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Evaluating Portfolio Value-At-Risk Using Semi-Parametric GARCH Models

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Author Info
Rombouts, J.V.K.
Verbeek, M.J.C.M. (Erasmus Research Institute of Management (ERIM), RSM Erasmus University)

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Abstract

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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Paper provided by 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 University Rotterdam. in its series Research Paper with number ERS-2004-107-F&A Revision_Date: 2009-07-29.

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Date of creation: 28 Jan 2009
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Handle: RePEc:dgr:eureri:30001977

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Related research
Keywords: multivariate GARCH; semi-parametric estimation; value-at-risk; asset allocation;

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This paper has been announced in the following NEP Reports: References listed on IDEAS
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  1. BAUWENS, Luc & LAURENT, SŽbastien & ROMBOUTS, Jeroen, 2003. "Multivariate GARCH models: a survey," CORE Discussion Papers 2003031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE). [Downloadable!]
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  2. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, 06. [Downloadable!] (restricted)
  3. Campbell, Rachel & Huisman, Ronald & Koedijk, Kees, 2001. "Optimal portfolio selection in a Value-at-Risk framework," Journal of Banking & Finance, Elsevier, vol. 25(9), pages 1789-1804, September. [Downloadable!] (restricted)
  4. Christian Gourieroux & J. P. Laurent & Olivier Scaillet, 2000. "Sensitivity Analysis of Values at Risk," Econometric Society World Congress 2000 Contributed Papers 0162, Econometric Society. [Downloadable!]
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  5. Billio, Monica & Pelizzon, Loriana, 2000. "Value-at-Risk: a multivariate switching regime approach," Journal of Empirical Finance, Elsevier, vol. 7(5), pages 531-554, December. [Downloadable!] (restricted)
  6. Alexander, Gordon J. & Baptista, Alexandre M., 2002. "Economic implications of using a mean-VaR model for portfolio selection: A comparison with mean-variance analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 26(7-8), pages 1159-1193, July. [Downloadable!] (restricted)
  7. Pierre Giot & Sébastien Laurent, 2003. "Value-at-risk for long and short trading positions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(6), pages 641-663. [Downloadable!]
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  8. Tim Bollerslev & Jeffrey Wooldridge, 1992. "Quasi-maximum likelihood estimation and inference in dynamic models with time-varying covariances," Econometric Reviews, Taylor and Francis Journals, vol. 11(2), pages 143-172. [Downloadable!] (restricted)
  9. Hafner, C.M. & Rombouts, J.V.K., 2004. "Semiparametric multivariate volatility models," Econometric Institute Report EI 2004-21 Revision_Date:, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
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  10. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-50, July.
  11. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).
  12. Peter de Goeij, 2004. "Modeling the Conditional Covariance Between Stock and Bond Returns: A Multivariate GARCH Approach," Journal of Financial Econometrics, Oxford University Press, vol. 2(4), pages 531-564. [Downloadable!] (restricted)
  13. Giovanni Barone Adesi & Patrick Gagliardini & Giovanni Urga, 2004. "Testing Asset Pricing Models With Coskewness," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 474-485, October. [Downloadable!] (restricted)
  14. Jianqing Fan & Juan Gu, 2003. "Semiparametric estimation of Value at Risk," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 261-290, December. [Downloadable!] (restricted)
  15. Jeff Fleming, 2001. "The Economic Value of Volatility Timing," Journal of Finance, American Finance Association, vol. 56(1), pages 329-352, 02. [Downloadable!] (restricted)
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  1. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109. [Downloadable!]
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