Sovereign Credit Risk, Liquidity, and ECB Interventionpeople.stern.nyu.edu/msubrahm/papers/SovereignCredit.pdf · 2016. 8. 9. · Sovereign Credit Risk, Liquidity, and ECB Intervention:

Sovereign Credit Risk, Liquidity, and ECB Intervention:Deus ex Machina?I

Journal of Financial Economics, forthcoming

Loriana Pelizzona,b,∗, Marti G. Subrahmanyamc, Davide Tomiod, Jun Unob,e

aSAFE Center - Goethe University, Theodor W. Adorno Platz 3, 60323 Frankfurt am Main, Germany.bCa’ Foscari University, Fondamenta San Giobbe 873, 30121 Venezia, Italy.

cNew York University - Leonard N. Stern School of Business, 44 West 4th St., NY 10012-1126 New York, USA.dCopenhagen Business School, Solbjerg Plads 3, 2000 Frederiksberg, Denmark.

eWaseda University, 1-4-1 Nihombashi, Chuo-ku Tokyo 103-0027, Japan.

Abstract

We examine the dynamic relation between credit risk and liquidity in the Italian sovereign bond market during theEuro-zone crisis and the subsequent European Central Bank (ECB) interventions. Credit risk drives the liquidity ofthe market: a 10% change in the credit default swap (CDS) spread leads to a 13% change in the bid-ask spread, therelation being stronger when the CDS spread exceeds 500 bp. The Long-Term Refinancing Operations (LTRO) ofthe ECB weakened the sensitivity of market makers’ liquidity provision to credit risk, highlighting the importanceof funding liquidity measures as determinants of market liquidity.

Keywords: Liquidity, Credit Risk, Euro-zone Sovereign Bonds, Financial Crisis, MTS Bond MarketJEL: G01, G12, G14.

IWe thank Einaudi Institute of Economics and Finance, the NYU Stern Center for Global Economy and Business, and the NYU-Salomon Center, the project SYRTO of the European Union under the 7th Framework Programme (FP7-SSH/2007-2013 - Grant Agreementn 320270), the project MISURA, funded by the Italian MIUR, the Waseda University Center for Finance Research, the Center for FinancialFrictions (FRIC) under grant no. DNRF102 from the Danish National Research Foundation, and the SAFE Center, funded by the State ofHessen initiative for research, LOEWE, for their financial support. Part of the research in this paper was conducted while Davide Tomio wasemployed by the SAFE Center, whose support is gratefully acknowledged. We thank Antje Berndt, Monica Billio, Rohit Deo, Rama Cont,Peter Feldhutter, Eric Ghysels, Bernd Schwaab, Kenneth Singleton, Clara Vega, and participants at the CREDIT 2013 Conference, Venice,the American Finance Association 2014 meetings, Philadelphia, the NYU-Stern Volatility 2014 Conference, the Financial ManagementAssociation conference in Tokyo 2014, the 2nd Conference on Global Financial Stability and Prosperity (Sydney), the European FinanceAssociation 2014 Conference, the First International Conference on Sovereign Bond Markets, the Multinational Finance Society Confer-ence, and seminars at the Federal Reserve Bank of New York, the Board of Governors of the Federal Reserve System, the European CentralBank, the Bank of England, the Bank of Italy, the Italian Tesoro (Department of Treasury), Goethe University, University of Mannheim,Frankfurt School of Economics and Finance, Einaudi Institute of Economics and Finance, and the Vienna University of Economics andBusiness Administration, for their insightful comments. We thank Stefano Bellani, Mitja Blazincic, Alberto Campari, Alfonso Dufour,Carlo Draghi, Peter Eggleston, Sven Gerhardt, and Davide Menini for sharing their thorough understanding of market practice with us. Wealso thank the MTS group for providing us with access to their datasets. The views expressed in the paper are solely those of the authors.We are responsible for all remaining errors.

∗Corresponding author.Email address: [email protected] (Loriana Pelizzon)

Preprint submitted to Elsevier February 11, 2016

1. Introduction

The challenges facing the governments of the GIIPScountries (Greece, Ireland, Italy, Portugal and Spain) inrefinancing their debt marked the genesis of the Euro-zone sovereign debt crisis. Following a series of creditrating downgrades of three countries on the Euro-zoneperiphery, Greece, Ireland and Portugal, in the springof 2010, the crisis spread throughout the Euro-zone.The instability in the Euro-zone sovereign bond marketreached its apogee during the summer of 2011, when thecredit ratings of two of the larger countries in the Euro-zone periphery, Italy and Spain, were also downgraded.This culminated in serious hurdles being faced by sev-eral Euro-zone countries, causing their bond yields tospike to unsustainable levels. The crisis has abated tosome extent, due in part to fiscal measures undertakenby the European Union (EU) and the International Mon-etary Fund (IMF), but mostly thanks to the interventionby the European Central Bank (ECB) through a seriesof policy actions, including the Long-Term Refinanc-ing Operations (LTRO) program, starting in December2011.

The discussion in the academic and policy-makingliteratures on the Euro-zone crisis has mainly focusedon market aggregates such as bond yields, relativespreads, and credit default swap (CDS) spreads and thereaction of the market to intervention by the Troika ofthe ECB, the EU and the IMF. Although the analysisof yields and spreads is useful, it is equally relevant forpolicy makers and market participants to understand thedynamics of market liquidity in the European sovereigndebt markets, i.e., the drivers of market liquidity, par-ticularly given the impact market liquidity has on bondyields, as documented in the previous literature on assetprices.

In this paper, we address the latter issue and analyzethe inter-relation between market liquidity and creditrisk, the effect of the funding liquidity of the marketmakers, and how this inter-relation changed thanks tothe ECB interventions. We drive our analysis by de-veloping a simple model that formalizes several chan-nels through which credit risk affects market liquid-ity. Our empirical analysis shows that credit risk af-fects market liquidity, and that this relation shifts con-ditional on the level of the CDS spread: it is strongerwhen the CDS spread exceeds 500 bp, a threshold usedas an indicator by clearing houses in setting margins.Moreover, we show that the LTRO intervention by theECB, which funneled funding liquidity into the bankingsystem, weakened the sensitivity of market liquidity tocredit risk.

The linkage between credit risk and market liquid-ity is an important topic because a liquid market is ofparamount importance for both the success of the imple-mentation of central bank interventions, whether in theform of interest rate setting, liquidity provision funding,or quantitative easing, and their unwinding. Moreover,as we show in this paper, monetary policy has an impacton the interplay between credit risk and market liquidityitself.

The main focus of our research in this paper is todetermine the dynamic relation between market liquid-ity and credit risk, as well as other risk factors such asglobal systemic risk, market volatility, and the fund-ing liquidity risk of market makers. We study the ef-fects of the ECB measures in the context of this dy-namic relation. We employ the time-series of a rangeof liquidity metrics, as well as CDS spreads, a mea-sure of credit quality, to analyze the liquidity of Italiansovereign bonds during the period from July 1, 2010 toDecember 31, 2012. We allow the data to help us un-cover how the relation between credit risk and liquiditydepends on the endogenous level of the CDS spread. Inaddition, we examine how these relationships were in-fluenced by the interventions of the ECB.

We motivate our empirical analysis with a simplemodel of a risk averse market maker, holding an inven-tory of a risky asset and setting her optimal marginalquotes (and, therefore, the optimal bid-ask spread), inthe presence of margin constraints and borrowing costs.The margins, set by a clearing house, depend on the riskof the asset, as measured by the CDS spread, and theactions of the central bank. The CDS market is funda-mental to the market maker’s and the clearing house’sdecisions, since it is from the CDS market that they de-duce the future volatility of the asset return. In addition,the market maker can pledge her assets at the centralbank to finance her positions at rates influenced by thecentral bank’s actions. The model provides several em-pirical predictions that we test in the empirical sectionof the paper.

First, we test the empirical prediction that the rela-tion between the credit risk of a sovereign bond and itsliquidity is statistically significant and, specifically, thatthe credit risk, as measured by the CDS spread, leadsthe liquidity, and not the other way around. We findthat a 10% change in credit risk is followed by a 13%change in market liquidity. Further, we find that the co-efficients of both contemporaneous and lagged changesin the CDS spread are statistically and economically sig-nificant in explaining the market liquidity of sovereignbonds, even after controlling for the lagged liquidityvariable and the contemporaneous changes in other fac-

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tors. In particular, we test whether global risk and fund-ing liquidity factors also affect market liquidity.

Second, we examine whether the relation betweencredit risk and market liquidity is conditional on thelevel of the CDS spread, i.e., whether it is significantlyaltered when the CDS spread crosses a certain thresh-old. We let the data identify the presence of such a CDSthreshold effect, and find that the relation between mar-ket liquidity and credit risk is different, depending onwhether the Italian CDS spread is below or above 500bp. We find not only that a change in the CDS spreadhas a larger impact on market liquidity when the CDSspread is above 500 bp, but that this relation is instanta-neous, while the lead-lag relation is stronger for lowerlevels of the CDS spread. We interpret this finding, to-gether with a change in the margins for bonds, in lightof the predictions made by Brunnermeier and Pedersen(2009).

Third, we analyze the impact of ECB interventionon the relation between credit risk and liquidity. Thethreshold effect in CDS levels is present only until De-cember 21, 2011. In fact, our test for an endogenousstructural break indicates that, on December 21, 2011(when the ECB allotted the funds of the LTRO pro-gram), the relation between the two variables changessignificantly. Thereafter, during 2012, after the largeamount of funding liquidity from the LTRO programhas become available to market makers and market par-ticipants, changes in market liquidity still respond tochanges in credit risk, but with a lagged effect, and witha significantly lower intensity, while the only contem-poraneous variable that affects market liquidity signif-icantly is the global funding liquidity variable proxiedby the Euro-US Dollar cross-currency basis swap spread(CCBSS).1

The Euro-zone sovereign crisis provides us with anunusual laboratory in which to study how the interac-tion between credit risk and illiquidity played out, in amore comprehensive framework than has been used inprevious studies of corporate or other sovereign bondmarkets. In contrast to research on corporate bonds,which are generally traded over-the-counter (OTC), wehave the advantage of investigating an exchange-tradedmarket, using a unique, tick-by-tick data set obtainedfrom the Mercato dei Titoli di Stato (MTS), the world’slargest electronic trading platform for sovereign bonds.

