Relevance of Maximum Drawdown in the Investment Fund Selection Problem When Utility is Nonadditive

This paper explores the circumstances under which maximum drawdown becomes relevant to a rational investor’s choice of an investment fund. We adopt the framework of the nonadditive expected utility theory of Schmeidler, and consider the consequence of extreme uncertainty over cash flow and also of extreme uncertainty aversion. We show that an investor facing extreme uncertainty makes a choice based on maximum drawdown. We also show that an extremely uncertainty-averse investor makes a choice based on maximum drawdown even if uncertainty is not extreme. An implication for the mean-variance analysis of Markowitz is discussed as well.