Euclidean (dis)similarity in financial network analysis

Abstract

Interdependence among financial return series primarily originate from correlation between underlying assets. However, correlation fully describes interdependence only if the financial system behaves linearly and if an assumption of multivariate normal distribution additionally holds true. At the same time, with intrinsic z score normalization, correlation ignores means (expected return) and variances (risk) when calibrating the interdependence. Such oversight raises the significant question of whether security return networks can be realistically modelled and interpreted by market correlations. This paper proposes the Euclidean (dis)similarity metric which enables incorporation of risk and return along with the primary correlation component. We apply this metric to explain the collective behavior of the MSCI world market and compare the results with other correlation networks. Findings show that realized volatility accounts for 71% of the observed topology whereas correlation explains only 29% of market structure. No evidence was found supporting the importance of expected return. Power law exponents and degree distributions reveal that the centrality of hub nodes are considerably higher in the Euclidean as opposed to correlation networks. Accordingly, the importance and influence of central countries (like US and Japan hubs) in the spreading of high volatility is considerably higher than what correlation networks report.