In this paper we examine the usefulness of multivariate semi-parametric GARCH models for portfolio selection under a Value-at-Risk (VaR) constraint. First, 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. Finally, we examine the economic value of the multivariate GARCH models by determining optimal portfolios based on maximizing expected returns subject to a VaR constraint, over a period of 500 consecutive days. Again, the superiority and robustness of the semi-parametric model is confirmed.
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Paper provided by HEC Montréal, Institut d'économie appliquée in its series Cahiers de recherche with number
04-14.
Length: 30 pages Date of creation: Dec 2004 Date of revision: Handle: RePEc:iea:carech:0414
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Rombouts, J.V.K. & Verbeek, M.J.C.M, 2004.
"Evaluating Portfolio Value-At-Risk Using Semi-Parametric GARCH Models,"
Research Paper
ERS-2004-107-F&A Revision, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus Uni.
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