Bank Solvency and Funding Cost
New Data and New Results
  • 1 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund
  • | 2 0000000404811396https://isni.org/isni/0000000404811396International Monetary Fund

Contributor Notes

This paper presents new evidence on the empirical relationship between bank solvency and funding costs. Building on a newly constructed dataset drawing on supervisory data for 54 large banks from six advanced countries over 2004–2013, we use a simultaneous equation approach to estimate the contemporaneous interaction between solvency and liquidity. Our results show that liquidity and solvency interactions can be more material than suggested by the existing empirical literature. A 100 bps increase in regulatory capital ratios is associated with a decrease of bank funding costs of about 105 bps. A 100 bps increase in funding costs reduces regulatory capital buffers by 32 bps. We also find evidence of non-linear effects between solvency and funding costs. Understanding the impact of solvency on funding costs is particularly relevant for stress testing. Our analysis suggests that neglecting the dynamic features of the solvency-liquidity nexus in the 2014 EU-wide stress test could have led to a significant underestimation of the impact of stress on bank capital ratios.

Abstract

This paper presents new evidence on the empirical relationship between bank solvency and funding costs. Building on a newly constructed dataset drawing on supervisory data for 54 large banks from six advanced countries over 2004–2013, we use a simultaneous equation approach to estimate the contemporaneous interaction between solvency and liquidity. Our results show that liquidity and solvency interactions can be more material than suggested by the existing empirical literature. A 100 bps increase in regulatory capital ratios is associated with a decrease of bank funding costs of about 105 bps. A 100 bps increase in funding costs reduces regulatory capital buffers by 32 bps. We also find evidence of non-linear effects between solvency and funding costs. Understanding the impact of solvency on funding costs is particularly relevant for stress testing. Our analysis suggests that neglecting the dynamic features of the solvency-liquidity nexus in the 2014 EU-wide stress test could have led to a significant underestimation of the impact of stress on bank capital ratios.

I. Introduction

The global financial crisis appears to have been a liquidity crisis, not just a solvency crisis.1 Yet the failure to adequately model interlinkages and the nexus between solvency risk and liquidity risk led to a dramatic underestimation of risks. Liquidity risk manifests primarily through a liquidity crunch as firms’ access to funding markets is impaired, or a pricing crunch, as lenders are unwilling to lend unless they receive much higher spreads. We extract funding liquidity risk from observing the costs that banks are required to pay to secure market liquidity. A sudden increase in bank funding costs can have an adverse impact on financial stability through the depletion of banks’ capital buffers. To preserve financial stability, it is important to assess banks’ vulnerability to changes in funding costs. The reason is twofold. First, to the extent funding costs reflect counterparty credit risk, it is of particular interest for supervisors to determine the level of capital buffers that should be held to keep funding costs at bay if and when market conditions deteriorate. Second, funding costs are linked not only to banks’ initial capital position but also they determine their capital position going forward, paving the way for adverse dynamics. The magnitude of this effect is likely to depend on the bank’s behavioral reaction to rising funding costs. On the one hand, it may react by setting higher lending rates to its borrowers. Yet this action reduces the bank’s market share and its franchise value. On the other hand, the bank might not be able to pass-through additional funding costs to new lending so its internal capital generation capacity is reduced. Even if some pass-through is possible, the erosion of profits is likely to be substantial given the shorter time to repricing of liabilities relative to assets with the margin impact on the carrying values of assets outweighing that of new asset generation. 2

The dynamics of adverse economic conditions on banks’ capital position can be examined through a stress testing exercise. Typically, bank stress tests measure the resilience of banks to hypothetical adverse scenarios. While stressed conditions capture a deterioration of banks’ economic conditions such as a severe recession and a sharp correction in asset prices, they do not reflect the gradual increase in funding costs that banks experience as their capital buffers are depleted. The analysis presented in this paper suggests that stress test models that do not consider the dynamics between solvency and funding costs are likely to underestimate the impact of stress on bank solvency and financial stability.3 First, higher funding costs erode bank capital buffers in the short-term due to the back-book effect.4 Second, capital buffers are further depleted in the long-term as risk sensitive investors’ demand for a higher compensation to bear risk, sets off adverse dynamics and lengthens the persistence of funding shocks.

This paper aims to answer two questions. First, what is the magnitude of the interaction between funding costs and solvency? Second, how can the estimated effects be used for stress testing purposes? To address these two issues, we construct a new dataset and test for the importance of the two-way interaction between funding conditions and bank solvency. Our results lend support to the joint determination of funding costs and bank solvency. We also provide some evidence of non-linear interactions between funding costs and solvency risk, and find that this relationship has not changed significantly during the crisis.

While these results are somewhat consistent with the literature on bank solvency and funding costs, we extend the literature in two directions. First, we build a unique dataset consisting of supervisory reporting data of 54 large banks over 2004–20135 shared across supervisory agencies from six countries.6 We check that the data is of higher quality than the publicly available sources used in other studies. Second, we focus on the endogenous determination of solvency and funding costs, contrary to the approach taken in most studies which investigate funding cost drivers. To this end, we study the interaction between solvency and liquidity using a simultaneous equation approach based on a set of exogenous instrumental variables, rather than using lagged values of endogenous variables as under a VAR specification. This is motivated by our concern that, given the endogeneity of capital and funding costs discussed above, an OLS-based regression is likely to yield biased coefficients. A priori, the direction of the bias is uncertain. On the one hand, one might argue that banks perceived by bondholders to be riskier might face both higher funding costs and hence seek to maintain higher capital ratios to address market’s perceived risk. And if this perception is unobserved in the empirical analysis, then OLS estimates are likely to underestimate the negative impact of funding costs on solvency. On the other hand, OLS estimates can overstate this negative relationship if positive shocks to solvency, which are likely to also affect funding costs, remain unobserved. Concretely, if markets expect that a strong bank will become safer by raising its capital ratio, current funding costs might decline more than warranted by its current capital position. But if this expectation is unobserved, then OLS estimates will overstate the negative relationship between solvency and funding costs. Our results provide evidence that OLS underestimates the impact of capital on funding costs. Whereas a multivariate OLS-based panel regression on our dataset yields a positive relationship between banks’ capital position and funding costs, our simultaneous equation-based analysis suggests a large negative impact of capital on the cost of funding.

