Tangency portfolios using graph neural networks.

Abstract

According to modern portfolio theory, the weights of tangency portfolios are solely determined by the expected returns and the covariance matrix of asset returns. However, estimating expected returns and the covariance matrix poses significant challenges, especially when the number of assets is large. Considering the supply-demand relationships between companies issuing stocks, we propose that incorporating industry chain relationships can enhance the accurate estimation of the covariance matrix. Specifically, we present a method that employs Graph Neural Networks (GNNs) to estimate tangency portfolio weights by aggregating stock features based on the industry chain graph and using the aggregated features to estimate the expected returns and the covariance matrix. In addition to incorporating additional industry information, we propose two strategies to enhance the efficiency of estimation: 1) Calculating the dynamic modularity of the stock relationship graph using aggregated node features and constraining the estimated correlations to exhibit a clustered structure by minimizing modularity. 2) Adding a historical ranking regularization to the expected returns. We validate our approach on two daily stock datasets, demonstrating that our method effectively predicts portfolio returns and Sharpe ratios.