Learning about Beta: time-varying factor loadings, expected returns and the conditional CAPM

This paper explores the theoretical and empirical implications of time-varying and unobservable beta. Investors infer factor loadings from the history of returns via the Kalman filter. Due to learning, the history of beta matters. Even though the conditional CAPM holds, standard OLS tests can reject the model if the evolution of investor's expectations is not properly modelled. The authors use their methodology to explain returns on the twenty-five size and book-to-market sorted portfolios. Their learning version of the conditional CAPM produces pricing errors that are significantly smaller than standard conditional or unconditional CAPM and the model is not rejected by the data.