Nonlinear Pricing Kernels, Kurtosis Preference, and Evidence from the Cross Section of Equity Returns

ABSTRACT This paper investigates nonlinear pricing kernels in which the risk factor is endogenously determined and preferences restrict the definition of the pricing kernel. These kernels potentially generate the empirical performance of nonlinear and multifactor models, while maintaining empirical power and avoiding ad hoc specifications of factors or functional form. Our test results indicate that preference‐restricted nonlinear pricing kernels are both admissible for the cross section of returns and are able to significantly improve upon linear single‐ and multifactor kernels. Further, the nonlinearities in the pricing kernel drive out the importance of the factors in the linear multi‐factor model.