Comparing Asset Pricing Models by the Conditional Hansen-Jagannathan Distance

We compare nonnested parametric specifications of the stochastic discount factor (SDF) using the conditional Hansen-Jagannathan (HJ-) distance. This distance measures the discrepancy between a parametric model-implied SDF and the admissible SDF's satisfying all the conditional (dynamic) no-arbitrage restrictions, instead of just few unconditional no-arbitrage restrictions for managed portfolios chosen through the instrument selection. We estimate the conditional HJ-distance by a generalized method of moments estimator and establish its large sample properties for model selection purposes. We compare empirically several SDF models including multifactor beta pricing specifications and some recently proposed SDF models that are conditionally linear in consumption growth.