Chapter

8 Bank Business Correlations

Author(s):
Jörg Decressin, Wim Fonteyne, and Hamid Faruqee
Published Date:
September 2007
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This chapter1 investigates bank business correlations within individual countries and across countries in Europe. In doing so, it seeks to disentangle the relative importance of EU-wide versus country-specific drivers of bank soundness and profitability in order to gain insights into the state of banking system integration and to aid in the design of financial stability arrangements. A growing literature measures comovements between EU banks, typically finding that EU-wide macroeconomic and banking-specific shocks are significant and that some risks have increased since EMU.2 These results are generally derived from market-based indicators, notably DD measures.3 The contribution here is the following:

  • An analysis of bank balance sheet and profitability indicators, rather than market-based indicators: The former are less distorted by day-to-day market volatility, but are available at a much lower frequency (annually for most institutions) and with longer delays. They are also an important input for supervisors, who cannot rely on market data only.

  • New methods to gauge comovements, notably cluster analysis, that require few assumptions.4

  • A quantification of the importance of EU-wide shocks relative to national shocks—this part of the analysis is also done for DD measures of 11 of the internationally active large banking groups (ILBGs) operating across borders in Europe.

The key finding is that developments in balance sheet and profitability indicators for Europe’s 100 largest banks do not cluster naturally around countries. In various ways, the EU-wide dynamics in these indicators appear to be as important as the country-specific dynamics. Hence, detecting potential risks and vulnerabilities in national financial systems and resolving instabilities if and when they arise are likely to require a strong cross-border perspective.

Data and Summary Statistics

The dataset comprises indicators for Europe’s 100 largest banks from BankScope over a continuous sample period spanning 1997–2004. A few of Europe’s largest banks are excluded because of changes in accounting standards and other reasons (Table 8.1).5 Nonetheless, the distribution of banks across countries is broadly in line with countries’ significance in world financial markets, with few exceptions (Table 8.2). Together these banks account for over half of EU-15 banking system assets. The specific indicators comprise the (after-tax) return on assets (ROA) and equity (ROE); the capital-to-assets ratio (CAP); the gross-operating-revenues-to-assets ratio (OPREVA); and the natural logarithms of gross operating revenue (OPREV), assets (ASSETS), and equity (EQUITY). The availability of further data, notably on capital adequacy, asset quality, and liquidity was much more limited.

