Master Thesis Msc. Finance
Bank risk-taking
and the yield curve slope
Student number: 1883534
Name: Jasper Hinne
Study program: Msc. Finance
University: Rijksuniversiteit Groningen
Faculty: Faculty of Economics and Business
Supervisor: dr. Y.R. Kruse
Field Keywords: Banking & Insurance
2 1. Introduction
The recent crisis put a renewed focus on banking behavior. While it is too short sighted to only blame the behavior of the banks, many agree that the risk-taking behavior of some of these banks played a major role. Banks carry a wide variety of risks, of which the three main financial risks are credit risk, interest rate risk and market risk. And within these risks, two thirds is credit risk and a quarter interest rate risk (Kuritzkes and Schuermann, 2010). So when one talks about banking risk, the main interest is upon the loan portfolio and the maturities of assets and liabilities. This is inherent to banks as the main role of the banking system is to transform the maturities from a lot of small and short maturity deposits to fewer and longer maturity loans. While they take on risks, they expect to make a return by the difference of interest rates between these short-term deposits and long-term loans. Within these long term loans, banks have better information than outsiders with regards to the likelihood that the loan gets paid back. This is an important observation as it gives rise to asymmetric information. Miles and Du (2015) suggest that is one of the main drivers for banks to take on excessive risk and lend more.
Central banks and other policymakers like governments and financial regulators have two main tools at their disposal to influence the financial environment, and so through which they can attempt to limit the risk-taking behavior of these banks. Firstly they can put limits on a banks’ capital structure, as is done through the Basel accords. However the Basel II accord is argued to have caused, or at least worsen the situation. For one it has a procyclical effect, so in good times they need to hold less equity and therefor have less reserves for when bad times come (Gordy and Howell, 2006; Poledna Thumer, Farmer, and Geanakoplos, 2014). Among others, Miles, Yang, and Marcheggiano (2013) also argue that the sheer level of minimal equity was too low in Basel II, as even in Basel III it is at half of the desirable level, taking into account the costs that it entails with such a high level of equity requirements. These observations paved the way for Basel II.5 and currently Basel III being implemented. This is a gradual process so a research into the effectiveness has yet to follow. Banks are reluctant to comply with rising capital requirements, as they generate high rate of returns with high leverage, so when leverage is forced to decrease, so do their rate of returns. Debt is also cheaper, in part because most banks have government guarantees on deposits so they do not require a higher interest rate to compensate for the risk in high leverage. This combination of asymmetric information and limited liability make it so that banks take on more risks and less equity than would be possible for non-bank firms.
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rates and the risk-taking of banks. The link between monetary policy and its effects on interest rates has been extensively studied (see, e.g., Wright 2012; Borio and Zhu, 2012). This effect on the interest rates can in turn have an effect on the risk-taking of banks, as is done by Delis and Kouretas (2011) and Altunbas, Gambacorta, and Marques-Ibanez (2010). They focus mainly on the short-term interest rates and the banking interest rates. There has not been a research trying to link the effect of the entire yield curve to the risk-taking of banks, considering all possible tools. This paper tries to fill this gap by incorporating a model with the yield curve as well as segregating the yield curve in its components. Additionally subsample analyses for periods, size and specialization are performed for robustness. The measuring of risks is mainly done by assessing the credit risk a bank takes, focusing on the composition of the portfolio of loans and the loan loss reserves a banks holds.
The main point of focus with regards to bank risk is on the loan portfolio and solutions are based on capital structure. However banks can game this capital structure with their insider knowledge and redistribute funds to optimally comply with regulations, while not necessarily reducing the risky position it assumes, as seen in the recent crisis by the large off-balance sheet accounts as a way to deal with the higher capital requirements. This paper therefor incorporates an additional measure of risk, also considering the loan loss reserves a bank builds up, to off-set the credit risk. A bank could have a better loan portfolio, including more creditworthy customers, but when it has no reserves to withstand downside credit risk, it might actually assume a more risk-taking position as opposed to a bank that has ample reserves. This might give an indication for the substitution effect that might result from the tightening of regulation.
This paper is structured as follows; section 2 gives a literature overview of the research in this field, as well as giving the hypotheses. Section 3 explains the research method and the variables used. Section 4 presents results and additional robustness tests. Section 5 concludes and gives the practical implications of this research.
2. Literature review
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The economic environment can also play a role with regards to the risk-taking of banks. Interest rates play a large role in this. Delis and Kouretas (2011) and Altunbas, Gambacorta, and Marques-Ibanez (2010) empirically showed in their study that low interest rates substantially increase bank risk-taking. When interest rates drop, insurance companies and hedge funds, who generally have a long-term fixed interest commitment, cannot finance their position anymore with the lower safe interest rates and need to seek out riskier investments in order not to default (Rajan, 2006). Banks that transfer interest rate risk in these insurance companies and hedge funds indirectly also become riskier. Rajan (2006) also mentions the “search for yield” theory, where low interest rates, especially after a period of high interest rates, will induce banks to maintain their previous yield by compensating with riskier loans. Another reason how low interest rates influence bank risk-taking is that a low interest rate overestimates a firm value, because the discount factor is lower than the long-term “real” interest rate (Damodaran, 2008), which can then result in underestimations of asset risk (Borio and Zhu, 2012).
While all the evidence suggest that low interest rates indeed increase bank risk-taking behavior, the difference between short- and long term interest rates is relatively left in the dark. The yield curve slope measures the relative difference between short- and long term interest rates. This yield curve is intuitively important for the profitability of the bank, because a bank transforms short maturity deposits to long maturity loans. This means that a bank borrows for a short term interest rate and loans for a long term interest rate, so differences in the yield curve result in different income patterns, which are usually measured by the net interest margin (NIM). This positive relationship between yield curve slope and bank profitability is backed up by evidence of Alessandri and Nelson (2015). They found that in the long run, both the level and the slope of the yield curve contribute positively to profitability. In the short run however, a rise of the yield curve level reduces the NIM. An overview of all related literature is shown in Appendix A.
