Comparative Study of Correlations in Financial Markets

We elucidate correlations among stock price movements in S&P 500 and Tokyo Stock Exchange (TSE) taking advantage of the concept of community in networks. The correlation matrix, purified by random matrix theory, is regarded as the adjacency matrix for a stock correlation network. The network thus constructed has links with weights of either sign depending on whether stocks are correlated (positive) or anticorrelated (negative). Community is defined here as a group of stocks related to each other with positive correlation coefficients. The community detection allows us to find that the stocks in S&P 500 are split up into four communities with two conflicting triangular relations. In TSE, there exists three communities of stocks forming a conflicting triangle. We thus see that the frustrated correlation structure is common to the well-developed financial markets.