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) (𝐵𝑇 11𝑄) performs best overall. While some other tail risk measures excel at specialized tasks, 𝐵𝑇 11𝑄 performs well in all tests: First, 𝐵𝑇 11𝑄 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.