The slope of the yield curve, profitability and bank
risk-taking; evidence from the US
Willem Jongbloed Master Thesis 13th of June, 2016
Abstract
This paper exposes the slope of the yield curve to be a determinant factor in banks’ risk-taking behavior, and provides evidence that profitability from maturity transformation plays a role in this relationship. The research thereby contributes with an alternative explanation for increased credit risk exposure among banks in pre-crisis years, which by existing research is attributed to a prolonged period of low interest rate levels and expansionary monetary policy. A large panel dataset containing quarterly observations on 1415 US banks between 2001 and 2008 is subjected to a bank-specific ordinary least squares regression analysis on risk behavior, as well as a sensitivity analysis to monitor monetary policy implications. The results provide evidence for a positive impact of the slope of the yield curve on risk-taking, and that this effect is amplified by a risk-taking channel of profitability with regards banks’ non-performing loan ratios. These findings recommend consideration of the yield curve slope when setting the monetary target rate.
Keywords: slope of the yield curve, profitability, net interest margin, bank risk-taking, US banks, panel data, monetary policy.
Student number: 1893939 Supervisor: dr. Y.R. Kruse
Program: MSc Finance
2 1. Introduction
In performing their indispensable role as financial intermediaries, banks rely heavily on interest rates to earn profits from the practice of maturity (or term) transformation. By taking on short-term deposits to fund the provision of long-short-term loans, they derive their profits from the spread between short- and long-term interest rates. As such, a bank’s profitability – recorded on its income statement as net interest income – is directly affected by the slope of the yield curve representing this spread. Currently however, there is an expanding discussion on additional effects of interest rates, specifically on the consequences of managerial responses to certain levels of interest rates. Studies such as Delis and Kouretas (2011), Dell’Ariccia et al. (2014), and Drakos et al. (2014) argue that a period of low interest rates may raise the risk-taking incentives of a bank, in an attempt to achieve higher yields. An important assumption being made is that a prolonged period of low interest rates usually occurs on both ends of the yield curve, flattening the slope of the curve and limiting the income from maturity transformation. Consequently, the urge to engage in riskier investments with higher payoffs is said to gain ground. The debate has attracted significant attention since the recent financial crisis, with strong accusations that risk-taking behavior, following a period of low interest rates in the mid 2000’s, has ultimately led to bank failures and the collapse of the financial system. Among others, Borio & Zhu (2008) additionally point out the role of monetary policy as a ‘risk-taking channel’, as choosing an expansionary policy may backfire and cause banks to take risky actions and increase their exposure to credit risk.
This paper questions whether the level of interest rates is the primary source of bank risk-taking and proposes that the role of profitability that lies in the term spread is being underestimated. From a sample of bank risk-taking and interest rates in the US during the pre-crisis years, it can be observed in Figure 1 that low interest rates are not necessarily associated with a flatter yield curve. In fact, the interest rate spread picks up as the monetary rate declines, and it is during this period of wider term spreads that banks experience a higher ratio of non-performing loans. This leads to wondering whether the achievable profits from a favorable term spread, more importantly than the low levels of interest rates, have motivated banks to soften their risk standards. While it is not the intention of this paper to disprove the above assumption that a flat yield curve creates an appetite for risk, it should be explored if there is reason to suggest that a steep yield curve has a similar impact on bank risk-taking.
3 have. In similar fashion, De Nicoló et al. (2010) mention the existence of a risk-taking effect when rates are high, provided that the bank operates with limited liability and is poorly capitalized. These examples provide a theoretical basis to expect that the prospects of increased earnings from maturity transformation when the slope of the yield curve is high, may in fact incentivize banks to exploit the opportunity of additional income and accept higher levels of risk doing so. As opposed to existing analyses, the focus should therefore be on the interest rate spread, rather than interest rate levels, when investigating drivers of risk-taking behavior among banks. A better understanding of the term spread as a source of risk-taking may then lead to more accurate recommendations regarding the formation of monetary policy (Mink, 2011).
The current paper adds to existing literature by proposing that (i) an empirical assessment of the slope of the yield curve and its direct relation to bank risk-taking has so far not been explored, that (ii) this relationship can be expected to be positive, and that (iii) if the relationship is indeed positive, profitability is expected to be an intermediate channel of risk-taking. In other words, the aim is to
Figure 1. Market-level interest rates and risk-taking in the US. The figure reports the long-term Treasury Bill
4 analyze whether bank risk-taking is incentivized by higher profitability as the slope of the yield curve is high. In doing so, the research monitors a range of measures of the yield curve slope and their relation to the risk-taking behavior of a sample of US banks between 2001 and 2008. Measurements of the net interest margin may confirm profitability to be an intermediate channel of risk, and an assessment of the monetary rate provides possible policy implications from this new perspective of bank risk-taking.
1.1 Theoretical background
A leading study in the aforementioned debate is that of Delis and Kouretas (2011), which contributes empirical evidence from a sample of European banks and shows that low interest rates spur risk taking behavior. They build on the propositions by Dell’ Ariccia and Marquez (2006), Rajan (2006), and Keeley (1990) that low interest rates are coupled with intensified competition and a reduced incentive to bear the costs of screening borrowers for quality. It is further suggested by Delis and Kouretas (2011) that combined with the decline in interest rate volatility associated with low rates, an increased pressure on bank margins releases risk budgets and incentives for banks to search for higher yields in riskier projects. Banks do so by lowering their lending standards and investing in riskier loans that carry a greater risk of default. Following Dell’ Ariccia and Marquez (2006), this strategy is then thought to significantly affect the bank’s credit risk position, and on a national scale can result in a heightened risk of a financial crisis.
The role of monetary policy receives significant attention in the discussion. Between 2001 and 2004, the US government elected a low interest rate (expansionary) policy to boost consumer confidence and promote home ownership (see Federal Funds rate in Figure 1), which resulted in banks relaxing their lending standards and making the subprime loans that built up to the default crisis (see, e.g., Keys et al., 2010; Mian and Sufi, 2009). This connection between government policy and bank risk-taking is thus, not surprisingly, of interest to researchers such as Brissimis and Delis (2010), Borio and Zhu (2008), and Ioannidou et al. (2009), who find that monetary policy is strongly related to the issuance of inferior loans. The monetary interest rate is indeed an important base rate for other short-term interest rates, and it is a key economic indicator as it translates governmental targets with regards to inflation, investment and unemployment. But in those pre-crisis years, as the central bank responded with an expansionary policy to market participants’ pleadings for financial alleviation, the result was an increased appetite for credit risk among banks (Jimenez et al., 2008). This has led theorists to question the risk implications of monetary policy.
5 address the issue by assessing the level of several interest rates, the role of profitability that lies in the slope of the yield curve is however still not considered. This spread is an important determinant for the actual performance of the bank (see Alessandri and Nelson, 2015) and can play a key role in bank management decisions regarding lending standards and interest rate pricing.
The practice of maturity transformation forms the core business of traditional commercial banking. The interest income earned on loans in excess of the interest paid on deposits makes up the net interest income that is recorded as profit. A bank’s profitability from maturity transformation is then described as the net interest margin; how the net interest income compares to the value of the interest-earning assets. The slope of the yield curve plays a crucial role in this income strategy, as it represents the spread between the short- and long-term market interest rates. The rates banks eventually pass through to borrowers and lenders are based on these market rates and subject to fluctuations in the market. Changes in the slope of the yield curve thus have a direct effect on the net interest income that ends up on the balance sheet as profit, as well as on the net interest margin that marks the bank’s profitability (see e.g., Ho and Saunders, 1981; Saunders and Schumacher ,2000; Memmel, 2011; Entrop et al., 2015). Consequently, if banks derive their profit margins from the term spread, and the state of this margin – as assumed by Delis and Kouretas (2011) and references therein – provides incentive for risk-taking, then profitability is arguably the intermediary in a two-step relationship between the interest rate environment and bank risk-taking. This ‘risk-taking channel of profitability’, which as opposed to the monetary policy channel of Borio and Zhu (2008) is determined by the slope and not the level of interest rates, may be an alternative explanation for the observed trend of risk-taking in the period of interest. A key element of this proposition however is that banks have a reason to raise, not lower, their risk appetite when the term spread is in their favor. Such reasons will be considered in the following section.
