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The Quarterly Review of Economics and Finance 63 (2017) 204–218
Contents lists available at ScienceDirect
The Quarterly Review of Economics and Finance
j ourna l h om epage: www.elsev ier .com/ locate /qre f
ooking beyond banks’ average interest rate risk: Determinants of igh exposures
. Entropa, L. von la Hausseb,∗, M. Wilkensb
Faculty of Business Administration and Economics, University of Passau, 94032 Passau, Germany School of Business and Economics, University of Augsburg, 86159 Augsburg, Germany
r t i c l e i n f o
rticle history: eceived 14 January 2015 eceived in revised form 21 February 2016 ccepted 11 April 2016 vailable online 19 April 2016
EL classification: 21 43
a b s t r a c t
This paper studies the magnitude and determinants of interest rate risk (IRR) of listed U.S. bank holding companies. As our first contribution, we test whether banks avoid exposures to IRR as prescribed in classic bank hedging literature. To do so, we use a state space model and Kalman filter techniques to estimate time-series of interest rate betas from bank stock returns. While the interest rate exposures of banks average close to zero, we find that individual banks at times exhibit high and significant exposures to interest rate risk. As our second contribution, we relate these high betas to lagged bank characteristics from accounting data, applying logit regressions and unconditional quantile regressions. We find that high exposures are partly systemic and comove with bank characteristics like size or leverage. This has
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eywords: nterest rate risk anks
implications for the monitoring of interest rate risk by regulators and investors as well as for the ongoing debates on the appropriate capitalization of banks.
© 2016 Board of Trustees of the University of Illinois. Published by Elsevier Inc. All rights reserved.
ail exposures inancial crisis
. Introduction
We study the exposures to interest rate risk (IRR) of U.S. bank olding companies, since IRR is a systematic risk basic to all banking ctivities. Classic bank hedging literature suggests that elimination f easily hedgeable systematic risks is the optimal risk policy.1 We xamine whether banks follow this advice by maintaining low IRR xposures or, on the contrary, show economically significant IRR xposures at times. We further analyze if such high IRR exposures re related to unobserved system-wide factors and/or individual agged bank characteristics. Insights gained from our analyses can id regulators when surveilling banks’ IRR and investors when judg- ng banks’ riskiness.
We contribute empirically to the existing research by adding the ime-series dimension of IRR exposures to the analyses. Our empir-
cal approach is based on Flannery and James (1984), who estimate ach bank’s interest rate beta from first-stage OLS regressions of ank stock returns and explain the resulting cross-section of IRR
∗ Corresponding author at: Finance and Banking, School of Business and conomics, University of Augsburg, Universitaetsstrasse 16, D-86159 Augsburg, ermany. Tel.: +49 821 5984118; fax: +49 821 5914223.
E-mail addresses: [email protected] (O. Entrop), [email protected] L. von la Hausse), [email protected] (M. Wilkens).
1 See, e.g. Diamond and Dybvig (1983) and Froot and Stein (1998).
ttp://dx.doi.org/10.1016/j.qref.2016.04.008 062-9769/© 2016 Board of Trustees of the University of Illinois. Published by Elsevier In
exposures with bank characteristics in a second-stage OLS regres- sion. We extend this analysis in the time dimension by estimating banks’ time-varying IRR betas in an econometrically consistent way using Kalman filter techniques. This allows us to circumvent econo- metric issues that emerge when using constant parameter or rolling window OLS in a context where changing sensitivities are to be expected.
Besides the theoretical implications for banks’ optimal level of interest rate risk, the existing literature has not yet voiced expec- tations regarding the family or general shape of the distribution of IRR betas over banks and over time. Thus, we find the distribu- tion of banks’ IRR betas resulting from our Kalman filter approach interesting with regard to some features that are related to our research questions: the distribution is highly leptokurtic and cen- tered around both a mean and a median close to zero. This implies that banks on average show low IRR exposures in accordance with the above-mentioned hedging theory. However, looking at the tails
of the exposure distribution, we find that there are economically significant (i.e. high2) IRR betas for individual banks at some points in time.
2 We term both highly negative and highly positive IRR betas as high here and in the rest of the paper, as they pose high IRR exposures in absolute terms. If there is a need to differentiate between the direction of the exposure, this will be indicated.
c. All rights reserved.
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In fact, modern banking theory acknowledges and leaves room or banks retaining high exposures to IRR:3 according to Allen nd Santomero (1997), financial intermediation has increased in pite of a reduction in transaction costs and asymmetric informa- ion. Nevertheless, financial intermediation activities shift towards
anaging and sharing risks and facilitating participation in ever ore complex capital markets. These services entail risk manage- ent and trading by financial intermediaries themselves. Going a
tep further, there are papers on the allocation of aggregate risk in he economy (e.g. Hanson, Shleifer, Stein, & Vishny, 2014; Hellwig, 994, 1998) that recognize and rationalize risk-taking. Empirical esearch, too, has never doubted that banks take high net positions n IRR. As one of the latest works in this field, Begenau, Piazzesi, and chneider (2013) explicitly estimate the net interest rate exposure f banks’ portfolios using on- and off-balance sheet data.
We next analyze whether high IRR betas in the tails of the expo- ure distribution are related to lagged bank characteristics and/or ystemic effects or whether they are mere spurious phenomena esulting from estimation error and posing no threat to banks or he banking system. As a first step, we check the switching behav- or of banks in and out of the high exposure tails. Banks’ business
odels and tactical and strategic decisions in terms of risk manage- ent usually do not change too rapidly over time. Thus, IRR betas
ossibly related to them should not fluctuate too strongly in and ut of high exposure quantiles either. We find that there is quite a igh degree of stability with respect to banks’ positions in the expo- ure distribution. In fact, more than 64% of observations in high beta uantiles are followed by an observation in a high beta quantile of he same sign (controlling for the panel structure of our data).
As a next step in analyzing the relationships of IRR betas with ank characteristics, we apply two different approaches: logit-style egressions and unconditional quantile regressions developed by irpo, Fortin, and Lemieux (2009). The former can give an indi- ation of what bank characteristics influence the probability of a ank-quarter being in the high beta quantiles of the exposure dis- ribution. The latter allow for a differentiated analysis of links of he entire distribution of high IRR betas with bank characteristics, ecause relationships between the dependent variable and covari- tes are estimated at every unconditional quantile of the dependent ariable.
We find only few weak relationships for the center of the IRR eta distribution, where low IRR exposures prevail. This makes ense economically, because these low exposures are the result of anks following the above-mentioned classic bank hedging theory. anks following implications of this theory shield themselves from
RR by hedging activities, thereby decoupling IRR exposures from heir sources.
In contrast, high IRR betas in the tails of the exposure distri- ution show economically meaningful and statistically significant elationships with lagged bank characteristics and time-fixed ffects for both approaches, logit and quantile regressions. This ndicates that high IRR betas are not purely random or spurious ffects that can be ignored. They rather represent a consequence of he development of individual banks’ characteristics, e.g. the degree f leverage or the intensity of derivative usage, that are also to ome degree associated with business models or risk management olicies. High IRR betas are also significantly related to time-fixed ffects representing unobserved systemic shifts that broadly affect
he cross-section of banks.
Summarizing the individual results, leverage shows a symmet- ic effect on both high beta tails of the exposure distribution: it is
3 An earlier stage model by Deshmukh, Greenbaum, and Kanatas (1983), too, ratio- alizes risk-neutral banks taking on interest rate risk as a reaction to levels of loan nd borrowing rates and associated volatilities.
omics and Finance 63 (2017) 204–218 205
related to an increase in the probability of exhibiting both highly negative or highly positive IRR betas in quantile regressions. Sim- ilarly, for quantile regressions, leverage is linked to increases of both negative and positive tail quantiles of IRR betas as well. This symmetric boost for high IRR exposures from leverage is visible for the financial crisis period, too. This finding corroborates the need for adequate and comprehensive capitalization of banks also with regard to term transformation and IRR on the banking book and thus adds to current discussions on further developments of capital regulation.
Greater bank size shows an asymmetric effect on the tails of the exposure distribution: it is associated with a higher (lower) prob- ability of exhibiting highly negative (positive) IRR betas in logit regressions. Although less pronounced for times of crisis, uncon- ditional quantile regression results mirror this asymmetric effect and show a shift to more negative IRR betas for greater size as well. This indicates that greater size, although traditionally asso- ciated with positive effects on risk, like greater potential for scale economies in risk management and regional and product diversi- fication, is related to a shift towards more negative IRR exposures that are characteristic for traditional (i.e. positive) term transfor- mation. These findings should be taken into consideration in the ongoing discussions on financial stability.
Another interesting link concerns the intensity of interest rate derivative usage. Over the entire sample period, but not for the crisis subperiod, it is related positively to the positive beta tail (both in terms of probability and tail values). As this is the part of the IRR beta distribution where banks have decoupled themselves from the traditional term transformation, this link serves as an indication of banks’ intention when using IRR derivatives.
Other variables show more mixed results for the different approaches and (sub)sample periods. For example, the positive link of a greater traditional term transformation with the nega- tive tail of the exposure distribution (both in terms of probability and tail values) is significant throughout only for the crisis sub- period. Nevertheless, this result for maturity mismatch is in line with the latest theoretical literature on financial intermediation (e.g. Brunnermeier & Oehmke, 2013; Farhi & Tirole, 2012), which sees an aggregate maturity mismatch at the heart of the recent banking crisis.
Overall, our approach sheds further light on the extent and determinants of IRR exposures of banks. We show that at some points in time some banks have economically significant IRR expo- sures that are related to system-wide unobserved effects and bank characteristics like leverage, size, intensity of derivative usage or term transformation. This indicates that banks’ significant IRR exposures can be identified to some degree by such leading indi- cators of high exposures, thereby helping regulators and investors to evaluate the IRR exposures of banks. Our findings also add to ongoing discussions on adequate bank capitalization and size.
The rest of the paper is organized as follows: Sections 2 and 3 give a short overview of the related literature and describe the data. Estimation of IRR betas is covered in Section 4. Section 5 contains the second-stage analyses explaining high IRR betas with lagged bank characteristics, which in turn are described in Section 5.1. Section 5.2 describes the regression design for the second stage. Sections 5.3 and 5.4 show results for logit and unconditional quan- tile regressions, including robustness (Section 5.4.2) and financial crisis subperiod analyses (Section 5.4.3). Section 6 concludes with possible applications of our findings.
