Assessing Specification Errors in Stochastic Discount Factor Models




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    • Hansen is from the University of Chicago, The National Opinion Research Center, and National Bureau of Economic Research. Jagannathan is from the Carlson School of Management and Visitor, Research Department, Federal Reserve Bank of Minneapolis. Comments by Renee Adams, Edward Allen, Fischer Black, John Cochrane, John Heaton, Peter Knez, Erzo Luttmer, Marc Roston, S. Viswanathan, two referees, and the editor of the journal are gratefully acknowledged. Expert research assistance was provided by Marc Roston and Amir Yaron. Hansen received funding from the National Science Foundation in support of this research. Jagannathan acknowledges partial financial support from the National Science Foundation, grant SBR-9409824. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.


In this article we develop alternative ways to compare asset pricing models when it is understood that their implied stochastic discount factors do not price all portfolios correctly. Unlike comparisons based on χ2 statistics associated with null hypotheses that models are correct, our measures of model performance do not reward variability of discount factor proxies. One of our measures is designed to exploit fully the implications of arbitrage-free pricing of derivative claims. We demonstrate empirically the usefulness of our methods in assessing some alternative stochastic factor models that have been proposed in asset pricing literature.