The impact of the term-spread on bank risk-taking in
the United States: an empirical research
Master thesis Finance Student: Niels Vermuë1
Supervisor: dr. J.O. Mierau June 2015
Abstract
This study empirically investigates the relation between the macro-economic term spread and micro-economic bank risk-taking in the United States between 1999 and 2014. Since banks essentially transform short-term liabilities in long-term assets, a steeper yield curve is expected to incentivise banks to engage more in maturity transformation, thereby increasing leverage and risk-taking. By means of regression analysis on a large set of panel data, this study finds that a higher term spread indeed increases bank risk-taking. Time- and bank-fixed effects are taken into account, as well as macro-economic control variables. The results are robust for different time-frames, different interest measures, and an alternative measure of bank risk. They suggest that monetary policy and financial stability are more entwined than previously thought.
Keywords: Bank risk-taking, monetary policy, term spread
JEL classification: D22, E43, E44, E52, G21
1 University of Groningen, Faculty of Economics and Business Studentnumber: 1883232
1. Introduction
In August 2007, BNP Paribas froze three of its hedge funds, containing packages of sub-prime loans. It was the first major bank that acknowledged the risk of its exposure to the sub-prime mortgage market. One month later, British bank Northern Rock faced severe liquidity issues due to the imploding of the housing market. All of a sudden, the value of its assets decreased substantially and financial aid by the government was essential. The following distrust among deposit holders would lead to the first bank run in Britain since 150 years. In January 2008, analysts in the United States reported the largest drop in US home sales since decades (The Guardian, 2015). These were the first evident signs of what was occurring: a global financial crisis.
This crisis triggered the attention of scholars and practitioners for the functioning of the financial system and the role of banks within the system. Financial regulation and supervision fell short in preventing the serious malfunctioning of the system (Apel and Claussen, 2012). In the United States this resulted in many ‘too-big-to-fail’ institutions receiving governmental financial aid, whereas others went bankrupt. Mainly in the United States and Europe, excessive risk-taking by banks caused severe damage to economies. Many researchers have recently shown that for bank risk-taking, low interest rate environments act as an important factor.2
Figure 1. The target federal funds rate
This figure graphically presents the Federal Reserve target interbank overnight rate between January 2000 and September 2014 (Federal Reserve Bank of New York, 2015). It illustrates the low interest environment that preceded the financial crisis, and the current low target rate.
As Fig. 1 illustrates, the target federal funds rate as set by the Federal Reserve System was extremely low in the run-up to the financial crisis. This policy was mainly the result of fear for
economic slowdown due to low consumer confidence following the 9/11 terrorist attack and the dotcom bubble in the early 2000s (Altunbas, Gambacorta, and Marques-Ibanez, 2010; Gambacorta, 2009). At the time, the financial stability aspect of monetary policy was not seen as particularly threatening yet (Altunbas et al., 2010). These low rates however, led banks to search for yield (Rajan, 2006). This is because low interest rates are usually linked to a reduction in margin between lending and deposit rates, which puts pressure on a bank’s bottom line (Delis and Kouretas, 2011). Next to incentivising yield-searching, these low rates increased valuations, incomes and cash flows. This in turn led to increasing equity values of banks, and so encouraged larger position-taking (Gambacorta, 2009). Because of the crisis, scholars and policy makers are fully focused on the link between monetary policy and the risk-taking of banks nowadays (Altunbas et al., 2010). Despite the proven effect of low interest rates on bank risk-taking, the federal funds target rate currently is again very low for an extended period of time. This raises the question whether lessons have been learned from the prior crisis.
The effect of short-term interest rates on bank risk-taking is not the only important relation to look at. The term spread, which is the difference in yield on long- and short-term Treasury securities, might be important as well. The relation between the term spread and bank risk-taking is not thoroughly studied yet in an empirical way. Following the theoretical reasoning of Adrian and Shin (2010), a positive relationship is expected. The reasoning for this theory lies in the core of what banks do, namely maturity transformation. In essence, banks take short-term liabilities (i.e. deposits) and transform these in long-term assets (i.e. loans). The margin between the cost of funding and the return on loans is an important source of income. When the term spread diverges (i.e. becomes steeper), the profitability of banks increases. The increase in profit, combined with the incentive to engage more in maturity transformation, could also increase risk. The rise in income increases forward-looking measures of bank capital. As a result, banks are able to expand their balance sheets and grant loans they would not make before the rise in bank capital. When banks start expanding their balance sheets, the price of risk decreases (Adrian and Shin, 2010). Another potential effect of increasing maturity transformation is an increasing liquidity risk. Since long-term assets are less liquid than short-term assets, the occurrence of a bank run becomes more plausible, as is illustrated by the case of Northern Rock in Britain.
Prior research has mainly put focus on the levels of short-term interest rates without considering the relative gap between the short- and long-term rate. Since this gap is crucial for the profit of a bank, measuring the effect of the term spread on bank risk-taking is interesting.
bias, by showing that not including today’s inactive banks in the data set leads to an underestimation of the measured term spread impact.
The remainder of this research is structured as follows. First, existing literature on banking, interest rates and the term spread is reviewed. Second, the research methodology is presented. Third, the used data are described. Fourth, the results are presented. In the concluding section, the results and limitations are discussed and the implications of the findings for financial policymakers are presented.
2. Literature review
The term spread is constructed out of the long-term and short-term yield on Treasury securities. Hence, the gap between those two rates is the important factor. To the best of my knowledge, there is no empirical research that investigates the relation between the term spread and bank risk-taking directly yet. Therefore, analysing the relation between the two stand-alone components of the term spread and bank risk-taking is an useful starting point.
Many scholars have shown that the stand-alone short-term rate influences bank risk-taking. This fact, combined with the near perfect negative correlation that Adrian and Shin (2010) find for the United States between the federal funds target rate and the term spread, makes the short-term interest rate an important part of this literature review. However, since many authors (see, e.g., Jiménez, Ongena, Peydró, and Saurina, 2013; Maddaloni and Peydró, 2011) show that the stand-alone long-term rate has no significant effect on bank risk-taking, this variable is less relevant for this study.
2.1 The concept of banking, the term spread, and bank risk-taking
The traditional role of banks is to take deposits and grant loans (Hull, 2012). By doing so, banks serve society through mobilizing short-term financing and enabling individuals and companies to invest in long-term assets. This process is called maturity transformation. In this model, the difference in interest rates that banks charge borrowers and pay depositors is an important source of income.