But how does this yield curve slope and level relate to the risk-taking of banks? This research tries to answer this question with the following hypothesis:
1. H0: A higher yield curve slope increases bank risk-taking
H1: A higher yield curve slope does not increase bank risk-taking
Monetary policy does have a significant influence on the yield curve level and slope (Bomfin, 2003) and therefor identifying what relationship the slope has to bank risk-taking can help policymakers improve monetary policies and regulations to reduce the unwanted risk taking behavior. To determine the individual factors of short term and long term interest rates, additional hypothesis will be tested:
2. H0: A higher short-term interest rate decreases bank risk-taking
H1: A higher short-term interest rate does not decrease bank risk-taking
3. H0: A higher long-term interest rate increases bank risk-taking
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Furthermore there might also be differences between periods, as the crisis instigated many changes in the area of bank risk-taking and regulations. These unique financial conditions brought about many changes in the banking regulations and policies. As a result banks are likely to react differently to changes in the yield curve slope. For one, during the crisis a high yield curve slope means large differences between short-term and long-term yields. As a result firms are facing relatively high costs of loaning and default more often during an economic downturn. A higher slope therefor would increase the non-performing loans (NPL’s) within a bank. Conversely after the crisis the yield curve slope rose again, so the differences between both the periods can be readily observed, however the direction after the crisis is ambiguous. Some research suggests that the search for yield will still encourage banks for an increase in risk-taking (Rajan, 2006), however this was tested when high yields became low yields, while after the crisis low yields are rising again. Therefor these fourth and fifth hypotheses will be tested:
4. H0: During the crisis a higher yield curve slope increases bank risk-taking
H1: During the crisis a higher yield curve slope does not increase bank risk-taking
5. H0: After the crisis a higher yield curve slope increases bank risk-taking
H1: After the crisis a higher yield curve slope does not increase bank risk-taking
In the now famous concept of too-big-to-fail as described by Boyd, Jagannathan, and Kwak (2009) there are also likely to be differences between large and small banks. The moral hazard problem of size suggests that larger banks are more risk-taking. The effect the yield curve slope has on the differences between large and small banks is not yet researched, but the effect is likely to be larger for large banks, since they show the overall tendency to be more risk-taking. This leads to the following hypothesis:
6. H0: A higher yield curve slope makes large banks to take more risk than small banks
H1: A higher yield curve slope does not make large banks to take more risk than small banks
Lastly Fiordelisis and Mare (2013) and Groeneveld and de Vries (2009) among others suggest that there are significant differences between the risk profiles of commercial, savings, and cooperative banks. The role they play within the financial system and mainly the portfolio characteristics suggest that commercial banks have larger and more long-term oriented loans. This would lead to a higher persistence of their risk profiles. Additionally the higher level of surveyability of the savings and cooperative banks might result in a better screening of creditworthiness and therefor increments in the yield curve slope are paired with a better response in the risk portfolio, not increasing the risk-taking as much as commercial banks. This results in the following hypothesis:
7. H0: A higher yield curve slope makes commercial banks to take more risk than savings and cooperative
banks
H1: A higher yield curve slope does not make commercial banks to take more risk than savings and
6 3. Research method
To perform a successful analysis between the relationship of the slope of the yield curve and the bank risk-taking, both the variables need to be further examined. After the variables have proper measurements, some additional explanatory variables pass the review. A summary of the descriptive statistics of the variables are presented in Appendix B. Then the boundaries for the dataset are demarcated and finally the model is laid out along with several robustness checks.
3.1 Yield curve slope
Literature is fairly consistent in the way the slope is measured. Altunbas, Gambacorta, and Marques-Ibanez (2010) for instance use the slope in their research as a robustness check and calculate it by taking the slope of the ten year yield and an unspecified short term interest rate. Alessandri and Nelson (2015) in their research to relate the yield curve with profitability use the three month yield and the ten year yield. Estrella and Hardouvelis (1991) were one of the first to empirically establish a yield curve inversion as a sign for a recession, for which they also used the three month and ten year interest rates as short and long term interest rates respectively. This research will therefor follow common practice and use the three month and ten year yields to calculate the yield curve slope.
3.2 Bank risk-taking
Literature is less consistent with regards to the measure of bank risk-taking. Delis and Kouretas (2011) for instance use the ratio of risky assets as part of total assets, and for robustness also use non-performing loans as part of the total amount of loans. This approach is very focused on the assets of the bank and the amount of actual risk taken can vary between banks. This would mean that bank risk-taking comes from accepting below standard assets, which might be a result of information asymmetry reduction between banks (Dell’ariccia and Marquez, 2003).
A more market oriented approach for bank-risk taking comes from Altunbas, Gambacorta, and Marques-Ibanez (2010), who use the expected default frequency (EDF), which measures the probability of default of a company within a year, measured by Moody’s KMV. This measure is directly tested by Munves, Hamilton, and Gokbayrak (2009) and performed quite well as an indicator. It is a more forward looking measure, as it assesses future default probabilities, but default might not be directly linked to risk-taking, which is why they also tried to decompose individual bank risk from systematic risk. The capital asset pricing model (CAPM) is used to calculate beta coefficients per bank to extract the idiosyncratic risk. This is also a forward looking measure, as it calculates how the market perceives the bank-risk taking but is more a measure of market risk. For this reason the main focus is on using non-performing loans as a ratio of gross loans as the measure of risk taking.
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3.3 Explanatory control variables 3.3.1 Size
Boyd, Jagannathan, and Kwak (2009) developed the now well-known concept of too-big-to-fail and hypothesized that large banks had limited liability and therefor were incentivized to take larger risky positions than they would without any insurance, because when a bank would otherwise fail, the large banks expected the government to bail them out. Therefor failing was much less of a risk and riskier positions yielded higher returns. Bhagat, Bolton, and Lu (2015) find the same effect for the pre-crisis period and during the crisis, however this effect seems to be lost in the post-crisis period (after 2010). This size effect into risk will be controlled for by taking the natural logarithm of the total assets of the bank. A positive effect is to be expected before and during the crisis according to well-developed theory, with no significant effect after the crisis.
3.3.2 Profitability
Size is not the only factor that influences the risk taking behavior of banks. Profitability also has an influence on the risk profile of banks. The direction however is under scrutiny. Traditional theory suggests that profitable banks should have a lower risk profile, because in downside risk they have far more shareholder value to lose (Keeley, 1990). However in the light of the recent crisis it became apparent that very profitable banks exposed themselves to risky investments and were at least as risk-taking as less profitable banks. Martynova, Ratnovski, and Vlahu (2015) in an attempt to explain this paradox suggest that banks that are more profitable diversify away from their core business and use the excess returns to fund riskier side activities. They can do this on a larger scale than less profitable banks, so while their incentives to take on more risk might be lower, this can be trumped by the scale of the riskier investments. Following this line of theory, a positive relationship between profitability and the risk profile is to be expected, as measured by both return on average assets (RoAA) and return on average equity (RoAE). Both measures are experimented with, but RoAE proves to be not significant. This might be a result of banks increasing their leverage to compensate a drop in RoAA, so RoAE would remain unaffected (Alessandri and Nelson, 2015).
3.3.3 Liquidity
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3.3.4 Net interest margin
The concept of the net interest margin is an important one in banking. One of the main traditional roles of banking is maturity transformation in which they borrow short and lend long. The difference between the short- and long interest rates is how they finance their operations and cover the interest and credit risks among other risks the bank takes. In an attempt to hedge against changes in the yield curve, banks hedge and become less reliant on the difference between short and long term interest rates, however Alessandri and Nelson (2015) find that there is still a systematic effect between market interest rates and the profitability of banks. While a decrease in the net interest margin depresses the RoA, they found the RoE to be unaffected. Banks increase the leverage to compensate, which might leave them more open to market and credit risks. Additionally with the introduction of Basel III the question remains whether they are able to continue to increase leverage as a response to declining margins. A negative effect is to be expected, with a flattening of the curve increasing risk due to additional leverage and a “search-for-yield” as described by Rajan (2006).
