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Multivariate GARCH with dynamic beta

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  • M. Raddant
  • F. Wagner

Abstract

We investigate a solution for the problems related to the application of multivariate GARCH models to markets with a large number of stocks by restricting the form of the conditional covariance matrix and by introducing a system of recursion formals. The model is based on a decomposition of the conditional covariance matrix into two components and requires only six parameters to be estimated. The first component can be interpreted as the market factor, all remaining components are assumed to be equal. This allow the analytical calculation of the inverse covariance matrix. The factors are dynamic and therefore enable to describe dynamic beta coefficients. We compare the estimated covariances for the S&P500 market with those of other GARCH models and find that they are competitive, despite the low number of parameters. As applications we use the daily values of beta coefficients to confirm a transition of the market in 2006. Furthermore we discuss the relationship of our model with the leverage effect.

Suggested Citation

  • M. Raddant & F. Wagner, 2022. "Multivariate GARCH with dynamic beta," The European Journal of Finance, Taylor & Francis Journals, vol. 28(13-15), pages 1324-1343, October.
    • Handle: RePEc:taf:eurjfi:v:28:y:2022:i:13-15:p:1324-1343
    DOI: 10.1080/1351847X.2021.1882523
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    References listed on IDEAS

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    1. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    2. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    3. Matthias Raddant & Friedrich Wagner, 2017. "Transitions in the stock markets of the US, UK and Germany," Quantitative Finance, Taylor & Francis Journals, vol. 17(2), pages 289-297, February.
    4. repec:bla:jfinan:v:44:y:1989:i:5:p:1115-53 is not listed on IDEAS
    5. Cavit Pakel & Neil Shephard & Kevin Sheppard & Robert F. Engle, 2021. "Fitting Vast Dimensional Time-Varying Covariance Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(3), pages 652-668, July.
    6. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    7. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    9. Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-131, February.
    10. F. Wagner & M. Milaković & S. Alfarano, 2010. "What distinguishes individual stocks from the index?," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 73(1), pages 23-28, January.
    11. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
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