The role of pricing errors in linear asset pricing models with strong, semi-strong, and latent factors

This paper examines the role of pricing errors in linear factor pricing models, allowing for observed strong and semi-strong factors, and latent weak factors. It focusses on the estimation of ∅k = λk − μk which plays a pivotal role, not only in the estimation of risk premia but also in tests of market efficiency, where λk and μk are respectively the risk premium and the mean of the kth risk factor. It proposes a two-step estimator of ∅k with Shanken type bias-correction, and derives its asymptotic distribution under a general setting that allows for idiosyncratic pricing errors, weak missing factors, as well as weak error cross-sectional dependence. The implications of semi-strong factors for the asymptotic distribution of the proposed estimator are also investigated. Small sample results from extensive Monte Carlo experiments show that the proposed estimator has the correct size with good power properties. The paper also provides an empirical application to a large number of U.S. securities with risk factors selected from a large number of potential risk factors according to their strength.