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Chapter 8 Bank Solvency and Funding Cost: New Data and New Results

Author(s):
Li Lian Ong, and Andreas A. Jobst
Published Date:
September 2020
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Author(s)
Stefan W. Schmitz Michael Valderrama and Laura Schmitz

This chapter is based on IMF Working Paper 17/116 (Schmitz, Sigmund, and Valderrama 2017). Similar results with an extended data set and additional robustness checks can be found in Schmitz, Sigmund, and Valderrama (forthcoming).

This chapter 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 2004–13, the chapter uses a simultaneous equation approach to estimate the contemporaneous interaction between solvency and liquidity. The results show that liquidity and solvency interactions can be more material than suggested by the existing empirical literature. A 100-basis-point increase in regulatory capital ratios is associated with a decrease of bank funding costs of about 105 basis points. A 100-basis-point increase in funding costs reduces regulatory capital buffers by 32 basis points. The chapter also finds evidence of nonlinear effects between solvency and funding costs. Understanding the impact of solvency on funding costs is particularly relevant for stress testing. The 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.

1. 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. The chapter extracts 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 they also 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 chapter 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 b ack-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 of adverse dynamics and lengthens the persistence of funding shocks.

This chapter 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, a new dataset and test for the importance of the two-way interaction between funding conditions and bank solvency is constructed. The results lend support to the joint determination of funding costs and bank solvency. The chapter also provides some evidence of nonlinear interactions between funding costs and solvency risk, and finds 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, the study extends the literature in two directions. First, it builds a unique dataset consisting of supervisory reporting data of 54 large banks over 2004–135 shared across supervisory agencies from six countries.6 The data is checked to ensure it is of higher quality than the publicly available sources used in other studies. Second, the study focuses 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, the study examines 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 vector autoregression specification. This is motivated by concern that, given the endogeneity of capital and funding costs discussed previously, an ordinary least squares (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 the 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. The results provide evidence that OLS underestimates the impact of capital on funding costs. Whereas a multivariate O LS- based panel regression on the dataset yields a positive relationship between banks’ capital position and funding costs, the simultaneous equation-based analysis suggests a large negative impact of capital on the cost of funding.

The results suggest more sizable effects than those found in the literature. The study finds that a 100-basis-point increase in regulatory capital is associated with a 105-basis-point 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 An application of the empirical work is illustrated to inform stress testing projections of bank capital ratios under stressed conditions, using the 2014 EU- wide stress test exercise.

The rest of the chapter is structured as follows. Section 2 reviews the existing literature. Section 3 introduces the new dataset and presents the econometric approach. Section 4 shows the main findings on the interaction between regulatory capital and funding costs. Section 5 explores the robustness of the results to a market-based definition of bank solvency, and to banks’ bearing capacity for liquidity risk. Section 6 illustrates the dynamic impact of the solvency-funding interaction in a stress testing framework. Section 7 concludes with some policy implications.

2. Related Literature

This chapter 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. An-naert and others 2013 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 1-percentage-point drop in weekly bank stock returns (associated with higher implied market-based leverage), is associated with a 64-basis-point rise in a bank’s credit default swap (CDS) spread. Similarly, Hasan, Liu, and Zhang 2016 show that solvency has significant impact on bank funding costs using a sample of 161 global banks from 23 countries over 2001–11. An increase of 1 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 and others 2016 examine the sensitivity of bank funding costs to bank solvency, drawing on the Federal Deposit Insurance Corporation 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 federal 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 5 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 nonlinear, with higher sensitivity of funding cost at lower levels of bank solvency.

Afonso, Kovner, and Schoar 2011 conduct an event study around Lehman Brothers’ bankruptcy using transaction-level data containing all transfers by US banking institutions through Fedwire. They find that the worst-performing large banks access the federal funds market least, whereas small banks access the market at an increase in funding spreads of over 96 basis points. 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 US banks over the 2007– 09 financial crisis.

A different estimation method is applied by Babihuga and Spaltro 2014. In the context of a panel error correction model, they estimate the long-and short-term effects of bank-specific and macro variables on funding costs using a panel of 52 banks in 14 advanced economies over 2001–12. In the long term, a 1-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 with rising bank funding costs two quarters ahead. Gray, Wehrhahn, and Savage 2012 use a contingent claims analysis approach to compute a fair value credit default swap (FVCDS) spread 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 nonlinear relationship between funding costs and bank capital. Under the baseline scenario, banks’ weighted average expected default frequency (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 nonlinear relationship between market-based solvency and funding costs.

Within the second strand of the literature, Pierret 2014 uses fixed-effect panel vector autoregressive regressions to model the nexus between solvency and liquidity risk of banks in a set of 49 US banks examined over 2000 to 2013. The main result suggests an asymmetric relationship: higher solvency risk, measured by the expected capital shortfall SRISK9 defined by Acharya and others (2010), Archarya, Engle, and Richardson (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 1 percent increase in short-term debt see their expected capital shortfall ratio increase by 0.9 percentage point, suggesting that banks funded with more short-term debt face higher solvency risk. This chapter is more closely related to Distinguin, Roulet, and Tarazi 2013, and Schmitz, Sigmund, and Valderrama (forthcoming). Distinguin, Roulet, and Tarazi (2013) use a simultaneous equation approach to study the endogenous interaction between solvency and funding volumes on a panel of 870 US and European publicly traded commercial banks over 2000–06. For the solvency part, they use regulatory capital ratios as proxy. On the funding side, they focus on the inverse of the net stable funding ratio 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. Schmitz, Sigmund, and Valderrama (forthcoming) use an extended dataset with around 300 more data points before the financial crisis in 2007. With these additional data, they perform further robustness checks (cross validation and separate models for higher and lower capitalized banks). Their results, however, are very much in line with our finding.

The approach taken in this chapter differs insofar as it focuses on funding costs rather than on funding volumes, and in that the relationship between solvency and funding costs on a newly constructed dataset drawing on supervisory returns is investigated. This chapter also calibrates the impact of incorporating the solvency-funding costs’ interaction on banks’ resilience using the 2014 European Banking Authority (EBA) stress testing framework.

3. 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 nonlinear 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.

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 fourth quarter of 2004 to the fourth quarter of 2013. 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 fltering 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). The analysis proxies funding costs by the marginal cost of long-term, unsecured, wholesale funding. It uses 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, secondary market spreads could be used on active bonds to approximate the cost of wholesale funding. However, time series analysis drawing on this variable is challenging, as bond features change over time (for example, 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. The analysis used 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 (that is, shortening of tenors or a reduction of lines) rather than to significantly higher rates. Third, unconventional monetary policy, including full allotment and quantitative easing, limited the variation and information content of short-term market rates as a proxy for banks’ marginal funding costs, although the impact of unconventional monetary policy in the analysis is expected to be rather limited. The measures are available to all banks in the respective economies; thus, it is not expected that it will systematically affect the variation of CDS spreads across banks. Data on individual emergency liquidity assistance could reduce the bank’s CDS and affect the estimates. Tough central banks try to keep emergency liquidity assistance confidential, confidence is high that no bank in the sample received it.

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 (for example, for some of the smaller European banks). To account for this unobserved heterogeneity, bank-specific fixed effects are used. Second, CDS spreads may not be representative of bank funding costs under stress if the bank is shut out of the funding market. This chapter takes 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, it is not expected that this will systematically bias CDS spreads over the sample period. In any case, to measure funding costs effectively, 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, Jacobs, and Oviedo 2009), and used as a framework to calibrate Basel III regulatory capital. This motivates this study’s choice of solvency risk, that is, Core Tier 1 ratio (CT1), which reflects high-quality regulatory capital relative to risk-weighted assets (RWAs).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. This concern is addressed 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 those of nonfinancial companies.15 This is a consequence of the perceived public-good characteristics of financial stability and the ensuing specific regulatory framework banks operate in. The study captures 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. The study transforms the standard rating scale into a1 (best rating or AAA) to 24 (worst rating) numerical scale (S&P). Third, the distance to default is typically higher for banks than for nonfinancial 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 that of nonbank 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, the study includes 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 nonfinancial companies and a broader range of variables needs to be considered. To address the robustness of the study’s results to different measures of bank resilience, the estimation is rerun using a market-based measure of bank default probability over five years, namely the EDF estimated by Moody’s Credit Edge.16 A wide range of bank-specific variables are considered as potential determinants of bank solvency and funding cost. Two balance sheet variables are used, which play key roles in solvency stress tests, that is, loan loss provisions (LLPs) in percent of total assets as a measure of asset quality, and net income (NI) in percent of total assets as a proxy for banks’ return on assets and its organic recapitalization capacity. Provisions have a direct impact on bank solvency through their effect on RWAs. However, this proxy has known shortcomings. Banks have some leeway in determining loan loss provisions and can use it as a signaling device to the market, to accommodate regulators, to smooth earnings over time, and for tax optimization 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 4, the EDF measure, which is more market oriented. The study also controls for banks’ resilience to liquidity shocks, which is monitored regularly by the regulatory authorities. Liquidity risk is defined 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 rollover 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. The study addresses the potential regime shift around the outbreak of the global financial crises in 2008 by using the following control variables. First, a non-bank, non-country-specific variable was included that proxies for market sentiment in the interbank market. The London Interbank Offered Rate (LIBOR)-overnight index swap (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, the study controls for substantial changes in monetary policies and for the introduction of unconventional measures that were designed to dampen bank funding costs by using the 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 the sample and the reliance of individual banks on these central bank measures differ, this information is not publicly available in a systematic manner. The model allows for bank-specific fixed effects to capture such unobservable differences. Third, a market measure of volatility is included to capture global risk aversion.18 This is motivated by evidence that a common systemic risk factor can reduce the discrepancy between modeled and actual returns for corporate bondholders (Chen, Collin-Dufresne, and Goldstein 2009). The study proxies 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 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 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 capitalization changed abruptly with Lehman’s bankruptcy. The dummy variable is defined as 0 from the fourth quarter of 2004 to the third quarter of 2008 and as 1 from the fourth quarter of 2008 to the fourth quarter of 2013. Despite the control variables, it is possible that the interaction between solvency and funding costs changed over time; for example, a stronger sensitivity of wholesale investors to solvency risk post-Lehman is expected. Therefore, the study also runs its equations separately for two subsamples ( pre-and post-Lehman’s default) to check for robustness.

To control for the macroeconomic environment, the study uses 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, the study constructs a dummy variable to capture large swings in regulatory capital (ΔCT1_d). Specifically, an increase of CT1 by more than 20 percent quarter-over-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 the fourth quarter of 2008 seem to be well captured by this dummy. A five-year government CDS (CDS_gov) is used 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 creditworthiness of the guarantor.

