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

We develop a new approach to identify model misspecifications based on Minimum Discrepancy (MD) projections that correct asset pricing models with the use of nonlinear functions of basis assets returns. These nonlinear corrections make our method more effective than the Hansen and Jagannathan distance in detecting sources of model specifications, especially in economies where nonlinear risk is priced. A theoretical example illustrates our point, with an economy where the true SDF prices coskewness risk with respect to the market portfolio (Kraus and Litzemberger (1976)). We suggest diagnosing the CAPM model under this economy, and show that while the HJ distance can not identify the exact source of model misspecification (a quadratic term in the market return), there are nonlinear projections in the class of MD problems that correctly capture this term. We also derive the asymptotic distributions of the estimators for the Cressie Read family of discrepancies, and illustrate their use with an empirical assessment of the CCAPM