Mind the Gap: Disentangling Credit and Liquidity in Risk Spreads

Euro-area sovereign bond and interbank interest rate spreads widened sharply in the 2007-2009 Global Financial Crisis and over the subsequent European Debt Crisis, greatly increasing financing costs. Such rate volatility could represent concerns over asset liquidity or issuer solvency. To precisely identify the relative contribution of these two effects in interest rate spreads, this paper uses a model-free measure of euro-area bond market liquidity. Liquidity accounts for 36% of the trough-to-peak sovereign spread widening during the Financial Crisis and 21% in the Debt Crisis, after controlling for default risk. Aggregate bond liquidity also explains a substantial portion of interbank spreads.

The 2007-2009 Global Financial Crisis and the European Debt Crisis were marked by extraordinary interest rate spread widening and heightened volatility in asset prices, contributing to a broad tightening of financial conditions. One example is the increase in euro-area government bond spreads, which rose by more than an order of magnitude in the Financial Crisis, to levels not seen since the introduction of the common currency in 1999. During the Debt Crisis, spreads rose even higher. In the money market, spreads between unsecured interbank borrowing rates (EURIBOR) and overnight-indexed swap (OIS) rates of comparable maturities also rose by more than an order of magnitude in the Financial Crisis. EURIBOR-OIS spreads reached their widest levels since the inception of the OIS market, and peaked to an all-time high in October 2008.
Despite the enormity of these interest rate movements, there has been a lack of consensus on the dominant driver. One hurdle to identification is the difficulty in precisely capturing the risk components in prices. This paper documents a model-free measure of euro-area market liquidity, constructed directly from asset prices, that is used to parse these historic movements in euro-area sovereign bond and interbank interest rate spreads. The results show that aggregate market liquidity and default risk are primary contributors to movements in euro-area sovereign debt and money market spreads. However, their relative importance differs by country and over time. An equal-weighted average across countries and maturities attributes 36% of the trough-to-peak sovereign bond spread widening over the Financial Crisis to deteriorating liquidity and 22% to heightened default risk. In the Sovereign Debt Crisis, liquidity and credit continue to have substantial roles in explaining spread widening, but their importance shifts to 21% and 32%, respectively. Aggregate bond market liquidity also explains a substantial portion of interbank interest rate spreads over and above the effects of interbank credit and liquidity, and the results show that its role increases over time.
Beyond the expected path of future short-horizon interest rates, it is difficult to empirically determine what drives sovereign bond yields or interbank rates, especially at times of market stress. Two possible influences that are explored in this paper are credit, reflecting compensation for heightened default risk (Afonso, Kovner andSchoar (2011), Filipović andTrolle (2013), Taylor and Williams (2009) , Beber, Brandt andKavajecz (2009), andMcAndrews, Sarkar andWang (2008)), and market liquidity, reflecting trading conditions in asset markets (Michaud and Upper (2008), Acharya and Skeie (2011)). The years after 2007 are an ideal period to study the liquidity and credit components of sovereign and interbank spreads because they were so variable both over time and in the cross section. In contrast, before 2007, these spreads were roughly constant near zero, making identification almost impossible.
Understanding the default and liquidity components in interest rates is important for portfolio allocation and policy decisions. Investors with the longest horizons should prefer to hold higher yielding assets if the elevated yields represent compensation for deteriorating market conditions, but not necessarily if they represent a greater risk of loss due to default. Amihud and Mendelson (1986) and Longstaff (2009) both propose models with different types of investors, in which the longer-horizon investors receive a premium for holding less liquid assets. From the perspective of policymakers, efforts to improve market functioning could help to dampen the effects of poor asset market liquidity on yields, mitigating the knock-on effects of higher financing costs. For example, an exchange of more-liquid for less-liquid bonds (such as in the Federal Reserve's securities lending facility) could reduce liquidity premia. On the other hand, if higher yields are largely attributable to a credit shock, then this argues for addressing solvency. This paper first documents the tremendous deterioration in euro-area market liquidity during the Global Financial Crisis and the Sovereign Debt Crisis, using the yield differential Electronic copy available at: https://ssrn.com/abstract=1486240 between two duration-matched bonds with an identical credit guarantee to construct a measure of euro-area market liquidity. This yield spread identifies any deviation in an asset's price from its hold-to-maturity value, fully capturing market liquidity effects impounded in prices. Specifically, the yield of a German federal government bond is compared to that of its less-liquid agency counterpart, KfW (Kreditanstalt für Wiederaufbau). The German federal government bond systematically commands a premium across maturity points over the sample period. I refer to this yield differential as the K-spread. While this paper is the first to construct the K-spread, comparing two types of government-guaranteed securities goes back to Longstaff (2004), who explained the yield differential between Refcorp (Resolution Funding Corporation) and U.S. Treasury bonds as a measure of Treasury market liquidity. In this paper, the K-spread is used to identify the contribution of aggregate market liquidity to the unprecedented widening of various interest rate spreads across euro-area countries.
Prior to the Global Financial Crisis, the K-spread typically remained below 10 basis points.
During the Crisis, the spread became unusually wide and volatile. At the 5-year maturity, it spiked as high as 90 basis points in December 2008. The spread also widened sharply in the more recent Sovereign Debt Crisis, but remained below its Financial Crisis peak. The K-spread is a model-free identification of euro-area market liquidity -it does not rely on a single interpretation of liquidity frictions. It is also tradable in that an investor can form a portfolio comprised of a long KfW bond position and a corresponding short German federal bond position. This position earns the "liquidity spread" and hedges against credit fluctuations. This paper uses the K-spread and other measures to parse euro-area sovereign bond and interbank interest rate spreads into liquidity and credit components over the Global Financial Crisis and the European Debt crisis. Researchers have proposed theoretical models in which liquidity can Electronic copy available at: https://ssrn.com/abstract=1486240 have an important effect on bond yields, especially during a crisis Skeie (2011), Favero, Pagano andvon Thadden (2010) and Manganelli and Wolswijk (2009)). Separately, there is evidence of a common factor driving liquidity premia across markets ((Chordia, Sarkar and Subrahmanyam (2005) and Brunnermeier and Pedersen (2009)). In the decomposition of euro-area sovereign yields spreads, the single K-spread's identification of liquidity relies on commonality across the different member countries' sovereign bond markets. The results show a strong and significant influence of aggregate market liquidity on sovereign spreads that is robust to controlling for country-specific default risk. The common liquidity component in spreads also explains more variation than is explained by several extant country-specific liquidity measures jointly. The finding that liquidity is an important driver of bond spreads during the Financial Crisis is familiar in the corporate bond literature (e.g. Bongaerts, de Jong and Driessen (2013)). This paper highlights the importance of a single liquidity factor for sovereign bond and interbank spreads during crises. Brunnermeier and Pedersen (2009) and Bolton, Santos and Scheinkman (2011), model the relationship between aggregate market liquidity and idiosyncratic funding liquidity to explain market features seen in the early stages of the Financial Crisis. To consider a possible link between aggregate bond market liquidity and money markets, I use the K-spread to decompose unsecured interbank rates, assuming proportionality in bond and funding market liquidity. In order to measure credit and liquidity specific to the interbank market, I obtain a novel dataset of high-frequency interbank transactions. I find that the K-spread, constructed in the sovereign bond market, explains a substantial share of interbank spreads beyond what is captured by the interbank measures of credit and liquidity. Both sovereign and interbank spreads are affected by a common liquidity factor. One possible explanation is the close link between the liquidity of sovereign bonds used as collateral in funding markets and the funding rates themselves. 1 The plan for the remainder of the paper is as follows. Section 1 introduces the data including the liquidity measure's construction. Section 2 parses the euro-area sovereign bond yield spreads into liquidity and credit components. Section 3 identifies these two effects in interbank interest rate spreads. Section 4 concludes with the paper's contributions and implications.

