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


  • Robert F. Dittmar

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    • Dittmar is at the Kelley School of Business, Indiana University, Bloomington, Indiana. This paper is based on the author's dissertation at the University of North Carolina. Thanks to Dong-Hyun Ahn, Ravi Bansal, Utpal Bhattacharya, Mike Cliff, Jennifer Conrad, Amy Ditt-mar, Wayne Ferson, Ron Gallant, the journal editor, Richard Green, Mustafa Gultekin, Campbell Harvey, Karl Lins, Steve Monahan, Steve Slezak, George Tauchen, Marc Zenner, and an anonymous referee for valuable comments. Thanks also to seminar participants at Case Western Reserve University; Indiana University; the Office of the Comptroller of the Currency; Penn State University; the 1999 Western Finance Association meetings (Santa Monica); and the Universities of Cincinnati, Miami, Minnesota, North Carolina, Utah, Virginia, and Western Ontario for helpful comments and discussions. The author also thanks Eugene Fama and Kenneth French for making their data available. Any remaining errors are solely the author's responsibility.


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.