Networks and Contagion in Financial Markets
(This article follows on from a more general post on the study of networks in economics)
In this model, as well as those concepts Jackson discussed in the broader discussion on networks, we have the concepts of diversification and integration to separate the breadth and depth of connectivity of one organisation to others. A company/organisation/ country with many connections to others would be highly diversified; where those interests represented a higher proportion of their overall connectivity, they would be highly integrated.
The world for this model was simple:
– Organisations held equity in other organisations
– The remainder of an organisation belonged to the initial investors
– Prices were taken as given
– The level of diversification and integration was determined outside of the model
Then, an algorithm, that goes like this:
1. If the value of a particular firm fell below a critical level, it would fail (first failure).
2. If another firm suffered a critical loss value (externally identified at e.g. 1/2/5/10%) from the extent of devalued investments into the first firm, it too would fail.
3. If a third firm then suffered the same critical loss value from the extent of devalued investments in either of the first two firms, it would also fail.
And so on.
(The model was gently critiqued for not allowing for endogeneity or for considering the potential positive impacts of the failure of one firm on another, in the case of the fall of a competitor. The model did not consider effect of an increase in value of firm i, leading to an increase in the value of firm j who had invested in i, then leading to an increase in the value of firm i who had invested in firm j.)
Jackson et al. ran simulations, setting a level of integration, a level of diversification, and a critical loss value.
And they found the following:
– where firms were not diversified at all, one failure did not lead to others. This is hardly surprising. If a firm’s value is not linked to any other firm’s value, there will be no knock-on effects of the first.
– as diversification increases, as does the cascade effect, although this is lower for lower critical loss values. Again, no big shock: if a firm’s value is linked to others, and is more sensitive to losses (lower critical loss value), one failure will have a greater negative impact on others.
– there is a point at which this reverses. For larger levels of diversification, the contagion reduces. (Remember, this is for a given level of integration. In the example given, each firm has 5% of the value in another).
What about integration, then? Here, too, we saw ‘non-monotonic effects’ – or, for a given critical loss value, and a given level of diversification, we saw an increase in contagion, followed by a decrease in contagion, for increasing levels of integration.
So, a highly-networked banking sector will be stable, and a highly independent banking sector will be stable, but a sector with few and modest equity shares is a toxic combination for a cascade. In a world where financial markets often resemble the latter, with no clear incentive to move towards either of the former, this may be a cause concern for policy-makers.