Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may University of Konstanz CoFEValeri Voev ‡ University of Aarhus CREATESAbstract This paper proposes a methodology for modelling time series of realized covariance matrices in order to forecast multivariate risks. The approach allows for flexible dynamic dependence patterns and guarantees positive definiteness of the resulting forecasts without imposing parameter restrictions. We provide an empirical application of the model, in which we show by means of stochastic dominance tests that the returns from an optimal portfolio based on the model's forecasts second-order dominate returns of portfolios optimized on the basis of traditional MGARCH models. This result implies that any risk-averse investor, regardless of the type of utility function, would be better-off using our model.JEL classification: C32, C53, G11

We introduce a multivariate generalized autoregressive conditional heteroskedasticity (GARCH) model that incorporates realized measures of variances and covariances. Realized measures extract information about the current levels of volatilities and correlations from high-frequency data, which is particularly useful for modeling financial returns during periods of rapid changes in the underlying covariance structure. When applied to market returns in conjunction with returns on an individual asset, the model yields a dynamic model specification of the conditional regression coefficient that is known as the beta. We apply the model to a large set of assets and find the conditional betas to be far more variable than usually found with rolling-window regressions based exclusively on daily returns. In the empirical part of the paper, we examine the cross-sectional as well as the time variation of the conditional beta series during the financial crises.REALIZED BETA GARCH 775 we avoid such issues by incorporating realized measures and the use of measurement equations. The measurement equations tie realized measures to latent volatilities and correlations, and this leads to a useful regularization of the model. This particular structure was chosen for a number of reasons. First, the model provides a good empirical fit for the wide range of assets used in our empirical study; second, the structure of the model is amenable to a deeper analysis of secondary quantities such as betas; third, the model is simple to estimate, which is particularly important when a large set of assets are to be analyzed, as is the case in our empirical analysis.The proposed model has a hierarchical structure in which the market return and a corresponding realized measure form the core of the model. The model can be extended to an arbitrarily large set of individual returns, by adding a conditional model for an individual return and two realized measures, one being a realized measure of return volatility, and the other a realized measure of the correlation between the individual return and the market. This yields a flexible model with a dynamic covariance structure that is constantly revised by using the information contained in the realized measures.The concept of realized betas is not new. Bollerslev and Zhang (2003) carried out a large-scale estimation of the Fama-French three-factor model using high-frequency (5-minute) data on 6400 stocks over a period of 7 years. Their analysis showed that high-frequency data can improve the pricing accuracy of asset pricing models. Their approach differs from ours in important ways. For instance, they model raw realized factor loadings and use simple time series processes to forecast these. Thus there is no explicit link between realized and conditional moments of returns in their framework. Nor do they explicitly account for the measurement error (sampling error) in the realized quantities. Another related paper is Andersen et al. (2006), who study the time variation in realized variances, covariances an...

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