Does Diversification Improve the Performance of German Banks? Evidence from Individual Bank Loan Portfolios

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1 Does Diversification Improve the Performance of German Banks? Evidence from Individual Bank Loan Portfolios Evelyn Hayden 1 Banking Analysis and Inspections Division Österreichische Nationalbank Otto-Wagner-Platz 3, POB 61, A-1011 Wien Tel.: +43 (0) Evelyn.Hayden@oenb.at Daniel Porath 1 Bank Examinations Deutsche Bundesbank Postfach , D Frankfurt am Main Tel.: +49 (0) Daniel.Porath@bundesbank.de Natalja v. Westernhagen 1 Department of Banking and Financial Supervision Deutsche Bundesbank Postfach , D Frankfurt am Main Tel.: +49 (0) Natalja.von-Westernhagen@bundesbank.de Abstract: Should banks be diversified or focused? Does diversification indeed lead to increased performance and therefore greater safety of banks as traditional portfolio and banking theory would suggest? In this paper we try to shed some light on these questions by empirically investigating the situation of German banks. By exploiting a unique data set of individual bank loan portfolios for the period , we analyze the link between banks portfolio diversification across different industries, broader economic sectors and geographical regions and banks profitability. Up to the authors knowledge this is the first paper studying the effect of all three types of diversification jointly, and also the first one based on micro-level data of German banks. The evidence we present indicates that on average each kind of diversification harms banks return, i.e. in general focus increases profitability. Moreover, our results suggest that banks do not use diversification to move on a constant risk-return efficiency level, which implies that overall German banks are not risk-return efficient. Next, the impact of all types of diversification on banks return changes with the risk level. While the effect of sectoral focus on return declines monotonely with increasing risk, there is mixed evidence for either a monotonely decreasing or a U-shaped relationship for regional focus and rather distinct indication for a U-shape with respect to industrial focus. Besides, for our data diversification significantly improves banks profits only in the case of moderate risk levels and industrial diversification. Hence, from a policy point of view our results suggest that bank regulations which might tend to increase the level of industrial, sectoral or geographical diversification should be evaluated carefully. Keywords: Focus, Diversification, Monitoring, Bank Return, Bank Risk JEL Classification: G21, G28, G32 1 This paper represents the authors personal opinion and does not necessarily reflect the views of Österreichische Nationalbank or Deutsche Bundesbank or their staff.

2 Content: 1 Introduction Data DATA SOURCES DIVERSIFICATION MEASURES BALANCE-SHEET VARIABLES Empirical Framework AVERAGE IMPACT OF DIVERSIFICATION CONSISTENCY WITH PORTFOLIO THEORY DIVERSIFICATION, MONITORING EFFECTIVENESS AND RETURNS Conclusions References

3 1 Introduction Should banks diversify their portfolios across different industrial or even broader economic sectors and geographic regions, or should they focus on a few related fields? Does diversification indeed lead to increased performance and therefore greater safety of banks as traditional portfolio and banking theory would suggest? In this paper we try to shed some light on these questions by empirically investigating the situation of German banks. The focus vs. diversification issue is important in the context of banks as they face several regulations that create either incentives to diversify or focus their portfolios, i.e. the imposition of capital requirements tied to the risk of the banks assets or asset investment restrictions. Hence, policy makers should be especially interested to ask whether banks benefit or loose from diversification. Experts on financial institutions generally argue that banks, which are typically highly levered, should diversify to reduce their chance of costly financial distress; also, several models of intermediation suggest that diversification makes it cheaper for institutions to achieve credibility in their role as screeners or monitors of borrowers (see e.g. Diamond (1984) and Boyd and Prescott (1986)). On the other hand, corporate finance theory suggests that any firm should focus so as to take greatest advantage of management s expertise and reduce agency problems, leaving investors to diversify on their own (see e.g. Jensen (1986), Berger and Ofek (1996), or Denis et al. (1997)). Since real world cases can be found in support of either view, the question arises which circumstances favor one strategy or the other. Winton (1999) presents a theoretical framework to investigate the above issue. He argues that the benefit from diversification should be greatest when banks loans have medium levels of downside risk, i.e. the banks probabilities of default are moderate. To see this, assume that the banks abilities to monitor loans is constant across different sectors. Such pure diversification increases the central tendency of the banks return distribution, which generally reduces their chance of failure. However, if the loans have sufficiently low exposure to sector downturns, specialized banks have a low probability of failure anyway and the benefits of diversification are small. What s more, diversification can actually increase the banks default probabilities if their loans have sufficiently high downside risk, since then a downturn in one sector is enough to make a bank fail, and a diversified bank is exposed to more sectors than a specialized one. Furthermore, diversification involves moving into economic sectors or geographic regions that differ from the banks home base, therefore implying a lower monitoring effectiveness in these areas at least in the beginning. Also, some papers suggests that a bank entering a sector with several established banks faces increased adverse selection in its pool of borrowers (see e.g. Gehrig (1998) and Shaffer (1998)). So overall, 2

