Systemic Importance and the Contagion Phenomenon in a Network of Banks
On September 13, the Reserve Bank of India identified HDFC bank as a Domestic Systematically Important Bank (D-SIB). This status, referred to colloquially as “too big to fail”, refers to banks that are determined to have the potential to “send shocks through the [domestic] financial system” (BIS) in the event of their failure. Specifically, criteria for classification as a D-SIB include size (relative to domestic GDP), interconnectedness, and complexity (taken directly from the Basel Committee’s Framework).
Interconnectedness of a bank in an economy is an important criterion, and it can be visualized using graph theory. Consider each bank as a node, and connections between banks to represent the presence and magnitude of transactions between banks. (Here, this would be a weighted directed graph.) Because of the nature of bank transactions, the directedness and weights of edges with respect to one node will indicate the size of one bank—larger banks will tend to carry out more transactions of higher magnitudes with more banks. If we are able to construct a graph of this sort, we can identify the largeness of a bank just by the number and weights of the edges connected to a node. Large banks that are “too big to fail” (D-SIBs) will be connected to many other banks and have edge weights corresponding to high volumes of transactions. In the research paper (Yao et al.) linked, the degree of systemic importance is in part determined by a matrix of interbank credit exposure—this actually encodes a directed weighted (multi)graph because it acts as an adjacency matrix and is hence a quantitative measure of interconnectedness.
The phenomenon of D-SIB failure “sending shocks through the financial system” is an example of contagion in a network. If a D-SIB is connected to many other banks and fails, a large number of those banks will lose a significant volume of transactions, causing some of them to suffer and fail. Then banks connected to those failing banks will also start to suffer. An example of this interconnected market is the interbank lending market, the “contagion-induced” collapse of which caused the financial crisis of 2007-2008. Here, we see that the interconnectedness of a network is often a consequence of certain banks controlling a large stake of the market, and that this interconnectedness leaves certain markets susceptible to contagion-induced collapses. This is why governments and regulatory bodies identify such banks as D-SIB so that additional restrictions and regulations may be imposed on the bank to prevent failure.
In class, it was also discussed that certain graphs can possess “subgraphs” (different from components as these sets of nodes and edges are connected to each other) that differ in their levels of connectedness from other subgraphs. For example, a graph with 12 nodes can have 3 subgraphs that are fully connected, with only one edge between each pair of those subgraphs. If this graph represents a model of banks in a market, the theory of contagion can also be applied to it.
(It should be noted that graphs of bank markets are almost always fully connected but with differing edge weights, because the likelihood that two banks in a domestic market don’t trade with each other at all is practically nil. In order to closely match the model of connectedness I have described, draw a similar looking graph that places an edge between 2 banks if their transactions are above a threshold value—hence banks are connected if they have a high volume of transactions, and are not connected if they don’t trade as much.)
In the above 12-node model, imagine a bank in one of the fully-connected subgraphs fails. Because of its connectedness to 3 other banks, those three banks will suffer. Then, as in contagion theory, those 3 banks, being dependent on each other, will suffer even more. As the failing node is either connected to two other subgraphs by one edge, or not at all, the contagion effects in the other two subgraphs will be minimal.
This understanding of connectivity among banks can give insight into not only how much the economy will suffer as a result of a D-SIB failing, but which parts and actors in the economy will suffer relative to others. In class, we distinguished highly connected subgraphs from each other when the only connections between them were local bridges (edges that are part of no triangle). This distinction allows for a rigorous means of describing connectivity among nodes; this in turn allows us to qualitatively and quantitatively gauge local impacts of D-SIB failure within a domestic market.
Resources:
News Article: http://www.financialexpress.com/money/hdfc-bank-too-big-to-fail-why-this-crucial-tag-stamped-on-just-3-banks-in-india-read-all-about-it/853007/
Basel Committee Framework: http://www.bis.org/publ/bcbs224.pdf
Research Paper describing quantitative criteria for systemic importance: http://ac.els-cdn.com/S1877050915014842/1-s2.0-S1877050915014842-main.pdf?_tid=b9745f84-9a6f-11e7-b2ec-00000aacb362&acdnat=1505519210_5255fdd7ee3aee273a16bc6b15dd1dc6