ABSTRACT Index tracking is a well-known passive management strategy that seeks to match the performance of a benchmark index. To the best of our knowledge, the existing literatures for sparse index tracking are mainly focus on the penalized least squares (LS) regression under the no-short selling constraint. In this paper, we propose an efficient sparse portfolio that based on composite quantile regression to simultaneously perform stock selection and capital allocation for high-dimensional index tracking. A special consideration is made concerning the budget constraint that has been ignored by the existing LS-type procedures. Furthermore, we develop a specialized linear programming algorithm for the implementation of the proposed method. Through the simulation, we show that the proposed method outperforms (or at least matches) existing procedures in terms of prediction accuracy and variable selection. Finally, we apply the proposed method to track the SP 500 index in the New York Stock Exchange.

中文翻译：

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基于复合分位数回归的高效稀疏投资组合用于高维指数跟踪

摘要 指数跟踪是一种著名的被动管理策略，旨在与基准指数的表现相匹配。据我们所知，现有的稀疏指数跟踪文献主要集中在无卖空约束下的惩罚最小二乘（LS）回归。在本文中，我们提出了一种基于复合分位数回归的高效稀疏投资组合，可同时执行股票选择和资本配置以进行高维指数跟踪。对现有 LS 类程序忽略的预算约束进行了特殊考虑。此外，我们开发了一种专门的线性规划算法来实现所提出的方法。通过模拟，我们表明，所提出的方法在预测准确性和变量选择方面优于（或至少匹配）现有程序。最后，我们应用所提出的方法来跟踪纽约证券交易所的 SP 500 指数。