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

Abstract

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, the authors 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. They find evidence for one to six pervasive factors in the cross section of New York Stock Exchange and American Stock Exchange stock returns. Copyright 1993 by American Finance Association.