Data
The sample period for this paper is January Crisis. This section describes the euro-area sovereign debt and EURIBOR-OIS spreads, and discusses the construction of the various measures of liquidity and credit used in this paper.

Sovereign Bond Yield Spreads
Starting with the sovereign bond market, the data sample includes 77 country-maturity pairs: the government debt securities for 11 euro-area member countries (Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, the Netherlands, Portugal, and Spain) at seven specific maturity points (1, 2, 3, 4, 5, 7, and 10 years). 2 To precisely compare these yields, I estimate a smoothed zero-coupon yield curve, for each maturity m, each country c, and each day t, by applying the six-parameter model of Svensson (1994) to the prices of all euro-denominated 1 Sovereign bonds are often used as collateral in euro repo transactions (e.g. the central bank's liquidity operations). Market liquidity premia in the cash bond market will drive EURIBOR rates higher via their collateral value in the repo market; unsecured funding is a close substitute for repo funding. 2 The Greek data end in January 2010. There are insufficient transactions for reliable analysis in the period around the debt restructuring. Germany is the largest economy in the euro area, and is one of the three largest euro-area government debt markets in par value outstanding, along with France and Italy. However, Germany has maintained a lower debt-to-GDP ratio than France and Italy since the 1999 monetary union. Additionally, at the time of the Financial Crisis, Germany's sovereign bond market was the only euro-area bond market with a complementary futures market. 5 The yield spread could alternatively be constructed relative to the euro-area average yield, giving very similar results.

Interbank Interest Rate Spreads
In the money market, I consider euro interbank borrowing rates (EURIBOR). EURIBOR is the reference rate at which large euro-area banks borrow some notional amount of euro currency, uncollateralized, for a specified term. 6 EURIBOR contains a common risk-free term structure and risk components. To remove the common component, I consider the spreads of EURIBOR relative to the euro overnight-index swap (OIS) rate, which I take as a proxy for the risk-free rate. An OIS is a money market derivative, with a payoff determined by the future path of overnight interest rates plus a pure term premium. There is no payment required at inception of the contract. For any maturity of OIS contract, the fixed rate reflects a sequence of refreshed overnight bank credits. For these and other reasons, 7 default and liquidity premia in OIS rates are negligible (Brunnermeier (2009) and Packer and Baba (2009)), allowing for the EURIBOR-OIS spread to be interpreted as interbank risk premia.
I consider the 1-, 3-, 6-, and 12-month maturity EURIBOR-OIS interest rate spreads, which are the EURIBOR maturities commonly referenced in financial contracts. Panel A of Figure 2 shows a steep decline in the level of EURIBOR rates of roughly 450 basis points across the different maturities over the sample period. This drop was largely driven by the ECB's crisis- futures, and many mortgage rates in the euro area reference EURIBOR.

