An Economic Index of Riskiness

Abstract

Define the riskiness of a gamble as the reciprocal of the absolute risk aversion (ARA) of an individual with constant ARA who is indifferent between taking and not taking that gamble. We characterize this index by axioms, chief among them a “duality” axiom that, roughly speaking, asserts that less risk‐averse individuals accept riskier gambles. The index is positively homogeneous, continuous, and subadditive; respects first‐ and second‐order stochastic dominance; and for normally distributed gambles is half of variance/mean. Examples are calculated, additional properties are derived, and the index is compared with others.