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On the Measurement of Economic Tail Risk

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  • Steven Kou
  • Xianhua Peng
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    Abstract

    This paper attempts to provide a decision-theoretic foundation for the measurement of economic tail risk, which is not only closely related to utility theory but also relevant to statistical model uncertainty. The main result is that the only tail risk measure that satisfies a set of economic axioms proposed by Schmeidler (1989, Econometrica) and the statistical property of elicitability (i.e. there exists an objective function such that minimizing the expected objective function yields the risk measure; see Gneiting (2011, J. Amer. Stat. Assoc.)) is median shortfall, which is the median of tail loss distribution. Elicitability is important for backtesting. Median shortfall has a desirable property of distributional robustness with respect to model misspecification. We also extend the result to address model uncertainty by incorporating multiple scenarios. As an application, we argue that median shortfall is a better alternative than expected shortfall for setting capital requirements in Basel Accords.

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    File URL: http://arxiv.org/pdf/1401.4787
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1401.4787.

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    Date of creation: Jan 2014
    Date of revision: Feb 2014
    Handle: RePEc:arx:papers:1401.4787

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    Web page: http://arxiv.org/

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