1.2 From slope to risk
This paper’s two-step reasoning of a positive relationship between the slope of the yield curve and bank risk-taking requires an understanding of both the ‘slope-profitability’ and ‘profitability-risk-taking’ relationships. Before discussing whether from a managerial point of view it can be assumed that profitability levels influence risk-taking decisions, It should initially be explored how banks interpret the yield curve and decide on the pricing of their loans and deposits.
6 with a simultaneous new deposit, the bank has to borrow funds in the money market. This long position in the money market exposes the bank to refinancing risk if the short-term market interest rate rises, and for bearing this ‘yield curve risk’ banks independently demand an optimal interest mark-up when they set their loan rates (see also Gambacorta, 2008; Entrop et al., 2011; Memmel, 2011). Depending on the bank management’s risk aversion, market power, the magnitude of the transactions, loan and deposit demand, and the volatility of interest rates, the size of this mark-up determines the interest rate eventually charged to the bank’s customers. Banks thus partly have an own hand in determining their profitability, as adjusting their deposit and loan rates depends on both the ‘true’ market interest rate spread and the mark-up that they deem necessary to cover for their yield curve risk in the short run.
The above implies that a change in the interest rate spread affects profitability. Though many theorists agree on this positive relationship between short-long spreads and net interest margins based on the workings of maturity transformation1, Gambacorta (2008) and Alessandri and Nelson (2015) argue that this relationship is more complex and specifically differentiate between the short- and long-run transmissions of market interest rate fluctuations to loan rates. They point out that due to repricing frictions on loan rates in the short run – banks can’t simply adjust their loan rates on a daily basis – rising market interest rates will initially translate into higher funding costs resulting from deposit rates that are adjusted much quicker, implying a depressed net interest margin. It is not until banks have responded with the pass through of repriced long-term loan rates, that the net interest margin shows a positive response to rising market rates. By similar logic, for a given short-term interest rate, a rising long-term market rate will cause the bank to pass through higher loan rates, eventually improving the net interest margin in the long run. So although banks already account for yield curve risk when setting loan and deposit rates, repricing frictions will prevent them from swiftly passing through adjustments on their mark-ups. Nevertheless, in the long run, a rising slope of the yield curve will have a positive impact on the net interest margin.
Having clarified the slope-profitability nexus, the question remains how profitability from maturity transformation affects bank risk-taking, and whether this relationship can be expected to be positive. Martynova et al. (2015) provide a fitting discussion on the subject and question the traditional consensus that higher profitability reduces risk-taking to preserve shareholder value (Keeley, 1990). By differentiating between a bank’s core business and its engagement in risky side activities, they argue that a more profitable core business allows a bank more leverage and incentive to take side risks. Although such a differentiation between business activities does not apply to the concept of risky lending in this paper (since lending is considered a core activity), the argumentation that a well performing bank is more comfortable with additional risk is of interest. In this respect,
7 Calem and Rob (1999) show in a U-shaped pattern that banks tend to first lower their risk appetite, but as profits grow and capital continues to build, capital requirements become relatively less restrictive and the bank is more willing to take an occasional loss, raising the share of risky assets in its portfolio. This ‘diminishing value of risk’ would suggest that rising interest rate spreads can provide a cushion to take on riskier loans with even higher payoffs. Another capital-based approach, which highlights the high starting point of Calem and Rob’s U-curve is provided by Blum (1999), who suggests that banks engage in risk-taking in order to generate the profits necessary to answer to capital requirements in the first place. Such under-capitalized banks would be extra motivated to haul in excess profits when a higher interest rate spread offers the chance. This theory is also in line with the ‘under-capitalized’ motives for risk taking put forward by De Nicoló et al. (2010) and the distributional effects of capitalization observed by Delis and Kouretas (2011).
Besides a capital-based view on the motivation for risk-taking in profitable times, the ownership structure of a bank is equally of concern. Limited liability among shareholders and managers, as well as asymmetric information between shareholders and managers, are potential ingredients for excessive risk-taking. Jensen and Meckling (1976) analyze these agency problems in detail and explain that the incentive of a bank manager is to maximize his own utility. As the losses on a risky investment are not carried by bank management and accrue to a large group of individual shareholders, both management and shareholders have a lower incentive to take into account the ultimate welfare of the bank and its depositors. In this respect, De Nicoló et al. (2010, p.4) describe that “a leveraged bank will prefer a risky investment that yields a higher private payoff in case of positive outcomes – but involves large losses for depositors in case of failure – to a more prudent investment that generates a higher net present value.” Such incentives would be especially present when the core business becomes relatively more profitable as the yield curve slopes up. For a profit-maximizing bank in that case, the opportunity cost of holding risk-free assets increases as it forgoes the option to earn higher payoffs from the favorable interest rate environment, up to the point where it becomes more profitable to increase risky lending. Finally, Laeven and Levine (2009) lean more to the risk appetite of shareholders by differentiating between diversified owners who have a small fraction of their personal wealth invested in the bank (high incentive for risk), and non-shareholder managers with bank-specific human capital skills and private benefits of control (low incentive for risk). They conclude that banks with an emphasis on diversified ownership structure therefore tend to exercise higher risk-taking.
8 payoffs – which increases as the term spread becomes steeper. In his theoretical model, this cost advantage facilitates increased income from maturity transformation, from which they can increase their leverage at a lower cost. With a relatively lower amount of equity, the risk of insolvency is thereby increased when the bank’s assets drop in value. Additionally, the cost advantage allows banks to engage in portfolio diversification and lower their lending standards in a competitive market, with increased exposure to credit risk as a result. The effects of deposit insurance in case of a higher term spread is further amplified when a bank possesses greater market power, as such a ‘too-big-to-fail’ status (Boyd and Runckle, 1993) provides greater certainty of a bailout and improves the borrowing cost advantage of a bank.
In conclusion, the arguments of (under- or over-) capitalization, ownership structure and moral hazard provide sufficient basis for expecting banks to take on more risk when the term spread is high, even though this more profitable position of the yield curve would traditionally suggest the opposite. As such, the first hypothesis to be tested by this research can be formulated as:
H1: the slope of the yield curve is positively related to bank risk-taking.
Additionally, it is shown that a steeper yield curve translates into higher profit margins for the bank via the net interest margin from maturity transformation (Alessandri and Nelson, 2015). This increased profitability may contribute to the positive relationship mentioned in the first hypothesis. As such, the significance of a risk-taking channel of profitability is tested by answering whether:
H2: bank profitability from maturity transformation amplifies the impact of the slope of the yield curve on bank risk-taking.
Similar to the approach by Delis and Kouretas (2011), the emphasis of this research is primarily on exposing the above relationships from the perspective of bank behavior. It is only after drawing conclusions on the risk-taking responses of banks to the interest rate spread, that inferences should be made on the consequences of monetary policy formation. This is done by performing a sensitivity analysis on the effects of expansionary monetary policy on banks’ interpretation of the yield curve slope. It is then expected that the conclusions from this paper contribute in a complementary fashion to existing theories on the risk-taking channel of monetary policy, by proposing that the term spread, in addition to the level of the interest rates, should be considered by policy makers when determining the target monetary rate.
