Abstract
We propose a clustering method for large dimensional data to classify the 365 largest euro area financial institutions according to their business model. The proposed clustering approach is applied to granular supervisory data on banks’ activities and combines also dimensionality reduction and outlier detection. We identify four business models, namely wholesale funded, securities holding, traditional commercial and complex commercial banks while identifying as outliers the banks that follow idiosyncratic business models. Evidence is provided that the sets of banks following the distinct business models differ with respect to performance and risk indicators.
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Notes
Loans to the real economy equal EUR 712 bln while the sum of loan commitments and financial guarantees to the real economy equal EUR 404 bln, according to the bank’s 2016 financial statement: https://invest.bnpparibas.com/sites/default/files/documents/etats_financiers_31.12.16_en.pdf.
Source: Bank of Greece statistics on the aggregate balance sheet of Greek credit institutions.
For example, deposits from other banks or customers are generally an important source of funding for Landesbanken, however the percentage varies considerably. Specifically, some Landesbanken rely almost exclusively on deposits for their funding, either from other banks or from customers while for some other this is not the case e.g. the Oldenburgische Landesbank had according to its 2017 financial statement more than 85% of its funding via deposits, while this percentage is less than 50% for Landesbank Baden-Württemberg—again as shown in the bank’s 2017 financial statement. Consequently, consideration of additional granular information on the remaining part of the liability side is needed in order to classify these banks meaningfully to a business model.
Tywoniak et al., 2007 use also customer satisfaction ratings, although this seems to be better suited as a performance variable which could be investigated ex post. Reger & Huff (1993) should be considered separately in this strand of the literature as they focus on the cognitive dimension of the managers and utilises data originating from interviews with bankers. As regards the criteria used to determine the differences among strategic groups, DeSarbo & Grewal (2008) include performance, efficiency and size in the outcome set. Halaj & Zochowski (2009) also incorporate risk indicators (‘irregular loans’) arguing that this allows to position banks in a risk-return space, an idea which is especially relevant for the banking sector.
The number of clusters is chosen using the pseudo F-index, as proposed in Calinski & Harabasz (1974), which quantifies the trade-off between parsimony and ability to discriminate between clusters.
The standard reference on finite mixture models is McLachlan & Peel (2000). Recently, the literature has provided robust versions estimating mixtures of multivariate skew-normal (Lin et al., 2016) and skew-t distributions (Murray et al., 2014a) by maximum likelihood and the EM algorithm respectively. A distribution-free alternative is provided in Yang et al., (2017) using trimmed likelihood. Lucas et al., (2017) estimate via EM dynamic mixtures of normal or t distributions with time-varying means and possibly covariance matrices and find that the choice of Student’s t causes clusters to be more robust to outliers due to fat tails.
It should be noted that there exist few variables presenting values higher than unity, like notional amounts of derivatives.
We also experimented with including size variables in the input set, however, this did not alter significantly the results as the ensuing factors still were mainly related to the compositional input variables.
Hartigan suggested specifically that when \({\mathrm{H}}_{\mathrm{c}}>10\), the number of clusters should be selected to be equal to c + 1. Chang and Mirkin (2010) find that this criterion works well also for different values than 10.
Details can be found at the link https://github.com/MatFar88/A-clustering-methodology-for-European-banks-business-models.
Specifically, the singular values for three factors were 17.3, 3.7 and 0.4 while for the two-factor case they were equal to 16.0 and 3.
The choice of the percentage identified as outliers was based on the examination of the set of banks which were selected in the outlier set and on the visual examination of results in the low dimensional space. The results presented later are not sensitive to small deviations of this parameter value (these results are available upon request).
A stability analysis of the derived classification is presented in "Appendix B".
Therefore, it is clear that the two types which sometimes are lumped together as ‘investment banks’, namely the securities holding banks and the wholesale funded ones should be distinguished because their activities differ substantially.
We have preferred to label this business model as “complex” rather than “diversified”, as the latter label would imply that they are safer against risks. On the other hand, both names refer to the variety of the activities in which these banks are engaged to. The characterisation “universal” could also be fitting for this class of banks.
Similar is the result obtained by De Meo et al., (2018) for a sample of 77 European banks.
Cernov & Urbano (2018) examine a large sample of 5292 European banks and find also that retail banks represent the majority. Their results are driven by the large set of cooperative banks and savings and loans associations (usually quite small institutions) that dominate the sample (57% of the number of institutions but only 9.3% as regards the share of assets). Therefore, it is not straightforward to map these results into ours.
Specifically, the median carrying amount of hedge accounting derivatives on the asset side of the “wholesale-funded” cluster is 1.05% of the total assets while this number is less than 0.25% for the remaining clusters. The carrying amount of derivatives in the “Held for trading” portfolio is 0.96% for the “wholesale-funded” cluster while it is less than 0.57% for the remaining clusters.
Fair valued financial commitments and guarantees are also included under this item.
In a few cases, our sample includes a large bank at a consolidated level (e.g. Unicredit in Italy) and a (usually much smaller) subsidiary of that bank in another country.
