Chart 10 offers support for the latter hypothesis. It suggests a positive relationship between bank size and pre-crisis expectations of official sector support. 33 Size matters. Historically, the safety net was perceived to be fur-lined for those above a certain size. This evidence is discouraging from a systemic risk perspective. It suggests incentives to generate and propagate risks may have been strongest among those posing greatest systemic threat. Basel vaccinated the naturally immune at the expense of the contagious: the celebate were inoculated, the promiscuous intoxicated. Latterly, this defect has begun to be addressed. For example, the US and Swiss authorities have announced plans to introduce tighter regulatory requirements for systemic institutions. There is further to go internationally. Work is needed to give systemic regulation practical effect. A number of calibration devices have been proposed. 34 With richer data on network topology, calibrated simulation models could help gauge financial institutions’ marginal contribution to systemic risk. This is standard practice in management of the electricity grid and eco-systems. Finance needs to catch up. (c)  Restructuring the network  In Herbert Simon’s The Architecture of Complexity, he tells the parable of two watchmakers, Hora and Tempus. 35 Both produce watches composed of 1000 parts. Both watches are, in this sense, equally complex. They are also of equal quality and sell at the same price. But Hora’s business prospers, while Tempus’s founders. Why? 32  For example, Pikitch et al (2004). 33  Proxied by Fitch ratings agency’s support ratings for institutions.
For Bank A, not knowing the links in the chain means that judging the default prospects of Bank B becomes a lottery. Indeed, in some ways it is worse than a lottery, whose odds are at least known. In this example, Bank A faces uncertainty in the Knightian sense, as distinct from risk, about the true network structure. Counterparty risk is not just unknown; it is almost unknowable. And the higher the dimensionality of the network, the greater that uncertainty. It is possible to formalise this intuition with some simple numerical examples. 17 Consider two states of the world, pre-crisis and crisis. And consider the impact of network complexity on CDS pricing. Once we introduce Knightian uncertainty, asset prices are no longer determinate; they are defined by a range rather than a point. So the range of equilibrium CDS spreads can be taken as a metric of the uncertainty, and hence distortion, arising from different network structures. Chart 4 plots a pre-crisis world where it is assumed that counterparty default probabilities, and the uncertainty around them, are low. Subject to those assumptions, it illustrates how the range of CDS spreads is affected by Bank B’s number of counterparties. Larger numbers of  17  The following is based on work in progress at the Bank on asset pricing under network Knightian uncertainty, by Sebastiano Daros and Kemal Ercevik. 8  BIS Review 53/2009  counterparties are marginally beneficial. There is a “law of large numbers” benefit.