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Adjusted Expected Shortfall

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  • Burzoni, Matteo
  • Munari, Cosimo
  • Wang, Ruodu

Abstract

We introduce and study the main properties of a class of convex risk measures that refine Expected Shortfall by simultaneously controlling the expected losses associated with different portions of the tail distribution. The corresponding adjusted Expected Shortfalls quantify risk as the minimum amount of capital that has to be raised and injected into a financial position X to ensure that Expected Shortfall ESp(X) does not exceed a pre-specified threshold g(p) for every probability level p∈[0,1]. Through the choice of the benchmark risk profile g one can tailor the risk assessment to the specific application of interest. We devote special attention to the study of risk profiles defined by the Expected Shortfall of a benchmark random loss, in which case our risk measures are intimately linked to second-order stochastic dominance.

Suggested Citation

  • Burzoni, Matteo & Munari, Cosimo & Wang, Ruodu, 2022. "Adjusted Expected Shortfall," Journal of Banking & Finance, Elsevier, vol. 134(C).
    • Handle: RePEc:eee:jbfina:v:134:y:2022:i:c:s0378426621002491
    DOI: 10.1016/j.jbankfin.2021.106297
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    Cited by:

    1. Jianming Xia, 2023. "Benchmark Beating with the Increasing Convex Order," Papers 2311.01692, arXiv.org.
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    4. Ardakani, Omid M., 2023. "Coherent measure of portfolio risk," Finance Research Letters, Elsevier, vol. 57(C).
    5. Max Nendel & Jan Streicher, 2023. "An axiomatic approach to default risk and model uncertainty in rating systems," Papers 2303.08217, arXiv.org, revised Sep 2023.
    6. Zaevski, Tsvetelin S. & Nedeltchev, Dragomir C., 2023. "From BASEL III to BASEL IV and beyond: Expected shortfall and expectile risk measures," International Review of Financial Analysis, Elsevier, vol. 87(C).
    7. Maria Arduca & Cosimo Munari, 2021. "Risk measures beyond frictionless markets," Papers 2111.08294, arXiv.org.
    8. Gómez, Fabio & Tang, Qihe & Tong, Zhiwei, 2022. "The gradient allocation principle based on the higher moment risk measure," Journal of Banking & Finance, Elsevier, vol. 143(C).
    9. Yan Fang & Jian Li & Yinglin Liu & Yunfan Zhao, 2023. "Semiparametric estimation of expected shortfall and its application in finance," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(4), pages 835-851, July.
    10. Zou, Zhenfeng & Wu, Qinyu & Xia, Zichao & Hu, Taizhong, 2023. "Adjusted Rényi entropic Value-at-Risk," European Journal of Operational Research, Elsevier, vol. 306(1), pages 255-268.
    11. Xia Han & Ruodu Wang & Qinyu Wu, 2023. "Monotonic mean-deviation risk measures," Papers 2312.01034, arXiv.org.

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