The term spread, also referred to as the yield curve, is a well-known indicator of the business cycle (Estrella and Mishkin, 1997). Diebold, Rudebusch and Aruoba (2006) show that the shape of the curve strongly depends on the macro-economic variables inflation, real economic activity, and monetary policy instruments. The Treasury components of the spread are considered risk-free, which is why they are important for banks. Risk-free rates determine the cost of funds and the reward for lending. As a result, the term spread highly influences the profit a bank makes. If the term spread steepens, either short-term funding has become relatively cheaper, or long-term lending has become relatively more rewarding. If the slope of the term spread remains steep for an extended amount of time, banks earn high absolute net interest margins. Adrian, Estrella, and Shin (2010) indeed confirm empirically that the term spread increases the net interest margin of banks in the US. In theory, this subsequently increases their equity value and thus the risk-taking capacity of banks. The balance sheet expansion that might follow then decreases the market price of risk (Adrian and Shin, 2010).
2.2 Theory on the short-term interest rate and bank risk-taking
Monetary policy has a huge impact on the economy. Central banks like the American Federal Reserve System conduct their policy by setting the short-term interest rate. This ‘transmission mechanism’ operates through several channels like the traditional channel, the balance sheet channel and the bank-lending channel (see, e.g., Bernanke and Gerlter, 1995; Paligorova and Jiménez, 2012). Simply put, they are known for contributing to the expansion of credit when set interest rates are low (Gambacorta, 2009).
Fuelled by the financial crisis that started in 2007 and the preceding extended period of low interest rates, recent literature suggests that there is another channel through which monetary policy impacts the economy. For this channel, Borio and Zhu (2012) introduced the term ‘risk-taking channel’ of monetary policy. The risk-taking channel implies that banks are willing to take on more risk when interest rates remain persistently low (Paligorova and Jiménez, 2012). A vast body of empirical research indeed finds that lower interest rates lead to higher bank risk-taking in varying countries over time, hereby confirming the existence of the risk-taking channel.3 These findings on
the importance of the short-term rate oppose the perspective that prevailed until the early 2000s, stating that short-term rates mattered only to the extent that they determined long-term rates (Adrian and Shin, 2010).
However, the question remains why low short-term interest rates increase bank risk-taking. Scholars provide several explanations, of which the most prominent ones mentioned in existing
literature are the following:
First, when interest rates are low, banks can start ‘searching for yield’ through more risky investments with higher expected returns in a mean-variance portfolio perspective (Rajan, 2006). Banks that for example have to meet a specific rate of return may start moving from government bonds towards riskier high-yield investments (Apel and Claussen, 2012; Gambacorta, 2009). Second, low nominal interest rates are generally associated with a decreasing margin between borrowing rates and lending rates. Therefore, it reduces a banks charter value. As a consequence, banks soften their lending standards in search for yield, thereby increasing the level of risky assets in their portfolio (Keeley, 1990; Paligorova and Santos, 2013). Third, if the long-term rate follows the short-term rate and thus decreases, the value of (long-short-term) assets can increase more than the value of (short-term) liabilities. This is because a bank’s (long-term) assets are more sensitive to discount rate changes due to their longer duration (Adrian and Shin, 2010). In theory, equity value increases directly when this situation occurs, which frees up balance sheet capacity and hence leads to a greater loan supply. This increases banks' risk appetite. With the increased balance sheet capacity, banks also tend to take on lower quality projects that did not meet lending standards before the low interest period (Adrian and Shin, 2010). Similarly, Dell′Ariccia and Marquez (2006) suggest that low interest rates lead to a decreasing adverse selection problem, which decreases a banks incentive to screen loan applicants. Last, following increasing asset prices in low interest rate environments, collateral values increase. This affects measures of risk for loan applicants like the probability of default and loss-given-default. As a result, periods with lower asset price volatility may alter the risk perception and may release risk budgets (Altunbas et al., 2010; Bernanke and Kuttner, 2005; Delis and Kouretas, 2011; Gambacorta, 2009).
2.3 Empirical evidence on the short-term interest rate and bank risk-taking
Delis and Kouretas (2011) investigate the risk-taking behaviour of banks in Europe by looking at the extended period of low interest rates prior to the recent financial crisis. They find a strong negative relationship between multiple interest rates and bank taking. They proxy bank risk-taking by ratios of risky assets to total assets and non-performing loans to total loans (‘non-performing loans’ or ‘NPL’). They find that the low interest environment unambiguously resulted in riskier asset portfolios and deteriorating loan quality. They control for time-variant, bank-specific, and macro-economic variables.
correcting for it. This could mean that in their sample the inactiveness of banks cannot be assigned to increased bank risk-taking. However, it is interesting to check if the survivorship bias is present in the sample of this paper.
Ioannidou, Ongena, and Peydró (2014) study if expansive monetary policy impacts bank risk-taking in Bolivia between 1999 and 2003, and find a strong negative relationship. They use loan level information from the Bolivian credit register and control for several bank-specific variables, macro-economic variables, and potential bank-heterogeneity. Bank risk is amongst others measured by non-performing loans. They find that a lower US federal funds rate - the Bolivian Boliviano is pegged to the dollar - increases lending to ex-ante observable riskier borrowers with weak past performance or a low rating. In addition, banks do not price the additional risk since the relative interest premium that risky borrowers pay over safe borrowers declines. Another result of their research is that a decrease in the federal funds rate lowers the default rate on existing loans. This implies that credit risk in a bank’s portfolio decreases in the short-run after the rate goes down and is highest when the rate increases after an extended period of low levels.
Jiménez et al. (2013) conduct a similar research for Spain between 2002 and 2008. In their regressions, they control for bank-specific variables, macro-economic variables, time-varying and bank-varying effects. They also find that a lower overnight interest rate induces banks to grant more loans to firms with a bad non-performing loan history. For a lower long-term interest rate, they do not find such an effect.
Gambacorta (2009) is mainly interested in the duration of low levels of interest rates and the effect this has on bank risk. For the US and Europe, he finds a positive relation between consecutive quarters of low interest rates and bank risk-taking. He investigates whether bank risk that materialized during 2007-2008 can be explained by variables in the six years prior to this crisis. Bank risk-taking is measured by a bank’s expected default frequency (EDF), which is a forward-looking indicator of credit risk. In his ordinary least squares regression, Gambacorta controls for bank-specific variables and economic variables. The inclusion of the term spread as one of the macro-economic control variables is interesting. For this variable, he finds a negative but insignificant effect. However, in his model the linkage between the term spread and risk-taking is not of central importance. Gambacorta’s finding illustrates the importance of isolating the term spread-impact.