The choice of instrumental variables for identification purposes in the simultaneous equation system (8.2) is of key importance. Variables that fulfill the economic preconditions were selected; that is, they are directly related to one endogenous variable but interact with the second one only indirectly via the first one. They fulfill the exclusion restriction. In line with the literature, drivers of CDS spreads include proxies of profitability and asset quality. LLPs are used as the instrumental variable for identification in the CT1 equation in Specification 1. LLPs 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, that is, indirectly via CT1. Similarly, net income NI is used as an exogenous variable in the solvency equation. The main channel through which solvency affects NI is via funding costs, which are captured in the model setup. Other determinants of NI like commission income (fees and turnover); staff costs, IT-costs, LLP, participations, and return on own portfolio are not directly affected by solvency. In addition, country-wide loan growth is included only in the CT1 equation. In Specification 2 a dummy variable is added that captures deliberate management action to change CT1 in the CT1 equation regulatory capital (ΔCT1_d). It affects FVCDS only via CT1. 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 are used 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 8.1. shows data coverage for the variables used in the estimation, whereas Table 8.2 presents the summary statistics.

Table 8.1.Data Coverage
VariableAvailable Observations (Number)Available Observations (In Percent)
Dependent variable
CT1163281.7
EDF162581.3
FVCDS162581.3
CET1115958.0
Tier 147723.9
FVOAS76438.2
ptb118459.3
tee145873.0
Bank characteristics
assets_usd184792.4
NPL136568.3
LLR156978.5
LLP183992.0
LTD171986.0
st_debt156578.3
excess_reserves182391.2
fx liabilities27613.8
NIE183992.0
Nil181590.8
Nl183992.0
Fitch131165.6
Moodys139569.8
S&P151475.8
Country variables
ER_regime1998100.0
CDS_gov151575.8
loan_growth1997100.0
Sources: Bloomberg, LP; IMF International Financial Statistics database; Moody’s KMV; national supervisory data; and Thomson Reuters.Note: Coverage of key variables for the sample of European and North American banks from 2004:Q4 to 2013:Q4. assets_usd = total assets in US dollars; CDS_gov = sovereign credit default swap spread; CET1 = Core Equity Tier 1 ratio; CT1 = Core Tier 1 ratio; EDF = expected default frequency; ER_regime = IMF’s de facto classification of exchange rate arrangements (scalar); FVCDS = fair value credit default swap spread; FVOAS = fair value option adjusted spread; fix liabilities = liabilities in foreign currency to total liabilities; NI = net income; NIE = net interest expense; NII = net interest income; LLP = loan loss provisions; LLR = loan loss provisions to total assets; LTD = loan-to-deposit ratio; NPR = net-profit-to-total-assets ratio; ptb = price-to-tangible-book-equity ratio; tce = tangible common equity to total assets.
Sources: Bloomberg, LP; IMF International Financial Statistics database; Moody’s KMV; national supervisory data; and Thomson Reuters.Note: Coverage of key variables for the sample of European and North American banks from 2004:Q4 to 2013:Q4. assets_usd = total assets in US dollars; CDS_gov = sovereign credit default swap spread; CET1 = Core Equity Tier 1 ratio; CT1 = Core Tier 1 ratio; EDF = expected default frequency; ER_regime = IMF’s de facto classification of exchange rate arrangements (scalar); FVCDS = fair value credit default swap spread; FVOAS = fair value option adjusted spread; fix liabilities = liabilities in foreign currency to total liabilities; NI = net income; NIE = net interest expense; NII = net interest income; LLP = loan loss provisions; LLR = loan loss provisions to total assets; LTD = loan-to-deposit ratio; NPR = net-profit-to-total-assets ratio; ptb = price-to-tangible-book-equity ratio; tce = tangible common equity to total assets.
Table 8.2.Summary Statistics of the Dependent and Independent Variables
VariableMinFirst QuartileMedianMeanThird QuartileMaxNAsStandard Deviation
CT1-13.77.99.410.511.6111.23669.8
EDF0.00.10.30.90.921.43731.6
FVCDS0.00.41.32.02.517.43812.2
ACT12_sign-525.30.00.0-0.10.1757.842328.2
AEDF2_sign-87.40.00.00.10.0158.34566.8
AFVCDS2_sign-73.30.00.00.10.1132.04275.9
CET1-13.76.47.97.810.019.78394.0
Tier 14.48.610.414.712.1114.6129918.1
ptb10.291.4145.4163.7217.9577.981493.1
tee0.0343.2483.5485.9647.81726.0540249.4
assets_usd28781623594012460151480.1
LLP-0.20.00.10.10.22.01830.2
Nl-4.70.10.20.10.32.11600.3
Fitch2.04.04.04.96.010.06871.7
Moodys1.04.05.05.37.015.06032.3
S&P2.05.05.05.77.011.04841.8
ACT1_d0.00.00.00.00.01.04230.2
CDS_gov0.00.20.40.40.51.94830.3
loan_growth-7.7-0.11.31.02.28.211.9
VIX11.013.618.320.524.358.309.5
LIBOR_OIS0.10.10.20.30.42.100.4
Crisis_d0010.61100.5
Sources: Bloomberg, L.P.; Datastream; International Financial Statistics; Moody’s KMV; and national supervisory data.Note: Summary descriptive statistics of the sample of European and North American banks from 2004:Q4 to 2013:Q4. All variables are expressed in percent, except assets in billions of US dollars, agency ratings in a numerical scale (from 1 for AAA to 24 for D), and two dummy variables, i.e. ∆CT1_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); ∆CT12_sign (square quarter-on-quarter growth rate of CT1, sign preserving); ∆EDF2_sign (square quarter-on-quarter growth rate of EDF, sign preserving); ∆FVCDS2_sign (square quarter-on-quarter growth rate of FVCDS, sign preserving); CET1 (Core 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, Moody’s, S&P (agency bank’s rating with government uplift mapped to a numerical scale from 1 (AAA) to 24 (D)); ∆CT1_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 2008:Q4 to 2013:Q4; 0 otherwise). CDS = credit default swap; EDF = expected default frequency; FVCDS = fair value credit default swap spread; max = maximum; min = minimum; NAs = number of missing observations; RWAs = risk-weighted assets.
Sources: Bloomberg, L.P.; Datastream; International Financial Statistics; Moody’s KMV; and national supervisory data.Note: Summary descriptive statistics of the sample of European and North American banks from 2004:Q4 to 2013:Q4. All variables are expressed in percent, except assets in billions of US dollars, agency ratings in a numerical scale (from 1 for AAA to 24 for D), and two dummy variables, i.e. ∆CT1_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); ∆CT12_sign (square quarter-on-quarter growth rate of CT1, sign preserving); ∆EDF2_sign (square quarter-on-quarter growth rate of EDF, sign preserving); ∆FVCDS2_sign (square quarter-on-quarter growth rate of FVCDS, sign preserving); CET1 (Core 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, Moody’s, S&P (agency bank’s rating with government uplift mapped to a numerical scale from 1 (AAA) to 24 (D)); ∆CT1_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 2008:Q4 to 2013:Q4; 0 otherwise). CDS = credit default swap; EDF = expected default frequency; FVCDS = fair value credit default swap spread; max = maximum; min = minimum; NAs = number of missing observations; RWAs = risk-weighted assets.

Note that most of the variables are denoted in percentage points. This also holds for CDS spreads. The median value stood at 131 basis points 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 8.3 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 profit-and-loss 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 turnover); staff costs, IT costs, LLPs, participations, return on own portfolio, and a number of other factors also play a role.20

Table 8.3.Cross-Correlation Matrix of the Dependent and Independent Variables
∆CT1_dCDS_govCT1Crisis_dEDFFVCDSLIBOR_OISLiRiskloan_ growthLLPNlOISS&P∆CT12_sign∆FVCDS2_signVIX
∆CT1_d1.000.00-0.050.000.050.070.220.08-0.030.11-0.100.02-0.030.040.030.18
CDS_gov0.001.000.100.530.410.390.02-0.09-0.310.05-0.01-0.500.120.040.030.21
CT1-0.050.101.000.200.090.12-0.03-0.02-0.06-0.04-0.02-0.19-0.060.13-0.040.00
Crisis_d0.000.530.201.000.400.480.11-0.10-0.520.19-0.17-0.910.260.04-0.050.40
EDF0.050.410.090.401.000.860.12-0.05-0.370.30-0.21-0.380.280.030.190.26
FVCDS0.070.390.120.480.861.000.33-0.06-0.450.35-0.32-0.490.280.040.240.40
LIBOR_OIS0.220.02-0.030.110.120.331.00-0.03-0.240.29-0.29-0.17-0.09-0.020.110.85
LiRisk0.08-0.09-0.02-0.10-0.05-0.06-0.031.000.06-0.05-0.030.08-0.12-0.010.00-0.05
loan_growth-0.03-0.31-0.06-0.52-0.37-0.45-0.240.061.00-0.310.210.49-0.110.01-0.08-0.43
LLP0.110.05-0.040.190.300.350.29-0.05-0.311.00-0.42-0.200.260.010.020.36
Nl-0.10-0.01-0.02-0.17-0.21-0.32-0.29-0.030.21-0.421.000.19-0.04-0.01-0.24-0.32
OIS0.02-0.50-0.19-0.91-0.38-0.49-0.170.080.49-0.200.191.00-0.24-0.030.02-0.40
S&P-0.030.12-0.060.260.280.28-0.09-0.12-0.110.26-0.04-0.241.00-0.010.00-0.03
∆CT12_sign0.040.040.130.040.030.04-0.02-0.010.010.01-0.01-0.03-0.011.000.02-0.01
∆FVCDS2_sign0.030.03-0.04-0.050.190.240.110.00-0.080.02-0.240.020.000.021.000.08
VIX0.180.210.000.400.260.400.85-0.05-0.430.36-0.32-0.40-0.03-0.010.081.00
Sources: Bloomberg, L.P.; Datastream; International Financial Statistics; Moody’s KMV; and national supervisory data.Note: Correlation matrix of key variables for the sample of European and North American banks from 2004:Q4 to 2013:Q4. All variables are expressed in percent, except assets in billions of US dollars, S&P ratings in a numerical scale (1 for AAA, and 24 for D), and the dummy variables ∆CT1_d and Crisis_d (values: 0,1). Key variables include: ∆CT1_d (dummy variable with 1 if quarter-on-guarter growth of CT1 is >20%;0 otherwise); CDS_gov (five-year government CDS); CT1 (Core Tier 1 to RWAs); Crisis_d (dummy variable with 1 for 2008:Q4 to 2013:Q4;0 otherwise); EDF (Moody’s five-year expected default freguency); FVCDS (Moody’s five-year fair value credit spread); LIBOR-OIS (3m libor usd to overnight index swap); LiRisk (ratio of cash, centra bank excess reserves, and sovereign debt with risk weights of 0 and 20% to short-term wholesale liabilities with remaining maturity of less than three months); loan_growth (guarter-on-guarter growth of loans to the private sector); LLP (loan loss provisions to total assets); Nl (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)); ∆CT12_sign (sguare guarter-on-guarter growth rate of CT1, sign preserving); ∆FVCDS2_sign (sguare guarter-on-guarter growth rate of FVCDS, sign preserving); and VIX (implied volatility of S&P 500 index options). CDS = five-year credit default swap spread; EDF = expected default freguency; FVCDS = fair value credit default swap; RWAs = risk-weighted assets.
Sources: Bloomberg, L.P.; Datastream; International Financial Statistics; Moody’s KMV; and national supervisory data.Note: Correlation matrix of key variables for the sample of European and North American banks from 2004:Q4 to 2013:Q4. All variables are expressed in percent, except assets in billions of US dollars, S&P ratings in a numerical scale (1 for AAA, and 24 for D), and the dummy variables ∆CT1_d and Crisis_d (values: 0,1). Key variables include: ∆CT1_d (dummy variable with 1 if quarter-on-guarter growth of CT1 is >20%;0 otherwise); CDS_gov (five-year government CDS); CT1 (Core Tier 1 to RWAs); Crisis_d (dummy variable with 1 for 2008:Q4 to 2013:Q4;0 otherwise); EDF (Moody’s five-year expected default freguency); FVCDS (Moody’s five-year fair value credit spread); LIBOR-OIS (3m libor usd to overnight index swap); LiRisk (ratio of cash, centra bank excess reserves, and sovereign debt with risk weights of 0 and 20% to short-term wholesale liabilities with remaining maturity of less than three months); loan_growth (guarter-on-guarter growth of loans to the private sector); LLP (loan loss provisions to total assets); Nl (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)); ∆CT12_sign (sguare guarter-on-guarter growth rate of CT1, sign preserving); ∆FVCDS2_sign (sguare guarter-on-guarter growth rate of FVCDS, sign preserving); and VIX (implied volatility of S&P 500 index options). CDS = five-year credit default swap spread; EDF = expected default freguency; FVCDS = fair value credit default swap; RWAs = risk-weighted assets.