2. Related literature
As mentioned above, our analysis rests on the basis of the fun- damental paper by Flannery and James (1984), who investigated
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06 O. Entrop et al. / The Quarterly Review o
ow changes in the value of banks’ equity are linked to interest ates. In a first stage, they therefore estimated one interest rate eta for each bank’s time series of stock returns in a two-factor odel specification based on Stone (1974). They found banks’ stock
eturns to be negatively related to increases in the level of interest ates. In a second-stage OLS regression, they related the resulting ross-section of OLS-based IRR betas from the first-stage to bank haracteristics. They found that the relation of bank stock returns ith interest rates expressed by IRR betas is stronger for banks with igher maturity gaps. The authors interpret this finding as banks eing exposed to IRR from term transformation.
This approach has since been the basis for many studies of nterest rate risk that found the same results, e.g. Saunders and ourougou (1990) or Kwan (1991),4 but also for studies broadening he scope of the analyses to include many more variables related to anks’ risk management practices and business models. Additional ariables have partly been employed as control variables, but some tudies sought to dig deeper into sources of IRR and thus focused n the relationships of newly added variables with IRR exposures.
One area that has captured special attention is related to deriva- ive usage. Two important papers in this area are Choi and Elyasiani 1997) and Hirtle (1997). Choi and Elyasiani (1997) use foreign xchange risk as an additional factor and show that IRR betas f bank holding companies are generally negative but positively elated to interest rate derivative usage. A similar result is found y Hirtle (1997) who measures IRR betas for each bank at yearly
ntervals to arrive at a panel structure for the second-stage analy- es. They show that on-balance sheet portfolio composition is an mportant determinant of interest rate risk but that derivative con- racts played an important role for the later subsection of the study early 1990s). For that period a higher degree of interest derivative ontract usage is related to higher IRR.
Schrand and Unal (1998) analyze the relation between credit nd interest rate risk for banks’ risk management. Their version of isk management, coordinated risk management, views credit risk ith associated selection and monitoring tasks as a core-business
isk, as related high-information activities allow banks to earn rents or superior evaluation capabilities with regard to the contained nsystematic risk. In contrast, homogenous risks like IRR based n efficient (observable) market prices hardly allow banks to earn ents when taking these risks. Coordinated risk management thus ntails hedging homogenous risks like IRR and increasing core busi- ess risks like credit risk, when total risk is limited by regulatory estrictions. In a somewhat related study Bessler and Kurmann 2014) show that both credit risk and IRR are risk factors priced in anks’ stock returns, although with changing degrees of importance nd changing signs.
. Data
Our sample consists of traded U.S. bank holding companies BHCs)5 that file quarterly FR Y-9C reports with the Board of Gov- rnors of the Federal Reserve System (FED). Return data of these anks and a value-weighted U.S. total market index are obtained rom Thomson Reuters Datastream.6 Information on government ond interest rates from Gurkaynak, Sack, and Wright (2006) are ade available via the FED. This data and returns are used below
o estimate time-varying IRR betas individually for each BHC. Resulting IRR betas are then related to bank characteristics con-
isting of on- and off-balance sheet data from quarterly regulatory
4 For a comprehensive survey of the literature, see Staikouras (2006). 5 We use the expressions “BHC” and “bank” interchangeably. When referring to
anking subsidiaries of BHCs, we use the term “commercial bank”. 6 We follow Ince and Porter (2006) in screening the return data.
omics and Finance 63 (2017) 204–218
reports. Consolidated financial data at the BHC level are made avail- able in FR Y-9C reports; additionally, we aggregate subsidiary data contained in the Call Reports, available via the Chicago FED and the FDIC, by summing across commercial banks of each BHC to gain additional information on, e.g. type and maturity of deposits.7
We restrict our analysis to domestic BHCs with charter type BHC. To ensure consistent time-series, we drop lower-tier BHCs (defined as being owned by another BHC by more than 50% of equity) and BHCs with total consolidated assets of less than $500 million (in 2006:Q1 dollar terms).8 To avoid including IRR measures biased by near default, we drop bank-quarters marked as liquida- tion, inactivity or failure (with and without resolution arranged by a regulatory agency) and bank-quarters exhibiting negative values of equity or leverage ratios of above 66 (25 observations).9 To fil- ter remaining BHCs for business models nonrepresentative of the concept of commercial banking, we exclude bank-quarters with loan-to-deposit ratios greater than five (10 observations) and with non-interest income amounting to five times interest income (99 observations). Following Whited and Wu (2006) we require indi- vidual banks’ time-series of matched FR Y-9C, Call Report and IRR beta data to be at least eight quarters in length.
The sample period lasts from 1995:Q2 to 2012:Q4, with the main restricting factor being the availability of data on fair values of inter- est rate derivative contracts. This results in an unbalanced panel of 354 unique BHCs and 12,610 bank-quarters. The average time span covered for a BHC is 35.6 quarters and one quarter contains 177.6 BHCs on average. This is in line with recent studies that also com- bine regulatory data on the BHC (and commercial bank) level with market data on these banks (Brunnermeier, Dong, & Palia, 2012; English, Van den Heuvel, & Zakrajsek, 2012; Zagonov, 2011).
Overall, our BHC sample strongly resembles characteristics of the entire commercial banking system. On average, our sample con- tains more than 80% of commercial banks’ aggregate total assets as reported in the FED’s H.8 release. Time-series descriptive statis- tics of total assets-weighted balance sheet ratios of our sample are quite similar to the ones that can be calculated from the H.8 release. Deviations (less than 10pp), e.g. for the reliance on deposit finance or the share of total loans to total assets resemble the greater size of BHCs compared to smaller commercial banks not included in our sample. Correlations over time between respective ratios exceed 80%, with the only exception being the loans-to-assets ratio, with a correlation of 65%.
4. Estimation of time-varying IRR exposures
4.1. Research design
As our first research question, we ask if banks show IRR exposures according to classic bank hedging literature. To draw inferences on banks’ IRR exposures, we estimate IRR betas from
7 We follow, e.g. Kashyap, Rajan, and Stein (2002) and Begenau et al. (2013), acknowledging the same biases in these variables (like the double counting of inter- subsidiary business or the omission of non-bank activities).
8 See Micro Report Series Description, http://www.federalreserve.gov/ reportforms/mdrm/pdf/BHCF.PDF “Beginning March 31, 2006, the FR Y-9C and the FR Y-9LP filing threshold was increased from $150 million to $500 million or more and the reporting exception that required each lower-tier bank holding company with total consolidated assets of $1 billion or more to file the FR Y-9C was eliminated.”.
9 This equals dropping bank-quarters with equity capital ratios of below 1.5% and includes bank-quarters with a risk-adjusted Tier 1 capital ratio below 5%.
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imension to obtain time-varying IRR betas, we set up the following tate space model for each bank i
i,s = ˇi,M,srM,s + ˇi,IR,srIR,s + �ri �i,s (1)
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here ri,s is bank i’s total return, rM,s is the total return of the Datas- ream value-weighted U.S. total market index and rIR,s is the relative hange of the U.S. 10-, 5-, or 2-year government bond spot rate in eek s.10 �i,s represents an independently and standard normally istributed series of measurement errors. Transition equations for he unobserved states conditional on week s, ˇi,M,s and ˇi,IR,s, are ach set up as a random walk and are obtained via Kalman filtering ith diffuse initialization of the initial states.11 �i,s is a vector of two
ndependent disturbances that are independently and standard ormally distributed. �i,s and �i,s are uncorrelated at all times. The yperparameters �ri , �i,M and �i,IR scale the variances of the error erms and are estimated with functional restrictions to avoid neg- tivity using maximum likelihood.
In the setup outlined above, we model the instability of factor oadings over time by a state space system with a random walk in he transition equation for the unobserved states, as similar appli- ations have shown this approach to yield superior results.12 The esulting filtered states ˇi,M,s and ˇi,IR,s derived from applying the alman filter represent the sensitivity of bank i’s stock return in eek s to the market and interest rate factor, respectively.13
The thus assumed instability of factor loadings over time has ecome a common notion in economic and econometric literature, lthough mostly applied to market risk.14 Elliott and Müller (2006) rgue that under the assumption of permanent changes of ˇM,s or IR,s, a constant parameter representing an average (which is the esult of conventional time-series OLS regressions used in earlier tudies of IRR) has no interpretation when the true marginal effect s time dependent. Viewing a bank as a portfolio subject to per-
anent change in composition on both the asset and liability side, nd considering the results of studies of market timing or derivative sage by bank managers,15 this assumption is not hard to defend.
Earlier studies relying on rolling window OLS to obtain time- arying sensitivities face the difficulty of having to assume arameter constancy and stationarity in the residuals of the return- enerating model, while arbitrarily choosing an optimal window ength for which this assumption is supposed to be valid. Further conometric issues can arise if overlapping windows are used in he estimation.
Accordingly, the Kalman filter approach applied here leads to ore precision in the 2-factor models in Eq. (1) for our sample of
HCs. Specificially, cross-sectional averages of root mean squared rrors (RMSE) of conditional 2-factor models in the shape of Eq. (1) ased on beta coefficients from 50 (253) weeks rolling window OLS
stimation are 5.8% (9.2%) above RMSEs resulting from the Kalman lter approach (difference in means statistically significant above he 1% level). Additionally, the Kalman filter betas’ edge in fit in the
10 I.e. negative IRR betas indicate a ceteris paribus negative bank stock return for ncreases in the respective interest rate. 11 States estimated on less than two years (=104 weekly observations) of bank eturn data after diffuse initialization are dropped from further analyses. 12 See, e.g. Mamaysky, Spiegel, and Zhang (2008), Mergner and Bulla (2008) and houdhry and Wu (2008). 13 In contrast to smoothed states which are estimated on the entire sample data, he filtered state at time s is conditional on information up to time s only. 14 See, e.g. Jagannathan and Wang (1996) for theory and Patton and Verardo (2012) or a recent application. This direction of future IRR research for banks has already een initiated by Kane and Unal (1988) and Kane and Unal (1990). 15 See, e.g. Faulkender (2005), Hirtle (1997) and Schrand (1997).
omics and Finance 63 (2017) 204–218 207
conditional factor models is not simply achieved by a higher ran- dom oscillation of betas: the cross-sectional average of time series standard deviations of IRR betas from Kalman filtering is almost 40% lower than that of rolling window OLS (difference in means statistically significant above the 1% level). This strongly indicates that the Kalman filter approach applied here yields coefficients that are more stable and less contaminated by noise and thus convey greater explanatory power and information on BHCs exposures to IRR. This ensures robustness of the results presented below with regard to measurement error of IRR betas in comparison with the estimation approaches traditionally applied in the literature.
