The effect of the term spread
on the risk-‐taking behavior of banks
in the US bank market
M. A. Enthoven Student number: s1905007
Master’s Thesis Finance Supervisor: J. O. Mierau
16th January 2015
Abstract
This paper explores the effect of the term spread on bank risk-‐taking. Where previous studies focused mainly on short-‐term (monetary policy) interest rates, this paper argues that the difference between long-‐term and short-‐term interest rates is fundamental to the leverage and risk-‐taking in a bank. Using a dataset of US commercial banks across time (1999-‐2013), this paper finds that a larger term spread leads to increased levels of bank-‐risk (NPL). Results show to be consistent across a fixed effects model and a multi-‐level (hierarchical) model and robust to most choices made in the research process.
Keywords: Interest rate, term spread, bank risk, NPL JEL classification: E43, E44, G21
1. Introduction
The recent financial crisis has shown that excessive risk-‐taking of banks can lead to a collapse of the financial system and the closing down of many banks across the United States. Prior to the crisis, the Federal Reserve lowered the federal funds rate several times in order to create liquidity and ward off a recession. Increased liquidity caused US banks to supply so-‐called ‘cheap money’ through (mortgage) loans to subprime borrowers who later appeared to be unable to pay them off. Excessive bank risk-‐taking ultimately led to the financial crisis and the economic recession. However, what causes banks to take excessive risk in general?
A sound basis of empirical research1 supports the argument that interest rate changes are
among one of the most important determinants of bank risk. Central banks, such as the Federal Reserve, can fix short-‐term interest rate levels by setting monetary policy rates. Recent literature emphasizes that unusual low short-‐term interest rate levels preceding the crisis, as set by the federal funds rate, contributed to the crisis through stimulation of leverage and excessive bank risk-‐taking. This process is also known as ‘the risk-‐taking channel of monetary policy’ and has been researched intensively during the last decade. Even though the risk-‐taking channel of monetary policy explains the effect of short-‐term interest rates on bank risk-‐taking, it could be more relevant to look at the interest rate spread since the interest rate spread is a measure of the profitability of banks. The practical relevance of using the interest rate spread rather than a standalone short-‐term interest rate level is best explained by the concept of ‘maturity transformation’.
When banks participate in maturity transformation, they finance long-‐term assets with short-‐ term debt (Mink, 2011). Many investors are willing to invest capital on a short-‐term basis, but capital for large investment projects is needed on a long-‐term basis. Banks fill in this gap as they take on debt (deposits) in return for a short-‐term interest rate, and extend credit (loans) in return for a long-‐ term interest rate. Bank profits consist of this difference between interest rates, which is called the term spread. So a larger term spread gives banks additional incentive to engage in maturity transformation. However, increased levels of maturity transformation also make banks more risky because increases in short-‐term interest rates (debt) may rise faster than they are able to obtain in the profits on long-‐term loans. Larger term spreads are expected to result in increased levels of leverage and thereby larger risks of sudden illiquidity and/or bank runs. Since bank risk-‐taking
becomes more profitable with a larger term spread, this relation is interesting to investigate more thoroughly (Mink, 2011).
The term spread is often depicted by the yield curve that shows the relationship between the yield, i.e. interest rate, and time to maturity on fixed-‐income securities. In most situations, investors want to be compensated for additional risks that increase with the time to maturity. Thereby long-‐ term interest rates will be higher than short-‐term rates. This causes the yield curve to be upward sloping, i.e. the term spread to be positive. A steeper yield curve is related to positive investor expectations towards future economic growth, which could lead to excessive risk-‐taking. Even though there is a large amount of research about the determinants of the yield curve, this is beyond the scope of this paper. This study focuses on the effect that the term spread has on bank risk-‐taking. Note that throughout this paper the terms: interest rate spread, term spread and yield curve (slope) are used interchangeably.
Much research about the influence of monetary policy on short-‐term interest rates and bank risk-‐taking has been done, but only a small amount of literature focuses on the role of the interest rate spread in explaining bank risk. This paper looks deeper into the mechanism of the yield curve and how it affects bank risk. A sample of US banks across time will be used to test the hypothesis that a steeper yield curve, i.e. larger term spread, has a positive and significant effect on bank risk-‐taking. Panel data analysis will test whether a positive relation between the macro-‐economic term spread and micro-‐economic bank risk-‐taking still holds when bank-‐ and time-‐fixed effects are used. Furthermore the model uses country-‐level data to control for variables that may otherwise bias the research. The fixed effects model will be extended to a multi-‐level mixed model to improve estimation. In the last part of the paper, robustness checks are performed to cross-‐reference the regression results. The main empirical results show that a larger term spread leads to an increased level of bank risk-‐taking across US commercial bank market from 1999 to 2013.