3.3.5 Capitalization
As described above, the leverage effect might have an influence on the risk profile. Bhagat, Bolton, and Lu (2015) discuss the link between capitalization as equity over total assets and the risk-taking of financial institutions and find that they use leverage as a tool in taking, in which an increase in leverage is parallel to more risk-taking. This is an endogenous relationship and should be treated as such. In an extension to this relationship Blum (1999) researched the capital adequacy requirements with respect to the banking risk. He found that for that period a tightening in capital restrictions goes combined with an increase in bank riskiness, because equity tomorrow is more costly and is therefore compensated by increasing risk-taking today. In light of the implementation of Basel II between 2004 and 2008, Basel II.5 afterwards and currently the gradual implementation of Basel III the capitalization of banks with regard to the risk they take is of great importance, while the effectiveness of Basel II for instance is under scrutiny (see, e.g., Hakenes and Schnabel 2011; Poledna, Thumer, Farmer, and Geanakoplos, 2012).
3.3.6 GDP growth
There are also macroeconomic factors that influence the risk profile of banks in different countries. These factors are incorporated by country dummies to assess their validity. The GDP growth is one of those factors. It is well developed that during economic growth the lending standards are loosened (see, e.g., Dell’Ariccia and Marquez, 2003; Männasoo and Mayes, 2009) and as a result the bank is more risk-taking. They take GDP growth and other macroeconomic factors as a given and set their individual strategies accordingly, so macroeconomic factors are assumed to be exogenous.
3.3.7 Banking importance
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Larrain (2006) showed that in countries with higher banking credit, the volatility of industrial output is lower, which means that banks conversely would seek more risky assets to compensate for the more inelastic demand for credit. Maddaloni and Peydró (2011) additionally find some evidence to the difference between the banking importance as size of the total economy and the risk they take, with risk being disproportionally high for the size of their assets.
3.3.8 Bank Concentration
The concentration of banking is used as a measure of competition in banking, measured by the ratio of the total assets of the five biggest banks to the total assets of all banks in the country. The traditional theory states that a lower banking concentration, which means more competition, goes paired with more risk-taking because banks have to compete more with each other with the deposit rates and therefor have a lower NIM which they in turn have to compensate with more risk to remain profitable (Rajan, 2006). Boyd and Nicolo (2005) however found that the risk on this deposit only partly explains the effect of competition and find that a higher concentration also gives fundamental incentives to take more risk. These mixed results are backed up by Jimenez, Lopez, and Saurina (2013) who find a non-linear relationship between banking concentration and the risk-taking of banks.
3.4 Data
To examine the relationship between the yield curve slope and bank risk-taking, an unbalanced panel data set is created. The banks under consideration are retrieved from BankScope and consider developed economies in the Euro-area and the US. This results in 14,450 banks within 16 countries (Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxemburg, Portugal, Spain, Sweden, The Netherlands, UK, and USA). However, there is some double counting with holding companies; additionally we only want commercial, savings or cooperative banks, for they are the only banks that take deposits, which is needed in the measurement for risk-taking. This leaves out other specialization banks, like investment banks, real estate banks, central banks, and holding companies, which reduces the list to 10,399 banks. This includes a plethora of banks with minimal amount of assets. Therefor the list is reduced to only consider banks with total assets of over one billion dollar. This substantially reduces the data set to 2,280 banks. We consider the period 2005-2015 to optimally investigate the crisis and post-crisis situation. This also coincides with data availability being largest within this period. Descriptive statistics of the countries and size of banks is found in Appendix C.
Since the panel data is from two different regions, two yield curve slopes need to be constructed, for both the Euro region as well as the US. The EU yield curve is constructed from the European Central Bank (ECB) database, which have readily available daily yields from September 6, 2004 up until current yields. The US treasury yield data goes back as far as 1990 for all maturities, and is retrieved from the U.S. department of treasury site. Since the model requires earlier rates as instrumental variables, monthly averages of 3-month Euribor from the global-rates site are used to estimate the true 3-month Euribor for the period 2002 up until 2004.
10 4. Results
4.1 OLS estimation
A first glance at the relationship between the yield curve slope and bank risk-taking is taken by means of a simple OLS-regression without any control variables as follows:
(1)
(2)
Where NPLi,t is the non-performing loans, the measure of risk-taking of bank i, at time in years t. The NPL is measured in terms of impaired loans as proportion of total gross loans. RMi,t is the reserve ratio, measured as the loan
loss reserves over the impaired loan for bank i at time in years t. Sloc,t is the slope per continent at time t and ui,t is
the error term for bank i at time t. The results are presented in table 1. The NPL shows a positive relationship, while the reserve ratio shows a negative relationship. This gives the first indication that a higher yield curve slope indeed increases the risk-taking of banks.
Table 1. Simple OLS regression
Non-performing loans Reserve ratio
α 3.097*** (33.924) 165.402*** (65.215) Slope 0.396*** (8.477) -27.282*** (-21.278) Observations 13688 12883 Adjusted R2 0.005 0.034 DW-statistic 0.227 0.550
The table reports the coefficients of the explanatory variable and the constant. The number in parentheses are the t-statistics of the coefficients. α is the constant, Slope is the slope of the yield curve which is relevant for each individual bank, adjusted R2 measures the goodness of fit and the DW-statistic is the Durbin-Watson statistic as a measure of
autocorrelation.
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4.2 GMM estimation
This model is not complete, since a lot more variables influence the risk-taking behavior of banks. The low R2 indicates a bad goodness of fit. The low DW-statistic indicates there is autocorrelation present between the regressor and the error-term. An extension to this model including all control variables is estimated by the following equations:
( )
(3)
( )
(4)
Where NPLi,t is the non-performing loans, the measure of risk-taking of bank i, at time in years t.. RMi,t is the reserve
r for bank i at time in years t. On the right hand side lagged NPL and RM terms are included to measure the persistence of risky assets, where δ=0 means there is no persistence and last years’ results have no influence on the next. δ=1 means there is no change in the risk-taking, while a value between 0 and 1 means the previous years are gradually less important. Sloc,t measures the yield curve slope, where c is a continent dummy that is either 0 or 1
whether the bank is in US or in Europe to match it with the correct yield curve slope. NIM, RoA, Liq, Size and Cap are the banks individual characteristics for net interest margin, return on average assets, liquidity, the natural logarithm of size and the capitalization for bank i at time t. To measure macroeconomic variables GDP, Imp and Con are used for GDP growth, bank importance and concentration for country k at time t. αi,t describes the individual
intercept for each entity i at time t, which indicates fixed effects for both entity and time, to take into account that both every entity as well as time period might have their own means. ui,t is the error term for bank i at time t. The
reason to include a lagged dependent variable is that the risky assets in the bank portfolio are not completely liquid and therefor persist through time to some degree, even when explanatory variables changes are taken into account by the bank. Furthermore as described in the discussion about the control variables, the model is flooded by endogeneity. This endogeneity means that the control variables are correlated with the error estimate ui,t. The two most common reasons for endogeneity are omitted variables and a causality loop in which the dependent variable and explanatory variables influence each other. This causality issue is likely to be the main reason for endogeneity, since banks are able to adjust both the risk-taking and other individual characteristics to find a balance. In particular, the capitalization, liquidity, profitability and yield slopes are used as instruments.