Our classification results remain unchanged to a level higher than 95% when a different reference date within the 2014Q4–2015Q3 time period is used. This is expected as in a short time frame the composition of banks’ activities is not expected to change significantly. This is consistent also with the approach adopted in the literature. For example, Lucas et al., (2017) assume a fixed cluster assignment although their data set spans a larger time period while Mergaerts & Vennet (2016) find that ‘between’ variation (differences across banks) exceeds the ‘within’ variation (changes over time within banks) for a sample of banks from 30 European countries. Finally, also studies which define business models with respect to governance structures assume constancy of business models (e.g. Becchetti et al., 2016).
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Appendix
Appendix
1.1 Appendix A—FINREP templates used as input set
Table
7 presents the templates which are used as the input set along with the number of variables from each template. The EBA templates along with the definitions of the contained data can be found at the EBA website: https://www.eba.europa.eu/regulation-and-policy/supervisory-reporting.
F 01.01 and all F 04 templates provide the breakdown of assets across accounting portfolios, with additional breakdowns on instruments and counterparties. F 05 provides the breakdown of loans by product (credit card loans, collateralized loans, project finance etc.). The liability side is covered by the F 08 template, which breaks down liabilities by accounting portfolio (the largest percentage of banks’ liabilities are valued at amortised cost), instrument and counterparty. Off-balance sheet items, primarily loan commitments and guarantees are contained in template F 09.01. Finally, templates F 10 and F 11.01 provide detailed information on derivatives, distinguishing between trading and hedge accounting derivatives. The information is further broken down by type of derivatives (interest rate, equity, foreign exchange, credit and commodity) and by the type of market in which the derivatives are traded (OTC or organised markets).
1.2 Appendix B
In this Appendix, we have examined the stability properties of the classification derived, according to the principles described in von Luxburg (2010). We have done this by re-running the clustering algorithm in the reduced sample of 329 banks, i.e., excluding the banks that were identified as outliers by the application of the algorithm in the initial sample of 365 banks.
In general, the issue of clustering stability is an open area of research as, especially in high dimensional spaces, the solution depends on the initialization of parameters (see Tortora (2011)). We have focused, therefore, to examine the stability properties of the classification that we have used in the statistical analysis. Our investigation, reported below, shows that the classification is locally stable in the reduced sample of 329 banks that excludes the outliers.
Specifically, our results show that starting from random initialisations defined as perturbed versions of the cluster memberships obtained in the total sample (in which x% of bank memberships into clusters are randomly re-assigned), our clustering algorithm (without the outlier detection step) does not proceed further in the large majority of cases, as the initial values (which are close to the ones we use in the statistical analysis) represent a local minimum. The initial objective function, i.e., the variance within clusters in the reduced space, is now minimised in the space with the reduced sample size: this is why, when x is small, the initial objective is sometimes lower than our original one, meaning that a small perturbation of the initial solution could lead to a lower value of the objective function in this reduced space. However, this drawback disappears quickly as x% reaches and goes beyond 5%, i.e., when we examine non-negligible departures from the classification used in the paper. More importantly, in the small number of cases where the algorithm starts to run after the perturbed initialization is given, the final solution has always a higher objective value compared to the minimised objective value that we obtain in the statistical analysis. In other words, the optimization then gets trapped in a local minimum that is worse than our original optimum. Therefore, we can conclude that our classification is very close to a global minimum if we search within an area relatively close to our initial classification (or in other words, a local minimum in the reduced space). This can be further appreciated in Fig. 14, which contains the detailed results of our investigation for what concerns the initial and the final objective value across 10,000 simulated runs.
More specifically, randomizing 1% of memberships (3 banks), the procedure goes to the second step 0% of the times. When 2% of memberships are re-assigned (7 banks), the procedure goes to the second step 0.0012% of the times (12 times). Furthermore, when 5% of memberships are re-assigned (16 banks) the procedure goes to the second step 6.62% of the times and it always gets trapped in a worse local minimum than the one we obtain in the statistical analysis, i.e., the final objective is never lower. Similarly, for x > 5%, the final objective attained when the algorithm goes to the second step is never lower than the value of the objective function corresponding to the classification we derive in the statistical analysis.
Boxplots of the objective function values when the clustering algorithm is applied to perturbed initialisations in the reduced sample, excluding the outlier banks. The x-axis contains the x% proportion of banks which are randomly re-assigned compared to the classification used in the paper. Subplot (a) contains the initial value of the objective function which is run 10,000 times for each x%. Subplot (b) contains the final value for the cases when the algorithm starts to run (i.e., the subset of the 10,000 runs in which the initialisation does not represent itself a local minimum). The red line shows the value of the minimized objective function under the classification used in the paper. (Color figure online)
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Farnè, M., Vouldis, A.T. Banks’ business models in the euro area: a cluster analysis in high dimensions. Ann Oper Res 305, 23–57 (2021). https://doi.org/10.1007/s10479-021-04045-9
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DOI: https://doi.org/10.1007/s10479-021-04045-9