Maddaloni and Peydró (2011) find robust evidence that loose monetary policy softens banks’ lending standards for both firms and households in the US and Europe between 2002-2008. Thereby, they find that this mainly goes for short-term rates, rather than long-term rates, which is in line with Jiménez et al. (2013). They also find that the long consecutive period of low monetary policy rates has a big influence on bank risk-taking.
the years 1991-2008. They run ordinary least squares regressions on panel data in which they proxy bank risk by lending standards. As control variables they use several macro-economic variables and time-fixed effects. Interestingly, they also include the term spread as one of their macro-economic controls. Next to confirming the negative effect of the short-term rate on lending standards, they find that the slope of the term spread (measured by the 10-year government bond rate minus the federal funds rate) has a significant negative impact on a bank’s lending standards. This paper builds on their findings by further exploring the relation. It is worth exploring the relation in more depth since they use the term spread merely as a control factor.
Dell’Ariccia, Laeven and Suarez (2014) also find that the short-term interest rate leads to increased bank risk-taking in the United States. They analyse the internal ratings that banks assign to business loans. These internal ratings are highly correlated with the non-performing loans measure of bank risk. Through conducting least squares regressions, they find robust evidence that a lower 3-month federal funds rate leads to more ex-ante riskier borrowers obtaining loans. Table 1 sums up the empirical findings in the literature regarding the interest rate and bank risk-taking nexus.
Table 1: Empirical studies investigating the interest rate – bank risk-taking nexus
This table reports empirical findings from several scholars on the short-term interest rate and bank risk-taking nexus. The studies differ in region, period, bank risk measure, and data frequency.
NPL stands for non-performing loans, and EDF stands for expected default frequency.
Author(s) Region Period Bank risk measure Data Main findings
Delis and Kouretas (2011)
EU 2001-2008 Risky assets, NPL Quarterly, Yearly
Low levels of short-term interest rates lead to increased levels of risky assets and non-performing loans
Ioannidou, Ongena, and Peydró (2014)
Bolivia 1999-2003 NPL Monthly Low levels of short-term interest rates lead
to increased loan-granting to ex-ante riskier borrowers and reduce rates charged to these borrowers
Jiménez, Ongena, Peydró, and Saurina (2013)
Spain 2002-2008 Loan granting and credit amount
Monthly Low levels of short-term interest rates decrease bank risk-taking in the short-run but increase bank credit risk in the medium term
Gambacorta (2009)
US, EU 2007-2008 EDF Quarterly Extended consecutive periods of low
short-term interest rates increase bank risk-taking
Maddaloni and Peydró (2011)
US, EU 1991-2008 Lending standards Quarterly Low levels of short-term interest rates and extended consecutive periods of low short-term rates increase bank risk-taking Dell’Ariccia,
Laeven, and Suarez (2014)
US 1997-2011 Loan risk rating Quarterly Low levels of short-term interest rates lead to increased loan-granting to ex-ante riskier borrowers
2.4 Term spread and bank risk-taking hypothesis
short-term rate translates directly in a steeper yield curve (Adrian and Shin, 2010; Mink, 2011), the same reasoning as for the short-term rate could apply for the term spread. The second way is through an absolute increase of the gap, even when rates go up. This is the case when the long-term component rises faster than the short-term component. In both situations, the steeper yield curve could incentivise banks to engage more in maturity transformation as argued by Adrian and Shin (2010). Increased profits boost the equity capital positions of banks, which enables them to take on more leverage. Loans that were not granted before the capital increase then potentially are and the market price of risk comes down. Mink (2011) even suggests that the effect of the short-term rate on the term spread adds a new component to the risk-taking channel of monetary policy. Following the established line of reasoning, the hypothesis tested in this research is:
‘An increasing term spread leads to higher risk-taking by the banking sector in the United States’.
3. Methodology
To test the hypothesis of this study, the applied methodology is based on the short-term interest rate and bank risk-taking literature, as described in Section 2.
3.1 The model
Following the literature4, the starting statistical estimation method is the basic ordinary least
squares (OLS) regression:
𝑟𝑖,𝑡 = 𝛼 + 𝛽1 𝑖𝑟𝑡+ 𝛾𝐵𝑖,𝑡+ 𝛾𝐶𝑡+ 𝜀𝑖,𝑡 (1)
In this regression, bank risk is expressed as a function of a constant, the level of interest rates 𝑖𝑟 at time 𝑡, a set of bank specific control variables 𝐵 for bank 𝑖 at time 𝑡, a set of macro-economic control variables 𝐶 at time 𝑡 and an error term for bank 𝑖 at time 𝑡.
This research investigates the impact of the term spread on bank risk-taking. After replacing the interest rate by the term spread, denoted as 𝑇𝑆, the starting relevant ordinary least squares for testing the hypothesis is Eq. (2). As common in literature, the term spread is defined as Eq. (3).
𝑟𝑖,𝑡 = 𝛼 + 𝛽1 𝑇𝑆𝑡+ 𝛾𝐵𝑖,𝑡+ 𝛾𝐶𝑡+ 𝜀𝑖,𝑡 (2)
𝑇𝑒𝑟𝑚 𝑠𝑝𝑟𝑒𝑎𝑑𝑡= 10 𝑦𝑒𝑎𝑟 𝑇𝑟𝑒𝑎𝑠𝑢𝑟𝑦 𝑟𝑎𝑡𝑒𝑡− 𝐹𝑒𝑑𝑒𝑟𝑎𝑙 𝑓𝑢𝑛𝑑𝑠 𝑖𝑛𝑡𝑒𝑟𝑏𝑎𝑛𝑘 𝑜𝑣𝑒𝑟𝑛𝑖𝑔ℎ𝑡 𝑟𝑎𝑡𝑒𝑡 (3) Macro-economic variables that are likely to influence the level of bank risk-taking are real economic activity and inflation. An increase in the former reduces bank risk, since economic prosperity increases project profitability and so decreases credit risk (Kashyap, Stein, and Wilcox, 1993). The latter decreases bank risk as well, assumedly due to its reduction of the real debt level (Jiménez et
al., 2013).
