Does the Term Structure Affect Bank Risk-Taking?
Evidence from the Eurozone
Master’s thesis, MSc Finance
University of Groningen, Faculty of Economics and Business June 2015
Enzio de Geus Student number 1760297 e-mail: enzio.degeus@gmail.com
First supervisor Dr. Jochen Mierau Second supervisor
Abstract
Banks borrow short and lend long, leading to increased profitability if the term spread grows. This, in turn, may cause banks to take on more risk. This study examines the proposition empirically using a sample of euro area banks and finds some evidence that supports this proposition. Though risk assets unexpectedly decrease as the term spread grows, non-performing loans and insolvency probabilities generally increase.
Additionally, the distributional effects of the term spread on bank risk due to bank- level characteristics suggest that the impact of the term spread is amplified for lowly capitalized banks. Banks with high total assets are less prone to be affected by the adverse effects of the term spread. The results are not uniform for the entire euro area, as German banks are largely unaffected while for example Italian banks are very affected.
1. Introduction
The amount of risk banks take on can have severe welfare implications for our society. When too much risk materializes, it can cripple the financial system and thereby affect the real economy. Policymakers and regulators must therefore have insight in the factors that drive bank risk-taking. Interest rates are such a factor, and recent lines of research have studied its effects on bank risk. Up to now, however, no research has focused on the term spread, the difference between long-term and short- term rates. In this paper, I analyze the relationship between the term spread and bank risk. Banks borrow short and lend long, leading to increased profitability if the term spread grows. This, in turn, may cause banks to take on more risk. The empirical results use a data set of euro area banks and give a first indication that bank risk indeed increases with the term spread.
Again, policy considerations motivate this research. The recent financial crisis has given ample motivation to search for factors that impact risk in the banking industry. For instance, Delis and Kouretas (2011) and Jiménez, Ongena, Peydró, and Saurina (2014) are among the researchers who study the effects of low interest rates on bank risk-taking. This study operates in the same spirit, but instead focuses on the effects that the difference between long-term and short-term rates (the term spread) has on bank risk.
I use three different variables to measure bank risk. The amount of risky assets and the amount of non-performing loans proxy risk-taking behavior by banks. I also proxy the insolvency probability of banks. The theory is that all these risk indicators increase with the term spread. However, in contradiction to the theoretical considerations, the results suggest that risk assets are negatively related to the term spread. The following mechanism could explain this unexpected finding. The premise is that banks aim to satisfy a target return on equity. When the term spread grows larger, banks can achieve the target with relatively low risk assets. That would explain why we observe a negative relationship between the term spread and risk assets.
On the other hand, the term spread has a positive influence on both non- performing loans and the insolvency probability. These results do not hold for the entire euro area: e.g. Germany is relatively unaffected. However, Italy is heavily affected. Finally, this study gives insight in bank-level distributional effects of the relationship between the term spread and bank risk. Lowly capitalized banks see an on average amplified relationship between the term spread and bank risk.
The rest of the paper is organized as follows. Section 2 presents a literature review of closely related studies, goes on to explain the theory that motivates this particular research, and explicitly states the hypotheses I will test. Section 3 describes the data set. Section 4 explains the main methodology I will employ. Section 5 shows the results and my interpretation of those results. Furthermore, it provides some robustness checks. Finally, section 6 gives some policy considerations and concludes the study.
2. Literature review and theory 2.1. Literature review
To my knowledge, no empirical research has ever been published on the relationship between the slope of the term structure and bank risk-taking. Closely related, however, is empirical research that investigates the relationship between interest rates and bank risk-taking. As a consequence of the low-interest rate environment since the beginning of the new millennium, recent years have generated much research on the subject. I will mention three of these studies that are particularly salient: research by Delis and Kouretas (2011), Jiménez et al. (2014), and Maddaloni and Peydró (2011).
So do banks in low interest rate environments take on more risk in a search for yield?
The literature seems to agree that this is indeed the case.
Delis and Kouretas (2011) research the relationship between interest rates and bank risk-taking in the Eurozone over the period 2001-2008. They find strong empirical evidence that low-interest rate environments indeed increase bank risk- taking. More specifically, banks increase risk assets as a portion of total assets, and have more non-performing loans as a portion of gross loans. These results are robust over a number of different interest rate specifications. Furthermore, Delis and Kouretas (2011) find distributional effects of interest rates on bank risk-taking due to individual bank characteristics: the impact of interest rates on risk assets is diminished for banks with higher equity capital and is amplified for banks with higher off-balance sheet items.
Jiménez et al. (2014) find similar results using both a different approach and a different data set. Their focus is on the effects of expansionary monetary policy and thus the ‘risk-taking channel of monetary policy’, a term introduced by Borio and Zhu (2012). The strength of this study lies in its unique data set. Spain’s national bank, Banco de España, granted access to monthly, exhaustive bank loan data on virtually all individual loans given in the Spanish banking system over the period 2002-2009.
Jiménez et al. (2014) find evidence that a lower overnight rate induces lowly capitalized banks to grant more loan applications to ex-ante risky firms (at least more so than highly capitalized banks), where firm risk is measured with the presence of a bad credit history with non-performing loans. Moreover, when granting applications to these firms (when overnight rates are lower), lowly capitalized banks further commit more credit and require less collateral, and their granted loan applications overall face a higher future likelihood of default. A striking similarity between Jiménez et al.’s (2014) and Delis and Kouretas’ (2011) findings is the following: not only do lower interest rates increase risk-taking, but the effect is also amplified for banks with low equity capital.
