Properties of Portfolio-Based Estimates of Market Risk Premia

Abstract

We use simulation to assess the performance of conventional financial econometric methods in recovering accurate estimates of market risk premia. In this study, we focus particular attention on the properties of standard cross-sectional risk premium estimation methods using portfolios and make several contributions. First, we confirm a general finding reported elsewhere that standard cross-sectional regression methods can produce accurate point estimates of market risk premia under ideal conditions, but they typically have very large standard errors. Our simulations show that existing standard error adjustments generally have limited practical importance. We propose a bootstrap approach and show that it can produce suitable standard errors. Second, when the market index is misspecified, we demonstrate that the biases in market risk premium estimates can be huge, even when the market proxy is highly correlated with the true market portfolio. We show that the pure cross-sectional method, in which in-sample mean excess returns are regressed against in-sample portfolio betas, is generally superior to the Fama-MacBeth method in estimating market risk premia with the least bias. We also demonstrate that the optimal number of portfolios to use in cross-sectional regressions depends critically on the estimation method, the accuracy of the market proxy, and whether the aim is to compute the best point estimate of the market risk premium or the standard error of the estimate. Finally, as an alternative to the cross-sectional method, we find that the mean of an excess index return provides a more efficient estimate of the market risk premium compared with a cross-sectional estimate, but only when the market index employed for both closely approximates the true market portfolio.