4.2. Estimated time-varying IRR betas
Results from the estimation described above allow us to draw conclusions on our first research question: to what extent are banks exposed to IRR and to what extent are they acting in accordance with classic bank hedging theory? Table 1, Panel A shows sum- mary statistics of the pooled distributions of quarterly IRR betas for different maturities of the interest rate factor used in Eq. (1).16
The distributions are centered around the slightly negative but close-to-zero means and medians. While statistically significantly different from zero, magnitudes of average IRR betas are economi- cally insignificant: a standard deviation shock of weekly relative changes in, e.g. the 10-year spot rates indicates an annualized return for the average IRR beta of around −0.5%.
To offer more perspective on the behavior of betas within banks over time, Table 1, Panel B shows the cross-sectional distribution of standard deviations of banks’ IRR beta time-series. Average volatil- ity is 0.128, which is more than five times the average IRR exposure. There are banks in our sample that exhibit lower or even higher volatility of IRR exposures over time.
To gain deeper insight into the persistence of IRR betas we define an ordinal variable, D1090, that takes on the value of 1 (−1) for bank- quarters with highly positive (negative) IRR betas, defined as being above the 90%-quantile (below the 10%-quantile), and 0 for the remaining low IRR betas in the center quantiles. Table 1, Panel C shows transition frequencies controlling for the panel structure of the data and each bank’s individual observation history. We find that high exposures are quite stable: 64% of bank-quarters with high exposures (positive and negative) are followed again by a high exposure of the same sign. Of the remaining bank-quarters 7% keep a high exposure value but of opposite sign and 28% are followed by a low exposure. Low IRR-betas are even more stable: 93% of bank- quarters with low IRR betas are followed by bank quarters with low IRR betas. In the rest of the cases the IRR exposures change to a high exposure.
These relative frequencies of changes in IRR betas from high to low and vice versa show that IRR betas estimated for our sample are, in general, not switching frequently between high and low expo- sures but are developing quite stably. This degree of persistence can be seen as a first indication of IRR betas being related to banks’ busi- ness models and (IRR) risk strategies, as they also generally tend to evolve slowly over time.17
It can be seen from the results, too, that the distribution is negatively skewed and highly leptokurtic. This means that com- pared with a normal distribution, its mass tends to lie close to
16 As each quarter’s last weekly IRR beta is later matched to end-of-quarter bank characteristics, we already present results and base the following arguments on each quarter’s last weekly IRR betas to conserve space. As is expected from a measure without unit like a regression coefficient, distributions of IRR betas at the weekly frequency are highly similar and this approach does not change conclusions drawn in this section. Descriptive statistics of IRR betas at the weekly frequency can be obtained from the authors on request.
17 We thank an anonymous referee for pointing this out.
208 O. Entrop et al. / The Quarterly Review of Economics and Finance 63 (2017) 204–218
Table 1 Summary statistics of estimated IRR betas.
Panel A: pooled distribution Percentile Mean Std. dev. Skew. Kurt.
Maturity of interest rate factor 1% 10% 50% 90% 99%
10 years −0.588 −0.175 −0.022 0.140 0.505 −0.022 0.245 −3.3 543.7 5 years −0.767 −0.154 −0.017 0.113 0.506 −0.024 0.250 −3.4 205.8 2 years −0.631 −0.132 −0.017 0.086 0.463 −0.025 0.222 −3.6 200.5
Panel B: cross-sectional distribution of standard deviations of banks’ IRR beta time-series Percentile Mean Std. dev. Skew. Kurt.
Maturity of interest rate factor 1% 10% 50% 90% 99%
10 years 0.014 0.027 0.067 0.255 1.019 0.128 0.200 5.7 49.6 5 years 0.009 0.022 0.054 0.270 1.022 0.123 0.212 4.9 37.3 2 years 0.005 0.015 0.045 0.245 1.061 0.110 0.202 4.9 37.2
Panel C: transition frequencies for ordinal variable D1090 D1090 Following bank quarter
Preceding bank quarter −1 0 1 −1 64.1 28.3 7.5 0 3.3 93.4 3.3 1 7.0 28.5 64.5
Panel A shows summary statistics of the pooled IRR betas estimated from the state space systems characterized by Eqs. (1) and (2) for three different maturities of the interest rate factor, IR. The first 104 weekly values for each bank are dropped to allow for the diffuse initialization of the Kalman filter. The last value of the weekly IRR betas of each quarter is matched with accounting data from the preceding quarter. This r 2012:Q4. Panel B shows descriptive statistics of the cross-sectional distribution of standar an ordinal variable, D1090, that takes on the value of 1 (−1) for bank-quarters with highly 10%-quantile), and 0 for the low IRR betas in the center quantiles controlling for the pane
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and Strahan (1997), these reductions in traditional business risk together with the too-big-to-fail argument might incline big banks to take greater risks to increase expected return.
ig. 1. Development of the cross-sectional distribution of banks’ IRR beta over time. he figure shows the development of the cross-sectional distribution of banks’ IRR etas on the basis of the mean, 10%- and 90%-quantiles over the sample period.
he center and in the tails. IRR betas in the tails constitute eco- omically high exposures: a standard deviation shock of weekly elative changes in the 10-year (5-year, 2-year) spot rates indicates n annualized return, e.g. for the 10%-quantile of IRR betas of −4.3% −5.7%, −7.0%).
Fig. 1 shows the development of the cross-sectional distribu- ion of banks’ IRR betas over time. Cross-sectional averages of IRR etas are pretty much close to zero over the entire sample period, xcept for the later stage of the financial crisis. Over time there are hases with a low cross-sectional dispersion of IRR betas and less xtreme values in the tails of the distribution, e.g. in the middle of he 2000s. At the beginning of our sample period and especially in
he aftermath of the outbreak of the financial crisis, IRR exposures n the tails are more pronounced.
Based on the results obtained so far, the answer to our first esearch question is the following: on average banks follow the
esults in a sample of 12,610 bank-quarters from 354 unique BHCs from 1995:Q2 to d deviations of banks’ IRR beta time-series. Panel C shows transition frequencies of
positive (negative) IRR betas, defined as being above the 90%-quantile (below the l structure of the data and each bank’s individual observation history.
arguments of the classic bank hedging literature with regard to systematic risks and avoid IRR exposures. Therefore, IRR seems to pose little danger for banks or the banking system as a whole. Nevertheless, we also find economically significant high IRR expo- sures that could matter to regulators and investors. This leads to our second research question: are high exposures purely ran- dom or are they linked to bank characteristics or systemic effects? In the latter cases they need to be taken into account when making investment decisions and they need to be surveilled by regulators.
5. Relationships of high IRR betas with bank characteristics and systemic effects
5.1. Bank characteristics as explanatory variables
To provide an understanding of the interrelationships deter- mining high IRR exposures, our empirical investigation relates time-varying IRR betas to time-fixed effects and lagged bank characteristics consisting of on- and off-balance sheet data from quarterly regulatory reports. We use a broad set of bank character- istics to capture as many aspects of banks’ business and risk profile as possible.18
The size of a bank, here described by the natural logarithm of the CPI-adjusted gross total assets (SIZE), is a natural choice since it is assumed to be linked to risk through many different channels that are a challenge to capture individually. On the one hand, risk reductions can be achieved by big banks through regional/global or product diversification as well as more efficient risk management or risk sharing via economies of scale and lower capital mar- ket participation costs. On the other hand, according to Demsetz
18 For detailed definitions of the explanatory variables, see Appendix A.
O. Entrop et al. / The Quarterly Review of Economics and Finance 63 (2017) 204–218 209
Table 2 Summary statistics of bank characteristics.
Variable Mean Standard deviation Percentile Skewness Kurtosis
1% 50% 99%
SIZE 22.139 1.507 20.148 21.72 27.462 1.419 5.212 LEV 11.791 3.442 6.334 11.316 22.061 3.836 42.692 LIQ 0.269 0.123 0.063 0.248 0.662 1.481 7.286 TL/TD 0.894 0.200 0.366 0.896 1.447 0.863 16.978 DTrD/TLi 0.140 0.085 0.019 0.120 0.395 1.124 4.566 TCI/TL 0.181 0.118 0.008 0.157 0.605 1.882 8.845 BUSCOMRAT 0.144 0.063 0.030 0.134 0.318 0.805 3.939 loanHHI 0.559 0.159 0.277 0.549 0.948 0.375 2.515 NII/II 0.256 0.244 0.016 0.192 1.319 3.796 24.114 ALMM 0.063 0.159 −0.301 0.056 0.447 0.040 5.015 IRCnom 0.331 2.355 0.000 0.006 11.107 11.458 154.814
.231
T he det f 12,61
c r o
a b e h r r
b d d c o p a o l fi
o o n G I i
w e c p o r l ( v a r f l a f
m e
derivatives and IRR can be formulated, because it depends on the underlying intention, which can be either hedging or speculation.
IRCfvNET × 100 0.032 0.237 −0 able reports the summary statistics of the independent variables. Appendix A lists t or IRCfvNET are multiplied by 100 to facilitate comparisons. The sample consists of
Financial leverage, the ratio of total assets to total book equity apital (LEV), is usually inversely associated with asset risk. When isk is measured from the perspective of equity holders, as it is in ur case, the expected sign of the relationship is reversed.
The ratio of liquid assets to total assets (LIQ) is usually viewed s a buffer to insure against higher risk. In the case of IRR of anks, this relationship might break down or be inverted. For xample, an investment in liquid assets with short maturities or igh repricing frequency instead of giving out long-term fixed- ate loans is a way to avoid negative effects of increasing interest ates.
The extent to which traditional loan business and the entire ank is financed by the deposit base is proxied by the loan-to- eposit ratio (TL/TD) and the ratio of total demand and transaction eposits to total liabilities (DTrD/TLi), respectively. Deposit finan- ing is linked to lower IRR: both the Regulation Q ban on interest n these deposits and the stickiness and partial asymmetry in the ass-through of banks’ retail rates documented, e.g. by Cottarelli nd Kourelis (1994), Karagiannis, Panagopoulos, and Vlamis (2010) r Gropp, Kok, and Lichtenberger (2014), allows for lower costs and ower IRR when relying more strongly on deposits as a source of nancing.