Maddaloni and Peydró (2011) analyze the effects of low short-term (monetary policy) interest rates and low long-term interest rates on both euro area and U.S.
lending standards. They find a statistically and economically significant effect for the former, but not for the latter. Furthermore, they observe that high securitization activity, weak supervision for bank capital, and too low for too long monetary policy
rates amplify the softening effect of low short-term interest rates on lending standards.
This effect was most pronounced for mortgages.
All in all, the literature seems to agree that low (short-term) interest rates indeed have a positive effect on bank risk-taking. However, the literature is silent on the related but separate matter of the relation between the slope of the term structure and risk-taking, both on a theoretical and an empirical level. The next section will address the theoretical issues.
2.2. Theory
One of the core tasks of banks is to transform short-term deposits into long-term loans. Naturally, this also entails a risk because when depositors come to claim their money, it may not actually be there. If so, it will probably only be there after quite a while. The profitability of this strategy increases as the difference between the short- term interest rate and the long-term interest rate increases (i.e., the term spread).
Then, if there is enough demand, banks can now take on borrowers whose creditworthiness is inferior to that of the borrowers they could taken on before the increase of the term spread, because the increased profitability of each loan makes borrower projects more likely to still warrant expected profits. Hence, the objective of this project is to study whether bank risk taking increases as the term spread increases.
Hypothesis 1: An increase in the term spread increases bank risk.
There are a number of ways to assess increased risk empirically. This study uses the amount of risky assets, the amount of non-performing loans, and a proxy of bank insolvency probability. The first two measures review bank risk-taking more purely, as these measures proxy bank behavior. However, the insolvency probability is of interest as well, since increased insolvency probability due to a factor common to all banks gives insight in systemic risk.
The analyses suggested above become more insightful if we could establish that some bank-level characteristics moderate the relationship between the term spread and bank risk. For instance, Jiménez et al. (2014) note that risk-taking is more likely to be excessive for banks with relatively little equity capital, since they do not internalize as much of the losses when compared to highly capitalized banks. Such a
moral hazard leads these banks to grant loan applications to ex-ante risky firms. That is why I also research the following hypothesis:
Hypothesis 1a: The positive effect of the term spread on bank risk is amplified for lowly capitalized banks.
Another bank-level balance sheet characteristic is the size of its total assets.
Laeven, Ratnovski, and Tong (2014) report that large banks tend to have lower capital, less-stable funding, more market-based activities, and be more organizationally complex than small banks. They suggest that large banks may therefore have a distinct, more fragile business model. Large banks, in other words, are riskier. This leads to another hypothesis:
Hypothesis 1b: The positive effect of the term spread on bank risk is amplified for large banks.
A further bank-level characteristic that could have an influence on the relationship between the term spread and bank risk is technical efficiency. Delis and Kouretas (2011) note that technically efficient banks may be more capable in managing risks. This leads to an additional hypothesis:
Hypothesis 1c: The positive effect of the term spread on bank risk is diminished for highly efficient banks.
3. Data
The main data set is a large unbalanced panel used to examine the relationship between the term structure and bank risk-taking. This sample consists of yearly observations for the period 2001-2013. I obtain the annual bank-level data from the Bankscope database. These data only include commercial banks, savings banks, and cooperative banks from 16 different euro area countries. Other types of banks do not borrow short and therefore fall outside the scope of the theoretical considerations. It could be argued, however, that investment banks should be included on the basis of these considerations, since some in fact do fund themselves with short maturity
liabilities. After analysis of a sample of euro area investment banks, I conclude that some indeed borrow short and lend long, but others do not. The latter category is more concerned with fee generating activities, like equity issues or mergers and acquisitions. Thus, the category of investment banks does not purely conform to the theoretical considerations. That is why I omit them from the sample.
Table 1. Descriptive statistics.
(1) (2) (3) (4) (5)
Variable N Mean Standard deviation Min Max
Term structure 35,028 1.425 1.177 -0.650 21.93
Risk assets 21,888 0.933 0.0812 0.0336 1
Non-performing loans 6,928 0.0676 0.0570 0 0.928
Z-score 27,105 3.849 1.096 -2.889 9.234
Capitalization 27,245 0.0867 0.0860 -0.458 1
Efficiency 27,043 0.694 0.248 0 9.500
Size 27,264 13.13 1.449 5.775 21.67
The table reports summary statistics for the variables used in the empirical analysis. The variables are as follows:
term structure is the difference between 10-year government bonds rates and 3-month Euribor rates, risk assets is the ratio of risk assets to total assets, non-performing loans is the ratio of non-performing loans to total loan to gross loans, z-score is the natural logarithm of the return on average assets plus the capital assets ratio divided by the standard deviation of the return on average assets (ln[(ROAA+CAR)/σ(ROAA)]), capitalization is the ratio of capital assets to total assets, efficiency is the ratio of total revenue to total expenses, and size is the natural logarithm of total assets.
I use unconsolidated accounts, so that country-specific effects of the yield curve are isolated and not contaminated by revenues of foreign subsidiaries. I only use consolidated accounts if no unconsolidated accounts are available, thereby avoiding double counting.1 Concerning the euro area countries, Latvia, Lithuania, and Estonia are excluded. Latvia and Lithuania only entered the euro zone after the sample period, while Estonia did not have the required term structure data available.
These term structure data are country-specific and obtained from Eurostat.
Data are available for 2,695 banks, and given the sample period of 2001-2013, there is a maximum of 35,035 bank-year observations. However, due to the data availability of the different dependent variables, the analyses either use 27,105 observations, 21,888 observations or 6,928 observations. Especially this last total of
1 More specifically, I use Bankscope consolidation codes U1, U2, C1, and A1. This approach is consistent with Duprey and Lé (2015).
bank-year observations may give rise to concern, but this issue is given due attention in the robustness checks.
