Assessing Misspecifications in Asset Pricing Models with Nonlinear Projections of Pricing Kernels

We develop a new approach to evaluate asset pricing models (APMs) based on Minimum Discrepancy (MD) projections that generalize the Hansen-Jagannathan (HJ, 1997) distance to account for an arbitrary number of moments of asset returns. The Minimum Discrepancy projections correct APMs to become admissible stochastic discount factors (SDF) through nonlinear functions of the basis assets returns, contrasting with the linear corrections from the HJ method. These nonlinear corrections make our method more effective than available methods in detecting sources of model specifications, specially in economies with nonlinear priced risk, or when the APMs being tested contain nonlinear functions of basis assets. We provide a geometric interpretation and also a theoretical example to illustrate our point. In the example, the CAPM is diagnosed in an economy where the true SDF prices coskewness risk with respect to the market portfolio (Kraus and Litzemberger (1976)). It is shown that while methods that use the HJ distance can not identify the correct source of misspecification of the CAPM in this economy (a quadratic term in the market return), there are nonlinear projections in the class of MD problems that correctly capture the misspecified term. Also, in order to explore the empirical structure of the MD projections, we provide a full example of estimation and diagnosis of the CCAPM model based on several discrepancy measures