Mutual Fund Theorem for Ambiguity-Averse Investors and the Optimality of the Market Portfolio

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 Rufino (2013) in an ambiguity-inclusive CARA-normal setup. We extend the mutual fund theorem to accommodate ambiguity, identify a necessary and sufficient condition for a given portfolio to be optimal for some ambiuityaverse investor, characterize all the ambiguity structure under which the given portfolio is optimal, and find the minimal ones in two senses to be made precise. We also calculate the minimal ambiguity structures based on the U.S. equity market data and find the smallest coefficient of ambiguity aversion with which the market portfolio is optimal is equal to 9.31.