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Backtesting Marginal Expected Shortfall and Related Systemic Risk Measures

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  • Denisa Banulescu-Radu

    (Laboratoire d'Economie d'Orleans, University of Orléans, 45067 Orléans, France)

  • Christophe Hurlin

    (Laboratoire d'Economie d'Orleans, University of Orléans, 45067 Orléans, France)

  • Jérémy Leymarie

    (Data Science, Economics and Finance Faculty, EDHEC Business School, 59100 Roubaix, France)

  • Olivier Scaillet

    (Geneva School of Economics and Management and Geneva Finance Research Institute, University of Geneva, 1211 Geneva, Switzerland; Swiss Finance Institute, 8006 Zürich, Switzerland)

Abstract

This paper proposes an original approach for backtesting systemic risk measures. This backtesting approach makes it possible to assess the systemic risk measure forecasts used to identify the financial institutions that contribute the most to the overall risk in the financial system. Our procedure is based on simple tests similar to those generally used to backtest the standard market risk measures such as value-at-risk or expected shortfall. We introduce a concept of violation associated with the marginal expected shortfall (MES), and we define unconditional coverage and independence tests for these violations. We can generalize these tests to any MES-based systemic risk measures such as the systemic expected shortfall (SES), the systemic risk measure (SRISK), or the delta conditional value-at-risk ( Δ CoVaR). We study their asymptotic properties in the presence of estimation risk and investigate their finite sample performance via Monte Carlo simulations. An empirical application to a panel of U.S. financial institutions is conducted to assess the validity of MES, SRISK, and Δ CoVaR forecasts issued from a bivariate GARCH model with a dynamic conditional correlation structure. Our results show that this model provides valid forecasts for MES and SRISK when considering a medium-term horizon. Finally, we propose an early warning system indicator for future systemic crises deduced from these backtests. Our indicator quantifies how much is the measurement error issued by a systemic risk forecast at a given point in time which can serve for the early detection of global market reversals.

Suggested Citation

  • Denisa Banulescu-Radu & Christophe Hurlin & Jérémy Leymarie & Olivier Scaillet, 2021. "Backtesting Marginal Expected Shortfall and Related Systemic Risk Measures," Management Science, INFORMS, vol. 67(9), pages 5730-5754, September.
    • Handle: RePEc:inm:ormnsc:v:67:y:2021:i:9:p:5730-5754
    DOI: 10.1287/mnsc.2020.3751
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    Cited by:

    1. Chen, Qihao & Huang, Zhuo & Liang, Fang, 2023. "Measuring systemic risk with high-frequency data: A realized GARCH approach," Finance Research Letters, Elsevier, vol. 54(C).
    2. Tong Pu & Yifei Zhang & Yiying Zhang, 2024. "On Joint Marginal Expected Shortfall and Associated Contribution Risk Measures," Papers 2405.07549, arXiv.org.
    3. Sullivan Hu'e & Christophe Hurlin & Yang Lu, 2024. "Backtesting Expected Shortfall: Accounting for both duration and severity with bivariate orthogonal polynomials," Papers 2405.02012, arXiv.org, revised May 2024.
    4. Michele Leonardo Bianchi & Giovanni De Luca & Giorgia Rivieccio, 2020. "CoVaR with volatility clustering, heavy tails and non-linear dependence," Papers 2009.10764, arXiv.org.
    5. Adasi Manu, Sylvester & Qi, Yaxuan, 2023. "CEO social connections and bank systemic risk: The “dark side” of social networks," Journal of Banking & Finance, Elsevier, vol. 156(C).
    6. Qin, Xiao & Zhou, Chen, 2021. "Systemic risk allocation using the asymptotic marginal expected shortfall," Journal of Banking & Finance, Elsevier, vol. 126(C).
    7. Gribkova, N.V. & Su, J. & Zitikis, R., 2022. "Inference for the tail conditional allocation: Large sample properties, insurance risk assessment, and compound sums of concomitants," Insurance: Mathematics and Economics, Elsevier, vol. 107(C), pages 199-222.
    8. Tobias Fissler & Yannick Hoga, 2021. "Backtesting Systemic Risk Forecasts using Multi-Objective Elicitability," Papers 2104.10673, arXiv.org, revised Feb 2022.
    9. Yannick Hoga & Matei Demetrescu, 2023. "Monitoring Value-at-Risk and Expected Shortfall Forecasts," Management Science, INFORMS, vol. 69(5), pages 2954-2971, May.
    10. Le, Trung H., 2020. "Forecasting value at risk and expected shortfall with mixed data sampling," International Journal of Forecasting, Elsevier, vol. 36(4), pages 1362-1379.
    11. Loïc Cantin & Christian Francq & Jean-Michel Zakoïan, 2022. "Estimating dynamic systemic risk measures," Working Papers 2022-11, Center for Research in Economics and Statistics.
    12. Colonnello, Stefano & Koetter, Michael & Wagner, Konstantin, 2023. "Compensation regulation in banking: Executive director behavior and bank performance after the EU bonus cap," Journal of Accounting and Economics, Elsevier, vol. 76(1).
    13. Ye, Wuyi & Zhou, Yi & Chen, Pengzhan & Wu, Bin, 2024. "A simulation-based method for estimating systemic risk measures," European Journal of Operational Research, Elsevier, vol. 313(1), pages 312-324.
    14. Fang, Sheng & Cao, Guangxi & Egan, Paul, 2023. "Forecasting and backtesting systemic risk in the cryptocurrency market," Finance Research Letters, Elsevier, vol. 54(C).
    15. Bianchi, Michele Leonardo & De Luca, Giovanni & Rivieccio, Giorgia, 2023. "Non-Gaussian models for CoVaR estimation," International Journal of Forecasting, Elsevier, vol. 39(1), pages 391-404.

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    More about this item

    Keywords

    backtesting; banking regulation; hypothesis testing; risk management; systemic risk;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G28 - Financial Economics - - Financial Institutions and Services - - - Government Policy and Regulation

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