UNIVERSITY OF GRONINGEN
Faculty of Economics and Business, Master of Science degree Economics
International Diversification in Banking
Author: M.W. Diepeveen
May 2008
MASTER OF SCIENCE THESIS ECONOMICS
Supervisors: Dr. L. Dam and Dr. I.P.P. van Lelyveld
ABSTRACT
In this paper we use a widely applicable correlation matrix approach for determining the magnitudes of international credit risk diversification effects for 43 of the largest banking groups in the world. Our results indicate that international diversification benefits are substantial and differ greatly among our sample of multinational banking groups.
Keywords: diversification, economic capital, credit risk, Value-at-Risk, the business cycle Jel classification: A23, E32, E58, G11, G21
1 INTRODUCTION
Currently there is a debate to what extent diversification effects should be incorporated into the calculations of capital requirements for banks under the second pillar of the New Capital Adequacy Framework, commonly referred to as Basel II.1 Basel II’s predecessor, Basel I, largely ignored the existence of diversification benefits
for banks when calculating regulatory capital to cover risks. Diversification effects exist in a banking group when the aggregate risk profile of the banking group is lower than the simple sum of the risk profiles of the entities belonging to the group, where higher degrees of diversification indicate lower actual risk profiles. International diversification potential exists when banks carry a considerable degree of country specific risks in their lending portfolios. A banking group consisting of banks from different countries can in theory diversify away these country specific risks, leading to lower than simple-sum aggregate risk for the banking group. If, for example, a subsidiary in Argentina suffers great losses due to bad local economic conditions, this does not necessarily mean that a subsidiary in Spain will perform badly as well. Moreover, the Spanish subsidiary may perform very well, compensating for the losses of the Argentine subsidiary at group level and hence the diversification effect for the banking group.
Diversification effects are of particular interest in the banking sector, since banks are highly leveraged and therefore the banking industry is fragile. Banks face systematic and idiosyncratic risks, and in theory all idiosyncratic risk can be diversified away. Allowing for diversification benefits in bank regulation may lead to lower capital charges for low-risk institutions as the actual risk of banks may be lower than that measured under Basel I regulation. Capturing diversification effects allows for better insight into the actual risks of banks, which should aid prevention of costly bank failures. This paper is therefore of interest to risk managers, bank supervisors, and to society as a whole as banking crises can be very costly.2
Regulators are currently reluctant to acknowledge diversification effects for two main reasons: (1) no consensus exists among risk managers and banking supervisors as of yet on how diversification effects should be measured and therefore what the magnitudes are of diversification effects; and (2) because banking groups are regulated at the national and not the international level, allocating diversification effects in terms of lower capital charges is problematic. The focus of this paper is on the first of these two problems. The second problem exists because country business units belonging to a banking group operate in different countries and are subject to local regulation. In case diversification effects are acknowledged and this materializes into lower capital charges for the banking group as a whole, the question is where exactly this diversification effect occurs and therefore which country business unit belonging to the banking group may hold lower capital. Therefore, because banking groups are not regulated at the aggregate level, but their country business units are subject to different jurisdictions, materializing diversification effects in terms of lower capital charges is problematic. Allowing for diversification effects requires supra-national banking regulation, which is currently lacking.
This paper contributes to the empirical literature on international diversification in banking by determining the magnitudes of international credit risk diversification benefits for 43 of the world’s largest banking groups. We
1 Diversification effects are currently considered to a limited extent within risks. Diversification between risks or
geographical diversification is only considered under the second pillar.
2 Consider as an illustration the current credit crisis which was triggered by subprime mortgage crisis in the United States. In
consider one risk type, credit risk, as this is the most important risk in banking. We use a widely applicable correlation matrix approach for estimating geographic credit risk diversification effects in internationally active banking groups, in which correlations are estimated between country business cycles to estimate the dependencies across countries between credit risks at the national level. This approach can be traced back to Markowitz and his portfolio theory of investments, considering diversification in the joint distribution of portfolio returns. Several studies exist that study diversification effects in banking, but to our knowledge this is a first and unique attempt at quantifying diversification benefits using a correlation matrix approach that can be widely applied to real-world multinational banking groups.
2.
EXISTING LITERATURE
The empirical literature on diversification in banking consists of the following three broad categories:3 (1)
international portfolio diversification; (2) diversification in banking within countries; and (3) international diversification in banking. This paper contributes to the third of these three categories by applying a new approach for measuring international diversification in banking.
In the first category of empirical literature on diversification in banking, following the pioneering work of Markowitz (1952), an extensive literature has studied the effects of diversification in asset portfolios and later on extended this research into an international context.4 Early studies in this field of international portfolio diversification include Grubel (1968) , Levy and Sarnat (1970) and Lessard (1973), all finding large international diversification effects as portfolio diversification depends on the correlations between return distributions of individual securities, which tend to be lower between than within countries. In a more recent study on international portfolio diversification, Buch et al (2005) apply a mean-variance portfolio model to study international diversification gains in asset portfolios of banks located in France, Germany, the United Kingdom, and the United States using aggregate data on cross-border claims of banks during 1995-1999. They study the diversification gains from international banking related to counterparty location or country risks, which consist primarily of transfer, political, and currency risk, focusing on the driving forces behind the possible barriers to the internationalization of bank portfolios. Their main finding is that cross-border diversification entails considerable gains, since banks are likely to benefit from diversifying risks on their balance sheet by lending internationally through an improvement in the risk-return trade-off due to the diversification of country-specific risks. The concept of diversification considered in portfolios of securities is a well understood phenomenon, but this concept is less clear when applied to banking activity.
The second category of literature on diversification covers the field of diversification in banking within countries. Acharya et al (2002) study the effect of focus versus diversification on the return and the risk of banks using data from 105 Italian banks during 1993-1999. Measuring focus and diversification by employing a Herfindahl-Hirschman index and focusing on diversification across different industries, sectors and local geographical regions within Italy, their main finding is that local geographical diversification did not necessarily improve the risk-return trade-off of banks so that diversification of bank assets is not guaranteed to produce superior performance and/or greater safety for banks. Similarly, Morgan and Samolyk (2002) find that broader geographical presence of banks within the United States is not associated with higher returns or lower risk. According to both studies, diversification in banking within countries is limited, possibly caused by strong co-movement of fundamental economic variables within countries.
