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Consistent Measures of Risk

Author

Listed:
  • Casper G. de Vries
  • Mandira Sarma
  • Bjørn N. Jorgensen
  • Jean-Pierre Zigrand

    ()

  • Jon Danielsson

    ()

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. Infact, 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. 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. Infact, 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.KEY WORDS: stochastic dominance, risk measures, preference ordering,utility theoryJEL Classification: D81, G00, G11

Suggested Citation

  • Casper G. de Vries & Mandira Sarma & Bjørn N. Jorgensen & Jean-Pierre Zigrand & Jon Danielsson, 2006. "Consistent Measures of Risk," FMG Discussion Papers dp565, Financial Markets Group.
  • Handle: RePEc:fmg:fmgdps:dp565
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    References listed on IDEAS

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    1. Kaplanski, Guy & Kroll, Yoram, 2002. "VaR Risk Measures versus Traditional Risk Measures: an Analysis and Survey," MPRA Paper 80070, University Library of Munich, Germany.
    2. Bawa, Vijay S., 1975. "Optimal rules for ordering uncertain prospects," Journal of Financial Economics, Elsevier, vol. 2(1), pages 95-121, March.
    3. Casper G. de Vries & Gennady Samorodnitsky & Bjørn N. Jorgensen & Sarma Mandira & Jon Danielsson, 2005. "Subadditivity Re–Examined: the Case for Value-at-Risk," FMG Discussion Papers dp549, Financial Markets Group.
    4. De Giorgi, Enrico, 2005. "Reward-risk portfolio selection and stochastic dominance," Journal of Banking & Finance, Elsevier, vol. 29(4), pages 895-926, April.
    5. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-126, March.
    6. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    7. G. Hanoch & H. Levy, 1969. "The Efficiency Analysis of Choices Involving Risk," Review of Economic Studies, Oxford University Press, vol. 36(3), pages 335-346.
    8. Philippe Artzner & Freddy Delbaen & Jean-Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228.
    9. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    10. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March.
    11. Carlo Acerbi & Claudio Nordio & Carlo Sirtori, 2001. "Expected Shortfall as a Tool for Financial Risk Management," Papers cond-mat/0102304, arXiv.org.
    12. Leigh Tesfatsion, 1976. "Stochastic Dominance and the Maximization of Expected Utility," Review of Economic Studies, Oxford University Press, vol. 43(2), pages 301-315.
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    Cited by:

    1. Caporin, Massimiliano & Costola, Michele & Jannin, Gregory & Maillet, Bertrand, 2018. "“On the (Ab)use of Omega?”," Journal of Empirical Finance, Elsevier, vol. 46(C), pages 11-33.
    2. repec:eee:finlet:v:23:y:2017:i:c:p:1-11 is not listed on IDEAS

    More about this item

    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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