Potential stationarity-related concerns are addressed by performing the so-called meta unit root tests by Choi 2001, which include 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 8.1. 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 figure 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. Panels 2 and 3 display the distribution of five-year EDF and five-year CDS market-based measures. The CDS first quartile is located at 45 basis points, the second quartile is located at 131 basis points, and the third quartile is located at 249 basis points. The figure 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 m arket-based measures has become wider relative to that for regulatory capital measures, pointing at higher discrimination by investors across banks’ creditworthiness.

Cross-Sectional Distribution of Bank Solvency and Funding Costs

Sources: National supervisory data; and Moody’s KMV.

Note: Evolution of the distribution of regulatory capital measures and market-based indicators across time. Panel 1 shows the distribution of Core Tier 1 capital ratios (CT1). Panels 2 and 3 show the distribution of five-year expected default frequency (EDF) and five-year 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 8.2 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.

Evolution of Bank Solvency and Funding Costs

Sources: National supervisory data; and Moody’s KMV.

Note: This panel shows the evolution of solvency ratios and funding costs for the sample of European and North American banks from 2004:Q4 to 2013:Q4. The reason behind the jump in Core Tier 1 in the bottom charts in 2008:Q1 is that the data for the Core Tier 1 ratios of the Dutch banks are reported from that time onwards and the average capital ratio of these banks is higher. EDF = expected default frequency; FVCDS = fair value credit default swap; RWA = risk-weighted assets.

A Simultaneous Equation Approach

To capture the contemporaneous realizations of bank solvency and bank funding costs, the study estimates 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. The following model is estimated:

In the analysis, Y is the vector of the two endogenous variables (that is, 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 macroeco-nomic conditions), and global variables (to capture global financial conditions and investors’ risk appetite).

Rewriting (8.1) in reduced form simplifies the problem:

Statistically, several conditions need to hold in order to extract the matrices B and Γ from the estimated matrix Π, that is, to solve the identification problem. If it is possible to deduce the structural parameters in equation (8.1) from the reduced form parameters in equation (8.2), then the model is identified. To identify the two endogenous variables, at least two exogenous sources of variation in bank solvency and funding costs need to be found. Ten, two-and three-stage least squares can be applied. The two-stage least squares (2SLS) procedure has two steps. For each structural equation in (8.1), each dependent variable is regressed on all exogenous variables in the system and the predicted values are obtained for them.21 In the second step, the other dependent variable is regressed 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 to account for the correlation structure of errors in each structural equation. Either the 2SLS or 3SLS results are reported, depending on the results of the statistical tests.

The statistical justifcation of the estimation approach can be tested by a series of standard tests in the context of 2SLS and 3SLS. First, the relevance of the instruments must be tested to avoid the weak instrument problem (see Staiger and Stock 1997 for more details). For each specification, the F-statistic and the p-value are reported, testing the joint relevance of the instruments for each equation. Second, instrument exogeneity is tested for with two tests: the J-test is performed for each equation to check for exogeneity of the instruments Bhargava (1991). Also, the Lagrange multiplier test (LMF) suggested by Kiviet (1986) is applied. If the null hypothesis is not rejected for at least one equation in the system, these tests support the application of 2SLS as an instrumental variable estimator. Third, endogeneity of the (right-hand side) solvency and liquidity variables is tested for. Here, the analysis does not use the classical Hausman test that tests if all coefficients of two estimators (2SLS vs. OLS) are different. Instead the regression-based Durbin-Wu-Hausman test that tests whether the coefficients of the (right-hand side) endogenous variable(s) are different is applied. 22 Finally, the Hausman overidentification test is applied to test the null hypothesis of 3SLS versus the alternative of 2SLS (provided 2SLS is validated by the exogeneity of instruments).

These estimates are compared with those obtained with a simple OLS estimator. The OLS model yields substantial biases and counterintuitive results, especially for the endogenous variables (see analyses in Sections 4 and 5). Ultimately, the study’s 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 do 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.

4. Estimation Results

Table 8.4 summarizes the results for the simultaneous panel estimation for the regulatory solvency measure CT1 and bank funding costs proxied by CDS spreads (in Section 5 the robustness of the results are checked by replacing the regulatory ratio by the market-based measure of solvency EDF). Table 8.4 shows results across various specifications for solvency and funding costs. For each specification, the first column shows the results of the bank solvency equation. The second column presents the results of the funding cost equation.

Table 8.4.Bank Regulatory Capital and Funding Costs
Specification 1Specification 2Specification 3
CT1FVCDSCT1FVCDSCT1FVCDS
Endogenous variables
CT1-1.048***

(0.273)
-1.129***

(0.235)
-0.848***

(0.282)
FVCDS-0.320***

(0.095)
-0.324***

(0.086)
-0.186***

(0.0719)
∆CT12_sign0.0761

(0.0544)
∆FVCDS2_sign-0.00963

(0.0249)
Exogenous variables
Bank specific
LLP-1.600***

(0.346)
-1.593***

(0.312)
-1.844***

(0.386)
Nl-0.144

(0.174)
-0.547**

(0.224)
-0.141

(0.157)
-0.565***

(0.141)
-0.104

(0.199)
-0.627***

(0.206)
S&P (lag 1)0.379***

(0.127)
0.299***

(0.075)
0.326***

(0.119)
∆CT1_d0.078

(0.268)
0.0352

(0.285)
Country specific
CDS_gov3.707***

(0.613)
4.137***

(0.407)
4.073***

(0.593)
loan_growth0.005

(0.040)
0.005

(0.037)
0.0360

(0.0372)
Global variables
LIBOR_OIS0.492

(0.328)
0.0171***

(0.315)
0.0122***

(0.00470)
VIX-0.064***

(0.022)
-0.0313

(0.0285)
Crisis_d3.230***

(0.180)
2.264***

(0.766)
3.260***

(0.165)
2.97142***

(0.782)
3.221***

(0.188)
1.676*

(0.956)
Constant7.466***

(0.881)
8.123***

(2.009)
7.470***

(1.007)
9.418***

(2.931)
7.001***

(0.935)
7.548***

(2.257)
Bank FEYesYesYesYesYesYes
Adj R20.9840.8250.9840.8250.9840.824
Obs782782772772772772
McElroy R20.8960.8840.755
Source: Authors’ calculations.Note: This table shows the results of estimating the system (1) using 2SLS. 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 include 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 (∆CT1_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 2004:Q4 to 2013:Q4. Adj R2 = adjusted R2; Bank FE = bank-fixed effects; CDS = credit default swap; CT1 = Core Tier 1 ratio; FVCDS = fair value credit default swap spread; LLP = loan loss provisions to total assets; NI = net income; OIS = overnight index swap; VIX = Chicago Board Options Exchange Volatility Index.
Source: Authors’ calculations.Note: This table shows the results of estimating the system (1) using 2SLS. 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 include 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 (∆CT1_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 2004:Q4 to 2013:Q4. Adj R2 = adjusted R2; Bank FE = bank-fixed effects; CDS = credit default swap; CT1 = Core Tier 1 ratio; FVCDS = fair value credit default swap spread; LLP = loan loss provisions to total assets; NI = net income; OIS = overnight index swap; VIX = Chicago Board Options Exchange Volatility Index.

To explain the solvency equation, the following variables are used: loan loss provisions, net income, aggregate credit growth, and a crisis dummy. Loan loss provisions can be in-fuenced by regulatory, tax, and profit-smoothing considerations. Regardless of their motivation, higher provisions reduce profits and regulatory capital.23 Country-level loan growth is included as a macro control variable. If the market is growing, banks tend to increase capital to compete for market share and to protect their franchise value. A priori, the effect of loan growth on banks’ CDS spreads is ambiguous. On the one hand, high loan growth could be associated with low CDS spreads if it is interpreted as sign of strong market growth, solid macroeconomic fundamentals, and sound profitability. On the other hand, it can also be associated with high CDS spreads when it is interpreted as a sign of low credit standards, reckless lending, and mispricing of risk. A positive effect is expected of the crisis dummy on regulatory capital. With the Lehman collapse the market expectations regarding CT1 shifted from around 6 percent to 10 percent (“10 is the new 6”). Postcrisis CT1 ratios are, on average, about 323 basis points higher than they were before the crisis.

In the funding cost equation, bank net income is also included as a key determinant. Net income is expected to be associated with lower funding costs, as banks’ capacity to generate earnings and repay outstanding debt increases. Also, a set of market-based variables is included, namely the bank’s S&P’s rating, the sovereign CDS spread, the LIBOR- OIS spread, and the VIX. These variables are, however, excluded from the solvency equation, as arguably, they do not impact directly CT1 or RWA. They do so indirectly via funding costs. A bank’s ratings directly affect the pricing of its credit derivative, but not its regulatory capital.24 Higher sovereign spreads often lead to higher bank spreads as the value of the implicit government guarantee is reduced. But they do not systematically affect banks’ regulatory capital. This is because bonds of the local sovereign have a zero-risk weight and are often held on hold-to-maturity portfolios. Tensions in interbank markets affect bank CDS spreads by rising wholesale funding costs. Finally, higher market volatility increases investors’ risk premia, pushing up funding costs.

