Abstract
We propose a new model that estimates the long- and short-run components of the variances and covariances. The advantage of our model to the existing DCC-based models is that it uses the same form for both the variances and covariances and estimates these moments simultaneously. We apply this model to obtain long- and short-run factor betas for industry test portfolios. We find that the risk premium related to the short-run market beta is significantly positive, irrespective of the choice of test portfolio. Further, the risk premia for the short-run betas of all the risk factors are significant outside recessions.
Highlights
In this paper, we propose a new bivariate component GARCH-mixed data sampling (MIDAS) model that decomposes return variances and covariances into a long-run and a short-run component
We find that the cross-sectional dispersion in short-run betas increases in recessions
We find that the data frequency matters for estimation of the risk premium: none of the risk premia estimated at weekly frequency are significant
Summary
We propose a new bivariate component GARCH-MIDAS model that decomposes return variances and covariances into a long-run (persistent) and a short-run (transitory) component. 4.3 Cross-sectional regressions To evaluate our component GARCH model, we compare its pricing ability with that of two alternative models for estimating betas: the traditional rolling-window OLS regressions (unconditional betas) and the bivariate GARCH model For these comparisons, we use both weekly and monthly returns. The total betas from the component GARCH model give significant risk premia for SMB and HML (only at the 10% level for the latter) Overall, none of these estimations give a significantly positive risk premium for the market beta, which is consistent with findings from the previous literature. For the component GARCH model (Panel B of Table 5), the short- and long-run SMB risk premia are significantly positive and slightly larger in expansions than for the entire sample period. Excluding recessions from our sample, i.e. only considering expansions, makes the risk premia for all the betas, except for the long-run market beta, significant and have the expected sign
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