An Unconditional Asset-Pricing Test and the Role of Firm Size as an Instrumental Variable for Risk


  • K. C. CHAN,


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    • College of Business, Ohio State University and Graduate School of Business, University of Chicago, respectively. We are grateful to James Bodurtha, Eugene Fama, Wayne Ferson, Larry Harris, Gur Huberman, Shmuel Kandel, Ed Kane, Robert Kohn, Merton Miller, Marc Reinganum, Robert Stambaugh, Rene Stulz, George Tiao, Sheridan Titman, Walter Wasserfallen, an anonymous referee, workshop participants at the University of Chicago, Ohio State University, University of California, Berkeley, and UCLA, and the participants at the Symposium for Stock Market Regularities (Brussels), the Western Finance Association Meeting (Colorado Springs), and the European Finance Association Meeting (Dublin, Ireland) for helpful comments and suggestions, as well as the Center for Research in Security Prices for support.


In an intertemporal economy where both risk (stock beta) and expected return are time varying, the authors derive a linear relation between the unconditional beta and the unconditional return under certain stationarity assumptions about the stochastic process of size-portfolio betas. The model suggests the use of long time periods to estimate the unconditional portfolio betas. The authors find that, after controlling for the betas thus estimated, a firm-size proxy, such as the logarithm of the firm size, does not have explanatory power for the averaged returns across the size-ranked portfolios.