The next section describes theoretical and empirical literature on interest rates and bank-‐risk taking. Section 3 explains the research methodology and Section 4 explains the dataset that is used for this study. Section 5 presents the empirical results and reports the robustness of these results. Finally, Section 6 will draw the main conclusions and limitations of this paper and provides further recommendations.
2. Literature
rate spread and bank risk. Section 2.1 describes the literature that focuses on the general effect of (short-‐term) interest rates on bank risk-‐taking. Next, Section 2.2 discusses how banks operate and that interest rate spreads may be a determinant of bank risk.
2.1. Monetary policy and the risk-‐taking channel
The transmission of monetary policy and the way that it influences economic activity is a popular topic of research. Monetary policies have large effects on short-‐term interest rates (Evans and Marshall, 1998). The Federal Reserve can set a target federal funds rate that corresponds to a certain short-‐term interest rate. The process through which interest rates affect the riskiness of bank loan portfolios is called the risk-‐taking channel (Paligorova and Sierra, 2012). Borio and Zhu (2012) argue that insufficient attention has been paid to the link between monetary policy and the pricing of risk. The recent crisis is the best reminder that long periods of financial stability can be replaced by a sudden emergence of financial strains. Policymakers should become more aware about risk consequences of monetary policy measures. There are two ways through which the risk-‐taking channel of monetary policy works:
1) Through the search for yield. Expectations of low interest rates soften lending standards and lead to the extension of lower-‐quality credit. In addition, interest rate differences between risky and non-‐risky borrowers may converge which inadequately reflects the cost of risk (Rajan, 2006).
2) Through the excessive expansion of banks’ balance sheets through leverage. Accommodative monetary policy is viewed as a sign of financial stability, which leads to increased levels of leverage (Gambacorta, 2009). The attraction of excessive levels of debt (i.e. deposits) is risky because a small fluctuation in risk aversion of the investors may lead to large financial imbalances, reduced liquidity and forced asset (i.e. loan) sales (Paligorova and Sierra, 2012).
Table 1 shows recent empirical papers that have investigated the relation between short-‐ term interest rates and bank risk-‐taking across the EU, US, Spain, and Bolivia. These papers provide a basis for the argument that (short-‐term) interest rates are important determinants for bank risk-‐ taking, which is a fundamental assumption for this research.
Table 1 -‐ Studies researching interest rate effects on bank risk-‐taking.
Author Market Period Data Conclusions
Dell’Ariccia, Laeven, and Suarez (2013)
US 1997-‐2011 Quarterly A low short-‐term interest rate environment increases bank risk taking.
Altunbas, Gambacorta, and Marques-‐Ibanez (2010)
EU 1999-‐2005 Annually Lower EDF banks have ability to offer larger amounts of credit and are better protected against monetary policy changes.
Jimenez, Ongena, Peydró, and Saurina (2014)
Spain 1984-‐2006 Quarterly Prior to loan origination, lower short-‐term interest rates soften lending standards. More loans go to bad borrowers and loans with higher hazard rates are granted.
Gambacorta (2009) EU and US 1998-‐2008 Quarterly Low interest rates over an extended period cause an increase in expected bank-‐risk.
Maddaloni and
Peydró (2011) EU and US 2002-‐2008 Quarterly Low short-‐term (monetary policy) rates soften lending standards rather than low long-‐term interest rates.
Ioannidou, Ongena, and Peydró-‐Alcalde (2008)
Bolivia 1993-‐2003 Monthly A decrease in the US federal funds rate prior to loan origination raises the monthly probability of default on individual bank loans.
Table 1 presents literature in the field of monetary policy and bank risk-‐taking. Authors, markets, sample periods, data type and the main conclusions are shown.
Gambacorta (2009) takes most previous literature2 into consideration when investigating the
interest rate-‐bank risk nexus for EU and US listed banks. He finds a significant link between an extended period of low interest rates prior to the crisis and bank risk-‐taking. The regression model used includes measures of bank-‐risk, interest rates and control variables and serves as a useful starting point for the model used in this paper. Maddaloni and Peydró (2011) add additional information by finding that lower short-‐term rates soften lending standards more than long-‐term interest rates do. Altunbas, Gambacorta, and Marques-‐Ibanez (2010) focus on EU banks to show that the markets’ perception of bank risk as measured by the Expected Default Frequency (EDF) plays an important role in determining bank’ loan supply and in protecting them from monetary policy changes. Shocks in short-‐term (monetary) interest rates have smaller effects for banks with low levels of bank risk. This paper analyses the link between bank risk and monetary policy effects, which is a reverse relationship from previous papers. Thus in the analyses, attention towards reverse causality is important.
Altogether, this set of literature gives a firm basis for the assumption that short-‐term interest rates as set by monetary policy are negatively related to bank risk-‐taking.