Control variables should only be added if they influence the dependent variable, the independent variable of interest (i.e. the term spread), and if they are not outcomes of the regression themselves. Otherwise they are bad controls (Angrist and Pischke, 2008). Bikbov and Chernov (2010) and Diebold et al. (2006) show that real economic activity and inflation affect the term spread. Thereby, they are unlikely to be a direct result of the term spread. Given the above, there is a strong rationale to include economic activity (i.e. GDP growth) and inflation as macro-economic controls. They therefore are represented in the formula by 𝐶𝑡.
Different from most existing literature on interest rates, only macro-economic control variables are used in the regressions. Although bank specific controls are widely used, their inclusion is ambiguous. In this study, only the effect of the macro-economic term spread on micro-economic bank risk-taking is of interest. As mentioned, control variables should only be added if they - next to the dependent variable - also influence the independent variable of interest (Angrist and Pischke, 2008). Micro-economic individual bank characteristics are unlikely to influence the macro-economic term spread. The underlying assumption for this is that the Federal Reserve System does not take into account (aggregated) individual bank characteristics when deciding upon its monetary policy. The goals of its policy are promoting maximum sustainable output, employment, and stable prices (FRBSF, 2015). The aim of this is affecting the demand for goods and services. Since these goals are economy wide, banking sector factors are not leading in determining policy. As Altunbas et al. (2010) pointed out, at least until recently the financial stability aspect of monetary policy was not seen as particularly important. Therefore, bank specific controls are deleted from Eq. (2):
𝑟𝑖,𝑡 = 𝛼 + 𝛽1 𝑇𝑆𝑡+ 𝛾𝐶𝑡+ 𝜀𝑖,𝑡 (4)
This study focuses on how banks react to macro-economic changes. It is plausible that the group of investigated banks is heterogeneous. This means that unobserved individual characteristics of banks could influence individual banks' risk-taking (see e.g., Altunbas, Gambacorta, and Marques-Ibanez, 2012). For example, Jiménez et al. (2013) find that less capitalized banks in Spain grant more loans to ex-ante riskier borrowers if monetary policy loosens. This suggests that this has to be controlled for by holding constant the average effect for each individual bank.
control for unobserved time-varying common shocks that might affect monetary policy and bank risk -taking.
Eq. (4) does not take into account the mentioned individual bank-specific heterogeneity and changing circumstances for banks over time. A bias due to omitted variables therefore may occur. This means bank-specific characteristics and/or time varying factors may be correlated with the bank risk predictors. Adding time- and bank-fixed effects to the model solves these issues. They are denoted as 𝜏𝑡
and
𝜆𝑖 respectively. Adding both the time- and bank-fixed effects results in Eq. (5):𝑟𝑖,𝑡 = 𝛼 + 𝛽1 𝑇𝑆𝑡+ 𝛾𝐶𝑡+ 𝜏𝑡+ 𝜆𝑖+ 𝜀𝑖,𝑡 (5)
The time-fixed effects are constructed by including a dummy variable for each year 𝑡 except for one year to avoid the dummy variable trap.5 In Eq. (5), bank risk is a function of a constant, the
level of the term spread 𝑇𝑆, the macro-economic control variables real economic activity and inflation 𝐶, bank-fixed effects 𝜆, time-fixed effects 𝜏 and an error term 𝜀.
3.2 Dependent variable
Several measures for individual bank risk-taking are employed in existing literature. Examples are non-performing loans to total loans, the amount of risky assets to total assets, the z-score, and Moody’s’ exclusive expected default frequency. In addition, some scholars deduct bank risk-taking from information on individual loan levels (see, e.g., Ioannidou et al., 2014; Jiménez et al., 2013). Most measures are backward-looking accounting measures, whereas a measure like the expected default frequency is a forward looking risk indicator. Following Delis & Kouretas (2011) and Jiménez et al. (2013), this study uses the ratio of non-performing loans to total loans as main measure of bank risk. It is a direct proxy of credit risk, for which a high value is associated with higher credit risk (Delis and Kouretas, 2011).6 Non-performing loans seems a good proxy, since credit risk is the most
important risk banks face. Inserting non-performing loans in Eq. (5) yields the following baseline model:
𝑁𝑃𝐿𝑖,𝑡 = 𝛼 + 𝛽1 𝑇𝑆𝑡+ 𝛾𝐶𝑡+ 𝜏𝑡+ 𝜆𝑖+ 𝜀𝑖,𝑡 (6)
3.3 Robustness
To ensure validity of the results, several robustness checks are performed on baseline Eq. (6). First, the model is run with the z-score as alternative measure of bank risk-taking. Second, another term spread measure is applied. The long-term component of the spread remains the same, whereas
the overnight component will be replaced by the 3-month Treasury rate. Third, the baseline equation is run with the federal funds rate replacing the term spread. Hereby the goal is to test whether the model is able to confirm the findings that are discussed in Section 2. Fourth, the model is run for the separate periods 1999-2006 and 2007-2014. These different time frames allow checking if dynamics in the relation changed, which is particularly interesting because of the financial crisis that unfolded in 2007. Fifth, the BBB spread (i.e. investment grade corporate debt spread) replaces the term spread in the baseline equation. Since banks are assumed to predominantly transform short-term retail deposits into long-term corporate loans, this spread might be even more relevant for risk taking. Lastly, the baseline regression is also run on (i) a set of inactive banks, and (ii) a set of inactive banks combined with active banks. This last robustness check takes the survivorship bias into account, which is relevant because it potentially distorts the real impact of the term spread on bank risk-taking.
4. Data
In this section, the used panel data are described. First, the construction process of the main data set is elaborated upon. Second, the data set of inactive banks is introduced which serves for robustness purposes. Third, descriptive statistics and a correlation matrix of the main regression variables are reviewed. Lastly, data on the robustness variables is elaborated upon.
4.1 Data set
In this study, data on banks from the United States are used. The impact of the 2007 financial crisis illustrated the role the US banking industry has globally. Because the banking industry of the US is leading in the world of financial services, it is a logical country to focus on. Thereby, the US is well suited for investigation since it has a good availability of data.
The main dependent variable of this study is non-performing loans. Data on this variable are obtained directly from Bureau van Dijk’s Bankscope (referred to as ‘Bankscope’). Data on the macro-economic variables term spread, GDP growth and inflation are obtained from Thomson Reuters’ Datastream (referred to as ‘Datastream’). GDP growth and inflation are obtained directly, whereas the term spread is constructed manually.