4 diversification is more likely to be unattractive, particularly when the bank s home sector loans have either low or high downside risk. Although the issue of focus versus diversification has a long history in the corporate finance literature, it has not been addressed thoroughly in an empirical context for financial institutions and banks. The existing literature mainly focuses on geographic diversification and on US data and also provides mixed results. Using more aggregated measures of bank diversification, for example Hughes et al. (1996) and Berger and DeYoung (2001) examine geographic diversification for US banks, while Caprio and Wilson (1997) investigate cross-country evidence for a relationship between on-balance sheet concentration and bank insolvency. Besides, Dahl and Logan (2003) and Buch at al (2004) suggest that there are benefits from international diversification, while according to Klein and Saidenberg (1998) and Morgan and Samolyk (2003) geographic diversification of US banks is not necessarily associated with an increase in profitability. In line with the later DeLong (2001) finds that geographically focused bank mergers in the U.S. produce superior performance, and finally Stiroh and Rumble (2003) and Stiroh (2004) show that a shift towards non-interest income does not offer large diversification benefits. Therefore, there is clearly a need for more empirical evidence on the effects of diversification on banks performance based on individual bank level data for European countries. The leading study in this respect is probably the one by Acharya et al (2004), who examine the effect of sectoral and industrial loan diversification on the performance of Italian banks. Their results are consistent with Winton s theory of a deterioration in the effectiveness of banks monitoring at high levels of risk. Besides, Acharya et al find that both industrial and sectoral loan diversification reduce banks returns while endogenously producing riskier loans for high risk banks in their sample, so that diversification of banks assets is not guaranteed to produce superior return performance and/or greater safety for Italian banks. Now the question arises whether the Italian results are valid for other European countries, too. Our study attempts to fill this gap by studying the situation for the German banking industry. Based on a unique data set of the German national bank with data on individual bank loan portfolios disaggregated at a very fine and micro level available for the period we assess the impact of sectoral, industrial and geographical diversification on banks profitability by looking on three major aspects. First, we are interested in the average effect of banks portfolio diversification across industries, sectors and regions on banks returns. Second, we try to get an insight on whether diversification is used as an instrument to induce shifts in banks risk-return efficiency. Third, we test how monitoring effectiveness for low, medium and high risk banks impacts on the relationship between banks portfolio diversification and banks returns. Thereby in contrast to previous studies we apply a Value at Risk approach to measure banks risk and derive unexpected losses for each 3

5 individual bank, as in our opinion unexpected losses are better suited to capture banks riskiness than the more common proxy of expected losses. Our main findings are the following: First, we find that portfolio diversification across different sectors, industries and regions rather tends to worsen banks profitability than to lead to improved returns. The highest benefits are associated with geographical focus, whereby benefits from industrial focus appear to be only moderate. Second, there is evidence that instead of moving along a constant risk-return efficiency level banks use diversification in order to change their risk-return profile. As banks with highly risky credit portfolios are not systematically more profitable than banks with low risk portfolios, it seems that overall banks are not risk-return efficient. Third, the profitability benefits associated with diversification strongly depend on the banks risk level. Besides, the type of focus plays a crucial role. While the effect of sectoral focus on return declines monotonely with increasing risk, there is mixed evidence for either a monotonely decreasing or a U-shaped relationship for regional focus and rather distinct indication for a U-shape with respect to industrial focus. Therefore, at least partly our results confirm Winton s theory of diversification benefits being highest for moderate risk levels. Finally, for our data diversification significantly improves banks profitability only in the case of moderate risk levels and industrial diversification. Hence, from a policy point of view our findings suggest that bank regulations which might tend to increase the level of industrial, sectoral or geographical diversification should be evaluated carefully. The remaining of the paper is structured as follows: Section 2 describes our data, in Section 3 we present the empirical results and Section 4 concludes. 4

6 2 Data 2.1 Data Sources The main data source for our analysis comes from the database of the credit register for loans of 1.5 million Euro (formerly 3 million Deutsche Mark) or more at Deutsche Bundesbank. German banks have to report quarterly all claims which have exceeded the threshold of 1.5 million Euro. Bank claims are fairly broadly defined, covering details on types of claims 2, types of respective borrowers by industries and sectors, international claims by individual foreign countries and regions 3. Additionally to balance-sheet bank activities claims also incorporate information on off-balance-sheet activities 4. This credit register data set on exposures of individual banks is combined with financial data from the second data source of the Bundesbank called BAKIS (BAKred 5 Information System). BAKIS incorporates information which stems from bank balance sheets and from supervisory reports of all German banks. Since the data on bank balance sheets is mostly of annual frequency, we finally use annual data for the time period from 1996 to Both the credit register and BAKIS represent unique data sources which have never been exploited before to investigate the relationship between diversification and performance of German banks. Our data sample does not only include banks but also their subsidiaries and amounts to 3760 individual entities. However, as small banks usually grant only few large loans, the reported loans from the credit register sometimes only cover a rather low fraction of the total credit volume outstanding according to the banks balance sheets. This implies that it might be misleading to analyze the diversification structure of these small banks based on the information from the credit register, as the decomposition of the total portfolio could differ significantly from the one of the large loans. Therefore, we only focus on those banks in our study where the ratio of the reported loans versus the total amount of loans according to the balance sheet exceeds 50%. 6 We further excluded affiliates of German banks abroad, mortgage banks and special purpose banks from our analysis. This reduces the number of eligible banks to E.g. among on-balance sheet activities lease receivables, mortgage loans, publicly guaranteed loans, interbank loans (with a residual maturity up to one year) are listed separately. 3 The following items are deemed not to be credit exposures: shares in other enterprises irrespective of how they are shown in the balance sheet and securities in the trading portfolio (Deutsche Bundesbank, 1998). 4 Off-balance-sheet items include derivatives (other than written option positions), guarantees assumed in respect of these, and other off-balance-sheet transactions (Deutsche Bundesbank, 1998). 5 The BAKred is the former synonym for BAFin (Bundesanstalt für Finanzdienstleistungsaufsicht) the Federal Banking Supervisory Office in Germany. 6 For these banks the average coverage rate is about 70%. 5

