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

A. Mbairadjim Moussa, Jules Sadefo Kamdem and M. Terraza

Economic Modelling, 2014, vol. 39, issue C, 247-256

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.

Keywords: Risk management; Value-at-risk; Expected shortfall; Fuzzy random variables; Heavy-tailed distributions (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecmode:v:39:y:2014:i:c:p:247-256

DOI: 10.1016/j.econmod.2014.02.036

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