Since the main data set only incorporates currently active banks, the so-called survivorship bias could be an issue that taints the results of this study. Indeed, some banks are not included in the sample because of mergers, acquisitions, or failures. To ascertain if the omission of these banks influence the results, I create and analyze a separate data set that adds inactive banks to the active bank sample. The results of these analyses are described in the section for robustness checks.
Table 1 provides the descriptive statistics for the main data set. It contains all the variables that are in this study, along with some explanatory notes. For instance,
3.1. The term spread
This study is empirically investigates a possible relationship between the term spread and bank risk. Theoretically speaking, the term spread may have a different value for each point in time. It is therefore necessary to approximate the slope of the term structure using a relevant single slope measure.
Banks borrow short and lend long: debt obligations are often deposits that are instantly claimable, while most loan assets have a maturity of many years. That is why this study uses the difference between 10-year government bonds yield and 3- month Euribor rates to construct a relevant yield curve measure. The data I use are obtainable from Eurostat and concern annual averages. Since these rates concern different markets (government bonds market and money market), some may consider it unorthodox to plot them in a single term structure. However, given the fact that these rates to a large extent determine interest income and interest costs for a bank, these rates are nevertheless the relevant rates for the banking industry; the Euribor is highly correlated with deposit rates, while the 10-year government bond rates heavily influence lending rates.
Notice also that the approach only provides a country-specific term structure.
However, this result is appropriate because banks are mostly subject to the conditions in their country of residence. In this regard, bank-specific term structures are virtually impossible to obtain.
As can be seen in Table 1, the mean term spread is about 1.43%. There are even some instances of a negative term spread. The reported maximum value for the
term spread - 21,93% - seems almost impossibly high, but can readily be explained:
this spread concerns Greek banks during 2012. During that year, the fiscal problems of the Greek government led to particularly high bond rates. The highest average term spread was in 2009, when it reached 2.36%. In 2008, the average term spread was negative (-0.43%). See Figure A.1 in the appendix for a graph that plots mean term spreads against each year in the sample.
3.2. Bank risk
This study employs three different proxies for the bank risk: risk assets, non- performing loans, and the z-score. All of the necessary data for these measures is obtained from the Bankscope database. The first measure, denoted as risk assets, is the ratio of risk assets to total assets. Bank risk assets is defined as total assets minus cash and cash equivalents, balances due from other banks, and government securities.
Conversely, risk assets could be defined as all those assets that are subject to change in value as a consequence of deteriorated credit quality. The assumption that government securities and balances due from other banks are risk-free should in practice be unproblematic. Higher values of risk assets are of course associated with riskier bank portfolios.
The mean value of risk assets in the sample is 0.933, while its highest reported value is 1 and its lowest reported value is as small as 0.0336. Investigating the mean of each year in the sample period shows that 2004 has the highest mean value for risk assets (0.955) and 2013 the lowest (0.907). This 5% difference shows that risk assets varies significantly over the years. Moreover, since 2010 the risk assets ratio dropped by 3%. These findings can be associated with the flight to quality idea.
The second measure, non-performing loans, is actually the ratio of non- performing loans to gross loans. This measure shows to what extent the existing loan portfolio is subject to repayment issues, with higher values leading to more adverse implications for both earnings and loan asset market values. As such, it is a good proxy for credit risk.
Compared to all the other variables, non-performing assets has by far the least amount of observations (6,928 while all other variables have over 20,000 observations). This lesser amount of observations has research implications, since the missing observations may have a systematic cause and could therefore influence
0.2.4.6.81Risk assets / Total assets
0.00 5.00 10.00 15.00 20.00
Term spread
0.2.4.6.81Non-performing loans ratio
0.00 5.00 10.00 15.00 20.00
Term spread
-50510Z-score
0.00 5.00 10.00 15.00 20.00
Term spread
Fig. 1. The term spread and risk variables. The figures each show a scatterplot together with a regression line between the term spread and all three risk variables employed in this study. Risk assets show an unexpected negative relationship with the term spread. Non-performing loans show the expected positive relationship with the term spread. Finally, the z- score exhibits the expected negative relationship with the term spread.
research findings. Due attention will be given to this fact during robustness checks.
An interesting fact to note here, however, is that though the year 2002 has the highest non-performing loan ratio (0.081), the total amount of observations for that year is only 18 out of the possible 2,695. Closer inspection reveals that only from the year 2006 and onwards the amount of non-performing loans observations is satisfactory, with the amount of observations per year climbing from 450 to more than 1600. From these years, 2010 gives the highest average ratio (0.077). Interestingly enough, 2007 provides the lowest mean (0.059).
The third measure for bank risk-taking is the z-score. As opposed to the other measures, the z-score measures insolvency risk (Roy, 1952), where insolvency is a state in which losses are greater than equity. The z-score is defined as the return on average assets (ROAA) plus the capital assets ratio (CAR), divided by the standard deviation of asset returns. It thus measures the inverse of the probability of insolvency. To see why, note that the probability of insolvency can be expressed as Prob(-ROAA<CAR). Then, if profits are normally distributed, the inverse of the probability of insolvency is equal to (ROAA+CAR)/σ(ROAA), where σ(ROAA) is the standard deviation of return on average assets. Since the z-score measures the inverse of the insolvency probability, naturally higher z-scores imply less insolvency risk.
Laeven and Levine (2009) note that the z-score is highly skewed. Following these authors, I use the natural logarithm of z-score, which is approximately normally distributed. In the remainder of this paper, the term ‘z-score’ will refer to the natural logarithm of the z-score.
