标题： 高维投资组合分析与TE和权重约束 显示英文标题

标题： Portfolio Analysis in High Dimensions with TE and Weight Constraints

摘要： 本文探讨了在高维资产集合中形成约束最优投资组合的统计特性。 我们研究了具有跟踪误差约束的投资组合，同时具有跟踪误差和权重限制的投资组合，以及仅受权重限制的投资组合。 跟踪误差衡量投资组合相对于基准（通常是指数）的表现，而权重约束则根据监管要求或基金说明书确定资产配置。 我们的方法采用了一种新颖的统计学习技术，将因子模型与节点回归相结合，称为受限残差节点最优权重回归（CROWN）方法。 我们展示了其在大维度下的估计一致性，即使资产数量超过投资组合的时间跨度。 提供了约束投资组合权重、风险和夏普比率的收敛速率结果，模拟和实证证据突显了该方法的卓越性能。 显示英文摘要

摘要： This paper explores the statistical properties of forming constrained optimal portfolios within a high-dimensional set of assets. We examine portfolios with tracking error constraints, those with simultaneous tracking error and weight restrictions, and portfolios constrained solely by weight. Tracking error measures portfolio performance against a benchmark (typically an index), while weight constraints determine asset allocation based on regulatory requirements or fund prospectuses. Our approach employs a novel statistical learning technique that integrates factor models with nodewise regression, named the Constrained Residual Nodewise Optimal Weight Regression (CROWN) method. We demonstrate its estimation consistency in large dimensions, even when assets outnumber the portfolio's time span. Convergence rate results for constrained portfolio weights, risk, and Sharpe Ratio are provided, and simulation and empirical evidence highlight the method's outstanding performance.