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 2022, 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：本文运用拓扑数据分析工具，提出了一种面向稀疏投资组合构建的数据驱动聚类选股策略。我们的资产选择策略利用股价波动的拓扑特征，为稀疏指数跟踪投资组合（马科维茨投资组合）选取拓扑特征相似（相异）的资产子集。我们在持续同调图与持续同调景观空间中引入了新的距离度量方法，该度量充分考虑时间序列的时间维度特性，并作为聚类算法的输入。通过对2009年至2022年标普500指数的实证分析（包括针对COVID-19疫情数据的专项研究），验证了我们方法的鲁棒性。将拓扑数据分析与聚类算法相融合的策略，显著提升了稀疏投资组合在不同市场情境下各项绩效指标的表现。