9 2. Methodology and data
The considered empirical model for this research explores primarily the relationship between the slope of the yield curve and bank risk-taking. It is of the following form:
𝑟𝑖𝑡 = 𝛼 + 𝛽1𝑆𝑖𝑡+ 𝛽2𝑏𝑖𝑡+ 𝛽3𝑐𝑖𝑡+ 𝑢𝑖𝑡 (1)
where dependent variable, r, represents the measure of bank risk-taking, and is written as a function of the slope of the yield curve, S, a set of bank-level control variables, b, and a set of regulatory and structural control variables, c. The model closely resembles that of Delis and Kouretas (2011), but considers specifically the interest rate spread rather than the level of interest rates. As the dataset concerns US banks only, country-level control variables have been replaced by a set of regulatory and state-level structural control variables (see section 2.3). In line with the theoretical proposition of this paper, the model is expanded with the net interest margin in further analysis to assess the role of profitability as an intermediate channel of risk-taking (see section 3.2). A sensitivity analysis on the implications of monetary policy concludes the research. Below follows a discussion on the dataset and variables. Table 1 provides descriptive statistics of the variables used throughout the analysis. Table 2 reports the correlation matrix of these variables.
The analysis is performed on a large unbalanced panel dataset containing quarterly data on a selection of US banks over the period 2001-2008. The data includes active commercial, savings and cooperative banks only, following the argumentation of Delis and Kouretas (2011) that other types of banks are not engaged in the type of commercial maturity transformation activities discussed in this paper. To limit the size of the dataset, only the upper quartile of all banks in terms of total assets are considered (at the end of 2001). Most of the data is collected from the Bankscope database2, which, after applying the above selection criteria, provides information on 1435 banks. Another 20 banks have been excluded from the analysis due to either a limited availability of information on multiple variables, outlier issues concerning the bank-level measure of the slope variable (see section 2.2), or because their existence does not extend across the full time frame of the sample. The latter justification for exclusion implies that the dataset is free of survivorship bias due to bank failures, mergers or acquisitions. The final dataset contains information on 1415 banks.
Choosing the United States as a background for this research is justified by the intention to identify the source of risk-taking at the heart of the financial crisis. Since the recent debate regarding auxiliary effects of interest rate levels on risk-taking has had a notable focus on the causes of the global recession, it can only be considered appropriate to (possibly) expose an alternative explanation for risk-taking close to the source. From similar reasoning, the time frame is chosen for the purpose of
10 comparison between the low interest rates that have so far been seen as the cause of the crisis, and the higher term spread observed in the same period that is proposed here as the underlying source of risk-taking.
A note on the use of quarterly data. Although there exists some disagreement on the speed and scale of the pass-through of market interest rate fluctuations to loan rates3, it can surely be argued that banks adjust their loan rates more frequently than on a yearly basis. In this respect, the use of annual data on the interest rate spread is arguably not sufficient to analyze its effect on bank risk-taking. Delis and Kouretas (2011) suggest that their focus on longer term levels of interest rates, rather than short-term responses to changes in the interest rates, justifies the use of annual data in assessing the effects on risk-taking. Though considering the long-term nature of the extended loans to possibly riskier borrowers, a short-term response of risk taking to changing interest rate levels may have long lasting effects on the bank’s credit position. Where an annual dataset may overlook such an intermediate risk-taking response, using quarterly dataset will capture more detailed variations and can enrich the
3
Gerali et al. (2010) and Gertler and Karadi (2011) provide opposing views on the magnitude of the pass-through of monetary shocks to customer-end interest rates.
Table 1
Descriptive statistics.
Variable Mean Std. deviation Min Max Observations
Z-score 4.341 1.083 -3.246 10.093 45173 NPL ratio 0.745 1.328 0.000 42.300 44791 Risk assets 96.802 2.023 61.470 100.000 45232 Slope market 1 1.237 1.404 -0.774 3.291 45280 Slope market 2 1.518 1.399 -0.617 3.590 45280 Slope market 3 1.730 1.275 -0.437 3.503 45280 Slope market 4 1.779 1.367 -0.236 3.859 45280 Slope market 5 2.060 1.350 -0.113 4.050 45280 Slope market 6 2.273 1.242 0.080 4.003 45280 Slope bank 1.626 1.210 -14.700 115.430 45154
Net interest margin 3.977 1.794 -20.355 48.912 45232
Size 13.346 1.133 7.965 21.293 45232
Capitalization 10.332 4.228 -1.049 87.049 45232
Lagged profitability 0.607 8.568 -44.058 1142.000 43791
Efficiency 137.439 180.677 -29477.270 13281.250 45227
Off-balance sheet items 142.937 5139.737 0.000 288644.600 45232
Supervision 2.988 1.059 1.000 6.000 45280
District 6.447 3.345 1.000 12.000 45248
Concentration 0.210 0.213 0.023 1.000 45248
11
Table 2 Correlation Matrix.
Z-score NPL ratio Risk assets Slope market 1 Slope market 2 Slope market 3 Slope market 4 Slope market 5 Slope
market 6 Slope bank
Net interest
margin Size Capitalization
Lagged
profitability Efficiency
Off-balance
sheet items Supervision District Concentration
Z-score 1.000 NPL ratio -0.251 1.000 Risk assets 0.020 0.033 1.000 Slope market 1 -0.045 0.009 -0.097 1.000 Slope market 2 -0.095 0.053 -0.082 0.955 1.000 Slope market 3 -0.112 0.076 -0.077 0.928 0.979 1.000 Slope market 4 -0.046 0.011 -0.097 0.996 0.944 0.927 1.000 Slope market 5 -0.097 0.057 -0.082 0.956 0.996 0.985 0.953 1.000 Slope market 6 -0.114 0.079 -0.076 0.917 0.963 0.995 0.925 0.977 1.000 Slope bank -0.032 0.049 -0.139 0.073 0.053 0.046 0.074 0.055 0.047 1.000
Net interest margin -0.100 0.083 -0.234 0.051 0.040 0.032 0.052 0.041 0.033 0.392 1.000
Size -0.002 0.025 0.030 -0.105 -0.080 -0.074 -0.108 -0.084 -0.077 -0.100 -0.053 1.000
Capitalization 0.090 0.033 0.124 -0.055 -0.051 -0.046 -0.056 -0.052 -0.046 0.116 0.138 -0.041 1.000
Lagged profitability 0.025 -0.015 0.009 -0.001 -0.002 -0.002 -0.001 -0.002 -0.001 0.039 0.010 -0.017 0.060 1.000
Efficiency 0.009 -0.005 -0.032 0.026 0.023 0.019 0.024 0.021 0.017 0.109 0.223 0.018 0.022 0.011 1.000
Off-balance sheet items 0.016 -0.011 0.014 -0.012 -0.011 -0.010 -0.012 -0.011 -0.010 0.036 -0.003 -0.018 0.063 0.842 0.003 1.000
Supervision -0.010 0.015 -0.100 -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 0.046 0.006 0.128 -0.048 0.001 -0.006 0.001 1.000
District -0.087 0.041 -0.202 -0.001 -0.001 -0.001 -0.001 -0.001 -0.001 0.029 0.228 0.004 -0.058 -0.013 0.052 -0.022 0.088 1.000
12 explanatory power of the model. The following sections go into the selection of the specific variables.