1This spread represents the additional premium paid per period fora cross-currency swap between Euribor and US Dollar Libor. Marketparticipants view it as a measure of the macro-liquidity imbalances incurrency flows between the Euro and the US Dollar, the global reservecurrency.

With respect to the US Treasury and other sovereignbond markets, the presence of a common currency forsovereign issuers means that the ECB is completely in-dependent of the Italian government. Hence, the centralbank’s monetary policy has a qualitatively different im-pact on its sovereign credit risk, as well as on the marketliquidity of its sovereign bonds, compared to countrieswhose central banks are somewhat within the control ofthe sovereign.

To our knowledge, ours is the first paper to empiri-cally investigate the dynamic relation between marketliquidity and credit risk in the sovereign bond market,particularly during a period of crisis. The existing lit-erature has highlighted the theoretical relation betweenbond yields and market liquidity, as well as that betweenfunding liquidity and market liquidity (as modeled byBrunnermeier and Pedersen, 2009). We contribute tothis literature by exploring the role of central bank in-terventions, and show both theoretically and empiricallythat they affect the relation between sovereign credit riskand market liquidity. The laboratory for our analysis isthe Italian sovereign bond market, particularly aroundthe Euro-zone crisis, starting from July 2010. Italy hasthe largest sovereign bond market in the Euro-zone (andthe third largest in the world after the US and Japan) interms of amount outstanding, and is also a market thatexperienced substantial stress during the recent crisis.It is important to emphasize that such an analysis can-not be performed in other large sovereign bond markets,such as those of Germany or France, since they were notas much affected by the sovereign credit risk concerns.

In Section 2 of the paper, we survey the literature onsovereign bonds, particularly the papers relating to liq-uidity issues. In Section 3, we present a model of marketmaker behavior in the setting of the bid-ask spread andderive its empirical implications. In Section 4, we pro-vide a description of the MTS market architecture andthe features of our database. In Section 5, we presentour descriptive statistics. Our analysis and results arepresented in Section 6, and Section 7 presents severalrobustness checks. Section 8 concludes.

2. Literature Survey

The dynamic relation between credit risk and themarket liquidity of sovereign bond markets has receivedlimited attention in the literature, thus far. The extantliterature on bond market liquidity seldom focuses onsovereign bond markets, with the exception of the USTreasury bond market; yet, even in this case, most pa-pers cover periods before the current financial crisis and

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address limited issues related to the pricing of liquid-ity in the bond yields.2 It is, therefore, fair to say thatthe relation between sovereign credit risk and marketliquidity has not yet been investigated in the US Trea-sury market, possibly because US sovereign risk wasnot an issue until the recent credit downgrade by Stan-dard & Poor’s. The liquidity in the US Treasury bondmarket has been investigated by Chakravarty and Sarkar(1999), using data from the National Association ofInsurance Commissioners, and Fleming (2003), usingGovPX data. Fleming and Remolona (1999), Pasquar-iello and Vega (2007), and Goyenko, Subrahmanyam,and Ukhov (2011) study the responses of the US Trea-sury markets to unanticipated macro-economic newsannouncements. In a related paper, Pasquariello, Roush,and Vega (2011) study the impact of outright (i.e., per-manent) open-market operations carried out by the Fed-eral Reserve Bank of New York on the microstructure ofthe secondary US Treasury market. Furthermore, thereare a few papers in the literature analyzing data fromthe electronic trading platform in the US known as Bro-kerTec, such as Fleming and Mizrach (2009) and Engle,Fleming, Ghysels, and Nguyen (2011).

There are a handful of papers on the Europeansovereign bond markets, and again, these papers gen-erally examine a limited time period, mostly prior tothe global financial crisis, and largely focus on the im-pact of market liquidity on bond yields; see for exam-ple Coluzzi, Ginebri, and Turco (2008), Dufour andNguyen (2012), Beber, Brandt, and Kavajecz (2009),Favero, Pagano, and von Thadden (2010) and Bai, Jul-liard, and Yuan (2012). More recent work has high-lighted the effects of ECB interventions on bond yields,market liquidity, and arbitrage relationships betweenfixed income securities. Ghysels, Idier, Manganelli, andVergote (2014) study the effect of the Security Mar-kets Programme (SMP) intervention on bond returns,while Corradin and Rodriguez-Moreno (2014) docu-ment the existence of unexploited arbitrage opportuni-ties between European sovereign bonds denominated inEuros and Dollars, as a consequence of the SMP. Eserand Schwaab (2013) and Mesters, Schwaab, and Koop-man (2014) show long- and short-term effects of theECB interventions on European bond yields. Finally,

2Specifically, the existing literature documents the direct impactof liquidity (e.g., Dick-Nielsen, Feldhutter, and Lando, 2012, amongothers) on bond yields and prices, but not the impact of credit riskon liquidity, or how credit risk affects the bond yields through bondliquidity. In this spirit, we need to establish the relation between creditrisk and liquidity in order to then, in turn, quantify its effect on bondyields. An effort in this direction is made by Jankowitsch, Nagler, andSubrahmanyam (2014).

Corradin and Maddaloni (2015) and Boissel, Derrien,Ors, and Thesmar (2014) investigate the relation be-tween sovereign risk and repo market rates during theEuropean sovereign crisis.

There is a vast literature on liquidity effects in the UScorporate bond market, examining data from the TradeReporting and Compliance Engine (TRACE) databasemaintained by the Financial Industry Regulatory Au-thority and using liquidity measures for different timeperiods, including the global financial crisis. This lit-erature is relevant to our research both because it an-alyzes a variety of liquidity measures and because itdeals with a relatively illiquid market with a vast ar-ray of securities. For example, Friewald, Jankowitsch,and Subrahmanyam (2012a) show that liquidity effectsare more pronounced in periods of financial crisis, es-pecially for bonds with high credit risk. Similar re-sults have been obtained by Dick-Nielsen, Feldhutter,and Lando (2012), who investigate the effect of creditrisk (credit ratings) on the market liquidity of corporatebonds.3

In a theoretical contribution to the literature on therelation between corporate credit risk and liquidity, Er-icsson and Renault (2006) show both theoretically andempirically that bond illiquidity is positively correlatedwith the likelihood of default. He and Milbradt (2014)provide a theoretical framework for the analysis of cor-porate bonds traded in OTC markets and show that athinner market liquidity, following a cash flow decline,feeds back into the shareholders’ decision to default,making a company more likely to default. A final theo-retical paper related to our analysis is by Brunnermeierand Pedersen (2009), who investigate the relation be-tween funding liquidity and market liquidity.

To the best of our knowledge, there are no theoreticalmodels that investigate the relation between sovereigncredit risk and market liquidity. The models in Eric-sson and Renault (2006) and He and Milbradt (2014)cannot be applied straightforwardly to the sovereignframework because of the nature of the credit event.There are, in fact, no bankruptcy or strategic defaultchoices in the sovereign context (see Augustin, Sub-rahmanyam, Tang, and Wang, 2014, Section 7.1), al-though the outcome of debt renegotiation, e.g., the re-covery rate, could arguably be affected by the liquid-

3Other recent papers quantifying liquidity in this market providerelated evidence. See, for example, Edwards, Harris, and Piwowar(2007), Mahanti, Nashikkar, Subrahmanyam, Chacko, and Mallik(2008), Zhou and Ronen (2009), Jankowitsch, Nashikkar, and Sub-rahmanyam (2011), Bao, Pan, and Wang (2011), Nashikkar, Subrah-manyam, and Mahanti (2011), Lin, Wang, and Wu (2011), Feldhutter(2012), and Jankowitsch, Nagler, and Subrahmanyam (2014).

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ity of the secondary market. From a theoretical per-spective, one channel that definitely applies to the rela-tion between sovereign credit risk and market liquidityis that of the market maker’s inventory concerns, as inthe model proposed by Stoll (1978). In this paper weextend Stoll’s (1978) model by including further deter-minants of market liquidity, i.e., margins and a policyeffect, whereby both margins and borrowing rates areinfluenced by the policy maker’s actions (i.e., by thecentral bank). Our model is designed to specificallycapture the effects that credit risk has on the marketliquidity of bonds. A comprehensive theoretical modelwhere sovereign credit risk, via debt renegotiations, af-fects market liquidity could be formulated; yet, suchmodel lies beyond the scope of this paper. Nonethe-less, in our empirical investigation, we allow and testfor both the effects of credit risk on liquidity and liquid-ity on credit risk.

There are several important differences between theprior literature and the evidence we present in this pa-per. First, we are among the first to focus on the relationbetween liquidity (rather than yield spreads) in the cashbond market and credit risk, especially in the context ofsovereign credit risk. Second, while most of the pre-vious literature spans past, and thus more normal, timeperiods in the US and Euro-zone markets, the sampleperiod we consider includes the most relevant periodof the Euro-zone sovereign crisis. Third, our focus ison the interaction between credit risk and liquidity, i.e.,how credit risk affects illiquidity and vice versa. Fourth,we examine the impact of monetary policy interventionson the linkage between credit risk and liquidity, in thecontext of ECB policies over the past few years, to mea-sure and document their differential effects. Finally, wecontribute to the literature a model that links the bid-askspread in the bond market to the CDS market.

