Does the Ross Recovery Theorem Work Empirically?

Abstract

Starting with the fundamental relationship that state prices are the product of physical probabilities and the stochastic discount factor, Ross (2015) shows that, given strong assumptions, knowing state prices suffices for backing out physical probabilities and the stochastic discount factor at the same time. We find that such recovered physical distributions based on the S&P 500 index are incompatible with future realized returns and fail to predict realized returns and variances. These negative results remain even when we add economically reasonable constraints. Simple benchmark methods based on a power utility agent or on the historical return distribution cannot be rejected.

Keywords: Ross recovery, stochastic discount factor, risk-neutral density, transition state prices, physical probabilities