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Destabilizing properties of a VaR or probability-of-ruin constraint when variances may be infinite


  • Eisenberg, Larry


Despite the use of VaR as a means to control risk, regulations that constrain VaR can have an effect opposite of their intent: to increase risk taking by firms that are doing poorly. Hence VaR constraint regulations can have a destabilizing effect on the financial system. A VaR constraint on the probability that future firm equity value will be less than a floor is a constraint on the probability-of-ruin when the floor is zero. The marginal price of risk with this constraint is coherent and also additive. For a wide class of distributions, the firm--when it is doing poorly--may pay a premium for a lottery that will increase the risk of its portfolio and the opposite when the firm is doing well.

Suggested Citation

  • Eisenberg, Larry, 2011. "Destabilizing properties of a VaR or probability-of-ruin constraint when variances may be infinite," Journal of Financial Stability, Elsevier, vol. 7(1), pages 10-18, January.
  • Handle: RePEc:eee:finsta:v:7:y:2011:i:1:p:10-18

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    References listed on IDEAS

    1. Amir Dembo & Jean-Dominique Deuschel & Darrell Duffie, 2004. "Large portfolio losses," Finance and Stochastics, Springer, vol. 8(1), pages 3-16, January.
    2. Gabaix, Xavier & Gopikrishnan, Parameswaran & Plerou, Vasiliki & Stanley, H.Eugene, 2003. "Understanding the cubic and half-cubic laws of financial fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 1-5.
    3. Larry Eisenberg & Thomas H. Noe, 2001. "Systemic Risk in Financial Systems," Management Science, INFORMS, vol. 47(2), pages 236-249, February.
    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. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78 World Scientific Publishing Co. Pte. Ltd..
    6. R. Jarrow & A. Purnanandam, 2007. "The valuation of a firm’s investment opportunities: a reduced form credit risk perspective," Review of Derivatives Research, Springer, vol. 10(1), pages 39-58, January.
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