No Arbitrage and Arbitrage Pricing: A New Approach




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    • The Fuqua School of Business, Duke University. We owe a special debt to Ron Gallant and George Tauchen for the valuable time that they have spent in discussions with us. We thank two anonymous referees and the editor, René Stulz, for detailed comments that have improved the paper considerably. We thank Peter Bossaerts, Francisco Delgado, George Constantinides, Campbell Harvey, Burton Hollifield, David Hsieh, Ravi Jagannathan, Ellen McGratten, Victor Ng, Sanjay Srivastava, and seminar participants at Duke, Michigan, and Wisconsin, the WFA meetings in San Francisco, and the AFA meetings in Anaheim for their comments, and Campbell Harvey and Tom Smith for providing us with their data. The Business Associates Fund of the Fuqua School of Business provided financial support.


We argue that arbitrage-pricing theories (APT) imply the existence of a low-dimensional nonnegative nonlinear pricing kernel. In contrast to standard constructs of the APT, we do not assume a linear factor structure on the payoffs. This allows us to price both primitive and derivative securities. Semi-nonparametric techniques are used to estimate the pricing kernel and test the theory. Empirical results using size-based portfolio returns and yields on bonds reject the nested capital asset-pricing model and linear APT and support the nonlinear APT. Diagnostics show that the nonlinear model is more capable of explaining variations in small firm returns.