Table 8.1.EU-15: Listing of Banks, 1997–2004
Foreign Earnings Share1
AB Spintab (publ)
Abbey National Plc
Alliance & Leicester Plc
Allied Irish Banks plc
Alpha Bank AE
Anglo Irish Bank Corporation Plc
Baden-Wuerttembergische Bank AG
Banca Antonveneta-Banca Antoniana Popolare Veneta SpA
Banca Intesa SpA17.2%
Banca Lombarda e Piemontese SpA
Banca Monte dei Paschi di Siena SpA-Gruppo Monte dei
Paschi di Siena
Banca Nazionale del Lavoro SpA—BNL
Banca Popolare dell’Emilia Romagna
Banca Popolare di Milano SCaRL
Banca Popolare Italiana-Banca Popolare Italiana -
Banca Popolare di Lodi
Banco Bilbao Vizcaya Argentaria SA46.5%
Banco de Sabadell SA
Banco Español de Crédito SA, BANESTO
Banco Espirito Santo SA
Banco Popular Espanol SA
Bankgesellschaft Berlin AG
Bankinter SA
Banque Générale du Luxembourg SA
Barclays Bank Plc17.9%
Bayerische Hypo-und Vereinsbank AG50.2%
Bayerische Landesbank
BHW Holding AG
BNP Paribas44.9%
BRF Kredit A/S
Britannia Building Society
Caisse Centrale du Crédit Immobilier de France—3CIF
Caisse des Dépôts et Consignations-Groupe Caisse des Dépôts
Caixa d’Estalvis de Catalunya-Caja de Ahorros de Cataluña
Caixa Geral de Depositos
Caja de Ahorros de Galicia—Caixa Galicia
Caja de Ahorros de Valencia Castellon y Alicante BANCAJA
Caja de Ahorros del Mediterraneo CAM
Caja de Ahorros y Pensiones de Barcelona, LA CAIXA
Caja Madrid-Caja de Ahorros y Monte de Piedad de Madrid
Calyon
Capitalia SpA
CCF
Cheltenham & Gloucester Plc
Commerzbank AG23.9%
Crédit Agricole S.A.32.3%
Crédit du Nord
Crédit Foncier de France
Crédit Industriel d’Alsace et de Lorraine—Banque CIAL
Crédit Industriel et Commercial—CIC
Crédit Lyonnais
Credit Mutuel Centre Est Europe (Bancassurance)
Danske Bank A/S23.2%
DekaBank Deutsche Girozentrale
Dexia
Dresdner Bank AG37.9%
Espirito Santo Financial Group S.A.
FoereningsSparbanken AB
Fortis66.3%
Groupe Caisse d’Epargne
Halifax Plc
HSBC Holdings Plc73.0%
IKB Deutsche Industriebank AG
ING Groep NV75.3%
IXIS Corporate & Investment Bank
KBC Group-KBC Groep NV/KBC Groupe SA
Kredietbank S.A. Luxembourgeoise KBL
Landesbank Baden-Wuerttemberg
Landesbank Hessen-Thueringen Girozentrale—HELABA
Landwirtschaftliche Rentenbank
Lehman Brothers International (Europe)
Lloyds TSB Group Plc3.6%
LRP Landesbank Rheinland-Pfalz
Mediobanca SpA
Millennium bcp-Banco Comercial Português, SA
Natexis Banques Populaires
National Bank of Greece SA
National Westminster Bank Plc—NatWest
Nationwide Building Society
Nomura International Plc
Norddeutsche Landesbank Girozentrale NORD/LB
Nordea Bank Danmark Group A/S
Nordea Bank Finland Plc
Northern Rock Plc
OP Bank Group Central Cooperative
Rabobank Group-Rabobank Nederland
Realkredit Danmark A/S
Royal Bank of Scotland Plc (The)21.8%
San Paolo IMI11.5%
Santander Central Hispano Group-Banco
Santander Central Hispano55.8%
Skandinaviska Enskilda Banken AB54.6%
SNS Reaal Groep NV
Société Générale45.5%
Stadshypotek AB
Standard Chartered Plc
Svenska Handelsbanken
UFJ International plc
Ulster Bank Limited
UniCredito Italiano SpA28.8%
WestLB AG
WGZ-Bank AG Westdeutsche Genossenschafts-Zentralbank
Source: BankScope database.

Data are for 2004. Source: Deutsche Bank Research, EU Monitor 31.

Source: BankScope database.

Data are for 2004. Source: Deutsche Bank Research, EU Monitor 31.

Table 8.2.EU-15: Country Distribution of Banks, 1997–2004
NumberTop 20
United Kingdom174
France165
Netherlands32
Spain122
Belgium32
Germany165
Denmark40
Italy120
Sweden50
Finland20
Ireland20
Portugal30
Greece20
Luxembourg30
Austria00
Total10020
Source: BankScope database.
Source: BankScope database.

While in some ways the dataset is representative of the banking industry as a whole, Europe’s largest banks engage in much more cross-border business than the many smaller banks. The key summary statistics are very similar to those for the industry as a whole during 1997–2004: (after-tax) returns on assets and equity of about 0.5 percent and 11.5 percent, respectively, and a capital-to-assets ratio of about 4.5 percent.6 For 2004 specifically, almost all the figures lie very close to ECB (2005a) data for the euro area and the EU-25 (Table 8.3). But the share of foreign earnings at the largest (top 20) banks—typically in the 30–60 percent range (see Table 8.1)—is likely to be much larger than that of the more than 7,000 smaller banks.

