When investing for retirement over long time horizons, advisors can choose from two apparently conflicting approaches. They can follow the advice of Wharton professor Jeremy Siegel, who has steadfastly advocated equity-centric portfolios, most notably in his highly popular book, *Stocks for the Long Run*. Or they can listen to Boston University professor Zvi Bodie, who says equities are simply too risky over the long term, and the core of a retirement portfolio should be Treasury Inflation Protected Securities (TIPS).

Siegel and Bodie cannot both be correct. Understanding which approach is best for long-term investors, however, requires an analysis of the subtle risk and return tradeoffs an investor faces. A sophisticated Monte Carlo simulation reveals how to reconcile these apparently conflicting conceptual models, as I demonstrate below.

But before getting to that, let’s review Bodie’s and Siegel’s positions.

In 1995, Bodie published a paper in *The Financial Analyst’s Journal* in which he challenged the idea that stocks become less risky for investors over a long time horizon. His alternative approach, which he also describes in a book called *Worry Free Investing*, is to place the core of retirement savings in inflation-protected bonds (TIPS), with very modest exposure to equities. Bodie’s argument is that a portfolio of equities does not, in fact, become less risky the longer you hold it. While stocks have beaten bonds on average over history, there are multi-decadal periods in which bonds have beaten equities (see here). Bodie received renewed attention for his proposal after the massive stock market decline in 2008.

Bodie has debated the logic of ‘stocks for the long run’ with Siegel for years. Siegel’s thesis is that stocks thrash bonds over long periods of time so soundly that investors need substantial exposure to equities in order to accumulate meaningful wealth. Siegel puts heavy emphasis on the fact that stocks have beaten bonds by more than 3% per year, on average, from 1871 through 2008. A range of analysis suggests that equities will out-perform bonds, on average, in the future as well. Even given that that the historical period upon which he draws has provided equity investors with returns that are too high to be used on a forward-looking basis, Siegel has repeatedly projected that stocks will out-perform bonds by 3% per year over future decades. Siegel believes that the most recent years’ poor relative performance in equities is an extremely rare historical anomaly and that investors need to maintain substantial buy-and-hold exposure to equities.

Bodie counters that an equity focus is just too risky and is a poor way to hedge against future income needs of individuals. Instead, he says inflation-indexed bonds are a good proxy for individual investors’ future income needs, so the real question is the extent to which a mix of stocks and bonds can match that the future performance of TIPS.

**Checking the numbers**

The S&P500 has a substantially higher expected return than an aggregate bond index—about 4.5 percentage points of average excess annual return (see here). But stocks are also more volatile than the bond index. If we take reasonable forward-looking estimates of the risks and returns for a bond index (AGG) and the S&P500 (SPY), we can easily estimate the probability that stocks will cumulatively beat bonds over a specific holding period.

More importantly, however, we need to look at the probability that equities will under-perform TIPS (TIP). To assess that probability, we need to account for the correlations among TIPS, nominal bonds (AGG), and equities (represented here by the S&P500). A Monte Carlo Simulation – which generates forward-looking estimates of risk and return for the various asset classes – can do just that.

This is important because historical returns from the market are not necessarily a reasonable basis for the future. It is likely that the equity risk premium will be smaller and that correlations between asset classes will be higher than in the past. I used the Quantext Portfolio Planner (QPP) to generate these projections. To underscore the value of such comparisons, I have generated Monte Carlo simulations using data available only through May 2008. This will allow us to consider the forward-looking projections vs. what actually happened in 2008-2009.

The chart below shows the cumulative probability that equities (the S&P500, SPY) will under-perform or out-perform TIPS and nominal bonds (AGG) by a certain amount. This is a generalized long-term probability, and does not include tactical considerations of current value. In other words, we are showing a general illustration of the equity risk premium, but from a probabilistic perspective. This type of chart takes a little explaining. The horizontal axis shows the percentile of the outcome and the vertical axis shows the cumulative return of the S&P500 vs. bonds. One curve shows the S&P500’s performance against TIPS and the other shows the S&P500 against the AGG. The model estimates that the S&P500 has a 5% chance of returns 30% less than TIPS over a one-year time horizon. The model also estimates that the S&P500 has a 5% chance of returns 22% less than AGG in a single year. These results are not too surprising. We all know that in a single year, there are significant odds that equities will greatly under-perform bonds.