金融市场下非负稀疏组LASSO在股指跟踪中的研究

Nonnegative Sparse Group Lasso with an Application in Financial Index Tracking

作为一种流行的被动投资组合管理策略,指数跟踪主要侧重于复制或跟踪金融指数的表现.以股指为例,传统的投资策略通常考虑指数所有成分股的完全复制.然而,随着指数成分股数量的增加,完全复制通常会受到流动性差以及成本高的影响.因此,投资者倾向于购买部分成分股进行资产配置.此外,在股票市场中,股票之间还存在明显的“组群”效应.基于此,本文提出了非负稀疏组LASSO方法,用于成分股的选择和权重系数的估计.在有限维组的情况下,我们给出了模型变量选择和参数估计一致性的几乎充要的条件.为了得到模型的解,我们推导出一种基于坐标下降的计算方法.最后,实证结果表明,非负稀疏组LASSO优于具有“组效应”的其他目前的流行方法,例如非负弹性网.

Index tracking mainly focuses on replicating or tracking the performance of a financial index which is also a popular passive portfolio management strategy.The classical methods often consider the full replication consisted of all asserts of an index.However,the full replication often suffers from small and illiquid positions and high cost as the number of asserts increasing.Thus,the investors intend to purchase sparse portfolios.In stock markets,besides,there are still apparently existing group effects among stocks.This paper proposes the nonnegative sparse group lasso method for model selection and estimation to grouped variables without overlapping.We provide almost necessary and sufficient conditions for the variable selection and estimation consistency of the method in finite dimensional group cases.To get the solutions of the model,we derive a computational method based on coordinate decent algorithm.To track the index,the nonnegative sparse group lasso outperforms other current methods with group effects such as nonnegative elastic net,according to tracking error.