2.1 Bank risk-taking
Three measures of bank risk-taking are employed to provide a wide base of information from which conclusions can be drawn regarding a bank’s risk behavior. The (i) ratio of risk assets to total assets and the (ii) ratio of non-performing loans to total loans are familiar from the Delis and Kouretas (2011) model. The first reflects a bank’s holdings of assets that are susceptible to fluctuations due to market conditions. The percentage of total assets not including cash, balances due from other banks and government issued assets, represents a bank’s holding of these relatively risky assets, termed by Delis and Kouretas (2011) as risk assets. It may be insightful to consider the reverse argumentation that a bank lowers its risk position by raising its cash holdings, thereby providing itself with a cushion for bad times. A lower ratio of risk assets to total assets thus implies lower risk-taking by a bank. The 45232 observations for this variable exhibit a fairly high mean value of 96.8%, with the lowest mean reported in 2001 (95.6%) and the highest mean in 2007 (97.1%). It is noticeable that US banks maintain a high level of risk assets compared to the European sample by Delis and Kouretas (2011), with an average of 77.6%. Our US sample also shows less variability in this ratio over the seven year time frame (a 1.57% increase versus a 5.1% increase). A possible explanation is that US banks have relatively lower holdings of government securities than is customary in Europe. The majority of US government issued assets is held by intragovernmental holdings such as social security funds. Only a small portion of the more than 19 trillion USD worth of government securities ends up on banks’ balance sheets.4 The low variability in risk assets may imply that US banks mainly exert their risk-taking behavior in other ways, such as through the loan quality acceptance determined in its lending standards, rather than raising or lowering their holdings of risk-free assets.
The second proxy, the NPL ratio, is such a qualitative indication of risky lending. A higher level of defaulting loans tells us something about the quality of the outstanding loans. If a substantial part of bank assets turns out to be non-performing, this will result in losses to the bank, affecting the bank’s credit position. The 44791 observations for this variable exhibit a mean value of 0.74%, with a minimum mean value of 0.53% in 2006 and a maximum mean value of 1.35% in 2008. This change in the NPL ratio (a 154.7% increase) in the years up to the financial crisis is indeed more significant than the change in risk assets (the 1.57% increase). It should be noted that the NPL-ratio as a measure of risk-taking is by itself lagged. As it takes time before a borrower defaults on his loan (Iaonnidou et al., 2015), and then another short period before the loan is written off as non-performing (most commonly a 90-day window), the NPL-ratio effectively measures risk that is taken at an earlier stage.
This paper adds another proxy for bank risk-taking; the (iii) z-score of distance to insolvency. As applied by Agoraki et al. (2011), Drakos et al. (2014), and Laeven and Levine (2009), the
13 probability of insolvency, a state in which losses exceed equity, can be expressed as the probability that −𝑅𝑂𝐴 < 𝐶𝐴𝑅. The z-score is then defined as the inverse probability of insolvency, which is measured as
𝑍𝑠𝑐𝑜𝑟𝑒 = 𝑙𝑛 [(𝑅𝑂𝐴+𝐶𝐴𝑅)𝜎(𝑅𝑂𝐴) ] (2)
where ROA is the return on assets, CAR is the capital assets ratio, or capitalization, and 𝜎(𝑅𝑂𝐴) is the standard deviation of ROA from the previous three periods.5
A higher z-score implies a low probability of insolvency and thus a more stable bank. Compared to the NPL ratio being a measure of default probability of the borrower (credit risk), the z-score is considered a more direct measure of the bank’s overall default probability (insolvency risk). Contrary to the argument by Delis and Kouretas (2011) that insolvency risk does not relate to the theoretical considerations of bank risk-taking, Mink (2011) argues that due to the use of less equity to finance their assets, levered banks run a greater risk of insolvency when the value of these assets declines as a result of defaulting borrowers. This paper therefore argues that insolvency risk is an extension of the risk decisions taken by bank management, and that it is considered an appropriate tool to gauge the consequences of an increasing yield curve slope to risk-taking behavior. The 45173 observations for this variable show a mean value of 4.34, with a maximum mean value of 4.55 in 2006 and a minimum mean value of 3.88 in 2008. Just like the NPL ratio, the z-score means show a significant decrease (increase in risk taking) in the years up to the financial crisis.
2.2 Slope of the yield curve
The primary focus of this paper is to analyze the effect of the interest rate spread on banks’ risk-taking behavior. As the yield curve depicts the interest rates for different maturities, its slope is indicative for the spread between short- and long-term interest rates that are determined in the market or set by the central bank. A variety of rates is commonly used to calculate this spread, or they are combined into indices. The St. Louis Federal Reserve district office for example, publishes a financial stress index that incorporates a variety of interest rates and yield spreads, including the difference between 10-year and 3-month Treasury bond rates. This Treasury bill rate (government issued bonds that are considered to have near risk-free returns), the 3-month LIBOR (the London Interbank Offered Rate is an estimation of the charged rate for borrowing from other banks) and the Federal Funds rate (the overnight lending rate that is determined by the Federal Open Market Committee through open market operations) are among the most important rates to measure financial market expectations and to construct the yield curve on which banks base their lending and borrowing rates. For this research,
14 six market-level spreads common to all banks in the sample are constructed, as well as a bank-level spread (with a cross-sectional dimension) of lending and borrowing rates that are eventually charged by each bank to its clients. Table 3 provides an overview of these seven indicators of the yield curve slope.
The market-level spreads are constructed by alternately subtracting three short maturity rates from two long maturity rates, all five of which are provided by the Federal Reserve Bank research database. Besides for the purpose of a robustness check, the main motive for constructing a variety of market-level estimates of the interest rate spread is to capture several sources of changes in the interest rate environment. Treasury bills are government issued debt products and represent the risk-free alternative to any investor. The rates on T-Bills are commonly used as a benchmark rate, reflecting the public’s economic market expectations over the life of their maturities. The interest rate swap rate and LIBOR on the other hand, are determined by the supply and demand of interbank transactions. Banks typically exchange interest rates on fixed and floating payments to hedge against interest rate risks, so these interbank rates reflect the banks’ expectations of interest rate variability. Finally, the Federal Funds rate is the overnight lending rate for funds maintained at the Federal Reserve. This rate is particularly interesting, because it translates the central bank’s monetary policy as the Federal Open Market Committee aims to steer it towards a target rate through open market operations. The rate has an impact on the broad economy and is therefore an important base rate for all other interest rates. By constructing the market-level interest rate spreads using the above rates, we thus include the market expectations of both the public and depository institutions, as well as the monetary policy targets expressed by the Federal Reserve Bank. At this point it is assumed unknown if, and which, one of these perspectives has a stronger effect on bank risk-taking. The indicators of the slope of the yield curve may turn out to express varying effects on bank risk-taking.
Besides the analysis of market-level interest rate spreads, this paper follows the argumentation
Table 3
Measures of the slope of the yield curve.
Variable Measured as
(a) Market-level interest rate spreads
Slope market 1 10-year Treasury bill rate - 3-month LIBOR Slope market 2 10-year Treasury bill rate - Federal Funds rate Slope market 3 10-year Treasury bill rate - 3-month Treasury bill rate Slope market 4 10-year interest swap rate - 3-month LIBOR Slope market 5 10-year interest swap rate - Federal Funds rate Slope market 6 10-year interest swap rate - 3-month Treasury bill rate (b) Bank-level interest rate spread
Slope bank (Total interest income / net loans) - (total interest expense / total customer deposits)
15 by Delis and Kouretas (2011) that the charged rates by each bank to its customers is of great importance to the analysis. These bank-level interest rates eventually determine the net interest income generated by the bank (Entrop et al., 2005) and may thus be an important determinant in the risk-taking decisions of bank management. The bank-level interest rate spread is constructed by subtracting the bank-level deposit rate from the bank level lending rate, measured as the ratio of total interest expense to total customer deposits and the ratio of total interest income to net loans, respectively. In producing this variable, 11 outliers were encountered with unusual ratios of interest to loans or deposits, resulting in abnormally high banks spreads. These 11 banks are among the 20 banks excluded from the dataset. The 45154 observations for this variable show a mean value of 1.63%, with slowly decreasing mean values from 1.80% in 2001 to 1.42% in 2008.
