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 that it estimates these moments simultaneously. We apply this model to obtain long- and short-run factor betas for industry test portfolios, where the risk factors are the market, SMB, and HML portfolios. We use these betas in cross-sectional analysis of the risk premia. Among other things, 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
A vast literature is devoted to investigating the cross-sectional relationship between expected returns and risk
We find that the data frequency matters for estimation of the risk premium: None of the risk premia estimated at weekly frequencies is significant, which is in contrast to the risk premia obtained at the monthly frequency
The risk premia associated with both the long- and short-run small-minus-big portfolio (SMB) betas are significant, only the risk premium associated with the short-run market beta is significantly positive
Summary
A vast literature is devoted to investigating the cross-sectional relationship between expected returns and risk (see, e.g., Engle, Bollerslev, and Wooldridge, 1988; Harvey, 1989; Schwert and Seguin, 1990; Ang, Hocrick, Xing, and Zhang, 2006; Bali, 2008). We suggest a new conditional asset-pricing model by using the mixed-data-sampling approach in a component bivariate GARCH model This new framework allows us to simultaneously obtain long- and short-run factor-beta components. Baele and Londono (2013) use Colacito, Engle, and Ghysels’s (2011) dynamic conditional correlation (DCC) MIDAS model to obtain long-run betas. They find that DCCMIDAS betas are superior to ordinary betas in limiting the downside risk and ex-post market exposure for the minimum-variance strategy. We apply our component GARCH model to each factor and an asset (industry portfolio) to estimate long- and short-run variances and covariances.
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