Specification 1 is the baseline specification. It yields 782 observations from 38 banks. Bank funding costs are statistically and economically significantly associated with bank solvency. A 100-basis-point increase of a bank’s CDS spread is associated with a reduction of its CT1 ratio by 32 basis points.25 This result is robust across specifications. Loan loss provisions are also significant; higher loan loss provisions are negatively correlated with regulatory capital. The crisis dummy is statistically significant, has the expected sign, and an economically meaningful magnitude. The McElroy R2 is high at 90 percent. 26

The CT1 ratio is statistically significant in the bank funding cost equation A 100-basis-point higher CT1 ratio is associated with a decrease of bank funding costs by 105 basis points. This effect is robust to alternative specifications. In addition, net income has a statistically and economically significant impact on bank funding costs. Sovereign risk is also significant, pointing at the existence of a sovereign-bank nexus, while the bank rating has the expected sign and is statistically significant. Tensions in

the interbank market increase bank funding costs as expected.27 Global risk aversion is significant, though with a negative sign, which we attribute to the correlation between LIBOR-OIS and VIX (Table 8.3). The crisis dummy is statistically significant, too. The McElroy R2 of 81 percent suggests that the explanatory value of the system is high. As an additional goodness-of-fit test results are provided for the adjusted R2 of 82 percent, which suggests that the equation explains most of the variation in bank funding costs.

In Specification 2, the study examines whether taking into consideration deliberate management actions to improve bank solvency has any impact on the results. Capital increases directly affect CT1, but systematically covary with bank CDS spreads only through changes in CT1. It turns out that the variable capturing sharp increases of capital is not statistically significant. The results for the endogenous variables and the other exogenous variables are basically unchanged; though the coefficient of CT1 in the funding cost equation is slightly higher at -113 basis points. Specification 2 was enhanced by including banks’ funding structure, as one would expect that the risk premium component in funding costs increases with the funding tenor (Hull and White 2000). Ceteris paribus, the CT1 ratios of banks with larger shares of short-term funding are likely to be less affected by an increase in five-year CDS spreads than those of banks with larger shares of long-term funding. This effect was tested for by including the share of short-term debt in total assets and the interaction term between this variable and the variable FVCDS as the explanatory variable in both equations. The analysis finds that the main results for the endogenous variables are robust with respect to the signs and the significance levels. At the same time, the coefficient of FVCDS in the solvency equation increases to -1.1 from -0.32. This effect is partly counterbalanced by the positive sign of the interaction term (0.06). An increase of the FVCDS of, say, 105 basis points decreases the CT1 ratio by 100 basis points if the bank has no short-term debt at all. If short-term debt amounts to 10 per cent of total assets (the average in the sample), the effect is reduced by 60 basis points to about 50 basis points. This has roughly the same magnitude that the corresponding parameter has in Specification 2 in Table 8.4. Regarding the other parameters in the specification, the crisis dummy remains unchanged, the LLP becomes insignificant, but NI becomes significant. Regarding the funding equation, the parameter of the CT1 ratio increases to -0.87 from -1.13. The coefficients of the other variables (NI, S&P, CDS_gov) remain unchanged. The variable VIX is now insignificant, the coefficient of the LIBOR_OIS spread decreases from 1.71 to 1.03 and that of the crisis dummy from 2.97 to 1.97.

To allow for nonlinear effects, the squared values of the endogenous variables are added in Specification 3.28 These variables are calculated as squared quarter-over-quarter first differences while maintaining the direction of the change (that is, the transformation is sign preserving). These variables are treated as additional endogenous variables and their ftted values of the underlying equations are included. CT1 remains significant in the funding cost equation, while CDS spreads remain significant in the solvency equation. We do not find supporting evidence of the existence of nonlinear effects between funding costs and regulatory capital, probably related to the lack of sensitivity of capital requirements to rising funding costs. The additional variables leave most other coefficients basically unaffected, except for the coefficient of loan loss provisions that becomes significantly higher. Schmitz, Sigmund, and Valderrama 2019 choose a different approach to account for potential non linearity between funding costs and regulatory capital. They split their sample in two parts—lower and higher capitalized banks based on the CT1 values in the second quarter of 2007. They find a stronger back-book effect for the lower capitalized banks. Thus, a higher FVCDS has a more pronounced negative effect on the CT1 ratio than for the better-capitalized banks where the FVCDS coefficient in the CT1 equation is closer to 0 and insignificant.

The tests’ statistics for the econometric specifications are generally satisfactory (Table 8.5). The quality-of-instruments test rejects the null of weak instruments in all equations if the contemporary S&P’s bank rating is included in the funding cost equation. Therefore, credit ratings are instrumented by their lagged value. The J-test and the LMF test fail to reject the null of exogenous instruments. The Durbin-Wu-Hausman test is consistent with the endogeneity of the (right-hand-side) dependent variables. The system overidentification test for the 3SLS method suggests a preference for 2SLS over 3SLS (and iterated 3SLS) for Specifications 1, 2, and 3.

Table 8.5.Test Results for Bank Regulatory Capital and Funding Costs
Specification 1Specification 2Specification 3
CT1FVCDSCT1FVCDSCT1FVCDS
Quality of instruments (H0: Instruments are weak)
F statistic1059.0081.771020.2778.46989.7976.44
p value0.000.000.000.000.000.00
Exogeneity of instruments (H0: 2SLS is valid)
J-test statistic0.550.081.020.131.251.06
p value0.280.750.060.750.040.07
LMF test statistic5.161.966.543.2714.2130.12
p value0.860.160.090.200.160.00
Regression-based Hausman for endogeneity of specific variables (H0: Specific variables are exogenous)
t value6.067.526.095.946.555.78
p value0.000.000.000.000.000.00
System Overid Test (provided 2SLS is valid, H0: 2SLS is preferred to 3SLS)
Hansen test statistic31.5453.0059.58
p value0.000.000.00
Source: Authors’ calculations.Note: This table shows the various specification tests for the results shown in Table 8.4. The analysis tests for the quality of instruments (F-test) and the exogeneity of instruments (J-test and Lagrange multiplier test). The endogeneity of the RHS endogenous variables (t-test) is tested and the Hansen system overidentification test is applied. CT1 = Core Tier 1 ratio; FVCDS = fair value credit default swap spread; LMF = language multiplier test; 2SLS = two-stage least squares.
Source: Authors’ calculations.Note: This table shows the various specification tests for the results shown in Table 8.4. The analysis tests for the quality of instruments (F-test) and the exogeneity of instruments (J-test and Lagrange multiplier test). The endogeneity of the RHS endogenous variables (t-test) is tested and the Hansen system overidentification test is applied. CT1 = Core Tier 1 ratio; FVCDS = fair value credit default swap spread; LMF = language multiplier test; 2SLS = two-stage least squares.

To gauge the direction of the likely bias of OLS due to the endogeneity of bank solvency and funding costs, three specifications using OLS (Table 8.6) were run. For Specif-cation 1, the study obtained statistically significant coefficients of 0.17 and 0.14 for the coefficients of CT1 and CDS spreads, respectively. Similar results are obtained for Specifications 2 and 3. Counterintuitively, the results suggest that higher funding costs are associated with higher CT1 ratios and that higher CT1 ratios are associated with higher funding costs. This reveals that without controlling for spurious correlations and unobservable shocks, OLS estimates significantly underestimate the negative relationship between funding costs and solvency. For Specification 1, the OLS coefficient of CDS in the solvency equation suggests a positive relationship between funding costs and bank capital with an estimated coefficient of 0.14 rather than the negative impact of -0.32 estimated under the simultaneous panel approach.

Table 8.6.Bank Regulatory Capital and Funding Costs(OLS Estimation)
Specification 1Specification 2Specification 3
CT1FVCDSCT1FVCDSCT1FVCDS
Endogenous variables
CT10.173***

(0.0366)
0.209***

(0.0376)
0.215***

(0.0382)
FVCDS0.141***

(0.0344)
0.145***

(0.0347)
0.171***

(0.0372)
∆CT12_sign-0.00588

(0.00628)
∆FVCDS2_sign-0.0153*

(0.00791)
Exogenous variables
Bank specific
LLP-2.224***

(0.291)
-2.197***

(0.295)
-2.348***

(0.304)
Nl0.148

(0.148)
-0.728***

(0.139)
0.148

(0.149)
-0.703***

(0.138)
0.0870

(0.152)
-0.702***

(0.138)
S&P (lag 1)0.0510

(0.0661)
0.123*

(0.0682)
0.117*

(0.0685)
∆CT1_d-0.106

(0.266)
-0.0988

(0.265)
Country specific
CDS_gov3.959***

(0.385)
3.623***

(0.395)
3.617***

(0.395)
loan_growth0.129***

(0.0295)
0.131***

(0.0297)
0.128***

(0.0297)
Global variables
LIBOR_OIS1.571***

(0.143)
0.0077***

(0.269)
0.0078***

(0.269)
VIX0.0446***

(0.0121)
0.0443***

(0.0121)
Crisis_d3.159***

(0.161)
-0.782***

(0.238)
3.212***

(0.165)
-1.271***

(0.269)
3.170***

(0.166)
-1.260***

(0.270)
Constant5.826***

(0.740)
1.002

(0.800)
5.705***

(0.850)
0.611

(0.909)
5.687***

(0.849)
0.571

(0.910)
Bank FEYesNoNoNoNoNo
Adj R20.7810.5440.7790.5550.7800.555
Obs782782772772772772
McElroy R20.9990.9900.760
Source: Authors’ calculations.Note: This table shows the 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 five-year 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 include 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 (∆CT1_d). Specification 3 includes nonlinear effects of funding costs (regulatory capital) on regulatory capital (funding costs). The results are based on quarterly data from 2004:Q4 to 2013:Q4. Adj = adjusted; Bank FE = bank-fixed effects; CDS_gov = sovereign credit default swap spread; CT1 = Core Tier 1 ratio; FVCDS = fair value credit default swap spread; LLP = loan loss provisions to total assets; NI = net income; Obs = observations; OIS = overnight indexed swap; OLS = ordinary least squares; S&P = Standard & Poor’s; VIX = Chicago Board Options Exchange Volatility Index.
Source: Authors’ calculations.Note: This table shows the 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 five-year 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 include 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 (∆CT1_d). Specification 3 includes nonlinear effects of funding costs (regulatory capital) on regulatory capital (funding costs). The results are based on quarterly data from 2004:Q4 to 2013:Q4. Adj = adjusted; Bank FE = bank-fixed effects; CDS_gov = sovereign credit default swap spread; CT1 = Core Tier 1 ratio; FVCDS = fair value credit default swap spread; LLP = loan loss provisions to total assets; NI = net income; Obs = observations; OIS = overnight indexed swap; OLS = ordinary least squares; S&P = Standard & Poor’s; VIX = Chicago Board Options Exchange Volatility Index.

5. Robustness Checks

This section offers additional support for the study’s findings that solvency and funding costs are determined simultaneously. Several robustness checks are performed using a market-based proxy for bank solvency, and introducing a measure of liquidity risk.

Introducing a Market-Based Measure of Bank Solvency

To check the robustness of the results to the solvency measure, the specifications shown in the previous section using the market-based EDF measure as a proxy of bank solvency were rerun. Table 8.7 shows the results.

