Realized autoregressive conditional betas by Mariia Artemova, Christian Francq and Sébastien Laurent
September 9, 12:45 am - 2:00 pm
Christian Francq
(ENSAE)
“Realized autoregressive conditional betas by Mariia Artemova, Christian Francq and Sébastien Laurent”
We propose a new model called RACB (Realized Autoregressive Conditional Beta) to model the dynamics of slope parameters (or betas) in a linear regression model with heteroscedastic errors. The proposed model is a quasi score-driven model obtained by modelling the joint distribution of the endogenous variable and the realized betas, conditional on the explanatory variables and under the assumption that the realized betas are unbiased estimators of the conditional betas.
The proposed model extends the Autoregressive Conditional Beta (ACB) model by conditioning the betas on lagged realized betas and by shrinking the conditional betas towards the realized betas.
We establish the key stochastic properties of the data generating process and the associated filter, and argue that the contraction condition for invertibility is not only sufficient but also almost necessary. We also show that when realized betas are not observed for certain observations, replacing them with the conditional betas is optimal in the Kullback–Leibler divergence sense.
Empirically, for 37 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.