Our results suggest more sizeable effects than those found in the literature. We find that a 100 bps increase in regulatory capital is associated with a 105 bps decrease in funding costs, which is a large effect relative to the existing literature, where the effect tends to be smaller, at an average of 50 basis points.7 We illustrate an application of our empirical work to inform stress testing projections of bank capital ratios under stressed conditions, using the 2014 EU-wide stress test exercise.

The rest of the paper is structured as follows. Section II reviews the existing literature. Section III introduces the new dataset and presents the econometric approach. Section IV shows the main findings on the interaction between regulatory capital and funding costs. Section V explores the robustness of the results to a market-based definition of bank solvency, and to banks’ bearing capacity for liquidity risk. Section VI illustrates the dynamic impact of the solvency-funding interaction in a stress testing framework. Section VII concludes with some policy implications.

II. Related Literature

This paper is related to the empirical literature on the relationship between bank solvency and funding conditions, where funding conditions are defined in terms of funding costs rather than in relation to bank access to funding markets.8 There are two main strands of literature: a broader set of papers seeking to explain the effect of banks’ balance sheet fundamentals on funding costs, and an emerging literature examining the two-way interaction between bank solvency and the cost of funding.

Within the first strand, one set of papers base their estimates on a multivariate panel estimation of large banks. Annaert et al. (2010) find that the interaction between solvency and funding costs is indeed significant in a sample of 31 large euro area banks over the pre-crisis period from 2004 through October 2008. A one percentage point drop in weekly bank stock returns (associated with higher implied market-based leverage), is associated with a 64 basis points rise in a bank’s CDS spread. Similarly, Hasan et al. (2016) show that solvency has significant impact on bank funding costs using a sample of 161 global banks from 23 countries over 2001–2011. An increase of one percentage point in market-based leverage raises CDS spreads by an average of 101 basis points. This effect is slightly more pronounced after 2007 when the sensitivity of the coefficient increases to 103 basis points. In addition, they also include costs of funds (proxied by interest expense over total assets) as an explanatory variable which turns out to be significant. However, this seems to point to an endogeneity problem as CDS spreads and funding costs are expected to be jointly determined. Likewise, Aymanns et al. (2016) examine the sensitivity of bank funding costs to bank solvency drawing on the FDIC call report covering 10,000 banks over the period 1993–2013. They perform a panel estimation to quantify the impact of changes in bank fundamentals on yearly balance-sheet measures of banks’ funding costs. The latter are captured by either wholesale funding (interest rate expenses on feds funds) or average funding costs (total interest expense over total liabilities). Their independent variables are bank fundamentals clustered by factor analysis. The constituent variables stem from four groups, solvency, liquidity, asset quality and profitability. They find a larger negative coefficient of bank solvency on wholesale funding costs, pointing at the higher credit risk sensitivity of wholesale investors relative to depositors. Their results suggest that the sensitivity of funding cost to bank capital is larger in bad times. Whereas the average effect is typically small, with a solvency shock of five percentage points leading to an average increase in interbank funding cost of about 20 basis points, this effect rises to 40 basis points in 2007 when wholesale funding providers’ sensitivity to solvency risk reached its peak. The analysis also shows that the relationship between funding cost and solvency is non-linear, with higher sensitivity of funding cost at lower levels of bank solvency. Afonso et al. (2011) conduct an event study around Lehman Brothers’ bankruptcy using transaction-level data containing all transfers by U.S. banking institutions through Fedwire. They find that the worst performing large banks access the federal funds market least, whereas the small banks access the market at an increase in funding spreads of over 96 bps. Acharya and Mora (2015) show that banks’ vulnerability to liquidity risk, defined as banks’ exposure to liquidity demand risk due to credit line drawdowns and materializing in higher deposit rates, is greater in magnitude for the class of banks with greater solvency problems proxied by lower asset quality. The study is conducted on a panel of 7,000 U.S. banks over the 2007–2009 financial crisis.

A different estimation method is applied by Babihuga and Spaltro (2014). In the context of a panel error correction model (PECM), they estimate the long- and short-run effects of bank-specific and macro variables on funding costs using a panel of 52 banks in 14 advanced economies over 2001–2012. In the long-run, a one percentage point increase in bank regulatory capital reduces funding costs by 26 basis points, though this relationship is somewhat reversed in the short-term, wherein an increase in bank capital is associated to rising bank funding costs two quarters ahead. Gray et al. (2012) use a contingent claims analysis (CCA) approach to compute a fair value credit spread (FVCDS) as a proxy of bank funding cost using a Merton-based approach. Combining FVCDS with an implied market-based capital ratio the authors find a non-linear relationship between funding costs and bank capital. Under the baseline scenario, banks’ weighted average EDF rises steadily at an accumulated pace of 75 percent by the end of the stress testing horizon. This is mapped to an equivalent 75 percent rise in FVCDS. Yet, under the adverse scenario, the projected accumulated increase of 150 percent in the EDF measure is linked to a larger rise in FVCDS revealing a non-linear relationship between market-based solvency and funding costs.

