AI 中文总结
本文通过结合马科维茨优化与Sobol指数的全局敏感性分析，探究投资组合脆弱性，发现目标收益与敏感性结构的转变规律，并提出脆弱前沿作为评估约束优化器稳健性的诊断工具。
AI 中文摘要
在均值-方差投资组合分析中，有效前沿代表了在假设基础参数稳定的情况下，预期收益与风险之间的最优权衡。本文研究投资组合脆弱性：当模型输入和构建选择同时受到扰动时，最优权重、风险调整后表现以及分散化的不稳定性。结合约束马科维茨优化与基于方差的全局敏感性分析（Sobol指数），我们绘制了输入不确定性和投资组合构建选择如何沿目标收益维度传播的图谱。使用多资产交易所交易基金（ETF）的实证 universe，我们发现敏感性结构存在明显转变：在基准实验中，较低目标收益由L2正则化主导，而激进的收益要求对权重上限和预期收益扰动的敏感性日益增加。这一转变与有效分散化的急剧下降和权重分散度的上升同时发生。我们将分析扩展到多 universe 脆弱性图谱，表明在共同绝对集中度规则下，最小的 universe 在激进收益区域由权重上限驱动，而更大的抽样 universe 通常仍由正则化驱动。脆弱前沿作为一种直接的诊断工具，用于评估约束优化器的结构稳健性，而无需改变潜在的分配规则。
英文摘要
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.
