Evaluating asset pricing models using the second Hansen-Jagannathan distance

We develop a specification test and a sequence of model selection procedures for non-nested, overlapping, and nested models based on the second Hansen-Jagannathan distance, which requires a good asset pricing model to not only have small pricing errors but also be arbitrage free. Our methods have reasonably good finite sample performances and are more powerful than existing ones in detecting misspecified models with small pricing errors but are not arbitrage-free and in differentiating models that have similar pricing errors of a given set of test assets. Using the Fama and French size and book-to-market portfolios, we reach dramatically different conclusions on model performances based on our approach and existing methods.