A Unifying Risk Measure

Abstract

This study arrives at a unifying risk measure (UrM) that explicitly embeds the relative valuation of any two assets. Relative to either of conditional volatility (CoV) or conditional skewness (CoS), the UrM is a more robust rubric for the implementation of choice under uncertainty. In stated respect, whereas the robustness of CoV (respectively, CoS) to investment decision making is predicated on equality (respectively, inequality) of conditional expected returns, formal theoretical predictions and empirical results show robustness of the UrM to investment decision making is independent of any and all orderings that subsist between conditional expected returns. For concreteness, whereas the UrM always performs at least as well as CoV (respectively, CoS), there exist conditions, in context of which with conditional expected returns equal (respectively, unequal), the higher volatility (respectively, lower return) asset is the optimal choice for all loss averse agents, and the UrM correctly infers the atypical choice.

Keywords: Risk Aversion, Risk Seeking, Uncertainty, Equilibrium, Conditional Volatility, Conditional Skewness

JEL Classification: G11, C00, D53, D81