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Multivariate Garch with dynamic beta

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  • Matthias Raddant
  • Friedrich 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. The model is a factor model and uses only six free GARCH parameters. One factor can be interpreted as the market component, the remaining factors are equal. This allow the analytical calculation of the inverse covariance matrix. The time-dependence of the factors enables the determination of dynamical beta coefficients. We compare the results from our model with the results of other GARCH models for the daily returns from the S\&P500 market and find that they are competitive. 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

  • Matthias Raddant & Friedrich Wagner, 2016. "Multivariate Garch with dynamic beta," Papers 1609.07051, arXiv.org, revised Nov 2019.
    • Handle: RePEc:arx:papers:1609.07051
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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. 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.
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    4. 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.
    5. 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.
    6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
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    8. 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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    10. 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.
    11. 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.
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