Contagion and equilibria in diversified financial networks

Diversified cross-shareholding networks are thought to be more resilient to shocks, but diversification also increases the channels by which a shock can spread. To resolve these competing intuitions we introduce a stochastic model of a diversified cross-shareholding network in which a firm's valuation depends on its cash endowment and the shares it owns in other firms. We show that a concentration of measure phenomenon emerges: almost all realized network instances drawn from any probability distribution in a wide class are resilient to contagion if endowments are sufficiently large. Furthermore, the size of a shock needed to trigger widespread financial distress increases with the exposure of firms to each other. Distributions in this class are characterized by the property that a firm's equity shares owned by others are weakly dependent yet lack “dominant” shareholders.