发表机构
Université Paris-Saclay; CentraleSupélec（巴黎-萨克雷大学; 中央高等电力学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究针对含小盘股投资组合的不定成对相关矩阵问题，提出端到端神经收缩方法，经模拟验证可显著降低波动率、提升夏普比率，且效果稳健。
AI 中文摘要
包含小盘股的股票 universe 包含近期上市和间歇性交易的证券，因此采用统一回溯期会丢弃大量可用信息。成对完整估计为每对资产保留最长重叠区间，但由于其条目基于不同样本计算，所得相关矩阵可能不定，这阻碍了其直接用于 Markowitz 优化，且不符合标准随机矩阵收缩的假设。我们将旋转不变神经协方差估计器适配至该场景：该模型计算感知掩码的边际矩和成对相关矩阵代理，处理其符号谱，并使用由重叠矩阵和特征向量载荷推导的因子对齐有效样本长度调节的双向门控循环单元，将所有特征值（包括负特征值）映射至正逆谱，重构的协方差为正定矩阵，并进行端到端训练以最小化五日已实现全局最小方差风险。我们在含时点选择、佣金、融资、公司行为和市场冲击的收盘拍卖模拟器中，针对2000年至2025年的26个滚动窗口模型，评估了最多1500只美国股票。在26年的样本外期间，该神经估计器较次优协方差估计器，将年化五日波动率降低约20%，并将夏普比率提高约40%。这些改进在已实现风险、风险调整后绩效和回撤控制方面一致，在考虑建模的执行摩擦后仍保持有效，且得到仅保留该神经估计器的99.9%模型置信集的支持。
英文摘要
Small-cap-inclusive equity universes contain recently listed and intermittently traded securities, so enforcing a common look-back discards a substantial fraction of the available information. Pairwise-complete estimation preserves the longest overlap for each asset pair, but the resulting correlation matrix can be indefinite because its entries are computed on different samples. This prevents direct use in Markowitz optimization and falls outside the assumptions of standard random-matrix shrinkage. We adapt a rotation-invariant neural covariance estimator to this setting. The model computes mask-aware marginal moments and a pairwise correlation matrix proxy, processes its signed spectrum, and uses a bidirectional gated recurrent unit conditioned on factor-aligned effective sample lengths derived from the overlap matrix and eigenvector loadings. It maps all eigenvalues, including negative ones, to a positive inverse spectrum. The reconstructed covariance is positive definite and is trained end-to-end to minimize five-day realized global-minimum-variance risk. We evaluate 26 expanding-window models from 2000 to 2025 on up to 1,500 U.S. equities in a closing-auction simulator with point-in-time selection, commissions, financing, corporate actions, and market impact. Across the 26-year out-of-sample period, the neural estimator reduces annualized five-day volatility by approximately 20\% and increases the Sharpe ratio by approximately 40\% relative to the next-best covariance estimator. These improvements are consistent across realized risk, risk-adjusted performance, and drawdown control, remain after the modeled execution frictions, and are supported by a 99.9\% Model Confidence Set that retains only the neural estimator.