Not surprisingly, the co-movement of fundamental economic variables is likely to be lower between countries than within countries, bringing us to the third category of empirical literature on diversification: international diversification in banking. Reflecting the rising interest in this topic over the last couple of years, several studies have recently emerged in this field of empirical literature. A distinctive component within this category is whether diversification is considered in a profit enhancing manner or in a risk reducing manner. Using a dataset of individual bank loan portfolios of 983 German banks for the period from 1996 to 2002, Hayden et al (2006)
3 García-Herrero and Vázquez (2007) make a similar broad distinction of categories for the empirical literature on
diversification in banking.
address the issue of focus versus diversification in banking by investigating whether geographic diversification leads to increased performance and therefore to safer banks. To do so, they analyze the link between bank profitability and portfolio diversification as measured by the Herfindahl-Hirschman index across different industries, broader economic sectors and geographic regions. Their results indicate that each kind of diversification tends to lower German banks’ returns so that focus generally leads to greater profitability. From this they conclude that diversification does not improve the performance of German banks and therefore does not lead to greater safety on the part of banks as traditional portfolio and banking theory would suggest. This line of argumentation implicitly assumes a direct negative link between bank return and risk, but the existence of such a link is not an obvious point in our belief. Similarly, risky portfolios of assets often earn higher average returns than their less risky counterparts, suggesting a trade-off between risk and return and therefore a positive link between them.
According to García-Herrero and Vázquez (2007), international diversification effects in banking can be substantial. Similar to Hayden et al (2006), they measure international geographical diversification in terms of the assets held by subsidiaries abroad, relative to those maintained by their parent banks in their home countries. They argue that, when business cycles are imperfectly correlated across countries, a bank with broad global exposures, particularly in its lending portfolio, should in principle be better able to diversify away country-specific risks. Using a bank-level dataset covering the operations of 38 major international banking groups from eight industrial countries and their subsidiaries overseas during 1995-2004, García-Herrero and Vázquez (2007) assess the potential geographical diversification gains of banks in terms of the assets held by subsidiaries abroad, relative to those maintained by their parent banks in their home countries. They do this by estimating the contribution of foreign subsidiaries’ assets to the risk-return performance of the consolidated banking group. Furthermore, García-Herrero and Vázquez (2007) examine the correlations of GDP growth, money market rates, and long-term government bond yields, reflecting the idea that macroeconomic conditions may be more synchronized within geographical regions due to similar economic fundamentals and exposure to common risk factors. By including two Herfindahl-Hirschman indices to the regression, measuring the concentration of the assets of each international bank within industrial and emerging countries, they capture the effect of international diversification within country groups. Their results show that international banks with larger allocations of assets overseas obtain substantially higher risk-adjusted returns, in particular when the share of assets in emerging market countries is relatively large.
these two groups of countries was generally low. Since banks carry a considerable degree of country-specific risks in their lending portfolios, they argue that the benefits of international diversification in banking could potentially be large, especially between industrial and emerging market economies. Griffith-Jones et al (2002) hypothesize that the levels of unexpected loss for a portfolio that is diversified across developed and developing markets will be lower than that for a portfolio that focuses exclusively on developed markets. They test this by using a modified CreditMetrics approach to simulate levels of unexpected loss for two portfolios: one with a loan portfolio that is evenly distributed across developed and developing regions; the second with a portfolio that is distributed across only the developed regions. Their results support their hypothesis: the unexpected loss simulated for the portfolio focused on developed country borrowers only are substantially higher on average than for the portfolio diversified across developed and developing countries. Griffith-Jones et al (2002) therefore argue that the Basel Committee should closely examine the practicalities of incorporating the benefits of international diversification in order to accurately reflect the actual risks that banks may face. Although providing strong support for the likelihood that diversification effects are substantial, Griffith-Jones et al (2002) do not provide real data to support their conclusion.
3
THEORY
Risk can be defined as the uncertainty about future outcomes, which is caused by the volatility of returns, and calculating risk is a way of quantifying this uncertainty. Applied to banking, the future revenue of financial transactions is hard to predict in practice, so the variability in past revenues is used to quantify the uncertainty of future outcomes. Because banks are highly leveraged, their profitability is highly sensitive to the risks of their operations. From a risk management perspective, the focus here is on downside risk: the risk of loss. Several different types of risk can be distinguished in banking, namely: credit risk, market risk, interest rate risk, operational risk, country risk, foreign exchange risk, solvency risk and liquidity risk. Any classification of risk types in banking is arbitrary to a degree, since these risks often are not clearly distinctive from one another, but overlap to a large extent.5 Credit risk is the main source of risks for banks as lending activity is the main activity
for most banks. Credit risk is defined as the risk that an obligor will default on his or her loan. More specifically, credit risk is defined as the risk of loss due to a debtor’s non-payment of a loan or other line of credit (either the principal or interest (coupon) or both). Banks employ their own models to rank potential and existing customers according to risk, and then apply appropriate strategies. Nevertheless, there is always a chance that a borrower will default on his or her loan. Credit risk typically accounts for approximately 50% of total economic capital and historically credit risk has been the main cause of bank failures.6
In the following subsections we discuss the theoretical basis for our empirical framework. We begin by discussing diversification, followed by a discussion of the concepts of Economic Capital and Value-at-Risk. In the final subsection of this section, we discuss alternative methods for measuring diversification.
3.1 Diversification
Diversification is a term used to denote the spreading of risks and finds its roots in investment theory, where diversification means that a portfolio of risky investments will be less risky compared to the level of risk of the individual investments, due to the correlation structure of the investments. In his pioneering work on the portfolio theory of investments, Markowitz (1952) found that if asset returns are not perfectly correlated, the aggregate risk of a portfolio of shares, measured by the standard deviation of the portfolio’s returns, may be lower than the aggregate risk of these shares considered and aggregated separately. Using this correlation structure of investments, risks can be mitigated. The remaining risk of a portfolio with a given return that cannot be ‘diversified’ away is called systematic risk. Translating Markowitz’ portfolio theory of investments to the international banking industry, the portfolio of assets is now the portfolio of national entities (or country business units) of a banking group. If the risks of these country business units are not perfectly correlated, international diversification effects exist for this banking group.
Quantifying the total diversification effect within a banking group may be done by simultaneously modelling the correlation between all relevant risk drivers at all possible aggregation levels. Following through on this approach would result in each business being assigned a set of risk drivers, some of which will relate to market risk, some to credit risk, some to operational risk, and so on. Sensitivities to each of the risk drivers can in principle be added up across all business units. The various risk drivers can be aggregated to arrive at an overall
5 See Chapter 2 of Van Lelyveld ed. (2006) for a classification of the main risks in banking and Chapter 1 of Bessis (2007)
for an extensive description of these risks.
