Testing Pricing Errors of Models with Latent Factors and Firm Characteristics as Covariances

This paper extends the methodology of statistically extracting latent factors in settings with return-predictive firm characteristics as conditional covariances (betas) between returns and factors. The main feature is that the pricing errors (alphas) are specified to be orthogonal to the affine-transformed firm characteristics as the betas with one component of pricing errors lying outside the space spanned by the firm characteristics. The specification is shown to make substantial differences with the extant literature as the zero pricing error hypothesis is strongly rejected for various models with commonly used firm characteristics.