Measuring tail risk
系统评估了文献中提出的尾部风险度量方法，发现Bollerslev和Todorov（2011b）的期权隐含度量在统计和经济有效性上表现最佳，能预测尾部事件、波动率、收益及实体经济。
We comprehensively investigate the usefulness of tail risk measures proposed in the literature. \nWe evaluate their statistical as well as their economic validity. The option-implied measure \nof Bollerslev and Todorov (2011b) (𝐵𝑇 11𝑄) performs best overall. While some other tail risk \nmeasures excel at specialized tasks, 𝐵𝑇 11𝑄 performs well in all tests: First, 𝐵𝑇 11𝑄 can predict \nboth future tail events and future tail volatility. Second, it has predictive power for returns \nin both the time series and the cross-section, as well as for real economic activity. Finally, a \nsimulation analysis shows that the main driver of performance is measurement error.