AI 中文总结
研究最小方差投资组合对协方差估计误差的脆弱性，通过施加块对角相关结构导出闭式表达式，提出稳健化方法，经模拟验证该方法能降低样本外方差和换手率，为稳健投资组合构建提供实用途径。
AI 中文摘要
最小方差投资组合对协方差估计误差高度敏感。本文表明，通过施加块对角相关结构，可得到使这种脆弱性明确的多头最小方差投资组合的闭式表达式。这些解析解表明脆弱性由相关结构与资产波动率相互作用产生的阈值效应驱动。基于此，我们提出稳健化方法，可解释为结构化收缩方案，能在保留主导风险结构的同时选择性减弱不稳定耦合。与全局收缩技术不同，该修正基于解析，调优最少且与最小方差解紧密相关。通过基于聚类的近似，该框架可自然扩展到一般协方差矩阵。控制模拟的实证结果突出了明显的状态依赖性。在同质波动率设置中，忽略相关性的收缩在风险与稳定性间实现最佳权衡。相比之下，在异质波动率下，考虑相关性的收缩通过引入稀疏性并避免高风险资产暴露表现最佳。在各状态下，相对于经典和基于聚类的基准，所提方法持续降低样本外方差和换手率，为稳健投资组合构建提供了原则性和实用性方法。
英文摘要
Minimum-variance portfolios are well known to be highly sensitive to covariance estimation error. In this paper, we show that by imposing a block diagonal correlation structure, we can derive closed-form expressions for long-only minimum-variance portfolios that make this fragility explicit. These analytical solutions reveal that fragility is driven by threshold effects arising from the interaction between correlation structure and the assets' volatilities. Motivated by the latter insight, we propose robustification approaches that can be interpreted as structured shrinkage schemes that selectively attenuate unstable coupling while preserving the dominant risk structure. Unlike global shrinkage techniques, the proposed corrections are analytically grounded, require minimal tuning, and remain closely aligned with the minimum-variance solution. The framework extends naturally to general covariance matrices through clustering-based approximations. Empirical results on controlled simulations highlight a clear regime dependence. In homogeneous volatility settings, correlation-oblivious shrinkage achieves the best trade-off between risk and stability. In contrast, under heterogeneous volatility, correlation-aware shrinkage performs best by inducing sparsity and avoiding exposure to high-risk assets. Across regimes, the proposed methods consistently reduce out-of-sample variance and turnover relative to classical and clustering-based benchmarks, providing a principled and practical approach to robust portfolio construction.
