"Equity Risk Premium: Expectations Great and Small," Richard A. Derrig and Elisha D. Orr, January 2004/AUTHORS' REPLY

North American Actuarial Journal,  Jan 2005  by Whelan, Shane F

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OTHER PATHS

The above considerations point to the conclusion that the path of the ERP in the United States forms a nonstationary series, casting doubt on many of the approaches used to forecast it that Derrig and Orr survey in their paper. Viewing the evolution of the ERP in the United States as just one realized path of a stochastic process as suggested in section 6, knowledge of the ERP can be augmented by considering other market histories. Consider, for instance, the Irish capital markets, which, though small, have a history of continuous trading as long as that of the U.S. markets.3 Especially relevant to this discussion is that the path of the ERP in the Irish market reinforces the above remarks on its nonstationarity, as illustrated in Figure 1. Inspection of the figure shows, without the need for formal statistical tests, that the series are obviously nonstationary. The variance of the returns in the latter half of the twentieth century is clearly significantly higher than that of the first half.

As noted by the authors, Dimson, Marsh, and Staunton (2002) provide the most complete synthesis to date of the twentieth-century experience of national capital markets, recording returns from the cash, bond, and equity markets in 16 countries that, in total, cover about 90% of the current world markets by capitalization. No doubt the path traced by the ERP in each of these markets will reinforce the above remarks. However, the domain of study perhaps can be cast even wider than just the paths traced by low-frequency returns of national markets over the long term. Investigations of the statistical properties of the return paths traced by equity markets have shown that many key properties are invariant with respect to a change in the timescale over which returns are measured (e.g., monthly returns exhibit the same patterns as daily or hourly returns), and markets as diverse as those for commodities, currencies, cash, bonds, and equities display remarkably similar properties. Gont (2001) provides an overview of key empirical regularities of the return paths of financial markets, pointing out, aside from their shared property of nonstationarity, that all returns over any timescale exhibit (a) a heavy-tailed distribution, where the variance exists but the kurtosis (fourth moment) does not, (b) a volatility that tends to cluster in time, and the decay from high bouts of volatility tends to follow a characteristic power law, (c) a negative correlation between the current return and future volatility, decaying to zero in a characteristic pattern as the time lag increases, (d) an asymmetry between large positive and negative movement, with the latter more frequent, and (e) a high correlation between volume traded and volatility. The invariance of these properties with respect to time scaling and between markets strongly suggests that the annual returns delivered by the U.S. markets over the long-term past are no different statistically from, say, hourly returns on the dollar-yen over the last few weeks. Modeling with the latter, however, reduces the problems associated with the paucity of data of the former. It is true that estimation of the ERP is based on the difference between two market returns (the risky and riskless), hut parallels can be drawn between the ERP and the minimum enticement for market players (in whatever market) to increase their mismatch risks.