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Proper Conditioning for Coherent VaR in Portfolio Management

  • 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)

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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File URL: http://dx.doi.org/10.1287/mnsc.1060.0632
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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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  1. Rustam Ibragimov, 2004. "Shifting paradigms: on the robustness of economic models to heavy-tailedness assumptions," Econometric Society 2004 Latin American Meetings 105, Econometric Society.
  2. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
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  4. Engle, Robert F & Manganelli, Simone, 1999. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," University of California at San Diego, Economics Working Paper Series qt06m3d6nv, Department of Economics, UC San Diego.
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  7. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January.
  8. Ortobelli, Sergio & Rachev, Svetlozar & Schwartz, Eduardo, 2000. "The Problem of Optimal Asset Allocation with Stable Distributed Returns," University of California at Los Angeles, Anderson Graduate School of Management qt3zd6q86c, Anderson Graduate School of Management, UCLA.
  9. Mittnik, Stefan & Paolella, Marc S. & Rachev, Svetlozar T., 2000. "Diagnosing and treating the fat tails in financial returns data," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 389-416, November.
  10. Merton, Robert C., 1987. "A simple model of capital market equilibrium with incomplete information," Working papers 1869-87., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  11. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
  12. Gordon J. Alexander & Alexandre M. Baptista, 2004. "A Comparison of VaR and CVaR Constraints on Portfolio Selection with the Mean-Variance Model," Management Science, INFORMS, vol. 50(9), pages 1261-1273, September.
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  14. repec:nys:sunysb:93-02 is not listed on IDEAS
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