The question of how to stabilize financial systems has attracted considerable attention
since the global financial crisis of 2007–2009. Recently, Beale et al. [Proc. Natl. Acad.
Sci. USA 108, 12647 (2011)] demonstrated that higher portfolio diversity
among banks would reduce systemic risk by decreasing the risk of simultaneous defaults at
the expense of a higher likelihood of individual defaults. In practice, however, a bank
default has an externality in that it undermines other banks’ balance sheets. This paper
explores how each of these different sources of risk, simultaneity risk and externality,
contributes to systemic risk. The results show that the allocation of external assets that
minimizes systemic risk varies with the topology of the financial network as long as asset
returns have negative correlations. In the model, a well-known centrality measure,
PageRank, reflects an appropriately defined “infectiveness” of a bank. An important result
is that the most infective bank needs not always to be the safest bank. Under certain
circumstances, the most infective node should act as a firewall to prevent large-scale
collective defaults. The introduction of a counteractive portfolio structure will
significantly reduce systemic risk.