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Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors

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Academic Editors: Marc S. Paolella and Michael McAleer
J. Risk Financial Manag. 2017, 10(1), 5; https://doi.org/10.3390/jrfm10010005
Received: 31 July 2016 / Revised: 28 December 2016 / Accepted: 24 January 2017 / Published: 2 February 2017
(This article belongs to the Special Issue Advances in Modeling Value at Risk and Expected Shortfall)
We provide an accurate closed-form expression for the expected shortfall of linear portfolios with elliptically distributed risk factors. Our results aim to correct inaccuracies that originate in Kamdem (2005) and are present also in at least thirty other papers referencing it, including the recent survey by Nadarajah et al. (2014) on estimation methods for expected shortfall. In particular, we show that the correction we provide in the popular multivariate Student t setting eliminates understatement of expected shortfall by a factor varying from at least four to more than 100 across different tail quantiles and degrees of freedom. As such, the resulting economic impact in financial risk management applications could be significant. We further correct such errors encountered also in closely related results in Kamdem (2007 and 2009) for mixtures of elliptical distributions. More generally, our findings point to the extra scrutiny required when deploying new methods for expected shortfall estimation in practice. View Full-Text
Keywords: expectedshortfall; ellipticaldistributions; multivariateStudent t distribution; mixturesof elliptical distributions; accurate closed-form expression expectedshortfall; ellipticaldistributions; multivariateStudent t distribution; mixturesof elliptical distributions; accurate closed-form expression
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Dobrev∗, D.; Nesmith, T.D.; Oh, D.H. Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors. J. Risk Financial Manag. 2017, 10, 5.

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