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Decision making with Conditional Value-at-Risk and spectral risk measures: The problem of comparative risk aversion

Author

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  • Brandtner, Mario
  • Kürsten, Wolfgang
Abstract
We analyze spectral risk measures with respect to comparative risk aversion following Arrow (1965) and Pratt (1964) on the one hand, and Ross (1981) on the other hand. The implications for two standard financial decision problems, namely the willingness to pay for insurance and portfolio selection, are studied. Within the framework of Arrow and Pratt, we show that the widely-applied spectral Arrow-Pratt-measure is not a consistent measure of Arrow-Pratt-risk aversion. A decision maker with a greater spectral Arrow-Pratt-measure may only be willing to pay less for insurance or to invest more in the risky asset than a decision maker with a smaller spectral Arrow-Pratt-measure. We further show how a proper measure of Arrow-Pratt-risk aversion should look like instead. Within the framework of Ross, we show that the popular subclasses of Conditional Value-at-Risk, and exponential and power spectral risk measures cannot be completely ordered with respect to Ross-risk aversion. As a consequence, these subclasses also exhibit counter-intuitive comparative static results. In the insurance problem, the willingness to pay for insurance may be decreasing with increasing risk parameter. In the portfolio selection problem, the investment in the risky asset may be increasing with increasing risk parameter. These shortcomings have to be considered before spectral risk measures can be applied for the purpose of optimal decision making and regulatory issues.

Suggested Citation

  • Brandtner, Mario & Kürsten, Wolfgang, 2014. "Decision making with Conditional Value-at-Risk and spectral risk measures: The problem of comparative risk aversion," VfS Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100615, Verein für Socialpolitik / German Economic Association.
    • Handle: RePEc:zbw:vfsc14:100615
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    References listed on IDEAS

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    Cited by:

    1. Günter Bamberg & Michael Krapp, 2016. "Is time consistency compatible with risk aversion?," Review of Managerial Science, Springer, vol. 10(2), pages 195-211, March.

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    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
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages

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