Journal of Network Theory in Finance

Using Shapley’s asymmetric power index to measure banks’ contributions to systemic risk

Rodney Garratt, Lewis Webber and Matthew Willison

  • The paper outlines a methodology for determining banks' contributions to systemic risk based on a generaliszation of the Shapley value concept - the asymmetric power index.
  • A bank's power index is increasing in the tendency for its failure to cause losses in the banking system to pass a critical threshold assumed to trigger a crisis.
  • Banks' power indexes depend on the compositions of their assets and their capital buffers.
  • The methodology can also be extended to take into account the risk of interbank contagion.


An individual bank can put the whole banking system at risk if its losses in response to shocks push losses for the system as a whole above a critical threshold. This paper outlines a methodology for determining the contribution of banks to this form of systemic risk. Our approach utilizes a generalization of the Shapley value in which the order of bank failures in response to a shock depends on the composition of the banks' asset portfolios and capital buffers. We show how changes in these factors affect banks' contributions to systemic risk taking into account interbank contagion. Finally, we examine the extent to which banks' contributions depend on the level of the critical threshold for a systemic event.

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