Compared to the bank-level slope of the yield curve, Figure 1 shows our market-level interest rate spreads having a more variable pattern. The market-level slopes are rising from 2001 to 2002 and then declining towards 2007, in same cases even to a state with an inverted yield curve (negative slope) which is known to be a strong predictor of an upcoming financial crisis. The slope of the yield curve shows a sharp increase again in 2008. A somewhat surprising result from figure 1 is that the bank-level interest rate spread is relatively unaffected by the variations in the market-level yield curve.
Figure 2. Market-level and bank-level slopes of the yield curve. The figure reports mean values of each measure of the
16 This observation is consistent with the Ho and Saunders (1981) theory that banks to some level already include a mark-up for interest rate volatility on their loan rates, but does not coincide with the idea that these mark-ups do vary with market interest rates in the long run. Following Alessandri and Nelson (2015), this bank-level interest rate spread would have been expected to be more volatile than the data shows. How the bank-level spread affects the net interest margin will however also depend on the value of the interest income relative to a bank’s borrowing costs in the money market, so the relatively constant slope does not fully inform us on the consequences for profitability and risk-taking. Finally it is observed from Figure 1 that slopes 1 through 3 lie slightly lower than slopes 4 through 6, indicating that the 10-year interest swap rate is lower than the 10-year Treasury bill rate. How this affects risk-taking will become apparent from the estimation results.
2.3 Control Variables
17 (2011) argue that “technically more efficient banks are more capable to manage risks”, where ‘technically’ refers to internal processes and procedures that can deliver an improved result at a given level of expenses (think of software performance or well-defined employee practices). Theoretically, a bank’s higher capability to manage risk can either motivate further risk-taking with increased credit risk exposure as a result (as observed by Delis and Kouretas, 2011), or the management of risk can mitigate the consequences of lowering lending standards. Finally, our banks’ non-traditional activities are considered in the ratio of off-balance sheet items to total assets. As mentioned above and shown by the high correlation of 0.842 in Table 2, these risky side activities (Martynova et al., 2015) heavily contribute to overall profitability. Following the theoretical argumentation of this paper, lagged profitability and off-balance sheet items are expected to incentivize further risk-taking behavior.
While sticking with the Delis and Kouretas (2011) model regarding bank-level control variables, including country-specific measures does not apply to the US-only dataset of this paper; these variables would take the same value for all banks.6 But agreeing with Laeven and Levine (2009) and Delis and Kouretas (2011) on the importance of regulatory and structural conditions as determinants of risk-taking, a replacing set of variables is developed by this paper. First, a ‘supervision’ variable is designed to replace Barth et al.’s (2008) measure of supervisory power and measure a bank’s level of accountability towards regulatory authorities. The US banking and regulatory system is rather complex, as regulation takes place at different levels and is performed by several institutions.7 To give a quick overview, banks operate either under a state or national charter and report to one or more controllers based on this charter. State banks are regulated primarily by the financial department or agency of that state, regarding lending practices, interest rate restrictions, auditing and inspection. Additionally, state banks can opt for supervision by the Federal Reserve System and/or request deposit insurance from the Federal Deposit Insurance Committee. This brings great advantages such as better access to capital, at the cost of surrendering to federal supervision. Alternatively, a national chartered bank is relieved from most state banking laws, but is required to become a Federal Reserve Member. National banks are in principle supervised by the Office of the Comptroller of the Currency (OCC), though some national banks additionally report to the Federal Reserve Board and/or the FDIC. Finally, banks can be required to additionally report to the New York State Department of Financial Services or foreign regulatory authorities. The supervision scoring model assigns an index value to each bank based on the number of authorities to which it reports. A
6 The country-level control variables employed by Delis and Kouretas (2011), based on World Bank data from the supervision and regulation survey of Barth et al. (2008), have been applied to the dataset of this paper and indeed showed the same scores across all banks and between different surveys (2003 and 2007): the capital stringency index scored 5 out of 8, supervisory power 13 out of 14 and market discipline 6 out of 9. 7
18 description of how the index is constructed is given in Appendix A. It is expected that banks with higher levels of supervisory subordination will have lower risk incentives.
Second, a geographical distinction is made by categorizing each bank to the federal district in which it operates. As the Federal Reserve Board delegates certain supervisory responsibilities to each of the twelve districts, these Federal Reserve Banks may vary in how they perform functions such as field inspections, charter approvals and credit law enforcement. This is especially the case because federal districts vary to a significant degree in population density and the volume of transactions.8 To illustrate with an example, a large national bank on Wall Street operates in a rather different supervisory climate compared to, for instance, the local state-chartered bank in Boseman, Montana. In terms of their client base, size and level of scrutiny, banks in different Federal districts may thus have varying risk incentives that are of interest to our model. Appendix B provides an overview of the federal districts, showing that a higher district number implies a more dispersed population. The expectation regarding locational effects on risk-taking is that this dispersion across the district makes it more difficult for that district’s Federal Reserve Bank to efficiently perform its regulatory tasks, such that bank risk-taking is less restricted.
Third, a measure of banking industry concentration is added. Boyd and De Nicoló (2005) find that “as competition declines banks earn more rents in their loan markets by charging higher loan rates, which imply higher bankruptcy risk for borrowers”. A more concentrated market is thus said to fuel risk-taking, while Delis and Kouretas (2011) find no such result in their 3-bank concentration ratio. To find an answer, this paper alternatively proposes the Herfindahl index which, as shown by Weinstock (1982), is calculated by adding the square of each bank’s market share and takes a value between 0 (an infinite number of banks) and 1 (a pure monopoly). The index is then constructed for each state, basing a bank’s market share on its total assets compared to the state’s total assets. Each bank is assigned the Herfindahl index of the state in which it operates.
3. Econometric analysis and results
The empirical analysis is initiated with a simple pooled regression of equation (1), thereby first ignoring any estimation issues or bank heterogeneity that can affect the accuracy of the estimation. The results of this ordinary pooled OLS model are reported in Appendix C.9 From this first impression, a careful observation can be made that the data seems to confirm the expectation that the slope of the yield curve positively relates to risk-taking10, that is, when the z-score or NPL-ratio are
8
The Federal Reserve Board of Governors reported district populations in 1996, ranging from 7.6 million in the Minneapolis district to 46.7 million in the San Francisco district. The district numbers run from the more densely populated districts in the east to the more disperse districts in the west.
9
A background check has proven that including the set of control variables does not alter the sign and significance of the measures of the slope of the yield curve.
