Sparse Portfolio Selection via Topological Data Analysis based Clustering
This work addresses portfolio optimization for investors by providing a novel data-driven method, though it is incremental as it builds on existing TDA and clustering techniques.
This paper tackled the problem of constructing sparse portfolios by using topological data analysis (TDA) and clustering to select stocks based on topological features of price movements, resulting in significantly enhanced performance across various measures in diverse market scenarios, including during the COVID-19 period from 2009 to 2022 on the S&P index.
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.