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Must ERP Forecasts Be Positive?

| | Posted in: Equity Premium

Should equity risk premium (ERP) forecasters assume in their models, because stocks always carry risk, that the premium cannot be negative? In their January 2016 paper entitled “Forecasting the Equity Risk Premium: The Ups and the Downs”, Nick Baltas and Dimitris Karyampas examine recent ERP forecasting research, with focus on simple models constrained to positive values. Their baseline model is a linear regression model that forecasts next-period S&P 500 Index excess return from either the index dividend-price ratio or the 3-month US treasury bill yield. They highlight advantages and disadvantages of models that do and do not constrain ERP to non-negative values for three types of market regimes: (1) up markets (positive actual ERP) versus down markets (negative actual ERP); (2) recessions versus expansions; and, (3) low volatility versus high volatility. Using monthly total returns for the S&P 500 Index and monthly levels of the predictive variables during January 1927 through December 2013 (with initial training period 20 years), they find that:

  • Over the entire sample period the average actual annualized ERP is 5.9%, with volatility 19.2%, Sharpe ratio 0.31 and skewness -0.42.
  • Regime frequencies during the January 1947 through December 2013 out-of-sample test period are:
    • 476 months (59%) positive and 328 months (41%) negative actual ERP.
    • Based on NBER determinations, 682 months (85%) of economic expansion and 122 months (14%) of recession.
    • Arbitrarily, 268 months (33%) each of low, medium and high-volatility.
  • Over the entire out-of-sample test period, models that constrain ERP forecasts to non-negative values outperform the unconstrained model.
  • However, during down markets, recessions and high-volatility regimes, constrained models are less accurate than the unconstrained model. Put differently, the constrained models do worse when it matters the most (generating substantial losses).
  • For a mean-variance investor who allocates dynamically between the stock market and a risk-free asset over the entire out-of-sample period, the stricter the shorting and leverage constraints and the more risk-averse the investor, the smaller the advantage of the constrained models.
  • Results are similar for other ERP forecasting variables.

In summary, evidence indicates that use of ERP forecast models constrained to non-negative values may worsen maximum drawdown during unfavorable market conditions compared to unconstrained models.

Cautions regarding findings include:

  • Many investors do not use mean-variance optimization to drive portfolio allocations.
  • Analyses assume that portfolio rebalancing frictions and costs of shorting are zero. Including realistic costs may affect findings.
  • Analyses assume that leverage is available at the risk-free rate. Many investors are unable to borrow so cheaply.
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