Accurate evaluation of expected shortfall for linear portfolios with elliptically distributed risk factors

Artikel

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Journal: Journal of Risk and Financial Management ; ISSN: 1911-8074 ; Volume: 10 ; Year: 2017 ; Issue: 1 ; Pages: 1-14 ; Basel: MDPI

Classification and Topics

• Classification: Management ; Specific Distributions; Specific Statistics ; Portfolio Choice; Investment Decisions
• Subject: expected shortfall ; elliptical distributions ; multivariate Student t distribution ; mixtures of elliptical distributions ; accurate closed-form expression

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Dobrev, Dobrislav ; Nesmith, Travis D. ; Oh, Dong Hwan
• Event: Veröffentlichung
• (who): MDPI
• (where): Basel
• (when): 2017

Further information

• DOI: doi:10.3390/jrfm10010005
• Handle: http://hdl.handle.net/10419/178585
• Last update: 10.03.2025, 11:43 AM CET