3. The Model and its Testable Implications

In this section, we review and extend the standardmodel by Stoll (1978), in order to guide and motivateour empirical analysis. The extension allows us to de-fine some simple concepts and gain an intuition aboutthe forces driving the choice, by a market maker of asovereign bond, of what bid-ask spread to quote on themarket. The market maker stands ready to buy from, orsell to, an external trader, extracts information regardingthe risk of the sovereign bond from the CDS market, andfaces margin constraints arising from her inventory. Theplayers in our model are i) the market maker, ii) other(external) traders buying or selling the bonds, iii) the

clearing house, and iv) the central bank. The main pur-pose of our model is to characterize how a change in theCDS spread is reflected in the bid-ask spread of a bondissued by the underlying entity.4 Figure 1 summarizesthe players and the mechanisms of our model.

INSERT FIGURE 1 HERE

Central to the development of our model is identify-ing how the actions of each of the actors are affectedby the credit risk of the bond that we are considering,and how, in turn, these actions affect the liquidity pro-vided by the market maker. The model in Stoll (1978)shows that an increase in the risk of the security is di-rectly reflected in the market liquidity provision choiceof the market maker (Inventory Risk in Figure 1). Inaddition to this direct channel, our model includes anindirect channel, through which the credit risk of thebond affects the liquidity provision choice of the marketmaker. The indirect channel relates to the dealer’s costof financing a bond in the repo market, including themargin requirements, when she has a non-positive in-ventory and she needs to sell a bond to a trader (Marginsin Figure 1). In the indirect channel, credit risk affectsthe liquidity provision by the market maker through theclearing house’s margin setting decision, which dependson the credit risk of the bond (Margin Setting in Fig-ure 1). This hypothesis is motivated by the “SovereignRisk Framework” adopted by LCH.Clearnet, the majorEuropean clearing house, and by other clearing houses,including Cassa di Compensazione e Garanzia, duringthe sovereign crisis: the framework states that the clear-ing house adjusts the margins based on a list of indica-tors, which includes the CDS spread and the bond yieldspread over the German bund, to account for losses in-curred in case of default by the issuer of the security(LCH.Clearnet, 2011).

The margin setting decision by the clearing house isalso affected by the policies of the central bank, i.e.,by i) the central bank’s key interest rates, ii) the centralbank’s interventions, and iii) its explicit requests to theclearing house (Funding Rate and Margin Frameworkin Figure 1). First, the (collateralized) borrowing rate,set by the central bank, affects the volume traded on therepo market, by affecting its supply and demand, and,thus, the risk bearing capacity of the clearing house (seeMancini, Ranaldo, and Wrampelmeyer, 2014, for a de-tailed account of the effects of the ECB’s interventionson the European Repo market).

4We thank the referee for suggesting we formalize our empiricalpredictions in a simple model.

5

Second, during the European debt crisis, the ECBenacted several extraordinary interventions: i) the Se-curity Market Program (SMP), initiated in May 2010,ii) LTRO, announced and implemented in December2011, iii) policy guidance, and iv) the outright mon-etary transactions (OMT), also announced in Decem-ber 2011.5 These interventions could affect the creditrisk of the Eurozone, the liquidity of its bond market,or the funding liquidity of its banks: any of these ef-fects should be taken into consideration by the clearinghouse, when setting margins. A similar implication canbe drawn from the model by Brunnermeier and Peder-sen (2009): the provision of funding liquidity relaxesthe market makers’ borrowing constraints and, conse-quently, the impact of margins on market liquidity.

Third, our hypothesis that central banks can affecteven more directly the relation between margin set-tings and credit risk is supported by documents fromthe International Monetary Fund (2013) and the Bankof Italy (2012). Following a substantial margin increaseby the clearing house LCH.Clearnet at a time of highcredit risk, the Italian and French central banks workedwith the clearing house to propose a shared methodol-ogy to ensure that margin requirements would dependsmoothly on the CDS spread. This prevents the clearinghouse from implementing abrupt margin increases, dis-rupting the liquidity of the sovereign bond market whenthe sovereign credit risk is already high (Bank of Italy,2012). The central banks requested the clearing house toavoid the possibility for margins to become procyclicalto sovereign risk. Finally, in our model, the central bankaffects the dealer’s option to seek financing, by pledgingthe securities she holds, through changing the rate atwhich she can obtain funds (Borrowing Costs in Figure1). One could also argue that the central bank’s policyinterventions themselves depend on the level of creditrisk of the system (the dotted line in Figure 1). Whilewe do not pursue this line of modelling, our predictionswould be robust to the inclusion of this additional chan-nel. Finally, our model aims at specifically capturing

5The SMP is a Eurosystem programme to purchase bonds—especially sovereign bonds—on the secondary markets. The last pur-chase under the SMP was made in February 2012. At its peak, inAugust 2011, the programme’s volume totalled around 210 billion.The LTRO interventions provided three-year funding of e489 bil-lion on December 21, 2011 and e523 billion on February 29, 2012.The long-term maturity of this massive funding action was unprece-dented in ECB policy history, and even globally. By policy guidancewe largely refer to the Mario Draghi speech on July 26, 2012, at theGlobal Investment Conference in London, where he stated: “The ECBis ready to do whatever it takes to preserve the euro. And believe me,it will be enough.” Outright monetary transactions is the programmeto purchase sovereign bonds that substitute the SMP programme.

the effect of credit risk on bond market liquidity. Whilea model emphasizing the effect of a shock to marketliquidity on credit risk in the sovereign context, possi-bly via debt renegotiation, could be developed, such amodel lies beyond the scope of this paper.

We only model explicitly the behavior of the marketmaker, and assume as exogenous the other players’ ac-tions. In our model, we assume that the dealer, or mar-ket maker, is continuously making the market for a se-curity; in this continuum in time, we choose an arbi-trary point at which we model her optimal quote-settingdecision. The dealer has an initial wealth of W0 andan inventory made up of the bond with a dollar valueequal to I. Moreover, she also invests a fraction k ofW0 in the market portfolio. She invests the remainderof her wealth, (1 − k)W0 − I at the risk-free rate r f , ifI < (1−k)W0, i.e., in case there is a surplus. However, ifI > (1 − k)W0 > 0, she borrows the residual amount, bypledging securities in her portfolio at the central bank,at a rate rb = r f + b. Additionally, if the inventory po-sition I is negative, she borrows the bond on the repomarket, where it is subject to a margin requirement m.We model the margin, m, as an upfront cost of borrow-ing the specific bond rather than, for example, any bondunder a general collateral agreement. In general, havingto post margin constitutes a (opportunity) cost for themarket maker, who would have otherwise allocated therequired capital differently.

In light of our assumptions, we indicate the marginset by the clearing house as m(b,CDS ), i.e., a genericfunction of the CDS and the central bank liquidity pol-icy, parametrized by the (collateralized) borrowing rateat the central bank. Following from the previous argu-ments, the margin setting decision depends on the creditrisk and the policy arguments as follow: ∂m(b,CDS )

∂CDS > 0,and ∂m(b,CDS )

∂b > 0. We interpret the request of the cen-tral bank to avoid procyclical margin setting policies asa shift in the sensitivity of the margins to the level of theCDS spread, for a given level of borrowing rate, i.e., ashift in ∂m(b,CDS )

∂CDS

∣∣∣b.

If the dealer does not trade on the chosen date, theterminal wealth from her initial portfolio will be

WI = W0k (1 + rM) + I (1 + r) +((1 − k)W0 − I)

(1 + r f

)if (1 − k)W0 > I > 0

((1 − k)W0 − (1 − m) I)(1 + r f

)if (1 − k)W0 > 0 > I

((1 − k)W0 − I) (1 + rb) if I > (1 − k)W0 > 0

,

where the market portfolio (expected) return is rM (rM)and variance σ2

m, and the bond (expected) net return is r

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(r).6 The (forward looking) variance of the bond return,which the market maker extracts from the CDS market,is σ2(CDS ).

After trading a dollar quantity Q, the dealer’s post-trading wealth is

WI+Q =W0k (1 + rM) + (I + Q) (1 + r) + CQ(1 + r f )+

((1 − k)W0 − (I + Q))(1 + r f

)if (1 − k)W0 > I + Q > 0

((1 − k)W0 − (1 − h) (I + Q))(1 + r f

)if (1 − k)W0 > I + Q > 0 > I

((1 − k)W0 − (I + Q)) (1 + rb)if I + Q > (1 − k)W0 > 0

where CQ is the dollar cost of entering into this trans-action and depends on Q. These costs can be pos-itive or negative, depending on whether the marginaltrade in the bond raises or lowers the dealer’s inventory-holding costs, and essentially captures the dealer’s ex-posure cost of holding a non-optimal portfolio. Thedealer has a constant absolute risk aversion utility func-tion, U(x) = −e−γx, and she will trade and price thetrade so that her expected utility from maintaining theexisting portfolio is equal to the expected utility fromtrading the dollar quantity Q:

E [U (WI)] = E[U

(WI+Q

)].