Within the second strand of the literature, Pierret (2014) uses fixed-effect panel vector autoregressive (PVAR) regressions to model the nexus between solvency and liquidity risk of banks in a set of 49 U.S. banks examined over 2000 to 2013. The main result suggests and asymmetric relationship: higher solvency risk, measured by the expected capital shortfall SRISK9 defined by Acharya et al. (2010, 2012) and Brownlees and Engle (2011), limits the access of the firm to short-term funding. Yet a firm with more liquidity risk exposure, proxied by short-term debt, has a higher risk of insolvency in a crisis. Specifically, a unit increase in the expected capital shortfall ratio reduces its short-term debt ratio by 1.1 percentage points, suggesting that riskier banks find their access to wholesale markets limited. On the other hand, banks posting a one percent increase in short-term debt see their expected capital shortfall ratio increase by 0.9 percentage points suggesting that banks funded with more short-term debt face higher solvency risk. Our paper is more closely related to Distinguin et al. (2013), which uses a simultaneous equation approach to study the endogenous interaction between solvency and funding volumes on a panel of 870 United States and European publicly traded commercial banks over 2000–2006. For the solvency part, they use regulatory capital ratios as proxy. On the funding side, they focus on the inverse of the NSFR and a so-called liquidity creation indicator. They show that banks creating more liquidity have lower regulatory capital levels, and banks with lower capital ratios post higher measures of liquidity transformation. Our approach differs insofar as we focus on funding costs rather than on funding volumes, and in that we investigate the relationship between solvency and funding costs on a newly constructed dataset drawing on supervisory returns. We also calibrate the impact of incorporating the solvency-funding costs interaction on banks’ resilience using the 2014 EBA stress testing framework.

III. The Relation Between Solvency Risk and Funding Costs

To assess the resilience of financial institutions to adverse shocks, it is important to understand the interaction between solvency and funding costs. This is particularly relevant in the design of stress tests where different types of shocks can affect regulatory ratios for capital and liquidity simultaneously.10

A sharp rise in bank funding costs is likely to have an adverse effect on bank capital by eroding net interest income. Yet the channels through which funding costs affect profits are not straightforward. A bank may react by absorbing higher cost of funding thus reducing its profitability. Alternatively, the bank may try to pass on the increased cost to customers by charging high lending rates on new lending. This action might also erode profitability as liabilities reprice faster than assets and the demand for new lending is depressed, compressing the income base.11 The effect of bank capital on funding costs is also complex due to the highly non-linear relation between bank asset value and solvency risk due to the short-put option embedded in bank assets. Moreover, the compensation required by investors to bear solvency risk depends on scarcity effects from compressed bond issuance under stress, on investors’ funding liquidity, and on systematic risk factors. This section uses a reduced-form approach and a broad set of controls as a useful starting point for the calibration of the impact of solvency stress on bank funding costs in supervisory stress tests.

A. Construction of a New Dataset

The variables included in the new dataset were collected specifically for the purpose of estimating the simultaneous interdependence of bank solvency and funding costs. The data consist of an unbalanced panel of 54 large banks from six countries that cover the period from 2004Q4 to 2013Q4. With 33 banks in the sample, the United States is the largest contributor to the sample. The sample also includes six Austrian, six Canadian, six Dutch, and three Nordic banks. The bank data were shared among regulatory agencies of the respective countries under strict confidentiality protocols and went through careful data filtering and quality checks.12

Measuring the solvency-funding cost nexus is complicated due to the different frequencies of regulatory data for funding costs and solvency. The frequency of the former is usually much higher (up to daily) than for the latter (usually quarterly). The empirical analysis focuses on quarterly data. Another challenge for the analysis is posed by the choice of proxies to capture funding costs and solvency risk.

Banks can refinance their operations in different funding markets by tapping retail deposits, unsecured wholesale funding (including unsecured corporate deposits as well as funds sources from money markets and bond markets), and secured funding (including repos, securities lending, and securitization). We proxy funding costs by the marginal cost of long-term unsecured wholesale funding. We use the five-year senior single name CDS spread for each bank in the sample. This is a reasonable proxy as the sample consists of large international banks where CDS liquidity is usually higher than for the average bank. Also, CDS spreads are market-implied risk-neutral probabilities, which are obtained under the assumption that investors are risk-neutral and desire no risk premia, and thus are immune to shifts in risk aversion sentiment.

Alternatively, we could use secondary market spreads on active bonds to approximate the cost of wholesale funding. However, time series analysis drawing on is variable is challenging as bond features change over time (e.g., face value, maturity, covenants). In contrast, time series data for CDS spreads are ready available and do not suffer from changes in the maturity structure of a bank’s debt.

Another option is to use a measure of short-term wholesale funding costs. We prefer using the five-year fair value CDS spreads and the reason is threefold. First, bank specific data on short-term funding costs often reflects quoted prices rather than actual transaction prices. Second, variations in counterparty risk perception often lead to a volume reaction (i.e., shortening of tenors or a reduction of lines) rather than to significantly higher rates. Third, unconventional monetary policy (UMP), including full allotment and QE, limited the variation and information content of short-term market rates as a proxy for banks’ marginal funding costs, although we expect the impact of UMP in our analysis to be rather limited. The measures are available to all banks in the respective economies; thus, we do not expect it to systematically affect the variation of CDS spreads across banks. Data on individual emergency liquidity assistance (ELA) could reduce the bank’s CDS and affect our estimates. Though central banks try to keep ELA confidential, we are quite confident that no bank in the sample received ELA.

