On the nature of certainty equivalent functionals |
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| Institution: | 1. 578C Heady Hall, Department of Economics & CARD, Iowa State University, Ames, IA 50011-1070, United States;2. 283 Heady Hall, Department of Economics, Iowa State University, Ames, IA 50011-1070, United States;1. Centre for Complex Systems Science, Commonwealth Scientific and Industrial Research Organisation, Australia;2. Centre for Applied Macroeconomic Analysis, Australian National University, Australia;3. IPAG Business School, 184 Bd Saint Germain, 75006 Paris, France;4. Research Institute for Economics and Business Administration, Kobe University, Japan;5. Research School of Economics, Australian National University, Australia;1. Faculty of Arts and Social Sciences, Sabanci University, Orhanli, Tuzla, 34956, Istanbul, Turkey;2. School of Economics, University of Surrey, Guildford, GU2 7XH, UK;1. University of Oviedo, Department of Statistics and Operations Research, C-Calvo Sotelo, s/n, 33007 Oviedo, Spain;2. Istituto Dalle Molle di Studi sull''Intelligenza Artificiale (IDSIA), Galleria 2, 6928 Manno (Lugano), Switzerland;1. University of Notre Dame, USA;2. Department of Economics and Finance, University of Guelph, Guelph, Ontario, Canada N1G 2W1 |
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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 association 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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