Looking closer at the loan portfolio of a bank, we use the share f commercial and industrial loans to total loans (TCI/TL), the share f unused business commitments to total assets plus unused busi- ess commitments (BUSCOMRAT based on Kashyap et al., 2002, and atev, Schuermann, & Strahan, 2009) and a Herfindahl–Hirschman-
ndex (loanHHI) from the loan category shares of commercial and ndustrial, agricultural, consumer, real estate and other loans.
The reason for focusing on commercial and industrial loans, hich are generally only second in importance to banks behind real
state loans, is twofold: on the one hand, compared with other loan ategories TCI/TL exhibits smaller correlations with the other inde- endent variables. A higher TCI/TL is thus to be interpreted on its wn but also as a decrease in the share of omitted loans, especially eal estate loans. On the other hand, commercial and industrial oans can be seen as a proxy for credit risk as in Schrand and Unal 1998); there, lending to commercial and industrial customers is iewed as a high-information activity, as banks can gain a compar- tive advantage in the evaluation of the contained unsystematic isk. Following their argument of banks using hedging techniques or coordinated risk management (i.e. hedging homogenous risks ike IRR and increasing core business risks like credit risk) instead of bsolute risk management, we expect a reduction of IRR exposures
or increased TCI/TL.
Unused commitments in general and unused business commit- ents, BUSCOMRAT, even more so, as they are drawn down less
venly, represent an almost plain form of IRR exposure when left
0.000 0.861 10.724 244.405
ailed definitions of the variables. Summary statistics besides skewness and kurtosis 0 bank-quarters from 354 unique BHCs from 1995:Q2 to 2012:Q4.
unhedged.19 In contrast, commitments can be seen as a kind of insurance of a bank against drops in its business for times of high interest rates that it sells to its customers with a fee. This fee allows the bank to hedge the associated downside risks — maybe even at a profit, depending on its bargaining power and the efficiency of its risk management. If the IRR hedge is set up properly, a bank can thus become more positively exposed to interest rate increases. Results of Kashyap et al. (2002) and Gatev et al. (2009) regarding liquidity risk of banks point in a similar direction. Kashyap et al. (2002) find a positive correlation between unused loan commit- ments and transaction deposits. This indicates that banks make use of the non-perfect correlation between the liquidity needs of depositors and commitment borrowers. Gatev et al. (2009) con- clude that safety-oriented funding inflows from depositors during crises “allow banks to supply credit when markets cannot or would not”.
The variable loanHHI is used to measure concentration on the asset side, which can have different effects on risk depending on the reason for concentration: if specialization or market power are the driving factors, risk can be reduced. Contrary effects can be expected if a lack of willingness (as a management decision), ability of the risk management function or feasibility (e.g. due to locational limitations) prevent a bank from diversifying more broadly into different loan segments.
The following four variables are rather directly linked to IRR: the ratio of non-interest income to interest income (NII/II) describes the relative reliance on different revenue sources. An inverse relation- ship to IRR betas is expected.
In constructing a consistent measure of the traditional maturity gap (ALMM), we follow Purnanandam (2007), but keep the sign information in the difference of assets less liabilities with a maturity or time to repricing of less than or equal to one year. Specifically, an estimated positive relationship indicates higher positive IRR betas for an asset-side excess and higher negative IRR betas for a liability- side excess.
The last two variables employed concern the intensity of use and net fair value position of interest rate derivatives: for the ratio of total notional value of interest rate derivatives over total assets (IRCnom) we sum the notional values over all contract types. No clear expectation regarding the relationship between use of
19 In this context, credit risk is often assumed to take a back seat as the bank can invoke the material adverse change clause at its own discretion to deny conversion of the commitment to a loan after a re-evaluation of the borrower.
210 O. Entrop et al. / The Quarterly Review of Economics and Finance 63 (2017) 204–218
Table 3 Correlations between the independent variables.
SIZE LEV LIQ TL/TD DTrD/TLi TCI/TL BUSCOMRAT loanHHI NII/II ALMM IRCnom
LEV −0.05 LIQ 0.12 0.13 TL/TD 0.12 −0.07 −0.73 DTrD/TLi −0.20 −0.10 0.06 −0.20 TCI/TL 0.18 −0.04 0.08 −0.07 0.06 BUSCOMRAT 0.50 −0.05 −0.19 0.23 −0.12 0.31 loanHHI −0.39 0.06 −0.12 0.13 −0.20 −0.51 −0.23 NII/II 0.46 −0.07 0.25 −0.08 −0.06 0.03 0.28 −0.12 ALMM 0.22 −0.13 −0.35 0.37 0.10 0.27 0.44 −0.14 0.08 IRCnom 0.44 0.05 0.21 0.00 −0.08 0.07 0.17 −0.17 0.17 0.12
T
R c
v p h t v o o b
s i 2 T t
l T o s u c m m a s e
t c
5
I q b s t h S t
v
p a
IRCfvNET 0.37 0.00 0.06 0.09 −0.05 able reports Pearson correlation coefficients between the independent variables.
ather, the estimated parameter on this variable provides an indi- ation of the realized effect of derivative usage.
Similarly, the gap or net position of positive less negative fair alues of interest rate contracts held both for trading and for pur- oses other than trading, scaled by total assets (IRCfvNET), is used ere to approximate current resulting net present value of deriva- ive IRR exposures beyond mere notional values. Positive net fair alues might be viewed as a proxy for counterparty risk, i.e. the risk f the counterparty not being able to meet its obligation. In terms f interest rate risk, this might entail unexpected exposures that anks consider to be hedged by interest rate derivatives.
Table 2 presents the summary statistics. Our analysis shares ome variables with other recent studies combining regulatory fil- ngs with market data (Brunnermeier et al., 2012; English et al., 012; Zagonov, 2011). In comparison with these, LEV, LIQ, DTrD/TLi, CI/TL, loanHHI, NII/II, IRCnom and IRCfvNET are quite similar in erms of location and dispersion parameters.
Average size of a bank is $32.2 billion, median size is $2.7 bil- ion (in 2006:Q1 terms). The ratio of total loans to total deposits, L/TD, is quite symmetrically distributed with more than 75% of bservations showing a deposit base broad enough to finance out- tanding loans. Demand and transaction deposits, DTrD/TLi, make p 14% on average (12% in median) of total liabilities. This is an indi- ation of the prevalence of the classic commercial banking business odel of deposit-financed loans in our sample. The maturity gap- easure, ALMM, is distributed around a positive mean of 6.3% with
significant portion of negative values. This shows that there is a ubstantial number of bank-quarters for which the usually assumed xcess of short-term liabilities over short-term assets prevails.
Table 3 shows the pairwise correlations of the bank characteris- ics. Most variables are correlated at very low levels and no pairwise orrelation reaches critical values.20
.2. Regression design
To analyze links of high IRR exposures, we relate time-varying RR betas to the above-described bank characteristics lagged by one uarter21 and time-fixed effects, �t. Significant links of high IRR etas with time-fixed effects show that there are common unob- erved factors that drive high exposures at times. This indicates he existence of systemic effects that influence IRR exposures of
ighly IRR-exposed banks at the same time in a similar manner. uch behavior of IRR exposures warrants surveillance by regula- ors. The same is true if high IRR betas are linked to lagged bank
20 This is also reflected in the variance inflation factors (VIF): mean VIF of the ariables is 1.76 with SIZE exhibiting the highest value of 2.81. 21 As in Brunnermeier et al. (2012) we link the last value of bank i’s market- erceived IRR exposure in quarter t, called ˇi,IR,t , to the bank characteristics reported t the end of the preceding quarter, t − 1.
0.08 0.18 −0.11 0.18 0.16 0.52
characteristics. Our aim is to not only establish such links but to look deeper into their directions and magnitudes.
As a first step, we analyze the probability that a bank-quarter’s IRR exposure lies in one of the high beta quantiles of the exposure distribution. This allows us to answer the first question relevant to investors and regulators in terms of IRR exposures:22 which bank characteristics are likely to result in high IRR exposures? We there- fore set two dummies, D10 and D90, that take on the value of 1 if the bank-quarter exhibits an IRR beta below the 10%-quantile or above the 90%-quantile of the exposure distribution, respectively, and 0 otherwise. We run logit regressions including time-fixed effects, �t, for D10 and D90 in the general form of Eq. (3):
logit(P(Di,q,t = 1)) = �0 + �1SIZEi,t−1 + �2LEVi,t−1 + �3LIQ i,t−1 + �4TL/TDi,t−1 + �5DTrD/TLii,t−1 + �6TCI/TLi,t−1 + �7BUSCOMRATi,t−1 + �8loanHHIi,t−1 + �9NII/IIi,t−1 + �10ALMMi,t−1 + �11IRCnomi,t−1 + �12IRCfvNETi,t−1 + �t (3)
To provide a deeper understanding of the links between high IRR exposures and the entire exposure distribution with bank charac- teristics and systemic effects, the focus of our study is on results from applying unconditional quantile regressions developed by Firpo et al. (2009) on Eq. (4).23
ˇi,IR,t = �0 + �1SIZEi,t−1 + �2LEVi,t−1 + �3LIQ i,t−1 + �4TL/TDi,t−1 + �5DTrD/TLii,t−1 + �6TCI/TLi,t−1 + �7BUSCOMRATi,t−1 + �8loanHHIi,t−1 + �9NII/IIi,t−1 + �10ALMMi,t−1 + �11IRCnomi,t−1 + �12IRCfvNETi,t−1 + �t + �i,t (4)
Unconditional quantile regressions developed by Firpo et al. (2009) show how an unconditional quantile of the pooled IRR beta dis- tribution is affected by a small increase in an explanatory variable (controlling for the effects of other included variables). These effects are measured by coefficients for the set of independent variables in Eq. (4) that are estimated in separate unconditional quantile regres- sions for each unconditional quantile of the dependent variable that is of interest. Thus, coefficients can differ in sign, magnitude and
significance for different unconditional quantiles of the depend- ent variable (IRR betas) representing heterogenous responses to independent variables (bank characteristics) at different quantiles.
22 We thank an anonymous referee for this suggestion. 23 We are grateful to Nicole Fortin for providing the accompanying STATA ado-file
on her homepage.
O. Entrop et al. / The Quarterly Review of Economics and Finance 63 (2017) 204–218 211
Table 4 Logit regressions for the 10%- and 90%-quantile.