6 Credit risk percentages of economic capital are stated annual reports of banks such as Citigroup, Rabobank, Deutche Bank,
economic capital estimate by assessing the variability of risk drivers and correlation values between them. Diversification may thus occur at several different levels, for example: (1) between sub-risks within a risk type; (2) between risk-types within a business unit; and (3) between business units within the group. The aggregate risk of the banking group should then be assessed using a bottom-up approach.7 Applying such an extensive
approach is far beyond the scope of this paper; our goal here is to take a first step towards such an approach. In this paper we therefore focus on the main source of risk for banks: credit risk. We attempt to quantify the international diversification benefits for banking groups for operating subsidiaries in different countries by focussing on geographic diversification between these country business units. If credit risk is not perfectly correlated across countries, credit risk diversification effects exist for multinational banking groups that operate across those countries and we are interested in the magnitude of these diversification effects.
3.2 Economic Capital and Value-at-Risk
Risk can have both positive and negative outcome, but we are only interested in the risk of loss and therefore in downside risk. An overall standard for measuring downside risk is Economic Capital, which can be defined as the amount of capital that a transaction or business unit requires in order to support the economic risk it originates, as perceived by the institution itself.8 As such, economic capital is a measure of risk, not of capital
held, and it is distinct from familiar accounting and regulatory capital measures. Economic capital is based on a probabilistic assessment of potential future loss and is therefore a more forward-looking measure of capital adequacy than traditional accounting measures. A diversification benefit exists when the aggregate economic capital of a banking group is lower than the simple sum of the stand-alone economic capital numbers assigned to the stand-alone country business units. Economic Capital is commonly measured by using the Value-at-Risk or VaR methodology.
3.2.1 Value-at-Risk
The VaR methodology is used to define the Value-at-Risk, which applies directly to the issue of capital adequacy and therefore to economic capital. The Value-at-Risk is the maximum loss at a given tolerance level and the tolerance level is the probability that the loss exceeds this maximum value, or in other words the default probability of the bank. The VaR methodology can be used to define economic capital, since economic capital is the risk-based capital required to absorb the potential loss at a given tolerance level. Economic capital is thus a buffer for the VaR.
Figure 1 shows a loss distribution for a bank in which several types of potential loss can be distinguished: (1) Expected Loss (EL); (2) Unexpected Loss (UL); and (3) TailVaR. The Expected Loss, or EL, is a statistical estimate of the average loss. The average loss is frequently used for assessing credit risk because it represents the statistical mean of losses across a (loan) portfolio and thus over all possible outcomes. The law of large numbers says that loss will be sometimes high or low, but the average is the Expected Loss. For a portfolio, there is always an expected number of defaults which is the mean of the distribution of defaults, but the actual loss of an individual transaction will nearly always differ from the Expected Loss, since it will be higher or lower. Statistical losses are therefore more a portfolio concept than an individual transaction concept.
7 See Groupe Consultatif (2005) for an extensive discussion.
Figure 1: Loss distribution and VaR
Provisions are used for hedging Expected Loss, differing from capital which provides a protection against deviations from this average. Capital should thus provide protection against Unexpected Loss only, while Expected Loss is being netted out of revenues. The Unexpected Loss, or UL, is the maximum loss that will be exceeded only in a small fraction of all cases: the tolerance level. Unexpected Loss is loss that deviates from the expected value. The VaR is the total of Expected and Unexpected Loss, given a certain tolerance level and the confidence (or tolerance) level is the probability of losses being greater than the VaR. This tolerance level is determined by the degree of risk aversion of the institution and may differ per institution. We are particularly interested in VaR amounts, since such realisations typically cause banking distress and are therefore of particular interest to risk managers and supervisors.
Another concept is TailVar, often referred to as ‘Expected Shortfall’, which is the expected loss conditional on breaching the VaR amount. As for instance Artzner et al (1999) have shown, this measure has desirable properties for a risk measure. Leaving out the confidence level and thus including the TailVaR in the VaR would drastically increase the VAR or economic capital measures. At the limit, total assets (or even more) of a bank could be lost, but this theoretical possibility is extremely unlikely to occur. As the tails of loss distributions are difficult to estimate, TailVar is as yet not widely applied in banking.
3.2.2 Economic Capital terminology
Economic capital, regulatory capital, minimum capital, and actual capital are concepts which are frequently used in the literature on banking risk and regulation.9 Often, however, these concepts are confused with one another.
The main distinctive component between these concepts is the point of view of the key stakeholders: - economic capital is the desired target level from the point of view of the firm itself;
- optimum capital is the level that maximizes social welfare;
- minimum capital is the floor imposed on the firm by regulatory rules; and - actual capital is the current level from the point of view of the firm itself.
The principle difference between economic capital and socially optimal capital is that the latter abstracts from unintentional incentives that arise, for example, from the provision of a safety net to banking institutions. Absent those incentives, optimum capital is the level of capital that a firm determines is prudent, desirable, and achievable in the short run. Calculations of optimum capital are hardly complete and exact, especially since some risks are very difficult to model and quantify. Therefore they are subject to a degree of subjectivity, making optimum capital difficult to replicate and validate. Minimum capital requirements reflect large first-order risk exposures and they are objective and verifiable due to the fact that the basic information and formulas used to compute the required amounts are generally well defined in advance. Calculations are straightforward: simplicity is often favoured over accuracy. Minimum capital is not intended as a level toward which the firm should aim or as a standard for internal risk management, but is merely a rough minimum standard. The actual capital of the firm is the amount of capital that it currently chooses to hold. It should appreciably exceed the minimum requirement and differs from economic capital in that it may include capital that is not held just for risk purposes, such as capital needed for acquisition transactions. In this study, we attempt to calculate the magnitude of economic capital as opposed to regulatory capital, since for regulatory capital no diversification effects are taken into account. We assume that credit risk is the only risk in banking, so economic capital consists of credit risk only and the VaR methodology displays the distribution associated with credit risk loss.
3.3 Measuring diversification
Theoretically, three methods exist for measuring diversification in the banking sector, differing in theoretical robustness and practicality: (1) a correlation matrix; (2) copulas; and (3) tail-correlations. The correlation matrix approach is a method that is used to aggregate the risk of individual assets belonging to a common portfolio to arrive at the aggregate risk of the portfolio. Recall our earlier definition, using Markowitz’ portfolio theory applied to banking, that diversification means that the aggregate credit risk of a portfolio of credit risks of subsidiaries of a banking group is lower than the simple sum of stand-alone risks of the subsidiaries, due to the correlation structure of the risk driver for credit risk at the national level for the individual subsidiaries. If this common factor (credit) risk driver of the individual subsidiaries (assets) is not perfectly correlated internationally, an international diversification benefit exists.
