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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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 |
work_keys_str_mv |
AT dobrislavdobrev accurateevaluationofexpectedshortfallforlinearportfolioswithellipticallydistributedriskfactors AT travisdnesmith accurateevaluationofexpectedshortfallforlinearportfolioswithellipticallydistributedriskfactors AT donghwanoh accurateevaluationofexpectedshortfallforlinearportfolioswithellipticallydistributedriskfactors |
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1725787314809995264 |