Maturity of interest rate factor
10 years 5 years 2 years
Variable Dummy D10 D90 D10 D90 D10 D90
SIZE 0.3487*** −0.2283** 0.4441*** −0.4283*** 0.4176*** −0.4405*** (0.1046) (0.1032) (0.1067) (0.1032) (0.1051) (0.1076)
LEV 0.0617*** 0.0838*** 0.0300** 0.0473*** 0.0202* 0.0176 (0.0139) (0.0126) (0.0130) (0.0116) (0.0121) (0.0110)
LIQ −3.1411*** 2.8720*** −2.3455** 1.8643** −2.4743** −0.7191 (0.9191) (0.9132) (0.9761) (0.9187) (1.0207) (0.9739)
TL/TD −1.0341* 0.4698 −1.2952* 0.7082 −1.6674*** −0.5552 (0.5379) (0.5872) (0.6525) (0.5449) (0.6025) (0.5995)
DTrD/TLi −1.2706 5.1562*** −1.2935 3.1729*** −0.2387 1.7093** (0.9001) (0.7855) (1.0049) (0.7757) (1.0395) (0.7911)
TCI/TL 0.4949 −0.8706 0.0421 1.2898 0.4508 0.8256 (1.0674) (0.9947) (1.0859) (1.0321) (1.1150) (1.0534)
BUSCOMRAT 1.4433 1.5433 0.3326 0.0783 −2.7660* 2.1890 (1.4636) (1.4312) (1.5519) (1.4445) (1.5565) (1.4909)
loanHHI 4.2011*** −1.5152** 4.1898*** −0.7752 3.7277*** 1.2591* (0.8007) (0.7141) (0.7967) (0.7293) (0.7857) (0.7400)
NII/II −0.2919 −0.2069 −0.6424* −0.4272 −0.6195* −0.9906** (0.3233) (0.3090) (0.3901) (0.3810) (0.3763) (0.3909)
ALMM −2.9661*** 1.4775*** −1.1337** 1.5847*** 0.3607 1.5395*** (0.5207) (0.4956) (0.4978) (0.4717) (0.4968) (0.4855)
IRCnom 0.0567 0.1047*** 0.0358 0.1321*** −0.0325 0.0898** (0.0404) (0.0369) (0.0401) (0.0394) (0.0460) (0.0449)
IRCfvNET −16.1406 29.0391 30.4330 14.9125 32.6255 88.9981*** (22.0194) (25.1204) (20.2711) (26.3361) (24.0162) (25.9466)
Observations 12,610 12,610 12,610 12,610 12,610 12,610 Quarter FE Yes Yes Yes Yes Yes Yes p > �2 0.00 0.00 0.00 0.00 0.00 0.00
Table reports results from panel random effects logit regressions on Eq. (3) including quarter-fixed effects with dichotomous dependent variables D10 and D90, respectively, that take on the value of 1 if the bank-quarter exhibits an IRR beta below the 10%-quantile or above the 90%-quantile, respectively, of the exposure distribution and 0 otherwise. Results are reported for the three different maturities of the interest rate factor, IR, in Eqs. (1) and (2). p > �2 indicates p-values from Wald �2 tests for model fit. T ifican i ective
a i e b i c u f I t e
e i t b e q t w t q t 1 u a
he shares of panel-level variance components to total variance are statistically sign n parentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, resp
The quantile regression approach thus additionally allows us to nalyze how changes in bank characteristics are linked to changes n the distribution of IRR betas in a non-linear way. Hence, besides stablishing links beyond mere location shifts (as already provided y OLS regressions), unconditional quantile regressions give an
nsight into possible scale/dispersion shifts, asymmetric effects or hanges in skewness linked to changes in covariates. Furthermore, nconditional quantile regressions are more robust to departures rom normality than linear estimators.24 As the distribution of RR betas to be analyzed here is skewed and highly leptokurtic, his econometric approach, which considers wider distributional ffects, seems appropriate for our research question.
In our sample we do find highly positive and highly negative xposures in the tails of the IRR beta distribution that we focus on n our analysis for links with bank characteristics. Including only hese high IRR betas in a regression would lead to a sample selection ias. But estimating the effects of bank characteristics on differ- nt quantiles of the IRR exposures distribution via unconditional uantile regressions allows us to analyze how bank characteris- ics (and time-fixed effects) are related to high IRR exposures that e find at the low and high quantiles. Thus, e.g. coefficients for
he 10%-quantile of the IRR beta distribution tell us how the 10%- uantile is affected by changes in bank characteristics by answering he question: does an increase in a bank characteristic lead to the
0%-quantile being higher, lower or unchanged? This then shows s, too, how the highly negative exposures in that quantile are ffected by the increase in the bank characteristic. Comparisons
24 See, e.g. Schaeck and Cihak (2014).
tly different from zero for all specifications above the 1%-level. Standard errors are ly.
with coefficients of this bank characteristic at other quantiles allow the detection of a possible heterogenous influence.
5.3. Logit analyses of estimated links between high IRR betas and bank characteristics
As described in the research approach in Section 5.2, a first impression of links between IRR exposures and bank characteristics can be gained from logit regressions on dichotomous dependent variables D10 and D90, respectively, that take on the value of 1 if the bank-quarter exhibits an IRR beta below the 10%-quantile or above the 90%-quantile of the exposure distribution, respectively, and 0 otherwise.
Table 4 reports results from panel random effects logit regres- sions on these dependent variables with right hand-side variables as in Eq. (3) including quarter-fixed effects. There, p-values from Wald �2 tests for model fit are all below the 1%-level. Results reported for the three different maturities of the interest rate factor, IR, in Eqs. (1) and (2) are quite similar in terms of sign, magni- tude and statistical significance. Such logit regressions show which bank characteristics are linked to the probability of bank-quarters exhibiting highly positive or highly negative IRR betas controlling for the panel structure of the data.
As can be seen from Table 4, higher leverage, LEV, is related to a symmetrical increase in the probability of exhibiting high IRR betas irrespective of their sign. This result is consistent with expectations
regarding the relationship with IRR betas measured from equity risk. Additionally, it is an indication that banks are not balancing IRR and risk from financial leverage from the perspective of equity holders, e.g. by decreasing the former when increasing the latter. To
2 f Econ
s o i l b r o a a
i t w e r a o t l c
( ( r c m u i o a s t g e s t s I
b b t a t i e b c b
( t o ( g b m i t
f b
applying conventional panel OLS estimators to Eq. (4). As discussed in Section 4.2, on average banks seem to follow
the suggestions of classic bank hedging literature and avoid IRR exposures. These bank-quarters at the center of the exposure
26 See, e.g. Black, Hancock, and Passmore (2007) for a recent study on this issue. 27 Standard errors are bootstrapped from 11,000 replications. Respective figures
for the 5-year and 2-year IRR betas are quite similar in terms of shape but show tighter confidence intervals.
28 Results are not reported here in detail to keep the paper’s focus on the tails of the exposure distribution, but can be obtained from the authors upon request. For the cross-section, the panel between estimator applied to Eq. (4) only shows significant links of mean IRR exposures with variables SIZE, loanHHI and IRCnom. The former is
12 O. Entrop et al. / The Quarterly Review o
ome degree this could be attributed to the capital treatment of IRR n the banking book that is currently still applicable. Although there s growing international momentum to incorporate some more or ess standardized form of capital charge for IRR that stems from the anking book into Pillar 1 or 2, regulations concerning this type of isk for the sampling period considered in this study mostly relied n banks’ internal measurement systems (mostly some form of bal- nce sheet simulation for predefined term structure shocks) or gap nalyses when examining banks.25
This lack of an – internationally aligned – comprehensive cap- tal charge for IRR from the banking book might incline banks o accept higher IRR exposures or at least keep the current level hen increasing leverage and thereby their own default risk. In an
xtreme scenario such an increase in leverage might result from eductions in the value of equity due to compressed asset values nd might go along with increased speculation on the development f interest rates via term transformation in an attempt to coun- erbalance lower profitability. Thus, our result on leverage can be inked to the ongoing discussion on the adequate capitalization and apital regulation of all sources of banks’ risks.
Greater SIZE, in contrast, is related asymmetrically to a higher lower) probability of bank-quarters exhibiting highly negative positive) IRR betas. This indicates that in spite of the expected eduction in risk that bigger banks can achieve through more effi- ient risk management from scale economies and lower capital arket participation costs and greater geographical and prod-
ct/income diversification, greater SIZE is associated with a shift n the probability of a bank showing positive IRR betas to that f its showing negative ones. This is in accordance with Demsetz nd Strahan (1997) who show a similar result. There and in our tudy, less overall business risk due to greater size, together with he too-big-to-fail argument, might incline bigger banks to accept reater IRR exposures to fill up their overall risk budget and increase xpected return. Such effects might pose a threat to global financial tability and need to be kept in check by regulators with coun- erbalancing measures like additional capital charges for global ystemically important banks (G-SIBs), as introduced within Basel II.
A similar asymmetrical structure is found for an excess of lia- ilities in the short-term portion of the balance sheet (indicated y a negative ALMM) and the degree of loan segment concentra- ion, loanHHI. The reverse relationship holds for the share of liquid ssets to total assets: the greater this ratio, the lower (higher) he probability of bank-quarters exhibiting highly negative (pos- tive) IRR betas. These results indicate that the probability of xhibiting highly negative (positive) IRR betas is higher (lower) for ank-quarters characterized by a higher degree of loan segment oncentration, excess of liabilities in the short-term portion of the alance sheet and less liquidity holding.
Especially interesting is the positive link found for the ALMM traditional, i.e. positive, term transformation indicated by nega- ive values for ALMM). Besides confirming the economic validity f IRR betas as a good IRR measure, this link shows that positive negative) term transformation as indicated from a balance sheet ap measure is associated with a shift in probability to show IRR etas in the negative (positive) tail of the IRR beta distribution as easured from equity return data. This indicates that banks’ equity
nvestors are taking risk from on-balance sheet term transforma- ion and associated IRR into account.
Other statistically significant asymmetrical relationships are ound for the ratio of demand and transaction deposits to total lia- ilities, DTrD/TLi, and the extent of interest rate derivative usage,
25 See, e.g. Federal Reserve Board of Governors (1996, 2010, 2015), Section 5010.37.
omics and Finance 63 (2017) 204–218
IRCnom. Bank-quarters with higher values for these variables are more likely to exhibit a highly positive IRR beta (with no significant link for highly negative IRR betas). This makes sense economically for DTrD/TLi, as the above-mentioned slow and asymmetric pass- through for deposit rates allows banks with a stronger deposit base to profit from rising market rates, as they can also smooth interest rates passed through to high-value relationship lending customers.26 It is also interesting that the probability of being in the positive IRR beta tail, where IRR exposures are opposite from what is expected for traditional term transformation, is related pos- itively to the intensity of IRR derivative usage. This result would be in line with the tendency to use IRR derivatives to hedge or maybe even overhedge IRR that stems from term transformation inherent in traditional deposit and lending business.
