Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors
AbstractWe 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
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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.
Dobrev∗ D, Nesmith TD, Oh DH. Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors. Journal of Risk and Financial Management. 2017; 10(1):5.Chicago/Turabian Style
Dobrev∗, Dobrislav; Nesmith, Travis D.; Oh, Dong H. 2017. "Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors." J. Risk Financial Manag. 10, no. 1: 5.
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