Graph analysis of stock correlation networks

Abstract

In this paper, networks of S&P 500 stocks are constructed based on the correlation matrices of daily log-returns of constituent stocks. Such networks can be used to study the interactions of stock returns. A new filtering method called Clique-Limited Graphs (CLG) is proposed to extract representative subgraphs from dense networks. CLG is an extension of the minimum spanning tree (MST) with a topological constraint that restricts the number of k-element cliques that involves each node in a given network. The goal is to retain more information without significantly increasing complexity. The proposed method is compared with the MST filtering method that provides a minimal representation of the dense network. Filtered networks are then clustered into groups of stocks to reduce dimensionality and obtain an approximate representation of the market network. Dynamic networks constructed based on rolling correlations between the stock clusters are used to study the evolution of the market network during stock market crashes. It is observed that the network was more unstable over the stock market crash during the Global Financial Crisis than that in March 2020. Finally, the application of network analysis in portfolio construction based on centrality measures is discussed.