7 2.2 Diversification Measures The data from the credit register provides considerable detail on the industrial, the broader sectoral and the geographic decomposition of the German bank claims. On the individual bank basis the following information on the portfolio decomposition is available: 1. The disaggregated industrial sector decomposition includes: (1) agricultural, forestry, and fishing products, (2) energy products, (3) iron and non iron material and ore, (4) ores and products based on non-metallic minerals, (5) chemicals, (6) metal products, apart from machinery and means of conveyance, (7) agricultural and industrial machinery, (8) office, EDP machinery, and others, (9) electric material, (10) transport, (11) food products, beverages, and tobacco-based products, (12) textile, leather, shoes, and clothing products, (13) paper, publishing, and printing products, (14) rubber and plastic products, (15) other industrial products, (16) construction, (17) services trade and similar, (18) hotel and public firms products, (19) internal transport services, (20) sea and air transport, (21) transport related services, (22) communication services, and (23) other sales related services. Note that in aggregate these exposures (collectively defined in the data as non financial and household exposures) constitute the dominant part of most banks portfolios. 2. The broader sectoral decomposition includes (1) financial institutions and banks, (2) non-financial corporations, (3) private households, (4) the public sector and (5) other counter-parties. 3. The geographic decomposition includes (1) Germany, six regions according to the IMF classification: (2) Industrial Countries, (3) Asia, (4) Africa, (5) the Middle East, (6) the Western Hemisphere, (7) Emerging Europe, and (8) Other. 7 To measure diversification (respectively focus) we use a Hirschmann Herfindahl Index. It is calculated as the sum of squares of exposures as a fraction of total exposure under a given classification and is represented by the following formula: HI n 2 X i = i= 1 X, where n gives the number of groups and X i measures exposure towards industry, sector or region i. The smallest respectively the largest possible value for the Herfindahl-Index is given by: 1/n = HI = 1. Hence, lending is the more concentrated the closer the Herfindahl-Index is to one and is perfectly diversified if the Herfindahl-Index equals 1/n. 7 For further details see Nestmann et al. (2003). 6

8 In our case, we construct three different kinds of Herfindahl Indices, one industrial (and household) sector Herfindahl Index (HI), one broad asset type (or sectoral) Herfindahl Index (HT), and one regional (or geographic) Herfindahl Index (HR). 2.3 Balance-Sheet Variables We employ the following (annual) variables obtained from the balance-sheet data for the banks in our sample over the time period Return measures: Operating Profit / Assets serves as the principal measure for return. All results displayed are based on this measure. However, we also performed robustness checks with other measures like e.g. Operating Profit / Equity. We found that, overall, the results are robust with respect to the employed return measure. Risk measures: The simplest method to measure risk would be to look at a balance sheet ratio like Doubtful and Non- Performing Loans / Total Loans, which could be interpreted as capturing the level of expected losses. However, we argue that risk is more accurately represented by unexpected losses, the reason why we focus on a Value at Risk (VaR) measure. The most widespread method to determine a bank s loan portfolio risk is the Value at Risk. The Value at Risk of bank i in period t, VaR it, is the maximum loss over a target horizon such that with a prespecified probability p the realized loss will be smaller. It can be determined from the distribution of the portfolio losses at the target horizon as the difference between the mean of the portfolio value and the value at the p-percentile. In our calculations p is 99.9%. This is motivated by the observation that banks typically work with percentiles higher than 99.5%. Since the following estimations are fixedeffects panel models where the levels of the variables are differenced out, the exact level of p will not affect our results. The values for the VaR have to be taken from the distribution of the portfolio value. We estimate the portfolio s value distribution using a simplified version of CreditMetrics. 8 The basic assumptions of CreditMetrics are that the returns of a creditor are normally distributed and that a default occurs when the return of a creditor falls under a certain threshold. The default threshold is determined by the probability of default (PD). 8 J.P. Morgan (1997) 7

