Realized Autoregressive Conditional Betas

Abstract

We propose a new model called RACB (Realized Autoregressive Conditional Beta) for the dynamics of slope coefficients, or betas, in linear regression models with heteroskedastic errors. RACB is a quasi score-driven model that jointly models returns and realized betas, conditional on the regressors. It extends the Autoregressive Conditional Beta (ACB) model by incorporating realized betas into the beta updating equation and shrinking the conditional betas toward the realized betas.

We develop a multistep quasi-maximum likelihood estimator for the RACB model and establish its large-sample properties. We also derive key stochastic properties of the data-generating process and the associated filter, and show that the contraction condition ensuring filter invertibility is not only sufficient but also almost necessary. When realized betas are missing, we show that replacing the unobserved realized betas with their conditional counterparts is optimal within a class of near-degenerate approximations and for the one-step tracking loss.

Empirically, for 90 large U.S. stocks in a Fama-French three-factor setting, the RACB model achieves the best performance in a tracking portfolio exercise as it is the most frequently retained model in the Model Confidence Set. Joint paper with Mariia Artemova and Christian Francq.