Inference of Partial Canonical Correlation Networks with Application to Stock Market Portfolio Selection

In recent years, association networks and their applications have received increasing interest. The relationships in a network should ideally be ascertained without any preconceptions about the existence of a connection a priori. This would allow interpretations to be based on the underlying structure rather than on assumptions. Furthermore, a method that discounts outside influence on the relationships is desirable. Partial correlation is one method that meets these criteria, however, this approach is limited to a single attribute. We propose that examining the multi-attribute partial canonical correlations is a superior strategy for capturing the complex relationships found in real world data. As a motivating application, we choose the problem of stock market portfolio selection. Diversification is a core principle of any sound investment strategy, the purpose being to minimize risk and maximize returns. To create a diverse portfolio, the interrelations between corporations and the industrial sectors that they comprise must be understood. To model these relationships we induce a partial canonical correlation network (PCCN) using recent market data and select portfolios algorithmically based on finding the least dependent but related companies. We compare the risk of portfolios selected from the PCCN, partial correlation networks, and randomly. We find that the PCCN based-approach results in comparatively less risky portfolios.