9 As our data set does not comprise rating information for individual loans, we use the average insolvency rate of the industry which is associated with the loan to proxy the default probability for a loan and calculate its return threshold. We further assume that the correlation between the returns of creditors can be approximated by the correlation of the industries insolvency rates. 9 Using equal probabilities of default for each bank, however, may bias the results, since for example focused banks may have more effective monitoring systems and therefore grant loans with lower PDs as compared to diversified banks. Therefore - because no information on the risk of loans on industry and individual bank level is available for German banks - we have to adjust the (observed) industry insolvency ratios by bank specific factors. To do so we define the industry insolvency ratio multiplied with a scale parameter which is related to a bank s loan loss provisions as a bank specific PD. As a result banks with high loan loss provisions (divided by the amount of total loans) are assigned higher PDs for loans of a specific industry than banks with lower provisions. It should be noted that loans to all industries of a bank are adjusted with the same scale factor because, unfortunately, the data does not allow for a more precise adjustment. 10 The current value of a bank s overall portfolio at the beginning of a period is given by the sum of the bank s individual exposures to each industry which we take from the credit register as described above. We then simulate returns using a multivariate normal distribution with mean zero and the correlation matrix from the insolvency data. Defaults occur when the simulated returns fall below the threshold given by the critical values which are derived from the annual industries insolvency rates. The simulated value of the portfolio at the end of the period is the value at the beginning of the period less 45% of the loans defaulting in the simulations, which implies that we assume a loss given default of 45% to follow the Basel II proposal (see Basel Committee on Banking Supervision (2004)). 11 We 9 The insolvency data were taken from the Statistisches Bundesamt. The industry codes of the insolvency data match with the industry codes of the credit register. The insolvency rate of a specific industry is calculated as the number of insolvencies divided by the total number of companies in the industry. The probability of default of a specific industry is then calculated as the average of the annual data from 1994 to The correlation between insolvencies of the industries is calculated with monthly data for the same period. 10 More precisely the scale parameter for bank i is defined as Scale it = Loan Loss Provisions it Total Loans it j InsolvencyRate Exposure jt jit Exposure jit j where i, t and j index the bank, the period and the industry. Loan Loss Provisions and Total Loans are taken from the balance sheet data, and Exposure from the credit register. Following Moody s KMV Credit Monitor we introduce a cap of 20% for the resulting PD, see Bohn et al (2005). 11 As mentioned above, the level of the VaR differences out in the fixed effect estimations, so the value of the LGD will not affect our results. 8

10 then repeat this exercise 50,000 times in order to obtain the simulated loss distribution of a single bank in a specific period. From the loss distribution we calculate the unexpected loss as the difference between the 99.9% percentile and the mean. Finally, the variable Risk it is calculated as Risk it = Unexpected Loss it /Assets it In order to obtain a panel of observations for Risk it we repeat the simulations for each bank and each period of our sample. Control variables: The return of banks might not only be dependent on the diversification and the risk of the respective banks but probably will also differ due to other criteria. In the estimation we will control for unobservable individual and time effects by using dummy variables. The bank specific dummies control for all effects which do not change over time for individual banks. These effects comprise e.g. characteristics which differ between banking groups, like regional constraints of German savings or cooperative banks or different ownership structures. In addition to these fixed effects we also control for characteristics which may change over time: Personal it = Personal Costs it / Assets it Size it = Ln(Assets it ). We follow Acharya et al (2004) and use the variable Personal it to proxy cost efficiency. The rationale is that banks with different cost efficiency levels may transform the benefits from diversification (or focus) in a different way. The variable Size it captures possible scale effects on return. The banks equity ratio is a common control variable in many empirical studies: Equity it = Equity it / Assets it Following the capital buffer theory equity ratios above the regulatory minimum requirement of 8% serve as a buffer that shields banks from insolvencies due to unexpected losses. The amount of the buffer depends on the banks risks and risk preferences. Accordingly, Equity it depends on Risk it and the Herfindahl Indices. We try to avoid biases arising from this dependency and thus estimate the influence of diversification on returns without controlling for equity. However, in order to compare our results with those from other studies (e.g. Acharya et al (2004)), we report results which include Equity it, too. 9

11 3 Empirical Framework Our aim is to assess the impact of diversification on banks profitability for German banks. We address this question by looking at three aspects. First of all we are interested in the average effect of diversification on return. Subsequently we try to answer the question whether the link between return and diversification is consistent with portfolio theory. Finally we test how monitoring effectiveness affects the relationship between diversification and return. 3.1 Average impact of diversification We investigate the average impact of diversification on banks performance in a panel regression where we regress return on the Hirschman-Herfindahl Indices. More precisely, we estimate the following equation: N Return it = α 0 + α 1 HT it + α 2 HR it + α 3 HI it + α n X nit + ϖ it, (1) n= 4 where Return it, HT it, HR it and HI it are measured as described in the previous section. X n is the set of control variables described above, which comprises time dummies, individual dummies, 12 Personal it,, Size it and - for reasons of comparability to other studies - Equity it.. Due to the presence of the dummy variables estimating (1) with OLS is equivalent to adopting the two-way fixed effects estimator. ω it is iid with mean zero and a constant variance. The coefficients α 1, α 2 and α 3 capture the average impact of focus on bank performance, which means that they are not conditioned on the banks risk levels. We estimate (1) with several restrictions. The results are reported in Table 1. In all specifications the coefficients for the Herfindahl Indices are positive, in most estimations they are also highly significant. The results are remarkably stable for the estimations (1a) (1d), however, they change when adding Equity it to the equation, see specification (1e). In specification (1e) the coefficients for the Herfindahl Indices are considerably lower in terms of absolute magnitude and in terms of significance level and at the same time Equity it is highly significant. Hence the inclusion of Equity it reduces the impact of the Herfindahl Index on Return it. This is consistent with our assumption that Equity it is determined by banks risk preferences and that hence the coefficients α 1, α 2 and α 3 in (1e) no longer reflect the average impact of focus on Return it. Independently from this assumption, the results of all specifications confirm a positive impact of geographical focus at a 1% confidence level and a positive impact of sectoral focus on at least a 10% level. Furthermore, concerning the magnitude 12 For ease of disposition the coefficients of the dummies will not be reported in the following. 10