The logit analyses applied so far give a first indication of the relationships of high IRR betas with bank characteristics. There are several interesting links between bank characteristics and the prob- ability of bank-quarters exhibiting highly negative and/or positive IRR betas. In the following section we will analyze these relation- ships more deeply by applying unconditional quantile regressions. There, we will also reflect on traditional research approaches based on OLS methods and relate the results to economic theory and earlier studies in this area.
5.4. Unconditional quantile regression analyses of estimated links between high IRR betas and bank characteristics
Unconditional quantile regressions show how the unconditional quantiles of a dependent variable – in our case banks’ quarterly IRR betas from 1995:Q2 till 2012:Q4 – are related to right hand-side variables – in our case bank characteristics. To show the different relationships that emerge when applying unconditional quantile regressions to our dataset, we begin this section with a graph- ical overview of results for the entire distribution of IRR betas before analyzing the results in more detail in the following sec- tions. Therefore, Fig. 2 shows the results, i.e. coefficients of the bank characteristics and their 95% confidence intervals, of applying unconditional quantile regressions to Eq. (4) for quantiles between 5% and 95% of the 10-year IRR beta.27
In Fig. 2, many variables show statistically significant links to IRR-betas at the low (high) quantiles, where highly negative (posi- tive) IRR betas are located, but most variables show no significant link at or around the median of IRR exposures, indicating that there is no location shift in the exposure distribution associated with these variables. These results are in accordance with results from
28
associated with a shift of the cross-sectional mean to the left, the latter are associated with a shift to the right. Other variables are not related. The fixed-effects panel estimator applied to Eq. (4) shows significant links over time only for three variables: higher loan segment concentration and a greater excess of short-term liabilities over short-term assets (i.e. a negative ALMM indicating traditional term transformation) are associated with a mean location shift of IRR betas to the left. A higher ratio of demand and transaction deposits to total liabilities shifts means to the right. Other variables are not related. Considering that we find the IRR beta distribution’s mean and median located close to zero, these results are not surprising.
O. Entrop et al. / The Quarterly Review of Economics and Finance 63 (2017) 204–218 213 −
.0 6
− .0
5 −
.0 4
− .0
3 −
.0 2
− .0
1
0 .2 .4 .6 .8 1 quantile of dependent variable
SIZE
− .0
2 −
.0 1
0 .0
1 .0
2
0 .2 .4 .6 .8 1 quantile of dependent variable
LEV
− .1
0 .1
.2 .3
.4
0 .2 .4 .6 .8 1 quantile of dependent variable
LIQ
− .1
0 .1
.2
0 .2 .4 .6 .8 1 quantile of dependent variable
TL/TD
0 .2
.4 .6
0 .2 .4 .6 .8 1 quantile of dependent variable
DTrD/TLi −
.2 −
.1 0
.1 .2
0 .2 .4 .6 .8 1 quantile of dependent variable
TCI/TL
− 1
− .5
0 .5
1
0 .2 .4 .6 .8 1 quantile of dependent variable
BUSCOMRAT
− .3
− .2
− .1
0 .1
.2
0 .2 .4 .6 .8 1 quantile of dependent variable
loanHHI
− .1
− .0
5 0
.0 5
.1
0 .2 .4 .6 .8 1 quantile of dependent variable
NII/II
− .0
5 0
.0 5
.1 .1
5 .2
0 .2 .4 .6 .8 1 quantile of dependent variable
ALMM
− .0
05 0
.0 05
.0 1
.0 15
.0 2
0 .2 .4 .6 .8 1 quantile of dependent variable
IRCnom
− 10
− 5
0 5
10
0 .2 .4 .6 .8 1 quantile of dependent variable
IRCfvNET
coefficient 95% confidence interval
F (solid b nal qu
d a b o b e r e b o g w e
5
r i o l t i o b f o s
ig. 2. Coefficients over quantiles for the full sample. The figure shows coefficients ootstrapped with 11,000 replications) of the independent variables for unconditio
istribution seem to be at least partially hedged against IRR that rises almost naturally from banks’ risk transformations. For these ank-quarters at the center of the exposure distribution, we find nly few significant and economically meaningful links with ank descriptive variables. This makes sense as a hedged position xhibits at most weakened links between the source of risk and its ealization. Again, this is why we focus below on the tails of the IRR xposure distribution, where we find economically significant IRR etas. Unconditional quantile regressions allow us to analyze links f bank characteristics at different degrees of exposure and thus et a better understanding of their differentiated relationships ith changes in location, scale, skewness and the shape of the IRR
xposure distribution in general.
.4.1. Unconditional quantile regression results Table 5 shows the detailed results of unconditional quantile
egressions for Eq. (4) at the 10%- and 90%-quantiles for the set of ndependent variables, including quarter fixed effects. This choice f quantiles is the result of a trade-off between accounting for the eptokurtic distribution of the IRR betas and analyzing quantiles hat include a sufficient number of data points for the results to be nterpretable and still be representative of a large enough share f the data to be economically meaningful. Standard errors are
ootstrapped from 11,000 replications. Overall, results for the dif- erent maturities of the interest rate factor used for the estimation f the IRR betas are quite similar in terms of sign, magnitude and tatistical significance.
line) and 95% confidence intervals (shaded area, calculated from standard errors antiles from the 5%- to the 95%-quantiles of the 10-year IRR beta (horizontal axis).
As with logit regressions in Section 5.3, we find symmetrical and asymmetrical links indicating increases or decreases in risk. The most prominent result for a symmetrical link is again leverage. LEV shows a significant negative loading for the 10%-quantile and a significant positive loading for the 90%-quantile with a signifi- cant difference between both loadings (also see Fig. 2 for graphical proof). This indicates that for both tails of the IRR exposure distribu- tion, increases in leverage are associated with higher IRR exposures. This result adds to the findings from logit regressions above in that not only the probability of exhibiting a high IRR beta is related to a high leverage but also the magnitude of IRR betas, i.e. given a high IRR beta an increase in leverage leads to even higher betas.
Further symmetrical effects increasing IRR in both tails – although not consistent with logit regression results – are found for BUSCOMRAT and loanHHI. As expected from Section 5.1, unused business commitments can alter IRR exposures in both directions depending on the degree of bargaining power and hedging effi- ciency. The results for loanHHI indicate that banks accepting a higher concentration of their loan business segments are similarly tolerating higher IRR exposures. Unfortunately, the reasons for this kind of parallel risk management strategy cannot be analyzed fur- ther from our data. Nevertheless, both results warrant stronger surveillance by regulators in terms of risk policies and processes
for banks that show higher levels of unused commitments and loan segment concentration.
We find the opposite symmetrical effect, i.e. decreasing IRR betas in both tails, for the degree of liquidity holding. Results
214 O. Entrop et al. / The Quarterly Review of Economics and Finance 63 (2017) 204–218
Table 5 Unconditional quantile regressions for the 10%- and 90%-quantile.
Maturity of interest rate factor
10 years 5 years 2 years
Variable Quantile 10% 90% 10% 90% 10% 90%
SIZE −0.0310*** −0.0167*** −0.0391*** −0.0111*** −0.0295*** −0.0077*** (0.0034) (0.0030) (0.0037) (0.0027) (0.0032) (0.0022)
LEV −0.0074*** 0.0080*** −0.0076*** 0.0075*** −0.0062*** 0.0061*** (0.0011) (0.0012) (0.0012) (0.0011) (0.0010) (0.0009)
LIQ 0.0903** −0.0174 0.117** −0.0760** 0.227*** −0.111*** (0.0455) (0.0398) (0.0491) (0.0364) (0.0393) (0.0310)
TL/TD −0.0143 −0.0282 −0.0452 0.0320 0.0322 −0.0038 (0.0307) (0.0194) (0.0307) (0.0200) (0.0203) (0.0153)
DTrD/TLi 0.194*** 0.192*** 0.197*** 0.113*** 0.177*** 0.0252 (0.0408) (0.0467) (0.0412) (0.0385) (0.0331) (0.0312)
TCI/TL 0.0322 −0.0489 0.0217 0.0189 0.0532** 0.0688** (0.0246) (0.0302) (0.0284) (0.0329) (0.0231) (0.0320)
BUSCOMRAT −0.253*** 0.388*** −0.245*** 0.304*** −0.0317 0.210*** (0.0624) (0.0682) (0.0714) (0.0631) (0.0538) (0.0519)
loanHHI −0.0732*** 0.0810*** −0.0805*** 0.0929*** −0.0533** 0.133*** (0.0237) (0.0237) (0.0242) (0.0237) (0.0207) (0.0230)
NII/II 0.0062 0.0179 0.0498*** −0.0354*** 0.0151 −0.0432*** (0.0145) (0.0146) (0.0141) (0.0108) (0.0121) (0.0085)
ALMM 0.0447* 0.0296 0.0800*** 0.0298 0.0311 0.0126 (0.0247) (0.0260) (0.0271) (0.0252) (0.0218) (0.0215)
IRCnom 0.0029* 0.0072*** 0.0034* 0.0059*** 0.0017 0.0031*** (0.0016) (0.0020) (0.0019) (0.0017) (0.0013) (0.0011)
IRCfvNET −0.921 3.658* −3.922* 2.404 −0.0604 3.143** (1.593) (2.046) (2.069) (1.780) (1.355) (1.554)
Constant 0.480*** 0.358*** 0.670*** 0.166** 0.386*** 0.122* (0.0914) (0.0812) (0.0969) (0.0740) (0.0779) (0.0624)
Observations 12,610 12,610 12,610 12,610 12,610 12,610 Quarter FE Yes Yes Yes Yes Yes Yes R2 0.077 0.050 0.080 0.050 0.078 0.054
Table reports results from unconditional quantile regressions on Eq. (4) at the 10%- and 90%-quantiles. The dependent variables are the matched quarterly IRR betas for the t rors a * hat si f
i t d a c d r f h
t d r n b i r a a m
b D a e t i a r l t
hree different maturities of the interest rate factor, IR, in Eqs. (1) and (2). Standard er *, and * indicate significance at the 1%, 5%, and 10% levels, respectively. Coefficients t or an interest rate factor maturity are italicized.
ndicate that liquidity drives the magnitude of high IRR betas owards zero, thereby reducing absolute IRR exposures and their istributional dispersion. This makes sense economically, as liquid ssets due to their flexibility and short-term repricing frequency arry little opportunity costs when interest rates rise. This result oes not hold consistently for all different maturities of the interest ate factor and is only in accordance with logit regression results or the negative tail, where a decrease in probability for exhibiting ighly negative IRR betas is found.
