Home > Good One, Investing, Theory > Some Useful Charts And Thoughts About Personal Investing

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.

50yrs pic

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:

  1. 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
  2. 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.

Categories: Good One, Investing, Theory
  1. Mark
    March 12, 2013 at 4:04 pm

    But tips are now yielding only 67bp at 30 years.

    • March 12, 2013 at 5:02 pm

      Right, but remember we’re talking about equilibrium here. You can add additional value as a manager by optimizing on the basis of true return expectations. This actually gives way more credit to equities than should be given, when THEIR long-term return right now is around 2% real, rather than 4.5%!

  2. Jim H.
    March 13, 2013 at 12:27 pm

    Excellent, thought-provoking work; you really hit this one out of the park. I’ve just been discussing the same subject (of sustainable withdrawal rates) with a relative who asked for some input. He wants a 4% withdrawal rate. I had to tell him it’s iffy at best.

    Two questions, if I may. What was your criterion for choosing to present the 80% TIPS / 20% stocks case, as opposed to (say) 50% TIPS / 50% stocks? Presumably the former mix performed better in your Monte Carlo simulation, but in what respect?

    Second, being uninformed about LDI, I don’t fully understand how it captured the upside in Chart 4. Presumably it’s something different than just (for example) applying a fixed 2.5% withdrawal rate to a 3-year moving average of portfolio value. Is there anything you or others have written, that you could recommend for more background on LDI? Thanks!

    • March 13, 2013 at 12:51 pm

      I selected 80% TIPS and 20% stocks because it is a mix that virtually guarantees the client will not run out of money in 50 years. 80% is the PV of a real amount of 2.5% received annually for 50 years, discounted at a 2% real rate…what a client would pay, approximately, for a 50-year inflation-adjusted annuity in such a case if they were available. So, this is the “conservative” outcome, but as you can see it truncates the upper tail too.

      In the LDI case, we still start with 80%/20%, but we make annual adjustments based on the relative changes in the assets and the liabilities (the 49-year annuity, 48-year annuity, etc). So it’s also like CPPI, frankly, which is how it captures the upside in Figure 4. You still have a 2.5% withdrawal rate, adjusted for inflation, of original portfolio value (in both cases).

      Off the top of my head, I can’t think of any single good piece on LDI. But the idea is actually very simple: instead of maximizing long-run return on assets, subject to risk constraints based on the variability of the asset portfolio, you maximize the ECONOMIC SURPLUS (assets-liabilities) subject to constraints on the variability of the surplus. Ergo, investments which track liabilities well tend to be preferred because they greatly reduce the variance of the surplus, and one is willing to sacrifice some return for that.

      That’s LDI in a nutshell!

  3. Jim H.
    March 13, 2013 at 6:20 pm


    In principle, TIPS should produce lower returns than conventional Treasuries since the government accepts the inflation risk. Less risk, lower return. I’ve seen estimates in the 50 to 100 basis point range, for the expected return a TIPS investor sacrifices to lay off inflation risk.

    This effect shows up in my simulated pre-1997 TIPS returns, and probably in yours as well.

    Realistically, thanks to reckless central bank policy, the next couple of decades should favor TIPS over conventional bonds, owing to nasty inflation surprises. But I’m troubled, when a 50-year horizon is assumed, about sacrificing 50 or 100 basis points of annual return over a half century that might bring another bond bull market when we’re 80 or 90 years old.

    Am I just greedy, or should I learn to stop worrying and love the TIPS?

    • March 13, 2013 at 9:37 pm

      I’ve never understood the reasoning behind why the investor should accept less return in a ‘risk premium’ because he has the risk of upward inflation, but the government shouldn’t pay more because they have the risk of downward inflation. The risks are symmetrical. I can see no reason that there should be any risk premium, and in fact it appears that the premium these days fluctuates from being slightly positive to slightly negative. I don’t believe that TIPS have a downward return bias, and the historical record bears that out too – the returns are nearly identical over a full cycle.

  1. December 30, 2013 at 9:33 am

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