This paper uses topological data analysis (TDA) tools and introduces a data-driven clustering-based stock selection strategy tailored for sparse portfolio construction. Our asset selection strategy exploits the topological features of stock price movements to select a subset of topologically similar (different) assets for a sparse index tracking (Markowitz) portfolio. We introduce new distance measures, which serve as an input to the clustering algorithm, on the space of persistence diagrams and landscapes that consider the time component of a time series. We conduct an empirical analysis on the S\&P index from 2009 to 2020, including a study on the COVID-19 data to validate the robustness of our methodology. Our strategy to integrate TDA with the clustering algorithm significantly enhanced the performance of sparse portfolios across various performance measures in diverse market scenarios.

翻译：本文利用拓扑数据分析（TDA）工具，提出了一种数据驱动的聚类选股策略，专门用于稀疏投资组合构建。该资产选择策略通过挖掘股票价格走势的拓扑特征，为稀疏指数跟踪（马科维茨）投资组合选取拓扑相似（相异）的资产子集。我们在持续图与持续景观空间上引入了新的距离度量（作为聚类算法的输入），这些度量充分考虑了时间序列的时间成分。基于2009年至2020年标普指数数据（包括新冠疫情数据的鲁棒性验证研究）进行了实证分析。结果表明，将TDA与聚类算法相融合的策略，在不同市场情境下均能显著提升稀疏投资组合的多维度绩效指标。