Most Popular ArticlesJeremy Siegel v. Zvi Bodie
July 21, 2009
Now comes the key point: the 5th percentile under-performance of equities relative to bonds (both TIPS and nominal bonds) is far greater after ten years than after one year! This belies the notion that stocks become less risky the longer you hold them—and this is precisely the point Bodie was making in his 1995 paper. If our liabilities are indeed well-matched by TIPS, these data show that the risk that equities will fall significantly short of meeting our liabilities doesn’t decrease with time, it increases!
A different way to explain this point is provided in the following excerpt from Bodie’s original paper:
The basis for the proposition that stocks are less risky in the long run appears to be the observation that the longer the time horizon, the smaller the probability of a shortfall. If the ex ante mean rate of return on stocks exceeds the risk-free rate of interest, it is indeed true that the probability of a shortfall declines with the length of the investment time horizon. For example, suppose the rate of return on stocks is lognormally distributed with a risk premium of 8% per year and an annualized standard deviation of 20%. With a time horizon of only 1 year, the probability of a shortfall is 34%, whereas at 20 years that probability is only 4%. But as has been shown in the literature, the probability of a shortfall is a flawed measure of risk because it completely ignores how large the potential shortfall might be. [emphasis added]
The two charts above from our Monte Carlo Simulation show this effect quite clearly. After one year, there is a 47% chance than TIPS will out-perform the S&P500 (this is the percentile at which the SPY-TIPS curve crosses 0% return). After ten years, there is only a 37.6% chance that TIPS will out-perform SPY. The probability of stocks under-performing bonds (including TIPS) diminishes in time. On the other hand, the severity of the potential shortfalls increases with time horizon as we have discussed: the 5th percentile after ten years is much worse for an equity investor than the 5th percentile after one year.
What this means for you
So where does this leave an investor trying to save for retirement? First, there is solid evidence to support the notion that stocks can be expected to out-perform bonds at the levels used in this discussion—and that is not a small factor. If stocks out-perform bonds by 4.5% per year, investors will be well-served by equities on average. The problem that most people do not understand is that this higher return comes with risk and that they are not likely to receive the ‘average’ – they will realize only one of many possible future outcomes. Any given generation of investors may end up with the best 1-in-50 outcome or the worst 1-in-50 outcome, or any of the possible outcomes in between.
The simulations described above show that the risk in equities is high enough that any investor has some probability of needing his or her money on a time horizon such that he or she may end up having been better off in bonds over even very long time horizons. This is related to the outcome in game theory known as ‘gambler’s ruin.’ Even when the odds may be on your side, you can still end up having to leave the game before you get ahead. After the bruising markets of 2008-2009, this is painfully obvious, and my analysis demonstrates this point before the actual market declined (remember that our Monte Carlo Simulations from Quantext Portfolio Planner used data available only through May 2008).
There is a tendency to look at the downturn in 2008-2009 as a ‘black swan’ – an event beyond our capacity to anticipate – but the chart above suggests that, as we look at ten-year periods, such an event was not outside of the realm of possibility using straightforward statistical models.
Equities provide the opportunity for reaping returns higher than we can obtain from bonds, but certainly not a guarantee of higher returns – even over long periods of time – and the potential severity of under-performance increases with the time horizon rather than decreasing. The ultimate ‘safe asset’ (in terms of market risk) for investors saving for retirement is TIPS, but these provide only a modest opportunity of building wealth beyond simply maintaining purchasing power. Bodie and Siegel can look at the same statistics and disagree on the best strategy for investors — and the disagreement is legitimate and not trivial to reconcile.
How to balance the risks
The tradeoff between higher and lower allocations to bonds vs. riskier asset classes is between risk tolerance and expected returns — there is no mystery and, in fact, surprisingly little disagreement on the statistics of risk and return among the participants in this many-faceted dialog. The real disagreement concerns which are the most appropriate choices for an investor to make.
Moshe Milevsky, in his 2008 book on retirement planning, finds (Figure 8.4) that a 65-year-old has his or her highest long-term sustainable income stream from a portfolio that is 70% in equities. In an article in May 2008, I suggested that a portfolio with 50% in bonds was a reasonable choice if the portfolio was diversified to include REIT’s and commodities and also had most of its bond exposure via TIPS. That portfolio (let’s just call it the QPP 50/50 Portfolio) had 40% of its assets in TIPS, 10% in commodities, and 5% in REIT’s, all of which provide considerable inflation protection. I specifically noted that a portfolio that was 50% allocated to the S&P500 and 50% allocated to bonds would have a considerably lower probability of successfully supporting the same retirement income. Zvi Bodie has proposed that a portfolio that is 90% in TIPS is the right solution for retirement investing.
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