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

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References

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  1. GIOT, Pierre & LAURENT, Sébastien, 2001. "Value-at-risk for long and short trading positions," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2001022, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, American Finance Association, vol. 55(3), pages 1263-1295, 06.
  3. BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen VK, . "Multivariate GARCH models: a survey," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -1847, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Billio, Monica & Pelizzon, Loriana, 2000. "Value-at-Risk: a multivariate switching regime approach," Journal of Empirical Finance, Elsevier, Elsevier, vol. 7(5), pages 531-554, December.
  5. Hafner, Christian M. & Rombouts, Jeroen V.K., 2007. "Semiparametric Multivariate Volatility Models," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 23(02), pages 251-280, April.
  6. Giovanni Barone Adesi & Patrick Gagliardini & Giovanni Urga, 2004. "Testing Asset Pricing Models With Coskewness," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 22, pages 474-485, October.
  7. C. Gourieroux & J.P. Laurent & O. Scaillet, 2000. "Sensitivity analysis of values at risk," THEMA Working Papers, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise 2000-04, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
  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, 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, Society for Financial Econometrics, vol. 2(4), pages 531-564.
  10. Campbell, Rachel & Huisman, Ronald & Koedijk, Kees, 2001. "Optimal portfolio selection in a Value-at-Risk framework," Journal of Banking & Finance, Elsevier, Elsevier, vol. 25(9), pages 1789-1804, September.
  11. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 20(3), pages 339-50, July.
  12. 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, Tilburg University urn:nbn:nl:ui:12-194709, Tilburg University.
  13. Paul H. Kupiec, 1995. "Techniques for verifying the accuracy of risk measurement models," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 95-24, Board of Governors of the Federal Reserve System (U.S.).
  14. Bauwens, Luc & Lubrano, Michel & Richard, Jean-Francois, 2000. "Bayesian Inference in Dynamic Econometric Models," OUP Catalogue, Oxford University Press, Oxford University Press, number 9780198773139, October.
  15. Jianqing Fan & Juan Gu, 2003. "Semiparametric estimation of Value at Risk," Econometrics Journal, Royal Economic Society, Royal Economic Society, vol. 6(2), pages 261-290, December.
  16. Christian Gourieroux & Jean-Paul Laurent & Olivier Scaillet, 2000. "Sensitivity Analysis of Values at Risk," Working Papers, Centre de Recherche en Economie et Statistique 2000-05, Centre de Recherche en Economie et Statistique.
  17. Jeff Fleming, 2001. "The Economic Value of Volatility Timing," Journal of Finance, American Finance Association, American Finance Association, vol. 56(1), pages 329-352, 02.
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Citations

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Cited by:
  1. SBRANA, Giacomo & SILVESTRINI, Andrea, 2010. "Aggregation of exponential smoothing processes with an application to portfolio risk evaluation," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2010039, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  2. Sébastien Laurent & Luc Bauwens & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 21(1), pages 79-109.
  3. 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, Elsevier, vol. 408(C), pages 62-71.
  4. Pei Pei, 2010. "Backtesting Portfolio Value-at-Risk with Estimated Portfolio Weights," Caepr Working Papers, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington 2010-010, Center for Applied Economics and Policy Research, Economics Department, Indiana University Bloomington.

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