New bounds for tail risk measures

This paper introduces new upper bounds for tail risk measures, such as value-at-risk and expected shortfall, based on Bhattacharyya (1987) inequality. These enhanced bounds for losses consider higher-order moments like skewness and kurtosis, which sets them apart from the conventional one-sided Vysochanskii and Petunin (1980) and Cantelli (1928) inequalities. While the simplicity and reliance on estimating only the first two moments can make the latter bounds attractive, the practicality and effectiveness of the new bounds position them as a compelling alternative for risk measurement. We empirically analyze S&P 100 index stocks to illustrate our findings. Our results suggest tighter Basel multipliers and reduced minimum capital requirements.