The correlation coefficient reflects the statistical dependency between random variables, measuring the degree of linear dependency between two (or more) random variables and can have a value of between one and minus one. Diversification occurs when correlation coefficients are less than one (imperfect correlation). A correlation of
9 Estrella (2000) provides a brief and clear overview of the first three of these concepts and their main distinctive
minus one implies that two variables move in exactly the opposite direction and then complete diversification (or hedge) is said to occur. Correlation is thus crucial for determining diversification benefits.
A major advantage of the correlation matrix approach is that it is easy and understandable in its use. Correlation is often straightforward to calculate, since for many bivariate distributions it is a simple matter of calculating the variances and covariances and then to derive the correlation coefficient. A weakness of the correlation matrix approach is that it may lead to overestimation of diversification benefits, since the correlation coefficient is a measure of average dependency between two variables and therefore does not capture the dependency among variables under extreme circumstances.10
High losses typically occur when usually imperfectly correlated loss events happen at the same time. That is, correlations between risk drivers may increase in bad economic times and therefore average correlation, which does not take into account the increase in correlation that may occur in times of stress, may underestimate aggregate credit risk of a banking group and subsequently overestimate the diversification benefit.11
A method that does allow for calculation of diversification under extreme events is the use of copulas. A copula is a function that links the distribution function of different random variables within a stochastic dependence context to form a set of joint distributions. Modelling marginal distributions together with copulas provides a mode for the aggregate portfolio accounting for dependence between lines of business. Copulas have the advantage that they can be used to accurately combine other distributions other than from the ‘normal family’ and that they can recognise dependencies that change in the tail of the distribution, but no consensus has been reached yet on which copula to use in specific applications or on how to test the accuracy of a specific copula.12
Furthermore, Kole et al (2007) find copulas to be inaccurate in several circumstances as diversification is sometimes overestimated and some times underestimated.13 Copulas also become very complex when a large
number of distributions have to be combined, as is the case in our analysis. Furthermore, significant amounts of data must be available to accurately use the copula function. Working with copulas is therefore often problematic in practical situations.14
A third method for measuring diversification is the use of , or conditional-, correlations. When using tail-correlations, the focus is on that part of the distribution which is around the confidence level, thereby including extreme events. An adjusted correlation matrix is estimated using ‘expert opinion’, starting with experience analysis on dependencies between risks in ‘normal’ cases. The use of an adjusted correlation matrix filled with tail-correlations will only get reliable results in a small part of the distribution. If we are only interested in the tail (above the confidence level), the use of a tail correlation matrix can be a good alternative for the ‘normal’ correlation matrix. An advantage of the tail-correlation method is that it accurately estimates the dependency in the tail, so diversification is not likely to be overestimated as with the ‘normal’ correlation matrix approach.15
10 See for example Longin and Solnik (2002) or Bae et al. (2002).
11 Groupe Consultatif (2005) criticise the use of a ‘standard’ correlation matrix for estimating diversification benefits, since
extreme events can impact risks that are normally independent, so using a matrix filled with correlation factors that describe the average dependency across the whole distribution will be lower than the dependency in the tail.
12 Hyung and de Vries (2005) consider this issue by comparing the benefits of portfolio diversification for downside risk in
case returns are normally distributed with the case of fat-tailed distributed returns.
13 Kole et al find that the Gaussian copula overestimates diversification and the Gumbel copula underestimates
diversification.
14 See Embrechts et al (2002) for a review of the pro’s and cons of ‘normal’ correlation as a measure of dependency and a
discussion of the use of copulas as an alternative.
15 Hyung and de Vries (2005) consider this issue for the case of securities portfolios by comparing the benefits of portfolio
Problematic with the tail-correlation method, however, is that the estimation of the tail-correlation between two risks, or the estimation of the correlation between two risks under extreme circumstances, is subject to the same uncertainties as the selecting of copula functions. It will be hard to get enough data for a reliable estimation. By definition, extreme situations will not occur frequently and extreme events that do occur in the future have not occurred yet in the past. Therefore, despite its theoretical accuracy, working with tail correlations is often difficult in practice.
4 METHODOLOGY
We use a correlation matrix approach for estimating international credit risk diversification effects in multinational banking groups. Recall that we focus on geographic credit risk diversification. That is, we consider geographic diversification benefits for banking groups when operating one or more significant foreign subsidiaries, ignoring the other levels at which diversification occurs and focussing on the main source of risk in banking: credit risk. We assume that banks carry a considerable degree of country-specific risks in their lending portfolios, so that macroeconomic variables that drive these country specific risks may be used for calculating international diversification benefits.
To measure the degree of credit risk of individual banks, we use the variable loan-loss provisions and we assume that credit risk of banks is driven by the business cycle of the country they are located. We therefore use the output gap as input for the correlation matrix to calculate international credit risk diversification effects in our sample of multinational banking groups. Ultimately, a diversification benefit exists when the aggregate credit risk of a banking group is lower than the simple sum of the stand-alone credit risks of its country business units. The following subsections discuss our use of the correlation matrix approach, the motivation for the choice of proxies, and the way in which we aggregate stand-alone risks in order to calculate diversification benefits.
4.1 The Correlation matrix approach
As an example of the correlation matrix approach, consider Banco Santander Central Hispano, a banking group with a Spanish parent and with subsidiaries active in several European, Central- and South American countries and in the United States. Consider this banking group in a reduced form, where it consists of three country business units: one in Spain (ES), one in Brazil (BR), and one in the United States (US). Each country business unit constitutes of all business units belonging to banking group Santander that are active in that particular country. Figure 2 gives a graphical representation of the correlation matrix approach for calculating diversification effects for Banking Group Santander in this simplified example. Each country business unit has its own degree of individual credit risk exposure. Furthermore, macroeconomic forces determine the way in which these individual exposures are linked across countries, which is measured by the correlation between these macroeconomic forces. If the correlation between the macroeconomic credit risk drivers of these countries is large, little diversification benefit exists for this banking group in terms of international credit risk as these risks move together and the aggregate credit risk of the banking group is close to the simple-sum of stand-alone credit risks of the country business units. As correlations between the macroeconomic risk drivers drop, diversification benefits become larger.
For regulatory purposes, when diversification effects are not considered, the aggregate credit risk of the banking group is calculated by simple sum of the stand-alone credit risk amounts (i.e. all correlation factors are set to 1). When diversification effects are considered, the aggregate credit risk should be calculated using actual correlation factors of the underlying risk driver for country credit risk.
loan-loss provisions and we use the standardized output gap as proxy for the international risk driver for credit risk. Both choices are motivated in the following two subsections.