In Appendix A, we show that the absolute bid-askspread, calculated as the relative bid-ask spread for pur-chasing a quantity Q = p0 multiplied by the price of thebond p0, is

BA =γp2

0σ2(CDS )

1 + r f+ b

p0 −W0 (1 − k)1 + r f

+ m(b,CDS )p0. (1)

The market maker observes the CDS price (CDS ) on theCDS derivative market and extracts the (forward look-ing) volatility of the bond σ(CDS ). We model the re-lation between the standard deviation of returns and theCDS price by approximating it with a linear function,as in Brenner and Subrahmanyan (1988), thus derivingσ(CDS ) as:

σ(CDS ) =(1 + r f

) CDSp0 n (0)

, (2)

6Since we aim to gain an understanding of the day-to-day changein a liquidity measure, we model the return of the bond as normallydistributed between one period (day) and the next. This is a plausibleassumption as long as the bond is neither near the maturity date nor indefault, which is reasonable for our sample of Italian sovereign bonds.

where n(0) ≈ 0.4 is the probability density function ofthe standard normal distribution evaluated at 0.7

Re-writing the absolute bid ask spread as a functionof the CDS price, we obtain the relation between the de-pendent variable of interest, the absolute bid-ask spread,and its determinants, the CDS price, and the policy pa-rameters set by clearing houses and the central bank:

BA(b,CDS ) = δCDS 2 + m (b,CDS ) p0 + bη, (3)

where γ(1+r f )n(0)2 = δ > 0 and p0−W0(1−k)

1+r f= η > 0, and

where we emphasize that the margin setting decision bythe clearing house depends both on the borrowing costset by the central bank and on the level of the CDS.8

Equation (3) features the two channels through whichthe first determinant of market liquidity, the CDS price,affects the bid-ask spread. The first channel, representedby the first term in the equation (δCDS 2), is a direct one,arising from the market maker’s update of the (forwardlooking) bond volatility, as extracted from the deriva-tive market. The second channel, the second term inthe equation (m (b,CDS ) p0), is an indirect effect of theCDS price through the margin setting decision by theclearing houses, since the clearing houses, like the mar-ket maker, extract information about the riskiness of thebond from the CDS market. Our model rationalizes howchanges in margins, which depend on the level of theCDS spread (or price), affect the relation between creditrisk and liquidity.

A second determinant of market liquidity is the cen-tral bank’s monetary policy, which affects both the mar-ket maker’s borrowing costs, through the third term inthe equation (bη), and the second (indirect) channelthrough which the CDS price affects the liquidity: themargin settings. The monetary policy affects the marginsetting decision by the clearing house, which influencesthe market maker’s decision via the second term in theequation (m (b,CDS ) p0). In the next subsection, we de-rive the empirical predictions of the model that we testin the data.

3.1. Empirical PredictionsEmpirical Prediction 1. The illiquidity of the bondmarket increases with credit risk.

7This is a partial equilibrium analysis; in a general equilibriummodel, a change in volatility via CDS would also change p0, as theunderlying asset price would in a general version of the Black-Scholesmodel. In our model, therefore, we assume that the asset price isexogenous, and focus on changes in the return volatility. All detailedcalculations deriving the model can be found in Appendix A.

8The second inequality follows from the requirement that the mar-ket maker borrows the residual amount, when buying a bond, bypledging the security at the central bank, as modeled in Appendix A.

7

This follows from Equation (3), as ∂BA∂CDS > 0, since

δ > 0, η > 0, and ∂m(b,CDS )∂CDS > 0. We expect an in-

crease in credit risk to raise the market illiquidity of thebond. As in the Stoll (1978) model, and in line withother inventory models of market microstructure, ourmodel predicts that an increase in the risk of a secu-rity, e.g., credit risk, implies a riskier inventory, leadingto a withdrawal of liquidity offered to the market by themarket maker.

Since we expect the change in credit risk to be a rel-evant variable in characterizing the dynamics of liquid-ity in the market through the market makers’ inventoryconcerns, we investigate the lead-lag relation betweencredit risk and illiquidity, and the directionality of thisrelation.9

Moreover, our first empirical prediction is in line withrisk management practices based on value-at-risk (VaR)models used widely by market participants, particularlythe market makers. A portfolio with an excessivelylarge VaR, due to credit risk, erodes the dealers’ bufferrisk capacity, which results in the dealer setting higherbid-ask spreads.10

Empirical Prediction 2. The dynamic relation be-tween credit risk and market illiquidity shifts condi-tional on the level of the CDS spread.

We derive from Equation (3) the sensitivity of the bid-ask spread to the CDS spread, ∂BA

∂CDS = 2δCDS +∂m(b,CDS )∂CDS . This sensitivity depends on the CDS spread

through two channels: the direct risk channel, and theindirect margin setting channel; Empirical Prediction 2focuses on the latter. As documented in LCH.Clearnet(2011), the “Sovereign Risk Framework” states that themargin-setting decisions depend on the level of CDSand, particularly, that the clearing house deems that therisk of a security has increased significantly if the 5-year CDS spread increases above 500bp. In our model,this dependence would translate into a shift in ∂m(b,CDS )

∂CDS ,when the CDS spread crosses the 500bp threshold.11

9We address the contemporaneous interaction between the twovariables in detail in Section Int.1 of the internet appendix, via in-strumental variables analysis.

10This link also has implications for the dynamics of the relationbetween credit risk and market liquidity: The VaR is calculated at theend of day t−1. In periods of market stress, however, the VaR is oftenmonitored at an intraday frequency, implying that day-t liquidity willdepend on the contemporaneous, day-t, credit risk.

11Other related conceptual arguments can be advanced for such ashift in the relation. First, during the Euro-zone crisis, the adversechange in credit quality was generally accompanied or followed bydowngrades in the credit rating, altering the clientele of investors who

To test this empirical prediction, we employ thethreshold test proposed by Hansen (2000) to investi-gate i) whether a structural break in the level of CDSis present in the relation between credit risk and liquid-ity, ii) if this threshold corresponds to 500 bp, and iii)how the relation between credit risk and market liquid-ity changes, below and above the threshold.12

Empirical Prediction 3. The monetary policy inter-ventions of the central bank affect the dynamic relationbetween credit risk and market liquidity.

A central bank intervention that targets the access tofunding liquidity by banks and market makers would, inour model, affect the sensitivity of the bid-ask spread tothe CDS spread by changing the clearing houses marginsetting decision, i.e., through ∂m(b,CDS )

∂CDS . In the contextof the relation between credit risk and liquidity, there-fore, a successful intervention would be one that affectsthe sensitivity of the market makers to changes in creditrisk by providing them with improved funding liquid-ity. Therefore, we especially expect the LTRO to havean impact, due to the nature of its large funding liquidityshock, qualifying it as a significant structural break, thusaffecting the market liquidity in the sovereign bond mar-ket through the availability of funding liquidity to mar-ket makers. As in Brunnermeier and Pedersen (2009),we expect the margin channel to be have a larger impacton the market maker’s liquidity provision when she isfunding-liquidity constrained. The availability of mas-sive amounts of medium-term funding from the ECB,at unusually low interest rates, should have shifted theincentives of dealers to hold sovereign bonds.

Our third empirical prediction investigates the pres-ence of regime shifts in the estimated relation betweencredit risk and market liquidity around the dates of sig-nificant policy interventions by the ECB. Due to thelarge number of such interventions (SMP, LTRO, OMT,policy guidance, as described above) during the Euro-zone crisis, we choose to allow the data to endogenouslyinform us of the presence of structural breaks that in-dicates whether these interventions indeed affected therelation between credit risk and market liquidity. To in-vestigate this issue, we perform a SupWald structuralbreak test, a modified Chow test with an unknown break

were able to hold Italian sovereign bonds. Second, in the presence of asharp decline in credit quality, internal (and external) models of risk-weighting and illiquidity used by banks, a major investor segment,would necessarily predict an increase in the capital required to supportthe higher level of risk.

12Appendix B presents the details of the econometrical procedure.

8

point (see Chow, 1960; Andrews, 1993; Hansen, 1997).Appendix B presents the procedure in detail.

As argued earlier, the ECB interventions and itsmoral suasion towards the clearing houses could affectthe sensitivity of the market liquidity to the credit riskvia the indirect margin channel and, thus, affect the find-ings established in the previous empirical predictions.Therefore, we replicate the analysis in Empirical Pre-diction 1 and 2, for the two periods identified by the sta-tistical procedure. Thus, for the two periods separately,we i) quantify the sensitivity of the bid ask spread tothe CDS spread, and ii) test whether the relation shifts,when the CDS spread is above a threshold.

4. MTS Market Structure and Description of Vari-ables

Our data consist of all real-time quotes, orders, andtransactions that took place on the MTS Europeansovereign bond market during our period of study, andare provided by the MTS Group. These high-frequencydata cover trades and quotes for the fixed income secu-rities issued by twelve national treasuries and their localequivalents: Austria, Belgium, Finland, France, Ger-many, Greece, Ireland, Italy, the Netherlands, Portugal,Slovenia, and Spain. The MTS system is the largest in-terdealer market for Euro-denominated sovereign bondsand is made up of many markets, including the Eu-roMTS (the “European market”), EuroCredit MTS, andseveral domestic MTS markets. In this study, we willfocus on the liquidity of Italian sovereign bonds, regard-less of whether the trading or quoting activity took placeon the domestic or the European market. The MTStrading system is an automated quote-driven electroniclimit order interdealer market, in which market makers’quotes can be “hit” or “lifted” by other market partici-pants via market orders. EuroMTS is the reference elec-tronic market for European benchmark bonds.13

The sample period of our study is from July 1, 2010to December 31, 2012.14 The time period we analyze

13Benchmark bonds are bonds with an outstanding value higherthan e5 billion. Section Int.2 of the internet appendix provides de-tails of the market architecture, trading protocol, and data released forthe MTS market; see also Dufour and Skinner (2004).

14Our data set from July 2010 to May 2011 includes only intradayupdates of the three best bid and ask quotes. From June 1, 2011, wehave detailed tick-by-tick, second-by-second, data. The end date isdictated by a major change in market structure that was implementedin December 2012, and that changed the role of market makers actingin the European section of the MTS market. Fortuitously, the periodwe consider covers a large part of the Euro-zone crisis. A more de-tailed description of the differences between the datasets can be foundin the internet appendix, Section Int.2.

provides a good window in which to study the behaviorof European sovereign bond markets during the most re-cent part of the Euro-zone sovereign debt crisis and theperiod leading up to it. Our data set consists of 189 Ital-ian sovereign bonds. Table 1 presents the distributionof these bonds in terms of maturity and coupon rate,among original maturity groups as well as bond types.In terms of maturity groups, the bonds are grouped to-gether based on the integer closest to their original ma-turity. As Table 1 shows, the large majority (in num-bers) of the bonds analyzed have short maturities (from0 to 5 years). All bonds considered in this analysis be-long to one of the following types: Buoni Ordinari delTesoro (BOT), which correspond to Treasury bills, Cer-tificato del Tesoro Zero-coupon (CTZ), correspondingto zero-coupon bonds, Certificati di Credito del Tesoro(CCT), or floating notes, and Buoni del Tesoro Polien-nali (BTP), which are coupon-bearing Treasury bonds.The vast majority of the bonds in our sample belongto the BOT and BTP types. We exclude inflation andindex-linked securities from our analysis.

