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Evaluating Portfolio Value-at-Risk using Semi-Parametric GARCH Models

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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File URL: http://www.hec.ca/iea/cahiers/2004/iea0414_jrom.pdf
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Paper provided by HEC Montréal, Institut d'économie appliquée in its series Cahiers de recherche with number 04-14.

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Length: 30 pages
Date of creation: Dec 2004
Date of revision:
Handle: RePEc:iea:carech:0414
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  1. 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.
  2. de Goeij, P. C. & Marquering, W., 2004. "Modeling the conditional covariance between stock and bond returns : A multivariate GARCH approach," Other publications TiSEM 94fe5ada-715a-4339-b94c-f, Tilburg University, School of Economics and Management.
  3. GIOT, Pierre & LAURENT, Sébastien, . "Value-at-Risk for long and short trading positions," CORE Discussion Papers RP -1707, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen VK, . "Multivariate GARCH models: a survey," CORE Discussion Papers RP -1847, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. 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.
  6. 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.).
  7. 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.
  8. Gourieroux, C. & Laurent, J. P. & Scaillet, O., 2000. "Sensitivity analysis of Values at Risk," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 225-245, November.
  9. Jianqing Fan & Juan Gu, 2003. "Semiparametric estimation of Value at Risk," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 261-290, December.
  10. Pierre Giot and S»bastien Laurent, 2001. "Value-At-Risk For Long And Short Trading Positions," Computing in Economics and Finance 2001 94, Society for Computational Economics.
  11. Christian Gourieroux & Jean-Paul Laurent & Olivier Scaillet, 2000. "Sensitivity Analysis of Values at Risk," Working Papers 2000-05, Centre de Recherche en Economie et Statistique.
  12. Bauwens, Luc & Lubrano, Michel & Richard, Jean-Francois, 2000. "Bayesian Inference in Dynamic Econometric Models," OUP Catalogue, Oxford University Press, number 9780198773139, March.
  13. Hafner, Christian M. & Rombouts, Jeroen V.K., 2007. "Semiparametric Multivariate Volatility Models," Econometric Theory, Cambridge University Press, vol. 23(02), pages 251-280, April.
  14. Jeff Fleming, 2001. "The Economic Value of Volatility Timing," Journal of Finance, American Finance Association, vol. 56(1), pages 329-352, 02.
  15. 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.
  16. 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.
  17. 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.
  18. Peter de Goeij, 2004. "Modeling the Conditional Covariance Between Stock and Bond Returns: A Multivariate GARCH Approach," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(4), pages 531-564.
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