2.2. The term spread and bank risk-‐taking
The previous selection of literature provides a firm argument that interest-‐rates, especially short-‐term interest rates as set by monetary policy, have considerable effects on the risk-‐taking behavior of banks. However, this paper is more interested in the way in which banks work. Even though short-‐term (monetary policy) interest rates are a crucial part of bank operations, this does not provide the complete picture. Present business models of banks in the simplest form consist of incomes in terms of long-‐term interests received on outstanding loans and expenditures paid on deposits in terms of short-‐term interest rates. Since the spread between the long-‐term and short-‐ term rate is decisive for the profitability of banks, it is interesting to explore whether banks will take more risk if they have more profitable prospects (a larger term spread).
Mink (2011) provides theoretical reasons for this positive relationship. A steeper yield curve gives shareholders more cost advantage incentive for bank leverage instead of shareholder leverage due to the bank’s superior maturity transformation ability. Risk–taking increases since engaging in maturity transformation provides banks with a larger borrowing cost advantage and more leverage will be used. Through leverage, banks use more debt instead of equity when financing their assets, which leads to higher liquidity risks. Mink (2011) suggests a new risk-‐taking channel of monetary
policy in which lower policy rates lead to a larger term spread that eventually results in increased bank risk-‐taking.
Where Mink (2011) provides the theoretical background, Maddaloni and Peydró (2011) find empirically significant results that a higher slope of the yield curve leads to a softening of lending standards. Even though the relationship between softened loan-‐lending standards and bank risk is not one-‐on-‐one, it is expected that softened loan lending standards leave room for more risk-‐taking. Gambacorta (2009) finds that a steeper yield curve increases bank profits through the maturity transformation function. In addition, the yield curve shows to have a negative but very insignificant effect on bank risk. However, this paper uses the expected default frequency (EDF) as a bank risk measure rather than the amount of non-‐performing loans to total loans (NPL) that will be used in this paper. NPL considers realized credit risk rather than the forward-‐looking bank risk measure EDF. Therefore the outcome of Gambacorta does not need to be in contrast to this research (Fiordelisi, Marques-‐Ibanez, Molyneux, 2011). Espinoza and Prasad (2010) find that the NPL decreases if interest rates and risk aversion levels increase.
Whereas the effect of the interest rate on bank risk behavior has been frequently researched, there is a rather small amount of research investigating the interest-‐rate differentials and its effects on bank risk. A larger term spread softens lending standards (Maddaloni and Peydró, 2011), but does this also mean that a larger term spread increases bank risk?
A brief view on the US term spread and national level of non-‐performing loans to total gross loans from 1999-‐2013 shows a positive correlation of 52.88%. Even though this does not provide any statistically significant information, it does further motivate the fact that the spread-‐risk relation is interesting to further explore. Therefore the hypothesis of this paper is that a larger term spread leads to larger amounts of bank risk-‐taking as measured by loan portfolio risk (NPL).
Section 2.1 showed that monetary policy and (short-‐term) interest rate levels are important determinants of bank risk-‐taking. Section 2.2 suggested that the business model of banks depends on the interest rate spread rather than solely short-‐term interest rate levels. Therefore the research question for this paper states: Does the term spread have an effect on bank risk-‐taking? In Section 3 the research methodology to test the relationship of the term spread on bank risk will be explained and the choice, selection, summary statistics and correlation of the US data will be described.
3. Methodology
3.1. The fixed effects model
To empirically analyze the influence of term spreads on bank risk-‐taking in the US, I first look at background literature. Studies related to this paper make use of panel data sets to analyze the interest rate effects across banks and time3. Analyzing the models of related literature provides a
strong argument that a regression model with control variables serves as a useful starting point for this study. These studies generally include two types of control variables: control variables at a country-‐level (GDP growth, inflation, housing prices and stock market prices) and control variables at the bank-‐level (such as bank size, liquidity and return on assets). Control variables are important to add in order to solve the omitted variable bias. The term spread may seem to be a good estimator for bank risk-‐taking, but there could be other variables that are correlated with both the term spread and bank risk-‐taking. Not incorporating these variables will lead to a model that over-‐ or underestimates the real effect of the term spread on bank risk-‐taking. Since this research is mainly interested in the effect of the macro-‐economic term spread on the micro-‐economic risk-‐taking of banks, bank-‐level control variables will be excluded from the methodology. Individual bank characteristics will not be expected to have a substantial influence on the national US term-‐spread as loan demand is largely independent of bank-‐specific characteristics and mostly dependent on macro-‐ economic factors (Altunbas, Gambacorta, and Marques-‐Ibanez, 2010). Thus factors such as the inflation rate & GDP growth are most relevant in explaining the behavior of bank interest rate spreads (Afanasieff, Lhacer, and Nakane, 2002). In order to investigate the relationship between the term spread and bank risk the following basic set-‐up is used:
1 𝑅𝑖𝑠𝑘!,! = 𝛼 + 𝛽1𝑆𝑝𝑟𝑒𝑎𝑑!+ 𝛾𝑋!,!+ 𝜏!+ 𝜆!+ 𝜀!,!
