Staff Reports

Learning about Beta: Time-Varying Factor Loadings, Expected Returns, and the Conditional CAPM

Previous title: “Learning about Beta: A New Look at CAPM Tests”
September 2004Number 193
Revised October 2008
JEL classification: G12, C11

Authors: Tobias Adrian and Francesco Franzoni

We complement the conditional capital asset pricing model (CAPM) by introducing unobservable long-run changes in risk factor loadings. In this environment, investors rationally “learn” the long-run level of factor loading by observing realized returns. As a direct consequence of this assumption, conditional betas are modeled 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 ratio, our learning-augmented conditional CAPM fails to be rejected.

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