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Multistep predictions for multivariate GARCH models: Closed form solution and the value for portfolio management

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  • Hlouskova, Jaroslava
  • Schmidheiny, Kurt
  • Wagner, Martin

Abstract

This paper derives the closed form solution for multistep predictions of the conditional means and covariances for multivariate ARMA-GARCH models. These predictions are useful e.g. in mean-variance portfolio analysis when the rebalancing frequency is lower than the data frequency. In this situation the conditional mean and the conditional covariance matrix of the cumulated higher frequency returns are required as inputs in the mean-variance portfolio problem. The empirical value of the result is evaluated by comparing the performance of quarterly and monthly rebalanced portfolios using monthly MSCI index data across a large set of GARCH models. Using correct multistep predictions generally results in lower risk and higher returns.

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  • Hlouskova, Jaroslava & Schmidheiny, Kurt & Wagner, Martin, 2009. "Multistep predictions for multivariate GARCH models: Closed form solution and the value for portfolio management," Journal of Empirical Finance, Elsevier, vol. 16(2), pages 330-336, March.
    • Handle: RePEc:eee:empfin:v:16:y:2009:i:2:p:330-336
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    Cited by:

    1. Carlos Trucíos & Mauricio Zevallos & Luiz K. Hotta & André A. P. Santos, 2019. "Covariance Prediction in Large Portfolio Allocation," Econometrics, MDPI, vol. 7(2), pages 1-24, May.
    2. Haas, Markus, 2010. "Covariance forecasts and long-run correlations in a Markov-switching model for dynamic correlations," Finance Research Letters, Elsevier, vol. 7(2), pages 86-97, June.
    3. Carlos Trucíos & João H. G. Mazzeu & Marc Hallin & Luiz K. Hotta & Pedro L. Valls Pereira & Mauricio Zevallos, 2022. "Forecasting Conditional Covariance Matrices in High-Dimensional Time Series: A General Dynamic Factor Approach," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(1), pages 40-52, December.
    4. Kajal Lahiri & Fushang Liu, 2006. "ARCH Models for Multi-period Forecast Uncertainty: A Reality Check Using a Panel of Density Forecasts," Advances in Econometrics, in: Econometric Analysis of Financial and Economic Time Series, pages 321-363, Emerald Group Publishing Limited.
    5. Francisco Rubio & Xavier Mestre & Daniel P. Palomar, 2011. "Performance analysis and optimal selection of large mean-variance portfolios under estimation risk," Papers 1110.3460, arXiv.org.
    6. Hlouskova, Jaroslava & Schmidheiny, Kurt & Wagner, Martin, 2009. "Multistep predictions for multivariate GARCH models: Closed form solution and the value for portfolio management," Journal of Empirical Finance, Elsevier, vol. 16(2), pages 330-336, March.

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    More about this item

    Keywords

    Multivariate GARCH models Volatility forecasts Portfolio optimization Minimum variance portfolio;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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