An Information - Theoretic Approach to Estimating Risk Premia

Abstract

This paper shows that factor risk premia can be consistently estimated using a semi-parametric estimate of the stochastic discount factor without requiring a correctly specified linear factor model. We use a minimum discrepancy objective function to construct a stochastic discount factor from asset returns using only the economic assumption of no arbitrage. The stochastic discount factor and factor risk-premia are estimated using only data on portfolio returns and factor realizations: The same data used when evaluating linear models. The econometrics are applications of standard extremum estimator arguments and the Delta Method, making inference simple. In simulations, the estimated risk-premia have low root mean squared errors and are comparable to classic two-pass estimates even when the model is correctly specified. Empirical estimates of popular traded factors are close to their mean excess returns. For non-traded factors, we find that intermediary leverage and consumption growth carry risk-premia, while employment growth does not. A final application shows that the estimated risk-premia can be used as an extra moment condition to discipline the creation of factor mimicking portfolios.