There are several caveats associated with the use of CDS as a measure of funding costs. First, market liquidity in CDS markets might be limited for specific banks in the sample (e.g., for some of the smaller European banks). To account for this unobserved heterogeneity, we use bank-specific fixed effects. Second, CDS spreads may not be representative of bank funding costs under stress if the bank is shut out of the funding market. We take the view, however, that even under this extreme scenario, they signal effectively the marginal shadow cost of funding and thus affect a bank’s internal fund transfer pricing. Third, CDS spreads may reflect counterparty concerns over the issuer of credit protection. Yet, in line with the aforementioned literature, we do not expect this to systematically bias CDS spreads over the sample period. In any case, to measure effectively funding costs, the actual funding structure of each bank should be considered and the cost of alternative funding sources calibrated.13

Turning to solvency risk, the link between equity and default probability has been widely established in structural models of firms’ default (Merton, 1974), tested empirically (Ericsson et al., 2009), and used as a framework to calibrate Basel III regulatory capital. This motivates our choice of solvency risk, i.e., core tier 1 ratio (CT1), which reflects high quality regulatory capital relative to risk weighted assets.14 Yet the relationship between solvency risk and capital structure is somewhat more complex in banks relative to corporate firms. First, most bank debt is short-term which introduces liquidity risk into solvency risk. We address this concern by introducing bank liquidity buffers as a control variable. Second, bank regulation and supervision, deposit guarantee schemes, and implicit government guarantees (including the underpriced liquidity insurance via access to central bank emergency liquidity assistance for illiquid and often insolvent banks) suggest that the default boundaries as well as explanatory variables for bank CDS spreads also differ from that of non-financial companies.15 This is a consequence of the perceived public good characteristics of financial stability and the ensuing specific regulatory framework banks operate in. We capture implicit government guarantees for bank debt by including a proxy for government credit risk reflected in its sovereign CDS spreads, as well as by considering a bank’s credit rating from S&P with the uplift based on government support. We transform the standard rating scale into a 1 (best rating or AAA) to 24 (worst rating) numerical scale (S&P). Third, the distance to default is typically higher for banks than for non-financial firms because banks not only have to maintain minimum regulatory capital ratios but also because the required capital buffer is commensurate with the underlying volatility of assets. In theory that should ensure that the recovery rate of a failing bank is higher than for non-bank financial companies. Lastly, the Merton model relies on observed values of asset volatility. Yet as attested during the global financial crisis, the underlying bank asset volatility is unobservable and can quickly rise if bank asset values fall, which implies that the default barrier can be reached faster than implied by the Merton approach. To capture the risk of underlying assets and bank capacity to generate future profits we include asset quality and net interest income as regressors. In sum, there are strong arguments to suggest that the model of bank solvency is more complex than that of non-financial companies and a broader range of variables needs to be considered. To address the robustness of our results to different measures of bank resilience, we re-run the estimation using a market-based measure of bank default probability over five years, namely the expected default frequency (EDF) estimated by Moody’s Credit Edge.16

We consider a wide range of bank specific variables as potential determinants of bank solvency and funding cost. We use two balance sheet variables which play key roles in solvency stress tests, i.e., loan loss provisions in percent of total assets (LLP) as a measure of asset quality, and net income in percent of total assets (NI) as a proxy for banks’ return on assets and its organic recapitalisation capacity. Provisions have a direct impact on bank solvency through their effect on risk weighted assets. We are aware, however, of the shortcomings of this proxy. Banks have some leeway in determining loan loss provisions and can use it as a signalling device to the market, to accommodate regulators, to smooth earnings over time and for tax optimisation purposes. In addition, regulations and accounting rules have an impact on the level and timing of the recognition of changes in banks’ capital adequacy.17 This recognition is part of the rationale for considering, as an alternative to the supervisory solvency ratio in Section IV, the EDF measure, which is more market oriented. We also control for banks’ resilience to liquidity shocks, which is monitored regularly by the regulatory authorities. We define liquidity risk (LiRisk) as a bank’s liquidity risk exposure measured by its short-term wholesale debt (liabilities with a remaining maturity of less than three months) over its liquidity risk bearing capacity defined as the stock of liquid assets (cash and central bank excess reserves, sovereign debt with risk-weights of 0 and 20 percent). A higher ratio implies that the bank is exposed to higher roll-over risk. Also, wholesale funding is more credit sensitive and is likely to react more strongly to an erosion of bank capital buffers. At the same time, banks might profit from maturity transformation to a larger extent by funding a larger share of long-term assets with short-term wholesale funding, supporting bank profitability and easing credit risk. The sign of the liquidity risk coefficient is likely to depend on the initial capital position of banks.

The cost of funding also depends on investors’ confidence in banks’ funding instruments and in changes to macroeconomic conditions. We address the potential regime shift around the outbreak of the global financial crises in 2008 by using the following control variables. First, we include a nonbank, non-country specific variable that proxies for market sentiment in the interbank market. The LIBOR-OIS spread is a widely-used gauge for tensions in money markets. It tends to be high in times of stress and low otherwise. Second, we control for substantial changes in monetary policies and for the introduction of unconventional measures which were designed to dampen bank funding costs by using the overnight index swap (OIS) as a proxy for the monetary policy stance at the global level. While the specifics of unconventional measures differ between the various currency areas in our sample and the reliance of individual banks on these central bank measures differ, this information is not publicly available in a systematic manner. In the model, we allow for bank specific fixed effects to capture such unobservable differences. Third, we include a market measure of volatility to capture global risk aversion.18 This is motivated by evidence that a common systemic risk factor can reduce the discrepancy between modelled and actual returns for corporate bondholders (Chen et al, 2009). We proxy global risk aversion by the VIX index. This is a reasonable assumption as the sample of banks includes internationally active banks holding international asset portfolios and raising funding from international creditors. Global risk attitude can have an impact on bank funding costs, especially for hedging products such as credit derivatives. It is worth noting that the market sentiment variables are assumed to affect directly funding costs, but not CT1 systematically, though an increase in the VIX could increase the underlying volatility of bank assets, particularly if banks hold large equity portfolios, impacting their risk-weighted assets (RWAs). Over time, the indirect effects are captured in the simultaneous equation approach via funding costs. Finally, we add a crisis dummy (Crisis_d) that captures significant changes in the interaction between funding costs and bank solvency as well as other time-varying control variables. Market expectations regarding bank capitalisation changed abruptly with Lehman’s bankruptcy. The dummy variable is defined as 0 from 2004Q4 to 2008Q3 and as 1 from 2008Q4 to 2013Q4. Despite the control variables, it is possible that the interaction between solvency and funding costs changed over time; e.g., we expect a stronger sensitivity of wholesale investors to solvency risk post-Lehman. We, therefore, also run our equations separately for two sub-samples (pre-and post-Lehman’s default) to check for robustness.