Table 8.7.Market-Based Bank Solvency and Funding Costs
Specification 1Specification 2Specification 3
EDFFVCDSEDFFVCDSEDFFVCDS
Endogenous variables
EDF1.403***

(0.119)
1.346***

(0.143)
1.644***

(0.110)
FVCDS0.659***

(0.0508)
0.588***

(0.0492)
0.549***

(0.0285)
∆EDF2_sign0.0440***

(0.0160)
∆FVCDS2_sign-0.0164*

(0.00875)
Exogenous variables
Bank specific
LLP0.0754

(0.120)
0.190

(0.124)
0.143

(0.123)
Nl-0.108

(0.0679)
0.123

(0.113)
-0.119

(0.0727)
0.0675

(0.125)
-0.209**

(0.0823)
0.374**

(0.147)
S&P0.0244

(0.0346)
0.0865*

(0.0449)
0.0559

(0.0379)
∆CT1_d-0.00478

(0.0371)
0.0303

(0.0720)
Country specific
CDS_gov0.180

(0.266)
0.634*

(0.360)
0.187

(0.308)
loan_growth-0.00908

(0.0126)
-0.0228*

(0.0125)
-0.00360

(0.00926)
Global variables
LIBOR_OIS-0.0184***

(0.00126)
0.0268***

(0.00217)
-0.0180***

(0.00142)
0.0268***

(0.00269)
-0.0181***

(0.00141)
0.0311***

(0.00290)
VIX0.0538***

(0.00512)
-0.0760***

(0.0110)
0.0557***

(0.00592)
-0.0735***

(0.0141)
0.0608***

(0.00600)
-0.101***

(0.0137)
Crisis_d-0.258***

(0.0770)
0.360***

(0.117)
-0.0622

(0.0986)
-0.0892

(0.188)
-0.0557

(0.103)
0.00788

(0.203)
Constant-1.039***

(0.141)
1.396***

(0.333)
-1.969***

(0.430)
2.933***

(0.616)
-1.911***

(0.435)
3.225***

(0.791)
Bank FEYesYesYesYesYesYes
Adj R20.7820.7740.7850.7760.7710.559
Obs946946773773771771
McElroy R20.9990.9900.723
Source: Authors’ calculations.Note: This table shows the results of estimating the system (1) using 3SLS. The table reports the estimated coefficients, t-statistics, adjusted R2, and McElroy R2. The dependent variables are market-based capital proxied by the five-year expected default frequency estimated by Moody’s (EDF) and five-year 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 include 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 (∆CT1_d). Specification 3 includes nonlinear effects of funding costs (market-based capital EDF) on market-based capital EDF (funding costs). The results are based on quarterly data from 2004:Q4 to 2013:Q4. Adj = adjusted; Bank FE = bank-fixed effects; EDF = expected default frequency; FVCDS = fair value credit default swap spread; LLP = loan loss provisions; OIS = overnight index swap; LMF = Lagrange multiplier test; NI = net income; Obs = observations; 2SLS = two-stage least squares; S&P = Standard & Poor’s; VIX = Chicago Board Options Exchange Volatility Index.
Source: Authors’ calculations.Note: This table shows the results of estimating the system (1) using 3SLS. The table reports the estimated coefficients, t-statistics, adjusted R2, and McElroy R2. The dependent variables are market-based capital proxied by the five-year expected default frequency estimated by Moody’s (EDF) and five-year 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 include 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 (∆CT1_d). Specification 3 includes nonlinear effects of funding costs (market-based capital EDF) on market-based capital EDF (funding costs). The results are based on quarterly data from 2004:Q4 to 2013:Q4. Adj = adjusted; Bank FE = bank-fixed effects; EDF = expected default frequency; FVCDS = fair value credit default swap spread; LLP = loan loss provisions; OIS = overnight index swap; LMF = Lagrange multiplier test; NI = net income; Obs = observations; 2SLS = two-stage least squares; S&P = Standard & Poor’s; VIX = Chicago Board Options Exchange Volatility Index.

In Specification 1, the analysis is based on 946 observations for 38 banks in six countries from the fourth quarter of 2004 to the fourth quarter of 2013. While the test for weak instruments suggests that the instruments used in Table 8.4 are weak, one would expect that the LIBOR- OIS spread and the VIX are more likely to covary with the market solvency measure than with regulatory capital. Therefore, these two variables are included in the solvency equations shown in Table 8.7. The results show that the impact of bank funding costs on the market measure of solvency is statistically and economically significant. A 100-basis-point increase of CDS spreads is associated with an average increase in the EDF of 66 basis points. The bank-specific variable-provisioning ratio and the country-specific variable loan growth are not statistically and economically significant. As suggested by the test for weak instruments, the market indicators LIBOR- OIS and VIX are significant in the solvency equations, too. The VIX now has the expected sign, but the LIBOR- OIS spread influences solvency negatively through funding cost, reflecting high correlation across markets. The crisis dummy is statistically significant, but has a negative sign. This is consistent with the results in Table 8.4, as CT1 and EDF have different signs. After controlling for higher funding costs, money market conditions, and general risk aversion, EDF is somewhat lower post-Lehman, pointing at the high capitalization efforts by banks covered in the sample (as demonstrated by the positive sign of the crisis dummy in the CT1 equations in Table 8.4). The R2 is high at 78 percent.

The association between the market measure of solvency and funding costs is positive and highly significant at the 1 percent level; the coefficient 1.40 is economically significant. A money market shock— as measured by a spike in the LIBOR-OIS spread—translates into an increase in bank funding costs. Global risk aversion (VIX) reduces bank funding costs. While the coefficient is statistically signif-cant, it has the wrong sign. We attribute this to the large spikes in LIBOR- OIS when VIX also spiked during the heights of the crisis. Changes in sovereign CDS do not directly affect bank funding costs. Finally, the crisis dummy is significant; after Lehman, funding costs are generally higher. The R2 is high at 77 percent. The McElroy R is very high, at just under 100 percent, which suggests that the specifications including market-based measures of solvency and liquidity are less relevant than the specifications including the regulatory solvency measure CT1.

In Specification 2, the study takes into consideration whether or not deliberate management action that aims at improving bank solvency has an impact on the results. It turns out that this variable is not statistically significant. The coefficients and standard errors of the other exogenous variables, LIBOR_OIS and VIX, remain largely unaffected. However, the crisis dummy is not statistically significant anymore. In addition, the coefficients and standard errors of the endogenous variables are basically unchanged.

Again, the squared changes of the endogenous variables in the current quarter are added to test for nonlinearities in Specification 3. By contrast to the results shown in Table 8.4, funding costs have a significant nonlinear impact on the solvency equation. As funding costs increase, banks’ distance to default decreases, pushing up solvency risk. The coefficients of the other endogenous variables remain statistically and economically significant, with very similar coef-fcients. The same holds true for the coefficients of the exogenous variables.

The test statistics are generally satisfactory (Table 8.8). The quality of instruments test rejects the null of weak instruments in all equations. The J-test and the LMF test fail to reject the null of exogenous instruments (except for the FVCDS equation in Specification 3, which is not important since the null is kept for the EDF equation in the same specification). The Durbin-Wu-Hausman test for the solvency equation is only significant at the 7 percent level in Specification 1 and not significant in Specification 2, however in-significant for the other specifications. It suggests that endogeneity is less of an issue for the market-based solvency measure. The system overidentification test is satisfactory for 3SLS across all specifications.

Table 8.8.Test Results for Market-Based Bank Solvency and Funding Costs
Specification 1Specification 2Specification 3
EDFFVCDSEDFFVCDSEDFFVCDS
Quality of instruments (H0: Instruments are weak)
F statistic41.3897.3733.8183.9533.7592.36
p value0.000.000.000.000.000.00
Exogeneity of instruments (H0: 2SLS is valid)
J-test statistic0.010.100.030.160.860.77
p value0.960.660.880.690.130.27
LMF test statistic0.112.510.273.979.7421.72
p value0.740.110.600.140.280.01
Regression-based Hausman for endogeneity of specific variables (H0: Specific variables are exogenous)
t value-1.83-3.87-0.25-2.953.89-3.44
p value0.070.000.800.000.000.00
System Overidentification Test (provided 2SLS is valid, H0: 2SLS is preferred to 3SLS)
Hansen test statistic4.965.880.01
p value0.170.210.99
Source: Authors’ calculations.Note: This table shows the various specification tests for the results shown in Table 8.6. We check for the quality of instruments (F-test) and the exogeneity of instruments (J-test and Lagrange multiplier test). The analysis tests for the quality of instruments (F-test) and the exogeneity of instruments (J-test and Lagrange multiplier test). The endogeneity of the RHS endogenous variables (t-test) is tested and the Hansen system overidentification test is applied. EDF = expected default frequency: FVCDS = fair value credit default swap spread; LMF = Lagrange multiplier test; SLS = two-stage least squares.
Source: Authors’ calculations.Note: This table shows the various specification tests for the results shown in Table 8.6. We check for the quality of instruments (F-test) and the exogeneity of instruments (J-test and Lagrange multiplier test). The analysis tests for the quality of instruments (F-test) and the exogeneity of instruments (J-test and Lagrange multiplier test). The endogeneity of the RHS endogenous variables (t-test) is tested and the Hansen system overidentification test is applied. EDF = expected default frequency: FVCDS = fair value credit default swap spread; LMF = Lagrange multiplier test; SLS = two-stage least squares.

The direction of the bias generated is assessed by running an OLS regression on the market-based solvency measure. Results are reported in Table 8.9. In line with the results obtained for the regulatory capital measure, OLS coefficients underestimate the impact of solvency risk on funding costs across all specifications, albeit to a smaller extent. For Specification 1, the OLS coefficient of CDS in the solvency equation at 0.59 lies below the 0.66 estimate under the simultaneous panel approach.

