An information-theoretic approach to estimating risk premia

Abstract

Evaluation of linear factor models in asset pricing requires estimation of two unknown quantities: the factor loadings and the factor risk premia. Using relative entropy minimization, this paper estimates factor risk premia with only no-arbitrage economic assumptions and without needing to estimate the factor loadings. The method proposed here is particularly useful when the factor model suffers from omitted variable bias, rendering classic Fama-MacBeth/GMM estimation infeasible. Asymptotics are derived and simulation exercises show that the accuracy of the method is comparable to, and frequently is higher than, leading techniques, even those designed explicitly to deal with omitted variables. Empirically, we find estimates of risk premia that are closer to those expected by financial economic theory, relative to estimates from classical estimation techniques. For example, we find that the risk premia on size, book-to-market, and momentum sorted portfolios are very close to the observed average excess returns of these portfolios. An exciting application of our methodology is to performance evaluation for active fund managers. We show that we are able to estimate a manager's "alpha" without specifying the manager's factor exposures.