19 employed as dependent variables. Contrary to the theoretical predictions of this paper and observations in Delis and Kouretas (2011), the yield curve slope holds a negative relationship with risk assets. It does however point to the suggestion in section 2.1 of a risk-taking preference for raising the credit risk exposure compared to a quantitative rise in risk assets. Furthermore, a pattern seems to be present when comparing the coefficients of the market-level slope of the yield curve. As market slopes 1 and 4, 2 and 5, and 3 and 6 produce nearly the same coefficients between each other, it can be concluded from Appendix C and Table 3 that there is no significant difference between the 10-year Treasury Bill rate and the 10-year interest swap rate as determinants for the long end of the slope of the yield curve11. It can also be seen that efficiency and off-balance sheet items don’t have a large effect on risk-taking, which is similar to the results produced by Delis and Kouretas (2011). Finally, the regulatory and structural control variables overall show to have a significant impact on risk-taking decisions. Though before drawing any further premature conclusions from this simple regression, a few estimation issues should be addressed. After consideration of these issues, both a fixed and random effects estimation will give a more appropriate indication of the relationships, followed by an augmentation of the model and sensitivity analysis.
3.1 The fixed- and random effects model
The pooled model in Appendix C is constructed in a raw fashion, disregarding any characteristics of the dataset that can produce biased results in an ordinary least squares (OLS) estimation. For instance, Table 2 shows a presence of multicollinearity due to the correlated relationship between lagged profitability and off-balance sheet items. As a consequence, estimates of the coefficients of these variables may become sensitive to small changes in the specification of the model and result in wrongful conclusions. To prevent such errors, it is decided to drop the off-balance sheet items variable in the further analysis. As the profits from non-traditional activities are represented in the overall profitability of the bank, conclusions concerning the effects of such activities can be inferred from the lagged profitability variable. Therefore this solution to multicollinearity is deemed justified. Table 2 also presents multicollinearity among the different measures of the market-level slope of the yield curve. However, these variables were already intended to enter the model alternately, as in the pooled sample of Appendix C.
Common to panel data is the presence of unobserved heterogeneity across firms. As described by Petersen (2009) and Hsiao (2014), firm heterogeneity implies that there is an effect explaining the variation in the dependent variable that is unobserved by the variables included in the model. For instance, Laeven and Levine (2009) find a positive impact on risk incentives by controlling for the comparative power of shareholders through voting rights and cash flow rates. Such governance characteristics are not covered in this research but may still exert an unobserved heterogeneous effect
11
20 on risk-taking. Controlling for such an effect empowers the explanatory value of the panel data model and can be done by either applying a fixed effects or random effects estimation method. The results of a Hausman test reject the appropriateness of a random effects estimation12 for our dataset – the assumption of uncorrelated explanatory variables and firm effects is violated – suggesting that the fixed effects estimation delivers more convincing standard errors. This creates a dilemma, as the fixed effects estimation prohibits the inclusion of time-invariant regressors such as the variables reflecting supervision and federal district (Hsiao, 2014). These variables cancel out in the transformational estimation process of a fixed effects model. However, to prevent losing the ability to draw conclusions from these regulatory variables, results from the random effects estimation are presented alongside fixed effects estimations in the following analysis, keeping in mind that these results are subject to inconsistencies. A redundant fixed effects test confirms the existence and significance of bank-specific effects13, which are controlled for in the fixed effects estimation by re-estimating equation (1) as follows:
𝑟𝑖𝑡 = 𝛼 + 𝛽1𝑆𝑖𝑡+ 𝛽2𝑏𝑖𝑡+ 𝛽3𝑐𝑖𝑡+ 𝜇𝑖+ 𝑢𝑖𝑡 (3)
where μ represents the cross-sectional fixed effects. In the random effects estimations, the bank-specific effects are instead captured in the error term 𝑢𝑖𝑡.
It is also imperative to test for and deal with the presence of heteroskedasticity and serial correlation. Breusch and Pagan (1979) explain that using OLS estimation in the presence of heteroskedastic disturbances may cause significant loss of efficiency and biased standard error estimation. The same consequences apply for the use of OLS in the presence of serial correlation; positive autocorrelation will lead to downward biased standard errors. After applying a two-sided Breusch-Pagan test to the model, the null hypothesis of homoskedasticity is rejected.14 Testing for serial correlation within cross-sectional data is a more complex ordeal, given the wide range of possible tests for autocorrelation and their respective limitations discussed by Born and Breitung (2016). Although they argue in favor of the significance of choosing the correct test to confirm autocorrelation, it is also acknowledged that “the assumption of serially uncorrelated disturbances is likely to be violated in classical linear panel data models”. The basic Durbin-Watson test for first-order autocorrelation is therefore assumed here as sufficient proof that positive autocorrelation is present.15 Methods of tackling heteroskedasticity and serial correlation vary widely across the literature. Petersen (2009) compares these approaches and shows that, in the presence of firm-fixed
12 The Hausman test rejects the use of random effects estimation across all combinations of dependent variables and yield curve slopes. In case of the random effects estimation using the z-score as dependent and market slope 1 as independent variables, the test reports 𝜒2= 129.76 with probability 0.000.
13 The redundant cross-sectional fixed effects test reports 𝜒2= 15064.00 with probability 0.000. 14 The Breusch-Pagan test statistic is reported as 𝜒2= 156313.1 with probability 0.000.
15
21 effects, the standard OLS and Fama-MacBeth methods produce biased standard errors. The commonly applied Newey-West HAC estimation (Newey and West, 1987), which is designed to simultaneously account for heteroskedasticity and serial correlation, is also proven to still have a small bias. Petersen (2009) proposes that “clustered standard errors are unbiased as they account for the residual dependence created by the firm effect.” As such, the White cross-section estimation method – which assumes cross-sectionally correlated (clustered) errors – is considered an acceptable estimation of robust standard errors, and is applied to the fixed- and random effects regressions in this analysis. The results are presented in Table 4.
Regarding the z-score and NPL-ratio as measures of risk-taking, the results confirm the theoretical expectation of a positive impact of the slope of the yield curve. Regressions I-III and V produce a significant negative coefficient for the slope, implying that as the market-level interest rate spread increases, the bank’s distance to insolvency decreases as a result of asset devaluation when the relatively riskier loans default (Mink, 2011). Similarly, regressions VII-IX and XI show significant positive coefficients for the slope, such that the ratio of non-performing loans rises as the market-level interest rate spread increases. However, just as in the pooled estimation, the yield curve slopes have significant negative relationships with the ratio of risk assets in a bank’s portfolio (regressions XIII-XV and XIII-XVII). These observations tell us that banks react to a more profitable interest rate environment, not by raising the amount of risk assets in their portfolios, but by including qualitatively riskier investments in their portfolios that worsen the credit risk position of the bank. Although Delis and Kouretas (2011) conclude an increase in the risk assets ratio from their assessment of interest rate levels, they do however derive the same conclusion from a differential response to lagged profitability between risk assets and the NPL ratio. The observed relationship is in line with the proposition by Mink (2011) that a higher term spread amplifies a bank’s borrowing cost advantage, giving rise to portfolio diversification (into riskier projects) and the lowering of lending standards (as also described by Dell’Ariccia and Marquez, 2006). That banks in such a scenario appear to even lower their ratio of risk assets – contrary to the insignificant appreciation of this ratio observed by Delis and Kouretas (2011) – is nevertheless somewhat puzzling and ‘overshoots’ the above theory of a shift in risk preferences. This can possibly be attributed to the ratio of risk assets already being at a substantial level (averaging at 96.8%) compared to the European sample of Delis and Kouretas (2011), such that an increase of credit risk exposure has to be balanced by an increase in relatively devalued riskless assets.
22 adjusted. As such, risk-taking decisions can be expected to be taken on the basis of variations in the market-level slope, rather than the bank-level rates eventually charged to customers.
