Hansen-Jagannathan distance with many assets

This paper examines the evaluation of asset pricing models with many test assets. The models are specified through a linear stochastic discount factor (SDF). We implement two interpretable regularization schemes to extend the Hansen-Jagannathan distance in a framework of a data-rich environment. These regularizations are shown to yield a relaxation of the asset pricing equation and, therefore, take into account the global misspecified nature of models in finance. We derive the asymptotic properties of the SDF parameter estimator and implement comparison tests of asset pricing models when the models are potentially misspecified. We treat separately the nested or non nested models. All results are obtained under the double asymptotic where the number of assets and the number of time series increase to infinity. Simulations show that the regularization helps to control the size of the tests while maintaining a good power in small samples.