Table 8.3.EU-15: Sample Characteristics Compared with Overall Banking System, 2004
Banking System
SampleEuro areaEU-25
ROA0.520.420.50
ROE11.7810.5412.21
CAP4.444.094.59
dROA0.100.110.09
dROE2.202.782.25
dCAP0.000.03–0.03
Sources: European Central Bank (2005a); IMF staff estimates; and BankScope.Notes: ROA = return on assets; ROE = return on equity; CAP = capital-to-assets ratio.
Sources: European Central Bank (2005a); IMF staff estimates; and BankScope.Notes: ROA = return on assets; ROE = return on equity; CAP = capital-to-assets ratio.

Clustering Europe’s Banks

Cluster analysis offers a starting point to determine “natural” groupings—clusters—among the banks of the EU-15. Concretely, let yTi denote a specific balance sheet or profitability indicator with time dimension T, such as the equity-to-asset ratio CAP, for bank i. Different clusters contain banks with “dissimilar” vectors yTi. Conversely, a single cluster regroups banks with “similar” vectors yTi. Clustering depends on the specification of the variable y, the measure of dissimilarity/similarity, and the clustering procedure. One drawback of cluster analysis is that output does not come with measures of confidence/significance, which makes it difficult to discriminate between the many different ways to perform clustering. The method should primarily be seen as an exploratory data analysis technique for “unsupervised” learning—the problem of finding groups in data without the help of any structural model.

Sensible priors and different specifications should deliver fairly robust hypotheses that can be tested further with more structured techniques. Specifically, the objective is to cluster the 100 banks into K clusters. Let d(yTi, yTj) denote the dissimilarity between the indicator y of two banks i and j as measured by specific distance functions: for yTi the function is 1- γ(yTi, YTj), where γ denotes the correlation coefficient; and for the first difference yTi, the function is the squared Euclidian distance (ΔyTi–ΔyTj)2. The clustering procedure—Partitioning Around Medoids (PAM)—then works as follows:

  • Step 1: Randomly select K banks to be medoids M—the most centrally located objects within the K clusters Ck—and form the K clusters by assigning each of the i = 1,2, … (100 - K) remaining banks to their “nearest” medoid; that is, minimize d(yTi, yTM); and compute the sum of dissimilarities, such as the squared-error criterion:

  • Step 2: Randomly swap a non-medoid bank with a medoid bank; form the new clusters; and recompute the squared error criterion, E2 Accept the new medoid if E2 <E1. Continue swapping until no further improvement is found.

According to the balance sheet and profitability indicators, bank business does not appear to have a compelling country component. Assuming that country-specific dynamics are important, a natural starting point is to postulate that the 100 banks fall into five country clusters. The reasons are that the five largest EU countries—France, Germany, Italy, Spain, and the United Kingdom—account for 73 of the 100 banks; that each of these countries has between 12 and 17 banks in the dataset; and that the other countries have at most five banks in the sample. With seven balance sheet variables, five clusters per variable, and two different clustering techniques (correlation coefficient and Euclidian distance), the output is (7*5*2 =) 70 clusters (Figures 8.1 and 8.2). For ease of analysis, these clusters only show the distribution of the 73 banks that belong to the five largest EU countries. Two characteristics of the output are noteworthy:7

Figure 8.1.EU-15: Cluster Analysis of Bank Variables (a)

(In percent)

Sources: BankScope; and IMF staff calculations.

Note: ROA = return on assets; ROE = return on equity; CAP = capital-to-assets ratio; OPREVA = gross-operating-revenue-to-assets ratio; OPREV = natural logarithm of gross operating revenue; ASSETS = natural logarithm of assets; EQUITY = natural logarithm of equity.

Figure 8.2.EU-15: Cluster Analysis of Bank Variables (b)

(In percent)

Sources: BankScope; and IMF staff calculations.

Note: ROA = return on assets; ROE = return on equity; CAP = capital-to-assets ratio; OPREVA = gross-operating-revenue-to-assets ratio; OPREV = natural logarithm of gross operating revenue; ASSETS = natural logarithm of assets; EQUITY = natural logarithm of equity.