With regards to the bank-level control variables, first a strong positive impact is observed from the size of the bank on both the NPL-ratio and ratio of risk assets, confirming Ioannidou et al. (2009) and Boyd and Runckle (1993) that larger banks are less risk averse. The observation contrasts however with the negative impact of bank size on risk-taking found in the interest rate level models by Delis and Kouretas (2011) and Agoraki et al. (2011), providing evidence that banks react differently to the spread than to the level of interest rates. Bank size also shows the expected negative relation to the z-score, though these coefficients are insignificant. Although the theoretical expectations of the impact
Table 4
Slope of the yield curve and bank risk-taking: fixed- and random effects regressions.
I II III IV V VI Constant 6.722 *** 7.404 *** 7.583 *** 4.920 ** 5.174 *** 4.589 *** (3.261) (2.969) (3.290) (2.409) (6.671) (5.359) Size -0.185 -0.226 -0.234 -0.065 -0.065 -0.029 (-1.204) (-1.254) (-1.410) (-0.428) (-0.901) (-0.380) Capitalization 0.033 *** 0.029 *** 0.029 *** 0.039 *** 0.026 *** 0.032 *** (5.210) (5.775) (5.566) (5.631) (4.432) (5.469) Lagged profitability 0.003 ** 0.003 ** 0.003 ** 0.003 ** 0.003 ** 0.003 ** (2.142) (2.271) (2.313) (2.130) (2.410) (2.417) Efficiency 0.000 * 0.000 * 0.000 * 0.000 * 0.000 ** 0.000 ** (1.734) (1.681) (1.685) (0.072) (2.026) (2.044) Supervision 0.007 0.004 (0.352) (0.229) District -0.026 *** -0.025 *** (-3.275) (-3.111) Concentration -0.959 ** -1.090 ** -1.126 ** -0.609 -0.282 * -0.212 (-2.227) (-2.227) (-2.453) (-1.338) (-1.879) (-1.295) Slope market 1 -0.053 ** -0.039 ** (-2.572) (-1.966) Slope market 2 -0.092 *** (-2.585) Slope market 3 -0.114 *** (-3.058) Slope bank 0.001 -0.006 (0.113) (-0.450) Observations 43704 43704 43704 43630 43704 43630 Banks 1414 1414 1414 1413 1414 1413 Adjusted R-squared 0.272 0.281 0.285 0.268 0.009 0.006 F-statistic 12.530 13.012 13.251 12.283 48.725 35.298
Note: table continues on next page.
23 of capitalization was considered ambiguous – referring to the motivations to increase risk either from an under-capitalized or over-capitalized perspective – the results show well-capitalized banks to significantly reduce their credit risk exposure with an improved z-score and NPL-ratio. This relates to the traditional view that higher capital levels leads to more cautious behavior to maintain shareholder value (Keeley, 1990; Delis and Kouretas, 2011). On the other hand, capitalization’s positive impact on the ratio of risk assets points to Calem and Rob’s (1999) proposition that highly capitalized banks become less risk averse as capital requirements become less restrictive. Both lagged profitability (besides a negligible positive effect on the z-score) and efficiency produce very small and mostly
Table 4, continued
Slope of the yield curve and bank risk-taking: fixed- and random effects regressions.
VII VIII IX X XI XII
Constant -5.731 *** -6.376 *** -6.772 *** -3.903 ** -3.009 *** -2.289 ** (-2.936) (-2.805) (-3.280) (-2.190) (-2.939) (-2.110) Size 0.484 *** 0.523 *** 0.545 *** 0.359 *** 0.285 *** 0.236 ** (3.453) (3.274) (3.774) (2.805) (3.277) (2.569) Capitalization -0.031 *** -0.028 *** -0.027 *** -0.038 *** -0.026 *** -0.030 *** (-3.607) (-2.953) (-2.903) (-3.807) (-4.203) (-4.105) Lagged profitability -0.002 -0.002 -0.002 -0.002 -0.002 -0.002 (-1.431) (-1.474) (-1.504) (-1.430) (-1.405) (-1.413) Efficiency -0.000 -0.000 -0.000 -0.000 -0.000 -0.000 (-0.099) (-0.148) (-0.149) (-0.009) (-0.167) (-0.109) Supervision -0.021 -0.016 (-0.487) (-0.399) District 0.014 0.013 (1.110) (1.069) Concentration 1.287 *** 1.408 *** 1.481 *** 0.974 ** 0.725 * 0.622 (2.747) (2.765) (3.153) (1.985) (1.910) (1.604) Slope market 1 0.053 *** 0.033 ** (2.764) (1.961) Slope market 2 0.091 *** (2.833) Slope market 3 0.122 *** (3.728) Slope bank 0.023 0.021 (0.536) (0.505) Observations 43322 43322 43322 43322 43322 43322 Banks 1410 1410 1410 1410 1410 1410 Adjusted R-squared 0.514 0.519 0.524 0.512 0.013 0.011 F-statistic 33.417 34.095 34.656 33.125 71.208 60.604
Note: tabel continues on next page.
24
Table 4, continued
Slope of the yield curve and bank risk-taking: fixed- and random effects regressions.
XIII XIV XV XVI XVII XVIII
Constant 87.787 *** 86.830 *** 86.613 *** 85.253 *** 91.029 *** 88.727 *** (151.683) (131.854) (122.872) (102.44) (173.163) (121.279) Size 0.669 *** 0.737 *** 0.753 *** 0.844 *** 0.534 *** 0.696 *** (16.087) (15.508) (15.019) (14.388) (15.306) (14.694) Capitalization 0.014 ** 0.016 *** 0.017 *** 0.022 *** 0.015 ** 0.023 *** (2.447) (2.835) (2.854) (3.221) (2.430) (3.207) Lagged profitability 0.000 0.000 0.000 0.000 ** 0.000 0.000 * (1.099) (1.055) (1.126) (2.088) (0.968) (1.689) Efficiency 0.000 0.000 0.000 0.000 0.000 0.000 (0.877) (0.855) (0.816) (0.751) (0.656) (0.393) Supervision -0.222 *** -0.240 *** (-5.909) (-6.191) District -0.111 *** -0.111 *** (-3.512) (-3.561) Concentration 0.126 0.290 0.328 * 0.579 *** -0.092 0.293 * (0.860) (1.588) (1.728) (2.847) (-0.606) (1.858) Slope market 1 -0.077 *** -0.090 *** (-3.826) (-4.467) Slope market 2 -0.064 *** (-3.455) Slope market 3 -0.066 *** (-3.203) Slope bank -0.043 -0.054 (-1.330) (-1.432) Observations 43750 43750 43750 43675 43750 43675 Banks 1414 1414 1414 1413 1414 1413 Adjusted R-squared 0.742 0.742 0.742 0.741 0.051 0.042 F-statistic 89.781 89.558 89.488 89.152 296.977 239.338 Risk assets
25 insignificant coefficients to explain variations in risk-taking.16 A bank’s risk-taking decision is thus not based on last period’s overall profitability, including income from off-balance sheet practices, nor on technical efficiencies resulting from well-established internal processes and procedures.
Concerning the regulatory and structural control variables, it is initially noticed that a greater level of accountability towards supervising authorities limits risk-taking intentions, although the effect is only significant in relation to the ratio of risk assets. This is because the ratio of risk assets is directly related to liquidity requirements of the supervising authority, while the z-score and NPL-ratio record risk-taking after the investment in problem loans has already been made. These measures are thus less affected by regulations. As far as location goes, banks as expected appear to be more inclined to take risk in the higher numbered federal districts, where the dispersion of banking activity is assumed to make inspection and law enforcement more difficult. Finally, concentration shows to have a strong positive impact on risk-taking, specifically regarding the NPL-ratio. This is in accordance with the theory of Boyd and De Nicoló (2005) that a more concentrated banking sector confronts borrowers with higher interest costs charged by banks (who have more market power), raising the chances of defaulting on their loan.
