Portfolio Analysis in High Dimensions with Tracking Error and Weight Constraints
本文提出一种名为CROWN的统计学习方法，在高维资产中构建受跟踪误差和权重约束的最优组合，证明其估计一致性，并通过模拟和实证验证了方法的优异表现。
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 C onstrained R esidual Nodewise O ptimal W eight 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.