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Fuzzy value-at-risk and expected shortfall for portfolios with heavy-tailed returns

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  • Mbairadjim Moussa, A.
  • Sadefo Kamdem, J.
  • Terraza, M.

Abstract

This paper is concerned with linear portfolio value-at-risk (VaR) and expected shortfall (ES) computation when the portfolio risk factors are leptokurtic, imprecise and/or vague. Following Yoshida (2009), the risk factors are modeled as fuzzy random variables in order to handle both their random variability and their vagueness. We discuss and extend the Yoshida model to some non-Gaussian distributions and provide associated ES. Secondly, assuming that the risk factors' degree of imprecision changes over time, original fuzzy portfolio VaR and ES models are introduced. For a given subjectivity level fixed by the investor, these models allow the computation of a pessimistic and an optimistic estimation of the value-at-risk and of the expected shortfall. Finally, some empirical examples carried out on three portfolios constituted by some chosen French stocks, show the effectiveness of the proposed methods.

Suggested Citation

  • Mbairadjim Moussa, A. & Sadefo Kamdem, J. & Terraza, M., 2014. "Fuzzy value-at-risk and expected shortfall for portfolios with heavy-tailed returns," Economic Modelling, Elsevier, vol. 39(C), pages 247-256.
    • Handle: RePEc:eee:ecmode:v:39:y:2014:i:c:p:247-256
    DOI: 10.1016/j.econmod.2014.02.036
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    10. Sadefo Kamdem, J., 2009. "[Delta]-VaR and [Delta]-TVaR for portfolios with mixture of elliptic distributions risk factors and DCC," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 325-336, June.
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    Cited by:

    1. Pablo J. Villacorta & Laura González-Vila Puchades & Jorge de Andrés-Sánchez, 2021. "Fuzzy Markovian Bonus-Malus Systems in Non-Life Insurance," Mathematics, MDPI, vol. 9(4), pages 1-23, February.
    2. Evangelos Vasileiou, 2022. "Inaccurate Value at Risk Estimations: Bad Modeling or Inappropriate Data?," Computational Economics, Springer;Society for Computational Economics, vol. 59(3), pages 1155-1171, March.
    3. Dobrislav Dobrev∗ & Travis D. Nesmith & Dong Hwan Oh, 2017. "Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors," JRFM, MDPI, vol. 10(1), pages 1-14, February.
    4. Jaworski, Piotr & Liberadzki, Kamil & Liberadzki, Marcin, 2017. "How does issuing contingent convertible bonds improve bank's solvency? A Value-at-Risk and Expected Shortfall approach," Economic Modelling, Elsevier, vol. 60(C), pages 162-168.
    5. Jules Sadefo Kamdem & Babel Raïssa Guemdjo Kamdem & Carlos Ougouyandjou, 2021. "S-ARMA Model and Wold Decomposition for Covariance Stationary Interval-Valued Time Series Processes," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 17(01), pages 191-213, March.
    6. Babel Raïssa Guemdjo Kamdem & Jules Sadefo-Kamdem & Carlos Ougouyandjou, 2020. "On Random Extended Intervals and their ARMA Processes," Working Papers hal-03169516, HAL.
    7. Alfred Mbairadjim Moussa & Jules Sadefo Kamdem, 2022. "A fuzzy multifactor asset pricing model," Annals of Operations Research, Springer, vol. 313(2), pages 1221-1241, June.
    8. Zhao, Lu-Tao & Wang, Dai-Song & Ren, Zhong-Yuan, 2024. "The impact of joint events on oil price volatility: Evidence from a dynamic graphical news analysis model," Economic Modelling, Elsevier, vol. 130(C).
    9. Qasim Noor & Tabasam Rashid & Syed Muhammad Husnine, 2021. "An extended TDM method under probabilistic interval-valued hesitant fuzzy environment for stock selection," PLOS ONE, Public Library of Science, vol. 16(5), pages 1-24, May.

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