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 new test statistic to determine the number of factors in an approximate factor model of asset returns. An approximate factor model does not require that diversifiable components of returns be uncorrelated across assets. We apply the test to monthly stock market return data to determine the number of pervasive return factors in the cross-section of New York Stock Exchange stock returns. The influence of the factors beyond the first is concentrated in January.
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