Multistep Predictions from Multivariate ARMA-GARCH: Models and their Value for Portfolio Management
AbstractIn 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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multivariate ARMA-GARCH models; volatility forecasts; portfolio optimization; minimum variance portfolio;
Find related papers by 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
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2002-11-10 (All new papers)
- NEP-ECM-2002-11-13 (Econometrics)
- NEP-ETS-2002-11-10 (Econometric Time Series)
- NEP-FMK-2002-11-10 (Financial Markets)
- NEP-RMG-2002-11-10 (Risk Management)
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