Tail Risk and Robust Portfolio Decisions

Abstract

Both asset return and consumption disasters exhibit slowly-decaying tail behavior admitting severe downside risk. To investigate the effects of tail risk on optimal portfolio choice, we solve for the dynamic investment strategy in a multi-asset incomplete market with ambiguous jump risk. Out of the fear of extreme tail events in the worst case scenario, an ambiguity-averse investor tends to reduce her jump exposure, and an extremely ambiguity-averse investor may not hold any risky asset. We estimate the model on international equity indices and compare optimal portfolios under normally distributed jumps and heavy-tailed jumps obeying a power-law. Under rational expectation, an investor with a constant relative risk aversion (CRRA) utility function incurs negligible losses from ignoring extreme tail events, once the first two moments of the jump distributions are preserved. In stark contrast, the investor with aversion to uncertain tail risk suffers sizable economic losses. We also find that uncertain consumption tail risk enhances the option implied volatility smirk and variance risk premia in market equilibrium.