Fig. 3.

The systemic risk presented by a given set of allocations is largely characterized by two distinct factors: (i) the distance between the banks’ allocations D and (ii) the imbalance of the average allocation G, defined as the distance between the average allocation and the individually optimal allocation. Shown is the expected cost C associated with 10⁵ randomly chosen allocations as described in Fig. 2. When the cost function is linear (s = 1), the configuration that minimizes system cost has the banks herding in selecting the portfolio that minimizes individual risk of failure, (A). As the cost function becomes more nonlinear (s = 1.2), the cost-minimizing distance between the banks becomes larger. Here, the configurations that minimize system cost are associated with having banks at an intermediate distance from each other, while still having low imbalance G (B). With stronger nonlinearity (s = 4), the cost-minimizing configuration puts banks as far apart from each other as possible in asset space—large D (although still keeping the average location as close as possible to the individual optimum, i.e., small G) (C). Regressing log(C) against D, D², and G explains 97% of the variation in cost at s = 1, 90% of the variation in cost at s = 1.2, and 99% of the variation in cost at s = 4.