Managing ambiguity in asset allocation

Abstract

This paper is about the issue of input parameter uncertainty in portfolio optimization in a discrete setting with finite states (such as the case in a world with different macroeconomic regimes). In such a setting, being unable to assign reliable point estimates to the probabilities (or frequencies) of the states creates the ambiguity. We first describe how this ambiguity can be modeled probabilistically. Then, we show how this added uncertainty can be dealt with in optimal asset allocation problems. In simple-yet-realistic example applications we demonstrate that without sacrificing much of the upside, ambiguity managed portfolios may enhance the uniformity of returns across different states when compared to portfolios constructed by traditional methods. We stress that a key conclusion to be taken from these methods builds the case for insurance-like and potentially negative-yielding investments such as bonds and commodities so as to hedge the unforeseeable macrouncertainties for a smoother portfolio performance. Finally, we offer a variety of problem domains in which ambiguity management can be nested including macroeconomic scenario-based asset allocation, investing with regime-switching models, momentum investing, and risk-based investing.