On the Nature of Certainty Equivalent Functionals
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2006-03
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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.
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06011
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working paper
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JEL Classification: C61, D81, G10
Length: 22 pages
Original release date: March 2006
This working paper is published as Hennessy, David A., and Harvey E. Lapan. "On the nature of certainty equivalent functionals." Journal of Mathematical Economics 43, no. 1 (2006): 1-10. doi:10.1016/j.jmateco.2006.06.006.