Gaëtan Fournier : gaetan.fournier[at]univ-amu.fr
Raghul Venkatesh : raghul.venkatesh[at]univ-amu.fr
Excessive risk-taking and financial linkages are at the root of the last financial crisis, and by such two of the key issues of financial regulation. The failure of financial institutions being likely to foster contagion both inside and outside the financial sector, financial regulation aims at preventing it by constraining the amount of risk each institution is allowed to take. Through prudential regulation under the form of capital requirement, regulators attempt to dampen the (financial and social) costs of bail-ins. We analyze in the paper how financial linkages -- in the form of cross-shareholding -- are likely to modify the risk exposure of each institution and how prudential regulation should account for it. We build a simple model in which each financial institution, financed through equity (held in part by the financial sector) and external debt, has to allocate its fund between a risky, a risk-free asset, and equity in other institutions. Assuming that an extreme adverse event, in the form of a loss in its risky asset, can hurt at most one institution, we pin down the minimal capital requirements a regulator should set to prevent any default. We show that these limits of risk-taking depend on an original centrality measure that relies on the cross-shareholding network twice : through direct complementarities and through a resource effect that creates heterogeneity among institutions. We show that absent this resource effect, a more integrated network generates less regulation for all institutions, and provide conditions on the network for it to be the case. In the presence of resource effects, simulations tend to show that even if integration can lead to more regulation for some, the average capital requirement decreases. On the contrary, network diversification increased average regulation in all of our simulations on random networks. We finally analyze the case of correlated investment portfolios and show that capital requirements can then become strategic substitutes, modifying our comparative statics on network integration.