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

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