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A Two-Parameter Model of Dispersion Aversion

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  • Chambers, Robert G.
  • Grant, Simon
  • Polak, Ben
  • Quiggin, John

Abstract

The idea of representing choice under uncertainty as a trade-off between mean returns and some measure of risk or uncertainty is fundamental to the analysis of investment decisions. In this paper, we show that preferences can be characterized in this way, even in the absence of ob jective probabilities. We develop a model of uncertainty averse preferences that is based on a mean and a measure of the dispersion of the state-wise utility of an act. The dispersion measure exhibits positive linear homogeneity, sub-additivity, translation invariance and complementary symmetry. Since preferences are only weakly separable in terms of these two summary statistics, the uncertainty premium need not be constant. We show that the standard results originally derived in the context of mean-variance analysis and expected utility theory apply in this more generally setting. In particular, we generalize the concept of decreasing absolute risk aversion and show that the usual comparative static results from EU theory remain valid. Further we derive two-fund separation and asset pricing results analogous to those that hold for the standard CAPM.

Suggested Citation

  • Chambers, Robert G. & Grant, Simon & Polak, Ben & Quiggin, John, 2011. "A Two-Parameter Model of Dispersion Aversion," Risk and Sustainable Management Group Working Papers 151196, University of Queensland, School of Economics.
  • Handle: RePEc:ags:uqsers:151196
    DOI: 10.22004/ag.econ.151196
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    Cited by:

    1. Qu, Xiangyu, 2017. "Subjective mean–variance preferences without expected utility," Mathematical Social Sciences, Elsevier, vol. 87(C), pages 31-39.
    2. Robert G. Chambers & Margarita Genius & Vangelis Tzouvelekas, 2012. "A Supply-Response Model Under Invariant Risk Preferences," Working Papers 1209, University of Crete, Department of Economics.
    3. Jingyi Xue, 2020. "Preferences with changing ambiguity aversion," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(1), pages 1-60, February.
    4. Chambers, Robert G. & Tzouvelekas, Vangelis, 2013. "Estimating population dynamics without population data," Journal of Environmental Economics and Management, Elsevier, vol. 66(3), pages 510-522.
    5. Baillon, Aurélien & Placido, Lætitia, 2019. "Testing constant absolute and relative ambiguity aversion," Journal of Economic Theory, Elsevier, vol. 181(C), pages 309-332.
    6. Cerreia-Vioglio, Simone & Maccheroni, Fabio & Marinacci, Massimo, 2022. "Ambiguity aversion and wealth effects," Journal of Economic Theory, Elsevier, vol. 199(C).
    7. Nunez, Manuel & Schneider, Mark, 2019. "Mean-dispersion preferences with a specific dispersion function," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 195-206.
    8. Stefan Trautmann & Peter P. Wakker, 2018. "Making the Anscombe-Aumann approach to ambiguity suitable for descriptive applications," Journal of Risk and Uncertainty, Springer, vol. 56(1), pages 83-116, February.

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    More about this item

    Keywords

    Risk and Uncertainty;

    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
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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