where 𝑅𝑖𝑠𝑘!,! is the amount of loan portfolio risk (as measured by NPL) at bank 𝑖 in year 𝑡. 𝑆𝑝𝑟𝑒𝑎𝑑! is the interest rate spread between the 10-‐year Treasury bond rate and the federal funds rate. 𝑋!,! stands for a set of control variables at a country level. To control for time-‐varying global business cycle effects, time-‐fixed effects are added to the model (𝜏!). This time-‐fixed effects across the 15-‐ year period will be measured by a set of 14 dummy variables to avoid the dummy variable trap. To control for time invariant bank heterogeneity, bank fixed effects (𝜆!) are added to the regression equation. At last the error term (𝜀!,! ) is included.
3 See, e.g., Dell’Ariccia, Laeven, and Suarez, 2013; Gambacorta, 2009; Jiménez, Lopez, and Saurina, 2013; Maddaloni and
Control variables are included in the term 𝑋!,! in order to solve the omitted variable bias. The control variables include the real GDP growth rate (𝐺𝐷𝑃𝑔𝑟𝑜𝑤𝑡ℎ!) and the inflation rate (𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛!). A Hausman test will check whether a fixed effects model is preferred over a random effects model. This leads to the following baseline regression equation:
2 𝑅𝑖𝑠𝑘!,! = 𝛼 + 𝛽1𝑆𝑝𝑟𝑒𝑎𝑑!+ 𝛾𝐺𝐷𝑃𝑔𝑟𝑜𝑤𝑡ℎ!+ 𝛿𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛!+ 𝜏!+ 𝜆!+ 𝜀!,!.
The baseline regression model estimates the effects of the independent variable term spread on bank-‐risk levels. However the fact that this is a macro-‐to-‐micro relationship makes estimation more challenging. The dependent variable 𝑅𝑖𝑠𝑘!,! varies across banks 𝑖 and time 𝑡, but the independent variables 𝑆𝑝𝑟𝑒𝑎𝑑!, 𝐺𝐷𝑃𝑔𝑟𝑜𝑤𝑡ℎ! and 𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛! are equal for all banks and only vary throughout time. Since there is no time invariant bank heterogeneity in the independent variables, but only in the dependent variable, the baseline (fixed-‐effect) regression model may not explain inter-‐bank variation most accurate. Therefore I will not only test the hypothesis through the baseline (fixed effects) model, but also through the use of a multilevel model (also called hierarchical model). 3.2. The multilevel (mixed) effects model
3 𝑅𝑖𝑠𝑘!,! = 𝜇 + 𝜀!,!
where the 𝑅𝑖𝑠𝑘!,! can be estimated by the mean of bank risk across all bank observations (the grand country mean, 𝜇) plus an error term for the individual variation from this mean (𝜀!,!). Because individual bank risk observations are nested within a particular bank, the mean bank risk level of each bank (𝑢!) can be calculated. Now the error term can be split into two different components: individual bank risk observations vary around their bank mean of bank risk, and bank means vary around the (grand) country mean of bank risk. Equation 4 shows the new variance components model:
4 𝑅𝑖𝑠𝑘!,! = 𝜇 + 𝑢!+ 𝜀!,!
where 𝑅𝑖𝑠𝑘!,! is determined by the grand country bank risk mean (𝜇), the deviation of a particular bank risk level from this grand country mean (𝑢!) and the deviation of an individual bank risk observation from its bank mean (𝜀!,!). Applying this model to regression equation 2 results in the following model:
5 𝑅𝑖𝑠𝑘!,! = 𝛼 + 𝛽𝑆𝑝𝑟𝑒𝑎𝑑!+ 𝛾𝐺𝐷𝑃𝑔𝑟𝑜𝑤𝑡ℎ!+ 𝛿𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛!+ 𝑢!+ 𝜀!,!
where the grand country mean 𝜇 will be called 𝛼 in order to serve as an intercept for the regression model. An assumption of this model is that the two random effects 𝑢! and 𝜀!,! are normally distributed with mean 𝜇 and variance 𝜎!. Similarly to the baseline regression equation for a fixed effects model (2), time-‐invariant bank heterogeneity should also be controlled. A plot of bank risk throughout time for all individual banks shows that individual banks have different slopes for bank risk over time. So allowing a time trend is expected to increase the estimation power of the model. This leads to the following estimation model:
6 𝑅𝑖𝑠𝑘!,! = 𝛼 + 𝛽𝑆𝑝𝑟𝑒𝑎𝑑!+ 𝛾𝐺𝐷𝑃𝑔𝑟𝑜𝑤𝑡ℎ!+ 𝛿𝐼𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛!+ 𝜃𝑌𝑒𝑎𝑟!+ 𝑢!+ 𝜀!,! where adding 𝜃𝑌𝑒𝑎𝑟! allows bank risk to have a slope over time. However, the included fixed time-‐ slope (𝜃𝑌𝑒𝑎𝑟!) assumes that this slope is identical for all banks across time. The estimation power of the model can be further increased if the time slope is fitted to a particular bank i. Including a random time slope leads to the final multilevel estimation model:
𝜃𝑌𝑒𝑎𝑟!) plus the deviation of a particular bank from that fixed part of the model (𝑢!), the deviation between the random intercept and the random slope of a bank (𝑢!𝑌𝑒𝑎𝑟!), and the residual deviation of a specific bank observation (𝜀!,!). In multilevel modeling this is called a level-‐2 regression with random intercepts and random slopes (Cohen, Cohen, West, and Aiken, 2013).