Figure 2: The Correlation matrix approach for measuring diversification, graphically displayed for a simplified version of banking group Banco Santander Central Hispano
4.1.1 Bank credit risk: loan-loss provisions
Credit risk is defined as the risk that an obligor will default on his or her loan. More specifically, credit risk is defined as the risk of loss due to a debtor’s non-payment of a loan or other line of credit (either the principal or interest (coupon) or both). Banks employ their own credit scoring models to rank potential and existing customers according to risk, and then apply appropriate strategies. Nevertheless, there is always a chance that a borrower will default on his or her loan. Since we consider a large number of banks for several years, we need a single measure of credit risk for banks that is widely available. This is not an easy exercise, however, as any measure of credit risk is subject to some degree of criticism and the choice for a widely available measure is often frustrated by the availability of data. The choice for our proxy brings us back to the basic operations of a bank, consisting of receiving money from customers in the form of deposits on the one hand and lending in the form of loans on the other. Different types of loans can be distinguished and they typically differ in the accompanying default risk of the loan.16 Since a bank knows there is always a possibility that a lender may
default on his or her loan, it sets aside funds to cover this expected loss. The funds set aside to cover expected loan-losses are called loan-loss provisions and they add up to the stock of loan-loss reserves, the actual buffer for loan-losses. Loan-loss provisions are recorded on the income statement as an operating expense and are then recorded on the balance sheet as loan-loss reserves additions. Since the amount of loan-loss provisions is a ‘flow’ variable, it is a more forward looking concept than the ‘stock’ variable loan-loss reserves and therefore a better proxy for current changes in credit risk. In case the amount of ‘provisioned’ funds for loan-losses increases, the bank regards its credit risk as having increased. We assume that the magnitude of loan-loss provisions is an indication of the degree of unexpected loss as well as expected loss.
The amount of loan-loss provisioning is a good and widely available proxy for bank-level credit risk, but it has its drawbacks too. Bikker and Metzemakers (2005) find that a problematic feature of provisioning may be that tax motives can distort an accountant’s incentive for provisioning. Provisioning for loan-losses is usually done in
16 For example mortgages are typically less risky assets (loans) than unsecured personal loans due to the issuer’s ultimate
order to buffer against expected future credit risk, but when tax motives play the upper hand, provisioning may be used for income smoothing purposes. Bikker and Metzemakers (2005) point out that provisioning may be affected by country-specific circumstances with respect to accounting, regulatory and tax rules. Nevertheless, they acknowledge the strong advantages of using loan-loss provisions to proxy for bank credit risk. They argue that provisions are directly linked to the quality of the loan portfolio and are therefore more susceptible to short-term fluctuations arising from the macroeconomic environment and developments in the solvency of individual counterparties. These properties of the variable loan-loss provisions make it a good widely available proxy for the degree of credit risk exposure of banks.
4.1.2 International risk driver for credit risk: the output gap
As discussed above, we choose loan-loss provisions as a proxy for the expected credit risk of a typical bank. Since we assume that banks carry a considerable degree of country-specific risks in their lending portfolios and thus in their credit risk exposure, which is captured by loan-loss provisions, we need a measure that drives these risks internationally in order to calculate the international correlation of these country specific risks. That is, we need a country-level common risk factor for determining the international correlation of credit risk. This common factor might differ per bank, but recall that we are not looking at one specific bank but rather we are applying a universal framework and therefore we are looking for the sensitivity of a typical bank to the common country factor. To proxy for such a common country factor, we use the ‘output gap’ (or GDP gap), which is the difference between potential GDP and actual GDP and thus is an indication of whether an economy is in an expansion or in a recession.
Measuring the cyclical dimension of credit risk is difficult, but, as the recurrence of banking crises suggests, it is fundamentally important. Data directly measuring country credit risk are scarce, and if available, such data is mostly qualitative in nature. Examples are country risk indicators constructed by rating agencies such as Moody’s, Standard and Poor’s and the Economist Intelligence Unit. Furthermore, these indicators are very stable over time and only tend to improve slightly in periods of economic boom and deteriorate in times of economic downturn.17 Banks use internal models to calculate risk and in doing so they are less likely to be constrained by
data availability. For example, risk managers have internal access to all the data that is used to construct the balance sheet and income statement. Outsiders can only obtain year-end data and have little additional information on how it was constructed and what the data looks like at a higher granularity or frequency. To construct a correlation matrix for international diversification calculation purposes, a bank may use daily or monthly series of total returns per region (country) where it operates over a period of years and correlate these data. For outsiders, obtaining such data is not possible so other more practical solutions must be considered. Conversely, detailed records of data on real gross domestic product, the necessary input for output gap determination, are kept for many countries and years. The way in which we construct the output gap is discussed in the next section.
The use of the output gap as a proxy for the international risk driver for credit risk implies that the degree of credit risk of a bank is directly linked to the state of the economy of the country it is located. Several studies support this proposition. Levy and Sarnat (1970) argue that, for credit risk, it can be observed that default rates across countries tend to vary together indicating that they are linked through and influenced by the business
cycle of those countries. Differences in default rates can therefore be indicated by differences in default cycles. If, for a portfolio of international subsidiaries, the default cycles of the countries in which they operate are highly correlated, little geographic credit risk diversification benefits exist for operating these foreign subsidiaries. If correlations across country business cycles are low, diversification benefits may be large.
Lowe (2002) points out that, regardless of the source and timing of the build up of credit risk, credit risk materializes during recessions. He argues that if these recessions are not completely correlated, room exists for diversification effects across geographical regions since the magnitude and timing of business cycles is not equal across regions. Recessions will not hit economies at the same time, so credit risk will not materialize at the same time across regions and hence the diversification effect. Moreover, Lowe (2002) argues that the point is not whether the net effect of credit risk materializes during a boom or during a recession, but rather that the timing of the materialization of credit risk is consistent.
In theory, the potential for credit risk diversification can be considerable, following Pesaran et al (2006). They argue that since the business conditions of borrowers are tied to the business cycle, demand is strong in an expansion, while during a recession, keeping a business profitable is more challenging. Therefore it should come as no surprise that the credit risk profile of a commercial bank is tied to the business cycle through its borrowers. Pesaran et al (2006) continue by stating that if business cycles are not perfectly correlated across countries and regions, diversification benefits can be obtained by internationalizing one’s exposure. They argue that financial institutions are ultimately exposed to macroeconomic fluctuations in the global economy because default probabilities are driven primarily by how firms are tied to the business cycle and how business cycles are linked across countries. Another interesting empirical study has been carried out by Carling et al (2007), in which the main finding is that macroeconomic variables have significant explanatory power for firm default risk in addition to a number of common financial ratios. Carling et al (2007) conclude that the output gap has significant explanatory power for the credit risk of firms, and is therefore a quantitatively important indicator of the evolution of credit risk over time.18 This is exactly the function that the output gap variable performs in this
paper.
