EQUITY RISK PREMIUM: EXPECTATIONS GREAT AND SMALL

North American Actuarial Journal,  Jan 2004  by Derrig, Richard A,  Orr, Elisha D

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It is dangerous for actuaries to engage in simplistic analyses of historical ERPs to generate ex ante forecasts that differ from the realized mean.27 The research we have catalogued in Appendix B, the common level ERPs estimated in Appendix G, and the building-block (historical) approach of Ibbotson and Ghen (2003) in Appendix D all discuss important concepts related to both ex post and es ante ERPs and cannot be ignored in reaching an informed estimate.

For example, Wcndt (2002) concluded that a linear relationship with interest rates is a better predictor of future returns than is a "constant" ERP based on the average historical return. he arrived at this conclusion by estimating a regression equation relating long bond yields with 15-year geometric mann mnrkct returns starting monthly in 1960.28 Wendt's findings arc misleading. First, there was no significant relationship between short-, intermediate-, or long-term income returns over 1926-2002 (or 1960-2002) and annual ERPs, as evidenced by simple regressions using Ibbotson data.29 second, if the linear structural equation indeed held, there would be no need for an ERP since the (15-year) return could be predicted within small error bars. Third, there is always a negative bias introduced when geometric averages arc used as dependent variables (Krennan and Schwartz 1985). Finally, the results are likely to be spurious clue to the high autocorrelations of the target and independent variables; an autocorrelation correction would eliminate any significant relationship of long yields to the ERP.

Actuaries also should be aware of the variability of both the ERP and risk-free rate estimates discussed in this paper (sec Tables 4 and 9). All too often, return estimates are made without noting the error bars, and that can lead to unexpected "surprises." As one example, recent research by Longstaff (2004) proposes that a 1991-2001 "flight to quality" has created a valuation premium (and lowered yields) in the entire yield curve of Treasuries. He finds a 10-16 basis point liquidity premium throughout the zero coupon Treasury yield curve. he translates that into a 10-15% pricing difference at the long end. This would imply a simple CAPM market estimate for the long horizon might be biased low.

Finally, actuaries should know that the research catalogued in Appendix B is not definitive. No simple model of ERP estimation has been universally accepted. Undoubtedly, there will be still more empirical and theoretical research into this data-rich financial topic. We await the potential advances in understanding the return process that the behavioral view may uncover.

18. PosT SCRIPT: APPENDICES A-D

We provide four appendices that catalogue the ERP approaches and estimates discussed in the paper. Actuaries, in particular, should rind the numerical values, and descriptions of assumptions underlying those values helpful for valuation work that adjusts for risk. Appendix A provides the annual data from 1926 through 2002 from Ibbotson Associates referred to throughout this paper. The equity risk premium shown is a simple difference of the arithmetic stock returns and the arithmetic U.S. Treasury bill total returns.