## Abstract

Many variables have been proposed as common risk factors driving asset returns, which we refer to as "empirical factors" to distinguish them from true latent factors. We examine how many true latent factors are correlated with the empirical factors by estimating the rank of the beta matrix corresponding to the empirical factors. We develop a new rank estimation method to handle data with a large number of asset returns. Our results from the analysis of the U.S. individual and portfolio stock returns are consistent with the notion that the three empirical factors of Fama and French (1993, FF) are correlated with three linearly independent true latent factors. Using more empirical factors in addition to the FF factors increases the rank of the beta matrix by one or two. Using twenty-six empirical factors for testing several models, we find that the only multifactor model that generates a full rank beta matrix is the FF three-factor model.