Measuring Tail Risk

Abstract

We comprehensively investigate the usefulness of tail risk measures proposed in the literature. We evaluate their statistical as well as their economic validity. The option-implied measure of Bollerslev and Todorov (2011b) (BT11Q) performs best overall. While some other tail risk measures excel at specialized tasks, BT11Q performs well in all tests: First, BT11Q can predict both future tail events and future tail volatility. Second, it has predictive power for returns in both the time series and the cross-section, as well as for real economic activity. Finally, a simulation analysis shows that the main driver of performance is measurement error.

Keywords: Tail Risk, Return Forecasting, Tail Event Forecasting

JEL Classification: G12, C58, G17, G10