Table 8.9.Market-Based Bank Solvency and Funding Costs (OLS Estimation)
Specification 1Specification 2Specification 3
EDFFVCDSEDFFVCDSEDFFVCDS
Endogenous variables
EDF0.994***

(0.0279)
0.971***

(0.0299)
1.026***

(0.0330)
FVCDS0.591***

(0.0163)
0.607***

(0.0181)
0.610***

(0.0195)
∆EDF2_sign-0.0173***

(0.00430)
∆FVCDS2_sign-0.00185

(0.00397)
Exogenous variables
Bank specific
LLP0.351**

(0.141)
0.351**

(0.155)
0.333**

(0.160)
NI-0.101

(0.0687)
-0.114

(0.0839)
-0.0782

(0.0753)
-0.149*

(0.0897)
-0.0856

(0.0771)
-0.174*

(0.0889)
S&P0.0984**

(0.0384)
0.179***

(0.0428)
0.168***

(0.0424)
∆CT1_d0.215

(0.143)
0.218

(0.143)
Country specific
CDS_gov0.938***

(0.222)
1.374***

(0.262)
1.323***

(0.261)
loan_growth-0.00203

(0.0141)
0.00406

(0.0154)
0.00371

(0.0155)
Global variables
LIBOR_OIS-0.0177***

(0.115)
0.0218***

(0.150)
-0.0188***

(0.142)
0.0216***

(0.176)
-0.0188***

(0.142)
0.0222***

(0.176)
VIX0.0539***

(0.00517)
-0.0471***

(0.00682)
0.0565***

(0.00612)
-0.0419***

(0.00784)
0.0565***

(0.00614)
-0.0450***

(0.00781)
Crisis_d-0.186***

(0.0689)
0.231**

(0.102)
-0.0636

(0.0998)
-0.327**

(0.155)
-0.0704

(0.101)
-0.318**

(0.153)
Constant-1.027***

(0.136)
0.605**

(0.256)
-2.086***

(0.427)
2.374***

(0.560)
-2.088***

(0.428)
2.447***

(0.554)
Bank FEYesYesYesYesYesYes
Adj R20.7870.8180.7870.8160.7870.821
Obs946946773773771771
McElroy R20.9990.9900.760
Source: Authors’ calculations.Note: This table shows the 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 five-year expected default frequency estimated by Moody’s (EDF) and five-year 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 include 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 (∆CT1_d). Specification 3 includes nonlinear effects of funding costs (market-based capital EDF) on market-based capital EDF (funding costs). The results are based on quarterly data from 2004:Q4 to 2013:Q4. Adj = adjusted; Bank FE = bank-fixed effects; CDS_gov = sovereign credit default swap spread; CT1 = Core Tier 1 ratio; FVCDS = fair value credit default swap spread; LLP = loan loss provisions to total assets; NI = net income; Obs = observations; OIS = overnight indexed swap; OLS = ordinary least squares; S&P = Standard & Poor’s; VIX = Chicago Board Options Exchange Volatility Index.
Source: Authors’ calculations.Note: This table shows the 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 five-year expected default frequency estimated by Moody’s (EDF) and five-year 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 include 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 (∆CT1_d). Specification 3 includes nonlinear effects of funding costs (market-based capital EDF) on market-based capital EDF (funding costs). The results are based on quarterly data from 2004:Q4 to 2013:Q4. Adj = adjusted; Bank FE = bank-fixed effects; CDS_gov = sovereign credit default swap spread; CT1 = Core Tier 1 ratio; FVCDS = fair value credit default swap spread; LLP = loan loss provisions to total assets; NI = net income; Obs = observations; OIS = overnight indexed swap; OLS = ordinary least squares; S&P = Standard & Poor’s; VIX = Chicago Board Options Exchange Volatility Index.

Introducing a Measure of Liquidity Risk

Funding costs are likely to be determined by banks’ exposure to liquidity risk as recently shown by Acharya and Mora 2015. Changes in the maturity or composition of banks’ funding can have important implications for measures of default risk. To address this concern, a measure of liquidity risk is introduced to control for banks’ liquidity-risk-bearing capacity. For the baseline specification using the regulatory capital measure, the results are shown in Table 8.10. The impact of regulatory capital on funding costs is robust to the introduction of the liquidity measure. The coefficient decreases just slightly from 1.048 to 1.028 but remains statistically significant at the 1 percent confidence level (Table 8.11). Table 8.12 reports the results for the market-based solvency measure. The liquidity indicator is not statistically significant across specifications. Again, the coefficient of baseline regressors is stable, with the impact of EDF slightly decreasing from 1.40 to 1.37 and remaining statistically significant at the 1 percent confidence level (Table 8.13).

Table 8.10.Bank Regulatory Capital and Funding Costs(Controlling for Liquidity Risk)
Specification 1Specification 2Specification 3
CT1FVCDSCT1FVCDSCT1FVCDS
Endogenous variables
CT1-1.028***

(0.251)
-1.055***

(0.342)
-0.939***

(0.270)
FVCDS-0.350***

(0.0975)
-0.390***

(0.101)
-0.219***

(0.0713)
ACT12_sign0.0835

(0.0551)
AFVCDS2_sign-0.0125

(0.0250)
Exogenous variables
Bank specific
LLP-1.476***

(0.341)
-1.432***

(0.348)
-1.746***

(0.385)
Nl-0.194

(0.173)
-0.578***

(0.211)
-0.209

(0.177)
-0.587***

(0.215)
-0.168

(0.201)
-0.635***

(0.208)
S&P (lag 1)0.281**

(0.112)
0.236**

(0.110)
0.293**

(0.116)
LiRisk0.0961**

(0.0434)
0.0998**

(0.0498)
0.0693

(0.0450)
ACT1_d0.158

(0.309)
0.0712

(0.291)
Country specific
CDS_gov4.154***

(0.662)
4.464***

(0.711)
4.465***

(0.685)
loan_growth-0.000355

(0.0407)
-0.00987

(0.0418)
0.0282

(0.0372)
Global variables
LIBOR_OIS0.0045

(0.303)
0.0117**

(0.460)
0.00766

(0.00475)
VIX-0.0360

(0.0312)
-0.0158

(0.0269)
Crisis_d3.254***

(0.177)
2.386***

(0.776)
3.287***

(0.184)
2.715**

(1.201)
3.236***

(0.186)
1.846*

(0.980)
Constant7.550***

(0.864)
8.146***

(1.848)
7.693***

(1.002)
8.840***

(2.569)
7.119***

(0.918)
8.122***

(2.162)
Bank FEYesYesYesYesYesYes
Adj R20.9870.8450.9870.846
Obs742742732732732732
McElroy R20.9140.9050.763
Source: Authors’ calculations.Note: This table shows the results of estimating the system (1) using 2SLS. The table reports the estimated coefficients, t-statistics, adjusted R2, and McElroy R2. The dependent variables are regulatory capital (CT1) and five-year 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 variable include 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 (∆CT1_d). Specification 3 includes nonlinear effects of funding costs (regulatory capital) on regulatory capital (funding costs). The results are based on quarterly data from 2004:Q4 to 2013:Q4. Adj = adjusted; Bank FE = bank-fixed effects; CDS_gov = sovereign credit default swap spread; CT1 = Core Tier 1 ratio; FVCDS = fair value credit default swap spread; OIS = overnight index swap; LLP = loan loss provisions to total assets; NI = net income; Obs = observations; 2SLS = two-stage least squares; S&P = Standard & Poor’s; VIX = Chicago Board Options Exchange Volatility Index.
Source: Authors’ calculations.Note: This table shows the results of estimating the system (1) using 2SLS. The table reports the estimated coefficients, t-statistics, adjusted R2, and McElroy R2. The dependent variables are regulatory capital (CT1) and five-year 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 variable include 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 (∆CT1_d). Specification 3 includes nonlinear effects of funding costs (regulatory capital) on regulatory capital (funding costs). The results are based on quarterly data from 2004:Q4 to 2013:Q4. Adj = adjusted; Bank FE = bank-fixed effects; CDS_gov = sovereign credit default swap spread; CT1 = Core Tier 1 ratio; FVCDS = fair value credit default swap spread; OIS = overnight index swap; LLP = loan loss provisions to total assets; NI = net income; Obs = observations; 2SLS = two-stage least squares; S&P = Standard & Poor’s; VIX = Chicago Board Options Exchange Volatility Index.
Table 8.11.Test Results for Bank Regulatory Capital and Funding Costs(Controlling for Liquidity Risk)
Specification 1Specification 2Specification 3
CT1FVCDSCT1FVCDSCT1FVCDS
Quality of instruments (H0: Instruments are weak)
F statistic1109.0485.791072.1082.851036.9282.09
p value0.000.000.000.000.000.00
Exogeneity of instruments (H0: 2SLS is valid)
J-test statistic0.730.060.930.100.951.04
p value0.210.770.100.800.170.05
LMF test statistic6.731.498.992.3710.4528.41
p value0.080.220.060.310.400.00
Regression-based Hausman for endogeneity of specific variables (H0: Specific variables are exogenous)
t value5.597.436.035.776.466.65
p value0.000.000.000.000.000.00
System Overidentification Test (provided 2SLS is valid, H0: 2SLS is preferred to 3SLS)
Hansen test statistic41.9949.2353.06
p value0.000.000.00
Source: Authors’ calculations.Note: This table shows the various specification tests for the results shown in Table 8.6. We check for the quality of instruments (F-test) and the exogeneity of instruments (J-test and Lagrange multiplier test). The analysis tests for the quality of instruments (F-test) and the exogeneity of instruments (J-test and Lagrange multiplier test). The endogeneity of the RHS endogenous variables (t-test) is tested, and the Hansen system overidentification test is applied. 2SLS = two-stage least squares; 3SLS = three-stage least squares; CT1 = Core Tier 1 ratio; FVCDS = fair value credit default swap spread; LMF = Lagrange multiplier test.
Source: Authors’ calculations.Note: This table shows the various specification tests for the results shown in Table 8.6. We check for the quality of instruments (F-test) and the exogeneity of instruments (J-test and Lagrange multiplier test). The analysis tests for the quality of instruments (F-test) and the exogeneity of instruments (J-test and Lagrange multiplier test). The endogeneity of the RHS endogenous variables (t-test) is tested, and the Hansen system overidentification test is applied. 2SLS = two-stage least squares; 3SLS = three-stage least squares; CT1 = Core Tier 1 ratio; FVCDS = fair value credit default swap spread; LMF = Lagrange multiplier test.
Table 8.13.Test Results for Market-Based Bank Solvency and Funding Costs(Controlling for Liquidity Risk)
Specification 1Specification 2Specification 3
EDFFVCDSEDFFVCDSEDFFVCDS
Quality of instruments (H0: Instruments are weak)
F statistic42.01101.9334.3288.6434.49101.90
p value0.000.000.000.000.000.00
Exogeneity of instruments (H0: 2SLS is valid)
J-test statistic0.020.120.040.150.800.71
p value0.980.590.930.670.210.31
LMF test statistic0.202.720.413.709.0520.18
p value0.900.100.810.160.530.03
Regression-based Hausman for endogeneity of specific variables (H0: Specific variables are exogenous)
t value-1.89-4.02-0.32-2.784.79-5.24
p value0.060.000.750.010.000.00
System Overidentification Test (provided 2SLS is valid, H0: 2SLS is preferred to 3SLS)
Hansen test statistic5.734.850.66
p value0.220.430.98
Source: Author’s calculations.Note: This table shows the various specification tests for the results shown in Table 8.9. The analysis tests for the quality of instruments (F-test) and the exo-geneity of instruments (J-test and Lagrange multiplier test). The endogeneity of the RHS endogenous variables (t-test) is tested and the Hansen system overidentification test is applied. 2SLS = two-stage least squares; EDF = expected default frequency; FVCDS = fair value credit default swap spread; LMF = Lagrange multiplier; SLS = two-stage least squares.
Source: Author’s calculations.Note: This table shows the various specification tests for the results shown in Table 8.9. The analysis tests for the quality of instruments (F-test) and the exo-geneity of instruments (J-test and Lagrange multiplier test). The endogeneity of the RHS endogenous variables (t-test) is tested and the Hansen system overidentification test is applied. 2SLS = two-stage least squares; EDF = expected default frequency; FVCDS = fair value credit default swap spread; LMF = Lagrange multiplier; SLS = two-stage least squares.

A caveat of the analysis is that a bank’s exposure to other risks may affect its liquidity. Any exposure may expose a bank to multiple risks and can erode a bank’s liquidity position or affect its funding costs, thereby increasing its liquidity risk.

