Tail Risk and Robust Portfolio Decisions

Abstract

Return jumps on equities exhibit slowly-decaying tail behavior admitting severe downside risk; moreover, heavy-tailed jump size distributions governing these rare events pose further challenges to econometric estimation. This paper formulates a portfolio choice problem in a multi-asset incomplete market characterized by ambiguous jumps and arbitrary tail assumptions. We derive the optimal portfolio in closed-form through a decomposition approach. We show that, due to fear of tail incidents, an investor diminishes portfolio diversification, and even more so under heavy-tailed jumps which intensify misspecification concerns. We then calibrate the model to international equity indices to quantify the economic consequences of tail risk. We find that, without jump ambiguity, a CRRA investor suffers negligible wealth losses from underestimating tail risk, given that the first two moments of the jump size distributions are preserved regardless of the tail properties. In stark contrast, sizable losses are encountered in the presence of jump ambiguity.

Keywords: Tail risk; Jump ambiguity; Robust decisions; Portfolio selection

JEL Classification: G01, G11, G12