Learning about beta: A new look at CAPM tests

When risk-factor loadings are time-varying and unobservable, investors are forced to form beliefs about the levels of their loadings. The learning process involved in forming these beliefs has normative implications for asset-pricing tests. This paper develops an equilibrium model of learning about time-varying beta. In the model, the capital asset pricing model (CAPM) works for investors' probability distribution. However, mis-pricing can be observed if econometricians estimate betas without accounting for the investors' learning process. The empirical implication for asset-pricing tests is that the factor loadings must be estimated as latent variables. We provide an empirical application of this methodology to the cross section of returns on ten book-to-market and ten size-sorted portfolios. For these assets, the data do not reject a learning-augmented version of CAPM. This model performs better than other common empirical specifications, including the Fama-French three-factor model