12 of the coefficients, all estimations reveal the same order with HR it having the highest and HI it having the lowest coefficient. Table 1: Two-way fixed effects estimation of Equation (1) with alternative restrictions, Dependent Variable: Return it, (1a) (1b) (1c) (1d) (1e) HT it 0.018*** (4.87) 0.020*** (5.74) 0.005* (1.65) HR i *** (4.38) 0.039*** (5.83) 0.017*** (2.81) HI it 0.006** (2.50) 0.005** (2.00) (0.47) Equity it 0.185*** (24.66) Size it *** (14.75) *** (-15.69) *** (-15.13) *** (-14.92) *** (-4.27) Personal it *** (-15.02) *** (-14.89) *** (-14.91) *** (-14.54) *** (-20.55) Constant 0.429*** (13.39) 0.480*** (15.66) 0.438*** (13.77) 0.476*** (15.22) 0.124*** (3.99) No. of obs. 3,529 3,529 3,529 3,529 3,529 T-values in brackets, *, **, *** denotes significance at 10%, 5% and 1%. Blanks indicate that the coefficient of the variable is restricted to zero. The positive coefficients of the Herfindahl Indices can be interpreted as a confirmation that (at least on average) the benefits arising from focusing loan portfolios exceed the benefits which are achievable with diversification. The highest benefits seem to be achievable with geographical focus, whereas benefits from industrial focus appear to be only moderate. In the following subsections we will analyze whether the results are in line with portfolio theory and/or how the quality of monitoring influences the link between diversification and returns. 3.2 Consistency with portfolio theory Portfolio theory describes the relationship between diversification, expected returns and risk in a liquid portfolio. For our purpose, the most important implication is that diversification is an instrument to increase expected returns for a given value of risk and therefore it may be used to induce shifts in banks risk-return efficiency. Alternatively, banks may use diversification in order to change their risk-return profile on the same efficiency level. In order to test which policy prevails we add the variable Risk it (measured as described above) to Equation (1): Return it = β 0 + β 1 HT it + β 2 HR it + β 3 HI it + β 4 Risk it + β n X nit?+ ε it. (2) N n= 5 11

13 Here the coefficients β 1, β 2, and β 3 capture the impact of a variation of focus on return conditioned on the banks risk level. If banks have operated on the same efficiency level the conditional coefficients take the value zero and β 4 is positive. Deviations of β 1, β 2, and β 3 from zero and/or non-negative values for β 4 indicate that banks have used diversification to change their risk-return efficiency. It should be noted that Risk it is endogenous in HT it, HR it and HI it. Therefore (1) can be interpreted as the reduced form of (2). Table 2: Two-way fixed effects estimation of Equation (2) with alternative restrictions, Dependent Variable: Return it, (2a) (2b) (2c) (2d) (2e) (2f) HT it 0.017*** (4.77) 0.020*** (5.63) (1.621) HR it 0.030*** (4.38) 0.039*** (5.82) 0.017*** (2.81) HI it 0.007*** (2.71) 0.006** (2.28) (0.55) Risk it * (-1.67) (-1.27) * (-1.67) ** (-2.02) * (-1.71) (-0.56) Equity it 0.109*** (24.60) Size it *** (-14.29) *** (-15.35) *** (-14.76) *** (-14.40) *** (-15.09) *** (-4.17) Personal it *** (-14.92) *** (-14.81) *** (-14.83) *** (-14.43) *** (-14.52) *** (-20.48) Constant 0.421** (13.00) 0.475*** (15.36) 0.431*** (13.45) 0.466*** (14.72) 0.480*** (15.45) 0.122*** (3.89) No. of obs. 3,529 3,529 3,529 3,529 3,529 3,529 T-values in brackets, *, **, *** denotes significance at 10%, 5% and 1%. Blanks indicate that the coefficient of the variable is restricted to zero. Table 2 reports the estimated coefficients. Interestingly, conditioning on risk does not change the results from (1), since the conditional coefficients β 1, β 2, and β 3 are almost equal to the average coefficients α 1, α 2 and α 3 in Table 1. Contemporaneously, Risk it is significantly negative in specifications (2a), (2c) and (2d). In the other specifications the coefficient for Risk it is insignificant. Note that the outcome does not seem to be caused by a potential multicollinearity between Risk it and the Herfindahl Indices as β 4 remains stable when the Herfindahl Indices are excluded from equation (2), see specification (2e). When adding Equity it to the equation (see specification (2f)), the coefficients of Risk it and of the Herfindahl Indices become insignificant. Again, we belief that this finding is induced by the fact that Equity it is depends on the banks risk preferences. Since there is no evidence for a positive relationship between risk and return banks do not seem to have used diversification to move on a constant risk-return efficiency level. Banks with highly risky credit portfolios were not systematically more profitable than banks with low risk portfolios. One consequence of this finding is that overall banks were not risk-return efficient. This conclusion is confirmed by the non-zero coefficients of the Herfindahl Indices. 12

