Capital Asset Pricing Under Ambiguity

Abstract

This paper generalizes the mean–variance preferences to mean–variance–ambiguity preferences by relaxing the standard assumption that probabilities are known and assuming that probabilities are themselves random. It introduces a new measure of uncertainty, one that consolidates risk and ambiguity, which is employed for extending the CAPM from risk to uncertainty by incorporating ambiguity. This model makes the distinction between systematic ambiguity and idiosyncratic ambiguity and proves that the ambiguity premium is proportional to the systematic ambiguity. The merit of this model is twofold: first, it can be tested empirically; second, it can serve for measuring the performance of portfolios relative to their uncertainty.

Keywords: Shadow Theory, Ambiguity, Ambiguity Measure, Uncertainty Measure, Ambiguity premium, mean-variance, mean-uncertainty, Capital Market Line (CML), Capital Asset Pricing Model (CAPM)