Tail Robustness Inversion in Portfolio Optimisation

Abstract

This study identifies and quantifies tail-robustness inversion: improving a simulated covariance-tail objective can increase realised portfolio risk. A prespecified walk-forward evaluation covers 49 value-weighted US industry portfolios, 648 monthly rebalances, and 13,614 daily out-of-sample returns from January 1972 through December 2025. Bootstrap covariance-tail expected-shortfall optimisation lowers its in-sample tail objective by 1.938% relative to Ledoit–Wolf minimum variance, with an objective no higher at any rebalance (647 improvements and one tie in the saved results). Yet average out-of-sample realised variance is 2.588% higher, with a paired block-bootstrap 95% confidence interval of [1.121%, 4.057%] for the increase. The inversion persists across all 12 reported specifications and all five chronological regimes in annualised volatility. Diversification constraints reduce the variance penalty, providing a practical direction for controlling the effect. The analysis also distinguishes the covariance fragility ratio’s descriptive value from its ability to forecast subsequent risk. Together, these findings provide a reproducible empirical counterexample to equating simulated tail protection with effective portfolio protection, and a structured validation approach for assessing covariance-based allocation methods before deployment.