To control for the macroeconomic environment, we use country-level credit growth (loan_growth) to capture loan demand in the local credit market. High private sector credit demand can be associated with periods of high capital ratios as banks frontload increases in CT1 to fund loan growth. One might argue that weak banks may be forced to boost their regulatory capital ratios to increase their resilience. To control for deliberate management actions, some of which were required by the supervisory agency to ease systemic risk, we construct a dummy variable to capture large swings in regulatory capital (ΔCT1_d). Specifically, an increase of CT1 by more than 20 per cent quarter-on-quarter in nominal terms serves as a proxy for deliberate management action.19 This might stem from share issuance, asset sales, or public support measures. In fact, the various public interventions in 2008Q4 seem to be well captured by this dummy. We use five-year government CDS (CDS_gov) as a proxy of spillovers between sovereign risk and bank funding costs. Sovereign bonds constitute the safest assets in the countries in the sample and corporate bonds are priced against them. Higher sovereign CDS spreads are usually associated with higher corporate bond spreads. For the banks the interaction can be amplified via the value of implicit and explicit government guarantees. The value of the guarantees decreases with the credit worthiness of the guarantor.

The choice of instrumental variables for identification purposes in the simultaneous equation system (2) is of key importance. We have selected variables that fulfil the economic preconditions; i.e., they are directly related to one endogenous variable, but interact with the second one only indirectly via the first one. They fulfil the exclusion restriction. In line with the literature, drivers of CDS spreads include proxies of profitability and asset quality. We use loan loss provisions (LLP) as instrumental variable for the identification in the CT1 equation in Specification 1. LLP are a proxy for asset quality and directly affect CT1 as lower credit quality increases risk weighted assets and, thus, the denominator of the CT1 ratio. LLPs affect FVCDS only indirectly via counterparty risk, i.e. indirectly via CT1. Similarly, we use net income (NI) as an exogenous variable in the solvency equation. The main channel through which solvency affects NI is via funding costs which we capture in our model set-up. Other determinants of NI like commission income (fees and turn-over); staff costs, IT-costs, LLPs, participations, return on own portfolio are not directly affected by solvency. In addition, we include country-wide loan growth only in the CT1 equation. In Specification 2 we add a dummy variable that captures deliberate management action to change CT1 in the CT1 equation regulatory capital (ΔCT1_d). It affects FVCDS only via CT1. We use the S&P rating (S&P (lag 1)), the sovereign CDS spread (CDS_gov), and the LIBOR-OIS spread for the identification of equation FVCDS in Specification 1. The lagged S&P rating directly affects banks’ CDS spreads; it can have an indirect impact on CT1 eventually via higher funding costs. Similarly, sovereign CDS spreads and the LIBOR-OIS spreads directly affect bank funding costs but not banks CT1 ratios.

Table 1 shows data coverage for the variables used in the estimation whereas Table 2 presents the summary statistics. Note that most of the variables are denoted in percentage points. This also holds for CDS spreads. The median value stood at 131 bps across all banks over the entire period. The quartiles of the EDF measure are: 0.08 percent (first), 0.3 percent (second) and 0.94 percent (third). In addition, Table 3 provides a cross-correlation matrix of the dependent and independent variables used in the analysis. Interestingly, regulatory and market-based measures of bank solvency are not highly correlated with a correlation coefficient below 10 percent. EDF measures are more closely linked to other market-based measures including CDS spreads of government bonds and S&P’s bank ratings. While the components of the P&L account are all linked in various ways, the correlation between NI and LLP at 40 percent is not particularly significant in our sample. This might be explained by the fact that there are many other determinants of NI so that the increasing LLPs do not mechanistically reduce NI. The latter is mostly determined by interest income (slope of the yield curve, bank specific funding costs) and commission income (fees and turn-over); staff costs, IT-costs, LLPs, participations, return on own portfolio and a number of other factors also play a role.20

Table 1.

Data Coverage

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Note: Coverage of key variables for the sample of European and North American banks from 2004Q4 to 2013Q4.Sources: National supervisory data; Bloomberg L.L.P., Thomson Reuters; Moody’s KMV; and IMF, International Financial Statistics database.
Table 2.

