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Estimation of Expected Shortfall Using Quantile Regression: A Comparison Study

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  • Eliana Christou

    (University of North Carolina at Charlotte)

  • Michael Grabchak

    (University of North Carolina at Charlotte)

Abstract

Expected Shortfall ( $$\mathrm {ES}$$ ES ) is one of the most heavily used measures of financial risk. It is defined as a scaled integral of the quantile of the profit-and-loss distribution up to a certainly confidence level. As such, quantile regression (QR) and the closely related expectile regression (ER) methods are natural techniques for estimating $$\mathrm {ES}$$ ES . In this paper, we survey QR and ER based estimators of ES and introduce several novel variants. We compare the performance of these methods through simulation and through a data analysis based on four major US market indices: the S&P 500 Index, the Russell 2000 Index, the Dow Jones Industrial Average, and the NASDAQ Composite Index. Our results suggest that QR and ER methods often work better than other, more standard, approaches.

Suggested Citation

  • Eliana Christou & Michael Grabchak, 2022. "Estimation of Expected Shortfall Using Quantile Regression: A Comparison Study," Computational Economics, Springer;Society for Computational Economics, vol. 60(2), pages 725-753, August.
    • Handle: RePEc:kap:compec:v:60:y:2022:i:2:d:10.1007_s10614-021-10164-z
    DOI: 10.1007/s10614-021-10164-z
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    References listed on IDEAS

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    1. James W. Taylor, 2008. "Using Exponentially Weighted Quantile Regression to Estimate Value at Risk and Expected Shortfall," Journal of Financial Econometrics, Oxford University Press, vol. 6(3), pages 382-406, Summer.
    2. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    3. Kong, Efang & Xia, Yingcun, 2012. "A Single-Index Quantile Regression Model And Its Estimation," Econometric Theory, Cambridge University Press, vol. 28(4), pages 730-768, August.
    4. Aigner, D J & Amemiya, Takeshi & Poirier, Dale J, 1976. "On the Estimation of Production Frontiers: Maximum Likelihood Estimation of the Parameters of a Discontinuous Density Function," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(2), pages 377-396, June.
    5. Saralees Nadarajah & Bo Zhang & Stephen Chan, 2014. "Estimation methods for expected shortfall," Quantitative Finance, Taylor & Francis Journals, vol. 14(2), pages 271-291, February.
    6. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    7. Koenker, Roger & Xiao, Zhijie, 2006. "Quantile Autoregression," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 980-990, September.
    8. Gneiting, Tilmann, 2011. "Making and Evaluating Point Forecasts," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 746-762.
    9. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    10. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    11. Wu, Tracy Z. & Yu, Keming & Yu, Yan, 2010. "Single-index quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1607-1621, August.
    12. Yan Fan & Wolfgang Karl Härdle & Weining Wang & Lixing Zhu, 2018. "Single-Index-Based CoVaR With Very High-Dimensional Covariates," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(2), pages 212-226, April.
    13. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    14. Eliana Christou & Michael Grabchak, 2019. "Estimation of value-at-risk using single index quantile regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(13), pages 2418-2433, October.
    15. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    16. James W. Taylor, 2008. "Estimating Value at Risk and Expected Shortfall Using Expectiles," Journal of Financial Econometrics, Oxford University Press, vol. 6(2), pages 231-252, Spring.
    Full references (including those not matched with items on IDEAS)

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