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means there is no exact solution, and the model is said to be over-identified. GMM then minimizes the cross-products in order to find the true parameter vectors. In order to find whether this minimizing process results in a model where these moment conditions are satisfied, a Sargan “J-test” is performed. It measures the distance of the sample from meeting the over-identifying conditions, so whether they are close enough to zero (Hansen, 1982). This results in the hypotheses;
H0 = The GMM model is correctly specified, so the over-identifying conditions are close to zero
H1 = The GMM model is misspecified or some conditions are invalid
The empirical results are reported in table 2. The coefficients for the yield curve slopes remains statistically significant and positive for both compared to the initial OLS with the non-performing loans and negative under the reserve ratio for both continents under both measures of profitability. This indicates that a larger yield curve slope would give rise to an increased risk-taking appetite of banks. The RoAE measure seems to be performing worse, both in significance of the factor itself as well as the model as a whole. There seems to be ground for the theory of Alesandri and Nelson (2015) who state that the RoAE is held constant by means of leverage to compensate for a loss in RoAA. The Durbin-Watson statistic for correlation gives values close enough to two to rule out auto-correlation between the explanatory variables and the error-term as is researched by Bhargave, Franzini, and Narendranathan (1982) for panel data. This indicates that implementing further lags is not required and the lagged variables are valid instruments. To test whether the model is over-identified, the Sargan test is performed. With no p-values within any reasonable confidence level α of 1-,5-, or 10%, the model is correctly specified and the orthogonality conditions are satisfied. The coefficients for δ are highly significant in all models, which means that risk is indeed persistent. However implementing further lags does not give significant results, so it also returns back to the equilibrium, as is indicated by the δ<1 (of about 0.5 and 0.4 for NPL and the reserve ratio respectively).
There are also differences in size between the Europe and US slopes. In the US banks seem to respond more heavily to changes in the yield curve slope indicated by the higher coefficients, which is also present in all further analyses. This is likely a result of the large differences in capital market structures between the Euro-area and the United States and their lending standards (Maddaloni and Peydró, 2011). This is also the main motivation to keep both of the yield curve slopes separate.
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takes the hit as opposed to the reserves. This substitution effect is very relevant with regards to the current implementation of Basel III. While the requirements for capitalization might be tightened, banks can substitute these by holding less of the liquid loan loss reserves.
14 Table 2. Yield curve slope and bank risk-taking GMM model
NPL & RoAA NPL & RoAE Reserves & RoAA Reserves & RoAE
Lagged NPL 0.500***
(3.338)
0.434*** (2.639)
Lagged reserve ratio 0.388***
(4.314) 0.372*** (3.770) Slope EU 1.487* (1.691) 3.050** (2.143) -0.446*** (-2.697) -0.367 (-1.526) Slope US 6.272** (2.133) 11.321** (2.358) -1.385*** (-3.193) -1.332** (-2.181) Size 1.787 (0.942) 1.640 (0.646) -1.624** (-2.203) 0.534 (0.228) Profitability -1.037*** (-3.297) -0.060 (-0.886) -0.054 (-0.617) 0.0177 (1.035) Liquidity 0.007 (0.323) 0.009 (0.349) -0.002 (-0.846) 0.000 (0.097) Capitalization -.0156 (-0.143) -0.127 (-0.807) -0.066** (-2.063) 0.024 (0.265) GDP growth -0.663*** (-3.106) -1.029*** (-3.338) 0.123*** (3.350) 0.106** (2.420) Bank importance 0.025* (1.943) 0.045** (2.287) -0.007*** (-3.184) -0.005 (-1.563) Concentration 0.374 (1.387) 0.863 (1.544) -0.078** (-2.515) -0.159** (-2.351) Observations 8185 8182 7254 7251 Adjusted R2 0.777 0.548 0.396 0.259 DW-statistic 2.036 2.121 1.777 2.069 Sargan J-statistic 1.493 1.085 2.480 1.174 p-value 0.474 0.581 0.289 0.556
The table reports the coefficients of the explanatory variables and their significance. The numbers in parentheses are the t-statistics of the coefficients. Lagged NPL is impaired loans over gross loans at time t-1, lagged reserve ratio is the loan loss reserves over impaired loans at time t-1, Slope EU/US is the yield curve slope of Europe and United States respectively, size is the natural logarithm of total assets, profitability is the return on average assets or return on average equity as denoted in the top row, liquidity is the liquid assets over short term borrowing and funding, capitalization is the percentage of equity over total assets, GDP growth is annual percentage growth of GDP at market prices based on constant local currency, bank importance is the domestic credit provided by banks over GDP, concentration is the assets of the five largest banks over assets of all banks. Adjusted R2 denotes the goodness of fit, the DW-statistic is the Durbin-Watson statistic, which measures the autocorrelation and the Sargan statistic and p-value measures over-identifying restrictions.
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4.2 Segregating the yield curve
In order to segregate the yield curve, the individual short- and long-term yields are first separately assessed and then jointly estimated. This will likely bring more clarification as to how the yield curve influences the risk assets. Most research is done with regards to the short-term interest, since this is most relevant for monetary policy. Wright (2012) researched the long-term interest rate with regards to a short-term interest rate at the zero lower bound and found that for instance the asset repurchasing that the Federal Fund and the European Central Bank are doing at the moment reduces the long-term interest rate. Empirical results are found in table 3. From the results it can be identified that models without both measures of interest rates do not seem to add much value to the understanding of the relationship between non-performing loans and yield rates, since there is no significant relationship identified. With the yield curve divided into short- and long-term yield but aggregated in a single model, significant results are found. The direction of the relationship remains significant where increases in short-term yield and decreases in long-term yield (so a diminishing of the slope) results in less risk-taking. Additionally the short-term yield seems to be leading, with a higher significance. The country specific variables for competition and bank importance, as well as profitability are similar to the original model, however the GDP growth relationship seems to be reversed, where a higher GDP growth results in more risk-taking as is predicted by Dell’Ariccia and Marquez (2003). The results for the reserves also seem to be robust with the original model, meaning that higher short-term interest rates indeed could reduce the risk-taking of banks.
