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Identifying systemically important financial institutions: a network approach

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Abstract

The Basel Committee on Banking Supervision has proposed a methodology to identify Systemically Important Financial Institutions based on a series of indicators that should account for the externalities that these institutions place into the system. In this article we argue that the methodology chosen by Basel III maintains the micro-prudential focus of Basel I and II. We show how the PageRank algorithm that operates behind the Google search engine can be modified and applied to identify Systemically Important Financial Institutions. Being a feedback measure of systemic importance, the PageRank algorithm evaluates more than individual exposures. The algorithm is able to capture the risks that individual institutions place into the system, while at the same time, taking into account how the exposures at the system-wide level affect the ranking of individual institutions. In accordance to the Basel III framework, we are able to distinguish between systemic importance due to exposures born on the asset and on the liability side of the balance sheet of banks.

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Notes

  1. See Kashyap et al. (2008), Bank of England (2009), Brunnermeier et al. (2009), Haldane (2009), Hellwig (2010), Trichet (2011), Haldane and May (2011) and Rosengren (2013).

  2. See Basel Committee on Banking Supervision (2013).

  3. The five categories are: size, cross‐jurisdictional activity, interconnectedness, substitutability financial institution infrastructure and complexity. Each category has the same weight (20%) in the overall measure which is rescaled such that an overall score is given in basis points. See Basel Committee on Banking Supervision (2013) for further details.

  4. We explicitly distinguish systemic risk, understood as a byproduct of banks’ bilateral first and higher order exposures in the interbank market, from contagion that results from correlations in bank asset returns as in Adrian and Brunnermeier (2008) or co-movement in the deposit flow as in Diamond and Dybvig (1983), as well as interconnectedness at the producer-supplier level (including financial interlinkages between banks and its non-financial borrowers/depositors) as in Acemoglu et al. (2010). Undoubtedly the two concepts are closely related and interbank exposures can be a major source of contagion; e.g. Allen and Gale (2000). The key distinguishing factor however, is that interbank exposures are first and higher order balance sheet interlinkages between financial institutions, i.e. horizontal exposures between peers rather than vertical exposures with clients or exposures due to losses in similar investment portfolios. In the event that a financial institution defaults, a void is immediately created in the balance sheet of several other banks through the direct and indirect horizontal linkages. This type of exposures represents a risk for the entire system that is typically several orders of magnitude higher than that resulting from other contagion mechanisms.

  5. Their analysis can in fact be performed using stock prices from companies of any industry, provided that they are publicly traded, regardless of whether they have or not direct bilateral balance sheet exposures. One of their findings for instance is that insurance companies emerge as systemically important towards the end of the sample. Despite the fact that both banks and insurances are financial intermediaries, insurance companies do not have direct balance sheet exposures against its peers while banks do. This means that the sources of systemic risk differ in both industries, which greatly influences design policies to control systemic risk (see Thimann 2014).

  6. While a bank can be a systemically important borrower and lender at the same time, this does not need to be the case. A bank can borrow relatively small amounts in the interbank market and yet be systemically important as a result of its lending activities. The risks for such a bank lie, and will be transmitted to the rest of the system, through the asset side of its balance sheet. On the contrary, banks borrowing large volumes face and distribute risks to the system through the liability side of the balance sheet.

  7. Dungey et al. (2013) compute their rankings based on a matrix correlations, which by definition is symmetric. In our case, to have a symmetric matrix of exposures, it is required that every borrowing transaction between any two banks i and j is perfectly matched by a lending transaction between the same banks. While two banks certainly can, and often do, lend and borrow from one another, a situation of perfect bilateral matching would render the interbank market a redundancy.

  8. Some recent contributions reaching similar conclusions include: Babus (2007), Gai and Kapadia (2010).

  9. See Newman (2002) and Meyers (2007) for examples of the spread of infectious diseases on human networks, and Pastor-Satorras and Vespignani (2001a, b, b) for the analysis of the spread of viruses on computer networks.

  10. The degree of a bank is the number of partners that every bank has. See Sect. 2 below for further details. Assortative mixing refers to the property by which nodes in a network establish a relationship with similar nodes, according to a certain characteristic (size, degree, geographical location, etc). Disassortative mixing refers to the opposite situation, i.e. nodes connecting to nodes belonging to different groups.

  11. The small world effect refers to the property observed in a large number of social networks by which the distance between any two nodes grows at a speed \( {\text{log }}\left( n \right) \) as n → ∞, where n is the number of nodes. Cont et al. (2013) question this finding in the context of interbank networks.

  12. In the case of bipartite networks, the adjacency matrix is typically not squared. The adjacency matrix of bipartite networks receives the name of incidence matrix to distinguish it from the adjacency matrix.

  13. In other networks, most notably the internet, it is common to have selfedges.

  14. See Freeman (1978) and Borgatti and Everett (2006).

  15. The weighted version of the degree centrality is known in the network literature as strength centrality, for homogeneity we maintain the same degree denomination also for weighted networks.

