http://www.jstor.org/stable/2329038

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. A test statistic is developed to determine the number of factors in an approximate factor model for asset returns that does not require that diversifiable components of returns be uncorrelated cross assets. The test is applied to a sample of monthly returns on common stock traded on the New York Stock Exchange (NYSE) and the American Stock Exchange (AMEX) for the period January 1967-December 1991. Evidence is found for one to 6 pervasive factors in the cross section of NYSE and AMEX stock returns. The influence of the factors beyond the first is particularly strong in January. In non-January months, only or 2 signficant factors are found.