We develop a new extreme value theory for panel data and use it to construct asymptotically valid confidence intervals (CIs) for conditional tail features such as conditional extreme quantile and conditional tail index. As a by-product, we also construct CIs for tail features of the coefficients in the random coefficient regression model. The new CIs are robustly valid without parametric assumptions and have excellent small sample coverage and length properties  . Applying the proposed method, we study the tail risk of the monthly U.S. stock returns and find that (i) the left tail features of stock returns and those of the Fama-French regression residuals heavily depend on other stock characteristics such as stock size; and (ii) the alpha's and beta's are strongly heterogeneous across stocks in the Fama-French regression. These findings suggest that the Fama-French model is insufficient to characterize the tail behavior of stock returns.
We develop a new extreme value theory for panel data to construct asymptotically valid confidence intervals (CIs) for conditional tail features such as conditional extreme quantile and conditional tail index. As a by-product, we also construct CIs for tail features of the coefficients in the random coefficient regression model. The new CIs are robustly valid without parametric assumptions and exhibit superior small sample coverage and length properties than alternative nonparametric approaches based on asymptotic normality . Applying the proposed method, we study the tail risk of the monthly U.S. stock returns and find that (i) the left tail features of stock returns and those of the Fama-French regression residuals heavily depend on other stock characteristics such as stock size; and (ii) the alpha's and beta's are strongly heterogeneous across stocks in the Fama-French regression. These findings suggest that the Fama-French model may be insufficient to characterize the tail behavior of stock returns.
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