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

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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.

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Bibliographic Info

Paper provided by Universitaet Bern, Departement Volkswirtschaft in its series Diskussionsschriften with number dp0212.

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Date of creation: Nov 2002
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Handle: RePEc:ube:dpvwib:dp0212

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Keywords: multivariate ARMA-GARCH models; volatility forecasts; portfolio optimization; minimum variance portfolio;

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  1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  2. repec:cup:etheor:v:11:y:1995:i:1:p:122-50 is not listed on IDEAS
  3. Baillie, R.T. & Bollerslev, R.T., 1990. "Prediction In Dynamic Models With Time Dependent Conditional Variances," Papers 8815, Michigan State - Econometrics and Economic Theory.
  4. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
  5. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  6. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  7. Menelaos Karanasos, . "Prediction in ARMA models with GARCH in Mean Effects," Discussion Papers 99/11, Department of Economics, University of York.
  8. Jeff Fleming, 2001. "The Economic Value of Volatility Timing," Journal of Finance, American Finance Association, vol. 56(1), pages 329-352, 02.
  9. Nilsson, Birger, 2002. "International Asset Pricing and the Benefits from World Market Diversification," Working Papers 2002:1, Lund University, Department of Economics.
  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 116-31, February.
  11. 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.
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