Efficient Factor Identification

Abstract

Of the hundreds of published asset pricing anomalies, few have been properly tested to determine if they are admissible as true risk factors. Anomalies need not be risk factors, but they are often deployed in subsequent empirical tests as if they are. I leverage the equivalence between the linear factor (beta) model and the stochastic discount factor frameworks to show that the usual (Fama-MacBeth) statistical tests do not correspond to the null hypothesis of interest. These tests demonstrate only that the candidate risk factor is a viable trading strategy, in that it possesses a positive risk-adjusted return. I show that it is neither necessary nor sufficient for a risk factor to be a trading strategy, however. The sufficient statistic for whether a set of candidates are true risk factors is the multivariate analog of the Sharpe ratio, which accounts for the covariance structure of the factors. I present an MCMC procedure that efficiently estimates the multivariate Sharpe ratio and provides valid finite-sample inference.