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Backtesting Portfolio Value-at-Risk with Estimated Portfolio Weights

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  • Pei Pei

    () (Indiana University Bloomington)

Abstract

This paper theoretically and empirically analyzes backtesting portfolio VaR with estimation risk in an intrinsically multivariate framework. For the first time in the literature, it takes into account the estimation of portfolio weights in forecasting portfolio VaR and its impact on backtesting. It shows that the estimation risk from estimating the portfolio weights as well as that from estimating the multivariate dynamic model of asset returns make the existing methods in a univariate framework inapplicable. And it proposes a general theory to quantify estimation risk applicable to the present problem and suggests practitioners a simple but effective way to carry out valid inference to overcome the effect of estimation risk in backtesting portfolio VaR. A simulation exercise illustrates our theoretical findings. In application, a portfolio of three stocks is considered.

Suggested Citation

  • 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.
  • Handle: RePEc:inu:caeprp:2010-010
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    References listed on IDEAS

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    1. Jeroen Rombouts & Marno Verbeek, 2009. "Evaluating portfolio Value-at-Risk using semi-parametric GARCH models," Quantitative Finance, Taylor & Francis Journals, vol. 9(6), pages 737-745.
    2. Silvennoinen, Annastiina & Teräsvirta, Timo, 2007. "Multivariate GARCH models," SSE/EFI Working Paper Series in Economics and Finance 669, Stockholm School of Economics, revised 18 Jan 2008.
    3. 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.
    4. Diebold, Francis X & Nerlove, Marc, 1989. "The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor Arch Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(1), pages 1-21, Jan.-Mar..
    5. 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.
    6. Harvey, Andrew & Ruiz, Esther & Sentana, Enrique, 1992. "Unobserved component time series models with Arch disturbances," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 129-157.
    7. Enrique Sentana, 1995. "Quadratic ARCH Models," Review of Economic Studies, Oxford University Press, vol. 62(4), pages 639-661.
    8. 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.
    9. Mc Cracken, Michael W., 2000. "Robust out-of-sample inference," Journal of Econometrics, Elsevier, vol. 99(2), pages 195-223, December.
    10. Luc Bauwens & Sébastien Laurent, 2002. "A New Class of Multivariate skew Densities, with Application to GARCH Models," Computing in Economics and Finance 2002 5, Society for Computational Economics.
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