Systemic Risk and Stability in Financial Networks

The recent financial crisis has rekindled interest in the relationship between the structure of the financial network and systemic risk. Two polar views on this relationship have been suggested in the academic literature and the policy world. The first maintains that the “incompleteness” of the financial network can be a source of instability, as individual banks are overly exposed to the liabilities of a handful of financial institutions. Thus, according to this argument, a more complete financial network, which limits the exposure of the banks to any one counterparty would be less prone to systemic failures. The second view, in stark contrast, hypothesizes that it is the highly interconnected nature of the financial system that contributes to its fragility, as it facilitates the spread of financial distress and solvency problems from one bank to the rest in an epidemic-like fashion.

In our recent NBER working paper, Systemic Risk and Stability in Financial Networks, my co-authors (Asuman Ozdaglar of MIT and Alireza Tahbaz-Salehi of Columbia Business School) and I provide a tractable theoretical framework for the study of the economic forces shaping the relationship between the structure of the financial network and systemic risk. We show that as long as the magnitude (or the number) of negative shocks is below a critical threshold, a more equal distribution of interbank obligations leads to less fragility. In particular, all else equal, the sparsely connected ring financial network (corresponding to a credit chain) is the most fragile of all configurations, whereas the highly interconnected complete financial network is the configuration least prone to contagion. In line with the observations made by Allen and Gale (2000), our results establish that, in the more complete networks, the losses of a distressed bank are passed to a larger number of counterparties, guaranteeing a more efficient use of the excess liquidity in the system in forestalling defaults.

We also show that when negative shocks are larger than a certain threshold, the second view on the relationship between the structure of the financial network and the extent of contagion prevails. In particular, completeness is no longer a guarantee for stability. Rather, in the face of large shocks, financial networks in which banks are only weakly connected to one another would be less prone to systemic failures. Such a “phase transition” is due to the fact that, the senior liabilities of banks, as well as the excess liquidity within the financial network, can act as shock absorbers. Weak interconnections guarantee that the more senior creditors of a distressed bank bear most of the losses and hence, protect the rest of the system against cascading defaults. Our model thus formalizes the robust-yet-fragile property of interconnected financial networks conjectured by Haldane (2009). On a broader level, our results highlight the possibility that the same features that make a financial network structure more stable under certain conditions may function as significant sources of systemic risk and instability under another.

The paper also provides an analysis of the efficiency of the financial networks that emerge in equilibrium. We assume that interbank interest rates adjust endogenously in order to reflect the risk that each bank’s decisions impose on its counterparties. Nevertheless, we show that equilibrium financial networks may be excessively prone to the risk of financial contagion. The intuition underlying this result is that even though banks fully internalize the effects of their lending (and risk-taking) decisions on their immediate creditors, they do not take into account the fact that their lending decisions may also put many other banks (such as their creditors’ creditors) at a greater risk of default. Thus, our results highlight the presence of a financial network externality, which cannot be internalized via simple bilateral contractual relations, thus providing an example of the view that financial stability is a “public good,” likely to be under-provided in equilibrium. We also show that the presence of this externality may manifest itself in equilibrium financial networks that (relative to the socially efficient level) are either too sparsely or too densely connected. The financial network externality and the consequent inefficiency also imply that there is room for welfare-improving government interventions. We leave the analysis of the optimal policy in this class of models to future work.

Finally, we establish a second form of phase transition when long-term returns are partially pledgeable. In particular, we show that if the fraction of the returns that is pledgeable is above a certain threshold, there are no network effects: the excess liquidity of the baking system can be efficiently reallocated to distressed banks and all defaults are avoided, regardless of the structure of the financial network. However, if the pledgeable fraction is below this threshold, network effects cannot be avoided, and the local structure of the financial network plays a defining role in the extent of financial contagion.

The full paper is available for download here.