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

Dobrislav Dobrev∗, Travis Nesmith and Dong Hwan Oh
Additional contact information
Dobrislav Dobrev∗: Board of Governors of the Federal Reserve System, 20th St. and Constitution Ave. N.W., Washington, DC 20551, USA
Dong Hwan Oh: Board of Governors of the Federal Reserve System, 20th St. and Constitution Ave. N.W., Washington, DC 20551, USA

JRFM, 2017, vol. 10, issue 1, 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 ?nancial risk management applications could be signi?cant. We further correct such errors encountered also in closely related results in Kamdem (2007 and 2009) for mixtures of elliptical distributions. More generally, our ?ndings point to the extra scrutiny required when deploying new methods for expected shortfall estimation in practice.

Keywords: expectedshortfall; ellipticaldistributions; multivariateStudent t distribution; mixturesof elliptical distributions; accurate closed-form expression (search for similar items in EconPapers)
JEL-codes: C E F2 F3 G (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
https://www.mdpi.com/1911-8074/10/1/5/pdf (application/pdf)
https://www.mdpi.com/1911-8074/10/1/5/ (text/html)

Related works:
Working Paper: Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors (2016)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jjrfmx:v:10:y:2017:i:1:p:5-:d:89239

Access Statistics for this article

JRFM is currently edited by Ms. Chelthy Cheng

More articles in JRFM from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().