In this paper we examine the usefulness of multivariate semi-parametric GARCH models for evaluating the Value-at-Risk (VaR) of a portfolio with arbitrary weights. We specify and estimate several alternative multivariate GARCH models for daily returns on the S&P 500 and Nasdaq indexes. Examining the within-sample VaRs of a set of given portfolios shows that the semi-parametric model performs uniformly well, while parametric models in several cases have unacceptable failure rates. Interestingly, distributional assumptions appear to have a much larger impact on the performance of the VaR estimates than the particular parametric specification chosen for the GARCH equations.

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Keywords GARCH models, Multivariate volatility, Risk management, Time series analysis
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Journal Quantitative Finance
Rombouts, J.V.K, & Verbeek, M.J.C.M. (2009). Evaluating portfolio Value-at-Risk using semi-parametric GARCH models. Quantitative Finance, 9(6), 737–745. doi:10.1080/14697680902785284