4.3 Period and first differences model
The main model is estimated for the entire time period between 2005 and 2015, but this period includes both the crisis and the after crisis period. It is also interesting to separate these into two separate groups. A simple equality test of the risk variables between periods indicates that at least the medians per period are statistically significant different (see Appendix E). To also test the influence on a per year basis, a first difference model as proposed by Arellano and Bond (1991) is used to estimate the model between the crisis period 2006 up until 2010 and the aftermath of the crisis in 2011 to 2015 and the model as a whole is re-estimated for the entire period to get an indication of the differences between both periods. Since there is no readily available data of the EU regions on interest rates before 2006 on daily basis, the average of monthly data is used instead to calculate the average interest rates for both the short and long term rates in the Europe region to incorporate lags of the yield curves as instrumental variables. Additionally the long term interest rates are on a per country basis. Taking the first differences of equation (3) and equation (4) yields
( )
(5)
( )
16
where the individual fixed effect term αi,t is no longer in the equation, however the error term Δui,t is correlated with Δδ(NPLi,t-1) by construction, because δ(NPLi,t-1) is a function of ui,t which are also in the first differenced terms. The
empirical results can be found in table 4. There are some interesting differences to be found with the original model. First and foremost the post crisis US yield curve slope sign has reversed. While during the crisis an increase of the yield curve resulted in more risk-taking, after the crisis this was the other way around. This is also shown by the per year effects being generally positive in the crisis period and negative afterwards for NPL’s (and vice versa for reserves). Possible explanations are found in the measurement of risk. Non-performing loans were likely more abundant during the crisis, because an increase of the yield curve slope meant loans are having to pay more interest and default more quickly. This relationship is not present in the reserves, where almost no significant effect is found. Only in the full differenced model the negative sign is found in the US yield curve, indicating that a higher curve results in less loan loss reserves for impaired loans. Additionally, the size variable was expected to be positive in the crisis period and no effect in the post-crisis period following Bhagat, Bolton, and Lu (2015). However no effect was found during the crisis and a negative effect in the post-crisis period, though the shift to less risk-taking of big firms after the crisis is present. Another telling effect is found for the liquidity. Firms with more abundance of liquid assets indeed take more risk, both during and after the crisis in terms of non-performing loans. The capital structure is only significant in the crisis period, so during the crisis less capitalized firms are also more risky. This effect is not found in the post-crisis period. A possible explanation for this is that in a response to the crisis the banks were regulated more strictly and higher capitalization is required when having a riskier loan portfolio.
4.4 Small and large banks
Another interesting distinction to make is that of size. There is an extensive amount of research into size effects with regards to the risk taking, mainly pointing out differences between small and large banks. The Dodd-Frank Wall Street Reform and Consumer Protection Act of 2010 deems banks with $50 billion in assets as systemically important. This boundary is also used in Beltratti and Stulz (2012) and Laeven, Ratnovski, and Tong (2015) who did research on the difference in performance and systemic risk respectively between small and large banks. For this dataset there are 148 banks with $50 billion or more in the last reported total assets and 2132 banks with less than $50 billion in last reported total assets. The tests for equality of medians for the non-performing loans are statistically significant, meaning that there are differences between the risk profiles of small and large banks. Only 2 out of 3 tests of equality are significant at the 5% level for the reserves, so further investigation is required (see Appendix F).
17
banks take more risk, as is apparent by the test of equality. Within the reserves there seems to be no significant relationship in relation to the yield curve. So while large banks have more loan impairments, they do not hold more loan loss reserves to back these risks up. The reserves are also not affected for the small and large banks by the yield curve when they are split up, while they are significant when combined with the large banks in a single model.
4.5 Bank specialization
Within the banking system there might be fundamental differences between the bank specialization as well. This research already focuses on a limited amount of banking specializations, excluding banks that do not both take deposits and provide corporate loans. This leaves commercial, savings and cooperative banks. Fiordelisi and Mare (2013) for instance found that cooperative banks default more often than commercial banks in financially stable periods. This is in contrast with the theory that these banks are more stable, because they have more soft information on the creditworthiness of these clients than commercial banks as is found by Groeneveld and de Vries (2009). This would indicate cooperative banks being less risk-taking than commercial banks. Savings banks provide loans to individuals or small and medium sized enterprises as opposed to the medium to large sized enterprises a commercial bank provides loans to. These portfolios are usually riskier as is also backed up by Jeon and Lim (2013). Appendix G shows that equality of medians tests are not significant for reserves and only one out of the two tests is significant for the NPL’s. This contradicts the evidence that there are significant differences in risk-taking, so additional research is warranted. This subsample analysis tests how the risk profiles of these different specializations are affected by the yield curve slope.
18 Table 3. Segregated yield curve GMM estimation
Short NPL Long NPL Mix NPL Short reserve Long reserve Mix reserve
Lagged NPL 0.482* (1.707) 0.768*** (4.209) 0.553*** (6.194) Lagged reserve ratio 0.355*** (4.277) 0.670*** (4.647) 0.689*** (4.039) Short yield EU -14.548 (-0.620) -1.037** (-2.396) 2.636*** (3.045) 2.821** (2.066) Short yield US -39.781 (-0.621) -2.161*** (-4.891) 7.297*** (3.072) 6.502** (2.111) Long yield EU 1.069 (0.380) -0.301 (-1.310) -0.417 (-1.625) -1.215* (-1.799) Long yield US 4.337 (0.821) 2.500*** (3.780) -0.957** (-2.342) 0.390 (1.605) Size -1.294 (0.460) -0.059 (-0.027) 1.034 (0.598) -0.575 (-1.122) 0.861* (1.787) 2.028* (1.891) Profitability -1.451* (-1.988) -0.691 (-0.917) -1.132*** (-3.242) 0.078 (0.889) -0.186* (-1.682) -0.163 (-1.322) Liquidity -0.042 (-0.592) -0.014 (-0.484) 0.005 (0.215) 0.002 (0.414) -0.007 (-1.258) -0.009 (-1.261) Capitalization -23.911 (-0.891) -3.254 (-0.253) -7.231 (-0.724) -1.261 (-0.582) 0.562 (0.277) 3.607 (1.123) GDP growth 1.691 (0.586) 0.369 (0.638) 0.282** (2.380) -0.254** (-2.353) 0.017 (0.498) -0.150 (-1.422) Bank importance -0.018 (-0.465) 0.001 (0.277) 0.007*** (2.986) 0.002 (1.408) -0.001 (-1.452) -0.002** (-2.156) Concentration -0.098 (-0.469) -0.483 (-0.715) 0.142* (1.653) -0.001 (-0.074) 0.109** (2.391) 0.248** (2.134) Observations 8185 8185 8185 7254 7254 7254 Adjusted R2 0.613 0.767 0.811 0.448 0.438 0.100 DW-statistic 2.205 2.193 2.082 2.121 2.081 1.899 Sargan J-statistic 0.650 3.165 12.008 0.250 0.485 1.989 p-value 0.722 0.205 0.217 0.883 0.785 0.575
The table reports the coefficients of the explanatory variables and their significance. The numbers in parentheses are the t-statistics of the coefficients. Lagged NPL is impaired loans over gross loans at time t-1, lagged reserve ratio is the loan loss reserves over impaired loans at time t-1, Short yield EU/US is the 3-month yield of Europe and United States respectively, Long yield EU/US is the 10-year yield of Europe and United States respectively, size is the natural logarithm of total assets, profitability is the return on average assets or return on average equity as denoted in the top row, liquidity is the liquid assets over short term borrowing and funding, capitalization is equity over total assets, GDP growth is annual percentage growth of GDP at market prices based on constant local currency, bank importance is the domestic credit provided by banks over GDP, concentration is the assets of the five largest banks over assets of all banks. Adjusted R2
denotes the goodness of fit, the DW-statistic is the Durbin-Watson statistic, which measures the autocorrelation and the Sargan statistic and p-value measures over-identifying restrictions.
