Topological structure features enhanced portfolios: integration of asset clustering and price prediction

Topology data analysis (TDA) explores the topological structure features of data from the geometric topology perspective. This study constructs investment portfolios by integrating asset clustering based on topological structure features and price prediction. First, we employ the Principal Component Analysis to reduce the dimensionality of nine topological features, and utilize the K-Medoids algorithm to cluster multiple assets based on the extracted principal components. Then, portfolios based on historical prices and predicted prices are constructed, respectively, with the latter effectively integrates the advantages of TDA and the predictive information. Based on closing prices of Chinese stock market, the performance of five TDA-based strategies are analysed and compared with five industry classification strategies. The results show that portfolios incorporating topological features outperform those based on industry classification, and portfolios integrating predicted prices further outperform those based on historical data. Specifically, the strategy combining TDA with volatility, and the strategy combining TDA with both predicted prices and Sharpe ratio, are particularly outstanding. This study verifies the core value of topological features in investment decision-making, providing a practical approach for portfolio construction.