Pricing Model Performance and the Two-Pass Cross-Sectional Regression Methodology

Raymond Kan, Cesare Robotti, and Jay Shanken
Working Paper 2009-11
March 2009

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Since Black, Jensen, and Scholes (1972) and Fama and MacBeth (1973), the two-pass cross-sectional regression (CSR) methodology has become the most popular approach for estimating and testing asset pricing models. Statistical inference with this method is typically conducted under the assumption that the models are correctly specified, that is, expected returns are exactly linear in asset betas. This assumption can be a problem in practice since all models are, at best, approximations of reality and are likely to be subject to a certain degree of misspecification. We propose a general methodology for computing misspecification-robust asymptotic standard errors of the risk premia estimates. We also derive the asymptotic distribution of the sample CSR R2 and develop a test of whether two competing linear beta pricing models have the same population R2. This test provides a formal alternative to the common heuristic of simply comparing the R2 estimates in evaluating relative model performance. Finally, we provide an empirical application, which demonstrates the importance of our new results when applied to a variety of asset pricing models.

JEL classification: G12

Key words: two-pass cross-sectional regressions, risk premia, model misspecification, model comparison, R2

The authors thank Wayne Ferson, Nikolay Gospodinov, Ravi Jagannathan, Yaxuan Qi, Guofu Zhou, and seminar participants at the Board of Governors of the Federal Reserve System, Concordia University, the Federal Reserve Banks of Atlanta and New York, and the University of Toronto for helpful discussions and comments. Kan gratefully acknowledges financial support from the National Bank Financial of Canada. The views expressed here are the authors' and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors' responsibility.

Please address questions regarding content to Raymond Kan, Joseph L. Rotman School of Management, University of Toronto, 105 St. George Street, Toronto, Ontario, Canada M5S 3E6; Cesare Robotti (contact author), Federal Reserve Bank of Atlanta, 1000 Peachtree Street, N.E., Atlanta, GA 30309-4470, 404-498-8543, 404-498-8810 (fax),; or Jay Shanken, Goizueta Business School, Emory University, 1300 Clifton Road, N.E., Atlanta, GA 30322.

For further information, contact the Public Affairs Department, Federal Reserve Bank of Atlanta, 1000 Peachtree Street, N.E., Atlanta, Georgia 30309-4470, 404-498-8020.