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Estimation risk for the VaR of portfolios driven by semi-parametric multivariate models

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  • Francq, Christian
  • Zakoïan, Jean-Michel

Abstract

Joint estimation of market and estimation risks in portfolios is investigated, when the individual returns follow a semi-parametric multivariate dynamic model and the asset composition is time-varying. Under ellipticity of the conditional distribution, asymptotic theory for the estimation of the conditional Value-at-Risk (VaR) is developed. An alternative method – the Filtered Historical Simulation – which does not rely on ellipticity, is also studied. Asymptotic confidence intervals for the conditional VaR, which allow for simultaneous quantification of the market and estimation risks, are derived. The particular case of minimum variance portfolios is analyzed in more detail. Potential usefulness, feasibility and drawbacks of the two approaches are illustrated via Monte-Carlo experiments and an empirical study based on stock returns.

Suggested Citation

  • Francq, Christian & Zakoïan, Jean-Michel, 2018. "Estimation risk for the VaR of portfolios driven by semi-parametric multivariate models," Journal of Econometrics, Elsevier, vol. 205(2), pages 381-401.
    • Handle: RePEc:eee:econom:v:205:y:2018:i:2:p:381-401
    DOI: 10.1016/j.jeconom.2018.03.018
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    Citations

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    Cited by:

    1. Eyden Samunderu & Yvonne T. Murahwa, 2021. "Return Based Risk Measures for Non-Normally Distributed Returns: An Alternative Modelling Approach," JRFM, MDPI, vol. 14(11), pages 1-48, November.
    2. Francq, Christian & Zakoïan, Jean-Michel, 2020. "Virtual Historical Simulation for estimating the conditional VaR of large portfolios," Journal of Econometrics, Elsevier, vol. 217(2), pages 356-380.
    3. Rombouts, Jeroen V.K. & Stentoft, Lars & Violante, Francesco, 2020. "Pricing individual stock options using both stock and market index information," Journal of Banking & Finance, Elsevier, vol. 111(C).
    4. Zhu, Pengfei & Tang, Yong & Wei, Yu & Dai, Yimin, 2019. "Portfolio strategy of International crude oil markets: A study based on multiwavelet denoising-integration MF-DCCA method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    5. Arnold Polanski & Evarist Stoja & Ching‐Wai (Jeremy) Chiu, 2021. "Tail risk interdependence," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(4), pages 5499-5511, October.
    6. Xu, Qifa & Chen, Lu & Jiang, Cuixia & Yu, Keming, 2020. "Mixed data sampling expectile regression with applications to measuring financial risk," Economic Modelling, Elsevier, vol. 91(C), pages 469-486.
    7. Zaichao Du & Pei Pei, 2020. "Backtesting portfolio value‐at‐risk with estimated portfolio weights," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(5), pages 605-619, September.
    8. Amiri , Hossein & Najafi Nejad , Mahmood & Mousavi , Seyede Mohadese, 2021. "Estimation of Value at Risk (VaR) Based On Lévy-GARCH Models: Evidence from Tehran Stock Exchange," Journal of Money and Economy, Monetary and Banking Research Institute, Central Bank of the Islamic Republic of Iran, vol. 16(2), pages 165-186, June.
    9. Samunderu, E. & Perret, J.K. & Geller, G., 2023. "The economic value rationale of fuel hedging: An empirical perspective from the global airline industry," Journal of Air Transport Management, Elsevier, vol. 106(C).

    More about this item

    Keywords

    Confidence intervals for VaR; Dynamic portfolio; Elliptical distribution; Filtered historical simulation; Minimum variance portfolio; Model risk; Multivariate GARCH;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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