Overall, our finding that the interaction between solvency and liquidity funding costs is economically and statistically significant is robust. The exact level of the parameters of solvency and funding costs should be investigated further for different samples of banks. Our sample consists of very large internationally active banks with a relatively short maturity structure, relatively high CDS-sensitive funding structure, and a relatively low risk density. Aldasoro and Park 2018 a pply and refine our approach to a proprietary balance sheet data for 13 Korean banks covering the period from the first quarter of 2015 to the second quarter of 2015. The data includes a specific reporting item, “marginal funding costs,” which the authors use instead of the CDS spread. They confirm our finding of an economically and statistically significant interaction. They find that a 100-basis-point increase in marginal funding costs is associated with a 155-basis-point increase in solvency risk; a 100-basis-point increase of the T1 ratio is associated with a 77-basis-point increase of marginal funding costs. Their findings are robust under various subsamples, alternative specifications, and alternative proxies for solvency. Similarly, IMF 2018 presents the results of an exploratory study into the solvency-liquidity interaction in stress tests. Based on three different approaches, the study confirms that the interaction is relevant for stress tests. It also finds that the back-book effect increases with banks’ maturity mismatch between assets and liabilities and with the share of unsecured wholesale funding; it decreases with banks’ risk density (measured as RWA over total assets) and their pass-through rates of higher bank-specific funding spreads to new loans.

6. Application to Stress Testing

This section illustrates the relevance of the empirical analysis for stress testing. The estimated relationship between solvency and funding costs are applied to project banks’ capital ratios under stress. The objective of stress testing is to assess banks’ resilience to adverse macroeconomic developments. While banks are routinely required to incorporate funding cost projections in their stress testing submissions, these are typically driven by risk factors linked to the scenario, notably the macroeconomic environment and the evolution of benchmark rates, but less so to idiosyncratic risk linked to banks’ capital positions under stress. The aim of this section is to provide an estimate of the additional impact of endogenizing the solvency-funding cost channel on banks’ capital ratios in a stressful environment. The analysis is based on the adverse macroeconomic scenario developed by the European Central Bank for the 2014 EU- wide stress test conducted by the EBA.

To illustrate the magnitude of the interaction between solvency and funding costs on banks’ capital ratios, the study used data on European banks disseminated by the EBA on the 2014 EU-wide stress test exercise.29 The EU-wide stress test was conducted on a sample of 124 EU banks under the assumption of a static balance sheet, which implies no new growth and a constant business mix and model throughout the time horizon of the exercise. The resilience of EU banks was assessed over a period of three years (2 014 –16 ).

Of the 15 EU banks covered in the sample, 11 were also included in the EU stress test exercise. The analysis focuses on this subset of banks. At the cutof date, the aggregate

CET1 ratio for the study’s sample stood at 14.5, which is significantly higher than the aggregate CET1 ratio for the entire sample at 11.1 percent. At the same time, the impact of stress on bank’s capital ratios is of similar magnitude across samples: 283 basis points for the study’s subset of banks relative to 270 basis points for the entire population of banks covered in the exercise. This section addresses the question of whether integrating second-round effects via the solvency and funding cost nexus would have had a significant impact on this capital shortfall.

The coefficients shown in Specification 1 (Table 8.4) are used to endogenize banks’ funding costs. While econometric results are cast in terms of CT1 rather than CET1 as the measure of regulatory capital, the undisclosed value of CT1 for the banks in the subsample is expected to be close to their CET1 as the weighted-sized gap between Tier 1 (a broader measure than CT1) and CET1 stood at only 100 basis points in 2013.30 The assumption is that the average funding structure of the 11 banks included in the EU stress test exercise is similar to that of the average bank in the study’s 15-bank sample.31 While this is a reasonable assumption given the composition of the two samples, individual results might be overestimated for banks that focus on retail funding and underestimated for banks with greater reliance on wholesale funding. The estimated relationship suggests that:

where ΔCT1i,t* denotes bank i’s change in regulatory capital at time t excluding the interaction effect, and ΔCT1i,tfc denotes the interaction effect. The marginal effect of capital (net income) in the funding equation is denoted by α (β), and the marginal effect of funding cost in the capital equation is denoted by 8.

Note that allowing for the interaction effect at time t carries forward to t + 1 due to its impact on ΔCT1i,t+1* and therefore on ΔFVCDSi,t+1.

The stress test horizon is denoted by {t, t + j}. Equation (8.3) can be iterated forward to calculate the impact of the interaction effect on bank i’s capital ratio at time t + j:

Interestingly, equation (8.4) reveals a hysteresis effect of solvency shocks in banks’ capital ratios. An initial disturbance to bank capital is long-lived due to its impact through the funding cost channel. The rate of decay is determined by the interaction between the elasticity of capital to funding costs (δ) and the elasticity of funding costs to capital (α).

Next, the analysis quantifes banks’ susceptibility to adverse solvency-funding cost dynamics for the selected 11 EU banks. To conduct the analysis, the individual bank projections of CET1 and NI were used, as projected by the EBA in 2014, as a starting point of the iterative process. The estimated coefficients for NI and regulatory capital (CT1) in the funding cost equation (FVCDS) are then used to parameterize the adverse dynamics between bank solvency and funding costs and their ultimate impact on bank’s capital ratios at the end of the stress test horizon.

In 2014, the weighted-average CET1 ratio for the study’s sample of banks decreases by 130 basis points under the adverse scenario, from a weighted average of 14.5 percent in 2013 to 13.2 percent in 2014. At the same time, the average NI falls by 40 basis points to –0.2 percent from 0.2 percent in 2013. Given the estimated elasticities of funding costs to

Table 8.12.Market-Based Bank Solvency and Funding Costs(Controlling for Liquidity Risk)
Specification 1Specification 2Specification 3
EDFFVCDSEDFFVCDSEDFFVCDS
Endogenous variables
EDF1.372***

(0.123)
1.276***

(0.148)
1.731***

(0.110)
FVCDS0.687***

(0.0559)
0.613***

(0.0528)
0.553***

(0.0272)
∆EDF2_sign0.0420**

(0.0164)
∆FVCDS2_sign-0.0196**

(0.00948)
Exogenous variables
Bank specific
LLP0.0551

(0.124)
0.194

(0.129)
0.0542

(0.119)
Nl-0.0951

(0.0705)
0.108

(0.115)
-0.104

(0.0755)
0.0290

(0.127)
-0.238***

(0.0871)
0.423***

(0.157)
S&P0.0166

(0.0330)
0.0835*

(0.0426)
0.0391

(0.0345)
LiRisk-0.000471

(0.00149)
-0.000592

(0.00405)
-0.000666

(0.0103)
∆CT1_d0.0180

(0.0434)
0.0231

(0.0701)
Country specific
CDS_gov0.142

(0.302)
0.749*

(0.431)
-0.0972

(0.363)
loan_growth-0.00660

(0.0128)
-0.0221*

(0.0121)
-0.00272

(0.00871)
Global variables
LIBOR_OIS-0.0181***

(0.00124)
0.0254***

(0.00234)
-0.0179***

(0.00140)
0.0245***

(0.00290)
-0.0181***

(0.00146)
0.0318***

(0.00315)
VIX0.0507***

(0.00540)
-0.0692***

(0.0118)
0.0529***

(0.00636)
-0.0624***

(0.0152)
0.0613***

(0.00638)
-0.106***

(0.0148)
Crisis_d-0.264***

(0.0776)
0.355***

(0.122)
-0.0583

(0.0992)
-0.147

(0.200)
-0.0574

(0.106)
0.0600

(0.216)
-1.032***

(0.141)
1.369***

(0.335)
-2.026***

(0.437)
2.894***

(0.595)
-1.919***

(0.446)
3.335***

(0.823)
Bank FEYesYesYesYesYesYes
Adj R20.7820.7750.7860.7870.7690.671
Obs905905733733733733
McElroy R20.9990.9900.760
Source: Authors’ calculations.Note: This table shows the results of estimating the system (1) using 3SLS. The table reports the estimated coefficients, t-statistics, adjusted R2, and McElroy R2. The dependent variables are market-based capital proxied by the five-year expected default frequency estimated by Moody’s (EDF) and five-year 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 include 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 (∆CT1_d). Specification 3 includes nonlinear effects of funding costs (market-based capital EDF) on market-based capital EDF (funding costs). The results are based on quarterly data from 2004:Q4 to 2013:Q4. Adj = adjusted; Bank FE = bank-fixed effects; CDS_gov = sovereign credit default swap spread; EDF = expected default frequency; FVCDS = fair value credit default swap spread; OIS = overnight index swap; LLP = loan loss provisions to total assets; NI = net income; Obs = observations; 2SLS = two-stage least squares; S&P = Standard & Poor’s; VIX = Chicago Board Options Exchange Volatility Index.
Source: Authors’ calculations.Note: This table shows the results of estimating the system (1) using 3SLS. The table reports the estimated coefficients, t-statistics, adjusted R2, and McElroy R2. The dependent variables are market-based capital proxied by the five-year expected default frequency estimated by Moody’s (EDF) and five-year 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 include 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 (∆CT1_d). Specification 3 includes nonlinear effects of funding costs (market-based capital EDF) on market-based capital EDF (funding costs). The results are based on quarterly data from 2004:Q4 to 2013:Q4. Adj = adjusted; Bank FE = bank-fixed effects; CDS_gov = sovereign credit default swap spread; EDF = expected default frequency; FVCDS = fair value credit default swap spread; OIS = overnight index swap; LLP = loan loss provisions to total assets; NI = net income; Obs = observations; 2SLS = two-stage least squares; S&P = Standard & Poor’s; VIX = Chicago Board Options Exchange Volatility Index.

CT1 and NI, the solvency shock triggers an increase in banks’ marginal wholesale funding cost of 160 basis points in 2014. This shock generates a further reduction of banks’ capital ratios by 51 basis points. The additional drop in capital buffers feeds into the stress test exercise as an idiosyncratic funding shock the following year. This iterative process continues throughout the stress test horizon. Table 8.14 reports the results at the bank level for the entire stress test horizon over 2014–16.

