Implied Ambiguity: Mean-Variance Efficiency and Pricing Errors

Abstract

We study the optimal portfolio choice problem for an ambiguity-averse investor having a utility function of the form of Klibanoff, Marinacci, and Mukerji (2005) and Maccheroni, Marinacci, and Ruffino (2013). We identify necessary and sufficient conditions for a given portfolio to be optimal for some ambiguity-averse investor. We also show that the smallest ambiguity aversion coefficient for the optimality of the given portfolio, which we term the implied ambiguity of the portfolio, is decreasing with respect to its Sharpe ratio. This relation can also be expressed in terms of the size of the pricing errors when the asset returns are regressed on the return of the portfolio. A numerical analysis is provided to find the ambiguity aversion implied by the U.S. equity market data.