Table 4. Crisis and post crisis first differences GMM estimation Crisis NPL 2006-2010 Post crisis NPL 2011-2015 Total NPL 2006-2015 Crisis reserve 2006-2010 Post crisis reserve 2011-2015 Total reserve 2006-2015 Lagged NPL 0.410*** (3.885) 0.912*** (6.315) 1.093*** (9.457) Lagged reserve ratio 0.237** (2.412) -0.239 (-1.006) -0.272** (-2.097) EU slope 0.991** (2.179) 0.375 (0.944) 1.324*** (2.804) -0.363 (-0.837) 0.028 (0.427) 0.158 (1.291) US Slope 1.907*** (3.174) -2.063*** (-2.934) 0.972*** (2.654) -0.910 (-1.283) 0.325 (1.593) -0.449** (-2.424) Size -0.532 (-0.225) -3.687*** (-3.104) -9.140** (-2.474) -1.001 (-0.830) 0.693 (0.865) 1.620** (2.472) Profitability -0.061 (-2.48) -0.257 (-1.076) -1.415*** (-2.806) 0.050 (0.471) 0.000 (0.011) 0.057 (0.987) Liquidity 0.027*** (4.612) 0.059** (2.524) 0.035** (2.517) -0.006 (-1.277) 0.001 (0.170) -0.000 (-0.042) Capitalization -0.425*** (-3.715) -0.092 (-0.609) -0.435* (-1.798) 0.051 (0.835) 0.016 (0.377) 0.047 (1.031) Net Interest Margin 0.219 (0.820) -0.230 (-0.635) -1.217** (-2.187) 0.029 (0.175) 0.310 (0.809) -0.016 (-0.122) GDP growth 0.537 (1.376) 0.142 (1.517) -0.655*** (-3.415) -0.266 (-1.036) 0.055* (1.831) 0.034 (1.063) Bank importance -0.033 (-1.099) 0.282*** (4.585) 0.131** (2.315) 0.042* (1.700) 0.010 (0.878) -0.001 (-0.168) Concentration 0.032 (0.724) 0.256*** (3.611) -0.001 (-0.009) -0.182 (-3.426) 0.073 (0.170) -0.055** (-2.144) 2006 2.436*** (3.110) 1.791*** (3.051) -1.006 (-1.172) -0.498* (-1.869) 2007 2.927*** (3.446) 2.034*** (3.930) -1.294 (-1.273) -0.869*** (-3.168) 2008 0.279 (0.987) -0.261 (-0.453) -0.026 (-0.185) -0.400*** (-3.675) 2009 1.282*** (3.158) -1.468 (-1.264) 0.330** (2.530) -0.359** (-2.061) 2010 3.241* (1.760) -6.163*** (-2.718) -1.406 (-1.056) -0.167 (-0.829) 2011 -1.075* (-1.945) -1.441 (-1.547) -0.332 (-1.546) -0.423** (-2.359) 2012 -1.624** (-2.192) -0.513 (-0.875) -0.023 (-0.132) -0.553*** (-4.311) 2013 -0.071 (-0.182) -0.138 (-0.301) 0.103 (0.879) -0.288** (-2.528) 2014 1.087*** (3.052) 0.876** (2.116) 0.243** (1.991) 0.056 (0.526) 2015 0.997** (2.391) 2.282*** (3.133) 0.453** (2.201) -0.052 (-0.332) Observations 3947 5113 9072 1511 4111 5644 Sargan J-statistic 10.170 12.016 9.402 5.479 3.287 1.055 p-value 0.118 0.100 0.152 0.140 0.349 0.788
The table reports the coefficients of the explanatory variables and their significance. The number in parentheses are the t-statistics of the coefficients. For a further description of the variables see table 3. The years depict the yearly fixed effect modifiers on the dependent variable.
Table 5. Small and large banks GMM subsample analysis
Small bank NPL Large bank NPL Small bank reserve Large bank reserve
Lagged NPL 0.366***
(3.755)
0.516*** (6.118)
Lagged reserve ratio 0.336***
(4.626) 0.132 (1.281) EU slope -0.572** (-2.143) 0.892*** (3.345) 0.084 (1.462) 0.016 (0.512) US Slope 0.251 (0.642) 4.648*** (4.853) 0.028 (0.315) -0.124 (-1.262) Size -0.655*** (-3.364) 0.016 (0.053) 0.049 (0.449) -0.159 (-0.949) Profitability -1.220*** (-4.057) -1.097*** (-3.491) 0.058 (1.054) -0.023 (-0.416) Liquidity 0.004 (0.192) -0.004 (-0.178) 0.009 (0.934) 0.001 (0.271) Capitalization -0.019 (-0.461) -0.099 (-1.267) 0.045 (1.296) 0.064* (1.714)
Net Interest Margin 0.291
(1.348) -0.162 (-0.637) -0.652* (-1.746) 0.214** (2.428) GDP growth -2.644*** (-5.160) -0.527*** (-4.892) -0.004 (-0.127) -0.043 (-1.130) Bank importance 0.034 (1.003) 0.017*** (4.389) 0.028** (2.177) 0.000 (0.032) Concentration 0.043 (0.425) 0.271*** (3.078) 0.095*** (2.570) -0.051** (-2.391) Observations 9412 994 5989 895 Adjusted R2 0.758 0.810 0.454 0.694 DW-statistic 1.825 2.064 1.784 1.194 Sargan J-statistic 5.236 4.642 11.700 4.773 p-value 0.155 0.461 0.165 0.311
The table reports the coefficients of the explanatory variables and their significance. The number in parentheses are the t-statistics of the coefficients. For a further description of the variables see table 3.
