Assessing Goodness-of-Fit of Asset Pricing Models: The Distribution of the Maximal R2





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    • Foster is from The University of Iowa, Smith is from the University of New South Wales, and Whaley is from Duke University. We are grateful for the helpful comments of seminar participants at the Australian Finance Association Conference, University of Arizona, Australian Graduate School of Management, Berkeley Program in Finance, University of British Columbia, University of California at Berkeley, University of Central Florida, University of Iowa, University of Michigan, Monash University, North Carolina State University, the Pacific Basin Finance Conference in Hong Kong, University of Pennsylvania, Queensland University of Technology, Rice University, the Second Conference on Financial Economics and Accounting at SUNY Buffalo, Stanford University, University of Western Australia, the Western Finance Association Annual Meetings in San Francisco, Fischer Black, Louis Chan, Bernard Dumas, Fred Feinberg, Campbell Harvey, Nancy Keeshan, Allan Kleidon, Andrew Lo, Kevin McCardle, Bob Nau, George Oldfield, Matthew Richardson, Jim Smith, René Stulz (the editor), S. Viswanathan, and an anonymous referee. Research support was received from the Business Associates' Fund (Smith and Whaley), Fuqua School of Business, Duke University. This research would not have been possible without the generous support of the North Carolina Super Computing Center.


The development of asset pricing models that rely on instrumental variables together with the increased availability of easily-accessible economic time-series have renewed interest in predicting security returns. Evaluating the significance of these new research findings, however, is no easy task. Because these asset pricing theory tests are not independent, classical methods of assessing goodness-of-fit are inappropriate. This study investigates the distribution of the maximal R2 when k of m regressors are used to predict security returns. We provide a simple procedure that adjusts critical R2 values to account for selecting variables by searching among potential regressors.