Summary Statistics of the Dependent and Independent Variables

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Notes: Summary descriptive statistics of the sample of European and North American banks from 2004Q4 to 2013Q4. Source: national supervisory data, Bloomberg, Datastream, Moody’s KMV, International Financial Statistics. All variables are expressed in percent, except assets in USD billion, agency ratings in a numerical scale (from 1 for AAA to 24 for D), and two dummy variables, i.e. ΔCT1_d and Crisis_d (values: 0, 1). Key variables include: CT1 (core Tier 1 to RWAs); EDF (Moody’s 5y expected default frequency); FVCDS (Moody’s 5y fair value credit spread); ΔCT1²_sign (square quarter-on-quarter growth rate of CT1, sign preserving); ΔEDF²_sign (square quarter-on-quarter growth rate of EDF, sign preserving); ΔFVCDS²_sign (square quarter-on-quarter growth rate of FVCDS, sign preserving); CET1 (common equity Tier 1 to RWAs); Tier 1 (Tier 1 equity to RWAs); ptb (price to tangible book equity); tce (tangible common equity to total assets); assets_usd (total assets in billion USD); LLP (loan loss provisions to total assets); NI (net income to total assets); Fitch, Moodys, S&P (agency bank’s rating with government uplift mapped to a numerical scale from 1 (AAA) to 24 (D)); ΔCT1_d (dummy variable with 1 if quarter_on_quarter growth of CT1 is >20%; 0 otherwise); CDS_gov (5y government CDS); loan_growth (quarter_on_quarter growth of loans to the private sector); VIX (implied volatility of S&P 500 index options); LIBOR-OIS (3m libor usd to overnight index swap); and Crisis_d (dummy variable with 1 for 2008Q4 to 2013Q4; 0 otherwise).
Table 3.

Cross-Correlation Matrix of the Dependent and Independent Variables

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Notes: Correlation matrix of key variables for the sample of European and North American banks from 2004Q4 to 2013Q4. Source: national supervisory data, Bloomberg, Datastream, Moody’s KMV, International Financial Statistics. All variables are expressed in percent, except assets in USD billion, S&P ratings in a numerical scale (1 for AAA, and 24 for D), and the dummy variables ΔCT1_d and Crisis_d (values: 0, 1). Key variables include: ΔCT1_d (dummy variable with 1 if quarter_on_quarter growth of CT1 is >20%; 0 otherwise); CDS_gov (5y government CDS); CT1 (core Tier 1 to RWAs); Crisis_d (dummy variable with 1 for 2008Q4 to 2013Q4; 0 otherwise); EDF (Moody’s 5y expected default frequency); FVCDS (Moody’s 5y fair value credit spread); LIBOR-OIS (3m libor usd to overnight index swap); LiRisk (ratio of cash, central bank excess reserves, and sovereign debt with risk wegiths of 0 and 20% to short-term wholesale liabilities with remaining maturity of less than 3 months); loan_growth (quarter_on_quarter growth of loans to the private sector); LLP (loan loss provisions to total assets); NI (net income to total assets); OIS (overnight index swap); S&P (agency bank rating with government uplift in a numerical scale from 1 (AAA) to 24 (D)); ΔCT1²_sign (square quarter-on-quarter growth rate of CT1, sign preserving); ΔFVCDS²_sign (square quarter-on-quarter growth rate of FVCDS, sign preserving); and VIX (implied volatility of S&P 500 index options).

Potential stationarity-related concerns are addressed by performing the so-called meta unit root tests by Choi (2001) which includes unit-root tests for each variable separately and tests the p-values from these tests to produce an overall result. The null hypothesis of a unit root is rejected in most tests. The distribution of banks’ solvency and funding costs is shown in Figure 1. CT1 ratios are presented in the top chart. Over the sample period, the first quartile is 7.89 percent, the third quartile is 11.55 percent, the mean is 10.5 percent and the median is 9.42 percent. The chart reveals banks’ efforts to build their capital buffers in the wake of the financial crisis with average CT1 ratios increasing almost twofold from 7.4 percent in 2007 to 13.7 percent in 2013. The distribution has widened somewhat across time and outliers on the top of the distribution have become gradually more prominent. The bottom charts display the distribution of five-year EDF and five-year CDS market-based measures. The CDS first quartile is located at 45 bps, the second quartile is located at 131 bps and the third quartile is located at 249 bps. The chart reveals that market-based measures for solvency and funding costs track each other quite closely, although in periods of stress, CDS spreads react more strongly than EDF measures. Interestingly, funding costs remain elevated, even after the financial crisis subsided, despite banks’ efforts to rebuild their regulatory capital ratios, suggesting that market-based hurdle rates may have increased in the wake of the crisis. This may be partly due to investors’ risk reassessment of banks’ underlying portfolios. The distribution of market-based measures has become wider relative to that for regulatory capital measures pointing at higher discrimination by investors across banks’ creditworthiness.

Figure 1.
Figure 1.

Cross-Sectional Distribution of Bank Solvency and Funding Costs

Citation: IMF Working Papers 2017, 116; 10.5089/9781484300664.001.A001

Note: Evolution of the distribution of regulatory capital measures and market-based indicator across time. Source: national supervisory data, and Moody’s KMV. The top chart shows the distribution of bank core Tier 1 capital ratio (CT1). The bottom charts show the distribution of 5y expected default frequency (EDF) and 5y CDS spreads (CDS). The boxplots include the mean (yellow dot), the 25th and 75th percentiles (shaded areas) and the 10th and 90th percentiles (whiskers).

Figure 2 displays the geographic evolution of the averages across banks of CT1, EDF, and CDS. Whereas North American banks’ funding stress has subsided in the wake of stronger regulatory capital ratios built after the crisis, European banks have been hit by higher funding costs despite their strong capital ratios, particularly during the sovereign debt crisis in 2012, pointing at the adverse dynamics between banks and sovereigns.

Figure 2.
Figure 2.

Evolution of Bank Solvency and Funding Costs

Citation: IMF Working Papers 2017, 116; 10.5089/9781484300664.001.A001

Notes: This panel shows the evolution of solvency ratios and funding costs for the sample of European and North American banks from 2004Q4 to 2013Q4. Source: national supervisory data, and Moody’s KMV. The reason behind the jump in CT1 in the bottom charts in Q1 2008 is that the data for the CT1 ratios of the Dutch banks are reported from that time onwards and the average capital ratio of these banks is higher.

