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

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...

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Main Authors: Dobrislav Dobrev∗, Travis D. Nesmith, Dong Hwan Oh
Format: Article
Language:English
Published: MDPI AG 2017-02-01
Series:Journal of Risk and Financial Management
Subjects:
Online Access:http://www.mdpi.com/1911-8074/10/1/5
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spelling doaj-d6f82c7969e2449480597832c3665d3e2020-11-24T22:16:58ZengMDPI AGJournal of Risk and Financial Management1911-80742017-02-01101510.3390/jrfm10010005jrfm10010005Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk FactorsDobrislav Dobrev∗0Travis D. Nesmith1Dong Hwan Oh2Board of Governors of the Federal Reserve System, 20th St. and Constitution Ave. N.W., Washington, DC 20551, USABoard of Governors of the Federal Reserve System, 20th St. and Constitution Ave. N.W., Washington, DC 20551, USABoard of Governors of the Federal Reserve System, 20th St. and Constitution Ave. N.W., Washington, DC 20551, USAWe 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.http://www.mdpi.com/1911-8074/10/1/5expectedshortfallellipticaldistributionsmultivariateStudent t distributionmixturesof elliptical distributionsaccurate closed-form expression
collection DOAJ
language English
format Article
sources DOAJ
author Dobrislav Dobrev∗
Travis D. Nesmith
Dong Hwan Oh
spellingShingle Dobrislav Dobrev∗
Travis D. Nesmith
Dong Hwan Oh
Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors
Journal of Risk and Financial Management
expectedshortfall
ellipticaldistributions
multivariateStudent t distribution
mixturesof elliptical distributions
accurate closed-form expression
author_facet Dobrislav Dobrev∗
Travis D. Nesmith
Dong Hwan Oh
author_sort Dobrislav Dobrev∗
title Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors
title_short Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors
title_full Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors
title_fullStr Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors
title_full_unstemmed Accurate Evaluation of Expected Shortfall for Linear Portfolios with Elliptically Distributed Risk Factors
title_sort accurate evaluation of expected shortfall for linear portfolios with elliptically distributed risk factors
publisher MDPI AG
series Journal of Risk and Financial Management
issn 1911-8074
publishDate 2017-02-01
description 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.
topic expectedshortfall
ellipticaldistributions
multivariateStudent t distribution
mixturesof elliptical distributions
accurate closed-form expression
url http://www.mdpi.com/1911-8074/10/1/5
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AT donghwanoh accurateevaluationofexpectedshortfallforlinearportfolioswithellipticallydistributedriskfactors
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