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Multistep Predictions from Multivariate ARMA-GARCH: Models and their Value for Portfolio Management

Author

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  • Jaroslava Hlouskova
  • Kurt Schmidheiny
  • Martin Wagner

Abstract

In this paper we derive the closed form solution for multistep predictions of the conditional means and their covariances from multivariate ARMA-GARCH models. These 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 covariance matrix of the sum of the higher frequency returns until the next rebalancing period is required as input in the mean variance portfolio problem. The closed form solution for this quantity is derived as well. We assess the empirical value of the result by evaluating and comparing the performance of quarterly and monthly rebalanced portfolios using monthly MSCI index data across a large set of ARMA-GARCH models. The results forcefully demonstrate the substantial value of multistep predictions for portfolio management.

Suggested Citation

  • Jaroslava Hlouskova & Kurt Schmidheiny & Martin Wagner, 2002. "Multistep Predictions from Multivariate ARMA-GARCH: Models and their Value for Portfolio Management," Diskussionsschriften dp0212, Universitaet Bern, Departement Volkswirtschaft.
  • Handle: RePEc:ube:dpvwib:dp0212
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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(01), pages 122-150, February.
    2. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    3. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    4. Menelaos Karanasos, "undated". "Prediction in ARMA models with GARCH in Mean Effects," Discussion Papers 99/11, Department of Economics, University of York.
    5. Jeff Fleming, 2001. "The Economic Value of Volatility Timing," Journal of Finance, American Finance Association, vol. 56(1), pages 329-352, February.
    6. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 247-264.
    7. Baillie, Richard T. & Bollerslev, Tim, 1992. "Prediction in dynamic models with time-dependent conditional variances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 91-113.
    8. repec:cup:etheor:v:11:y:1995:i:1:p:122-50 is not listed on IDEAS
    9. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    10. 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.
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    12. Foort HAMELINK, 2000. "Optimal International Diversification: Theory and Practice from a Swiss Investor’s Perspective," FAME Research Paper Series rp21, International Center for Financial Asset Management and Engineering.
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    More about this item

    Keywords

    multivariate ARMA-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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