A Two-Parameter Model of Dispersion Aversion
AbstractThe 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.
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Bibliographic InfoPaper provided by University of Queensland, School of Economics in its series Risk and Sustainable Management Group Working Papers with number 151196.
Date of creation: 04 Aug 2011
Date of revision:
uncertainty aversion; mean utility; dispersion of utility; weak-separability; Risk and Uncertainty; D81;
Find related papers by JEL classification:
- D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
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