  We propose a bootstrap-based robust high-confidence level upper bound (Robust
H-CLUB) for assessing the risks of large portfolios. The proposed approach
exploits rank-based and quantile-based estimators, and can be viewed as a
robust extension of the H-CLUB method (Fan et al., 2015). Such an extension
allows us to handle possibly misspecified models and heavy-tailed data. Under
mixing conditions, we analyze the proposed approach and demonstrate its
advantage over the H-CLUB. We further provide thorough numerical results to
back up the developed theory. We also apply the proposed method to analyze a
stock market dataset.
