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How Do Alphas and Betas Move? Uncertainty, Learning and Time Variation in Risk Loadings


  • This article was partly developed over a visiting period at the Department of Finance of the Carroll School of Management, Boston College. I thank Pierluigi Balduzzi and two anonymous referees for very useful suggestions. I am also grateful to participants to seminars at the University of Brescia, the Catholic University of Milan and to the ICMAIF 2010 and SIE 2010 conferences. All errors are mine.


I employ a parsimonious model with learning, but without conditioning information, to extract time-varying measures of market-risk sensitivities, pricing errors and pricing uncertainty. The evolution of these quantities has interesting implications for macroeconomic dynamics. Parameters estimated for US equity portfolios display significant low-frequency fluctuations, along patterns that change across size and book-to-market stocks. Time-varying betas display superior predictive accuracy for returns against constant and rolling-window OLS estimates. As to the relationship of betas with business-cycle variables, value stocks’ betas move pro-cyclically, unlike those of growth stocks. Investment growth, rather than consumption, predicts the betas of value and small-firm portfolios.