We find truly asymmetric effects for SIZE, DTrD/TLi and IRCnom hat remain unnoticed unless differentiated analyses are used for ifferent quantiles. For SIZE, which is also significantly negatively elated to IRR exposures at the central quantiles, we again find egative relationships that differ significantly from each other for oth unconditional tail quantiles analyzed here in more detail. An
ncrease in SIZE amplifies already existing negative exposures, but educes existing positive exposures. Size is therefore not related to
reduction in absolute IRR. Its effect could rather be characterized s an asymmetrical shift of the whole distribution to the left – being ore pronounced for the negative beta tail. A similar asymmetric effect, although of opposite direction,
ecomes evident with the significantly positive coefficient of TrD/TLi for all quantiles. An increase in the ratio of demand nd transaction deposits to total liabilities reduces negative IRR xposures and increases positive exposures. This leads to the dis- ribution of IRR betas being shifted to more positive values, which s in line with the above-mentioned literature on banks’ slow and
symmetric interest rate pass-through for deposit accounts and the elated smoothing of interest rates passed through to relationship- ending customers. This interpretation also holds when considering he positive tail results that are reflected in logit regression results.
re obtained via bootstrapping with 11,000 replications and given in parentheses. ***, gnificantly differ at or above the 5% significance level for the 10%- and 90%-quantiles
Examining the use of interest rate derivative contracts reveals an asymmetric picture similar to logit regression results: negative quantiles of IRR exposures are statistically unrelated, but positive quantiles increase with higher IRCnom, although coefficients do not differ significantly for the 10%- and 90%-quantile. Specifically, increased usage of interest rate derivative contracts shifts the dis- tribution of IRR betas to more positive values, indicating that banks that are more active in derivative markets are able to shield them- selves better against the negative impacts of rising interest rates. This is especially interesting as the right tail of the IRR beta dis- tribution resembles IRR exposures, contrary to what is expected for traditional term transformation. This adds to the logit regres- sion result in a way that indicates a tendency of banks avoiding IRR from traditional term transformation to use IRR derivatives to overhedge IRR.
Looking at the time-fixed effects, we find many statistically significant values that indicate systemic effects influencing banks together at points in time beyond the impact of the bank character- istics described above. We leave determining the nature and source of this influence for future research. Nevertheless, the existence of such a common behavior of high IRR exposures alone can be dan- gerous for the banking system as a whole and is thus a cause of concern for regulators.
5.4.2. Robustness To check our results for statistical artifacts, spurious correlations
or misspecifications, we apply the unconditional quantile models
above to a sample ranging only from 1997:Q2 to 2012 and use the refined maturity mismatch measure defined by English et al. (2012). It is constructed from more detailed information on matu- rity brackets of interest-bearing assets and liabilities available at
O. Entrop et al. / The Quarterly Review of Economics and Finance 63 (2017) 204–218 215
Table 6 Unconditional quantile regressions controlling for the financial crisis.
Quantile 10% 90%
Variable Regular Crisis Delta Regular Crisis Delta
SIZE −0.0369*** −0.0145*** *** −0.0256*** −0.0018 *** (0.0081) (0.0049) (0.0083) (0.0054)
LEV −0.0108*** −0.0030** *** 0.0045 0.0115*** *** (0.0024) (0.0013) (0.0028) (0.0018)
LIQ −0.1126 0.552*** *** −0.0078 −0.0281 (0.1117) (0.0664) (0.1286) (0.0851)
TL/TD −0.1050* 0.217*** *** −0.0106 −0.0239 (0.0628) (0.0357) (0.0659) (0.0442)
DTrD/TLi 0.1597* 0.140*** 0.0220 0.578*** *** (0.0916) (0.0538) (0.1490) (0.101)
TCI/TL 0.0258 0.0969 ** −0.0840 −0.0199 (0.0789) (0.0801) (0.1183) (0.0854)
BUSCOMRAT −0.2391 −0.163* 0.2998 0.663*** ** (0.1572) (0.0957) (0.2070) (0.140)
loanHHI −0.0257 −0.114*** * 0.0196 0.268*** *** (0.0640) (0.0403) (0.0763) (0.0508)
NII/II 0.0181 −0.0459** ** 0.0262 −0.0016 (0.0360) (0.0214) (0.0426) (0.0280)
ALMM −0.0157 0.0995** ** 0.0126 0.0504 (0.0714) (0.0457) (0.0858) (0.0572)
IRCnom 0.0053 0.0006 0.0097** 0.0026 * (0.0041) (0.0021) (0.0049) (0.0030)
IRCfvNET 1.3975 −10.32*** *** −1.0744 12.58*** *** (5.080) (3.396) (5.7497) (3.883)
Constant 0.782*** 0.672*** (0.113) (0.0924)
Observations 12,610 12,610 Quarter FE Yes Yes R2 0.089 0.060
Table reports results from unconditional quantile regressions on Eq. (4) at the 10%- and 90%-quantiles including interaction terms with a regular times dummy taking on the value of one for the regular-times subperiod from 1995:Q2 to 2007:Q2 and zero for the crisis subperiod from 2007:Q3 to 2012:Q4. The dependent variable is the matched quarterly IRR beta for the 10-year maturity of the interest rate factor, IR, in Eqs. (1) and (2). Columns termed “regular” and “crisis” report coefficients for the subperiods; the r m of t t s. Sta p ively.
t l u
t n r T
1 t c d a A e u d h c i
t u t r r
d e
each independent variable with a regular-times dummy. It takes on the value of one from the beginning of our sample in 1995:Q2 to 2007:Q2 and zero for the crisis subperiod from 2007:Q3 to 2012:Q4.29 The columns termed “crisis” and “regular” in Table 6
egular times coefficients are obtained and tested against the null of zero as the su erm. Columns termed “delta” show the level of significance of the interaction term arentheses. ***, **, and * indicate significance at the 1%, 5%, and 10% levels, respect
he commercial bank level Call Reports beginning 1997:Q2 to calcu- ate a weighted average maturity gap. Results remain qualitatively nchanged.
As the two bank characteristics related to interest rate deriva- ive contracts, IRCnom and IRCfvNET, are distributed rather on-normally, we test for a distortive influence on regression esults by eliminating them from the set of independent variables. his leaves the remaining results qualitatively unchanged.
Replacing IRCnom with a dummy that takes on the value of when the nominal value of interest rate derivatives is greater han 5% of total assets leads to qualitatively unchanged results. The hoice of the cut-off for the dummy is driven by a trade-off between iscretizing information contained in the derivative variable, while t the same time making sure its interpretation does not change.
pure user vs. non-user dummy, in contrast, might lead to differ- nt results because of different economic relationships. Banks that se derivatives only to a marginal degree might use derivatives for ifferent reasons, at different costs and with different success than eavy users. In this context, Stulz (2004) concludes that derivatives an create risk, especially if a firm uses derivatives episodically and s inexperienced in their use.
Although independent variables showed no sign of severe mul- icollinearity, results especially for SIZE might be influenced by the niform scaling of ratios by total assets as denominator. To test if his is an issue with our data, we replace SIZE with the natural loga- ithm of the CPI-adjusted market and book value of equity. Results
emain qualitatively unchanged.
As some of the variables employed above, like leverage or erivative usage, could have bidirectional relationships with IRR xposures, concerns for endogeneity of regressors might arise.
he coefficients of the respective bank characteristic and the respective interaction ndard errors are obtained via bootstrapping with 11,000 replications and given in
Concerning leverage, the use of book leverage is a first measure of precaution. The argument made above, that leaving out deriva- tive variables does not change results, is another indication that there is also no grave problem of identification in our sample caused by endogenous regressors. What contributes to this assess- ment is that we relate market information to quarterly-lagged accounting data. This way, any endogeneity-inducing bidirectional relationship would need to exist over this time-lag as well. As we see no economically sound argument to support such rela- tionships, we do not consider endogeneity to be an issue in our analyses.
5.4.3. Results for high exposures controlling for the financial crisis Next, we extend the analysis of the relationships by controlling
for the recent financial crisis. As market conditions have undergone drastic changes since the middle of 2007, it is highly interesting to see if and how the relationships found above are affected by the financial crisis.
To be able to draw inferences, we include interaction terms of
29 We base this approach on the crisis timeline of the Federal Reserve Bank of St. Louis (http://timeline.stlouisfed.org/). The rationale is that, although the direct consequences of the financial crisis might have slowly begun to attenuate by the end of 2009, the countermeasures taken by the FED and the US government lasted well into 2012 and some are still in place today.
2 f Econ
r i r i p
L d p s d c e T o f p i
a a a t b o s s s e t L e
b e d v
t w o c w i m f c
I p b p t e t r t h f t r
p c a b
16 O. Entrop et al. / The Quarterly Review o
eport the resulting coefficients for the 10-year maturity of the nterest rate factor in Eqs. (1) and (2) for the crisis subperiod and the egular times subperiod, respectively. Significance of differences n relationships between subperiods is represented by the level of -values of the interaction terms in the “delta” column.
As can be seen from Table 6, for most of the variables, like EV, SIZE, DTrD/TLi, BUSCOMRAT, loanHHI and IRCnom, relationships escribed in Section 5.4 are visible in terms of sign for both sub- eriods, but show different magnitudes and – related – levels of ignificance. For DTrD/TLi, BUSCOMRAT and loanHHI relationships escribed above for the entire sample period are significant for the risis subperiod indicating that their impact on IRR exposures is specially important during such a period of market uncertainty. he increased importance of deposits as a stable source of funding, f commitment lending during times when uncertainty about the uture availability of credit is widespread among customers, and of roduct diversification during and after the financial crisis is visible
n these results. For LEV and SIZE, relationships with the negative IRR beta tail
re consistently significant throughout our entire set of analyses nd for both subperiods. Although the direction of the differenti- ted relationships described above in Section 5.4 remains the same, here are differences in levels of significance for the positive IRR eta tail for the subperiods. The symmetrical IRR-increasing effect f leverage is there for the crisis subperiod, while the asymmetrical hift in IRR betas to more negative values associated with greater ize can be found for regular times. The reduction in strength of the hift of IRR betas to the left associated with greater size might be xplained with the increased probability and greater credibility for he denial of a public bail-out for bigger banks after the collapse of ehman Brothers and related regulation, e.g. banks’ “living wills”, nacted afterwards.