14 To sum up, the positive Herfindahl Indices in Table 2 indicate that banks with a higher focus tend to be more profitable than diversified banks and at the same time banks with a higher risk level seem to be less profitable. Accordingly, instead of moving along a constant risk-return efficiency level banks appear to have used diversification as an instrument to change their risk-return profile. 3.3 Diversification, monitoring effectiveness and returns Finally, we analyze how monitoring effectiveness affects the link between diversification and banks returns. In Winton s (1999) model effective loan monitoring is the force that prevails banks from failure by catching problem loans before the situation is going to deteriorate too much. Therefore, monitoring of loans allows banks to improve their loan returns and reduce their default probability. When choosing whether to diversify or not banks take into account the impact of diversification on their incentives to monitor their loans and on their probability of failure. For specialized banks which are exposed to sectors with low downside risk the benefits from diversification will only be slight since these banks have a low default probability anyway. Otherwise, if we consider diversified banks whose loans have sufficiently high downside risk, bank-owners (equity-holders or managers) have only little incentives to monitor, as then on an expected basis most benefits from monitoring accrue only to its creditors (uninsured depositors and providers of borrowed funds) and diversification can actually increase banks default probability. Accordingly, benefits from diversification are going to be greatest in the case when banks loans have moderate levels of downside risk and when banks monitoring incentives need strengthening. In terms of empirically testable hypotheses Winton s theory implies that the relationship between return and focus (respectively diversification) should be expected to be non-linear and U-shaped in risk. To try to capture this, we first reproduce the tests proposed by Acharya et al. (2004). They expand Equation (2) by non-linear terms: Return it = β 0 + β 1 HT it + β 2 HR it + β 3 HI it + β 4 Risk it + β N n= 5 n X nit + α 11 HT it *RISK i1 + α 12 HT it *RISK² it + α 21 HR it*risk it + α 22 HR it *RISK² it + α 31 HI it *RISK it + α 32 HI it *RISK² it +?ϖ it. (3) By calculating the first derivative of return on focus it is straightforward to see that a U-shape in risk is given if α 11 < 0, α 12 > 0, α 21 < 0, α 22 > 0, α 31 < 0 and α 32 > 0, see Acharya et al. (2004). 13

15 The estimated coefficients (see Table 3) follow the patterns associated with a U-shaped form, the only exception being the specification which contains Equity it. In all other equations the coefficients of the Herfindahl Indices interacted with RISK it are negative, whereas they are positive when interacted with RISK² it. Most of the coefficients are significant at the 5% or even at the 1% confidence level. Thus the results could be interpreted as strong evidence for a U-shaped relationship between focus and return dependent on the level of risk. Table 3: Two-way fixed effects estimation of Equation (3) with alternative restrictions, Dependent Variable: Return it (3a) (3b) (3c) (3d) (3e) HT it 0.023*** (5.64) 0.022*** (6.02) 0.008** (2.12) HT it *RISK it *** (-3.25) *** (-3.22) (0.25) HT it *RISK² it 0.293** (1.96) 0.215** (2.15) (0.74) HR it 0.029*** (3.89) 0.046*** (6.32) 0.022*** (3.19) HR it*risk it (-1.16) *** (-2.77) (-0.79) HR it *RISK² it 0.140** (2.11) 0.113** (2.02) (-0.63) HI it 0.011*** (3.58) 0.010*** (3.40) (0.48) HI it *RISK it * (-1.78) *** (-2.89) (0.25) HI it *RISK² it 0.603* (1.79) 0.702*** (3.86) (-0.19) Risk it 0.166** (2.05) 0.066* (1.74) 0.129* (1.84) *** (-2.68) 0.173** (2.38) Equity it 0.184*** (24.06) Size it *** (-14.12) *** (-15.26) *** (-14.84) *** (-14.41) *** (-4.14) Personal it *** (-15.23) *** (-14.92) *** (-14.94) *** (-14.71) *** (-20.48) Constant 0.415*** (12.72) 0.471*** (15.23) 0.428*** (13.32) 0.469*** (14.75) 0.117*** (3.67) No. of obs. 3,529 3,529 3,529 3,529 3,529 T-values in brackets, *, **, *** denotes significance at 10%, 5% and 1%. Blanks indicate that the coefficient of the variable is restricted to zero. However, to understand the economic significance of this potential U shaped relationship, Figure 1 plots the marginal effect d(return)/d(focus) for different values of risk for all three types of diversification based on the estimated coefficients from (3b), (3c) and (3d). The range of risk is taken to be between 0% and 50%, which represents the minimum and the maximum value over our entire sample period. Note that the mean (median) of risk is about 3.4% (2.6%), while the 90 th percentile is about 9%. As can be seen from Figure 1, in our sample the effect of a small increase in industrial focus (HI it ) on return for the mean (median) bank is rather small and positive. For risk levels above 10% the effect 14

16 becomes slightly negative, but returns to a positive and sharply rising impact at a risk level of about 22% (corresponding to the 99 th percentile of risk). Hence, we conclude that within the range of risk levels observed in our sample the marginal effect of industrial focus on return might indeed be U- shaped. On the other hand, for sectoral and geographical focus (HT it and HR it ) the result of the graphical analysis differs. Here an increase in focus leads to rising returns for banks with risk levels below 12% respectively 27%, too, but then the effect of focus stays negative and decreasing for all observed risk levels. Indeed, the effect only becomes positive again at hypothetical risk levels as high as 110% and 160%. Therefore, we suspect that the true impact of sectoral and geographical focus on return might rather be linearly or at least monotonely decreasing with risk than following a U-shaped relationship. Figure 1: The marginal effect of focus on return for different values of risk for HT, HR and HI based on the estimated coefficients from (3b), (3c) and (3d) 0,06 Non-monotonicity in Effect of Focus on Bank Returns as a Function of Bank Risk Effect of Focus on Return 0,04 0,02 0,00-0,02-0,04 HT HR HI -0,06 0,00 0,10 0,20 0,30 0,40 0,50 Risk (Unexpected Loss / Assets) To further explore this issue, we have to overcome the drawback of the above test, i.e. the restrictions imposed by the parameterization of the non-linearities between diversification, risk and return in (3). Richer patterns of non-linearity can be detected with nonparametric methods. To this end, we follow Acharya et al. (2004) and define a set of dummy variables which measure different risk levels. The dummy variables are: D 1 = 1 if Risk [0.10] < Risk it Risk [0.25] and zero otherwise, D 2 = 1 if Risk [0.25] < Risk it Risk [0.50] and zero otherwise, D 3 = 1 if Risk [0.50] < Risk it Risk [0.75] and zero otherwise, D 4 = 1 if Risk [0.75] < Risk it Risk [0.90] and zero otherwise, D 5 = 1 if Risk it Risk [0.90] and zero otherwise, where Risk [p] is the p th percentile of Risk it. We then interact the dummies with the Herfindahl Indices and regress the resulting variables on risk. The estimation results are given in Table 4. 15

