Economic indices of absolute and relative riskiness

Following Aumann and Serrano (J Polit Econ 116:810–836, 2008) who characterize by axioms an index of riskiness defined on absolute returns, we characterize a new index of riskiness defined on relative returns. Both indices are characterized by a similar principle of duality between risk and risk aversion, but while the index of absolute riskiness refers to absolute risk aversion, the index of relative riskiness refers to relative risk aversion. The similarities and differences between the two indices are studied.