On the Nature of Certainty Equivalent Functionals

David Hennessy and Harvey Lapan

ISU General Staff Papers from Iowa State University, Department of Economics

Abstract: We explore connections between the certainty equivalent return (CER) functional and the underlying utility function. Curvature properties of the functional depend upon how utility function attributes relate to Hyperbolic Absolute Risk Aversion (HARA) type utility functions. If the CER functional is concave, i.e., if risk tolerance is concave in wealth, then preferences are standard. The CER functional is linear in lotteries if utility is HARA and lottery payoffs are on a line in state space. Implications for the optimality of portfolio diversification are given. When utility is concave and Non-increasing Relative Risk Averse, then the CER functional is superadditive in lotteries. Depending upon the nature of covariation among lottery payoffs, CERs for Constant Absolute Risk Averse utility functions may be subadditive or superadditive in lotteries. Our approach lends itself to straightforward experiments to elicit higher order attributes on risk preferences.

Date: 2006-03-29
New Economics Papers: this item is included in nep-mic, nep-rmg and nep-upt
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Related works:
Journal Article: On the nature of certainty equivalent functionals (2006)
Working Paper: On the Nature of Certainty Equivalent Functionals (2006)
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