Navigating Complexity: Constrained Portfolio Analysis in High Dimensions with Tracking Error and Weight Constraints

Mehmet Caner, Qingliang Fan, Yingying Li
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Abstract

This paper analyzes the statistical properties of constrained portfolio formation in a high dimensional portfolio with a large number of assets. Namely, we consider portfolios with tracking error constraints, portfolios with tracking error jointly with weight (equality or inequality) restrictions, and portfolios with only weight restrictions. Tracking error is the portfolio's performance measured against a benchmark (an index usually), {\color{black}{and weight constraints refers to specific allocation of assets within the portfolio, which often come in the form of regulatory requirement or fund prospectus.}} We show how these portfolios can be estimated consistently in large dimensions, even when the number of assets is larger than the time span of the portfolio. We also provide rate of convergence results for weights of the constrained portfolio, risk of the constrained portfolio and the Sharpe Ratio of the constrained portfolio. To achieve those results we use a new machine learning technique that merges factor models with nodewise regression in statistics. Simulation results and empirics show very good performance of our method.
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驾驭复杂性:具有跟踪误差和权重约束的高维度受限投资组合分析
本文分析了具有大量资产的高维投资组合中受约束投资组合形式的统计特性。也就是说,我们考虑了具有跟踪误差约束的投资组合、具有跟踪误差与权重(相等或不相等)联合约束的投资组合以及仅具有权重约束的投资组合。跟踪误差是指投资组合相对于基准(通常是指数)的表现,{\color{black}{而权重限制是指投资组合内资产的具体分配,通常以监管要求或基金说明书的形式出现。}我们展示了这些投资组合如何在大维度上进行一致估计,即使资产数量大于投资组合的时间跨度。我们还提供了受约束投资组合权重、受约束投资组合风险和受约束投资组合夏普比率的收敛率结果。为了获得这些结果,我们使用了一种新的机器学习技术,该技术将因子模型与统计中的节点回归相结合。模拟结果和经验表明,我们的方法性能非常好。
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