Banks that became inactive during the analysed time frame are not included.
The time frame over which data is collected goes from 1999 to 2014 (i.e. 16 years). Because the time span has the financial crisis that unfolded in 2007 in the middle, it is well suited for time-differentiating comparisons ex-ante and ex-post crisis. The year 1999 is chosen as starting point because Bankscope does not provide information on non-performing loans for earlier years. To ensure that the outcomes of this study have the most value going forward, the final year choice was between the recent years 2013 and 2014. Since a balanced data set is preferable, the concern was that picking the year 2014 instead of 2013 would cause banks to drop out of the sample if they had not disclosed financial information yet. However, only 36 banks drop out the sample for this reason. Since the gain of one extra year of data is perceived more valuable than the loss of these banks (~0,6% of the sample), the year 2014 is chosen as final year.
The balanced data set contains 5,474 banks. Applying the above mentioned search criteria in Bankscope results in an unbalanced data set of 7,176 banks over 16 years. After balancing the set by erasing banks that do not have data on non-performing loans for all 16 years, 5,474 banks and 87,584 non-performing loan observations remain. This balanced data set is used as the main data set and is referred to as ‘the active data set’.
A second data set containing 3,149 inactive banks over 16 years is constructed to investigate whether the ‘survivorship bias’ exists. The survivorship bias might be a direct result of selecting banks that are still active. When all United States banks over time would have been taken into account, measured effects might be stronger. This is because defaulted banks might have reacted stronger to higher term spread levels, causing them to take on more risky portfolios and eventually become inactive.
The same search criteria have been applied to Bankscope for this set and the active data set. The only difference is that now only banks that are not active anymore are selected (i.e. they are bankrupt, in liquidation, dissolved or inactive without precision). Applying the mentioned search criteria in Bankscope results in information on 3,149 banks over 16 years. Obviously, this data set is completely unbalanced because these banks became inactive at different points in time. For example, in 2001 2,772 of the nowadays inactive US banks were still active, compared to 297 banks in 2013. This data set enables investigating possible differences in the relation between bank risk and the term spread for active- and inactive banks. It serves robustness purposes and is referred to as ‘the inactive data set’. To be able to draw conclusions about the survivorship bias, both datasets are also combined. This data set is referred to as ‘the combined data set’.
variables apply to all banks, which means there is one unique observation of these variables per year, applying to all banks. The use of annual data is in line with Ashcraft (2006), Delis and Kouretas (2011), and Gambacorta (2005). They compare yearly data to quarterly data and all find that yearly data is sufficient to identify the impact of monetary policy on bank risk. In addition, focus in this research is primarily on the level of the term spread and to a lesser extent on its change. Because risk taking by banks is considered a longer-term process, yearly observations seem well suited. Table 2 sums up the general descriptive facts of the two data sets and their combination.
4.2 Descriptive statistics and correlation coefficients
Table 3 presents the descriptive statistics of the active data set. The 5,474 analysed banks yield 87,584 observations over 16 years for non-performing loans. The macro-economic variables have 16 observations per year. The data seem fairly normal, with an average percentage of non-performing loans of 1.48%. Appendix A shows the values of the term spread, GDP growth, and inflation through time.
To obtain a first intuition about the relations, table 4 provides the correlation coefficients for the variables used in this research. Next to the variables mentioned in Table 3, it also includes correlations on the robustness measures z-score and federal funds rate.
The correlation coefficient between the term spread and non-performing loans is positive
Table 2: The data sets
This table reports information on the two data sets and the two sets combined. The active data set serves as the main data set of the study, whereas the inactive data set and the combined data set are constructed to investigate whether the survivorship bias is present.
The active data set The inactive data set The combined data set
Time-frame 1999-2014 1999-2014 1999-2014
# of banks 5,474 3,149 8,623
# of observations 87,584 26,629 114,213
Status banks Active Inactive Active + Inactive
Balanced Yes No No
Frequency Annual Annual Annual
Purpose Main set Robustness Robustness
Table 3: Descriptive statistics of the active data set
This table reports summary statistics on the active data set variables used in the empirical analysis. The variables are as follows: NPL is the ratio of non-performing loans to total loans, Term spread is the difference between the 10-year United States Treasury rate and the Federal Reserve interbank overnight rate,GDP growth is the change in GDP per year, and inflation is the CPI including all items. All observations are based on the period 1999-2014.
N Mean Standard
deviation
Minimum Maximum Year
NPL (%) 87,584 1.48 2.50 0 60.43 1999-2014
Term spread (%) 16 1.91 1.38 -0.45 3.51 1999-2014
GDP growth (%) 16 2.12 1.72 -2.78 4.69 1999-2014
and 44.4%, strengthening the intuition that a higher term spread goes hand in hand with higher bank risk-taking. The z-score, which is used as different measure for bank risk-taking, shows a negative relation with the term spread of -3.9%. This is in line with expectations since a lower z-score means higher bank risk. GDP growth and non-performing loans have a correlation coefficient of -41.4%, which is in line with the findings of Kashyap et al. (1993). Inflation, the other macro-economic control variable shows a correlation of -46% with non-performing loans. This is in line with the findings of Jiménez et al. (2013). The Federal Reserve interbank overnight rate has a high correlation of -72.9% with non-performing loans. This corresponds with the empirical findings on the interest rate and bank risk-taking nexus as shown in Section 2.3.
4.3 Robustness variables
To test the validity of the estimation model, several robustness checks are performed. The data gathering processes of the robustness check-variables are described here.