With 27,105 observations, the z-score is widely available. Its mean value, 3.849, provides the natural logarithm of the inverse probability of insolvency, which entails an insolvency probability of roughly 2.13%. The means of each year are remarkably close together: the z-score varies from 3.760 (2008) to 4.028 (2013). The associated insolvency probabilities are 2,33% and 1.78%, respectively.
Fig. 1 shows three simple scatterplots together with a with a fitted regression line on the relationship between the term spread and the three risk variables. Risk assets show an unexpected, negative relationship with the term spread. The other variables, non-performing loans and the z-score, exhibit the expected relationships.
Though these correlation results only show a very rough sketch of the true relationships, they constitute interesting first results. Moreover, to test whether the
term spread outliers (term spread > 10%) do not affect these results, I checked whether these graphs would look significantly different without the outliers. They do not.
3.3. Distributional effects of the term structure due to bank characteristics
To assess whether there are some distributional effects to be found in the relationship between the term structure and certain bank balance sheet characteristics, this study uses a three additional variables: capitalization, bank size, and efficiency.
Capitalization is the ratio of equity capital to total assets. Bank size is the natural logarithm of total assets. Efficiency is the ratio of total revenue to total expenses. I use these variables solely to create interaction terms. Thus, each variable only enters a regression to check for a possible distributional effect of that variable. All these variables are available through Bankscope.
4. Methodology
The general empirical model that will be estimated has the following form:
BRit =αi + γt + β1Sct + uit, (1)
where BR is bank risk for bank i at time t and S is the term spread for country c at time t. The parameter αi represents bank specific fixed effects. This parameter controls for factors that vary across banks but are time invariant within banks. The parameter γt represents time fixed effects that are common for each bank (and each country) but vary over time. The general empirical model of this study thus uses a two way fixed effects model.
In addition, for some specifications I expand the model in Eq. (1) by adding the term δct:
BRit =αi +γt +δct + β1Sct + uit, (2)
This model further controls for unobserved factors that are time varying within countries through country-specific linear time trends. If this were the case, neglecting
these factors would lead to biased estimates of parameters of Eq. (1) and therefore misleading conclusions. This is not the standard approach in the literature. Studies that research the relationship between some variable and bank risk-taking, for example Laeven and Levine (2009) or Delis and Kouretas (2011), generally use a set of regulatory, macroeconomic, and structural variables to control for potential omitted variable bias. There are, however, a number of downsides associated with such an approach. First, the inclusion of this set of variables can add as much as five or six variables to a regression. Adding this much variables to a model sharply increases the probability that a variable in that model is significant by chance alone. Second, the set of control variables may suffer from the bad control problem (Angrist and Pischke, 2008). For these reasons, I opt for the more parsimonious country-specific time trends.
5. Results
Table 2 reports the main results. These results consist of empirical estimations of Eq.
(1) and Eq. (2) for the data set of euro area banks, the two way fixed effects model and the two way fixed effects model with the addition of country-specific linear time trends, respectively. I include year fixed effects because for all specifications an F-test provides evidence that such terms are very significantly different from zero. Since a modified Wald test points to groupwise heteroskedasticity for the idiosyncratic error terms, all models employ heteroskedasticity-robust standard errors. Furthermore, a Hausman test establishes that a random effects model would not be suitable for the data.
The results cannot be interpreted straightforwardly. For instance, though risk assets shows highly significant parameter values in both models, the relationship with the term spread goes in the opposite direction: I have theoretical reasons for a positive relationship, but the empirical outcome shows a negative relation. Apparently, for a given bank, as the term spread varies across time by one unit, risk assets decreases somewhat. The economic mechanism behind this unexpected finding could be as follows. When profit maximization in an uncertain world is an unattainable ideal, banks instead strive for a target return on equity (or a comparable return measure).
When the term spread grows larger, banks can achieve the target with relatively low
risk assets. That would explain why we observe a negative relationship between the term spread and risk assets.
Non-performing loans, on the other hand, do follow the hypothesized direction, showing a positive relationship with the term spread. However, its economic effects are relatively small: for a given bank, as the term spread increases by 1%, the ratio of non-performing loans to total loans increase by 0.6% or less.
Moreover, the result of the model that includes country-specific linear time trends is marginally statistically significant.
5.1. Two way fixed effects regressions
Table 2. The term spread and bank risk-taking: two way fixed effects regressions.
(1) (2) (3) (4) (5) (6)
Variable RA NPL Z RA NPL Z
Term spread -0.017***
(0.002)
0.006***
(0.002)
-0.104***
(0.009)
-0.005***
(0.001)
0.002*
(0.002)
-0.037***
(0.012) Constant 0.938*** 0.0236 3.737*** 0.941*** 0.0867*** 3.728***
(0.002) (0.019) (0.010) (0.002) (0.023) (0.009)
Observations 21,886 6,926 27,103 21,886 6,926 27,103
R-squared 0.114 0.277 0.194 0.139 0.360 0.239
Number of banks 2,381 1,889 2,644 2,381 1,889 2,644
Bank FE YES YES YES YES YES YES
Year FE YES YES YES YES YES YES
Country-specific time trend
YES YES YES
The table reports coefficients, significance levels, and robust standard errors (in parentheses) of the term spread.
Risk variables are as follows: RA is the ratio of risk assets to total assets, NPL is the ratio of non-performing loans to total loans, and Z stands for the z-score, which is the natural logarithm of the return on average assets plus the capital assets ratio divided by the standard deviation of the return on average assets (ln[(ROAA+CAR)/σ(ROAA)]).
Models (1)-(3) are two way fixed effects models, using both bank and year fixed effects. Models (4)-(6) add country-specific linear time trends to the equation.
*** Statistical significance at the 1% level.
** Statistical significance at the 5% level.
* Statistical significance at the 10% level.