Regression equation 7 will be used as the baseline of the multi-‐level model and will also be checked for robustness. Robustness checks involve using the raw unbalanced panel, using US corporate BBB spreads rather than Treasury bond spreads, using an alternative measure of bank risk and using lagged values.
4. Data
Section 4.1 describes the selection and transformation of the sample and gives the descriptive statistics and relevant correlations. Next, the dependent variables (Section 4.2) and independent variables (Section 4.3) are explained more thoroughly.
4.1. Data selection, descriptive statistics and correlations
The recent crisis showed that the US banking market still sets the tone for worldwide financial markets. The US is known to be the leading player in the global financial industry, which is why US banks are selected for this study. In addition, US data availability is generally better than data availability of other regions. Different types of banks may have different implications for the spread-‐ risk nexus, which is why this study focuses on commercial banks. The database provides data from 1999 onwards. A sample of 6,304 banks across a 15-‐year time period (1999-‐2013) is selected as an initial sample. The dependent variable that measures bank risk is the amount of non-‐performing loans to total gross loans (NPL) and is available in approximately 90% of the observations. This dataset only includes banks with known NPL values across all 15 years and leaves out banks with missing NPL data. All other relevant variables do not have missing values and can be used directly. Important to notice is that the macro-‐economic measures (term spread, real GDP growth rate, and inflation rate) have only 15 unique values each and are uniformly applicable to all banks. The relevant variance for this research is created by the way that the large sample of banks reacts differently to 15 different term spread values.
perfectly balanced. However, data analysis software (Stata) has no problems with estimating this unbalanced panel. Table 2 contains the descriptive statistics of the data sample used for the baseline regressions of the fixed effects model and the multi-‐level model. Total assets are included because the effect of the term spread on bank risk across subsets of different sized banks may be interesting to look at. The bank risk measure NPL has a mean value of 1.68% and the term spread has a mean value of 1.73 percentage points. Analyzing the data points show that there are no substantially influential outliers that bias estimation results.
Table 2. -‐ Descriptive statistics for bank-‐year observations
Variable Observations Mean Std. deviation Min Max
NPL (%) 63,016 1.678 2.548 0.001 49.831 NPL (ln) 63,016 -‐0.403 1.565 -‐6.908 3.909 Term spread (pp) 63,016 1.732 1.220 -‐0.390 3.097 Real GDP growth (%) 63,016 2.043 1.787 -‐2.776 4.685 Inflation (%) 63,016 2.388 1.038 -‐0.356 3.839 Total assets (bln) 63,016 2.761 49.077 0.004 1945.467 Total assets (ln) 63,016 19.214 1.323 15.128 28.297
Table 2 contains the summary statistics for the panel dataset used in the baseline regressions. NPL and total assets are taken at its natural logarithm to solve for non-‐normality of these skewed variables.
In addition, Table 3 shows the correlation coefficients of all variables of the baseline regression. The NPLs of US commercial banks show to be positively correlated with the national term spread on 10-‐year Treasury bonds less the federal funds rate with a correlation coefficient of 0.226 (22.6%). This is congruent with the hypothesis of this paper. Furthermore, real GDP growth rates and inflation rates show to be significantly correlated with both the term spread and NPL and are included in the model as control variables. The observed negative correlation between real GDP growth rates and NPL is consistent with Jiménez, Lopez, and Saurina (2013). Moreover higher inflation rates imply tighter lending standards leading to decreases in loan portfolio risks. This is why the correlation of inflation and NPL is negative (-‐19.3%). At last the correlation between both control variables is somewhat high (45.9%) and could lead to possible collinearity. However, a cross-‐ reference using various data sources4 for GDP growth rates and inflation rates gave similar
correlation coefficient values. Moreover, related literature includes both variables and in case of severe collinearity the statistical software will automatically omit one of the variables.
Table 3 -‐ Correlation table.
Variable NPL (ln) Term spread (pp) GDP growth (%) Inflation (%)
NPL (ln) 1.000
Term spread (pp) 0.226 1.000 GDP growth (%) -‐0.210 -‐0.341 1.000 Inflation (%) -‐0.193 -‐0.549 0.459 1.000
Table 3 shows the correlation coefficients of the main variables of the balanced sample.