  • Banks of a single country are generally spread across various clusters. Only 19 of the 70 clusters include one-half or more of the banks of a single country, with seven such clusters containing one-half or more of the banks of at least one other country.

  • Dynamics that are shared by more than one country feature prominently. For 9 of the 14 variables, one cluster holds at least 26 of the 73 banks, well more than the highest number of banks of a single country in the sample, which is 17; the maximum number of banks in a single cluster is 39 banks. Alternatively, 55 out of 70 clusters contain banks from at least four of the five countries reviewed.

European, Country, and Idiosyncratic Bank Dynamics

The roles of European, country, and idiosyncratic developments in changing banks’ balance sheet structure and profitability can be gauged further. Focusing on the first difference of the various indicators, this section does so with the help of: (1) cross-correlations between pairs of banks; (2) a principal component approach to finding the areawide components in the various indicators; and (3) an analysis of variance decomposition based on regressions of bank-specific indicators on their European or country-specific counterparts—this is also done for DD measures for 11 ILBGs that operate across Europe’s borders.

Pair-Wise Cross-Correlations

A natural starting point to deepen the cluster analysis is to plot histograms of the bivariate cross-correlations of the various bank indicators. This is done both for banks that come from different countries and for banks that come from the same country. For each indicator, between 4,042 and 4,411 observations underlie the histograms for the cross-country bivariate correlations (for the top 20 banks, the number is 126–161); for the within-country sample, the number is 518–539). The correlation coefficients are given by:

The indicators appear highly correlated for pairs of banks from different countries—generally as high as those for pairs from the same country. For the cross-country sample and the changes in the ratio variables (dROA, dROE, dCAP, dOPREVA), between one-quarter and one-third appear positively or negatively correlated with a coefficient that exceeds 0.5 in absolute value (Table 8.4). For the changes in the level variables (dOPREV, dEQUITY, dASSETS) the share is much higher, reaching between one-third and one-half. Positive correlations account for at least two-thirds of these “large” correlations. For the sample of the top 20 banks, the fraction of large cross-country correlations is more similar to that of the large within-country correlations. Also, a greater fraction of the large correlations appear positive.

Table 8.4.EU-15: Pair-Wise Cross-Correlations(Percent that exceed 0.5 in absolute value)
Across CountriesWithin Countries
Full sample:
dROA26.424.9
dROE27.526.2
dCAP25.623.6
dOPREVA35.450.2
dOPREV35.379.5
dASSETS38.239.7
dEQUITY48.083.3
Top 20 banks:
dROA29.824.1
dROE31.134.5
dCAP28.624.1
dOPREVA45.23.7
dOPREV31.048.1
dASSETS31.141.4
dEQUITY38.551.7
Sources: BankScope; and IMF staff calculations.
Sources: BankScope; and IMF staff calculations.

Principal Component Analysis

Principal component analysis (PCA) starts from the premise that a few common factors may explain much of the variation in the indicators of the 100 banks. The analysis uses a K factor model,

where ft denotes a vector of the K common factors and ut a vector of mutually uncorrelated errors with mean zero and finite variance.8 The calculation of principal components is essentially a regression problem: it asks what linear function of the columns yit gives the best fit (highest R2) when it is regressed on the 100 columns yit. The loading matrix A can be estimated by minimizing the residual sum of squares:

subject to B’B=1K. The estimated matrix B is the principal component estimator of Λ and its columns result as the eigenvectors of the K largest eigenvalues of the matrix T1ΣΔytΔyt.