The z-score does exhibit the expected relationship. In both models, the terms are negative and statistically significant. Thus, there is empirical evidence that an increase in the term spread increases, on average, the insolvency probability of a given bank. The economic significance of these results differs slightly with respect to the model. Recall that the average bank in the sample has an insolvency probability of 2.13%. Model (3), the one without the country-specific linear time trend, tells us that the insolvency probability of the average bank increases to 2.36% if the term spread increases by one unit. Model (6), on the other hand, implies that the new insolvency
probability for the average bank is 2.21% if the term spread increases by 1%. Though these differences are small, they are not negligible.
5.3. Distributional effects
This study also sets out to research distributional effects. Therefore, I examine whether the term spread has a differential effect on bank risk owing to certain characteristics of bank balance sheets. To carry out this exercise, the following equation will be estimated:
Rit = αi + γt + δct + β1Sct + β2Bit + β3(Sct*Bit) + uit, (3)
where Bit is a bank-level control variable for bank i at time t and (Sct*Bit) is the interaction term of the term spread and the bank-level control variable.
Table 5 presents the correlation matrix of the term spread, the bank-level controls, and their interaction terms. Especially the term spread and the term spread- size interaction term have a high correlation (0.986). Some researchers take the multicollinearity of an interaction term with one of its constituents to be a serious problem. In an attempt to deal with such a problem, they ‘mean center’ constitutive terms (transforming terms to deviations from their means) and then generate the interaction terms using these newly transformed variables. This procedure then drastically reduces the correlation between interaction terms and their constituents.
Brambor, Clark, and Golder (2006), however, argue that mean centering is not a good approach. Mean centering simply does not mitigate multicollinearity. To see why, note that the procedure is simply an algebraic transformation. Hence, no new information is generated. If there are multicollinearity issues, this reflects the fact that there is not enough information in the data. The resulting standard errors may then be relatively large, but that only reflects the low amount of information. At any rate, multicollinearity between interaction terms and its constituents is not a problem.
Table 6 presents the estimation results of the distributional effects estimations.
For all these estimations, I use a regression model with two way fixed effects and country-specific time trends. I interpret the distributional effects results for each interaction term.
Table 5. Correlations between distributional characteristics, the term spread, and their products
Ts Cap Size Eff Ts * Cap Ts * Size Ts * Eff
Term spread (ts) 1.000
Capitalization (cap) 0.103 1.000
Size 0.004 -0.292 1.000
Efficiency (eff) -0.017 0.068 -0.158 1.000
Term spread * Cap 0.632 0.626 -0.163 0.037 1.000
Term spread * Size 0.986 0.060 0.132 -0.042 0.581 1.000
Term spread * Eff 0.817 0.115 -0.067 0.413 0.544 0.787 1.000
The table reports correlation coefficients for the term spread, bank-level control variables and their interaction terms. The term spread is the difference between 10-year government bonds rates and 3-month Euribor rates, capitalization is the ratio of capital assets to total assets, efficiency is the ratio of total revenue to total expenses, and size is the natural logarithm of total assets.
The findings suggest that high capitalization decreases the effect the term spread has on risk assets. As we have seen before, an increase in the term spread reduces risk assets. The evidence shows that relatively high levels of equity capital weaken this effect. Perhaps highly capitalized banks see less reason to unwind their more risky positions when the term spread increases, because their high amount of capital can absorb a loss while they retain a portfolio with potentially high earnings.
The model that uses non-performing loans as the dependent variable (model 4) corroborates the hypothesis that the positive effect of the term spread on bank risk is amplified for lowly capitalized banks. Though the sign of the capitalization interaction term is negative in this case, recall that the term spread instead has a positive effect on non-performing loans. Therefore, in the non-performing loans case, the presence of high equity capital diminishes the positive effect of the term spread on bank risk. The insolvency probability, however, has no significant interaction term.
Contrary to the hypothesis, large banks in terms of total assets do not amplify risk as the term spread increases. The ratio of risk assets to total assets is diminished for large banks if the term spread grows. The same occurs for non-performing loans and insolvency probabilities.
Efficient banks, in terms of a revenue cost ratio, have mixed results. Risk assets decrease less for highly efficient banks, while non-performing loans increase less for highly efficient banks. However, the insolvency probability in terms of the z- score is amplified for efficient banks.
Table 6. The term spread and bank risk-taking: distributional effects.
(1) (2) (3)
Dependent: Risk assets Term spread * Cap Term spread * Size Term spread * Eff
Term spread -0.009*** 0.006 -0.014***
(0.002) (0.005) (0.003)
Capitalization -0.118
(0.087)
Term spread * Cap 0.033**
(0.015)
Size 0.005
(0.006)
Term spread * Size -0.001**
(0.000)
Efficiency -0.023
(0.016)
Term spread * Eff 0.013***
(0.004)
Observations 21,886 21,886 21,856
R-squared 0.143 0.141 0.148
Number of ID 2,381 2,381 2,378
Bank FE YES YES YES
Year FE YES YES YES
Country-specific time trend YES YES YES
(4) (5) (6)
Dependent: Non-performing loans Term spread * Cap Term spread * Size Term spread * Eff
Term spread 0.007*** -0.025*** 0.005**
(0.002) (0.005) (0.002)
Capitalization 0.062
(0.076)
Term spread * Cap -0.033***
(0.013)
Size -0.017***
(0.006)
Term spread * Size 0.002***
(0.000)
Efficiency 0.018***
(0.005)
Term spread * Eff -0.004**
(0.002)
Observations 6,926 6,926 6,909
R-squared 0.367 0.376 0.365
Number of ID 1,889 1,889 1,887
Bank FE YES YES YES
Year FE YES YES YES
Country-specific time trend YES YES YES
(7) (8) (9) Dependent: Z-score Term spread * Cap Term spread * Size Term spread * Eff
Term spread -0.031*** -0.089*** -0.011
(0.007) (0.022) (0.015)
Capitalization 3.953***
(0.158)
Term spread * Cap 0.010
(0.036)
Size -0.455***
(0.030)
Term spread * Size 0.004***
(0.001)
Efficiency 0.027
(0.066)
Term spread * Eff -0.036**
(0.018)
Observations 27,103 27,103 26,952
R-squared 0.618 0.414 0.261
Number of ID 2,644 2,644 2,637
Bank FE YES YES YES
Year FE YES YES YES
Country-specific time trend YES YES YES
The table reports coefficients, significance levels, and robust standard errors (in parentheses) of the term spread, bank-level characteristics, and their interaction terms. Dependent variables are as follows: risk assets is the ratio of risk assets to total assets, non-performing loans is the ratio of non-performing loans to total loans, and z-score stands for the z-score, which is the natural logarithm of the return on average assets plus the capital assets ratio divided by the standard deviation of the return on average assets (ln[(ROAA+CAR)/σ(ROAA)]). Bank-level characteristics are the following: capitalization is the ratio of capital assets to total assets, efficiency is the ratio of total revenue to total expenses, and size is the natural logarithm of total assets. All models use two way fixed effects and country-specific time trends.
