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Consistent measures of risk

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  • Danielsson, Jon
  • Zigrand, Jean-Pierre
  • Jorgensen, Bjørn N.
  • Sarma, Mandira
  • de Vries, C. G.

Abstract

In this paper we compare overall as well as downside risk measures with respect to the criteria of first and second order stochastic dominance. While the downside risk measures, with the exception of tail conditional expectation, are consistent with first order stochastic dominance, overall risk measures are not, even if we restrict ourselves to two-parameter distributions. Most common risk measures preserve consistent preference orderings between prospects under the second order stochastic dominance rule, although for some of the downside risk measures such consistency holds deep enough in the tail only. In fact, the partial order induced by many risk measures is equivalent to sosd. Tail conditional expectation is not consistent with respect to second order stochastic dominance.

Suggested Citation

  • Danielsson, Jon & Zigrand, Jean-Pierre & Jorgensen, Bjørn N. & Sarma, Mandira & de Vries, C. G., 2006. "Consistent measures of risk," LSE Research Online Documents on Economics 24517, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:24517
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    References listed on IDEAS

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    3. Belhajjam, A. & Belbachir, M. & El Ouardirhi, S., 2017. "Robust multivairiate extreme value at risk allocation," Finance Research Letters, Elsevier, vol. 23(C), pages 1-11.

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    More about this item

    Keywords

    stochastic dominance; risk measures; preference ordering; utility theory;
    All these keywords.

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G00 - Financial Economics - - General - - - General

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