INSERT TABLE 1 HERE

4.1. Description of Variables

We measure bond liquidity for the MTS market by thedaily Bid-Ask Spread, defined as the difference betweenthe best ask and the best bid, per e100 of face value,proxying for the cost of immediacy that a trader willface when dealing with a small trade. We measure thebid-ask spread per bond at a five-minute frequency fromthe market open to the market close, namely from 8 AMto 5.30 PM, then average it per bond throughout theday, and finally average the daily bond measures acrossbonds to obtain a market-wide daily liquidity measure.

The Italian-sovereign-specific credit risk is measuredby the spread of a senior five-year dollar-denominatedCDS contract obtained from Bloomberg. The choice ofthis proxy for sovereign credit risk is debatable. An al-ternative potential proxy for Italian sovereign risk couldbe the BTP-Bund yield spread. We prefer to avoid us-ing the BTP-Bund yield spread because this variable islikely to be intimately connected to the bond quote andtransaction prices that are also used to calculate our liq-uidity measures. CDS spreads are obviously related tothe BTP-Bund yield spread (as Figure 2 shows), througharbitrage in the basis between them, but at least are de-termined in a different market.15

15We show in Section Int.3 of the internet appendix that there is nostatistically significant lead-lag relation between the two daily series,

9


Finally, in order to control for and characterize theeffect of global credit risk and funding liquidity, we em-ploy several macro-economic indicators, most of whichare common in the academic literature. The Euribor-DeTBill yield spread captures the (global) counterpartyand credit risk and, thus, an increase in the cost of fund-ing, and is measured as the difference between the three-month Euro-area Inter-Bank Offered Rate (Euribor) forthe Euro, covering dealings from 57 prime banks, andthe three-month yield of the three-month German Trea-sury bill. As banks are more uncertain, they chargeeach other higher rates on unsecured loans; similarly,looking for high-quality collateral, they purchase safeTreasury bills, lowering their yields. This measure isthe European counterpart of the TED spread used by,among others, Brunnermeier (2009). The USVIX, mea-suring global systemic risk, is the implied volatility in-dex of S&P 500 index options calculated by the ChicagoBoard Options Exchange (CBOE) and used widely as amarket sentiment indicator. The CCBSS represents theadditional premium paid per period for a cross-currencyswap between Euribor and US Dollar Libor, and servesas a proxy for funding liquidity.16 All these variableswere obtained from Bloomberg.

5. Descriptive Statistics

Table 2 presents the summary statistics for the mar-ket activity measures for Italian sovereign bonds tradedon the MTS market and system variables, between July2010 and December 2012, spanning the period of the

because the adjustment between them takes place on the same day.Also, in Section Int.4 of the internet appendix, we investigate whetherthe intraday volatility of the bond yield, as measured using the MTStransaction data, and the liquidity of the CDS market affect the liq-uidity, while controlling for the credit risk. These modifications donot significantly change the results, supporting our choice of the CDSspread as a measure of credit risk.

16The CCBSS can be thought of as the spread of the longer-term,multi-period equivalent of deviations from uncovered interest rate par-ity. When liquidity is available to arbitrageurs in all currencies, devia-tions from the (un)covered interest rate parity will be closed and prof-ited on, while lasting deviations can be interpreted as a sign of lack offunding liquidity. Baba, Packer, and Nagano (2008) and Baba (2009)show that cross-currency basis swaps are used by banks to financethemselves in foreign currencies when the interbank market in thehome currency is illiquid, Brunnermeier, Nagel, and Pedersen (2008)show that deviations from uncovered interest rate parity are partiallyexplained by shocks to funding liquidity. Acharya and Steffen (2015)and Ivashina, Scharfstein, and Stein (2012) investigate the fundingliquidity needs of European banks and relate them to the (un)coveredinterest rate parity.

Euro-zone sovereign crisis. The table reports statisticsfor the daily time-series of the market-wide variables:Trades, Volume, and Bid-Ask Spread were calculated ona daily bond basis and then averaged across bonds toobtain the time-series. Quoted Bonds is the time-seriesof the number of bonds quoted each day.

INSERT TABLE 2 HERE

The mean (median) number of bonds quoted each dayon the MTS is 89 (88), and the daily volume of tradingin the market is slightly below e2.9 billion (e2.6 bil-lion), which translates into a daily traded volume foreach quoted bond of about e32.6 million (e28.7 mil-lion). Based on these numbers, the daily trading volumein the Italian sovereign bond market (as represented bythe MTS) is much smaller than in the US Treasury mar-ket, by a couple of orders of magnitude, with the aver-age traded quantity in the latter being around $500 bil-lion per day (Bessembinder and Maxwell, 2008). Theaverage daily trading volume in the MTS Italian bondmarket is even smaller than in the US municipal mar-ket (around $15 billion), the US corporate bond market(around $15 billion), and the spot US securitized fixedincome market (around $2.7 billion in asset-backedsecurities, around $9.1 billion in collateralized mort-gage obligations, and around $13.4 billion in mortgage-backed securities).17

Our volume statistics are in line with the stylized factsdocumented in the previous literature, taken togetherwith the consistent shrinkage of overall market volumessince the Euro-zone crisis began. Darbha and Dufour(2013) report that the volume of the Italian segment ofthe MTS market as a whole, over their 1,641-day sam-ple, was e4,474 billion. This translates into an averagedaily volume of about e3.8 billion. Darbha and Dufourreport that the daily volume per bond shrank from e12million in 2004 to e7 million in 2007. Their sampleincludes only coupon-bearing bonds; thus, their figuresfor overall market volume are not directly comparableto ours.

The daily number of trades on the MTS Italiansovereign bond market is 352 in total (or about 4 perbond), which is similar to the 3.47 trades a day percorporate bond on TRACE, as reported in Friewald,Jankowitsch, and Subrahmanyam (2012a). Dufour andNguyen (2012) report an average of 10 trades per day

17Details for the corporate bond, municipal bond, and securitizedfixed income markets are provided in Friewald, Jankowitsch, andSubrahmanyam (2012a), Vickery and Wright (2010), and Friewald,Jankowitsch, and Subrahmanyam (2012b), respectively.

10

per Italian bond in an earlier period, between 2003 and2007. As with the trading volume, the number oftrades declined during the crisis period compared to ear-lier years. Our sample period covers the most stressedmonths of the Euro-zone crisis, when the creditworthi-ness of several European countries was seriously ques-tioned by market participants. As we will show later,the liquidity in the MTS market was intimately relatedto the evolution of spreads in the sovereign CDS mar-ket, and varied just as drastically, as the time-series plotsof the CDS spread and the Bid-Ask Spread in Figure 2show. Up to the end of 2011, at the peak of the crisis, thetwo series share a common trend, which is not repeatedin the second half of our sample.

The commonality in the two series in Figure 2 be-comes particularly evident, for example, when one con-siders the highest spike for the Bid-Ask Spread (e4.48per e100 of face value), which happened on Novem-ber 9, 2011. On the previous day, after the markets hadclosed, the Italian Prime Minister, Silvio Berlusconi,lost his majority in the parliament, which led to his res-ignation. The spike in the Bid-Ask Spread correspondsto a similar spike in the CDS Spread. The event clearlyhad medium-term effects, as both the Bid-Ask Spreadand the CDS Spread persisted at high levels for abouttwo months, before returning to more moderate quan-tities in January 2012. In mid-2012, however, the CDSSpread reached levels close to 500 bp, while the Bid-AskSpread oscillated around the time-series median valueof e0.30.

The reasons for choosing to present our results basedon the bid-ask spread as a measure of market liquid-ity bear mention. First, the quoted bid-ask spread is themost familiar and widespread measure of market liquid-ity. Thus, it allows for a direct comparison with the pre-vious and contemporaneous literature on liquidity. Sec-ond, the large number of quotes that are aggregated intoa single daily bid-ask spread time-series suggests thatmarket makers are very active, and ensures that the com-puted spread is a precise estimate of their willingness totrade, since the quotes are firm. Finally, high-frequencyquote updates indicate that accurate quoting in the MTSmarket is important for primary dealers under the super-vision of the Bank of Italy. These quotes are, moreover,also used by officials at the Italian Treasury to evaluate(and eventually even disqualify) sovereign bond marketmakers.18

18From July 1, 2010 until May 31, 2011, we use the MTS databasethat provides only the three best bid and ask prices. However, we havean overlapping sample of seven months of both the databases, andperform a comparison of the bid-ask liquidity measure we calculate,

The results of the Dickey-Fuller unit root test for thevariables used in our empirical investigation are pre-sented in Table 2 under the “Unit Root Test” columnsfor the levels of and differences in the variables. All ourtests for the control variables and the CDS spread sup-port the existence of a unit root, while the bid-ask spreadand the USVIX show a mean-reverting property. How-ever, (i) the first-order auto-correlation for the liquiditymeasure is 81%, and (ii) the unit root test did not re-ject the unit root null hypothesis when it was performedon the first part of the sample, for the period when theEuro-zone crisis first unfolded. In light of this fact, andin order to have a consistent, unique model for the wholedata sample and to ensure well-behaved residuals, weperform our analysis in first differences.

