Two-Pass Tests of Asset Pricing Models with Useless Factors


  • Kan is at the University of Toronto, Zhang is at the Hong Kong University of Science and Technology and the University of Alberta. We thank K. C. Chan, Sean Cleary, Jin-Chuan Duan, Wayne Ferson, Rene Garcia, Mark Huson, Vijay Jog, Youngsoo Kim, George Kirikos, Peter Klein, Bob Korkie, Anthony Lynch, Vikas Mehrotra, Angelo Melino, Randall Morek, Sergei Sarkis-sian, Ken Shah, Tim Simin, Robert Stambaugh, Rene Stulz (the editor), Mike Vetsuypens, Zhenyu Wang, John Wei, Min-Teh Yu, Guofu Zhou, Xiaodong Zhu, seminar participants at the Hong Kong University of Science and Technology, National Central University (Taiwan), Queen's University, Southern Methodist University, University of Alberta, University of California at Irvine, University of Toronto, participants at the 1996 Northern Finance Meetings in Quebec City and the 1997 Western Finance Meetings in San Diego, and particularly Naifu Chen and Ravi Jagannathan for their helpful comments and discussions. We would also like to thank Ravi Jagannathan and Zhenyu Wang for sharing their data set with us, and Teresa Chan and Martin Forest for their research assistance. All remaining errors are ours.


In this paper we investigate the properties of the standard two-pass methodology of testing beta pricing models with misspecified factors. In a setting where a factor is useless, defined as being independent of all the asset returns, we provide theoretical results and simulation evidence that the second-pass cross-sectional regression tends to find the beta risk of the useless factor priced more often than it should. More surprisingly, this misspecification bias exacerbates when the number of time series observations increases. Possible ways of detecting useless factors are also examined.