*** Statistical significance at the 1% level.
** Statistical significance at the 5% level.
* Statistical significance at the 10% level.
5.4. Robustness checks
In order to gain more support for the findings above, I perform some robustness checks. Here, I only report the most salient checks. A first exercise is to ascertain whether banks in different countries behave similarly when the term spread changes.
The motivation for this check is that euro area countries differ from each other with respect to a lot of factors, such as the economic structure and the regulatory climate.
Policymakers would want to know how their particular country is affected by the term spread. A second robustness exercise omits German banks from the sample, since they make up more than half of the sample. A third check looks into the effects of the
financial crisis and the possible structural break that it entails. The fourth robustness check looks into the non-performing loans subsample to see if this subsample is systematically different from the entire (active banks) sample. There, I estimate the effect of the term spread on risk assets and insolvency probabilities for the subsample.
The fifth and final exercise deals with the survivorship bias. In all of the previous analyses, I use only active banks. However, inactive banks (as a result of mergers, acquisitions, or failures) may be systematically different from active banks. That is why I test the impact of the term spread on a full sample that includes both active and inactive banks.
Table 7. The term spread and bank risk taking in major euro area countries
Risk assets Non-performing loans Z-score
Term spread Term spread Term spread
Germany -0.007*** -0.001 0.07
(0.001) (0.005) (0.004)
France -0.020** 0.003 -0.063**
(0.009) (0.004) (0.037)
Italy -0.12*** 0.005*** -0.040***
(0.001) (0.001) (0.003)
Spain 0.016 0.014** -0.001
(0.019) (0.007) (0.044)
The table reports coefficient estimates, associated statistical significance, and robust standard errors (in parentheses) of the term spread on the relationship with bank risk. The estimates are calculated using a two way fixed effects model along with a linear time trend. Risk assets is the ratio of risk assets to total assets, non- performing loans is the ratio of non-performing loans to total loans, and the z-score is the natural logarithm of the return on average assets plus the capital assets ratio divided by the standard deviation of the return on average assets (ln[(ROAA+CAR)/σ(ROAA)]).
*** Statistical significance at the 1% level.
** Statistical significance at the 5% level.
* Statistical significance at the 10% level.
The first exercise is to see whether the results I obtain from the full sample using two way fixed effects regressions, with added country-specific linear time trends, hold for major euro area countries (Germany, France, Italy, and Spain) separately. This analysis shows which major euro area countries are and are not resistant to larger term spreads, something policymakers and regulators would be very interested in. As can be seen in Table 7, the results are largely consistent with the full sample. Only Spain has no statistically significant coefficient when estimating risk assets. The significant cases for non-performing loans (Italy and Spain) are consistent
with previous results as well, as are the significant results for the z-score (France and Italy). Furthermore, these outcomes may be of relevance for national regulators, because the results show the term spread has slightly dissimilar effects for different countries. For instance, these figures suggest that Germany hasn’t got as much to fear from high term spreads.
The second check I perform omits German banks from the sample. The rationale is that German banks form more than half of all banks in the sample, potentially biasing the results towards circumstances specific to Germany. However, the results suggest that is not the case. Statistical and economic significance of these estimations are actually very similar to the results obtained in Table 2 (exact results are available upon request).
Table 8. The term spread and bank risk over different periods: 2001-2006 and 2007-2013
2001-2006 2007-2013
(1) (2) (3) (4) (5) (6)
Variable RA NPL Z RA NPL Z
Term spread -0.011 0.015 0.074** -0.018*** 0.006*** -0.101***
(0.012) (0.021) (0.035) (0.002) (0.001) (0.001)
Observations 8,262 599 10,264 13,624 6,327 16,839
R-squared 0.027 0.121 0.141 0.158 0.28 0.141
Number of
ID 2,036 456 2,328 2,306 1,885 2,619
The table reports coefficient estimates, associated statistical significance, and the robust standard error (in parentheses) of the term spread on the relationship with bank risk for different time periods: 2001-2006 and 2007- 2013. Risk assets is the ratio of risk assets to total assets, non-performing loans is the ratio of non-performing loans to total loans, and the z-score is the natural logarithm of the return on average assets plus the capital assets ratio divided by the standard deviation of the return on average assets (ln[(ROAA+CAR)/σ(ROAA)]).
*** Statistical significance at the 1% level.
** Statistical significance at the 5% level.
* Statistical significance at the 10% level.
