A critical look at the Aumann-Serrano and Foster-Hart measures of riskiness

Hart (J Polit Econ, 119(4):617–638, 2011) argues that the Aumann and Serrano (J Polit Econ, 116(5): 810–836, 2008) and Foster and Hart (J Polit Econ, 117(5):785–814, 2009) measures of riskiness have an objective and universal appeal with respect to a subset of expected utility preferences, $${{\mathcal {U}}}_H$$ U H . 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 $${{\mathcal {U}}}_H$$ U H . 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.