As shown in Figure 2, the Italian CDS spread for oursample period ranges from 127 bp to 592 bp, with amean of 321 bp and a standard deviation of 138 bp, in-dicating the large changes in this variable during the pe-riod under study. Figure 3 shows the evolution of themacro variables. The Euribor-DeTBill spread (Panel(a)) also presents a significant level of volatility, witha daily standard deviation of 0.36%, while the USVIX(Panel (b)) ranges from 13.45% to 48%. The CCBSSvariable (Panel (c)), which captures the general levelof funding liquidity in the system, and which shouldbe close to zero in the absence of funding constraints,ranges from 12bp to 107bp, indicating a large variabil-ity in the global liquidity conditions in the Euro-zone inthe period considered. All the funding and credit vari-ables suggest that the conditions in the Euro-zone finan-cial system were at their worst around the third quarterof 2011, but improved somewhat during the first quar-ter of 2012, then worsened, although to a lesser extent,around June 2012, and continued to decline towards theend of that year.


The correlations between the credit, funding liquid-ity and market liquidity variables are shown in Table 2Panel C. The correlations between the variables in lev-els are presented above the diagonal, while those forthe variables in differences are below the diagonal. Indifferences, bond market liquidity is most highly corre-lated with the Italian CDS Spread and the CCBSS.

using the two databases. The results show that there is almost nodifference between the two, for the purpose of computing the bid-askspread; see Section Int.2 of the internet appendix.

11

6. Results

In Section 3 we derived three empirical predictionsand, in this section, we investigate them, focusing on thedynamic relationships between credit risk and marketliquidity and the effect of the ECB’s deus ex machina. Inorder to test the first empirical prediction, regarding thedynamics of the relation between the credit risk of Ital-ian sovereign bonds, as measured by the CDS Spread,and the liquidity of the Italian sovereign bonds, as mea-sured by their Bid-Ask Spread, we first investigate, inSection 6.1, whether there is a lead-lag relation betweenthe two variables, using a Granger-causality test in aVector Auto Regression (VAR) setting.19

In Section 6.2, we focus on Empirical Prediction 2,and test for the presence of a threshold in the level of theCDS spread that shifts the relation between credit riskand market liquidity. We perform this analysis using thethreshold test proposed by Hansen (2000), and charac-terize how the relation between credit risk and marketliquidity changes below and above this threshold. Fi-nally, in Section 6.3, we investigate Empirical Predic-tion 3 and test whether and how the dynamics of therelation are affected by the ECB interventions. We usean endogenous structural break test described in detailin Appendix B, and study whether the injection of fund-ing liquidity by the central bank lowered the sensitivityof market liquidity to the worsening credit conditions ofthe Italian sovereign.

6.1. The Dynamics of Credit Risk and Liquidity

Empirical Prediction 1. The illiquidity of the bondmarket increases with credit risk.

In this section, we investigate Empirical Prediction1, testing whether the increase in credit risk drives thereduction of market liquidity or vice versa. While ourtheoretical model has been explicitly designed to char-acterize the effects that a change in the credit risk has onthe market liquidity, we cannot rule out that market liq-uidity has, in turn, an effect on credit risk. Therefore, toallow for this feedback loop, we implement this analysisby estimating a VAR system that allows us to performa Granger-causality test. Since global risk factors couldaffect market liquidity, on top of security-specific credit

19We conduct our analysis in changes, after winsorizing the data atthe 1% level to diminish the importance of outliers, such as the largechanges in bid-ask spread in the second half of 2011, in particular thatof November 9. For robustness, we repeat the analysis after winsoriz-ing the data at the 5% level. The results are mostly unchanged andreported in the internet appendix Section Int.5.

risk concerns, we include USVIX, the Euribor-DeTBillspread, and the CCBSS in our VAR specification as “ex-ogenous variables”. These variables are exogenous inthat we are not interested in studying the effect of theendogenous variables on their dynamics, only the oppo-site effect. We thus describe the system using a VARwith eXogenous variables (VARX) model.

The mathematical formulation of this Granger-causality test is based on linear regressions of thechange in the Bid-Ask Spread, ∆BAt, and the changein the CDS Spread, ∆CDS t, on their p lags. Specifi-cally, let ∆BAt and ∆CDS t be two stationary daily time-series, and Xt a time-series m−vector of stationary ex-ogenous variables. We can represent their linear inter-relationships using the following VARX model:(

∆BAt

∆CDS t

)=

(KBA

KCDS

)+

p∑i=1

(a11i a12i

a21i a22i

) (∆BAt−i

∆CDS t−i

)

+

q∑j=0

B j

∆X1t−q

∆X2t−q...

∆Xmt−q

+

(εBAt

εCDS t

), (4)

where εt ∼ N(0,Ω), the B js are 2-by-m matrices, andthe ai jp s are the p-lag coefficients of the model. Thisformulation allows for the presence of m contemporane-ous, and lagged (up to q), exogenous variables to controlfor factors that might affect the dynamics of the endoge-nous variables. We can conclude that ∆CDS Granger-causes ∆BA when the a12p s are contemporaneously dif-ferent from zero. Similarly, we can surmise that ∆BAGranger-causes ∆CDS when the a21p s are contempo-raneously different from zero. When both these state-ments are true, there is a feedback relation between thetwo time-series.

The lag length was chosen based on the correctedAkaike criterion, which suggests a lag length of 3 forthe endogenous variables and no lagged exogenous vari-ables. The results of the Granger-causality test, withp = 3 and q = 0, for the relation between the changesin the CDS Spread and the Bid-Ask Spread, are reportedin Table 3, where we report the F-test test statistics forthe contemporaneous significance of the cross-variableterms for each equation (the a12s for the bid-ask spreadequation under ∆BAt, and the a21s for the CDS spreadequation under ∆CDS t).20

INSERT TABLE 3 HERE

20Throughout the paper, statistical significance is always de-termined on the basis of t-tests that are calculated usingheteroskedasticity-robust standard errors.

12

As the table shows, in line with Empirical Prediction1 in Section 3, the CDS Spread Granger-causes liquidityin the bond market at a 1% level (the heteroskedasticity-robust F-test is 6.01 and the 1% confidence value is3.81, and the bootstrapped results provide identical sig-nificance levels), while the opposite directionality is notsignificant at any of the usual confidence levels (the p-value is 0.70). This result confirms Empirical Prediction1 and supports the inventory risk channel as a driver ofthe relation between credit risk and market liquidity.

The macro variables are significant in explaining thetwo variables. Specifically, the bond market illiquiditydepends positively on the availability of funding liquid-ity for European banks and on the sentiment of the mar-ket, as measured by the CCBS S and US VIX, respec-tively. In untabulated results, however, the contempora-neous dependence of the macro variables does not lowerthe significance of the effect of (lagged) credit risk onmarket liquidity, although it contributes towards lower-ing the residual cross-correlation.

In order to interpret the dynamics of the system,we calculate the impulse response functions (IRF) forthe relationships between the variables. We do thisfor the rescaled variables, so that they have a meanof 0 and a standard deviation of 1, for ease of in-terpretation. Figure 4 presents the results, for whichthe 5% confidence bands were bootstrapped based on5,000 repetitions. As shown in Panel (a) of the figure,a one-standard-deviation shock to the CDS Spread attime 0, corresponding to a 4.1% change, is followedby a change of 0.26 standard deviations in the Bid-Ask Spread, corresponding to a 5.2% increase in thesame direction, and is absorbed by both variables in twodays. Alternatively, the parameters imply that a 10%change in the CDS Spread (corresponding to a changeof 10%/4.1% = 2.43 standard deviations) is followedby a 2.43 · 5.2 = 12.7% change in the Bid-Ask Spread.The results are, hence, both statistically and economi-cally significant, and confirm the results of the Granger-causality tests presented above. The IRF in Panel (b)shows that a shock at time 0 to market liquidity lastsuntil time 1, but only affects market liquidity itself, in-dicating that the reaction of the CDS Spread to a shockin market liquidity is never different from zero, in linewith the findings of the Granger-causality tests.


Since the focus of this study is the dynamics of thecredit risk and bond market liquidity in relation to eachother, and past values of bid-ask spread do not affectcredit risk, as per Table 3, we focus solely on the bid-ask spread regression in the VARX system, augmenting

it with the contemporaneous change in credit risk. Thiscorresponds to a shift from a reduced-form to a struc-tural approach for the VAR, where the contemporane-ous causation runs from credit to liquidity. As the or-dering of the variables in this causation chain cannot betested in the VAR setting (see, e.g., Lutkepohl, 1993),we turn to instrumental variable (IV) methods to es-tablish whether feedback between the contemporaneousCDS Spread and Bid-Ask Spread changes—or, alterna-tively, other forms of endogeneity—is supported by thedata. We do so to ensure that our specification does notdisqualify the structural approach we take, or otherwisesuggest the opposite relation. In Section Int.1 of the in-ternet appendix, we show using several cohorts of validand strong instruments that the CDS Spread is indeednot endogenous to the system, and hence its inclusionas a regressor is justified: the regression parameter at-tached to it in the bid-ask spread regression is unbiasedand consistently estimated.

As both the lead-lag and the contemporaneous rela-tion indicate the direction of the Granger-causality, weonly need focus in the rest of the paper on the causal ef-fects on the liquidity measure (i.e., the ∆BAt equation),in order to determine the dynamics of the system. Thiswill be sufficient to capture the dynamics of the credit-liquidity relation (including the effect of ECB interven-tions), given the lack of statistical support for causalityin the opposite direction. Therefore, we regress changesin the liquidity measure, Bid-Ask Spread, on the con-temporaneous changes in the CDS Spread, and their re-spective lags, and on the contemporaneous macro vari-ables. Equation (5) presents our baseline regressionspecification for the remainder of the paper:

∆BAt = α0 +

3∑i=1

αi∆BAt−i +

1∑j=0

β j∆CDS t− j

+ β2CCBS S + β3US VIXt + εt, (5)

where ∆BAt is the change in the bond-market-wide bid-ask spread from day t − 1 to day t, and ∆CDS t isthe change in the CDS spread, as before. The sta-tistically insignificant lags of the CDS measure and∆EuriborDeT Billt have been dropped due to their lackof statistical significance. The results for Equation (5)are reported in Table 4 Panel A.

