investing environment). It is all very well and good to be optimistic, but the consequences of assuming a 7.2% real return sustained over 50 years when only a 4.5% return is realistic may be incredibly damaging to our clients’ long-term well-being and increase the chances of financial ruin to an unacceptably-high figure.

Notice that a 4% (real) withdrawal rate produces only a 68% success rate at the 30 year horizon for the all-equity portfolio! But the reality is worse than that, because a “success rate” doesn’t distinguish between the portfolios that failed at 30 years and those that failed spectacularly early on. It turns out that fully 10% of the all-equity portfolios in this simulation have been exhausted by year 19. Conversely, 90% of the portfolios of 80% TIPS and 20% equities made it at least as far as year 30 (this isn’t shown on the chart above, which doesn’t include TIPS). True, those portfolios had only a fraction of the upside an equity-heavy portfolio would have in the “lucky” case, but two further observations can be made:

- Shuffling off the mortal coil thirty years from now with an extra million bucks in the bank isn’t nearly as rewarding as it sounds like, while running out of money when you have ten years left to lift truly sucks; and
- By applying LDI concepts, some investors (depending on initial endowment) can preserve many of the features of “safe” portfolios while capturing a significant part of the upside of “risky” portfolios.

The chart below shows two “cones” that correspond to two different strategies. For each cone, the upper line corresponds to the 90th percentile Monte Carlo outcome for that strategy and portfolio, at each point in time; the lower line corresponds to the 10th percentile outcome; the dashed line represents the median. Put another way, the cones represent a trimmed-range of outcomes for the two strategies, over a 50-year time period (the x-axis is time). The blue lines represent an investor who maintains 80% in TIPS, 20% in stocks, over the investing horizon with a withdrawal rate of 2.5%. The red lines represent the same investor, with the same withdrawal rates, using “LDI” concepts.

While this paper concerned investors such as athletes who have very long investing lives and don’t have ongoing wages that are large in proportion to their investment portfolios (most 35-year-old investors **do**, which tends to decrease their inflation risk), the basic concepts can be applied to many types of investors in many situations.

And it should be.