The third important robustness check is to examine whether the financial crisis affects the results. In order to do so, I split up the data set into two periods: 2001-2006 and 2007-2013. Table 8 reports these analyses. Surprisingly enough, the coefficients for the term spread differ a lot from one period to the next. More specifically, the outcomes for the post-crisis period suggest the relationships similar to those reported in Table 2: the term spread positively affects non-performing loans, insolvency probabilities increase, but the relationship with the risk assets remains negative.
Moreover, for the post-crisis period, these results are highly significant statistically speaking, and the economic effects are slightly larger than for the full active sample.
However, all of these relationships falter in the pre-crisis sample. Here, the term spread has no statistically significant relation with any of the risk assets. These results suggest that the relationships we see for the full sample are largely the effect of the financial crisis (‘suggest’ in italics because we should be careful for a post hoc ergo propter hoc fallacy). To summarize, the results are not robust for the entire sample period, but do hold strong in the post-crisis period.
Table 9. Term spread and bank risk: subsample for non-performing loans observations
(1) (2) (3) (4)
Variable Risk assets Z-score Risk assets Z-score
Term spread -0.002 -0.008 -0.002* 0.014
(0.002) (0.012) (0.001) (0.013)
Observations 5,968 6,902 5,968 6,902
R-squared 0.326 0.117 0.403 0.180
Number of ID 1,726 1,884 1,726 1,884
Bank FE YES YES YES YES
Year FE YES YES YES YES
Country-specific time trend YES YES
The table reports coefficient estimates, associated statistical significance, and robust standard errors (in parentheses) of the term spread on the relationship with bank risk for the subsample that has non-performing loans observations. Risk assets is the ratio of risk assets to total assets and the z-score is the natural logarithm of the return on average assets plus the capital assets ratio divided by the standard deviation of the return on average assets (ln[(ROAA+CAR)/σ(ROAA)]).
*** Statistical significance at the 1% level.
** Statistical significance at the 5% level.
* Statistical significance at the 10% level.
The fourth robustness check deals with the issue of the remarkably fewer non- performing loans observations. Recall that the number of bank-year observations for non-performing loans is slightly fewer than 7,000, whereas both risk assets and the z- score boast more than 20,000 observations. Could this non-performing loans
‘subsample’ lead to systematically different estimations? The answer to this question is reported in Table 9. The coefficients in the table and their lack of statistical significance suggest that the non-performing loans subsample is indeed systematically different from the full sample. Furthermore, even if I split up this subsample into pre- and post-crisis time periods, the results are similar to those reported in Table 9. The reason for this systematic difference is beyond the scope of this study, but at any rate
we know that the results for the non-performing loans estimates above should be interpreted with care.
Table 10. Term spread and bank risk: active and inactive banks sample random effects regression
(1) (2) (3) (4) (5) (6)
VARIABLES RA NPL Z RA NPL Z
Term spread -0.019*** 0.016*** -0.107*** -0.003*** 0.001 -0.023**
(0.002) (0.001) (0.008) (0.001) (0.001) (0.010) Inactive dummy -0.002 0.012** -0.080 -0.001 -0.001 -0.072
(0.003) (0.005) (0.062) (0.003) (0.005) (0.061) Ts * In 0.005*** 0.008*** -0.003 0.005*** 0.007*** -0.001
(0.001) (0.002) (0.010) (0.001) (0.002) (0.009) Constant 0.938*** 0.0200*** 3.727*** 0.932*** 0.045*** 3.711***
(0.002) (0.00739) (0.024) (0.003) (0.007) (0.040)
Observations 25,250 7,946 31,377 25,250 7,946 31,377
Number of ID 3,195 2,191 3,459 3,195 2,191 3,459
Year dummies YES YES YES YES YES YES
Country-specific time trend
YES YES YES
The table reports coefficient estimates, associated statistical significance, and the robust standard error (in parentheses) of the term spread on the relationship with bank risk for the inactive banks sample. In opposition to all other analyses, a random effects model is used. Inactive dummy is a dummy variable that takes the value of 1 if a bank is inactive. Ts * In is an interaction variable of the term spread and the inactive dummy. Risk assets is the ratio of risk assets to total assets and the z-score is the natural logarithm of the return on average assets plus the capital assets ratio divided by the standard deviation of the return on average assets (ln[(ROAA+CAR)/σ(ROAA)]).
*** Statistical significance at the 1% level.
** Statistical significance at the 5% level.
* Statistical significance at the 10% level.
The fifth and final robustness analysis deals with survivorship bias. All of the other analyses use a data set consisting of currently active banks. However, these
‘surviving’ banks may be systematically different in certain respects to banks that ceased activities. To assess this, I estimate a model that uses a dummy variable for inactive banks and an interaction variable that multiplies the term spread and the inactive bank dummy. If the interaction term is not significant, the term spread has had no different effect on inactive banks and vice versa.
Brambor et al. (2006) recommend adding all constitutive terms when estimating an interaction model, because failing to do so can lead to biased estimates.
Since the inactive bank dummy is time-invariant and time-invariant variables have no
within variation, I cannot use a fixed effects model that uses all constitutive terms of the interaction variable. That is why I now employ a random effects model.
The results are listed in table 10. It suggests that inactive banks do not behave like active banks. We see the regular negative relationship between the term spread and risk assets. However, the effect is smaller for inactive banks. Furthermore, non- performing loans increase more for inactive than for active banks when the term spread grows. On the other hand, the term spread has no different effect on inactive banks than on active banks. All in all, I conclude that inactive are indeed systematically different from active banks. More specifically, these banks are riskier, meaning that the analyses with the active sample slightly underestimate the impact of the term spread on bank risk.