There are various data sources used for this research. The country-‐level variables (term spread, real GDP growth rate, and inflation rate) are obtained through Thomson Reuters’ Datastream. Bank-‐level data (NPL, total assets, return on average assets, and equity to total assets) are derived from Bureau van Dijk’s Bankscope Database. Since Bankscope only provides quarterly NPL data after 2009, this study uses annual NPL data. The bank-‐level variables ‘return on average assets’ and ‘equity to total assets’ will be used in order to calculate the z-‐score. The z-‐score is an alternative measure of bank risk that will be used as a robustness check in Section 5.2. Appendix A further explains all variables used.
4.2. The dependent variables: non-‐performing loans to total gross loans (NPL) and the z-‐score
Comparable literature use bank-‐risk measures like the expected default frequency (Gambacorta, 2009) and bank-‐loan risk ratings (Dell’Ariccia, Laeven, and Suarez, 2013). However both risk measures are calculated ex-‐ante, rather than ex-‐post. This research focuses on the effect that the term spread has on actual bank risk rather than expected bank risk. In addition, data on EDF and bank-‐loan risk ratings are unavailable without special licenses. In contrast, Jiménez, Lopez, and Saurina (2013) use an ex-‐post measure of credit risk, the non-‐performing loans ratio (NPL). This measure includes doubtful loans and loans that are more than 90 days overdue and is the most frequently used measure of problem loans throughout research literature (Berger and De Young, 1997). NPL measures loan portfolio risk (credit risk) and since credit risk is the main risk driver for most banks, NPL is a suitable measure for comparing a large sample of different banks.
To cross-‐check the robustness of the model, an alternative bank risk variable, the z-‐score, can also be used (Uhde and Heimeshoff, 2009). Higher levels demonstrate that a bank is more financially stable and bank risk is lower. The following equation is used for calculation of the z-‐score:
8 𝑍𝑠𝑐𝑜𝑟𝑒!,! = 𝑅𝑂𝐴!,!+ 𝐸/𝑇𝐴!,! 𝜎 !,! !"#
where 𝑅𝑂𝐴!,! is the average annual return on assets for bank i in year t. 𝐸/𝑇𝐴!,! is equity divided by total assets, which is a measure of bank leverage at a particular point in time. 𝜎 !,! !"# is the standard deviation of the return on assets. The z-‐score shows to be highly skewed, taking the natural logarithm of the z-‐score solves this and leads to a normally distributed variable (Laeven and Levine, 2009). In the remainder of this paper, ‘NPL’ and ‘z-‐score’ will refer to their log-‐transformed values, since these are used for regression.
4.3. The independent variables: term spread, real GDP growth and inflation
The term spread is an indicator of monetary policy and general financial conditions and rises when short-‐term interest rates are relatively low. There is a wide consensus that 10-‐year Treasury bond rates can be taken as the long-‐term interest rate and that (for the US yield curve) the federal funds rate serves as a good proxy for the short-‐term interest rate. This difference between long and short rates is often displayed in the yield curve. Therefore a typical yield curve is constructed using the 10-‐year Treasury bond rate and the federal funds rate, an overnight interbank borrowing rate. Datastream provides this measure directly as the ‘US interest rate spread: 10 years treasury bonds less federal funds rate’. Therefore no additional calculations were needed. The term spread is denoted as a nominal rate, but Dell'Ariccia, M., Laeven, and Suarez (2013) do not expect this to be a problem since the correlation between the nominal and real federal funds rate for their comparable time period is high (90%). Fig. 1 shows the movement of NPL and the term spread over time. The two variables show to move more parallel after 2007, which will be particularly interesting to explore.5
Figure 1 – Average NPL and the term spread over time.
The control variable GDP growth is taken at its real value, as inflation is controlled for separately. Moreover most related papers use real-‐ rather than nominal GDP growth rates. Since this study only involves US banks, real GDP growth rates are the same across banks and the real GDP growth has 15 unique values, i.e. one per year. Annual real GDP growth rate data and inflation rates were provided by the World Bank and extracted through Datastream. Annual inflation rates are based on the consumer price index (CPI).
In addition, it can also be interesting to know whether the spread of more vulnerable investment grade debt securities also impact bank risk-‐taking in a similar way. Section 5.2 will test the robustness of the spread-‐to-‐risk by using US corporate BBB debt securities.
5. Results
In this section, I present the main results from the regression analyses performed. First the most basic impact of the term spread on bank risk-‐taking will be tested. Control variables will be added to eliminate the potential omitted variable bias. Next, time-‐ and bank-‐specific effects are added to the model to control for time varying effects and time invariant bank heterogeneity. Also different subsets on asset size and time periods will be tested. The fixed effects model is extended to a multi-‐ level model that better estimates the pure effect of the term spread on bank risk-‐taking. At last, robustness checks will be performed to see whether the main results still hold when using an unbalanced panel, using a corporate BBB spread and using a different bank risk measure. At last lagged variables will be used to handle potential reverse causality. All robustness checks will be performed on the baseline regressions of the fixed effects-‐ and the multilevel model, regressions 5 and 12 respectively.
