🤖 AI Summary
This study investigates the robustness of Markowitz portfolios under estimation errors in input parameters and perturbations in optimization constraints. By integrating constrained mean-variance optimization with Sobol global sensitivity analysis, it systematically evaluates how target return levels influence weight stability, risk-adjusted performance, and diversification. The work introduces the novel concept of a “fragility frontier,” revealing that low-target-return regions are primarily governed by L2 regularization, whereas high-return regions exhibit heightened sensitivity to expected return perturbations and weight caps, accompanied by a sharp decline in diversification and increased weight dispersion. Empirical validation across a multi-asset ETF universe confirms the generality of this phenomenon, and the resulting fragility map offers a structural robustness diagnostic tool for constrained optimizers without requiring modifications to allocation rules.
📝 Abstract
In mean-variance portfolio analysis, the efficient frontier represents the optimal trade-off between expected return and risk, assuming stable underlying parameters. This paper investigates portfolio fragility: the instability of optimal weights, risk-adjusted performance, and diversification when model inputs and construction choices are jointly perturbed. Combining constrained Markowitz optimization with variance-based global sensitivity analysis (Sobol indices), we map out how input uncertainty and portfolio-construction choices propagate along the target-return dimension. Using an empirical universe of multi-asset exchange-traded funds (ETFs), we find a distinct transition in the sensitivity structure: in the baseline experiment, lower target returns are dominated by l2 regularization, whereas aggressive return requirements become increasingly sen- sitive to the weight cap and expected-return perturbations. This shift coincides with a sharp drop in effective diversification and a rise in weight dispersion. We extend the analysis to a multi-universe fragility atlas, showing that under a com- mon absolute concentration rule, the smallest universe is weight-cap-driven in the aggressive return region, while larger sampled universes remain more often regularization-driven. The fragile frontier serves as a direct diagnostic tool to evaluate the structural robustness of constrained optimizers without altering the underlying allocation rule.