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Predicting the Equity Risk Premium

| | Posted in: Equity Premium

Does a simple model based on the gap between the stock market earnings yield and an inflation-adjusted Treasury yield usefully predict the equity risk premium (ERP)? In their June 2012 paper entitled “Equities (Still) for the Long Run: A New Look at the Future Equity Premium”, Michael Crook and Brian Nick construct and test a model that compares an estimate of the future stock market earnings yield to real bond return expectations. They use the S&P 500 as a proxy for the stock market. They estimate the future stock market earnings yield as the inverse of Shiller’s cyclically adjust price-earnings ratio (P/E10). They use nominal Treasury yields with duration matched to forecast horizon and adjust this yield with inflation expectations from the Federal Reserve Bank of Cleveland. They apply simple inception-to-date linear regression to relate forecasted ERP to actual ERP. Using monthly S&P 500 Index total returns, Shiller’s P/E10 data, Treasury yields (10-year, 5-year and 2-year notes and bills) and the Cleveland Federal Reserve’s Index of Inflation (limiting the start of the sample period) during 1982 through April 2012, they find that:

  • Based on conventional statistical methods (R-squared statistics):
    • Relative to Treasury notes of matched duration, the model explains 10%/20%/40% of the future variability of 2-year/5-year/10-year annualized ERP.
    • Relative to Treasury bills, the model explains 30%/40%/70% of the future variability of 2-year/5-year/10-year annualized ERP.
  • ERP compression over the last decade is probably not a long-term structural change.
  • Stocks are presently cheap relative to Treasuries. Current ERP levels imply that stocks will outperform bonds by an annualized 6.7%, 6.4% and 5.8% over the next two, five and 10 years, respectively. A buy-and-hold equities strategy will likely be successful over the next decade.

In summary, evidence suggests that U.S. stocks are now priced attractively.

Cautions regarding findings include:

  • A multi-year annualized ERP forecast, which ignores intra-interval volatility, offers little support for tactical trading.
  • The sample period is short in terms of independent 10-year measurement intervals for P/E10 and multi-year annualized returns (only about three intervals for the former). The very large overlap in measurement intervals for monthly calculations may substantially inflate conventional correlations (and therefore R-squared statistics), thereby undermining hypothesis testing. This defect is worse for longer forecast horizons (greater measurement interval overlaps).
  • Use of indexes, which do not account for the costs of creating and maintaining tradable assets (trading frictions and management fees) may overstate achievable returns.
  • Testing multiple proxies (different Treasury instruments) for the risk-free rate on the same set of data introduces data snooping bias, such that the best proxy incorporates some luck.
  • It is arguable that an increase in the yield on each Treasury instrument, rather than a decrease in the stock market earnings yield, will close the gap between them.

For an alternative oriented toward tactical trading, see the Real Earnings Yield Model.

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