Figure 3 shows the mean annual NPL (%) and the annual term spread (pp) over time.
5.1. Main results
Table 4 shows the results from the regressions on US banks with perfect NPL data availability.6 NPL is the dependent (bank-‐risk) variable and the main independent variable is the term
spread (the difference between the 10-‐year Treasury bond rate and the federal funds rate). I start out with a simple linear regression using OLS. In Table 4, regressions 1 and 2 show that the spread indeed has a significant positive influence on the NPL-‐level. This is also true when control variables for real GDP growth and inflation are added to the regression equation. However, since we are using bank data throughout time it may be relevant to include bank-‐fixed effects and time-‐fixed effects. A significant Hausman test-‐statistic shows that using a fixed effects model is preferred over a random effects model. Also time-‐fixed effects can be considered. Testing for time-‐fixed effects shows that the null hypothesis can be rejected and time fixed-‐ effects are needed in this case. Regressions 3 and 4 in Table 4 show that including bank-‐ and time-‐fixed effect does still leave the term spread to have a positive significant influence on NPL. Regression equation 5 forms the baseline regression for this research and includes all previously mentioned variables.
The term spread coefficient of baseline regression 5 of the fixed effects model in Table 4 is significantly positive with a value of 0.052. The log-‐linear model shows that a one percentage point increase in the term spread leads a 5.2% (100 times 0.052) increase in bank risk as measured by NPL. The goodness of fit measure, adjusted R-‐squared, of baseline regression 5 is 18.0%. Even though this seems small, this is common in cross-‐section analysis since variations in individual behavior are difficult to fully explain (Gambacorta, 2009). Regression 6 solves for problems of serial correlation and group-‐wise heteroskedasticity (shown by a modified Wald test) by using bank-‐clustered standard errors. Comparing regression 5 and 6 shows that estimation coefficients remain unchanged, but that the standard errors and the F-‐statistics are generally lower. This variation in standard errors shows that the error/residual could be the sum of different variance components that can be further controlled.
Furthermore, regression results show that a higher real GDP growth rate reduces the bank risk. Gambacorta (2009) explains this by the fact that an increasing number of projects become profitable as a consequence of higher GDP growth levels. The coefficients of both GDP growth rates and inflation rates appear to be negative and significant for almost all regressions performed in Table 4. Regressions 7 and 8 test the term spread effect on bank risk for subsets of time periods. The results shows that a pre-‐crisis period (1999-‐2006) and a post-‐crisis period (2007-‐2013) deliver
substantially different results on the term spread-‐bank risk relationship. The estimation coefficient shows to be insignificant for the pre-‐crisis period (0.014), but largely significant for the post-‐crisis period (0.346). Post-‐crisis federal funds rates are exceptionally small, which leads term spreads to be larger. Larger term spreads are related to bank risk more strongly than smaller term spreads. A possible explanation of this is that larger term spreads lead to excessive leverage and bank risk-‐ taking.
Regression results for subsets of bank size, as measured through total assets, were considered. The term spread effect did not differ substantially between the largest-‐ and the smallest 25% US commercial banks and results are not included in Table 4 for the sake of simplicity. Table 4 shows that these first results are in line with the hypothesis proposed for this study, which states that a steeper yield curve (larger term spread) has a positive and significant effect on the risk-‐taking behavior of banks.
Table 4 -‐ Regression results (fixed-‐effects model).