The z-score is applied instead of non-performing loans as a proxy for bank risk-taking. The z-score is a measure directly related to the probability of a bank becoming insolvent (Hesse and Cihak, 2007). It measures the number of standard deviations the return of a bank has to fall in order to deplete equity. A higher z-score thus implies a lower insolvency risk. Lepetit and Strobel (2013) suggest that the most appropriate z-score for savings banks and banks in the United States is the following: 𝑍 − 𝑠𝑐𝑜𝑟𝑒𝑖,𝑡 =
𝑅𝑂𝐴𝐴𝑖,𝑡+ 𝐶𝐴𝑅𝑖,𝑡
𝜎 𝑖,𝑡 𝑅𝑂𝐴𝐴 (7)
Where 𝑅𝑂𝐴𝐴 is the return on average assets for bank 𝑖 in current period 𝑡, 𝐶𝐴𝑅 is the capital to assets ratio for bank 𝑖 in current period 𝑡, and 𝜎 𝑅𝑂𝐴𝐴 is the standard deviation of the 𝑅𝑂𝐴𝐴, calculated over the full time frame for bank 𝑖 in current period 𝑡. The 𝑅𝑂𝐴𝐴 and 𝐶𝐴𝑅 are obtained
Table 4: Correlation matrix of the active data set
This table reports correlation coefficients of the variables from the active data set. The variables are as follows: NPL is the ratio of non-performing loans to total loans, z-score is the capital asset ratio in current period t plus the return on average assets of bank i in current period t, divided by the standard deviation of the return on average assets over the full sample period for bank i,Term spread is the difference between the 10-year United States Treasury rate and the Federal Reserve interbank overnight rate, GDP growth is the change in GDP per year, inflation is the CPI including all items, and Fed funds rate is the Federal Reserve interbank overnight rate.
To obtain valid correlations between the dependent variables with large numbers of unique N’s and the independent variables with limited unique N’s, the values of the dependent variables have been converted to 16 average values (i.e. averages per year).
NPL Z-score Term spread GDP growth Inflation Fed funds
rate NPL 1 Z-score -0.1956 1 Term spread 0.4439 -0.0394 1 GDP growth -0.4135 0.0275 -0.5823 1 Inflation -0.4606 0.0936 -0.4083 0.4323 1
from Bankscope and the 𝜎 𝑅𝑂𝐴𝐴 is calculated manually, resulting in 87,584 z-score observations. The term spread (3-month) replaces the term spread as shown in Eq. (3). The long-term component remains unchanged, whereas the federal funds interbank overnight rate is replaced by the 3-month United States Treasury rate. This different spread is constructed manually.
The Federal Reserve interbank overnight rate replaces the term spread. The rate is obtained directly from Datastream and therefore does not need adjustments.
The BBB spread replaces the term spread. It is the spread between the yield on long-term and short-term investment grade corporate bond debt in the United States. The corporate bonds used to construct the spread are the 9-year and the 1-year corporate bond. The rates on these bonds are obtained from Datastream for the period 2009-2014 as a result of data availability (i.e. 6 years). The BBB spread is constructed manually.
Appendix B shows the descriptive statistics of the robustness variables. The data show normal patterns except for the z-score which has a fairly high maximum value. Analysing the data shows that this is caused by the way the measure is calculated. The values for the z-score increase gradually through the bank sample (i.e. there are not just a few evident extreme values). The high maximum value of the measure is a result of some banks having very low standard deviations of their returns over the analysed time frame. It is expected that this has an insignificant impact on the results, because of the large number of observations (87,584) of which the mean and median are approximately 35 and 30 respectively.
5. Results
In this section, evidence is presented of the impact of the term spread on bank risk-taking. Section 5.1 shows the main findings of this study. In the Section 5.2, robustness checks are performed to shed a light on the validity of the findings. In section 5.3, special attention is paid to the difference in impact of the term spread on active and inactive banks.
5.1 Main results active data set
variables are explanatory factors of bank risk-taking. From regression 3 and onwards, bank- and time-fixed effects enter the estimation model.7 Regression 3 and 4 show that after adding bank- and
time-fixed effects the term spread still has a positive and significant effect on bank risk-taking. However, regression 4 shows that the term spread coefficient decreases after adding time-fixed effects. This suggests that unexpected time-varying variation has an impact on bank risk-taking in the sample. In regression 5, the feature of controlling for heteroscedasticity is added (i.e. ‘Robust’). By rejecting the null hypothesis of homoscedasticity, the Breusch-Pagan test shows the presence of heteroscedasticity. This is coped with by including Huber-White robust standard errors, which helps to obtain more efficient estimates, because the true errors otherwise can be underestimated (Goldberger, 1962). Inference based on robust standard errors is less dependent on the assumption of normality (Maas and Hox, 2004). The standard errors decrease in regression 5 compared to regression 4, demonstrating an efficiency gain (i.e. lower uncertainty in estimates). Regression 4 and 5, which both represent the baseline Eq. (6), indicate that a 1% increase in the term spread leads to an increase in non-performing loans of 11%.
These strong empirical results confirm the theoretical reasoning of Adrian and Shin (2010) and have important implications for policy makers. Until recently, monetary policy was considered to have no significant influence on financial stability. Policy was mainly set with a focus on maximum sustainable output, employment, and price stability. Although many scholars have already shown that the short-term rate impacts risk taking, these findings indicate that the Federal Reserve System also has to take into account the slope of the yield curve. A larger gap mechanically increases the profits of banks on newly granted loans and forward looking equity value, and therefore their risk-taking capacity.
Appendix C graphically shows the relation between the term spread and non-performing loans. As can be seen, it seems that the term spread and non-performing loans are moving closer together from 2007 onwards. This is the year the financial crisis unfolded and it is interesting to compare the dynamics of the relation before and after the crisis. This is investigated in Section 5.2.
5.2 Robustness checks active data set
Appendix D reports the results of the performed robustness checks on the active data set. In regression 6 to 10, non-performing loans is the dependent variable, whereas regression 11 uses the z-score as its dependent variable.
Regression 6 shows the effect of the term spread on non-performing loans for the period 1999-2006. The measured impact is highly significant and 2.7%. Interestingly, regression 7 shows that the term spread impact is economically drastically stronger in the period following the financial crisis (53%). As graphically illustrated in Appendix C, the two variables seem to be much more related during- and after the crisis than before. This puts in perspective the measured impact of the term spread on bank risk-taking over the whole time period (11%), since it potentially is mainly caused by the period 2007-2014 where the target federal funds rate amounted zero the majority of the time. In addition, regression 7 shows that the impact of the macro-economic control variables changes drastically in the period 2007-2014, compared to both the whole time frame and the post-crisis period. The sign of the real economic activity measure becomes positive (28.8%) and the negative inflation coefficient increases substantially (-50.7%).
Regression 8 shows that irrespective of the rate used as the short-term component of the
Table 5: Main results active data set
This table reports regression coefficients and standard errors (in parentheses). The variables are as follows: NPL is the ratio of non-performing loans to total loans, Term spread (10yr-overnight) is the difference between the 10-year United States Treasury rate and the Federal Reserve interbank overnight rate,GDP growth is the change in GDP per year, and inflation is the CPI including all items. Baseline Eq. (6) is used for regression 4 and 5.
