标题： 端到端大型投资组合优化用于通过协方差清理的方差最小化神经网络 显示英文标题

标题： End-to-End Large Portfolio Optimization for Variance Minimization with Neural Networks through Covariance Cleaning

摘要： 我们开发了一个旋转不变的神经网络，通过联合学习如何对历史收益进行滞后转换，并如何对大型股票协方差矩阵的特征值和边缘波动率进行正则化，从而提供全局最小方差投资组合。这种显式的数学映射提供了每个模块作用的清晰可解释性，因此该模型不能被视为纯粹的黑箱。该架构模仿了全局最小方差解的解析形式，但对维度保持无偏，因此一个模型可以在几百只股票的面板上进行校准，并在不重新训练的情况下应用于一千只美国股票——这种横截面跳跃展示了稳健的样本外泛化能力。损失函数是未来实现的最小投资组合方差，并在真实每日收益上端到端优化。在2000年1月至2024年12月的样本外测试中，该估计器比最佳分析竞争对手（包括最先进的非线性收缩方法）系统性地实现了更低的实现波动率、更小的最大回撤和更高的夏普比率。此外，尽管该模型是端到端训练以生成无约束（多空）最小方差投资组合，但我们证明其学习到的协方差表示可以在长期限制下的一般优化器中使用，而对其相对于竞争估计器的性能优势几乎没有损失。当策略在高度现实的执行框架下执行时，这些收益依然存在，该框架模拟了拍卖中的市场订单、实证滑点、交易所费用和杠杆融资费用，并且在市场压力加剧的时期，这些收益依然稳定。 显示英文摘要

摘要： We develop a rotation-invariant neural network that provides the global minimum-variance portfolio by jointly learning how to lag-transform historical returns and how to regularise both the eigenvalues and the marginal volatilities of large equity covariance matrices. This explicit mathematical mapping offers clear interpretability of each module's role, so the model cannot be regarded as a pure black-box. The architecture mirrors the analytical form of the global minimum-variance solution yet remains agnostic to dimension, so a single model can be calibrated on panels of a few hundred stocks and applied, without retraining, to one thousand US equities-a cross-sectional jump that demonstrates robust out-of-sample generalisation. The loss function is the future realized minimum portfolio variance and is optimized end-to-end on real daily returns. In out-of-sample tests from January 2000 to December 2024 the estimator delivers systematically lower realised volatility, smaller maximum drawdowns, and higher Sharpe ratios than the best analytical competitors, including state-of-the-art non-linear shrinkage. Furthermore, although the model is trained end-to-end to produce an unconstrained (long-short) minimum-variance portfolio, we show that its learned covariance representation can be used in general optimizers under long-only constraints with virtually no loss in its performance advantage over competing estimators. These gains persist when the strategy is executed under a highly realistic implementation framework that models market orders at the auctions, empirical slippage, exchange fees, and financing charges for leverage, and they remain stable during episodes of acute market stress.