Comparing Asset Pricing Models by the Conditional Hansen-Jagannathan Distance

We compare non-nested parametric specifications of the Stochastic Discount Factor (SDF) in terms of their conditional Hansen-Jagannathan (HJ-) distance. This distance is defined as the discrepancy between a parametric SDF family identifying an asset pricing model and the set of admissible SDF's satisfying the conditional no-arbitrage restrictions for a set of traded assets. The conditional HJ-distance accounts for the models' ability to match the dynamic pricing restrictions for any set of managed portfolios, and not just a set of static restrictions for a specific choice of instruments like the often employed (unconditional) HJ-distance. We estimate the conditional HJ-distance by a kernel-based Generalized Method of Moments estimator and establish its large sample properties for model selection purposes. We demonstrate empirically the usefulness of our approach by comparing several SDF models including preference-based specifications, beta-pricing models and recently proposed SDF models that are conditionally linear in the priced risk factors