The K-spread Measure of Market Liquidity
Market liquidity is the premium demanded for buying or selling a large quantity of an asset, such as a sovereign bond, with immediacy. 8 Measuring this empirically is challenging. To identify the liquidity component of euro-area interest rate spreads, I construct a measure of market liquidity that compares the yields of German government bonds with German agency bonds, at specific maturities. German government bonds are highly liquid euro-area securities, backed by the full faith and credit of the German federal government. Their less-liquid counterparts are bonds issued by the German federal government-owned development bank, KfW, which was founded in 1948 to facilitate post-war reconstruction. A key feature of the KfW agency bonds, which safeguards 8 An important but conceptually distinct type of liquidity is funding liquidity, an institution's precautionary demand for term funding so as to have liquid assets on its balance sheet. In the interbank market, precautionary demand for funding is closely tied to market participants' creditworthiness. Credit and funding liquidity are thus particularly hard to disentangle and I do not attempt to do so; in this paper, credit incorporates both default risk and associated funding liquidity.
the liquidity measure against any credit effects, is that the German federal government has an explicit iron-clad guarantee -written into the German constitution -for all of KfW's current and future obligations, equally and without any difference in priority relative to the federal government bond issues. Credit and asset characteristics are entirely controlled for in the measure's construction.
To precisely compare the two classes of German yields, I first estimate a smoothed zerocoupon yield curve for the KfW bonds, on each day, using the same methodology as described for the sovereign yield curves in subsection 1.1. I then take the zero-coupon yield spread between the KfW bond and the corresponding German federal government bond at each of the seven maturity points considered. The m-year K-spread is defined as: Basel II capital ratios. The K-spread is treated as a directly observable liquidity measure. Its identifying assumption is that German sovereign and KfW yields have identical credit but that they load differently on the common liquidity factor.
Panel A of Figure 3 plots the K-spread at the 5-year maturity. The spread remains positive over the sample, reflecting the relative ease with which the federal government debt is traded as compared to the agency debt. The liquidity yield differential rises to a local peak of 47 basis points early in the sample period, around the collapse of Bear Stearns in March 2008, and then it reaches a global peak of 90 basis points later that year following Lehman Brothers' bankruptcy. The Kspread widened again during the Sovereign Debt Crisis, not quite reaching the same magnitude as in the Financial Crisis, but remaining elevated for a protracted period. Since the K-spread is constructed from observed bond prices, identification is not limited to any single model of liquidity frictions (e.g. asymmetric information). The K-spread's evolution reflects all information impounded in bond yields, including forward-looking future liquidity conditions, a potentially large dimension of liquidity not captured by market microstructure or transaction-based measures that are typically used to measure market liquidity.
There are some institutional differences between KfW and German federal government bonds that could contribute to their liquidity differential. Although they share the same creditworthiness, KfW and German federal government bonds are not fungible, even in the absence of any difference in characteristics. For instance, there is an active futures market for German 2-, 5-and 10-year federal government bonds, but the comparable-maturity KfW securities cannot be delivered into these futures contracts. 9 Federal government bond issuance is also larger and trading volume is higher than for KfW securities. 10 Moreover, euro repo funding rates are consistently slightly higher for KfW collateral than for German federal government collateral, reflecting the relative attractiveness of the federal government securities as collateral in funding markets. 11 The financing rate differential could be both a cause and a consequence of their greater liquidity (Brunnermeier and Pedersen (2009) and Gorton and Metrick (2012)).

Market Microstructure Liquidity Measures
In order to compare the proposed K-spread liquidity measure with traditional liquidity measures, and to allow for market-specific liquidity effects, I obtain detailed data on interbank borrowing and sovereign bond transactions. With these data, I construct a set of five microstructure liquidity measures, separately for the sovereign bond market and the interbank market. The measures are: trade size, trading volume, bid-ask spread, order flow, and the bid-ask spread scaled by trading volume (Bollen and Whaley (1998) liquidity index), each of which is expressed as a daily average value.
The sovereign bond transactions come from MTS, a large electronic European bond trading platform. 12 To allow for the independent variation of each country's liquidity at various horizons, I construct a separate microstructure measure for each of the 77 country-maturity pairs. Table 1 reports the country-level summary statistics. The measures are expressed relative to their maturity-