*, ** and *** represent statistical significance at p<0.1, p<0.05 and p<0.01.
1 2 3 4 5
VARIABLES NPL NPL NPL NPL NPL
Term spread (10yr-overnight) 0.320*** (0.00606) 0.170*** (0.00756) 0.170*** (0.00649) 0.110*** (0.0147) 0.110*** (0.00710) GDP growth -0.0840*** (0.00612) -0.0840*** (0.00525) -0.166*** (0.00992) -0.166*** (0.00561) Inflation -0.300*** (0.00942) -0.300*** (0.00809) -0.197*** (0.0101) -0.197*** (0.00717) Constant 0.868*** (0.0142) 2.042*** (0.0333) 2.042*** (0.0286) 1.739*** (0.0342) 1.739*** (0.0223) Bank-fixed effect Time-fixed effects Robust Yes Yes Yes Yes Yes Yes # of banks 5,474 5,474 5,474 5,474 5,474 # of observations 87,584 87,584 87,584 87,584 87,584 R-squared (within) 0.068 0.222 0.222 Period 1999-2014 1999-2014 1999-2014 1999-2014 1999-2014
term spread, the impact remains statistically significant and about equal (11% versus 12.6%). Regression 9 confirms the findings from the existing literature. Replacing the term spread with the short-term federal funds rate yields a strong negative relationship (-55.2%), which strengthens the reliability of the model. Regression 10 shows that for the corporate bond spread – between the years 2009 and 2014 –, the model still yields the expected outcome. The BBB spread has a relatively high coefficient of 37.2%, which seems plausible because banks are mainly expected to lend to companies. Therefore, the BBB spread may be a stronger determinant of bank risk-taking than the Treasury securities spread. In fact, the term spread shows an evenly significant but economically less strong coefficient of 15.1% over the same time span. For simplicity purposes this result is not reported in this study. The results of regression 11 show that, irrespective of the measure used to proxy bank risk-taking, the baseline Eq. (6) yields the expected result. A strong statistically and economically significant negative impact of the term spread on the z-score is found (-52.1%). As can be derived from Eq. (7), since a steeper yield curve results in higher bank profits and increased equity value, this finding implies that the standard deviations of the return on assets of banks become relatively larger when the spread increases.
5.3 Robustness checks inactive and combined data set
Appendix E reports the regression results of the inactive banks data set and the combined set. Regression 12 shows the results when controlling for GDP growth, inflation, and bank-fixed effects. Regression 13 in addition also controls for time-fixed effects and regression 14 adds robust Huber/White standard errors. The results show a very similar pattern compared to the fundamental regressions of this study shown in Table 5 in Section 5.1. Both, regression 5 and regression 14 show statistically and economically highly significant coefficients. Thereby, the signs of the three regressors are identical. However, the values of all coefficients in regression 14 are higher. The effect of the term spread is larger for this data set (16.4% versus 11%), which suggests a higher impact of the term spread on the risk-taking of banks that eventually became inactive. However, based on these results, it is not yet possible to make statements regarding the exact influence this has on the total bank set of the US. Therefore, in regression 15 the combined data set is used (i.e. the combination of the active- and the inactive set). The coefficient of the term spread now becomes 12%, which indicates an impact increase of 1%.
non-performing loans is mainly driven by new riskier loans, or by existing loans non-performing worse. It is apparent that there indeed is a survivorship bias when only active banks are considered. Hence, the above suggests that the measured impact of the term spread based on the active data set is understated. This finding is also important as it suggests that scholars have to take into account the potential survivorship bias in similar studies when interpreting results.
6. Conclusion
Fuelled by the financial crisis, monetary policy and bank-risk taking now have the full attention of scholars and practitioners. Recent literature proves that short-term rates lead to increased bank-risk taking. Since monetary authorities like the Federal Reserve System determine the short-term rate, this has important policy implications. The phenomenon of banks getting an increased risk appetite when short-term interest rates remain low is called the risk-taking channel of monetary policy.
However, the impact of the term spread on bank risk-taking has not been thoroughly researched yet. The main objective of this study is to test whether an increase in the slope of the yield curve increases bank risk-taking. This research finds that the term spread indeed is another influential factor, possibly because the slope of the spread directly affects a bank’s profits and risk-taking capacity.
Least squares regressions are applied on a large set of panel data of banks in the United States between 1999 and 2014. Bank risk-taking is measured by the ratio of non-performing loans to total loans and the term spread is constructed out of the yield on the 10-year United States Treasury rate and the federal funds interbank overnight rate. The applied regressions control for macro-economic control variables, time- and bank-fixed effects. Bank specific control variables are not included, since inclusion might lead to a bad control bias.
The findings are robust for a wide set of variations in estimations: instead of non-performing loans the z-score is applied, and instead of the term spread, the stand-alone federal funds rate, the BBB-spread, and the difference between the 10-year and 3-month United States Treasury yield are applied. Furthermore, the time frame before- and after the financial crisis is used.
Furthermore, an extra data set of inactive banks is constructed to investigate if the survivorship bias is present. It shows that these banks on average had much higher percentages of non-performing loans in their portfolios. This mainly materialized when the crisis erupted and could be a reason for their inactiveness. As a result, the measured coefficient of the term spread based on the active data set is understated. When controlling for this survivorship bias, the impact of the term spread is stronger.
This study suggests that monetary authorities such as the Federal Reserve have to take into account not only the term interest rate, but also the gap between the long-term and short-term interest rate when conducting monetary policy. This reinforces the suggestion of an addition to the risk-taking channel of monetary policy: one in which a larger term spread (through monetary policy) leads to increased risk-taking by banks.
The main limitations of this study are related to the data frequency, the estimation technique used, causality, and the number of explanatory variables included. Although scholars have shown that the use of yearly data is sufficient to measure the impact of monetary policy, it is interesting to see if the results of this study are confirmed when for example quarterly data is used. The estimation technique used is basic, which makes the results straightforward to interpret. However, combined with more frequent data, a dynamic model with lagged variables might provide more insights. In addition, there are also causality issues since it is possible that bank risk-taking affects future long- and short-term rates. Furthermore, there still might be an omitted variables bias. Supplementing the model with additional explanatory variables that affect both bank risk-taking and the yield curve could result in more accurate estimates of the impact the term spread has.
