On the Nature of Certainty Equivalent Functionals

We explore connections between the certainty equivalent return (CER) functional and theunderlying utility function. Curvature properties of the functional depend upon how utilityfunction 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 arestandard. The CER functional is linear in lotteries if utility is HARA and lottery payoffs are on aline in state space. Implications for the optimality of portfolio diversification are given. Whenutility is concave and Non-increasing Relative Risk Averse, then the CER functional issuperadditive in lotteries. Depending upon the nature of covariation among lottery payoffs,CERs for Constant Absolute Risk Averse utility functions may be subadditive or superadditive inlotteries. Our approach lends itself to straightforward experiments to elicit higher orderattributes on risk preferences.[...]