Credit Risk Measures
To Transactions on this platform comprise roughly 20% of all unsecured euro-denominated interbank transactions over the sample period. 14 Overnight funding transactions help banks meet their day-to-day funding needs. In the sample, 91% of transaction volume is agreed to for maturity on the following business day. The ECB's annual euro money market reports give detailed statistics on borrowing and lending each year. The maturity distribution has consistently shown that the largest share of transactions occurs at the overnight maturity.
In the sovereign bond market, I consider CDS spreads for each country and maturity in the sample. In the interbank market, I consider the CDS premia for each EURIBOR survey-member bank, as an alternative credit measure to bank-tiering. 15 (2008)). To approach the short horizon of the interbank spreads, I use the 1-year CDS premia. Then, I average the CDS premia over the member banks on each day, as in the calculation of EURIBOR. 16 All CDS data are obtained from Markit.
Panel B of Figure   spread of a euro-denominated CDS contract on the same issuer, giving the price of foreign exchange swaps embedded in CDS. To measure redenomination risk in this paper, I take each country's sovereign quanto CDS minus the German sovereign quanto CDS, following De Santis (2015). Panel A of Table 1 shows that the measure is positive for nearly all maturities and countries, consistent with the idea of a premium for protection against risk embedded in the euro currency. Finland and the Netherlands are the exceptions, the two countries with the smallest average CDS spreads. The correlation between quanto CDS and sovereign CDS spreads is 0.68, showing a relatively strong and positive relationship between redenomination and default risk. It makes sense that a higher likelihood of sovereign default increases the likelihood of departure from the currency union.

Credit versus Liquidity in Euro-Area Sovereign Bond Spreads
Next I turn to empirically investigate whether -and to what extent -credit and liquidity potentially drove the unprecedented variation in euro-area sovereign yield spreads. The aim in this estimation is to quantify the relative contribution of these variables to spread widening over the Global Financial Crisis and the European Debt Crisis, and to document differences by country.
With this in mind, I consider the following equation at the daily frequency: where cmt y is the sovereign yield spread for country c relative to the German benchmark, at the m-year maturity point on day t, mt κ is the KfW spread at the same maturity point, and cmt d is the deviation of the CDS spread from its benchmark German counterpart for that country and that maturity point. A natural concern in estimation is however that the variables are highly persistent and that spurious regression problems may arise. I consequently estimate equation (2)

in weekly
Electronic copy available at: https://ssrn.com/abstract=1486240 changes (not daily because of slight non-synchronicity). The equation is therefore: where w ∆ is the weekly difference operator. Equation (3) is estimated as a seemingly unrelated regression (SUR) over all country-maturity pairs. To gauge the relative responses, the coefficient estimates on liquidity, cm β , and credit, cm χ , are allowed to vary by country and maturity.
The results of equation (3) are shown in Table 3 Ammer and Cai (2011) argue that the cheapest-to-deliver option makes yield spreads move less than one-for-one with CDS spreads. The coefficients on CDS in Panel A of Table 3 are all highly significant and positive, but they are generally less than 1. As a robustness check, equation (3)  Sovereign spread movements were far larger in the Debt Crisis than in the Financial Crisis (shown in Figure 1, Panel B). CDS spreads also widen much more during the Debt Crisis (shown in Figure   3, Panel B), but even still liquidity plays a meaningful role in this period.

The K-spread versus Sovereign CDS Spreads in the Crisis Periods
Within the six months following Lehman's September 2008 failure, each sovereign spread in the sample widened to its highest level to date, at the time, since the introduction of the euro.
What drove the sudden discount demanded by investors to hold these bonds at this time?  influence for both liquidity and credit. An equal-weighted average across all countries and maturities shows that the K-spread explains 36% of the trough-to-peak spread widening and CDS spreads explain 22%. Weighting the shares by the average quantity of debt outstanding for each country and maturity tilts the importance further toward liquidity; liquidity and credit now account for 42% and 18% of yield spread widening, respectively.
Panel B of Figure 5 gives a similar analysis of the trough-to-peak yield spread widening over the Sovereign Debt Crisis, specifically from January 2010 to January 2012. The relative influence of credit and liquidity are calibrated to the coefficients estimated over the Sovereign Debt Crisis (

Sensitivity to Credit and Liquidity Shocks
To compare the sensitivity across countries to credit and liquidity shocks of a similar magnitude, I consider the change in the sovereign yield spread associated with a one standard deviation shock to each measure. The effects are calibrated using the full-sample coefficients ( could more than double the size of its yield spread. The effect of a one standard deviation credit shock ranges from having close to no effect for the countries situated along the y axis (Finland and the Netherlands), to more than 100 basis points of widening for Portugal and Ireland. It seems reasonable that countries closer to the default boundary would be more sensitive to further credit shocks. Portugal and Ireland both received around EUR 80 billion from the EU and the IMF to avoid defaulting during the Sovereign Debt Crisis.

