A Test for the Number of Factors in an Approximate Factor Model




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    • Connor is from the London School of Economics and Korajczyk is from Northwestern University. We would like to thank Peter Bossaerts, Gary Chamberlain, Richard Green, David Modest, Jay Shanken, René Stulz, Mark Watson, an anonymous referee, and seminar participants at London Business School, London School of Economics, and Nuffield College, Oxford for helpful comments. We also thank Theodore Sternberg and Robert Uhlaner for research assistance.


An important issue in applications of multifactor models of asset returns is the appropriate number of factors. Most extant tests for the number of factors are valid only for strict factor models, in which diversifiable returns are uncorrelated across assets. In this paper we develop a test statistic to determine the number of factors in an approximate factor model of asset returns, which does not require that diversifiable components of returns be uncorrelated across assets. We find evidence for one to six pervasive factors in the cross-section of New York Stock Exchange and American Stock Exchange stock returns.