B. A Simultaneous Equation Approach

To capture the contemporaneous realizations of bank solvency and bank funding costs, we estimate the solvency and funding equations using a simultaneous equation panel approach. For the purpose of stress testing, it is important to account for this endogeneity to avoid the underestimation of a solvency shock on financial stability.

We estimate the following model

YΓ=XB + U(1)

In our analysis, Y is the vector of the two endogenous variables (i.e., solvency and funding costs), and X is a vector of exogenous variables including bank specific variables (to capture governance structures or business models), country specific variables (to control for time-varying macroeconomic conditions), and global variables (to capture global financial conditions and investors’ risk appetite).

Rewriting (1) in reduced form simplifies the problem:

Y=XBΓ1+UΓ1=XΠ+V(2)

Statistically, several conditions need to hold in order to extract the matrices B and Γ from the estimated matrix Π, i.e., to solve the identification problem. If it is possible to deduce the structural parameters in equation (1) from the reduced form parameters in equation (2), then the model is identified. To identify the two endogenous variables, we need to find at least two exogenous sources of variation in bank solvency and funding costs. Then, we can apply two- and three-stage-least squares. The two-stage-least squares (2SLS) procedure has two steps. For each structural equation in (1), we regress each dependent variable on all exogenous variables in the system and obtain the predicted values for them.21 In the second step we regress the other dependent variable on the predicted value of the first dependent variable and on the remaining exogenous variables in the particular equation. The three-stage-least squares (3SLS) combines the 2SLS with seemingly unrelated regressions (SUR) to account for the correlation structure of errors in each structural equation. We report either the 2SLS or 3SLS results, depending on the results of the statistical tests.

The statistical justification of our estimation approach can be tested by a series of standard tests in the context of 2SLS and 3SLS. First, we must test the relevance of the instruments to avoid the weak instrument problem (see Staiger and Stock (1997) for more details). For each specification, we report the F-statistic and the p-value, testing the joint relevance of the instruments for each equation. Second, we test for instrument exogeneity with two tests: we perform the J-test for each equation to check for exogeneity of the instruments.22 We also apply the Lagrange multiplier test (LMF) suggested by Kiviet (1986). If the null hypothesis is not rejected for at least one equations in the system, these tests support the application of 2SLS as an IV instrumental variable estimator. Third, we test for endogeneity of the (right hand side) solvency and liquidity variables. Here we do not use the classical Hausman test that tests of all coefficients of two estimators (2SLS vs. OLS) are different but we apply the regression based Durwin-Wu- Hausman test that tests whether the coefficients of the (RHS) endogenous variable(s) are different. 23 Finally we apply Hausman overidentification test to test the null hypothesis of 3SLS versus the alternative of 2SLS (provided 2SLS is validated by the exogeneity of instruments).

We compare those estimates with those obtained with a simple OLS estimator. The OLS model yields substantial biases and counterintuitive results, especially for the endogenous variables (see Table 12 and 13). Ultimately, our approach is a balancing act between addressing the potential weaknesses of the instruments and the biases of the OLS approach. The 2SLS and 3SLS results shown in the next section yield economically more intuitive results than the OLS results. They also appear robust across specifications including using two different measures of solvency. Nevertheless, the results should be interpreted with caution given the intrinsic difficulties in finding good exogenous instruments.

Table 4.

Bank Regulatory Capital and Funding Costs

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Notes: This table shows that results of estimating the system (1) using 2 SLS. The table reports the estimated coefficients, t-statistics, adjusted R2, and McElroy R2. The dependent variables are regulatory capital (CT1) and 5y fair value CDS (FVCDS). The baseline specification (Specification 1) includes a set of bank specific variables to capture asset quality (LLP), the capacity to generate organic capital (NI), and the bank rating (S&P) lagged one period to address endogeneity. Country specific variables includes the value of sovereign support from implicit guarantees (CDS_gov) and credit growth to the private sector (loan_growth). Global variables include spreads in money markets (LIBOR-OIS), investor sentiment in equity markets (VIX), and a dummy for the global financial crisis (Crisis_d). Specification 2 includes the impact of deliberate management actions to raise regulatory capital (ΔCT1_d). Specification 3 includes non-linear effects of funding costs (regulatory capital) on regulatory capital (funding costs). The results are based on quarterly data from 2004Q4 to 2013Q4.
Table 5.

Test Results for Bank Regulatory Capital and Funding Costs

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Notes: This table shows that the various specification tests for the results shown in Table 4. We check for the quality of instruments (F-test) and the exogeneity of instruments (J-test and Lagrange multiplier test). We test the endogeneity of the RHS endogenous variables (t-test) and we apply the Hansen system overidentification test.
Table 6.

Market-Based Bank Solvency and Funding Costs

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Notes: This table shows that results of estimating the system (1) using 3 SLS. The table reports the estimated coefficients, t-statistics, adjusted R2, and McElroy R2. The dependent variables are market-based capital proxied by the 5y expected default frequency estimated by Moody’s (EDF) and 5y fair value CDS (FVCDS). The baseline specification (Specification 1) includes a set of bank specific variables to capture asset quality (LLP), the capacity to generate organic capital (NI), and the bank rating (S&P) lagged one period to address endogeneity. Country specific variables includes the value of sovereign support from implicit guarantees (CDS_gov) and credit growth to the private sector (loan_growth). Global variables include spreads in money markets (LIBOR-OIS), investor sentiment in equity markets (VIX), and a dummy for the global financial crisis (Crisis_d). Specification 2 includes the impact of deliberate management actions to raise regulatory capital (ΔCT1_d). Specification 3 includes non-linear effects of funding costs (market-based capital EDF) on market-based capital EDF (funding costs). The results are based on quarterly data from 2004Q4 to 2013Q4.
Table 7.