Controlling for Redenomination Risk
In the European Debt crisis, redenomination risk was a concern separate from default. De Santis (2015) proposes measuring this with the spread between non-German sovereign quanto CDS and German sovereign quanto CDS. I augment equation (3) In Table 4, the results are shown for the European Debt Crisis subsample (January 2010 through December 2014). Before 2010, there was virtually no trading in quanto CDS, and so the measure of redenomination risk is set to zero.
The average adjusted R-squared values over all countries and maturities when including redenomination risk in the estimation rises to 47% compared to 45% without. 19 The 10-year maturity contributes most to the increase in explained spread variation, suggesting that redenomination risk is most prevalent at a longer horizon. Of course, not all sovereigns are subject to the same level of redenomination risk. The quanto CDS coefficient estimates from equation (4) show that the Netherlands and Finland have virtually no priced redenomination risk, once controlling for credit and liquidity. There is a high degree of correlation between the measures of redenomination risk and default risk (Table 1, Panel C), and these two countries show the smallest effect of credit on yield spreads (subsection 2.2).
The positive correlation between the quanto CDS and sovereign CDS measures also suggests that the role for credit might be overestimated in countries with redenomination risk in the baseline specification. Comparing the significance and magnitude of the coefficient estimates from equation (4) with those in Panel C of Table 3, where quanto CDS spreads are not included, there is no systematic change across countries and maturities. The effect of redenomination risk on spreads is distinct from that of liquidity or credit, though its contribution is smaller.

Controlling for Country-Specific Liquidity
To compare the K-spread with traditional liquidity measures, and to addresses the potential concern that a measure with German origins may not fully capture other countries' liquidity effects, equation (4) is now expanded to also include the five country-specific market microstructure measures as defined in subsection 1.4: where cmt X is the vector of the five country-specific liquidity characteristics, relative to those of Germany. The coefficient cm Ξ measures yield spread sensitivity to the additional liquidity measures at each maturity point. For two of the microstructure measures, the bid-ask spread and the Bollen-Whaley index, a higher value indicates deteriorating liquidity, and so a positive coefficient estimate is consistent with an illiquidity discount in yields. For the remaining three measures (volume, trade size and order flow), a higher value denotes improving liquidity.  (2018)).

The Role of Aggregate Bond Market Liquidity in Euro-Area Interbank Spreads
The models of Brunnermeier and Pedersen (2009) and Bolton, Santos and Scheinkman (2011) describe a close relationship between bond and funding markets. This section empirically assesses the effect of aggregate bond liquidity in the funding market by using the K-spread to parse interbank rates.

Aggregate Bond Market Liquidity and Bank-Tiering Credit in Interbank Interest Rates
To examine euro-area money market spreads, I conduct a time-series regression of interbank spreads onto liquidity and credit measures. The specification is: where denotes the EURIBOR minus OIS spread at maturity m on day t, t κ is the K-Spread measure of euro-area sovereign bond market liquidity 20 , t d is the bank-tiering measure of credit risk, cds t d is the average EURIBOR bank CDS premium and t X is a vector containing the interbank market microstructure liquidity measures. Separate time series regressions are run for the 1-, 3-, 6-and 12-month EURIBOR-OIS maturities. As in the sovereign bond spread analysis, the regressions are run in weekly first differences, owing to spurious regression concerns. 21 Table 6 shows the estimation results for equation (6)  Within each panel, results for the four maturities are shown in four separate subpanels.
The first three columns of each subpanel in Panels A through C report univariate regression estimates for the K-spread, the bank-tiering credit measure, and the bank CDS measure. The estimates formed over the entire sample period (Panel A) reveal that each variable is significant and positive at the four maturity points. This is consistent with the intuition that a deterioration in either credit or aggregate market liquidity conditions would lead banks to charge one another a 20 Results are reported when using the 1-year maturity K-spread measure for the analysis of interbank spreads, but the estimation is not sensitive to the choice of maturity. 21 The explanatory variables are the same at all four maturities; so estimating the equation at the four maturities jointly by SUR gives numerically identical results.
higher borrowing premium. The fourth column shows the joint effect of credit and liquidity, estimated with a regression of EURIBOR-OIS spread changes onto both the K-spread changes and the bank-tiering credit measure changes. In comparison to the univariate case, the K-spread coefficient estimates ˆm β are nearly unchanged in size, but the bank-tiering credit estimates ˆm χ shrink by more than one third. Nonetheless, both estimates remain significant across maturities, showing a role for credit and liquidity in interbank spreads. Over the Sovereign Debt Crisis (Panel C), the estimated EURIBOR-OIS response to a one standard deviation shock to liquidity is 8 basis points, compared to a 1 basis point response to a credit shock, on average across maturities. These estimates show less sensitivity to both types of shocks than in the Financial Crisis. However, the relative importance of liquidity over credit is nearly double that of the Financial Crisis subsample. One argument for the relative increase in the importance of liquidity over credit is that some default risk shifted from the private sector to the public sector as banking systems were bailed out by their respective governments. Another possibility is that interbank market functioning was less robust over the Debt Crisis period than during the Financial Crisis. In particular, unsecured interbank borrowing may have been partly substituted by the ECB's extraordinary liquidity provision. 22