17 Table 4: Two-way fixed effects estimation of Equation (1) with interaction terms for different risk levels, alternative restrictions, Dependent Variable: Return it, (4a) (4b) (4c) (4d) (4e) HT it 0.026*** (2.89) 0.025*** (-0.10) D 1 *HT it (-0.40) *** (-6.56) 0.015* (1.93) D 2 *HT it * (-1.86) *** (-6.15) (0.02) D 3 *HT it * (-1.86) *** (-5.68) (0.73) D 4 *HT it ** (-2.53) *** (-5.43) (0.44) D 5 *HT it (-1.28) *** (-4.38) (0.20) HR it 0.038*** (3.73) 0.046*** (6.85) 0.046*** (5.00) D 1 *HR it (-0.61) *** (-7.08) ** (-2.47) D 2 *HR it (0.67) *** (-6.60) (-0.82) D 3 *HR it (0.81) *** (-6.19) (0.33) D 4 *HR it (1.30) *** (-5.92) (0.52) D 5 *HR it (0.51) *** (-5.23) (-1.13) HI it 0.016*** (3.00) 0.023*** (4.23) *** (-4.97) D 1 *HI it *** (-7.22) *** (-8.15) *** (-5.80) D 2 *HI it *** (-4.30) *** (-4.41) *** (-10.35) D 3 *HI it ** (-2.22) *** (-3.59) 0.029*** (4.62) D 4 *HI it *** (-2.60) (-4.00) 0.023*** (3.86) D 5 *HI it (-1.56) (-2.84) 0.031*** (4.77) Equity it 0.185*** (24.22) Size it *** (-13.77) *** (-14.90) *** (-14.47) *** (-12.94) *** (-6.36) Personal it *** (-14.65) *** (-15.63) *** (-15.71) *** (-13.20) *** (-19.58) Constant 0.373*** (12.19) 0.463*** (15.07) 0.422*** (13.31) 0.424*** (13.27) 0.151*** (5.22) No. of obs. 3,529 3,529 3,529 3,529 3,529 T-values in brackets, *, **, *** denotes significance at 10%, 5% and 1%. Blanks indicate that the coefficient of the variable is restricted to zero. It should be noted that the coefficients of the Herfindahl Indices which are not interacted with the dummy variables capture the impact of focus on return when risk is low. These coefficients are in general positive (again the only exception being the equation which includes equity) and highly significant. In the specifications where the Herfindahl Indices are analyzed separately, the coefficients of sectoral and geographical focus are significantly negative when interacted with the dummies. At the 16

18 same time they are slightly decreasing in magnitudes with rising risk (see (4b) and (4c)). This pattern confirms the hypothesis that for low risk banks benefits from focus are larger than for banks with higher levels of risk. Besides, again similar to the parametric analysis above, the overall influence of sectoral and geographical focus on return stays positive for all levels of risk, as the absolute magnitude of the (negative) coefficients of the terms interacted with the risk dummies are smaller than the (positive) baseline coefficient of the respective Herfindahl Index without interaction. On the other hand, for industrial focus the overall impact on return is negative for moderate levels of risk (compare i.e. the coefficients for HI it and D 1 *HI it in (4d)), and we can detect a U-shaped relationship to return as the overall impact of industrial focus increases to slightly positive (tough insignificant) levels for the riskiest banks. Although these patterns are less pronounced for the estimations (4a) and (4d), in all cases the coefficients reveal evidence for a nonlinear relationship between diversification and risk, with a strong positive impact of Herfindahl Indices for low risk banks and a moderate or insignificant impact for higher risk banks. The more sluggish results for sectoral and geographical diversification in specification (4a) as compared to (4b) and (4c) may be attributed to the reduction of degrees of freedom in the estimation. To sum up, the dummy variable approach gives strong evidence that the impact of a bank s portfolio diversification on its return strongly depends on the bank s risk level. Industrial, sectoral and geographical focus yield the highest benefits when risk is low. The benefits from focus decrease and, hence, the benefits from diversification increase with rising risk levels. For industrial focus the impact becomes insignificant for high risk levels. The finding of Tables 1 and 2, that on average industrial focus has a smaller impact on returns than sectoral and geographical focus, can be mostly attributed to banks with moderate risk. However, still it is difficult to test the hypothesis of a U-shaped form, since the classes which define the dummy variables are fixed heuristically and may be too rough to detect the underlying structure of the relationship between diversification, risk and return. In order to gain a more precise picture about the shape of the non-linearities we perform a second non-parametric procedure: We order the dataset according to the risk level. We then estimate (1) with a window of 1,000 observations that shifts from the lowest risk level to the highest risk level. More precisely, we first use a sub-sample of 1,000 observations with the lowest risk level to estimate (1), then shift the sample by one observation and repeat the estimation. The result is a series of roughly 2,500 estimations for α 1, α 2 and α 3 of equation (1) which are ordered according to the risk level. A plot of the series provides information about the impact of risk on the relationship between focus and return. Figure 2, 3 and 4 represent estimations for the specifications (1b), (1c) and (1d). 17