21 Table 6. Specialization GMM subsample analysis
Commercial NPL Savings NPL Cooperative NPL Commercial reserve Savings reserve Cooperative reserve Lagged NPL 0.645*** (3.845) 0.508*** (3.227) 0.345*** (2.681) Lagged reserve ratio 0.365** (2.498) 0.354** (2.037) 0.237* (1.827) EU slope 0.900** (2.178) 1.273* (1.947) 1.137** (2.522) -0.367** (-2.101) -0.128 (-1.041) 0.031 (0.356) US slope 4.889*** (3.291) 6.192** (2.464) 5.661*** (2.931) -1.309*** (-2.678) -0.900** (-2.515) -0.026 (-0.083) Size 4.275 (1.247) -0.819 (-0.365) -1.813 (-0.438) -2.026** (-2.135) -0.228 (-0.345) 1.061** (2.490) Profitability -0.991 (-1.317) -0.145 (-0.160) -0.955** (-2.461) 0.066 (0.667) -0.361 (-1.103) 0.047 (0.412) Liquidity 0.025 (0.559) -0.001 (-0.020) 0.034 (0.567) -0.006 (-0.785) 0.002 (0.687) -0.010 (-0.676) Capitalization 0.271 (1.345) -0.448 (-0.867) -0.193 (-1.292) -0.107** (-2.048) 0.001 (0.019) 0.024 (1.262) Net interest margin -2.699 (-0.861) -0.646 (-0.421) 0.435 (0.227) 0.181 (1.367) 0.276* (1.869) -0.210 (-0.833) GDP growth -0.534** (-2.189) -0.549** (-2.298) -0.471 (-1.436) 0.096** (2.123) 0.111 (1.425) 0.051 (0.867) Bank importance 0.020*** (3.347) 0.019** (2.305) 0.019** (2.513) -0.006*** (-2.682) -0.003** (-2.188) 0.000 (0.302) Concentration 0.257* (1.760) 0.394* (1.824) 0.277 (1.502) -0.082** (-2.469) -0.047 (-1.538) 0.007 (0.260) Observations 4320 1933 1930 3882 1714 1655 Adjusted R2 0.744 0.797 0.785 0.294 0.455 0.629 DW-statistic 1.956 1.969 1.969 1.743 1.776 1.389 Sargan J-statistic 4.177 0.653 5.353 6.959 4.432 6.459 p-value 0.243 0.884 0.148 0.138 0.351 0.167
The table reports the coefficients of the explanatory variables and their significance. The number in parentheses are the t-statistics of the coefficients. For a further description of the variables see table 3.
22
5. Conclusion and practical implications
In the current low short-term interest rate economy, the banking industry is especially of great importance. While most research is conducted with regards to the short term interest rate, there is not a lot of movement to be expected with the current near minimum short term interest rate. The slope of the yield curve however can still be influenced, which is the main focus of this research. An increase of the yield curve slope has, contrary to popular believes, an increase in the risk-taking of banks as a result. This has important implications when trying to reduce the risk taking of banks. While current monetary policy is focused on trying to stimulate the economy by keeping the short-term interest rate at its minimum in both the US and in Europe, this might be a stimulant for banks to increase their risky assets or reduce loan loss reserves. This is especially the case when this is not compensated by a lower long-term yield. A possible reason for this is that while banks do profit from higher net interest margins, the higher long-term yield means that loans default more often, because the firms they loan to have to pay a higher interest rate, which is especially difficult in financial downturns. Results of this research are robust under different measures of risk-taking, when considering non-performing loans and also when compensating for the loan loss reserves over impaired loans.
A side-note must be made to the overall result. While the positive relationship between risk and the yield curve slope is robust when segregating the yield curve in short- and long-term yields, a period analysis reveals that the leading determinant of the relationship was during the crisis, while after the crisis an increase in the yield curve slope might even reduce the NPL’s. It is very common to measure the risk-taking of banks by means of non-performing loans, and the analysis of specializations of banks show that banks can indeed adjust their NPL’s with the amount of information on clients, the relationship between actual risk-taking and the NPL might still not be accurate enough. The relationship between the yield curve slope and the NPL is shown to be reliant on the period. Possible future studies could look for common patterns between yield curve slopes and multiple pre- during- and post-crisis periods. This research tries to answer this ambiguity with an additional risk measure which should be less affected by defaults of firms as a result of economic downturns.
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Appendix
Appendix A. Literature overview
Name Period Region Subject Relationship
Acharya & Naqvi (2012)
Theoretical model Liquidity and Risk + Albertazzi &
Gambacorta (2006)
1981-2003 EU, UK, US Profitability and business cycle
+ Alessandri & Nelson
(2015)
1992-2002 UK Yield curve and profitability
Short term: - Long term: + Altunbas, Gambacorta,
Marquez-Ibanez (2010)
1998-2008 EU, UK, US Short-term interest rate and bank risk
- Bhagat, Bolton, Lu
(2015)
2002-2012 US Size and bank risk Leverage and bank risk
Size: + Leverage: + Bomfim (2003) 1989-2001 US Monetary policy and
yield curve
+ Borio & Zhu (2012) Literature review Monetary policy and
risk taking channel
Varying Boyd, de Nicolo, Jalal
(2005) 2003 1993-2004 US Non-developed countries Banking concentration and probability of failure US: + Non-developed: + Boyd, Jagannathan, Kwak (2009)
1986-2008 US Size (Toobigtofail) and moral hazard
Implied + Brissimis & Delis
(2009)
1994-2007 US, EU Monetary policy and bank profitability
Heterogeneous (+/-) Dell’ariccia, Laeven,
Marquez (2014)
1997-2009 US Interest rate - bank risk Interest rate - leverage Leverage - bank risk
- - + Estrella & Hardouvelis
(1991)
1955-1988 US Yield curve and economic activity
+ Gordy & Howells
(2006)
