The fundamental theorem of asset pricing, one of the cornerstones of neoclassical finance, establishes the equivalence between the absence of arbitrage and the existence of a positive stochastic discount factor (hereafter SDF) that correctly prices all assets. The main purpose of this paper is to develop asset pricing tests that fully reflect the implications of the fundamental theorem of as set pricing. Specifically, we develop a systematic approach for estimating, testing, and comparing asset pricing models based on the second Hansen Jagannathan distance (hereafter HJD).

The first and second HJDs developed by Hansen and Jagannathan (1997) measure specification errors of SDF models by least squares distances between an SDF model and the set of admissible SDFs that can correctly price a set of test assets. The first HJD considers the set of all admissible SDFs, which we denote as. The second HJD considers only the smaller set of strictly positive admissible SDFs, which we denote as. The positivity constraint of the second HJD guarantees the admissible SDFs to be arbitrage free and is important for pricing derivatives associated with the test assets. Hansen and Jagannathan (1997) show that while the first HJD represents the maximum pricing error of a portfolio of the test assets with a unit norm, the second HJD represents the minmax bound of the pricing errors of a portfolio of both the test assets and their related derivatives with a unit norm. Obviously, the second HJD represents a more stringent criterion for evaluating asset pricing models and is generally larger than the first HJD.