The PCA results suggest that area-wide developments potentially explain most of the proportion of changes in bank balance sheets and profitability (Table 8.5). Given the short time span, no more than two factors are considered here: one factor might capture areawide macroeconomic shocks and the other, say, regulatory and technological changes affecting the banking sector. The results suggest that the most important principal component explains between 25 and 50 percent of all the variance in Ayit; adding another component raises this to between 40 and 60 percent.9

Table 8.5.EU-15: Principal Component Analysis—Share of Variance Explained by 1 versus 2 Components
Full SampleTop 20 Banks
1 Component2 Components1 Component2 Components
(Explained variation of percent changes)
dOPREV43.160.041.866.7
dEQUITY41.458.038.762.1
dASSETS50.762.744.766.7
(Explained variation of changes in ratios to assets or equity)
dROA25.844.930.656.7
dROE24.246.028.855.6
dOPREVA39.758.547.770.4
dCAP22.140.930.859.1
Sources: BankScope; and IMF staff calculations.
Sources: BankScope; and IMF staff calculations.

Analysis of Variance

Bank Balance Sheet and Profitability Indicators

The variation of balance sheet and profitability indicators can be attributed to bank-specific, country-specific, and European developments. Presumably, the structure of supervision in Europe should take into account the relative importance of these developments. The following equations are fitted to the data:

Here yit stands for the particular indicator of bank i; β are slope parameters, which are country- and year-specific when denoted ct; and Yeart are time dummies. The R2 of equation (1) indicates the share of variations in y that that might be related contemporaneously to both EU-wide and country-specific developments—the unexplained variation in this equation reflects bank-specific shocks; for equation (2) it does the same for the share of variations that can be related only to EU-wide developments—it is a restricted version of equation (1) with βc= β for all countries c.

EU-wide factors appear as important as country-specific factors for the variations in many indicators, according to the findings. As outliers distort the results considerably, the focus here is on the evidence from subsamples comprising “reliable” data.10 These subsamples exclude those 10 percent of all data points that give rise to the largest errors in the full sample regressions (5 percent on each end). Several characteristics stand out (Table 8.6):

Table 8.6.EU-15: Variance Decomposition of Bank Variables
SubsampleFullTop 20 SubsampleTop 20 Full
EUEU&CYEUEU&CYEUEU&CYEUEU&CY
(Explained variation of percent changes)
dOPREV45.064.214.230.349.276.225.149.4
dEQUITY40.661.014.126.833.572.417.944.4
dASSETS56.072.614.751.950.172.624.551.6
(Explained variation of changes in ratios to assets or equity)
dROA11.639.74.221.025.251.416.346.2
dROE9.432.61.710.017.648.511.944.6
dOPREVA34.861.214.635.043.874.529.459.0
dCAP2.735.30.919.217.267.24.943.0
Memorandum items:
dOPINCA4.638.60.721.46.662.710.944.4
dINTEXA45.760.321.544.354.079.237.962.9
d(ROA+INTEXA)40.265.819.137.257.077.237.461.9
Sources: BankScope; and IMF staff calculations.Notes: This table shows R2 values from regressions of bank-specific variables for the top 20 of the full sample and for the top 20 of a subsample excluding outliers on European time dummies (EU) or on country time dummies (EU&CY). The first set of R2s shows the fraction of movements in bank-specific variables that is driven by European shocks; the second set shows the fraction explained by both European and country-specific shocks.
Sources: BankScope; and IMF staff calculations.Notes: This table shows R2 values from regressions of bank-specific variables for the top 20 of the full sample and for the top 20 of a subsample excluding outliers on European time dummies (EU) or on country time dummies (EU&CY). The first set of R2s shows the fraction of movements in bank-specific variables that is driven by European shocks; the second set shows the fraction explained by both European and country-specific shocks.
  • Areawide movements dominate changes in the level variables, accounting for close to 40–50 percent of all variations, more than the country-specific developments. This is a higher share than for the ratio variables. The level variables likely pick up some broader trends that are increasingly shared across countries, such as economic growth, financial deepening, technology, and inflation.

  • Areawide developments can account for some 30–40 percent of all variations in changes of the OPREVA, the same as country-specific developments. The much smaller role of such common dynamics in net income indicators (ROA and ROE) is entirely due to the removal of interest expenditure. Supplementary regressions show that over 40 percent of the variations in this expenditure ratio (INTEXA) can be attributed to area-wide factors and less than 20 percent to country-specific developments.

