Contagion and Bailouts in Financial Networks

Department of Economics and Decision Sciences

Speaker : Rakesh Vohra (UPenn)

Room T-007

Abstract: 

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 equity holding network in which a firm's valuation depends on its cash endowment and the shares it owns in other firms. Our stochastic model of holding networks is based on random matrices rather than Erdo-Renyi type random graphs. We show that a concentration of measure phenomenon emerges: almost all realized holding networks 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 default  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. 

As widespread default involves substantial deadweight costs, to counter them, a regulator can inject capital into failing firms. These injections have positive spillovers that can trigger a repayment cascade. But which firms should the regulator bailout so as to minimize the total injection of capital while ensuring solvency of all firms? While the problem is, in general, NP-hard, for a wide range of networks that arise from a stochastic model of the kind just described, we show that the optimal bailout can be implemented by a simple index policy in which a firm index depends only on its characteristics and its position in the network. Specific examples of the setting include core-periphery networks.

Joint work with: 1st paper: Victor Amelkin & Santosh Venkatesh, 2nd paper: Krishna Dsaratha & Santosh Venkatesh