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

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  • Jeroen V.K. Rombouts

    ()
    (IEA, HEC Montréal)

  • Marno Verbeek

Abstract

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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Bibliographic Info

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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Postal: Institut d'économie appliquée HEC Montréal 3000, Chemin de la Côte-Sainte-Catherine Montréal, Québec H3T 2A7
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Related research

Keywords: multivariate GARCH; semi-parametric estimation; Value-at-Risk; asset allocation.;

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References

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  1. 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.
  2. C. Gourieroux & J.P. Laurent & O. Scaillet, 2000. "Sensitivity analysis of values at risk," THEMA Working Papers 2000-04, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  3. 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.
  4. BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen, 2003. "Multivariate GARCH models: a survey," CORE Discussion Papers 2003031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Bauwens, Luc & Lubrano, Michel & Richard, Jean-Francois, 2000. "Bayesian Inference in Dynamic Econometric Models," OUP Catalogue, Oxford University Press, number 9780198773139.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. Goeij, P. C. de & Marquering, W., 2004. "Modeling the conditional covariance between stock and bond returns: A multivariate GARCH approach," Open Access publications from Tilburg University urn:nbn:nl:ui:12-194709, Tilburg University.
  11. Rombouts, Jeroen V. K. & Hafner, Christian M., 2004. "Semiparametric multivariate volatility models," Papers 2004,14, Humboldt-Universität Berlin, Center for Applied Statistics and Economics (CASE).
  12. 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.
  13. 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.
  14. 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.).
  15. 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).
  16. Jianqing Fan & Juan Gu, 2003. "Semiparametric estimation of Value at Risk," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 261-290, December.
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  18. Jeff Fleming, 2001. "The Economic Value of Volatility Timing," Journal of Finance, American Finance Association, vol. 56(1), pages 329-352, 02.
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Citations

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Cited by:
  1. BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen, 2003. "Multivariate GARCH models: a survey," CORE Discussion Papers 2003031, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. SBRANA, Giacomo & SILVESTRINI, Andrea, 2010. "Aggregation of exponential smoothing processes with an application to portfolio risk evaluation," CORE Discussion Papers 2010039, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Pei Pei, 2010. "Backtesting Portfolio Value-at-Risk with Estimated Portfolio Weights," Caepr Working Papers 2010-010, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.
  4. He, Kaijian & Wang, Lijun & Zou, Yingchao & Lai, Kin Keung, 2014. "Value at risk estimation with entropy-based wavelet analysis in exchange markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 408(C), pages 62-71.

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