Does Ambiguity Diversification Pay?

Abstract

With a focus on risk, classical portfolio theory assumes that probabilities of future outcomes are known. In reality, however, there is ambiguity in these probabilities. This paper studies the nature of the relationship between risk and ambiguity and proves that in most cases ambiguity cannot be diversified without increasing risk. This insight implies that holding a fully diversified portfolio is not necessarily optimal. It challenges the conventional wisdom which asserts that investors should hold such a portfolio.

Keywords: Ambiguity, Ambiguity Measure, Risk, Uncertainty, Knightian Uncertainty, Random Probabilities

JEL Classification: D81, G11, G12