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Proper Conditioning for Coherent VaR in Portfolio Management

Author

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  • René Garcia

    () (Département de Sciences Économiques, CIREQ, and CIRANO, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, Québec, Canada H3C 3J7)

  • Éric Renault

    () (Department of Economics, University of North Carolina, Chapel Hill, North Carolina 27599, CIRANO, and CIREQ)

  • Georges Tsafack

    () (Département de Sciences Économiques, CIREQ, and CIRANO, Université de Montréal, C.P. 6128, Succ. Centre-Ville, Montréal, Québec, Canada H3C 3J7)

Abstract

Value at risk (VaR) is a central concept in risk management. As stressed by Artzner et al. (1999, Coherent measures of risk, Math. Finance 9(3) 203-228), VaR may not possess the subadditivity property required to be a coherent measure of risk. The key idea of this paper is that, when tail thickness is responsible for violation of subadditivity, eliciting proper conditioning information may restore VaR rationale for decentralized risk management. The argument is threefold. First, since individual traders are hired because they possess a richer information on their specific market segment than senior management, they just have to follow consistently the prudential targets set by senior management to ensure that decentralized VaR control will work in a coherent way. The intuition is that if one could build a fictitious conditioning information set merging all individual pieces of information, it would be rich enough to restore VaR subadditivity. Second, in this decentralization context, we show that if senior management has access ex post to the portfolio shares of the individual traders, it amounts to recovering some of their private information. These shares can be used to improve backtesting to check that the prudential targets have been enforced by the traders. Finally, we stress that tail thickness required to violate subadditivity, even for small probabilities, remains an extreme situation because it corresponds to such poor conditioning information that expected loss appears to be infinite. We then conclude that lack of coherence of decentralized VaR management, that is VaR nonsubadditivity at the richest level of information, should be an exception rather than a rule.

Suggested Citation

  • René Garcia & Éric Renault & Georges Tsafack, 2007. "Proper Conditioning for Coherent VaR in Portfolio Management," Management Science, INFORMS, vol. 53(3), pages 483-494, March.
  • Handle: RePEc:inm:ormnsc:v:53:y:2007:i:3:p:483-494
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    File URL: http://dx.doi.org/10.1287/mnsc.1060.0632
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    References listed on IDEAS

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    Cited by:

    1. Almeida, Caio & Vicente, José, 2009. "Are interest rate options important for the assessment of interest rate risk?," Journal of Banking & Finance, Elsevier, vol. 33(8), pages 1376-1387, August.
    2. Steven Kou & Xianhua Peng, 2014. "On the Measurement of Economic Tail Risk," Papers 1401.4787, arXiv.org, revised Aug 2015.
    3. Borgonovo, Emanuele & Gatti, Stefano, 2013. "Risk analysis with contractual default. Does covenant breach matter?," European Journal of Operational Research, Elsevier, vol. 230(2), pages 431-443.
    4. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2012. "Bank regulation and stability: An examination of the Basel market risk framework," Discussion Papers 09/2012, Deutsche Bundesbank.
    5. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2013. "A comparison of the original and revised Basel market risk frameworks for regulating bank capital," Journal of Economic Behavior & Organization, Elsevier, vol. 85(C), pages 249-268.
    6. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, Elsevier.
    7. 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.
    8. Hill, Jonathan B. & Prokhorov, Artem, 2016. "GEL estimation for heavy-tailed GARCH models with robust empirical likelihood inference," Journal of Econometrics, Elsevier, vol. 190(1), pages 18-45.
    9. Nikolaus Hautsch & Julia Schaumburg & Melanie Schienle, 2015. "Financial Network Systemic Risk Contributions," Review of Finance, European Finance Association, pages 685-738.
    10. Al Janabi, Mazin A.M. & Arreola Hernandez, Jose & Berger, Theo & Nguyen, Duc Khuong, 2017. "Multivariate dependence and portfolio optimization algorithms under illiquid market scenarios," European Journal of Operational Research, Elsevier, vol. 259(3), pages 1121-1131.
    11. Alexander, Gordon J. & Baptista, Alexandre M. & Yan, Shu, 2014. "Bank regulation and international financial stability: A case against the 2006 Basel framework for controlling tail risk in trading books," Journal of International Money and Finance, Elsevier, vol. 43(C), pages 107-130.
    12. Ibragimov, Rustam & Prokhorov, Artem, 2016. "Heavy tails and copulas: Limits of diversification revisited," Economics Letters, Elsevier, vol. 149(C), pages 102-107.
    13. Michel Verlaine, 2010. "Risk Governance for funds," Cahiers du CEREFIGE 1003, CEREFIGE (Centre Europeen de Recherche en Economie Financiere et Gestion des Entreprises), Universite de Lorraine, revised 2010.
    14. repec:pal:jorsoc:v:61:y:2010:i:2:d:10.1057_jors.2008.144 is not listed on IDEAS
    15. Balbás, Alejandro, 2008. "Capital requirements: Are they the best solution?," DEE - Working Papers. Business Economics. WB wb087114, Universidad Carlos III de Madrid. Departamento de Economía de la Empresa.
    16. Michael Grabchak, 2014. "Does value-at-risk encourage diversification when losses follow tempered stable or more general Lévy processes?," Annals of Finance, Springer, vol. 10(4), pages 553-568, November.
    17. 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.

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