Controlling for Bank CDS and Interbank Market Liquidity Effects
To check that the estimation results are not driven by an idiosyncratic dynamic to the banktiering credit measure, I include bank CDS premia as an additional credit measure in equation (6).
The estimates are reported in the fifth column of each subpanel of Next, I consider the potential contribution of idiosyncratic interbank liquidity risk to EURIBOR-OIS spreads. The sixth column of Table 6 Table 6 shows the expanded specification, including all credit and liquidity measures, except without the K-spread measure of aggregate liquidity. Over all sample periods, the R-squared values shown in column 7 are less than half as large as those in column 6 when the K-spread is included.
Accounting for aggregate bond market liquidity explains more of the variation in EURIBOR-OIS spreads than all the interbank measures combined, regardless of the sample period. These results suggests that in a time of tight funding conditions, interbank spreads might be substantially narrowed through steps to improve aggregate market liquidity, independent of any credit effect. This paper first documents the large and persistent liquidity differential between yields on two duration-matched bonds that share an identical credit guarantee from the German federal government. I interpret this yield spread as a model-free measure of euro-area market liquidity, conceptually similar to the Refcorp spread proposed by Longstaff (2004). Formed directly from asset prices, this liquidity yield differential, the K-spread liquidity measure, recovers all information in bond yields that is not related to default risk.

