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Managing the risk based on entropic value-at-risk under a normal-Rayleigh distribution

Author

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  • Ahmed, Dilan
  • Soleymani, Fazlollah
  • Ullah, Malik Zaka
  • Hasan, Hataw

Abstract

Market observations basically reveal that the data do not follow a normal distribution and fat tails occur. On the other hand, the common measures of risk, like, value-at-risk (VaR) and conditional value-at-risk (CVaR) may not yield in reliable values in managing the risk of a portfolio under some conditions. To overcome these shortcomings, two ideas are furnished in this work. First, a mixture distribution is constructed based on the normal and Rayleigh distributions to provide fatter tails and to be more consistent on market data. And second, the entropic VaR (EVaR) is used to give reliable values for risk management. Finally, several simulation workouts on different stocks from real data are presented and compared to uphold the discussions of this work.

Suggested Citation

  • Ahmed, Dilan & Soleymani, Fazlollah & Ullah, Malik Zaka & Hasan, Hataw, 2021. "Managing the risk based on entropic value-at-risk under a normal-Rayleigh distribution," Applied Mathematics and Computation, Elsevier, vol. 402(C).
    • Handle: RePEc:eee:apmaco:v:402:y:2021:i:c:s0096300321001776
    DOI: 10.1016/j.amc.2021.126129
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    References listed on IDEAS

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    1. Ahmadi-Javid, Amir & Fallah-Tafti, Malihe, 2019. "Portfolio optimization with entropic value-at-risk," European Journal of Operational Research, Elsevier, vol. 279(1), pages 225-241.
    2. William T. Shaw, 2011. "Risk, VaR, CVaR and their associated Portfolio Optimizations when Asset Returns have a Multivariate Student T Distribution," Papers 1102.5665, arXiv.org.
    3. Leitao, Álvaro & Ortiz-Gracia, Luis, 2020. "Model-free computation of risk contributions in credit portfolios," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    6. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    7. Manfred Gilli & Evis këllezi, 2006. "An Application of Extreme Value Theory for Measuring Financial Risk," Computational Economics, Springer;Society for Computational Economics, vol. 27(2), pages 207-228, May.
    8. Steven Kou & Xianhua Peng, 2014. "Expected shortfall or median shortfall," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(01), pages 1-6.
    9. Matthias Fischer & Thorsten Moser & Marius Pfeuffer, 2018. "A Discussion on Recent Risk Measures with Application to Credit Risk: Calculating Risk Contributions and Identifying Risk Concentrations," Risks, MDPI, vol. 6(4), pages 1-28, December.
    10. Halkos, George E. & Tsirivis, Apostolos S., 2019. "Value-at-risk methodologies for effective energy portfolio risk management," Economic Analysis and Policy, Elsevier, vol. 62(C), pages 197-212.
    11. 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.
    12. Rezaul Karim & Pear Hossain & Sultana Begum & Forhad Hossain, 2011. "Rayleigh Mixture Distribution," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-17, November.
    13. Hamed Tabasi & Vahidreza Yousefi & Jolanta Tamošaitienė & Foroogh Ghasemi, 2019. "Estimating Conditional Value at Risk in the Tehran Stock Exchange Based on the Extreme Value Theory Using GARCH Models," Administrative Sciences, MDPI, vol. 9(2), pages 1-17, May.
    14. Pichler, Alois & Schlotter, Ruben, 2020. "Entropy based risk measures," European Journal of Operational Research, Elsevier, vol. 285(1), pages 223-236.
    15. Matthew Norton & Valentyn Khokhlov & Stan Uryasev, 2018. "Calculating CVaR and bPOE for Common Probability Distributions With Application to Portfolio Optimization and Density Estimation," Papers 1811.11301, arXiv.org, revised Feb 2019.
    16. Nicholas L. Georgakopoulos, 2018. "Illustrating Finance Policy with Mathematica," Quantitative Perspectives on Behavioral Economics and Finance, Palgrave Macmillan, number 978-3-319-95372-4, February.
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    Cited by:

    1. Wang, Gang-Jin & Zhu, Chun-Long, 2021. "BP-CVaR: A novel model of estimating CVaR with back propagation algorithm," Economics Letters, Elsevier, vol. 209(C).
    2. Malik Zaka Ullah & Fouad Othman Mallawi & Mir Asma & Stanford Shateyi, 2022. "On the Conditional Value at Risk Based on the Laplace Distribution with Application in GARCH Model," Mathematics, MDPI, vol. 10(16), pages 1-13, August.

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