  16. We are not the first to stress this issue. Albert and Barabási (2002), Newman (2004) and others have argued that the study of weighted networks has occupied a much smaller stage in the literature, than it probably should. Networks like the collaboration between authors, friendship networks, affiliation networks, biochemical and ecological networks, and the internet as well are networks in which the link between any two nodes might have different intensities. In other words, several networks are intrinsically weighted and in such cases, the network properties are better understood when using weighted instead of binary adjacency matrices.

  17. See Newman (2010) for further details.

  18. The term \(fd'_{out}\) is added to the matrix \(A\,\Phi\) to guarantee that the resulting matrix is irreducible.

  19. Notice that for α = 1, the irreducibility of the matrix \( \overline{\overline{P}}_{r} \) is no longer guaranteed. In this case the eigenvector in not uniquely defined. The same is true when the elements fi are not all larger than 0. For this reason, in most applications, f is chosen to be \( \frac{1}{n}1 \), such that fi > 0 is guaranteed ∀i = 1, …, n.

  20. The most widely used method to compute the eigenvector corresponding to the largest eigenvalue in the context of the PageRank is the power method.

  21. The former case corresponds to the eigencentrality measure, from which the PageRank measure is derived.

  22. When applying the algorithm, we set the parameter α = 0.85 and the elements fi = 1/n.

  23. The same principle applies to the matrix \( \overline{\overline{P}}_{l} \) of course.

  24. Acharya et al. (2012) argue that also market power is a potentially important factor driving the behavior of banks in the interbank market.

  25. Trust in the present context is directly related to the definition given in Fehr (2009): An individual trusts if she voluntarily places resources at the disposal of another party (the trustee) without any legal commitment from the latter. In addition, the act of trust is associated with an expectation that the act will pay off in terms of the investor’s goals. In particular, if the trustee is trustworthy the investor is better off than if trust were not placed, whereas if the trustee is not trustworthy the investor is worse off then if trust were not placed.

  26. As argued in Rochet and Tirole (1996) policies like lending of last resort reduce the incentives of banks to monitor their peers. This helps increasing the importance trust as a driver of interest rates.

  27. According to a 2007 ECB survey, the overnight market segment account for the 70% of the all unsecured market.

  28. The EONIA is a weighted average of all uncollateralised overnight loans processed by a portfolio of the most active credit institutions in the money market.

  29. ONL are contracts encompassing more than one day between two consecutive business days.

  30. We are aware that the e-MID dataset encompasses most of the transactions in which at least one partner in an Italian bank and thus it could potentially underestimate the relationships between foreign banks because they can transact using also other platforms. Unfortunately we do not have a dataset that contains all this information.

  31. To limit the potential noise in daily observations, we employ monthly averaged exposures.

  32. The Basel III was scheduled to be introduced from 2013 until 2015; however, changes from 1 April 2013 extended implementation until 31 March 2018 and again extended to 31 March 2019. This regulatory framework is not the actual methodology used to identify the SIFI but it is the first attempt of measuring the importance of interconnection between financial institutions.

  33. See Basel Committee on Banking Supervision (2013, 2015).

  34. We have experimented with several cutoff values and the results remain qualitatively unchanged.

  35. We first rank the banks according to their systemic importance in decreasing order using the two different methodologies: PageRank and Basel III. Then we identify those banks that belong to the upper 20-th percentile of the ranking (the upper bucket) according to both methodologies. Finally we compute the percentage of banks that enter into the PageRank and Basel III buckets simultaneously, i.e. the banks that both methodologies ‘agree’ that belong to the upper bucket of systemic importance.

  36. We denote the PageRank vector with the general notation π because the findings of Langville and Meyer (2004) apply to both the lending and the borrowing ranks.

  37. It is in fact to be expected, that the variability of the rankings in the lower percentiles of the PageRank distribution will be higher. For this reason we focus here only on relatively high percentiles of the PageRank distribution.

  38. We also perform this same analysis considering the banks that enter into the largest 5‐th PageRank percentile. Our conclusions regarding the choice of the parameter α and the stability of the results due to changes in α remain unchanged.

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Authors and Affiliations

  1. Department of Economics, University of Leuven, Louvain, Belgium

    Pablo Rovira Kaltwasser

  2. National Bank of Belgium, Brussels, Belgium

    Pablo Rovira Kaltwasser

  3. Department of Economics and Management, University of Pavia, via S. Felice 5, 27100, Pavia, Italy

    Alessandro Spelta

  4. Complexity Lab in Economics, Milan, Italy

    Alessandro Spelta

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  1. Pablo Rovira Kaltwasser
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Correspondence to Alessandro Spelta.

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We are indebted to the European Commission for their financial support through the EU FP7 RASTANEWS project (research Grant No. 320278), and to the Research Foundation Flanders (FWO) for their financial support through the research Grant 1510413 N. All errors are ours.

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Rovira Kaltwasser, P., Spelta, A. Identifying systemically important financial institutions: a network approach. Comput Manag Sci 16, 155–185 (2019). https://doi.org/10.1007/s10287-018-0327-8

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