In the appendix there is also Table B.1, which reports the results for a sample with both active and inactive banks.
6. Conclusion and policy implications
This study examines the effect of the term spread on bank risk. Understanding what drives bank risk is of great significance regulators, policymakers, and the population at large. The recent financial crisis has shown that free financial markets alone are undesirable, in part because of the massive externalities they can cause. To prevent massive welfare losses in the future, insight is needed in the factors that drive bank risk.
The results of the analyses above are a first indication that the term spread in such a factor. Banks borrow short and lend long, leading to increased profitability if the term spread grows. This, in turn, may cause banks to take on more risk. This study examines this proposition empirically using a sample of euro area banks and finds some evidence that supports this proposition. The results, however, are not entirely straightforward.
To start with an unexpected finding, the ratio of risk assets seems to have the opposite relationship to the term spread than hypothesized. The data reveal a tendency that risk assets decline after the term spread increases. For this unexpected finding I offer the following economic rationale: banks may strive for a target return on equity (or similar target measure). When the term spread increases, lower risk assets such as
government securities can achieve the target. This inference to the best explanation is consistent with the findings.
The ratio of non-performing loans to total loans generally increases with the term spread. This is consistent with the conjecture that because loans are more profitable when the term spread is high, banks can afford to grant loans to ex-ante more risky borrowers.
A feature that was quite robust over all specifications suggests that higher term spreads are associated with higher insolvency probabilities. Though still more research will be needed to further support this finding, the macroprudential policy implications are clear: if a high term spread implies a higher probability of bank insolvency, systemic risk in the financial sector increases as well. It could be that the term spread has to be added to models that assess systemic risk as an indicator.
The evidence also points to capitalization, bank size, and efficiency as important bank balance sheet characteristics that moderate the relationship between the term spread and bank risk. Highly capitalized banks are not as prone to the influence of the term spread as their lowly capitalized counterparts. As such, this would be an extra argument for increasing bank capital levels. The evidence for the case of large banks, however, is contrary to the hypothesis: banks with high total assets are less prone to be affected by the adverse effects of the term spread. Bank efficiency has mixed effects on bank risk.
A robustness check implies that the effects described above to not equally apply to all countries in the euro area. For instance, German banks seem relatively unaffected by the term spread, whereas Italian banks are among the most affected.
This study offers some opportunities to be extended. For instance, I have only empirically researched the theoretical propositions in the euro area, but it would be interesting to see if the relationships hold in other regions.
7. Appendix 7.1. Appendix A
Figure 1. The mean term spread per year. For each year in the sample period, a mean term spread is calculated. That mean is plotted for the period 2001-2013. The term spread is in percentages.
-1-.50.511.522.53Mean term spread
2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 Year
7.2 Appendix B
Table B.1. The term spread and bank risk: active and inactive banks in one sample
(1) (2) (3) (4) (5) (6)
Variables RA NPL Z RA NPL Z
Term spread -0.016*** 0.007*** -0.104*** -0.007*** 0.003* -0.032***
Constant
(0.002) 0.935***
(0.002) 0.0457***
(0.008) 3.701***
(0.002) 0.938***
(0.002) 0.106***
(0.011) 3.694***
(0.002) (0.011) (0.010) (0.002) (0.014) (0.009)
Observations 25,250 7,946 31,377 25,250 7,946 31,377
R-squared 0.089 0.271 0.155 0.105 0.341 0.197
Number of ID 3,195 2,191 3,459 3,195 2,191 3,459
Bank FE YES YES YES YES YES YES
Year FE YES YES YES YES YES YES
Country-specific time trend
YES YES YES
The table reports coefficient estimates, associated statistical significance, and the robust standard error (in parentheses) of the term spread on the relationship with bank risk for both active and inactive banks in one sample.
Risk assets is the ratio of risk assets to total assets and the z-score is the natural logarithm of the return on average assets plus the capital assets ratio divided by the standard deviation of the return on average assets (ln[(ROAA+CAR)/σ(ROAA)]).
*** Statistical significance at the 1% level.
** Statistical significance at the 5% level.
* Statistical significance at the 10% level.
References
Angrist, J., Pischke, J., 2008. Mostly Harmless Econometrics: An Empiricist's Companion. Princeton University Press, Princeton.
Borio, C., Zhu, H., 2012. Capital regulation, risk-taking and monetary policy: a missing link in the transmission mechanism? Journal of Financial Stability 8(4), 236-251.
Brambor, T., Clark, W., Golder, M., 2006. Understanding interaction models:
improving empirical analyses. Political Analysis 14(1), 63-82.
Delis, M., Kouretas, G., 2011. Interest rates and bank risk-taking. Journal of Banking
& Finance 35(4), 840-855.
Duprey, T., Lé, M., 2015. Bankscope dataset: getting started. Unpublished working paper. Paris School of Economics, Paris.
Jiménez, G., Ongena, S., Peydró, J., Saurina, J., 2014. Hazardous Times for Monetary Policy: What Do Twenty‐Three Million Bank Loans Say About the Effects of Monetary Policy on Credit Risk‐Taking?. Econometrica 82(2), 463-505.
Laeven, L., Levine, R., 2009. Bank governance, regulation and risk taking. Journal of Financial Economics 93, 259-275.
Laeven, M., Ratnovski, L., Tong, H., 2014. Bank size and systemic risk (No. 14).
International Monetary Fund.
Maddaloni, A., Peydró, J., 2011. Bank risk-taking, securitization, supervision, and low interest rates: Evidence from the Euro-area and the US lending standards. Review of Financial Studies 24(6), 2121-2165.
Roy, A.D., 1952. Safety first and the holding of assets. Econometrica 20, 431-449.