Bank Credit Tiering Measure Estimation
Default risk premia in unsecured interbank interest rates are unobservable, But, the difference in interbank borrowing rates at the same point in time controls for the common component and isolates the difference in risk premia between these borrowers. 24 The new banktiering credit measure takes the difference between two contemporaneous unsecured borrowing rates: the daily-average rate paid by banks in the highest quintile of credit and the daily-average rate paid by banks in the lowest quintile of credit. Considering only the spread between the two rates removes the common risks and market conditions that are faced by all market participants on the e-MID platform. The bank-tiering credit measure, t d , driven by the relative credit premia of the two bank types, is defined as follows: To motivate this approach, suppose that the spread between the interest rate that bank has to pay on day and the hypothetical risk-free interest rate is multiplicative of the form where is a bank fixed effect and is a time fixed effect. Normalize the average to one and let the cross-sectional dispersion of be θ. Then the average credit premium on any day is and the dispersion across banks on any day is . The average credit premium on day t is thus 24 In the unsecured interbank market, the lender is fully exposed to the credit risk of the borrower, and this is the only credit risk that the lender faces. The interbank rate thus prices the likelihood of repayment by the borrower. proportional to the dispersion in rates. 25 In this model, as the default risk of low credit institutions worsens, that of high credit institutions worsens proportionately more, and so an increase in the average rate difference between these two tiers of borrowers reflects an increase in the overall level of credit. The intuition is consistent with that of structural credit models. For instance, the model of Merton (1974) predicts that the credit premium is approximately proportional to rate volatility. It is also consistent with the idea that credit is largely driven by a systemic factor (Longstaff, Pan, Pedersen and Singleton (2011)).
To operationalize this bank-tiering measure, I use the unique database of signed interbank transactions from e-MID, an electronic interbank trading platform. These data show the negotiated rate and bank identities of the borrower and lender for each individual trade that takes place over the sample, plus the time stamp, maturity, volume, and the initiating side of each trade. 26 There are two key features of the e-MID platform that are important to the interpretation of the transaction rates. First, the lender in a trade is fully exposed to the default risk of a borrower in these trades that are facilitated but not backed by e-MID. This contrasts with trades in centrally cleared markets, such as futures, where the clearinghouse effectively becomes the counterparty to each trade.
Second, e-MID transactions are identity-transparent; a participant can view all limit orders posted by platform participants, alongside of their respective bank identities, and can choose to take the other side of any order that is posted. 27 A bank will initiate a market order to lend only if the posted 25 A simple example illustrates the model's multiplicative assumption. Suppose on a day with low credit and on a day with high credit, and suppose for the best credit bank and for the worst credit bank.
Then credit tiering on a good credit day would be and credit tiering on a bad credit day would be . 26 One distinct advantage of the new credit measure is that it is constructed from rates on actual unsecured interbank transactions and thus reflects true borrowing costs, whereas survey-derived rates such as EURIBOR and LIBOR may be affected by manipulation. A comparison of LIBOR and other measures of bank borrowing costs is reported in Kuo, Skeie and Vickery (2012). 27 In contrast, the MTS bond trading platform follows conventional price-time priority; trades are matched automatically based on the most attractive quote submitted, with priority given to the earliest submission. The borrowing rate sufficiently compensates the lender for the risk of the trade. It follows that the credit-relevant information on e-MID comes from the rates on limit orders to borrow (or equivalently market orders to lend), where trades are agreed to with the foreknowledge of the borrower's identity. 28 I use the rate and borrower identity information in e-MID limit order data to form a banktiering measure of credit, in the following 3 steps.
1. First, to estimate banks' credit quality, I run the following pooled regression: 29 and time indicators control for effects common to all rates, including interbank market-wide liquidity shocks. 30 The bank dummy coefficient, 2, j β , estimates the average credit quality of each bank. 31 Considering only the borrowing side of the quote avoids any contribution of noise counterparty's identity is revealed only after the trade is agreed to, which eliminates counterparty risk effects from bond trades on the MTS platform. 28 The intuition behind an identity-transparent platform for interbank markets is that the interbank loan is effectively the equivalent to the traded asset in an asset market. Just as a bond market participant would find it difficult to price a bond without knowing the identity of the bond issuer, an interbank market participant would be reluctant to lend unsecured funds to a mystery borrower. The relationship between counterparty default risk and the credit of an interbank trade is precisely what drives the transparent information structure of the e-MID platform. The importance of the borrower's identity is evident; 81% of interbank lending volume in the sample is via market order. Following the crisis, e-MID introduced a parallel platform where identities were not revealed, but there was very little market interest to transact "confidentially." 29 Estimation is necessary because each bank in the sample has a unique but generic identifier that does not reveal the bank's actual identity. A priori, I cannot tell which banks are good/bad credits from their e-MID identifiers alone. 30 Controlling for the day effect in equation (8)  as in equation (7). practice, these loans are not resold. Novation requests, or third party risk assumption for a transaction, occurred during the crisis. But, this was motivated by risk reduction of outstanding obligations, not to insure new transactions. 32 To check whether I have captured the difference between rates paid by high credit and low credit institutions, I consider the propensity to borrow via limit order versus market order for different credit quintiles. Low credit banks should prefer to borrow via limit order so that their identity is factored into the counterparty's lending rate; the lending bank will know that the borrower is low risk and will thus agree to a relatively low rate. It turns out that borrowing via market order as a fraction of total borrowing is 92% in the best credit quintile, compared to 57% in the lowest credit quintile. In fact, the propensity to borrow via limit order is monotonically increasing in credit quintile, supporting the idea that the grouping of banks by quintile has indeed separated the good credit banks from the bad credit banks.  Table 1. This table reports summary statistics for euro-area sovereign bonds, at the 2-, 5-, and 10-year maturities. Panel A reports the mean and standard deviation for sovereign zero-coupon bond yield spreads, CDS spreads, Quanto CDS and microstructure liquidity measures for 10 euro-area countries. Each measure is expressed as the country indicator's deviation from the German indicator. Panel B reports the K-spread's mean, standard deviation and its correlation with the microstructure liquidity indicators for Germany. Panel C reports correlations among the K-spread liquidity measure and the other sovereign bond market liquidity and credit indicators that are reported in Panel A. The correlations are run separately for each maturity, using all country data. The K-spread is formed as the KfW agency bond yield minus the German federal government bond yield. The CDS spread is each country's sovereign debt premium minus German sovereign debt premium. The Quanto CDS measure is each country's Quanto CDS spread minus the German Quanto CDS spread. The market microstructure liquidity measures are formed using sovereign bond transaction data from the MTS trading platform, as the country measure minus the German measure. All statistics are formed from daily frequency data. The sample period is from January 1, 2007 to December 31, 2014, except that the Greek data ends on January 1, 2010, and the Quanto CDS variable starts on January 1, 2011 for all countries.   Table 2. This table reports summary statistics for euro-area interbank money markets. Panel A gives the mean and standard deviation of the EURIBOR, the OIS rate and the EURIBOR-OIS interest rate spread at 1-, 3-, 6-, and 12-month maturities. Panel B reports the mean and standard deviation for the 1-year maturity Kspread liquidity measure, the overnight bank-tiering credit measure, the overnight interbank market microstructure liquidity measures and the one-year EURIBORmember bank average CDS premia. Correlations among these indicators are also reported. The K-spread is formed as the KfW agency bond yield minus the same maturity German federal government bond yield. The bank-tiering credit measure is formed as the average unsecured interbank borrowing rate paid by the highest risk quintile of banks minus that of the lowest risk quintile (estimated in Appendix 1) on each day, using transaction data on overnight interbank borrowing from the e-MID electronic interbank trading platform. The market microstructure liquidity measures are also formed as daily averages, using the overnight interbank data from e-MID. The bank CDS measure is the simple average of the EURIBOR panel banks' one-year CDS premia on each day. The sample period is from January 1, 2007 to December 31, 2014.   Table 3. This table reports the coefficient estimates, standard errors and adjusted R-squared values from the seemingly unrelated regression estimation of equation (3), at the 2-, 5-, and 10-year maturities, with all variables in weekly first differences. The dependent regression variable is changes in the sovereign bond yield spread of each country relative to that of Germany. Panels A through C report the joint estimation of changes in the K-spread and changes in each country's sovereign CDS spread, for three sample periods. The sample for Panel A is January 1 Table 4. This table reports the coefficient estimates, standard errors and adjusted R-squared values from the seemingly unrelated regression estimation of equation (4), at the 2-, 5-, and 10-year maturities, with all variables in weekly first differences. The dependent regression variable is changes in the sovereign bond yield spread of each country relative to that of Germany. Panels A through C report the joint estimation of changes in the K-spread, changes in each country's sovereign CDS spread, and changes in the Quanto CDS measure of redenomination risk. The equation is estimated over the sample period from January 1, 2010 to December 31, 2014, except that Quanto CDS are set to 0 prior to January 1, 2010 due to data limitations. Newey-West standard errors are in parentheses with the Newey (1994) lag length. *** indicates significance at the 1 percent level, ** at the 5 percent level, and * at the 10 percent level.   Table 5. This table reports the coefficient estimates, standard errors and adjusted R-squared values from the seemingly unrelated regression estimation of equation (5), at the 2-, 5-, and 10-year maturities, with all variables in weekly first differences. The dependent regression variable is changes in the sovereign bond yield spread of each country relative to that of Germany. The regression is a joint estimation on changes in the K-spread, changes in each country's sovereign CDS spread, changes in five country-specific microstructure liquidity measures, and changes in the Quanto CDS measure of redenomination risk. The equation is estimated over the sample period from January 1, 2007 to December 31, 2014, except that the Quanto CDS sample begins on January 1, 2010.. Newey-West standard errors are in parentheses with the Newey (1994) lag length. *** indicates significance at the 1 percent level, ** at the 5 percent level, and * at the 10 percent level.  Electronic copy available at: https://ssrn.com/abstract=1486240 Table 6. This table reports the results from regressing the EURIBOR-OIS spread at different maturities onto the one-year K-spread liquidity measure, the proposed overnight bank-tiering credit measure, the one-year bank CDS premia, and overnight interbank market microstructure liquidity measures, with all variables in weekly first-differences, as in equation (6). Panels A through C show the results for three sample periods. The sample for Panel A is January 1, 2007 through December 31, 2014, Panel B is January 1, 2007 through December 31, 2009 (the Global Financial Crisis), and Panel C is January 1, 2010 through December 31, 2014 (the European Debt Crisis). In Panels A through C, the first three columns for each EURIBOR-OIS maturity point report univariate results for the K-spread, the bank-tiering measure, and the CDS spread alone. Column four is a regression onto the K-spread and bank-tiering jointly. Column five is a joint estimation of the K-spread, bank-tiering and CDS. Column six includes all variables. Column seven is the comprehensive estimation, but without the K-spread. Newey-West standard errors are in parentheses with the Newey (1994) lag length. *** indicates significance at the 1 percent level, ** at the 5 percent level, and * at the 10 percent level.

