The behavioural components of risk aversion

Abstract

There have been few theoretical investigations of risk attitude within Cumulative Prospect Theory (CPT). Unlike expected utility theory, in CPT risk attitude is affected by loss aversion and decision weight distortions as well as utility curvature for both gains and losses. We introduce two variants of the risk premium—the total risk premium relative to expected value, and the behavioural risk premium relative to the imputed behavioural expected value. Approximate solutions for each using Pratt's [(1964). Risk aversion in the small and in the large. Econometrica, 32, 122–136] methodology show that the CPT risk premium is composed of two components: the first, analogous to the Pratt–Arrow coefficient of risk aversion, governs the contribution of the curvature of the value function to risk aversion; the second governs the first-order contribution of loss aversion. Both of these terms are made more complex by the introduction of decision weights. We analyse the contribution of each component and provide sufficient conditions to ensure risk aversion in CPT.