Factor Strengths, Pricing Errors, and Estimation of Risk Premia

This paper examines the implications of pricing errors and factors that are not strong for the Fama-MacBeth two-pass estimator of risk premia and its asymptotic distribution when T is fixed with n → ∞, and when both n and T → ∞, jointly. While the literature just distinguishes strong and weak factors we allow for degrees of strength using a recently developed measure. Our theoretical results have important practical implications for empirical asset pricing. Pricing errors and factor strength matter for consistent estimation of risk premia and subsequent inference, thus an estimate of factor strength is required before attempting to estimate risk. Finally, using a recently developed procedure we provide rolling estimates of factor strengths for the five Fama-French factors, and show that only the market factor can be viewed as strong.