Learning about beta: Time-varying factor loadings, expected returns, and the conditional CAPM

We amend the conditional CAPM to allow for unobservable long-run changes in risk factor loadings. In this environment, investors rationally “learn” the long-run level of factor loadings from the observation of realized returns. As a consequence of this assumption, we model conditional betas using the Kalman filter. Because of its focus on low-frequency variation in betas, our approach circumvents recent criticisms of the conditional CAPM. When tested on portfolios sorted by size and book-to-market, our learning-augmented conditional CAPM passes the specification tests.