Jose Menchero and Indrajit Mitra
We study the problem of augmenting fundamental risk models with statistical factors in order to capture the risk associated with omitted factors. The statistical factors are estimated by applying principal component analysis to the cross-sectional residuals. We show that in the limit of zero noise, the statistical factors can be precisely interpreted as fundamental factors that have been Gram-Schmidt orthogonalized to the existing fundamental factors. For finite noise, we determine the correlations between the true and estimated factor exposures and returns. This establishes a practical criterion for the successful detection of hidden factors.