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Mathematical Definition, Mapping, and Detection of (Anti)Fragility

  • Nassim N. Taleb
  • Raphael Douady
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    We provide a mathematical definition of fragility and antifragility as negative or positive sensitivity to a semi-measure of dispersion and volatility (a variant of negative or positive "vega") and examine the link to nonlinear effects. We integrate model error (and biases) into the fragile or antifragile context. Unlike risk, which is linked to psychological notions such as subjective preferences (hence cannot apply to a coffee cup) we offer a measure that is universal and concerns any object that has a probability distribution (whether such distribution is known or, critically, unknown). We propose a detection of fragility, robustness, and antifragility using a single "fast-and-frugal", model-free, probability free heuristic that also picks up exposure to model error. The heuristic lends itself to immediate implementation, and uncovers hidden risks related to company size, forecasting problems, and bank tail exposures (it explains the forecasting biases). While simple to implement, it outperforms stress testing and other such methods such as Value-at-Risk.

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    File URL: http://arxiv.org/pdf/1208.1189
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    Paper provided by arXiv.org in its series Papers with number 1208.1189.

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    Date of creation: Aug 2012
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    Handle: RePEc:arx:papers:1208.1189
    Contact details of provider: Web page: http://arxiv.org/

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    1. Makridakis, Spyros & Hibon, Michele, 2000. "The M3-Competition: results, conclusions and implications," International Journal of Forecasting, Elsevier, vol. 16(4), pages 451-476.
    2. Haug, Espen Gaarder & Taleb, Nassim Nicholas, 2011. "Option traders use (very) sophisticated heuristics, never the Black-Scholes-Merton formula," Journal of Economic Behavior & Organization, Elsevier, vol. 77(2), pages 97-106, February.
    3. Rothschild, Michael & Stiglitz, Joseph E., 1971. "Increasing risk II: Its economic consequences," Journal of Economic Theory, Elsevier, vol. 3(1), pages 66-84, March.
    4. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    5. Taleb, Nassim Nicholas, 2009. "Errors, robustness, and the fourth quadrant," International Journal of Forecasting, Elsevier, vol. 25(4), pages 744-759, October.
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