7. Appendices
Appendix C: The term spread and bank risk-taking
This figure graphically presents the relationship between the ratio of non-performing loans to total loans and the term spread, measured by the difference between the 10-year United States Treasury rate and the Federal Reserve interbank overnight rate. The data used for the graph consist of 16 data points for the term spread, and 16 average non-performing loans data points.
Appendix A: Macro-economic variables
This table reports the values of the macro-economic variables term spread, GDP growth, and inflation of the US in percentage points. The variables are obtained from Datastream. The term spread is constructed manually and is the difference between the 10-year United States Treasury rate and the Federal Reserve interbank overnight rate, GDP growth is obtained directly and is the change in GDP per year, inflation is obtained directly and is the CPI including all items. Year 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 Term spread (%) 0.34 -0.37 3.20 3.37 3.04 2.11 0.13 -0.45 0.39 3.51 3.14 3.03 2.72 1.64 2.26 2.42 GDP growth (%) 4.69 4.09 0.98 1.79 2.81 3.79 3.35 2.67 1.78 -0.29 -2.78 2.53 1.60 2.32 2.22 2.39 Inflation (%) 2.19 3.37 2.82 1.60 2.30 2.67 3.37 3.22 2.87 3.81 -0.32 1.64 3.14 2.08 1.46 1.61
Appendix B: Descriptive statistics robustness variables
This table reports summary statistics on the robustness variables used in the empirical analysis. The variables are as follows: Z-score is the capital asset ratio in current period t plus the return on average assets of bank i in current period t, divided by the standard deviation of the return on average assets over the full sample period for bank i,Term spread (3-month) is the difference between the 10-year United States Treasury rate and the 3-month United States Treasury rate, Fed funds rate is the Federal Reserve interbank overnight rate and the BBB spread is the difference between the 9-year and 1-year United States corporate bond market yield.
N Mean Standard
deviation
Minimum Maximum Year
Z-score 87,584 35.88 25.66 -3.566 292.3 1999-2014
Term spread (3-month) (%) 16 1.905 1.375 -0.450 3.510 1999-2014
Fed funds rate (%) 16 2.027 2.188 0.070 6.400 1999-2014
Appendix E: Robustness checks inactive & combined data set
This table reports regression coefficients and standard errors (in parentheses) for robustness checks on the inactive banks data set and the combined data set. The variables are as follows: NPL is the ratio of non-performing loans to total loans, Term spread (overnight) is the difference between the 10-year United States Treasury rate and the Federal Reserve interbank overnight, GDP growth is the change in GDP per year, inflation is the CPI including all items. Baseline Eq. (6) is used for regression 13, 14, and 15.
*, ** and *** represent statistical significance at p<0.1, p<0.05 and p<0.01.
12 13 14 15
VARIABLES NPL NPL NPL NPL
Term spread (overnight) 0.0328** 0.164*** 0.164*** 0.120***
(0.0132) (0.0296) (0.0194) (0.0132) GDP growth -0.201*** -0.290*** -0.290*** -0.185*** (0.0120) (0.0188) (0.0159) (0.00877) Inflation -0.367*** -0.303*** -0.303*** -0.214*** (0.0194) (0.0221) (0.0242) (0.00922) Constant 2.612*** 2.471*** 2.471*** 1.848*** (0.0696) (0.0788) (0.0889) (0.0317)
Bank-fixed effects Yes Yes Yes Yes
Time-fixed effects Yes Yes Yes
Robust Yes Yes
# of banks 3,148 3,148 3,148 8,622
# of observations 26,629 26,629 26,629 114,213
R-squared (within) 0.059 0.222 0.222 0.214
Period 1999-2014 1999-2014 1999-2014 1999-2014
Data set Inactive Inactive Inactive Combined
Appendix D: Robustness checks active data set
This table reports regression coefficients and standard errors (in parentheses) for robustness checks on the active data set. The variables are as follows: NPL is the ratio of non-performing loans to total loans, Term spread (overnight) is the difference between the 10-year United States Treasury rate and the Federal Reserve interbank overnight, Term spread (3month) is the difference between the 10-year United States Treasury rate and the 3-month United States Treasury rate. Fed funds rate is the Federal Reserve interbank overnight rate, the BBB spread is the difference between the 9-year and 1-year United States corporate bond market yield, GDP growth is the change in GDP per year, and inflation is the CPI including all items. Baseline Eq. (6) is used for all shown regressions.
*, ** and *** represent statistical significance at p<0.1, p<0.05 and p<0.01.
6 7 8 9 10 11
VARIABLES NPL NPL NPL NPL NPL Z-score
Term spread (overnight) 0.0267*** (0.00643)
0.530*** (0.0115)
-0.521*** (0.0345)
Term spread (3-month) 0.126***
(0.00815)
Fed funds rate -0.552***
(0.0117) BBB spread 0.372*** (0.0224) GDP growth -0.0408*** (0.00559) 0.288*** (0.00863) -0.158*** (0.00585) 0.256*** (0.00816) 0.024** (0.00743) -0.411*** (0.03593) Inflation -0.0156 (0.0158) -0.507*** (0.0119) -0.203*** (0.00723) -0.436*** (0.0109) 0.206*** (0.0143) 0.419*** (0.0270) Constant 0.784*** (0.0516) 1.579*** (0.0258) 1.701*** (0.0235) 3.246*** (0.0382) 1.171*** (0.0767) 35.78*** (0.0516)
Bank-fixed effects Yes Yes Yes Yes Yes Yes
Time-fixed effects Yes Yes Yes Yes Yes Yes
Robust Yes Yes Yes Yes Yes Yes
# of banks 5,474 5,474 5,474 5,474 5,474 5,474
# of observations 43,792 43,792 87,584 87,584 32,844 87,584
R-squared (within) 0.009 0.143 0.222 0.222 0.0544 0.018
Period 1999-2006 2007-2014 1999-2014 1999-2014 2009-2014 1999-2014
Appendix F: Non-performing loans development
This figure reports the development of the average percentage of non-performing loans to total loans per year between 1999-2014 in bank-portfolios from two different data sets. These are the set of active banks in a balanced format and the set of inactive banks in an unbalanced format. The figure provides an intuition for the different levels of impact the term spread possibly has had on active and inactive banks.
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