Two additional interesting effects involving highly negative IRR etas become apparent: results for LIQ show that the risk-reducing ffect we find for highly negative IRR betas in the entire sample is riven by the crisis subperiod, which is in line with recent literature iewing liquidity at the heart of the financial crisis.
In a similar manner, ALMM shows a significantly positive rela- ionship with the IRR exposure at the 10%-quantile since the crisis, hich is significantly different from regular times. Hence, an excess
f liabilities in the short-term portion of the balance sheet (indi- ated by a negative sign for the independent variable) is associated ith amplified negative exposure to increases in interest rates. This
s in line with the aforementioned latest research on an aggregate aturity mismatch being amplified by the extremely short-term
unding of securitization vehicles as a major cause of the financial risis.
The significantly different coefficients that have emerged for RCfvNET since the crisis indicate an increase in high IRR betas for ositive net fair values of interest rate derivative contracts. This can e seen as a consequence of the (perception of) increased counter- arty risk that resulted from the financial crisis. Stulz (2010) argues hat counterparty risk is present in credit default swap markets, ven though much of the direct risk due to the default of the coun- erparty is generally accounted for by collateral agreements. The ationale is that in the case of such a default, the surviving coun- erparty is exposed to risks that were considered hedged and thus as to buy new protection on the market. This way, higher positive
air values of interest rate derivatives, which were meant to pro- ect a bank, seem to have resulted in higher IRR exposures as the eliability of this protection deteriorated.
Overall, we find altered relationships between market-
erceived IRR exposures and bank characteristics for the financial risis subperiod. The significant increase in coefficients of liquidity nd maturity mismatch is a sign of markets realizing the associated uild-up of risk with respect to interest rates. Both effects are found
omics and Finance 63 (2017) 204–218
at the quantile of highly negatively exposed bank-quarters, making them even more relevant to investors and regulators.
6. Conclusion
We analyze interest rate risk exposures of U.S. bank holding companies from 1995 to 2012. As our first contribution we test whether banks show IRR exposures in accordance with classic bank hedging literature. Our approach for measuring IRR exposures is based on the traditional approach by Flannery and James (1984). We extend their model in the time dimension by applying Kalman filter techniques on a state space system that relates stock returns of banks to a market factor and an interest rate factor via unobserved time-varying sensitivities. The resulting time-varying IRR betas for each bank represent an econometrically consistent measure of the time-series of exposures to IRR as perceived by the market.
Over banks and over time we find means and medians of IRR betas slightly below but close to zero. Thus, the average IRR expo- sure of banks is in line with the theoretical bank hedging literature. This result at first glance depicts IRR exposures of banks to be a rather negligible source of risk, warranting little attention from reg- ulators or investors. Nevertheless, the IRR beta distribution shows high exposures that are economically significant.
Our second contribution to the existing literature on IRR is to provide a deeper understanding of these high IRR exposures with bank characteristics from regulatory accounting data. Banks’ busi- ness models or tactical and strategic decisions in terms of risk management do not change too rapidly over time. This is why we first analyze the switching behavior of banks in and out of the central exposure quantiles and high exposure tails. Results show a quite high degree of stability with respect to their position in the distribution: more than 64% of observations in high beta quan- tiles are followed by an observation in a high beta quantile of the same sign. Exposures in the central quantiles are even more stable.
Applying logit analyses and unconditional quantile regressions, we find differentiated relationships of highly positive and highly negative IRR exposures with lagged bank characteristics and time- fixed effects. The latter are partly significantly different from zero in both analytical approaches applied, indicating unobserved sys- temic effects that broadly affect the cross-section of banks.
Our results point to strong links between bank characteristics and IRR exposures that should be taken into account by regulators to promote the stability of the banking system and by investors to better assess banks’ riskiness. The first of our key findings is the symmetrical and risk-increasing relationship of leverage with probability and magnitude of IRR betas in both exposure tails. Besides being expected for a risk measure based on equity returns like IRR betas, this result can serve as an indication of banks not counterbalancing financial leverage risk and IRR. This might be related to a lack of an internationally aligned regulation for IRR from the banking book, allowing banks to take on IRR and increase their leverage at the same time. A risk-insensitive leverage ratio is not able to keep the degree of term transformation or maturity mis- match in check either. Against this background our results add to the ongoing discussion of optimal capitalization and capital charges for banks.
Similarly, the observed shift of IRR betas to more negative values linked to increases in size needs to be considered by regulators and investors. Results indicate a shift towards negative IRR betas resem- bling traditional term transformation. This indicates that bigger banks do not use their overall greater potential for diversification
or economies of scale to reduce total risk, but might even fill up under-used risk budgets by taking on greater IRR. To avoid negative effects on financial stability, such behavior – that might be inter- preted as reliance on public bail-outs – has to be kept in check, e.g.
O. Entrop et al. / The Quarterly Review of Economics and Finance 63 (2017) 204–218 217
Table A.1 Variable definitions
Variable Description Calculation Sources
SIZE Log of gross total assets, CPI-adjusted for 2006:Q1
ln (
(BHCK2170 + BHCK3123 + BHCK3128) ∗ 1000 ∗ CPI2006:I/CPIact )
U.S. FED FR Y-9C report, Bureau of Labor Statistics
LEV Total assets to total equity BHCK2170/BHCK3210 U.S. FED FR Y-9C report LIQ Liquid assets to total assets BHCK0010 + BHCK1754 + BHCK3545
+ {
BHCK0276 + BHCK0277 before 1997 : I BHCK1350 1997 : I–2001 : IV BHCKB987 + BHCKB989 after 2001 : IV
U.S. FED FR Y-9C report
TL/TD Total loans to total deposits (BHCK2122 + BHCK2123) / (BHDM6631 + BHDM6636 +BHFN6631 + BHDN6636)
U.S. FED FR Y-9C report
DTrD/TLi Demand and transaction deposits to total liabilities
rcon2215/rcon2948 Chicago FED Call Reports
TCI/TL Commercial and industrial loans to total loans
(BHCK1763 + BHCK1764) / (BHCK2122 + BHCK2123) U.S. FED FR Y-9C report
BUSCOMRAT Unused business commitments to total assets plus unused business commitments
(rcfd3423 − rcfd3815) / (rcfd3423 + rcfd2170 − rcfd3815) Chicago FED Call Reports
loanHHI Herfindahl-Hirschman-Index from the loan category shares
( TCI/TL
)2 + (
BHCK1590 BHCK2122+BHCK2123
)2 +(
BHCB538+BHCK2011 BHCK2122+BHCK2123
)2 + (
BHCK1410 BHCK2122+BHCK2123
)2 + (other loans share)2
U.S. FED FR Y-9C report
NII/II Non-interest income to interest income
BHCK4079/BHCK4107 U.S. FED FR Y-9C report
ALMM Short-term asset-liability mismatch
In accordance with Purnanandam (2007), but keeping the sign info Chicago FED Call Reports
IRCnom Nominal values of all interest rate contracts to total assets
(BHCK8693 + BHCK8697 + BHCK8701 + BHCK8705 + BHCK8709 +BHCK8713 + BHCK3450)/BHCK2170
U.S. FED FR Y-9C report
8741
b i
d t e s r f s m p c t s i f i i l
s b b t t t m a s r i a
A
IRCfvNET Net fair value position of all derivative contracts to total assets
(BHCK8733 + BHCK
y the application of Basel III risk buffers for global, systemically mportant banks and other nationally/regionally “bigger” banks.
Rather mixed results for other bank descriptive variables for the ifferent approaches and (sub)samples make an overall interpre- ation less imperative, but some are still worth noting to show the ffects of the financial crisis on IRR exposures of banks and relation- hips with bank characteristics. Positive net fair values of interest ate derivative contracts on the books, which can be seen as a proxy or counterparty risk, are related to an increase in high IRR expo- ures for the crisis subperiod. This link can be interpreted as the arket realizing reduced hedging efficiency via increased counter-
arty (wrong-way) risk of derivatives in the time after the financial risis. Our traditional maturity gap measure is significantly linked o the magnitude of negative tail IRR exposures only during the cri- is. For this subperiod, we find that traditional term transformation s associated with increased negative IRR exposures. Additionally, or this tail of IRR exposures, liquidity has a risk-reducing effect that s only valid for the crisis subperiod. These links reflect some find- ngs on causes for the financial crisis identified in recent literature, ike Farhi and Tirole (2012) and Brunnermeier and Oehmke (2013).
Overall, we show that high IRR betas are linked to unobserved ystemic effects in the financial markets and to the development of anks’ characteristics that can be assumed to partially reflect their usiness models and risk management strategies. Regulators need o focus especially on these high IRR exposures as they might pose a hreat for individual banks and possibly for the entire banking sys- em. Investors need to take high IRR exposures into account when
aking decisions, e.g. regarding portfolio optimization. Our logit nd quantile regression results can aid regulators and investors urveilling IRR by showing relationships with publicly available egulatory accounting information. We also add to current discuss- ons regarding optimal capitalization and capital charges for banks s well as current regulatory initiatives.
ppendix A. Variable definitions
Table A.1
− BHCK8737 − BHCK8745) /BHCK2170 U.S. FED FR Y-9C report
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- Looking beyond banks’ average interest rate risk: Determinants of high exposures
- 1 Introduction
- 2 Related literature
- 3 Data
- 4 Estimation of time-varying IRR exposures
- 4.1 Research design
- 4.2 Estimated time-varying IRR betas
- 5 Relationships of high IRR betas with bank characteristics and systemic effects
- 5.1 Bank characteristics as explanatory variables
- 5.2 Regression design
- 5.3 Logit analyses of estimated links between high IRR betas and bank characteristics
- 5.4 Unconditional quantile regression analyses of estimated links between high IRR betas and bank characteristics
- 5.4.1 Unconditional quantile regression results
- 5.4.2 Robustness
- 5.4.3 Results for high exposures controlling for the financial crisis
- 6 Conclusion
- Appendix A Variable definitions
- References
