Volatility of the Stochastic Discount Factor, and the Distinction between Risk-Neutral and Objective Probability Measures

Abstract

This paper derives a measure that characterizes the distance between the risk-neutral and the objective probability measures for any candidate asset pricing model. We formally show that the distance metric is equal to the volatility of the stochastic discount factor. This theoretical result gives an alternative interpretation to the Hansen-Jagannathan bounds: they provide a lower bound for the distance between the objective and the risk-neutral probability measures. Our empirical application provides support for the notion that the crash of 1987 has widened the wedge between the risk-neutral and the objective probability measures.