Figure 1. Euro-Area Government Bond Market
Panel A: Country Yields

5-Year Maturity
Panel B: Yield Spreads (Country Yields minus German Yield)

5-Year Maturity
Figure 1. This figure shows sovereign bond yield levels (Panel A), and yield spreads relative to Germany (Panel B), for each of the euro-area countries in the sample, at the 5-year maturity. These are based on zero-coupon yields, formed from smoothed curves fitted to all coupon securities, estimated separately for each country, on each day. The sample period is January 1, 2009 through December 31, 2014, except for Greece, which ends on January 1, 2010. The data are shown at the weekly frequency.

5-Year Maturity
Figure 3. This figure shows a time series of the 5-year maturity K-spread liquidity measure (Panel A) and the 5-year maturity sovereign CDS spread credit measure (Panel B), at a weekly frequency. The K-spread is constructed as the KfW yield minus the comparable-maturity German federal government yield (both zerocoupon yields, formed from smoothed curves fitted to all coupon securities, estimated separately for each day). Panel B shows the Credit Default Swap (CDS) spreads for the sovereign debt of each of the euro-area countries in the sample, relative to that of Germany. The sample period is January 1, 2009 through December 31, 2014, except for Greece, which ends on January 1, 2010. The data are shown at the weekly frequency.
Electronic copy available at: https://ssrn.com/abstract=1486240 Electronic copy available at: https://ssrn.com/abstract=1486240 . This figure plots the share of the trough-to-peak yield spread change that is attributable to the K-spread (y axis) versus the country CDS spread (x axis), for each country separately, on average over maturities. The plotted values are based on coefficient estimates from a regression of sovereign bond yield spreads onto the K-spread and the country sovereign CDS spreads. Panel A shows the trough-to-peak yield spread change from January 2007 to January 2009. The coefficient estimates are from Panel B in Table 3. Panel B shows the trough-to-peak yield spread change from January 2010 to January 2012. The coefficient estimates are from Panel C of Table 3. Greek data are only available for the Financial Crisis subsample.

Figure 6. Basis Point Change in Sovereign Spread Explained by One Standard Deviation
Shock to Credit and Liquidity (Full Sample Period) Figure 6. This figure plots the basis point change in country sovereign bond yield spreads (averaged across maturities) associated with a one standard deviation increase in the country CDS spread (x axis) versus a one standard deviation increase in the K-spread (y axis), both axes are on logarithmic scales. The plotted values are based on coefficient estimates from a regression of sovereign bond yield spreads onto the K-spread and the country sovereign CDS spreads, shown in Panel A of Table 3. The country sovereign CDS spread and the K-spread standard deviations are shown in Panels A and B of Table 1. The sample period covered by the estimation is January 1, 2007 to December 31, 2014.