Hart (2011) argues that the Aumann and Serrano (2008) and Foster and Hart (2009) measures of riskiness have an objective and universal appeal with respect to a subset of expected utility preferences, UH. We show that mean-riskiness decision-making criteria using either measure violate expected utility and are generally inconsistent with optimal portfolio choices made by investors with preferences in UH. We also demonstrate that riskiness measures satisfying Hart’s other behavioral requirements do not generally exist when his argument is generalized to incorporate non-expected utility preferences. Finally, we identify other attributes of the Aumann-Serrano and Foster-Hart measures that raise concerns over their operationalizability and usefulness in various decision making, risk management, and risk assessment settings.
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