Test Results for Market-Based Bank Solvency and Funding Costs

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Notes: This table shows that the various specification tests for the results shown in Table 6. We check for the quality of instruments (F-test) and the exogeneity of instruments (J-test and Lagrange multiplier test). We test the endogeneity of the RHS endogenous variables (t-test) and we apply the Hansen system overidentification test.
Table 8.

Bank Regulatory Capital and Funding Costs

(Controlling for Liquidity Risk)

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Notes: This table shows that results of estimating the system (1) using 2 SLS. The table reports the estimated coefficients, t-statistics, adjusted R2, and McElroy R2. The dependent variables are regulatory capital (CT1) and 5y fair value CDS (FVCDS). The baseline specification (Specification 1) includes a set of bank specific variables to capture asset quality (LLP), the capacity to generate organic capital (NI), the bank rating (S&P) lagged one period, and liquidity risk bearing capacity (LiRisk). Country specific variables includes the value of sovereign support from implicit guarantees (CDS_gov) and credit growth to the private sector (loan_growth). Global variables include spreads in money markets (LIBOR-OIS), investor sentiment in equity markets (VIX), and a dummy for the global financial crisis (Crisis_d). Specification 2 includes the impact of deliberate management actions to raise regulatory capital (ΔCT1_d). Specification 3 includes non-linear effects of funding costs (regulatory capital) on regulatory capital (funding costs). The results are based on quarterly data from 2004Q4 to 2013Q4.
Table 9.

Test Results for Bank Regulatory Capital and Funding Costs

(Controlling for Liquidity Risk)

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Notes: This table shows that the various specification tests for the results shown in Table 6. We check for the quality of instruments (F-test) and the exogeneity of instruments (J-test and Lagrange multiplier test). We test the endogeneity of the RHS endogenous variables (t-test) and we apply the Hansen system overidentification test.
Table 10.

Market-Based Bank Solvency and Funding Costs

(Controlling for Liquidity Risk)

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Notes: This table shows that results of estimating the system (1) using 3 SLS. The table reports the estimated coefficients, t-statistics, adjusted R2, and McElroy R2. The dependent variables are market-based capital proxied by the 5y expected default frequency estimated by Moody’s (EDF) and 5y fair value CDS (FVCDS). The baseline specification (Specification 1) includes a set of bank specific variables to capture asset quality (LLP), the capacity to generate organic capital (NI), the bank rating (S&P), and liquidity risk bearing capacity (LiRisk). Country specific variables includes the value of sovereign support from implicit guarantees (CDS_gov) and credit growth to the private sector (loan_growth). Global variables include spreads in money markets (LIBOR-OIS), investor sentiment in equity markets (VIX), and a dummy for the global financial crisis (Crisis_d). Specification 2 includes the impact of deliberate management actions to raise regulatory capital (ΔCT1_d). Specification 3 includes non-linear effects of funding costs (market-based capital EDF) on market-based capital EDF (funding costs). The results are based on quarterly data from 2004Q4 to 2013Q4.
Table 11.

Test Results for Market-Based Bank Solvency and Funding Costs

(Controlling for Liquidity Risk)

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Notes: This table shows that the various specification tests for the results shown in Table 9. We check for the quality of instruments (F-test) and the exogeneity of instruments (J-test and Lagrange multiplier test). We test the endogeneity of the RHS endogenous variables (t-test) and we apply the Hansen system overidentification test.
Table 12.

Bank Regulatory Capital and Funding Costs

(OLS Estimation)

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Notes: This table shows that results of estimating the system (1) using OLS. The table reports the estimated coefficients, t-statistics, adjusted R2, and McElroy R2. The dependent variables are regulatory capital (CT1) and 5y fair value CDS (FVCDS). The baseline specification (Specification 1) includes a set of bank specific variables to capture asset quality (LLP), the capacity to generate organic capital (NI), and the bank rating (S&P) lagged one period to address endogeneity. Country specific variables includes the value of sovereign support from implicit guarantees (CDS_gov) and credit growth to the private sector (loan_growth). Global variables include spreads in money markets (LIBOR-OIS), investor sentiment in equity markets (VIX), and a dummy for the global financial crisis (Crisis_d). Specification 2 includes the impact of deliberate management actions to raise regulatory capital (ΔCT1_d). Specification 3 includes non-linear effects of funding costs (regulatory capital) on regulatory capital (funding costs). The results are based on quarterly data from 2004Q4 to 2013Q4.
Table 13.

Market-Based Bank Solvency and Funding Costs

(OLS Estimation)

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Notes: This table shows that results of estimating the system (1) using OLS. The table reports the estimated coefficients, t-statistics, adjusted R2, and McElroy R2. The dependent variables are market-based capital proxied by the 5y expected default frequency estimated by Moody’s (EDF) and 5y fair value CDS (FVCDS). The baseline specification (Specification 1) includes a set of bank specific variables to capture asset quality (LLP), the capacity to generate organic capital (NI), and the bank rating (S&P) lagged one period to address endogeneity. Country specific variables includes the value of sovereign support from implicit guarantees (CDS_gov) and credit growth to the private sector (loan_growth). Global variables include spreads in money markets (LIBOR-OIS), investor sentiment in equity markets (VIX), and a dummy for the global financial crisis (Crisis_d). Specification 2 includes the impact of deliberate management actions to raise regulatory capital (ΔCT1_d). Specification 3 includes non-linear effects of funding costs (market-based capital EDF) on market-based capital EDF (funding costs). The results are based on quarterly data from 2004Q4 to 2013Q4.