Please use this identifier to cite or link to this item: http://hdl.handle.net/10419/178585
Authors: 
Dobrev, Dobrislav
Nesmith, Travis D.
Oh, Dong Hwan
Year of Publication: 
2017
Citation: 
[Journal:] Journal of Risk and Financial Management [ISSN:] 1911-8074 [Volume:] 10 [Year:] 2017 [Issue:] 1 [Pages:] 1-14
Abstract: 
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.
Subjects: 
expected shortfall
elliptical distributions
multivariate Student t distribution
mixtures of elliptical distributions
accurate closed-form expression
JEL: 
C46
G11
Persistent Identifier of the first edition: 
Creative Commons License: 
https://creativecommons.org/licenses/by/4.0/
Document Type: 
Article
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