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Subadditivity Re–Examined: the Case for Value-at-Risk

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  • Casper G. de Vries
  • Gennady Samorodnitsky
  • Bjørn N. Jorgensen
  • Sarma Mandira
  • Jon Danielsson

    ()

Abstract

This paper explores the potential for violations of VaR subadditivity both theoretically and by simulations, and finds that for most practical applications VaR is subadditive. Hence, there is no reason to choose a more complicated risk measure than VaR, solely for reasons of coherence.

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File URL: http://www.lse.ac.uk/fmg/workingPapers/discussionPapers/fmgdps/dp549.pdf
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Paper provided by Financial Markets Group in its series FMG Discussion Papers with number dp549.

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Date of creation: Nov 2005
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Handle: RePEc:fmg:fmgdps:dp549

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  1. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  2. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
  3. Jón Daníelsson & Casper G. de Vries, 1998. "Value-at-Risk and Extreme Returns," Tinbergen Institute Discussion Papers 98-017/2, Tinbergen Institute.
  4. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  5. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
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Cited by:
  1. Jon Danielsson & Jean-Pierre Zigrand & Bjørn N. Jorgensen & Mandira Sarma & C. G. de Vries, 2006. "Consistent measures of risk," LSE Research Online Documents on Economics 24517, London School of Economics and Political Science, LSE Library.
  2. Embrechts, Paul & Neslehová, Johanna & Wüthrich, Mario V., 2009. "Additivity properties for Value-at-Risk under Archimedean dependence and heavy-tailedness," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 164-169, April.
  3. Wagner P. Gaglianone & Luiz Renato Lima & Oliver Linton, 2008. "Evaluating Value-at-Risk Models via Quantile Regressions," Working Papers Series 161, Central Bank of Brazil, Research Department.
  4. Dominique Guegan & Bertrand K Hassani, 2014. "Distortion Risk Measures or the Transformation of Unimodal Distributions into Multimodal Functions," Documents de travail du Centre d'Economie de la Sorbonne 14008, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  5. Dirk Tasche, 2005. "Measuring sectoral diversification in an asymptotic multi-factor framework," Papers physics/0505142, arXiv.org, revised Jul 2006.
  6. Marie Kratz, 2013. "There is a VaR beyond usual approximations," Papers 1311.0270, arXiv.org.
  7. Georg Mainik & Ludger Rüschendorf, 2010. "On optimal portfolio diversification with respect to extreme risks," Finance and Stochastics, Springer, vol. 14(4), pages 593-623, December.
  8. Marie Kratz, 2013. "There is a VaR Beyond Usual Approximations," Post-Print hal-00880258, HAL.
  9. Bakshi, Gurdip & Panayotov, George, 2010. "First-passage probability, jump models, and intra-horizon risk," Journal of Financial Economics, Elsevier, vol. 95(1), pages 20-40, January.
  10. Genest, Christian & Gerber, Hans U. & Goovaerts, Marc J. & Laeven, Roger J.A., 2009. "Editorial to the special issue on modeling and measurement of multivariate risk in insurance and finance," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 143-145, April.
  11. Daníelsson, Jón & Jorgensen, Bjørn N. & Samorodnitsky, Gennady & Sarma, Mandira & de Vries, Casper G., 2013. "Fat tails, VaR and subadditivity," Journal of Econometrics, Elsevier, vol. 172(2), pages 283-291.
  12. Joaquin, Domingo Castelo, 2009. "Value at risk: Is a theoretically consistent axiomatic formulation possible?," The Quarterly Review of Economics and Finance, Elsevier, vol. 49(2), pages 725-729, May.
  13. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2012. "When more is less: Using multiple constraints to reduce tail risk," Journal of Banking & Finance, Elsevier, vol. 36(10), pages 2693-2716.
  14. Jaume Belles-Sampera & Montserrat Guillén & Miguel Santolino, 2013. "“Beyond Value-at-Risk: GlueVaR Distortion Risk Measures”," IREA Working Papers 201302, University of Barcelona, Research Institute of Applied Economics, revised Feb 2013.
  15. Kratz , Marie, 2013. "There is a VaR Beyond Usual Approximations," ESSEC Working Papers WP1317, ESSEC Research Center, ESSEC Business School.

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