But maps of the topology or wiring of the financial sector can be revealing about the strength, direction and complexity of the counterparty links between, and interactions among, financial firms. As one example, Chart 6 looks at the interbank connections between UK banks in 2013. 10 This suggests the wiring of the interbank network is messy and dense. The network’s epicentre is a small set of large banks with a very large number of connections – “superspreader” banks. There are, in addition, a large number of peripheral banks with few connections. In other words, the interbank system has all the properties of a classic scalefree network. Chart 7 looks at the pattern of interbank funding exposures among UK banks. It, too, suggests a complex web with scale-free properties. Networks with these properties are prone to failures among the super-spreader nodes. Since these are likely to be the entities most exposed to “too complex to manage” problems, this topology harbours a potential systemic vulnerability, the type of which was exposed in 2008. 9  “True Cost of complexity in the banking sector”, Simplicity Consulting (2012). 10  It is taken from Langfield, Liu and Ota (2014). Exposures comprise unsecured loans, marketable securities, CDS sold minus CDS bought, securities lending and repo and derivatives exposures. BIS central bankers’ speeches  7  Complex interactions are not confined to the banking sector. The non-bank (“shadow” banking) sector has become increasingly important over recent years.
This is particularly the case when the network has scale-free properties – in other words, a coreperiphery-type topology. These points can be brought to life using some simulations of the statistical distribution of a simple set of systems of systems. These are constructed by mixing together component distributions, which proxy the layers or sub-systems. These layers may themselves be complex. This mixing of layers, or distributions, is done using an assumed distribution of correlations, which may itself be non-normal and complex. In other words, there are multiple layers of complexity in this system of systems. The inputs to the simulations are shown in Table 1. Chart 1 shows a set of joint (system-wide) distributions from these simulations, where each line represents a probability contour of the distribution. 3 Chart 1a is the baseline case. It involves a mix of two normal distributions with a low correlation coefficient (0.3) where these correlations are themselves normally distributed. 4 This joint distribution represents a twolayer system of systems, with neither layer complex (hence the normal distribution for each) and where the correlation between the sub-systems is weak and regular. The resulting joint distribution is slightly more elliptical than the normal – meaning a greater likelihood of large positive or negative outcomes occurring simultaneously – but is otherwise unexceptional. 5 We can now add progressively greater degrees of complexity to this base case to assess its impact on the distribution of systemic risk.