On the Hansen-Jagannathan Distance with a No-Arbitrage Constraint

We provide an in-depth analysis of the theoretical properties of the Hansen-Jagannathan (HJ) distance that incorporates a no-arbitrage constraint. Under a multivariate elliptical distribution assumption, we present explicit expressions for the HJ-distance with a no-arbitrage constraint, the associated Lagrange multipliers, and the SDF parameters in the case of linear SDFs. This allows us to analyze the benefits and costs of using the HJ-distance with a no-arbitrage constraint to rank models. Finally, we demonstrate the practical relevance of our theoretical findings in an empirical illustration of some popular asset pricing models