Theoretical model and simulation Procyclicality of Basel II
+ Hakenes & Schnabel
(2011)
Theoretical model Bank size and risk Basel and risk taking
- (due to model choice) +
Jiménez, Lopez, Saurina (2013)
1988-2003 Spain Competition and bank risk
U-shape Larrain (2006) 1963-1999 59 countries Credit availability and
volatility
- Martynova, Ratnovski,
Vlahu (2015)
Theoretical model Profitability and bank risk taking
+ Miles and Du (2015) Theoretical model Capital structure limit
and risk
Interest rate and risk - - Poledna, Thurner,
Farmer, Geanakoplos
Theoretical model Regulation and bank risk
High leverage: + Low leverage: - Rajan (2006) 1970-2003 US, EU Financial development
and bank risk
+ Wright (2011) 2008-2010 US Monetary policy (asset
buyback) and long-term interest rate
Appendix B. Descriptive statistics variables
Europe US
Mean Median Standard deviation Min Max Mean Median Standard deviation Min Max
Slope 1.219 1.274 0.959 -1.314 3.072 1.905 2.100 1.117 -0.640 3.830
Short-term interest rate
1.689 1.082 1.600 -0.133 5.393 1.338 0.140 1.848 0 5.190
Long-term interest rate 2.908 3.315 1.170 0.134 4.776 3.248 3.220 1.035 1.430 5.260
Non-performing loans (NPL) 3.766 4.105 5.402 0 100 2.220 1.176 3.958 0 100 Reserves 2.292 1.514 3.277 0 100 1.657 1.314 3.003 0 100 Reserve ratio 1.183 0.532 1.433 0 9.910 1.596 0.945 1.727 0 9.910 Size 10.402 7.951 12.279 -2.137 15.124 9.602 7.392 11.532 2.279 14.545 Profitability 0.602 0.276 2.248 -29.860 185.572 0.935 0.905 2.339 -16.910 79.374 Liquidity 19.295 15.670 34.034 0 984.905 9.845 5.373 25.156 0.002 910.393
Net interest margin 2.848 2.231 1.765 -32.748 39.214 3.899 3.698 2.043 -32.750 35.294
Capitalization 0.094 0.070 0.067 -0.458 1.000 0.115 0.101 0.075 -0.374 0.994
GDP growth 1.328 1.179 2.306 -9.133 8.396 1.779 2.321 1.752 -2.776 3.786
Bank importance 170.165 140.560 55.223 0 253.502 207.484 227.134 66.486 0 253.502
Concentration 55.804 66.021 15.674 32.300 100.00 44.678 45.622 3.540 37.026 48.708
27 Appendix C. Descriptive statistics countries
Country Observations Banks Average Assets (mln USD) Median Assets (mln USD) Minimum (mln USD) Maximum (mln USD)
Austria 781 71 11,576 2744 1012 210,820 Belgium 319 29 40,270 5547 1185 297,967 Denmark 286 26 37,994 2789 1001 482,120 Finland 143 13 53,445 7853 1032 328,351 France 1881 171 86,773 11,529 151 2,171,141 Germany 7084 644 19,440 2238 1001 272,0312 Greece 88 8 48,252 39,910 2038 121,102 Ireland 143 13 33,879 15,156 2134 142,580 Italy 2156 196 19,667 2863 985 936,781 Luxembourg 561 51 12,219 5587 459 87,124 Portugal 187 17 40,681 9812 1233 229,589 Spain 825 75 66,404 5880 864 1,459,183 Sweden 286 26 36,589 2183 1009 301,965 The Netherlands 308 28 99,891 10,684 1356 912,932 UK 902 82 109,987 6620 1002 1,660,828 USA 9130 830 18,361 2306 1003 1,914,658 Total 25,080 2280 30,707 2754 151 2,720,312
All asset statistics are based upon the latest observed asset statistic to remove double-counting. The statistics show that there are not too significant differences in size per country, but there
Appendix D. Correlation matrix NPL Lagged NPL Reserve Lagged Reserve EU slope US slope EU short-term US short-term EU long-term US
long-term RoAA RoAE
Liquidit y Capitali zation Net interest margin Size Importa nce GDP growth Concent ration NPL 1 Lagged NPL 0.897 1 Reserve -0.220 -0.203 1 Lagged Reserve -0.208 -0.235 0.690 1 EU slope 0.474 0.402 -0.175 -0.186 1 US slope -0.242 -0.234 0.086 0.074 -0.556 1 EU short-term 0.055 0.044 -0.089 -0.063 0.120 -0.449 1 US short-term -0.211 -0.227 0.344 0.406 -0.241 -0.151 -0.195 1 EU long-term 0.398 0.336 -0.184 -0.179 0.842 -0.676 0.637 -0.293 1 US long-term -0.348 -0.354 0.331 0.370 -0.611 0.648 -0.494 0.655 -0.743 1 RoAA -0.300 -0.203 0.171 0.150 -0.276 0.138 -0.060 0.154 -0.247 0.224 1 RoAE -0.230 -0.159 0.111 0.095 -0.194 0.066 -0.007 0.100 -0.154 0.127 0.656 1 Liquidity 0.096 0.112 -0.087 -0.090 0.174 -0.297 0.284 -0.150 0.289 -0.343 -0.079 -0.027 1 Capitalization -0.034 0.004 0.055 0.049 -0.182 0.221 -0.179 0.069 -0.238 0.223 0.318 0.087 -0.109 1 NIM -0.129 -0.111 0.158 0.164 -0.342 0.409 -0.246 0.190 -0.399 0.459 0.422 0.185 -0.300 0.390 1 Size 0.071 0.067 -0.089 -0.102 0.239 -0.296 0.252 -0.158 0.323 -0.349 -0.110 -0.071 0.344 -0.262 -0.339 1 Importance 0.337 0.327 -0.270 -0.296 0.640 -0.657 0.343 -0.447 0.683 -0.847 -0.252 -0.167 0.347 -0.228 -0.454 0.380 1 GDP growth -0.340 -0.269 0.232 0.207 -0.482 0.069 0.075 0.349 -0.334 0.321 0.239 0.150 -0.068 0.098 0.163 -0.054 -0.356 1 Concentration 0.114 0.128 -0.195 -0.197 0.317 -0.336 0.163 -0.286 0.334 -0.478 -0.166 -0.125 0.136 -0.127 -0.235 0.286 0.644 -0.153 1
29 Appendix E. Test for equality of medians for crisis and post-crisis
Impaired Reserves
p-value Statistic p-value Statistic
Wilcoxon/Mann-Whitney 0.000 20.082 0.000 13.174 Median Chi-square 0.000 184.429 0.000 152.081 Kruskal Wallis 0.000 403.294 0.000 173.561 Crisis Post crisis Crisis Post crisis Median 1.781 2.659 0.703 0.595 Observations 5697 7102 5231 6936
Appendix F. Test for equality of medians for small and large banks
Impaired Reserves
p-value Statistic p-value Statistic
Wilcoxon/Mann-Whitney 0.000 12.305 0.031 2.163
Median Chi-square 0.000 116.476 0.131 2.279
Kruskal Wallis 0.000 151.414 0.031 4.678
Small Large Small Large
Median 1.559 2.645 0.682 0.670
Observations 14596 1415 12207 1371
Appendix G. Test for equality of medians for commercial, savings, and cooperative banks
Impaired Reserves
p-value Statistic p-value Statistic
Median Chi-square 0.109 4.438 0.476 1.484
Kruskal Wallis 0.016 8.305 0.529 1.275
Commercial Savings Cooperative Commercial Savings Cooperative
Median 1.687 1.586 1.637 0.676 0.677 0.689