Bangia et al (2007) find that the state of the economy is clearly one of the major drivers of systematic credit risk, especially as lower credit classes are much more sensitive to macroeconomic factors. They propose that underlying macroeconomic volatility is a key part of a useful conceptual framework for stress testing credit portfolios, and that credit migration matrices provide the specific linkages between underlying macroeconomic conditions and asset quality. Credit migration matrices characterize the expected changes in credit quality of obligors, and are cardinal inputs to many applications, including portfolio risk assessment, modelling the term structure of credit risk premia, and pricing of credit derivatives. Bangia et al (2007) find that these credit migration matrices are highly dependent on the business cycle.
Hackbarth et al (2006) develop a framework for analyzing the impact of macroeconomic conditions on credit risk and dynamic capital structure choice. Using this framework, they conclude that macroeconomic conditions have a large impact on credit risk and on firms’ financing decisions. Koopman and Lucas (2005) study the dynamic behaviour of the default rate and the credit spread in their relation to business cycle developments. They find evidence for several scenarios that there is a clear (positive) relation between spreads and business
18 The same conclusion holds for the yield curve and consumers’ expectations of future economic developments: they too
failures and a negative relation between GDP on the one hand and spreads and failures on the other hand. Simultaneously, however, they also conclude that the relation between defaults and GDP may be more complicated than assumed in many earlier papers on credit risk.
From the literature discussed above, we conclude that credit risk is linked to the output gap via default cycles. A bank’s credit risk is inherently subject to the default cycle, and the default cycle is clearly linked to the output gap. Since output data is widely available for multiple countries and years, we can conclude that it is a good and useful proxy for the common risk driver for credit risk at the national levels. In this paper, we therefore use the output gap as a proxy for credit risk at the national level. The way in which we construct the output gap and subsequently use the output gap to construct the correlation matrix, is discussed in Section 5.2.
4.2 Risk aggregation
To measure the degree of credit risk diversification effects for our sample of 43 banking groups consisting of different numbers of country business units, we use matrix multiplication in the correlation matrix approach. This section discusses the way in which the correlation matrix approach aggregates stand-alone risks to arrive at an aggregate risk number that is lower than the simple sum of stand-alone risks, signifying diversification. To measure the risk of a portfolio, the issue is to determine the risk of a sum of random but correlated losses. Risk is measured as the volatility of losses across the portfolio. That is, risk is the volatility of this sum of individual losses. The variance of portfolio loss of exposures can then be measured in two steps. First, a row vector of exposures is multiplied by the correlation matrix, resulting in a row vector. This vector is then multiplied by the transposed row vector of exposures. Both these steps are captured by the following simple formula:19 T L E*P*E 2 =
σ
(1) where σ2L is the portfolio variance of loss, E is the vector of exposures, Ρ is the correlation matrix, and ET is the
transposed row vector of exposures. A major advantage of this approach is that it can be applied to any number of exposures and output gap correlations, where the set of exposures is grouped into a row vector. Measuring the degree of international diversification within a banking group can then be done by comparing the loss variance using the normally computed correlation matrix with the outcome when a correlation matrix is used in which the correlation coefficients have all been set to one. The correlation coefficient of one indicates full correlation between the variables and therefore no diversification effect, which makes it the benchmark case to which the calculation of diversification is compared in order to determine the magnitude of the diversification effect. After obtaining and analyzing the magnitudes of diversification effects for our sample of 43 multinational banking groups, we will briefly consider the impact of several variables on the diversification outcome. We consider whether the size of banking groups and the number of country business units that it consists of are of influence on the international diversification outcome. Intuitively, as the amount of business units increases, a banking group’s activities are spread over more countries and one would expect a higher value for the diversification benefit. Following through on this analysis, we consider whether the diversification outcome is linked to the degree of international concentration of activities as measured by the Herfindahl-Hirschman Index (HHI) of total assets. The HHI index is a measure of concentration that is influenced not only by the amount of
country business units a banking group consists of (i.e. the amount of countries it is located in), but also by the size of these country business units. This can be an important point, as a banking group consisting of one extremely large country business unit and two extremely small country business units is likely to have a very small international diversification benefit. Thus we expect not only the location, but also the relative size of country business units of a banking group to be of influence on the result.
Finally, we also consider whether a sizeable difference exists for between the diversification result for banking groups that are active in OECD countries only and banking groups that operate at least one non-OECD country business unit. The reasoning behind this is that business cycles may be more synchronized among OECD countries than between non-OECD countries. For the most part, the country business units of all the 43 banking groups included in our data set are located in OECD countries. We will consider whether there is a substantial difference between the diversification result for the 29 banking groups that are located in OECD countries only and the result for the 14 banking groups operate at least one non-OECD country business unit. This reflects the intuitive idea that banking groups which are active in a heterogeneous set of countries in terms of macroeconomic credit risk drivers may have a relatively large diversification benefit.
To illustrate the way in which we calculate diversification effects for our sample of multinational banking groups, we now consider our approach applied as an example to an imaginary banking group that consists of three country business units. Note that this example can be changed into a case where a banking group consists of any other number of country business units. In order to keep things simple here, we stick to the simple example of a three entity case.
4.2.1 Three entity example
Consider for a particular year a vector of bank loan-loss provisions of subsidiaries belonging to a particular banking group consisting of three country business units and consider a correlation matrix filled with correlation coefficients between the standardized output gaps across the three countries in which these country business units operate. The variance of the portfolio of the credit risk exposures in a particular year can be calculated by the following matrix equation:
[
]
2 3 2 1 33 23 31 23 22 21 13 12 11 3 2 1 * * EC e e e e e e σ ρ ρ ρ ρ ρ ρ ρ ρ ρ = (2)where ei is the credit risk exposure of country business unit i, ρij is the correlation coefficient between the output
gap in countries i and j, and σ2
EC is the variance of portfolio loss from credit risk exposures, which is an
indication for the aggregate credit risk of the banking group when diversification has been taken into account. The row vector on the left hand side is the vector of bank loan-loss provisions of subsidiaries belonging to this banking group and the column vector on the right hand side is nothing more than its transpose. The 3x3 matrix in the middle is the correlation matrix filled with correlation coefficients. Note that equation (2) is a simply equation (1) specified for a three entity case. Furthermore, the subscript ‘EC’ (Economic Capital) is attached to the portfolio variance in equation (2), indicating that diversification effects are taken into account here.
