Global balance and systemic risk in financial correlation networks

The global balance index is used in the network literature to quantify how balanced a signed network is. In this paper we show that the global balance index of financial correlation networks can be used as a systemic risk measure. We define the global balance index of a network starting from a diffusive process that describes how the information spreads across nodes in a network, providing an alternative derivation to the usual combinatorial one. The steady state of this process is the solution of a linear system governed by the exponential of the replication matrix of the process. We provide a bridge between the numerical stability of this linear system, measured by the condition number in an opportune norm, and the structural predictability of the underlying signed network. The link between the condition number and related systemic risk measures, such as the market rank indicators, allows the global balance index to be interpreted as a new systemic risk measure. A comprehensive empirical application to real financial data finally confirms that the global balance index of financial correlation networks represents a valuable and effective systemic risk indicator.