A Comparison of Risk-Premium Forecasts implied by Parametric versus Nonparametric Conditional Mean Estimators

This paper computes parametric estimates of a time-varying risk premium model and compares the one-step-ahead forecasts implied by that model with those given by a nonparametric kernel estimator of the conditional mean function. The conditioning information used for the nonparametric analysis is that implied by the theoretical model of time-varying risk. Thus, the kernel estimator is used, in conjunction with a nonparametric diagnostic test for in-sample residual nonlinear structure, to assess the adequacy of the parametric model in capturing any structure in the excess returns. Our results support the parametric specification of an asset pricing model in which the conditional beta is the ratio of the relevant components of the conditional covariance matrix of returns modeled as a bivariate generalized ARCH process. Although the predictable component of the conditional moments is relatively small, the parametric estimator of the risk premia has somewhat more out-of-sample forecasting ability than does the kernel estimator. Hence, the superior in-sample performance of the latter may be attributed to overfitting.