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EQUITY RISK PREMIUM: EXPECTATIONS GREAT AND SMALL
North American Actuarial Journal, Jan 2004 by Derrig, Richard A, Orr, Elisha D
ABSTRACT
The equity risk premium (ERP) is an essential building block of the market value of risk. In theory, the collective action of all investors results in an equilibrium expectation for the return on the market portfolio excess of the risk-free return, the ERP. The ability of the valuation actuary to choose a sensible value for the ERP, whether as a required input to capital asset pricing model valuation, or any of its descendants, is as important as choosing risk-free rates and risk relatives (betas) to the ERP for the asset at hand.
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The historical realized ERP for the stock market appears to be at odds with pricing theory parameters for risk aversion. Since 1985, there has been a constant stream of research, each of which reviews theories of estimating market returns, examines historical data periods, or both. Those ERP value estimates vary widely from about -1% to about 9%, based on a geometric or arithmetic averaging, short or long horizons, short- or long-run expectations, unconditional or conditional distributions, domestic or international data, data periods, and real or nominal returns.
This paper examines the principal strains of the recent research on the ERP and catalogues the empirical values of the ERP implied by that research. In addition, the paper supplies several time series analyses of the standard Ibbotson Associates 1926-2002 ERP data using short Treasuries for the risk-free rate. Recommendations for ERP values to use in common actuarial valuation problems also are offered.
"What I actually think is that our prey, called the equity risk premium, is extremely elusive."
-Stephen A. Ross (2002, p. 22)
1. INTRODUCTION
The equity risk premium (ERP) is an essential building block of the market value of risk. In theory, the collective action of all investors results in an equilibrium expectation for the return on the market portfolio excess of the risk-free return, the ERP. The ability of the valuation actuary to choose a sensible value for the ERP-whether as a required input to capital asset pricing model (GAPM) valuation or any of its descendants'-is as important as choosing risk-free rates and risk relatives (betas) to the ERP for the asset at hand. Risky discount rates, asset allocation models, and project costs of capital are common actuarial uses of ERP as a benchmark rate.
The ERP should be of particular interest to actuaries. For pensions and annuities backed by bonds and stocks, the actuary needs to have an understanding of the ERP and its variability compared to fixed-horizon bonds. Variable products, including guaranteed minimum death benefits, require accurate projections of returns to ensure adequate future assets. With the latest research producing a relatively low ERP, the rationale for including equities in insurers' asset holdings is being tested.
In describing individual investment account guarantees, EaChance and Mitchell (2003) point out an underlying assumption of pension asset investing that, based only on the historical record, future equity returns will continue to outperform bonds; they clarify that those higher expected equity returns come with the additional higher risk of equity returns. Ralfe et al. (2003) support the risky equity view and discuss their pension experience with an all-bond portfolio. Recent projections in some literature of a zero or negative KRP challenge the assumptions underlying these views.
By reviewing some of the most recent and relevant work on the issue of the ERP, actuaries will have a better understanding of how these values were estimated, critical assumptions that allowed for such a low RRP, and the time period for the projection (see Appendix M). Actuaries can then make informed decisions for expected investment results going forward.
In 1985, Mehra and Prescott published their work on the eqttiiy rtsb premium puzzle the fact that the historical realized ERP for the stock market from 1889-1978 appeared to be at odds with and, relative to Treasury bills, far in excess of asset pricing theory values based on investors with reasonable risk aversion parameters. Since then, there has been a constant stream of research, each of which reviews theories of estimating market returns, examines historical data periods, or both (for example, see Gochrane 1997, Cornell 1999, or Equity Risk Premium Forum 2002). Those ERP value estimates vary widely, from about - 1% to about 9%, based on geometric or arithmetic averaging, short or long horizons, short-or long-run means, unconditional or conditional expectations, using domestic or international data, differing data periods, and real or nominal returns, Brealey and Myers (2000), in the sixth edition of their standard corporate finance textbook, believe a range of 6-8.5% for the U.S. ERP is reasonable for practical project valuation. Is that a fair estimate?
Current research on the RRP is plentiful. This paper covers a selection of mainstream articles and books that describe different approaches to estimating the ex ante RRP. We select examples of the research that cover the most important approaches to the ERP. We begin by describing the methodology of using historical returns to predict future estimates. We identify the many varieties of ERPs in order to alert the reader to the fact that numerical estimates of the ERP that appear different may instead be about the same under a common definition. We examine the well-known lbbotson Associates 1926-2002 data series for stationaty, that is, time invariance of the mean ERP. We show by several statistical tests that stationarity cannot he rejected and the best estimate going forward, ceteris paribus, is the realized mean. This paper will examine the principal strains of the recent research on the BRP and catalogue the empirical values of the ERP implied by that research (see Appendix B).
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