Factor Risk Premia and Variance Bounds

Abstract

We consider the implications for mean factor risk premia for the variance of admissible (normalized) stochastic discount factors, or pricing kernels. For given mean risk premia, we identify lower bounds on the variance of the pricing kernel which exceed the variance of the projection of the pricing kernel on the (augmented) asset return space: the “Hansen and Jagannathan” variance bound. These lower bounds increase with the covariability between the components of the pricing kernel and of the factors which are not explained by asset returns, and decrease with the distance between the factors and the (augmented) asset-return space. As an application, we show that the inflation risk premium generated by a consumption-based pricing kernel implies a standard deviation of the kernel which is up to 15% higher than the Hansen and Jagannathan bound.