one in the correlation matrix. This adjusted correlation matrix can be used to obtain the portfolio variance of the banking group portfolios in similar fashion as in equation (2):
[
]
2 3 2 1 3 2 1 * 1 1 1 1 1 1 1 1 1 * Sum e e e e e e =σ (3) where σ2Sum is the portfolio variance when individual credit risk exposures are aggregated using simple sum
(hence the subscript Sum). Note that the outcome of equation (3) is equal to the squared simple sum of the individual exposures. The diversification effect per banking group can be determined by comparing the outcome obtained when diversification is considered to the outcome obtained when diversification is ignored, that is by comparing equation (2) to equation (3). The percentage diversification effect per banking group for a particular year can then easily be calculated by computing
% 100 * SUM SUM EC DIV σ σ σ − − = , (4)
5
DATA
For our empirical framework, we use both bank-level data and macroeconomic data. At bank level, we use data on loan-loss provisions for each country business unit of 43 of the largest banking groups in the world which are active in 49 different countries. At macroeconomic level, we use data on real business cycles for the period 1950-2006 for all 49 countries in which the country business units of the banking groups are active. The following two sections describe our use of both these sources of data.
5.1 Bank-level data
We use a dataset that was constructed and used by De Haas and van Lelyveld (2008), in which, among other things, the activities of banking groups have been divided in significant country specific activities. The dataset includes data on the intra-group ownership structure and the balance sheets of 45 of the largest banking groups, which operate more than one significant foreign subsidiary. It was constructed using information taken from Bureau van Dijk’s BankScope database, from banks’ websites and based on correspondence with banks. It includes all subsidiaries of bank holdings for which the assets account for 0.5 per cent or more of the parent bank’s assets in 2004 and that are at least 50% owned by the parent bank. The sample period is 1992-2004 and only those banks are included for which at least three consecutive years of data were obtained. This excludes all Chinese and most Japanese banks. Included in the set are commercial banks, savings banks, co-operative banks, real estate/mortgage banks, and medium and long-term credit banks. Excluded are investment banks, securities houses, government-owned banks and non-banking credit institutions. All balance-sheet and income-statement variables in the dataset are stated in US dollars.20
Table 1: Geographical distribution of parent bank and subsidiaries of all banking groups
Bank Europe North America
South
America Asia Australia
Parent banks 83% 13% 0% 1% 3% Subsidiaries 73% 15% 2% 8% 2%
Table 1 provides information on the geographical distribution of the banks included in the sample and Figure 3 gives a graphical representation of this. A detailed list of all the banking groups included in the sample with the countries in which they operate a significant business unit is presented in Appendix A. Of the 49 countries in total where the country business units included in our sample are active, 28 are OECD countries and 20 are non-OECD countries. Of the total of 173 country business units included in the sample, 38 are located in non-non-OECD countries and the other 135 are located in OECD countries. Of the 43 banking groups included in our sample, 29 are active in OECD countries only and 14 banking groups operate at least one non-OECD country business unit. The size of the banking groups included in our sample may differ per year as subsidiaries are acquired or sold. Figure 4 gives an overview of the average amount of country business units per banking group in each year of our sample. The figure indicates that the amount of country business units per banking group has increased on average over time. At the end of our sample period (2004), each banking group consists of on average 4.7 country business units and thus operates in 4.7 countries on average.
Figure 3: Location of parent banks (triangles) and subsidiaries (circles)
Source: De Haas & van Lelyveld (2007)
As discussed in previous sections, we use the variable loan-loss provisions as a measure of each individual bank’s credit risk exposure. Before using the data on loan-loss provisions, we rescaled them to avoid the problematic use of negative values. Negative values for loan-loss provisions can be found when credit risk of institutions is believed to have reduced to such an extent that provisions are actually subtracted from loan-loss reserves. Proper use of our model, however, does not allow for negative values of individual exposures (loan-loss provisions) and therefore all values have been rescaled to a positive range.21
Figure 4: Yearly average number of country business unit’s per banking group
2. 5 3 3. 5 4 4. 5 5 av er ag e nu m be r o f b u' s pe r y e ar 1990 1995 2000 2005 year
21 Negative values for individual exposures can be used in our model, but they will lead to misinterpretation of the results.
Table 2: Descriptive statistics for country business unit variable loan-loss provisions over total assets over the
sample period 1992-2004
Variable* Obs. Mean Median Std. Dev. Min Max Skewness Kurtosis
Loanlossprovisions /
total assets 1084 0.061 0.059 0.008 0 0.146 2.643 30.613
Table 2 displays some descriptive statistics of yearly bank-level data for loan-loss provisions as a fraction of the corresponding bank’s total assets over the entire sample period 1992-2004. Correcting the data for bank size (in terms of total assets) provides an intuitively more appealing picture as the magnitudes of loan-loss provisions can be better compared across banks. For our empirical framework, however, we need the actual magnitudes of bank exposures so we do not correct for bank size. Figure 5 displays the time series on loan-loss provisions as a fraction of total assets in a boxplot.
Figure 5: Box plot for yearly bank-level loan-loss provisions divided by total assets over the period
1992- 2004. 0 .05 .1 .15 loan loss p ro visions / total assets 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 5.2 Macroeconomic data
This section discusses our raw macroeconomic data and subsequently the way in which we use these data to measure the output gap and to construct the correlation matrix filled with correlation coefficients between the output gaps of all countries included in the dataset for the period 1992-2004. To construct the business cycle, its trend, and eventually the standardized output gap, we use yearly time series data over the period 1950-2006, obtained from the ‘Total Economy Database 2007’ of the Groningen Growth and Development Centre (GGDC) for the 49 countries represented in the dataset. This period is longer than the observation period for the bank balance sheets (1992-2004), since we want to obtain the output gap per country for these years and this measure is obtained more accurately when using data with a longer time span.22 The total GDP series, from the GGDC
dataset that we use, is denominated in 1990 US$.23 For most countries, yearly data was available for the entire
22 Estimation of the trend of the business cycle is more accurate when using data with a longer time span. Using data with a
higher frequency could also contribute to the accuracy of the correlations, but we restrain from this due to a lack of
homogenous data covering all (or most of) the countries in the dataset for a sufficiently long period.
period, but for others only data from 1989 onward were available. Time series on yearly GDP series per country are displayed in Appendix B.
