Equity Risk Premium Forum: Term Structure, Mean Reversion, and CAPE Reconsidered
For more insights on the equity risk premium from Rob Arnott, Cliff Asness, Mary Ida Compton, Elroy Dimson, William N. Goetzmann, Roger G. Ibbotson, Antti Ilmanen, Martin Leibowitz, Rajnish Mehra, Thomas Philips, and Jeremy Siegel, check out Revisiting the Equity Risk Premium, from CFA Institute Research Foundation. “I see evidence of mean reversion over time horizons from 3 years up to 15 years. It’s similar to business cycles having turned from 4-year cycles into 10-year cycles. We have many questions on structural changes. The evidence is really fuzzy, and usable or actionable evidence is almost zilch because of all this horizon uncertainty.” — Antti Ilmanen Does the equity risk premium (ERP) vary depending on the term structure? Does reversion to the mean dictate that it will decrease the longer the time horizon? In the third installment of the Equity Risk Premium Forum discussion, Laurence B. Siegel and fellow participants Rob Arnott, Elroy Dimson, William N. Goetzmann, Roger G. Ibbotson, Antti Ilmanen, Martin Leibowitz, Rajnish Mehra, and Jeremy Siegel explore these questions as well as the effect of noise on the value premium, whether the CAPE works internationally, and how to test a stock–bond switching strategy, among other topics. Below is a lightly edited transcript of this portion of their conversation. Martin Leibowitz: We’ve been talking about “the” risk premium. Will Goetzmann pointed out, though, that over the course of time, the risk premium has declined, depending on whether you invest for 40 years or 400. The idea of the risk premium being a term structure is very important. Because what premium you would demand if you’re investing for 1 year will be different from when you’re investing for 5 years or, say, 100 years. We would expect that to be a declining curve. That’s very important, because investors can choose their time horizon, just as they can in bonds. Over a long time horizon, the risk that is relevant for them may be much less. Rajnish Mehra: No, Marty, that is not correct. You’re assuming mean reversion. If you have an IID [independent and identically distributed] process, then horizon shouldn’t matter. The result that Will got is precisely because there is a mean-reverting component in the dividend structure. If you have mean reversion, Marty, you are 100% correct. Risky assets will look less risky over time. But if the returns are IID draws, then the time horizon wouldn’t make a difference. Jeremy Siegel: That is true, but I’m making one correction. You have to have a degree of risk aversion over 1 for that. You need two conditions for getting a higher equity allocation for longer time periods: mean reversion and risk aversion greater than 1. Rob Arnott: Mean reversion has been a lively topic. It is weak on a short-term basis, which is one reason the CAPE is such a lousy predictor of one-year returns. But on longer horizons, it’s pretty good. Jeremy, you’ve written about this, where 30-year S&P volatility, when annualized, is distinctly lower than the volatility of 1-year returns. This comes from the fact that there is mean reversion over long horizons. For example, 10-year real returns for US stocks have a –38% serial correlation with subsequent 10-year earnings; and 10-year real earnings growth has a –57% correlation with subsequent 10-year earnings growth. That means there is mean reversion. But it acts over a long enough horizon that most people think that returns are IID. William N. Goetzmann: I just have to put in a word here. I spent the first 10 years of my early research career on the weakness of the mean reversion evidence. But then the 2013 Nobel Prize award cited Bob Shiller’s work demonstrating the predictability of stock returns. The evidence is always a bit marginal and depends on your assumptions and on where you get the data. And, as Amit Goyal and Ivo Welch have shown, sometimes it sort of falls in the statistically significant zone, and sometimes it kind of falls out of it. It depends on when you’re doing your measurement. So, it’s a bit of a chimera to say that we know for sure. I’m not entirely convinced that you would bet your wealth on this reversion process. Antti Ilmanen: When I look at the literature, I see evidence of mean reversion over time horizons from 3 years up to 15 years. It’s similar to business cycles having turned from 4-year cycles into 10-year cycles. We have many questions on structural changes. The evidence is really fuzzy, and usable or actionable evidence is almost zilch because of all this horizon uncertainty. By the way, I wanted to comment earlier on mean reversion in a different context, not about the premium but about the riskiness of stocks being related to the time horizon. There is a counterargument by Lubos Pastor and Robert F. Stambaugh that equity risk doesn’t decline with horizon. When you take into account parameter uncertainty — the fact that we don’t know how big the equity premium is — their analysis suggests that risk in equities doesn’t decline with the time horizon and, if anything, rises with it. Visualizing Returns over Time: Trumpets and Tulips Roger Ibbotson: Even if returns were IID, what you would get, of course, is a lognormal spreading out of wealth outcomes over time — times the square root of time. And the compounded return is divided by the square root of time. So, you get two entirely different shapes, depending on whether we’re talking about the compound return or just your ending wealth. Over time, ending wealth spreads out, in the shape of a tulip. The compound annual return, in contrast, is averaging out and looks more like a trumpet. The tulips and trumpets apply only if returns are IID. If there’s some other sort of return pattern, then the shapes will be different. Coping with Parameter Uncertainty J. Siegel: Antti, I want to return to what you said about Pastor and Stambaugh. Parameter uncertainty also applies to bond returns — you don’t know what the parameters are for the real rcapeisk-free
Equity Risk Premium Forum: Term Structure, Mean Reversion, and CAPE Reconsidered Read More »











