The “Best” Equity Risk Premium

What are the different ways of estimating the equity risk premium, and which one is the best? In the February 2010 update of his paper entitled “Equity Risk Premiums (ERP): Determinants, Estimation and Implications – A Post-crisis Update”, Aswath Damodaran offers a comprehensive overview of equity risk premium estimation and application. Using data from multiple countries (but focusing on the U.S.) over long periods, he concludes that:

• Determinants of the equity risk premium are: investor aversion to risk; macroeconomic risk; quantity and quality of investment information; investment liquidity; risk of catastrophe; and, investor irrationality.
• There are three general approaches to estimating the equity risk premium: (1) surveys of investors or experts (corporate managers and academics); (2) inference from historical return data; and, (3) implication from equity valuation calculations or behaviors of other asset classes.
• Survey-based estimates of the equity risk premium vary by type of individual polled:
  • Investor estimates tend to reflect the recent past rather than forecast the future and to vary by investor group and framing of the question.
  • Corporate managers estimates are somewhat lower than investor estimates.
  • Academic estimates indicate how much (high) historical risk premiums frame the thinking of academics.
• Historical premium estimates are backward looking and vary considerably with stock market movement (see the first table below) depending on:
  • Time period used for estimation.
  • Choice of risk-free rate and market index.
  • Method of averaging returns over time (arithmetic or geometric).
• Examples of implied equity risk premiums (moving down and up opposite the market) are those derived from:
  • Discounted cash flow (asset valuation) calculations.
  • Default spread for corporate bonds.
  • Options pricing (implied volatility).
• Extreme market moves result in large changes in all three kinds of equity risk premium estimates.
• In general, implied equity risk premiums based on asset valuation models have the greatest predictive power (see the second table below).

The following table, taken from the paper, compares historical equity risk premiums for the U.S. based on the mean return for stocks minus the mean returns for both 6-month Treasury bills (T.bills) and 10-year Treasury notes (T.bonds) over three sample periods using both arithmetic and geometric means. Across these choices, the historical equity risk premium varies from +7.53% to -7.22%. The single year 2008 has a substantial (downward) impact on results even for the longest sample period.

The next table, also from the paper, compares in two ways the predictive power of four estimates of the equity risk premium based on data for 1960-2009:

• The valuation-based implied equity risk premium at the end of the prior year.
• The average valuation-based implied equity risk premium over the previous five years.
• The historical equity risk premium through the end of the prior year.
• The premium implied by the Baa bond default spread.

Over the entire sample period, the implied equity risk premium at the end of the prior period is the best predictor of the implied equity risk premium in the next period, while the historical risk premium is the worst. The current implied equity risk premium is also the best predictor of the actual return premium of stocks over bonds for the next 10 years, and the historical risk premium is again the worst.

In summary, formal asset valuation models (extrapolations of historical return data) provide the most (least) predictive estimates of the future equity risk premium.

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