Evaluating Asset Pricing Models Using the Second Hansen-Jagannathan Distance

Abstract

We develop a systematic approach for evaluating asset pricing models based on the second Hansen-Jagannathan distance (HJD), which requires a good asset pricing model to not only have small pricing errors but also be arbitrage free. Our approach includes a specification test and a sequence of model selection procedures for non-nested, overlapping, and nested models. While the former can test whether a given model is correctly specified, the latter can compare relative performances of potentially misspecified models. Our methods are more powerful than existing ones in (i) detecting misspecified models that have small pricing errors but are not arbitrage free; and (ii) differentiating models that have similar pricing errors of a given set of test assets. Simulation studies show that our tests have reasonably good finite sample performances for typical sample sizes considered in the literature. Using the Fama-French size and book-to-market portfolios or hedge fund portfolios that exhibit option-like returns, we reach dramatically different conclusions on model performances based on our approach and existing methods.

Keywords: Stochastic Discount Factor, Specification Tests, Model Selection, HJ distance, Arbitrage

JEL Classification: C4, C5, G1