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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.

Keywords: uncertainty aversion ; mean utility ; dispersion of utility ; weak-separability

Subject(s): Risk and Uncertainty

Issue Date: Aug 04 2011

Publication Type: Working or Discussion Paper

PURL Identifier: http://purl.umn.edu/151196

Total Pages: 49

JEL Codes: D81

Series Statement: Risk and Uncertainty Program

R11/2

Record appears in: University of Queensland > School of Economics > Risk and Sustainable Management Group Working Papers





Author: Chambers, Robert G. ; Grant, Simon ; Polak, Ben ; Quiggin, John

Source: http://ageconsearch.umn.edu/record/151196?ln=en



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