3.2 The role of profitability
Having clarified that a steeper yield curve slope leads banks to take on loans with greater default risk, the next objective is to expose profitability from maturity transformation as a possible intermediate channel of risk-taking. To that purpose, equation (3) is reformulated to include the net interest margin, interacting with the market-level interest rate spread, such that the model takes the following form:
𝑟𝑖𝑡 = 𝛼 + 𝛽1𝑆𝑖𝑡+ 𝛽2𝑏𝑖𝑡+ 𝛽3𝑐𝑖𝑡+ 𝛽4𝑛𝑖𝑚𝑖𝑡+ 𝛽5(𝑛𝑖𝑚𝑖𝑡∗ 𝑆𝑖𝑡) + 𝜇𝑖+ 𝑢𝑖𝑡 (4)
where nim is the net interest margin, calculated as the ratio of net interest income (total interest income minus total interest expense) to the average interest earning assets. Specifying the model this way will tell us whether the impact of the term spread on risk-taking is to some extent diminished or amplified by the realization of a higher net interest margin. To perform the analysis, first a transformation to the interaction variable has to be applied in order to avoid multicollinearity with the variables from which it is constructed. This is done by subtracting from the ‘nim’ and ‘slope’ variables their mean values (‘mean centering’) before multiplying them to create the interaction term. After the transformation has been applied, the interaction variables are applied in the model along with the original (un-centered) ‘nim’ and ‘slope’ variables. Appendix D reports the correlation matrices before and after the transformation, showing that most of the multicollinearity issue is hereby resolved. A strong
16
26 correlation however remains between the net interest margin and its interaction with the bank-level interest rate spread. This is due to the way the bank-level measure of the yield curve slope is constructed, measuring interest income and expenses relative to the amount of outstanding loans and deposits. Since this net interest income also serves as a determinant for the net interest margin, correlation between these variables will always exist. The bank-level slope is therefore excluded from the ‘profitability-channel’ analysis of this section.
Equation (4) is executed using the same fixed effects OLS estimation as applied in section 3.1. The results are given in Table 5. To preserve space, only the regressions with market slopes 1 and 2 as indicators for the term spread (see Table 3) are reported for each measure of risk-taking.17 The findings indicate that the impact of the slope of the yield curve is unaffected by adding the net interest margin into the regression (compared to regressions I, II, VII, VIII, XIII and XIV in Table 4). Any changes in these coefficients are instead captured in the interaction variables, of which the impact and significance vary across measures of taking. First considering the z-score as the proxy for risk-taking, we see that the market-level slope worsens a bank’s risk of insolvency while the net interest margin improves it. The insignificant coefficient of the interaction variable indicates that these opposing effects are unrelated. In other words, the slope of the yield curve raises the probability of insolvency (through the asset devaluation proposed by Mink, 2011), but not through an intermediate channel of profitability from term transformation. The results do however provide evidence for such an effect in the case of the NPL-ratio, where the positive impact of the market slope is significantly amplified by a higher net interest margin. This is in line with this paper’s proposition of a risk-taking channel of profitability. Regarding risk assets, it can be observed that the net interest margin mitigates the previously unexpected negative impact of the yield curve slope. Since this mitigating effect on a decrease in risk assets is in essence the same as amplifying risk-taking, it is argued that these coefficients also provide evidence for a risk-taking channel of profitability. Finally, it is noted that changes in the coefficients of the control variables compared to Table 4 are negligible, and that the inferences made on these controls in section 3.1 remain unchanged.
3.3 Policy implications
So far it has been established that there exists evidence for an incentive to increase credit risk exposure when the interest rate spread is favorable, and that profitability can contribute to this incentive. With the knowledge that not only the level of interest rates, but also the spread between them carries a weight in risk-taking decisions, it is now of interest what the consequences are from setting a certain monetary rate. Referring back to the discussion on monetary policy in the introduction, risk models concerning monetary policy such as in Jimenez et al. (2008) have thus far only emphasized the consequences of specifically the level of the overnight central bank rate to banks’
27 risk behavior. Though Figure 1 has shown that this rate is not indicative for the market interest rate spread and the motivational influence of profitability to take risk, which are aspects that need to be addressed if the goal is to prevent banks from upping their credit risk load. To show that when setting
Table 5 I II III IV V VI Constant 6.503 *** 7.118 *** -6.009 *** -6.594 *** 88.747 *** 87.809 *** (3.295) (3.000) (-3.373) (-3.189) (167.493) (136.958) Size -0.177 -0.213 0.501 *** 0.535 *** 0.632 *** 0.699 *** (-1.177) (-1.223) (3.732) (3.535) (16.117) (15.258) Capitalization 0.033 *** 0.030 *** -0.029 *** -0.027 *** 0.013 ** 0.016 *** (5.241) (5.740) (-3.600) (-3.046) (2.317) (2.872) Lagged profitability 0.003 ** 0.003 ** -0.002 -0.002 0.000 0.000 (2.158) (2.286) (-1.426) (-1.466) (1.537) (1.533) Efficiency 0.000 * 0.000 * -0.000 -0.000 0.000 0.000 (1.743) (1.705) (-0.239) (-0.240) (1.336) (1.374) Concentration -0.947 ** -1.092 ** 1.227 *** 1.379 *** 0.090 0.234 (-2.235) (-2.231) (2.666) (2.690) (0.647) (1.369) Slope market 1 -0.054 *** 0.054 *** -0.073 *** (-2.611) (2.783) (-3.729) Slope market 2 -0.092 *** 0.092 *** -0.061 *** (-2.603) (2.810) (-3.372)
Net interest margin 0.027 ** 0.028 ** 0.011 0.012 -0.115 *** -0.116 *** (2.140) (2.206) (0.400) (0.434) (-4.203) (-4.395) NIM * Slope(x) -0.002 0.003 0.016 *** 0.011 *** 0.006 * 0.012 ** (-1.122) (1.107) (4.307) (3.461) (1.721) (2.057) Observations 43704 43704 43322 43322 43750 43750 Banks 1414 1414 1410 1410 1414 1414 Adjusted R-squared 0.273 0.281 0.515 0.520 0.744 0.744 F-statistic 12.537 13.021 33.496 34.105 90.644 90.520
The table reports coefficient estimates and t-statistics (in parentheses) of a range of fixed effects regressions. In regressions I and II the dependent variable is the z-score, in regressions III and IV the dependent variable is the NPL ratio, and in regressions V and VI the dependent variable is the ratio of risk assets to total assets. All regressions are estimated using White cross-section standard error correction. The explanatory variables are as follows: size is the natural logarithm of total assets, capitalization is the ratio of equity capital to total assets, lagged profitability is the lagged ratio of profits before taxes to total assets, efficiency is the ratio of total revenues to total expenses, concentration is the Herfindahl index of market concentration within a bank's state, slope market (1 and 2) is the market-level slope of the yield curve as reported in Table 3, net interest margin is the ratio of net interest income to average interest earning assets, and the final variable is the interaction of the net interest margin with the measure of slope applied in each regression. Adjusted R-squared denotes the precentage of the variance of the dependent variable that is explained by the model. The F-statistics denote goodness of fit, all of which are significant at the 1% confidence level. Statistical significance of the coefficients is reported as * (at the 10% level), ** (at the 5% level) or *** (at the 1% level).
Slope of the yield curve and bank risk-taking: fixed effects regressions including interaction effect of the net interest margin from maturity transformation.
