Before revision:  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;
After revision:  The new CIs are robustly valid without parametric assumptions and have excellent 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;