Tail Risk and Robust Portfolio Decisions

This paper formulates a portfolio choice problem in a multiasset 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 that intensify misspecification concerns. We then implement our model in international equity markets to quantify the impact of tail risk on portfolio selection, through comparisons between a normal and a slowly decaying jump size distribution. We find that, without jump ambiguity, constant relative risk aversion (CRRA) investors increase their jump exposures merely slightly and suffer 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 portfolio rebalancing and subsequent wealth losses are encountered in the presence of jump ambiguity.