Regression # 1 2 3 4 5 6 7 8
Estimation method OLS OLS OLS OLS OLS OLS OLS OLS
Information Basic
effect Controls added Bank-‐fixed effect added Time-‐ fixed effect added Baseline Baseline + clustured standard errors 1999-‐2006 2007-‐ 2013 𝑆𝑃𝑅𝐸𝐴𝐷! 0.289*** (0.005) 0.198*** (0.006) 0.203*** (0.005) 0.048*** (0.009) 0.052*** (0.008) 0.052*** (0.007) 0.014 (0.009) 0.346*** (0.007) 𝐺𝐷𝑃𝐺! -‐0.120*** (0.004) -‐0.118*** (0.003) -‐0.208*** (0.006) -‐0.241*** (0.005) -‐0.241*** (0.005) -‐0.070*** (0.006) 0.061*** (0.004) 𝐼𝑁𝐹𝐿𝐴𝑇𝐼𝑂𝑁! -‐0.068*** (0.007) -‐0.070*** (0.006) -‐0.004*** (0.010) -‐0.003 (0.012) -‐0.003 (0.006) -‐0.038** (0.019) -‐0.068*** (0.007)
Bank-‐fixed effects No No Yes No Yes Yes Yes Yes
Time-‐fixed effects No No No Yes Yes Yes Yes Yes
Observations 63016 63016 63016 63016 63016 63016 31925 31091
R-‐squared – within 0.051 0.072 0.054 0.180 0.256 0.256 0.012 0.199 R-‐squared (adj.) –overall 0.051 0.072 0.054 0.179 0.180 0.180 0.006 0.009
F-‐statistic 3382.19 1632.71 4537.81 984.44 1430.07 431.48 46.67 1082.65
Table 4. This table contains results of the regressions performed. The dependent bank-‐risk variable is NPL and the independent variable is the term spread. Real GDP growth and inflation are control variables. Regression 1 and 2 use OLS estimation for the main relationship between the term spread and NPL without the use of bank-‐ and time-‐fixed effects. Regression equations 3, 4 and 5 do include these effects and regression 5 is the baseline regression for this research. Regression 6 uses clustered standard errors and regression 7 and 8 look at different time periods. The unstandardized estimation coefficients of each variable or reported. * indicates significance at the 10% level, ** at the 5% level and *** at the 1% level. Standard errors for each variable are reported in brackets below the corresponding coefficient. Adjusted R-‐squared values shows the
Even though a Hausman test shows that using a fixed effects model are preferred over a random effects model, the Bruesch & Pagan Lagrangian multiplier test shows that there are, in fact, random effects. Using a multi-‐level (mixed) model for this macro-‐micro relationship takes both effects into account and yields more powerful estimation results for this particular research.
bank-‐specific time slope. The term spread coefficients remain positive and significant for all cases. Regression 12 is the baseline multilevel regression and shows that the coefficient for the spread has a value of 0.106. These results show larger and more significant term spread effects on bank risk than previously estimated by the fixed effects model. A one-‐percentage point increase in the term spread leads to a 10.6% (100 times 0.106) increase in NPL. The cross-‐reference of the spread-‐bank relation across two different econometric models provides a strong argument that a larger term spread indeed has a positive and significant influence on bank risk-‐taking. The multilevel mixed model shows that this relationship is more economically significant than the fixed effects model estimates. Moreover regression 13 shows that the multilevel model has hardly any difference between the predicted residuals and their bank-‐clustered versions because the residuals are accurately modeled. At last, regressions 14 and 15 in Table 5 show that the influence of the term spread on bank risk has become substantially larger since the outbreak of the financial crisis in 2007 as the post-‐crisis correlation coefficient of term spread (0.316) is larger than the pre-‐crisis coefficient (0.045).
Table 5 -‐ Regression results (multi-‐level model).
Regression # 9 10 11 12 13 14 15
Estimation method Multilevel Multilevel Multilevel Multilevel Multilevel Multilevel Multilevel
Information Variance from grand mean Variance from bank mean Fixed time
slope Baseline (Specific bank slope) Clustered standard errors Period 1999-‐2006 Period 2007-‐2013 𝑆𝑃𝑅𝐸𝐴𝐷! 0.198*** (0.006) 0.203*** (0.005) 0.106*** (0.005) 0.106*** (0.005) 0.106*** (0.005) 0.045*** (0.008) 0.316*** (0.007) 𝐺𝐷𝑃𝐺! -‐0.120*** (0.004) -‐0.119*** (0.003) -‐0.030*** (0.003) -‐0.030*** (0.003) -‐0.030*** (0.003) -‐0.068*** (0.006) 0.039*** (0.005) 𝐼𝑁𝐹𝐿𝐴𝑇𝐼𝑂𝑁! -‐0.068*** (0.007) -‐0.070*** (0.006) -‐0.078*** (0.006) -‐0.078*** (0.006) -‐0.078*** (0.005) -‐0.003 (0.018) -‐0.014** (0.006) 𝑌𝑒𝑎𝑟! 0.115*** (0.001) 0.115*** (0.001) 0.115*** (0.001) -‐0.016*** (0.004) 0.068*** (0.005) Observations 63016 63016 63016 63016 63016 31925 31091 Log likelihood -‐115278 -‐110486 -‐ 106734 -‐106733 -‐106733 -‐52682 -‐48842 Wald chi-‐squared 4898.44 6556.12 15481.71 15476.91 5267.01 287.99 5719.06 Table 5. This table contains results of the multilevel regressions performed. The dependent bank-‐risk variable is NPL and the independent variable is the term spread. Real GDP growth and inflation are control variables Regression 9 only allows for variance from the grand mean NPL and is therefore similar to regression 2 in Table 4. In regression 10 the multi-‐level model is extended and specifies for the variance from the bank mean NPL. Regression 11 allows mean NPL values to have a slope over time. Regression 12 forms the baseline of the multi-‐ level model and allows every bank to have a different slope for their NPL values over time. Regression 13 uses bank-‐specific clustured standard errors and regressions 14 and 15 look at different time periods. Note that R-‐squared statistics are not provided.