Comparing the parameters in Table 4 Panel A tothose in Table 3 shows that adding the contemporaneouschange in the CDS Spread does not modify our findings,with the exception of a lower level of statistical signif-icance for the other contemporaneous variables. Thiswas to be expected, since these other variables poten-

13

tially proxy for changes in the credit risk. Moreover, thedynamics of the bid-ask spread are well accounted for,since the residuals show no autocorrelation according tothe Durbin h-test and the Breusch-Godfrey serial corre-lation test (never significant at the 10% level or lowerfor lags up to 10, with one exception).

INSERT TABLE 4 HERE

As for the dynamics of the system, the change in theCDS Spread has a lagged effect on market liquidity, i.e.,the reaction of market liquidity, measured by the Bid-Ask Spread, to changes in the CDS Spread, occurs onthe next day. The Bid-Ask Spread also shows evidenceof an autoregressive component, being strongly relatedto the change in the Bid-Ask Spread that took place theday before, with a negative sign: this suggests an over-reaction adjustment dynamic in the Bid-Ask Spread, asshown already in the IRF of Figure 4 Panel (b). This ef-fect can be ascribed to the actions of the market makers,who adjust their quotes as a reaction, not only to thechanges in the traded price, but also to the changes inthe quotes of the other primary dealers. A 10% increasein the CDS spread on day t results in an increase in thebid-ask spread of 5.41% on day t and a further increaseof −0.352 · 5.41% + 7.94% = 6.04% on day t + 1, for acumulative increase of 11.45%.

Regarding the significance of the lagged ∆CDS term,a partial explanation can be found in the timing of VaR-based models in practice. Since the calculation of thedealer’s VaR generally takes place at the end of theday, the exposure to the credit risk is taken into accountby the dealer when deciding how much liquidity to of-fer only on the day following the credit shock, whichimplies the significance of the lagged change in creditrisk.21

6.2. The relation between Credit Risk and LiquidityConditional on the Level of Credit Risk


21One variable that could also affect the inventory levels of marketmakers (e.g., through the risk management practices of dealer desks),and therefore market liquidity, is the volatility of the bond yield. InSection Int.4 of the internet appendix, we repeat the analysis includ-ing this variable and our results are robust to this inclusion. Moreover,we also test whether the CDS Spread drives both changes in marketliquidity and bond return volatility or whether the effects are the otherway around, and show that it is the former relation that prevails, con-firming that the analysis we perform in this section is correct and ro-bust to the insertion of volatility into the pool of endogenous variables.

Turning to our Empirical Prediction 2, Equation (5)above implicitly assumes that the estimated relationholds independent of the level of credit risk, in partic-ular when the CDS Spread is above a particular thresh-old level. For the reasons highlighted in the theoreti-cal model presented in Section 3, on account of marginsetting, and downgrade concerns, it is possible that themarket makers’ liquidity provision would be more sen-sitive to changes in credit risk when the CDS Spreadbreaches a particular threshold. We investigate this em-pirical prediction by allowing the data to uncover thepresence of a threshold in the level of the CDS Spread,above which a different relation between changes inCDS and changes in market liquidity is observed. Weuse the test proposed by Hansen (2000), described indetail in Appendix B, to examine this hypothesis, esti-mating Equation (6) for different γ, where I

[CDS ≤ γ

]equals 1 if the condition is satisfied and 0 otherwise:

∆BAt = α0 +

3∑i=1

αi∆BAt−i

+ I[CDS ≤ γ

] 1∑j=0

β j∆CDS t− j

+ I

[CDS > γ

] 1∑j=0

β j∆CDS t− j

+ β2US VIXt + β3CCBS S + εt. (6)

Figure 5 shows, on the y-axis, the sum of squaredresiduals for the regression in Equation (6) as γ, shownon the x-axis, changes (the sum of squared residualsfor Equation (5) is plotted at γ = 0). The sum ofsquared residuals is minimized when γ = 496.55. Wetest for the identity between parameters above and be-low the threshold, or, equivalently, for the presence ofthe threshold, H0 : β0 = β0, β1 = β1 and, since the teststatistic asymptotic distribution is non-pivotal, we boot-strap it, as described in Hansen (1996). The test statisticfor the presence of the threshold we observe (25.05) issignificant at better than the 1% level, thus confirmingthe presence of a threshold.22


While the previous paragraphs confirm the presenceand location of the threshold, γ = 496.55 bp, Figure 6

22The histogram of the bootstrapped test distribution for this andsimilar tests referred to throughout the paper can be found in the in-ternet appendix, Section Int.6.

14

shows the test statistic needed to determine the confi-dence bounds around the point estimate we find. Thethreshold has a point estimate of 496.55, with a 5%confidence interval between 485 and 510, and is almostidentical for various alternative specifications of the re-lation (including whether or not lagged or macro vari-ables are included).


The confirmation of the presence of a structural shift inthe data when the CDS spread crosses a certain thresh-old is, therefore, robust and strongly supported by thedata, and indicates how important the level of the CDSSpread is for market liquidity.

This result confirms Empirical Prediction 2, andshows that the rules adopted by the clearing house toset margins as a function of the level of the CDS spreadhave an impact on the relation between credit risk andmarket liquidity. The application of the margin settingrule is shown in Figure 7, which depicts the time-seriesof bond-market bid-ask spread, CDS spread, and the av-erage margin on Italian bonds with between 3 monthsand 30 years to maturity, charged by a major clearinghouse, Cassa Compensazione e Garanzia, which usesthe same margins as those charged by LCH.Clearnet.The margin requirements changed only slightly betweenJune 2010 and November 2011, from 3.26% to 4.53%,while the CDS spread rose threefold from about 150 bpto 450 bp. However, the same clearing house nearlydoubled the margins to slightly below 9% on Novem-ber 9, 2011, the second time the spread hits and staysconsistently above 500 bp: in the sovereign risk frame-work, distributed by the LCH.Clearnet in October 2010(see LCH.Clearnet, 2011), one of the indicators used tojustify a hike in margin is indeed “a 500bp 5 year CDSspread”.

It is important to stress that market participants wereaware of the rule adopted by the clearing house, whichhad already enforced this margin setting rule for Irishsovereign bond on November 17, 2010, when the mar-gins on repo transactions were raised from 16-18% to31-33%. In that instance, LCH.Clearnet argued that thisdecision had been taken “in response to the sustainedperiod during which the yield differential of 10 yearIrish government debt against a AAA benchmark hastraded consistently over 500 bp.”23

23Source: http://www.lchclearnet.com/risk_

management/ltd/margin_rate_circulars/repoclear/

2010-11-17.asp and http://ftalphaville.ft.com//2010/

11/17/407351/dear-repoclear-member/


The very day that the clearing houses changed themargins charged on sovereign bonds, their market liq-uidity suddenly worsened, corresponding to a shift inthe level of the bid-ask spread, as predicted by Equation(3) in our model. Brunnermeier and Pedersen (2009) de-rive a similar prediction, that an increase in margins hasan effect on the security’s market liquidity, if the marketmakers’ budget constraint is binding. As Figure 3 Panel(c) shows, the CCBSS, measuring the funding liquid-ity needs of the market makers, was at its highest dur-ing the second half of 2011, when the margin changestook place. We interpret our findings as a confirmationof Brunnermeier and Pedersen (2009): In the secondhalf of 2011, when the funding liquidity of the marketmakers was at its lowest and their budget constraint wasbinding, a change in the margins charged on sovereignbonds led to a tightening of their market liquidity.

Having now identified the presence of a threshold andthe effect that it has on the level of bid-ask spread, weneed to determine how the sensitivity of market liquidityto credit risk is modified when the threshold is breached.Panel B of Table 4 reports the results for Equation (6),when γ = γ, or the threshold is the point estimate foundin the previous paragraphs, what we call for simplicitythe 500 bp threshold. The column “Test” in Panel Breports the test statistic for whether each pair of param-eters above and below the threshold is equal; e.g., thetest statistic for H0: β0 = β0 is 11.33, significant at the1% level.

As the panel shows, the relationships below andabove 500 bp are rather different from each other: con-temporaneous changes in the CDS Spread have a sig-nificantly larger economic impact on market liquidityabove the threshold of 500 bp than below. In particu-lar, the regression in Panel B indicates that the coeffi-cient of the contemporaneous change below the thresh-old is 0.32, but not significant, while that above it is2.85 and statistically significant. Looking at the laggedCDS variable, we find that, below the 500 bp threshold,market liquidity reacts with a lag to changes in the CDSSpread, with a significant impact of the autoregressivecomponent and the lagged component of the change inthe CDS. Above 500 bp, the relation is rather different:market liquidity reacts immediately to changes in theCDS Spread, with the impact being largely contempo-raneous, since the change in the CDS spread has no im-pact on the change in the market liquidity the followingday. The parameters suggest that an increase in the CDSSpread of 10% on day t, below (above) the thresholdof 500 bp, induces a contemporaneous increase in the

15

http://www.lchclearnet.com/risk_management/ltd/margin_rate_circulars/repoclear/2010-11-17.asp



http://ftalphaville.ft.com//2010/11/17/407351/dear-repoclear-member/

http://ftalphaville.ft.com//2010/11/17/407351/dear-repoclear-member/

Bid-Ask Spread of 3.2% (28.5%) on day t, and an in-crease (decrease) of −0.332 · 3.2% + 9.83% = 8.77%(−0.332 · 28.5% − 8.54% = −18%) on day t + 1,for a cumulative increase of 11.96% (10.46%). Al-though the cumulative t + 1 effects of a 10% increasein CDS spread are similar above and below the 500 bpthreshold, the dynamics of the system are very different:Above 500 bp, the market overreacts by increasing thebid-ask spread instantaneously, while below 500 bp themarket reacts moderately, and with a lag, to the increasein credit risk.

