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Proper Conditioning for Coherent VaR in Portfolio Management

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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.

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Bibliographic Info

Article provided by INFORMS in its journal Management Science.

Volume (Year): 53 (2007)
Issue (Month): 3 (March)
Pages: 483-494

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Handle: RePEc:inm:ormnsc:v:53:y:2007:i:3:p:483-494

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Keywords: value at risk; decentralized risk management; coherent measures of risk; subadditivity of VaR; heavy-tail distributions; stable distributions;

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Cited by:
  1. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2011. "Financial Risk Measurement for Financial Risk Management," PIER Working Paper Archive 11-037, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
  2. Caio Almeida & José Vicente, 2009. "Are Interest Rate Options Important for the Assessment of Interest Rate Risk?," Working Papers Series 179, Central Bank of Brazil, Research Department.
  3. 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, Research Centre.
  4. 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.
  5. Nikolaus Hautsch & Julia Schaumburg & Melanie Schienle, 2012. "Financial Network Systemic Risk Contributions," SFB 649 Discussion Papers SFB649DP2012-053, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  6. 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.
  7. 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.
  8. Steven Kou & Xianhua Peng, 2014. "On the Measurement of Economic Tail Risk," Papers 1401.4787, arXiv.org, revised Feb 2014.
  9. 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.
  10. 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.
  11. Alejandro Balbas, 2008. "Capital requirements: Are they the best solution?," Business Economics Working Papers wb087114, Universidad Carlos III, Departamento de Economía de la Empresa.

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