Critical Dependence Stress for Portfolio Diversification
I develop a variational framework for measuring the dependence stress needed to reverse a portfolio’s Expected Shortfall advantage while preserving individual loss distributions. I prove a quadratic law for the critical stress budget and characterize exactly when marginal restoration adds a premium. In a uniform benchmark, the asymptotic reversal budget is at least 30% higher than the initial-sensitivity prediction. Continuous flow–cut duality characterizes the premium’s sensitivity to background displacement costs, turning local risk sensitivity into a mathematically derived threshold for portfolio decision reversal.