  • Areawide evolutions appear more important in indicators for the top 20 banks.

  • Areawide factors appear to play a minor role for capitalization. The results for capitalization stand out and could point to the “residual” nature of retained earnings as well as to cross-country differences in regulatory and supervisory practices.

Distance-to-Default Indicators

Similarly to the balance sheet and profitability indicators, the variance in DD measures can be attributed to bank-specific, country-specific, and European components. The DD data cover 11 ILBGs from seven countries over 1991–2005 and are used at a daily as well as a monthly frequency (the average of days within a month).11 Given the large number of observations, rather than setting time dummies, the following regressions are run to identify the various components:

where y = DD and the subscript e denotes the average DD across all banks i.12

Among the ILBGs, EU-wide changes in DD measures account for the bulk of all DD changes. The R2 values of equation (4) are 60.5 and 61.1 percent, respectively, for daily and monthly DD data, suggesting that the majority of DD changes are common to all 11 banks.13 Allowing for country-specific intercepts and slopes by fitting equation (3) to the data raises these values to 68.4 and 69.3 percent, respectively, suggesting that country-specific dynamics account for some 8 percent of the variations only, much less than the EU-wide and bank-specific components.14

Conclusions

The analysis in this chapter provides evidence suggesting that shocks to EU banking systems are to a large extent shared across countries. The European component of bank business appears, from various perspectives, as strong as the national component. At the very least, the analysis points to strong parallelism in financial sector trends across Europe. It could also be evidence of progressing banking system integration and increasing integration of the environment in which banks function (such as increased business cycle correlation and a common monetary policy). Furthermore, the analysis might pick up commonality among similar types of banks across countries that is greater than the commonality among different types of banks within a country. However, without commonality in the factors affecting them, similar banks in different countries would not show the kind of correlation found in this analysis. The conclusion that bank developments across EU countries are to a large extent driven by common factors therefore appears compelling. It is also worth pointing out that the sample period (1997–2004) implies almost certainly an underestimation of the current importance of common factors for EU banks.

This chapter is based on the work in Decressin (2006).

See, for example, Chapters 6 and 7; De Nicolò and others (2005); and Brasili and Vulpes (2005). Gropp and Moerman (2003) focus on contagion to identify 12 systemically important banks in Europe. They show that significant contagious influence emanates from some smaller EU countries.

Gropp, Vesala, and Vulpes (2002) pioneered this type of analysis for euro area banks, demonstrating its usefulness as a complement to traditional balance-sheet-based analysis of risks.

For a cluster analysis of large, complex financial institutions of both the United States and Europe, see Hawkesby, Marsh, and Stevens (2005).

Specifically, banks that usually feature among Europe’s 100 largest and are not included here are the largest bank of Germany and the Netherlands and the two largest Austrian banks. As a result, Austria is not represented in the sample.

For data on the whole industry, see Decressin and Kudela (2005).

An alternative approach allows for different, hierarchical “levels” of clusters but reveals qualitatively similar results.

These assumptions for the error term can be relaxed as T, N become sufficiently large (Breitung and Eickmeier, 2005).

Since T=7, only six components are needed to explain 100 percent of the variance of a bank indicator.

One source of potential distortions that this technique addresses are the many mergers and acquisitions, which can cause very large changes to banks’ balance sheets and profit and loss accounts.

These banks (ABN Amro, ING, Santander, BBVA, HVB, Deutsche Bank, BNP Paribas, Fortis, KBC, HSBC, and Nordea) conduct much of their business abroad (see Schoenmaker and Oosterloo, 2005, and Chapter 7).

The DD data, used also in Chapter 7 and kindly provided by Alexander Tieman, were estimated using the procedure described in Vassalou and Xing (2004); see also De Nicolò and others (2005).

On omitting the 10 percent observations that are responsible for the largest errors, the R2 values are, respectively, 75.6 and 75.9 percent.

On omitting the 10 percent observations that are responsible for the largest errors, the R2 values are, respectively, 80.2 and 80.7 percent.

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