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Skewness as an explanation of gambling in cumulative prospect theory

Skewness of return has been suggested as a reason why agents might choose to gamble, ceteris paribus, in cumulative prospect theory (CPT). We investigate the relationship between moments of return in two models where agents choices over uncertain outcomes are determined as in CPT. We illustrate via examples that in CPT theory, as with expected utility theory, propositions that agents have a preference for skewness may be invalid.