Assessing Asset Pricing Model Misspecification with a Returns Decomposition

Abstract

Asset returns implicitly contain information about the systematic and nonsystematic risks in an economy. Based solely on the law of one price condition, we extract this information by using a mean-variance frontier decomposition of returns, and exploit it to improve the assessment of specification errors of stochastic discount factor models. Our empirical results document a large and significant mispricing of both the systematic and nonsystematic risks in industry returns, even for models not rejected by a test of over-identifying restrictions. Furthermore, models with smaller pricing errors on the pervasive portion of returns generally obtain larger pricing errors on the idiosyncratic portion of returns. We explain why this tradeoff is likely to occur and how it affects the evaluation of asset pricing models.