Hansen-Jagannathan distance with many assets
This paper proposes methods to estimate and compare asset pricing models in settings with a large number of test assets. Models are specified through a linear stochastic discount factor (SDF). We propose two regularization schemes to extend the Hansen-Jagannathan distance to high-dimensional environments. In addition to stabilizing the inversion of the covariance matrix, the proposed regularizations admit an economic interpretation as relaxing the exact pricing restrictions, thereby accommodating market frictions. We derive the asymptotic properties of the SDF parameter estimator under a double asymptotic framework in which both the cross-sectional and time dimensions grow. These results allow for inference on whether individual factors are priced. We further develop tests for comparing competing asset pricing models under misspeci cation, providing a formal procedure to identify the least misspecified model. The analysis covers both nested and non-nested specifications. An empirical application compares 4 models using a dataset of 647 test portfolios.