Using these raw data, we obtain the business cycle series per country by applying a full sample asymmetric Christiano-Fidzgerald frequency filter (band-pass filter) to the data with cycle periods set between two and eight years and with 3 lags to our dataset. The result is a trend with yearly fluctuations around it: the business cycle, as shown in the left panel of figure 6. This choice of filter, cycle periods, and lags is common practice for business cycle computations when using yearly time series data.24 The business cycle series are stated in levels (1990
US$), just like the GDP series. For correlation matrix multiplications, we use standardized series as these series are better comparable across countries. To obtain standardized output gap series per country, we calculate the fluctuations as a percentage of the trend. We first calculate the trend by subtracting the band pass filter series from the GDP series per country and then we divide the band-pass filter series by the trend to find the standardized output gap per country. The result for the Netherlands is shown in the right panel of figure 6. Standardized output gap series per country for all countries included in the dataset are displayed in Appendix C.
Figure 6: Measuring the output gap for the Netherlands
-6,000 -4,000 -2,000 0 2,000 4,000 6,000 0 100,000 200,000 300,000 400,000 50 55 60 65 70 75 80 85 90 95 00 05 GDP NL Trend Cycle The Netherlands Year B us ine ss c y cl e ( in 1 990 U S $) GD P and tre nd ( in 1 990 U S $) -4 -3 -2 -1 0 1 2 3 4 50 55 60 65 70 75 80 85 90 95 00 05 The Netherlands S tand ar d iz ed o u tp ut ga p ( % ) Year
Using these macroeconomic data on standardized output gaps, we construct a 49x49 correlation matrix, filled with correlation coefficients between the standardized output gaps across all countries. The correlation coefficient of a variable with itself is equal to one, so the entries on the matrix’ diagonal are all equal to unity.
6
RESULTS
Table 3 displays the results for the variable DIV over the entire sample, as ultimately generated through equation (4). Over the entire sample of 43 banking groups and 13 years, we find an average diversification benefit per banking group of 20.8%, a minimum diversification benefit of 1.7%, and a maximum of 58.1%. Thus among our sample of multinational banking groups, an average international credit risk diversification effect exists of 20.8% over the entire sample period. At the aggregate level, these banking groups diversify away country specific risks, leading to an aggregate credit risk of on average 20.8% lower than the simple sum of the credit risks of the stand-alone country business units belonging to these banking groups.
Table 3: Descriptive statistics for percentage diversification
Variable Obs. Mean Median Std. Dev. Min Max Skewness Kurtosis
DIV 326 0.208 0.167 0.136 0.017 0.581 0.558 2.266
Appendix D displays a table with banking group specific results for DIV (in percentages) averaged over the sample period 1992-2004 and at sample end (2004). The results in the table indicate that there are substantial differences in diversification benefits across the world’s largest banking groups, with a minimum average diversification benefit of 3.8% for Bank of America and a maximum average diversification benefit of 50.0% for Banco Comercial Português. Implications of allowing for the recognition of international diversification effects in banking regulation, in order to accommodate a more accurate assessment of aggregate risk profiles of banking groups, may thus differ substantially per banking group.
Figure 7: Diversification over total assets per banking groups and over the sample period
0 .2 .4 .6 0 1000000 2000000 3000000 4000000 (sum) totalassets
diversification (std. deviations) Fitted values
0 .2 .4 .6 di ve rs ifi ca tio n ( std . d ev ia tio ns) 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
figure 8 displays DIV when set out over the amount of subsidiaries (country business units) per banking group. The figure indicates that diversification is indeed higher for banking groups operating larger numbers of country business units, but again this pattern is not a straight line. An important note here is that the number of observations is lower for large numbers of country business units. For example, Appendix A indicates that there is only one banking group with ten country business units (HSBC) at sample end 2004 and figure 4 indicates that the average number of country business units has decreased during our sample period. As the number of observations falls for higher numbers of country business units, the corresponding results should be interpreted with greater care. This is especially true for the observations for eight or more country business units in the left hand panel of figure 8.
Figure 8: Diversification over the number of country business units per banking group and over international concentration per banking group as measured by the Herfindahl-Hirschman Index of total assets
0 .2 .4 .6 di ve rs ifi ca tio n (s td . dev ia tio ns ) 2 3 4 5 6 7 8 9 10 0 .2 .4 .6 .2 .4 .6 .8 1
HHI index banking group i year t diversification (std. deviations) Fitted values
In order to consider the relation between the international concentration of banking group activities and their degree of diversification, we determine the degree of concentration of operations per year for each banking group in the sample by calculating the Herfindahl-Hirschman Index (HHI) in terms of total assets,
∑
= i i j is
1 2 , .So si,j = TA(i) / TA(j), where si,j is the share in total assets of country business unit i in total assets of the entire
banking group j. Higher degrees of the HHI imply that banking group operations are concentrated in fewer countries, reducing the potential for international diversification. An important point to note here is that the HHI is not only influenced by the number of countries in which a banking group is active, but also the relative size of the operations of these banking groups as measured by their total assets. The right hand panel of Figure 8 displays a scatterplot for diversification over international concentration in terms of assets as measured by the Herfindahl-Hirschman index of total assets. There appears to be a negative trend, indicating that diversification reduces with concentration. Intuitively, one may expect this relation to be stronger, as the spreading of activities (which can be measured by assets) is the basis for diversification, i.e. international diversification benefits exist because risks are spread internationally.
of similar size. But the HHI does not consider the specific location of these country business units. If assets are spread over very different countries in terms of macroeconomic risk drivers, the international diversification will be higher as the correlation between the business cycles of these countries will be smaller. That is, if HHI is low (so spreading is high) then DIV may still be low when a banking group’s country business units are spread among countries that are similar in terms of macroeconomic risk drivers. Conversely, when the HHI is relatively high (so spreading is low) but the countries in which these country business units are located are very different, then DIV may be relatively high.
7
SUMMARY AND CONCLUSIONS
In this paper we use a widely applicable correlation matrix approach for calculating international diversification effects in the banking industry. We apply our framework to a sample of 43 of the largest banking groups in the World over the period 1992-2004, for which the country business units are treated as individual securities belonging to the portfolio ‘holding’ of the banking group. We focus on the most important risk in banking, i.e. credit risk. At bank-level, we use the variable loan-loss provisions to proxy for the degree of credit risk of individual banks. At macroeconomic level, we use the variable output gap to proxy for the international risk driver for credit risk. These two levels are linked through the assumption that banks carry a considerable degree of country specific risk in their lending portfolios.
Our results indicate that international credit risk diversification effects are substantial and differ considerably among the 43 multinational banking groups included in the sample. We find an average diversification benefit of 20.8% per banking group over the entire sample period, a minimum diversification benefit of 1.7%, and a maximum of 58.1%. Furthermore, average diversification has increased over the sample period 1992-2004, shows an increasing trend with the number of country business units, and appears to be negatively related to the degree of international concentration of banking groups in terms of total assets.
