Portfolio diversification and systemic risk in interbank networks

This paper contributes to a growing literature on the ambiguous effects of risk diversification. In our model, banks hold claims on each other's liabilities that are marked-to-market on the individual financial leverage of the obligor. The probability of systemic default is determined using a passage-problem approach in a network context and banks are able to internalize the network externalities of contagion through their holdings. Banks do not internalize the social costs to the real economy of a systemic default of the banking system. We investigate the optimal diversification strategy of banks in the face of opposite and persistent economic trends that are ex-ante unknown to banks. We find that the optimal level of risk diversification may be interior or extremal depending on banks exposure the external assets and that a tension arises whereby individual incentives favor a banking system that is over-diversified with respect to the level of diversification that is desirable in the social optimum.