Table 8.14.Impact of Bank Solvency and Funding Cost Interaction—2014 EBA Stress Test (Basis Points)
Estimated Elasticities201420152016
Bank NameFunding Costs to CET1Funding Costs to NilCET1 to Funding Costs∆Funding Costs∆CET1∆Funding Costs∆CET1∆Funding Costs∆CET1
Bankl-1.048-0.547-0.320213-68296295308-99
Bank 2-1.048-0.547-0.320103-3387228116-37
Bank 3-1.048-0.547-0.320311-99310299557-178
Bank4-1.048-0.547-0.32088-289623198-31
Bank 5-1.048-0.547-0.320225-7291-293-1
Bank6-1.048-0.547-0.320178-57159-51107-34
Bank 7-1.048-0.547-0.320335-107167-53153-49
Bank8-1.048-0.547-0.32059-1986-2869-22
Bank9-1.048-0.547-0.320595-191858-275976-312
Bank 10-1.048-0.547-0.320243-78351-112506-162
Bank 11-1.048-0.547-0.32093-3010-3-4213
Source: Authors’ calculations using European Banking Authority (EBA) stress test results and estimation results.Note: This table shows the additional impact of the interaction between funding costs and solvency ratios on banks’Common Equity Tier I (CET1) under EBAs adverse scenario over 2014–16. The sample of banks covers those banks included in the 2014 EU-wide exercise, which are also included in the sample. The analysis assumes constant asset size over the stress test horizon under EBAs static balance sheet assumption.
Source: Authors’ calculations using European Banking Authority (EBA) stress test results and estimation results.Note: This table shows the additional impact of the interaction between funding costs and solvency ratios on banks’Common Equity Tier I (CET1) under EBAs adverse scenario over 2014–16. The sample of banks covers those banks included in the 2014 EU-wide exercise, which are also included in the sample. The analysis assumes constant asset size over the stress test horizon under EBAs static balance sheet assumption.

The overall effect is significant. While macroeconomic stress reduces the aggregate capital ratio by 283 basis points over 2014–16, the overall impact, including the macro shock and the adverse dynamics of the solvency-funding cost nexus slashes banks’ average capital ratio by 414 basis points. This suggests that the impact of second-round effects of the solvency-funding cost nexus might erode banks’ capital ratios by about half of the capital shortfall estimated by the EBA. Figure 8.3 shows the factors contributing to the shortfall in the aggregate CET1 by year. For the average bank in the sample, the interaction effect on CET1 is 51 basis point in 2014, 43 basis points in 2015, and 37 basis points in 2016. 32 As a result of the adverse reinforcing dynamics, the relative impact of the interaction effect vis-à- vis the macro effect increases throughout the stress test horizon, from 40 percent in 2014 to over 50 percent in 2016.

Decomposition of Impact on CET1—2014 EBA Stress Test

Source: Author’s calculations using European Banking Authority stress test results and estimation results.

Note: CET1 = Core Equity Tier 1; EBA = European Banking Authority.

The impact on capital loss in monetary units is even larger, as weaker banks tend to post higher RWAs. Overall, the interaction effect triggers a reduction in aggregate capital by €3.8 billion in 2014, €3.3 billion in 2014, and €2.8 billion in 2014 for the study’s sample of banks. This represents around half of the aggregate capital losses estimated by the EBA for this subset of banks from adverse economic developments over the three-year horizon.

The effect of the interaction between solvency and funding costs is significant in part because the impact of funding cost rises nonlinearly over the stress test horizon. This is because net income and capital deteriorate further owing to adverse reinforcing dynamics. The EBA’s stressed capital ratios do include non bank-specific funding cost effects from adverse macroeconomic developments, risk aversion, and liquidity strains, but not the bank-specific feedback effect modeled in this chapter.33 The application to stress tests shows that banks with shorter funding tenors, and/or greater reliance on CDS-sensitive funding instruments (that is, unsecured wholesale funding) and/or lower-RWA-to-total-asset ratios are more affected by the feedback effect of solvency on funding costs. The study concludes that a bank’s funding structure is not only relevant for its funding liquidity risk exposure, but also for its exposure to solvency shocks. On the other hand, the cumulated impact could be more severe in a tail event, as bank funding structures might be further impaired under stress. In a crisis, wholesale funding tends to shift to shorter-dated tenors, increasing the amount of liabilities that need to be rolled over at higher funding rates.

7. Summary and Conclusions

While the existence of a relationship between bank solvency and funding costs is widely accepted in the literature, its estimated magnitude has been typically small. This study’s results suggest a larger impact of solvency on funding costs than suggested by earlier studies. The stability of the coefficients is confirmed when alternative measures of solvency risk and banks’ capacity to bear liquidity risk are considered. These new results could be in part due to the study’s newly constructed dataset, which exploits high-quality supervisory data. They could also be driven by the econometric strategy to implement a 3SLS simultaneous equation approach, by contrast to the OLS- based estimates that are prevalent in the existing literature. Indeed, the study’s results show that OLS underestimates the solvency-liquidity interaction nexus. This might be due to investors’ expectations that a weaker bank might raise capital to rebuild its capital buffer in order to ease funding pressures or meet regulatory expectations. While a simultaneous equation approach has its own challenges related to the difficulty of finding suitable instruments and avoiding overidentification, this study’s statistical tests and robustness checks provide some comfort on the estimated co-efficients in the interaction between solvency and funding costs. Still, the results should be interpreted with caution, bearing the limitations of the approach in mind.

The study’s results show that the interaction between solvency and funding shocks in supervisory stress test models is quantitatively relevant. The analysis suggests that, by incorporating the dynamic interaction between solvency and funding costs in the 2014 EU-wide stress test, stressed capital ratios could be depleted by a further half of the capital shortfall estimated in the original EBA analysis. This is a conservative estimate, as the EBA’s methodological approach partially incorporates rising funding costs linked to the scenario.34 The results are also highly relevant for cost-impact assessments of capital regulation, as the costs of higher capital requirements are partly offset by lower debt servicing costs. These results provide a foundation for calibrating that effect in quantitative cost-benefit analyses of bank regulation. The analysis also points at the merits of incorporating solvency and liquidity interactions in the design of prudential regulation. While the study’s results are encouraging, future research should assess their robustness using larger high-quality samples and, if feasible, a broader set of instruments to address remaining endogeneity concerns.

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1

Shleifer and Vishny (2011) argue that liquidity problems caused by fire sales contributed to the depth and propagation of the crisis.

2

This conjecture also holds, if the share of variable rate loans is high. The variable rates usually vary with market rates (for example, three-month LIBOR) plus a fixed margin. This does not allow banks to adjust variable rates to bank-specific increases in funding costs. Similarly, interest rate hedges insure against movements in market rate, but not in bank-specific markups on market rates.

3

With the caveat that if banks that anticipate holding riskier assets also post higher capital ratios, capital ratios would not reflect balance sheet strength but changes in riskiness of underlying assets. This would imply that we should not be able to observe a negative relationship between capital ratios and funding costs.

4

Kitamura, Muto, and Takei (2015) find that the median value of one-year-ahead pass-through for Japanese banks is 0.18.

5

Since not all of these banks are publicly traded, a restricted sample is used for some econometric specifications.

6

Due to the sensitivity of the data, strict confidentiality arrangements were in place.

7

A recent study by Aymanns and others (2016) finds that a solvency shock of 500 basis points lead to an average increase in interbank funding cost of about 20 basis points, with a peak impact of 40 basis points in 20 07.

8

Whereas the chapter’s baseline specification focuses on the cost of bank funding, robustness checks to include stress conditions on funding volumes are also included.

9

The SRISK measure is defined as the difference between the regulatory capital ratio applied to the expected value of assets in the event of a financial crisis and the expected market value of capital.

10

Cetina (2015) discusses the channels through which shocks can impact regulatory solvency and liquidity ratios simultaneously.

11

Beau and others (2014) provide a thorough discussion of the effect of a shock to bank funding costs on bank capital and financial stability.

12

Supervisory data is based on reported regulatory balance sheets and include confidential supervisory information gathered through supervisory processes.

13

The case studies discussed in BCBS (2013a) and BCBS (2013b) provide useful illustrations of this issue.

14

The instruments included in CT1 are well comparable across jurisdictions, while those included in Tier 1 and Tier 2 are comprised of instruments that are more country specific. Core Equity Tier 1 (CET1) would be even more comparable across jurisdictions, but was introduced only recently in Basel III. Thus, CET1 data is not available for our sample period.

16

Moody’s uses a Merton-based model whereby the equity of a firm is analogous to holding a call option on the firm’s assets and the required debt payment serves as the option’s strike price. See Sun, Munves, and Hamilton 2012 for further discussion of Moody’s methodology.

17

See BCBS 2015 for further details.

18

The high correlation between VIX and LIBOR- OIS reported in the appendix is an artifact of the enormous spikes in both around the Lehman failure. Before and after, the two did not move together. They indeed measure and capture different phenomena: the VIX captures a very broad change in volatility across all sectors of the economy (macroeco-nomic news in various parts of the world, changes in risk sentiment, geopolitical tensions); the LIBOR- OIS spread captures observed price behavior in levels in a subsegment of the economy (unsecured interbank markets). It is very bank specific and time specific.

19

This yields 70 observations for the dummy variable across all banks and quarters.

20

Even if variables LLP and NI were collinear, the estimated coefficients would still be consistent in the study’s estimation procedure. The standard error would be inflated but that would not affect the main finding, namely that solvency and funding costs are endogenously determined and that neglecting that interaction in stress tests leads to the systematic and significant underestimation of the effects on solvency of a given shock.

21

It is important to note that 2SLS in a simultaneous equation system has an important advantage over the classical single equation IV instrumental variable estimator: it does not use instruments that are outside of the system (that is, is not an exogenous variable in one of the equations).

22

See Nakamura and Nakamura (1981) for more details.

23

In contrast, the effect of provisions on funding costs depends on their motivation. Whereas higher provisioning rates designed to optimize taxation can increase intertemporal profits and push down funding costs, provisions triggered by borrowers’ lower credit quality is likely to be associated with higher funding costs.

24

Ratings are eventually considering bank solvency, but ratings change infrequently and often lag CT1 changes such that we assume that they are not simultaneously determined with solvency in each quarter.

25

The 32 basis points are an average across all banks in the sample; the impact of an increase in funding costs on an individual bank depends on the share of funding that is CDS sensitive (mostly unsecured wholesale funding), the ratio of RWAs to total assets, the term structure of funding, and the pass-through of higher funding costs to new assets. The banks in the sample are large internationally active banks with significant reliance on credit-sensitive funding instruments during the sample period. At the same time, competition in credit markets is high, constraining banks’ ability to pass through rising funding costs to customers. On balance, the magnitude of the coefficient is regarded as plausible, taking as a benchmark the largest bank of the sample.

26

The McElroy R2 provides a goodness-of-fit measure for systems of equations (McElroy 1977).

27

The variables that serve as instruments in the funding cost equations are significant. The study concludes that, given its assumptions, the results do not reject their usefulness as instruments.

28

However, this approach is treated as first approximation, as accounting for nonlinearities in linear models is not equivalent to constructing nonlinear models of the underlying processes.

30

Bank CT1 ratios are proxied by CET1 ratios, as the EBA’s CET1 projections are reported under the transitional arrangements of Basel III, which are close to CT1 ratios.

31

EBA 2014b does not disclose the liability composition of the banks included in the EU-wide stress test.

32

This estimate reflects the impact of an idiosyncratic funding shock whereby a bank’s cost of funds depends on its own capital position. By taking bank solvency into account, this element captures a key amplification channel evident during the global financial crisis. On the other hand, aggregate shocks to funding costs remain the same as under the EBA stress test scenario.

34

To the extent that stressed credit spreads under the adverse scenario reflect a weakened capital position of the banking system, the rise in wholesale funding costs projected under the EBA incorporates a “systemic” funding shock whereby banks’ cost of funds depends on the position of the system as a whole.

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