19 Figure 2: Coefficient of HT it for different risk levels (α 1 in equation (1), specification (1b)) 0,02 0,01 0-0,01 α1 α1 +/ 2σ -0,02-0, Number of Estimation Figure 3: Coefficient of HR it for different risk levels (α 2 in equation (1), specification (1c)) 0,05 0,04 0,03 0,02 α2 α2 +/ 2σ 0,01 0-0, Number of Estimation Figure 4: Coefficient of HI it for different risk levels (α 3 in equation (1), specification (1d)) 0,020 0,010 0,000 α3 α3 +/ 2σ -0,010-0, Number of Estimation 18

20 Like expected, all figures reveal that the coefficients for the Herfindahl Indices (α i ) vary with the risk level. Albeit the coefficients of the Herfindahl Indices partly fluctuate considerably, there is some evidence that the relationships are either U-shaped or monotonely decreasing. Besides, overall the depicted influences are comparable to those derived via the parametric and the dummy variables approach. Sectoral focus (HT it ), for example, has a positive coefficient for a low risk level. However, for increasing values of risk α 1 decreases and becomes slightly (and insignificantly) negative. Therefore, as with the former approaches the effect of sectoral focus on return seems to monotonely decrease with risk. On the other hand, the coefficient for regional focus (HR it ) now shows in contrast to former results a U-shape form. It is highly positive for the low risk, decreases for moderate risk levels (though remaining positive) and then rises again for high risk banks. Finally, industrial focus (HI it ) has a positive coefficient for low risk levels only. For moderate risk levels it is slightly but significantly negative, while the coefficient becomes insignificantly negative for highest risk. As such, the rolling window approach gives less distinct evidence for a U-shaped relationship between industrial focus and bank return than the above results. To sum up, in order to judge about the impact of banks portfolio diversification respectively focus on banks return for different risk levels we applied and compared three different approaches. We first introduced non-linear terms in the base specification and then applied two non-parametric tests by interacting the Herfindahl Indices with dummies for different risk levels and using a rolling window approach for each type of diversification. Table 5 tries to summarize the different results. Table 5 clearly demonstrates that the benefits from industrial, sectoral and geographical diversification systematically and strongly vary with the banks risk levels. Therefore, the decision of banks on whether to diversify their loan portfolio or not should be closely linked to their current risk level. Besides, the type of focus plays a crucial role. According to all three approaches sectoral focus, for example, is moderately beneficial for low risk banks, while its influence on return decreases monotonely for higher risk levels. This effect either stays positive for all banks or only becomes (insignificantly) negative for rather high risk levels. Concerning geographical focus, however, all results indicate a positive effect on return for all risk profiles. But while the parametric and the dummy variables approach report a monotone decline of this positive relationship for higher risk banks, the rolling window approach unambiguously depicts a U-shaped form. Also for industrial focus we find evidence for a U-shaped link to return, as the results show a positive influence for low risk, a significantly negative impact for moderate risk and almost no effect for very high risk banks. Hence, our analyses at least partly confirm Winton s theory of diversification benefits being highest for moderate risk levels. 19

21 Table 5: Comparison of the results on the impact of focus on return for different risk levels Risk Percentile Sectoral focus (HT it ) Parametric Approach (see Table 3, 3b) Dummy Var. Approach (see Table 4, 4b) Rolling Window Approach (see Figure 2) Geographical focus (HR it ) Parametric Approach (see Table 3, 3c) Dummy Var. Approach (see Table 4, 4c) Rolling Window Approach (see Figure 3) Industrial focus (HI it ) Parametric Approach (see Table 3, 3d) Dummy Var. Approach (see Table 4, 4d) Rolling Window Approach (see Figure 4) 0-1 th perc. (+)** (+)** (+)*** -10 th perc. -25 th perc. -50 th perc. -75 th perc. (+)** (+)** (+)** (+)** (+)*** (+)*** (+)*** (+)*** (+) # (+) # (-) (+)** (+)** (+)** (+)** (+)*** (+)*** (+)*** (+)*** (c) (+) # (+) (+) (i) (+)*** (+)*** (+)*** (+)*** (+)*** (-)*** (-)*** (-)*** (i) (i) (+) (-) (-) # -90 th perc. -99 th perc. (+)** (+/-)** (+)*** (+)*** (c) (-) (i) (+)** (+)** (+)*** (+)*** (c) (+) # (i) (+)*** (-)*** (d/i) (-) (+) (i) (-) (i) d / i / c indicate a decreasing / increasing / constant level for the respective risk interval. *, **, *** denote significance at 10%, 5% and 1%. # highlights that the interval α +/- 2σ does not intersect the x-axis th perc. (-)** (-)** (+)*** (i) 20