A Critique of the Stochastic Discount Factor Methodology RAYMOND KAN and GUOFU ZHOU* ABSTRACT In this paper, we point out that the widely used stochastic discount factor ~SDF! methodology ignores a fully specified model for asset returns. As a result, it suffers from two potential problems when asset returns follow a linear factor model. The first problem is that the risk premium estimate from the SDF methodology is unreliable. The second problem is that the specification test under the SDF meth- odology has very low power in detecting misspecified models. Traditional method- ologies typically incorporate a fully specified model for asset returns, and they can perform substantially better than the SDF methodology. ASSET PRICING THEORIES, such as those of Sharpe ~1964!, Lintner ~1965!, Black ~1972!, Merton ~1973!, Ross ~1976!, and Breeden ~1979!, show that the ex- pected return on a financial asset is a linear function of its covariances ~or betas! with some systematic risk factors. This implication has been tested extensively in the finance literature by the so-called “traditional methodol- ogies.” In the traditional methodologies, a data-generating process is first proposed for the returns, and then the restrictions imposed by an asset pric- ing model are tested as parametric constraints on the return-generating pro- cess. The approach taken by the traditional methodologies has a potential problem, which is that when the proposed return-generating process is mis- specified the test results could be misleading. Therefore, in applying the traditional methodologies, researchers typically have to justify that the pro- posed data-generating process provides a good description of the returns. For example, when the proposed return-generating process is a factor model, one would like the model to have high R 2 in explaining the returns on the test assets, especially when the test assets are well-diversified portfolios. As many of the earlier theories are special cases of the stochastic dis- count factor ~SDF! model, recent empirical asset pricing studies have been focused on testing the pricing restrictions in terms of the SDF model, rather *Kan is from the University of Toronto, Zhou is from Washington University in St. Louis. We thank Kerry Back, Philip Dybvig, Heber Farnsworth, Wayne Ferson, Campbell Harvey, Roger Huang, Ravi Jagannathan, Mark Loewenstein, Deborah Lucas, Akhtar Siddique, Hans Stoll, Zhenyu Wang, Chu Zhang, seminar participants at the National Central University of Taiwan, the University of Texas at Dallas, Washington University in St. Louis, and participants at the 1999 American Finance Association Meetings in New York for their helpful discussions and comments. Kan gratefully acknowledges financial support from the Social Sciences and Hu- manities Research Council of Canada. THE JOURNAL OF FINANCE • VOL. LIV, NO. 4 • AUGUST 1999 1221