The results that we derive in this sub-section formarket-wide measures are confirmed by the robustnessanalysis we perform in Section 7.1, where we groupbonds with similar maturities, as determined by coun-terparty clearing houses with regard to margin require-ments, and repeat the analysis regressing each groupmaturity on the corresponding maturity CDS spread.

Our conclusion, therefore, is that Empirical Predic-tion 2 is verified and that the dynamic relation betweencredit risk and market liquidity differs depending on thelevel of the CDS spread; specifically, in a stressed en-vironment, credit shocks have an immediate impact onmarket liquidity.24

6.3. Policy Intervention and Structural BreaksOur third empirical prediction is that the various in-

terventions that occurred during the period could havegenerated a structural break in the relation betweencredit risk and market liquidity. Therefore, the third re-search aim of this paper is to examine whether such astructural break can be detected statistically and relatedto policy changes. Again, we let the data alert us to thepresence of a structural break over time.


As we have described above, the period that we in-vestigate has been characterized by many events: theonset of the Euro-zone sovereign debt crisis, severalsovereign credit downgrades, a political crisis that in-duced changes in Euro-zone governments, and severalinterventions by European central banks, and, in par-ticular, by the ECB. Of course, by virtue of its status

24Since we have determined the presence of parameter discontinu-ity, we should verify how that discontinuity affects the lead-lag rela-tion investigated in Empirical Prediction 1 for the two samples. Ouranalysis shows that the same result applies whether the CDS level isbelow or above the threshold, as shown in Section Int.7 of the internetappendix.

as the central bank of the Euro-zone, the ECB has amajor influence on its sovereign bond markets. As de-scribed in Section 3, the ECB’s monetary interventiontakes many forms, ranging from formal guidance by itsboard members, in particular its president, to the injec-tion of liquidity into the major banks in the Euro-zone,which themselves hold these bonds, to direct purchasesof sovereign bonds in the cash markets.

The purpose of this section is not to quantify the di-rect effect of these interventions on the Euro-zone creditrisk (see Eser and Schwaab, 2013), or its bond mar-ket liquidity (see Ghysels, Idier, Manganelli, and Ver-gote, 2014), but to examine whether the relation be-tween credit risk and liquidity was significantly alteredby one or more of these interventions, as exemplifiedin the theoretical model presented above, by testing forthe presence of a structural break. The scant publicavailability of data concerning the quantity, issuer na-tionality, and timing of purchases of bonds in the SMPframework prevents us from quantifying the specific ef-fect of those purchases. Similarly, in the absence ofdetails of the extent of banks’ access to LTRO fundingand its usage, we are unable to investigate how the re-financing operation affected liquidity provision by themarket makers (most of which belong to major inter-national and national banks). However, since the sev-eral interventions and policy-relevant events took placeover finite and non-overlapping periods of time, we caninvestigate econometrically whether a structural breakin the relation between the two variables of interest oc-curred around the time of the announcement or imple-mentation of the interventions. This analysis is relevantfor our second empirical prediction for two main rea-sons: first, because if the data indeed exhibit structuralbreaks, our results will be biased if we ignore them, andsecond, because it will shed light on the relevant com-bination of conditions that affects the relation betweencredit risk and liquidity.

We investigate Empirical Prediction 3 by perform-ing the “structural change breaks” test proposed by An-drews (1993) (the supF test in that paper), on Equation(6), the details of which are presented in Appendix B.Briefly, the test corresponds roughly to a Chow (1960)test but, while in the Chow test the structural changebreak is specified exogenously, this “structural changebreak” allows us to leave the structural break date un-known a priori. The test corresponds to performing aChow test for the relation in question on each date inthe sample. The date that is most likely to constitute abreak in the data sample is found endogenously, iden-tified as the date with the largest Chow test value, andthe presence of a break itself is tested by comparing that

16

date’s (Chow) F-test statistic to a non-standard distri-bution. The test, therefore, verifies whether there is astructural break, at all, in the specified relation. If thenull hypothesis of “no structural break” can be rejected,the date with the largest corresponding Chow test statis-tic will be selected as the structural break. Figure 8shows the values of the Chow F-test statistic calculatedon each date, with the horizontal line showing the con-fidence band for the highest F-value.

We find that, from a statistical perspective, the testindicates a break, on December 21, 2011, for the rela-tion between the Bid-Ask Spread, and the CDS Spread,its lag, and the macro variables, and that this structuralbreak is significant at the 10% level. Although Decem-ber 21 is identified purely based on the statistical ev-idence as the date for which the (Chow) supF test ismost significant for the relevant relationships betweenthe Bid-Ask Spread and the CDS Spread, it coincidesexactly with the date of the allotment and the day beforethe settlement of the LTRO program by the ECB.25

Our evidence suggests that the relation between creditrisk and liquidity changed when the ECB providedLTRO funding to the banks. To the extent that the rela-tion measures the sensitivity of the market makers’ be-havior to changes in the (credit) risk of their portfolios,our finding supports our empirical prediction, that themarket makers were wary about providing liquidity tothe sovereign bond market.

They were particularly concerned that, should an ad-verse credit event have occurred, their inventory wouldhave suffered and they would have been left with noavailable funding liquidity. The large provision of fund-ing from the ECB constituted a structural break in thatrelation and had a clear impact on the sensitivity of mar-ket makers to changes in the credit riskiness of their in-ventories, as we quantify in the following paragraphs.

In order to account for this structural break in ourestimations, we split the sample into two periods, andagain perform the threshold test as per Equation (6)in both subsamples. That is, we test whether the rela-tion between the changes in the bid-ask spread, and thechanges in the CDS spread and its lag, varies above andbelow an endogenously found threshold. The bootstrapprocedure for the threshold test confirms the presenceof different relationships below and above the thresholdlevel of 500 bp for the CDS spread, in the first subsam-ple (July 1, 2010 to December 21, 2011), but fails to

25The policy implementation announcement of December 8,2011 with all the important dates for this measure can be foundonline at http://www.ecb.europa.eu/press/pr/date/2011/

html/pr111208_1.en.html

identify a threshold for the second subsample. Figure 9reports the test to identify confidence bands around thethreshold point estimates, for the first and second sub-sample, in Panel (a) and (b), respectively: the thresholdcan be identified around 500 bp for the first subsample,while no threshold can be found in the second subsam-ple.

This result suggests that, thanks to the assurance ofa massive amount of liquidity from the ECB and theECB’s request to the clearing house to avoid the pos-sibility for margins to become procyclical to sovereignrisk, the relation between changes in the CDS spreadand market liquidity was not altered when the ItalianCDS Spread breached the level of 500 bp after theLTRO intervention, in contrast to the period before theintervention.

INSERT FIGURES 8 AND 9 HERE

Panel A of Table 5 presents the results of the estima-tion for the first subsample, before December 21, 2011,and confirms the results we presented above. The maindifference is that, for the split sample, the relation be-tween the change in the CDS Spread and market liq-uidity, when the CDS Spread is above 500 bp, is evenstronger in the pre-LTRO regime, with a 10% increasein the CDS Spread translating into a 39% contempora-neous increase in the Bid-Ask Spread.

INSERT TABLE 5 HERE

Table 5 Panel B presents the results of the estimationfor the second subsample, after December 21, 2011, andshows that the presence of the autoregressive compo-nent in market liquidity is still apparent. However, thecontemporaneous relation between changes in the CDSSpread and changes in market liquidity is no longer sig-nificant, while there is a lagged adjustment of marketliquidity related to changes in the CDS Spread on theprevious day, with an economic intensity that is smallerthat in the full sample reported in Table 4, Panel A(0.566 vs. 0.794), and about a half of the correspond-ing parameter for the 2011 subsample, when the CDSis below 500 bp, reported in Table 5 Panel A (0.566 vs.1.028). Moreover, our analysis shows that the globalrisk variable, USVIX, affects market liquidity only forthe 2011 subsample, while, after the ECB interven-tion, the only significant variable is the funding liquiditymeasure, CCBSS.

The previous literature (e.g., Eser and Schwaab,2013; Ghysels, Idier, Manganelli, and Vergote, 2014)shows that the SMP had an effect on the yields ofthe bonds chosen for the program, following the large

17

http://www.ecb.europa.eu/press/pr/date/2011/html/pr111208_1.en.html

http://www.ecb.europa.eu/press/pr/date/2011/html/pr111208_1.en.html

buying pressure exerted by the central bank purchases.However, to the extent that the risk levels of themarket makers were maintained, the relation betweencredit risk and liquidity would have remained unaltered.Hence, the SMP, which was implemented in 2010, didnot, in fact, constitute a structural break for that de-pendence. The LTRO, on the contrary, constituted amassive intervention targeting the availability of fund-ing liquidity and, as such, was ideal for affecting howthe banks disposed of their available capital, makingthem less sensitive to changes in credit risk, when pro-viding liquidity to the market. We tested whether otherstructural breaks would emerge from the data after De-cember 21, 2011, and no date emerged as statisticallysignificant.

It is worth stressing that, although margins were in-creased again in June, July, and August 2012 (in Augustto the same level as in November 2011), Figure 7 showsthat the market illiquidity did not increase then as it didin November 2011, as a result of the hike in margins,but rather stayed constant. The large infusion of fund-ing liquidity resulting from the LTRO, confirmed by thelow levels of CCBSS after January 2012 shown in Fig-ure 3 Panel (c), loosened the market makers’ fundingconstraints, so that, consistent with Brunnermeier andPedersen’s (2009) prediction, we show empirically thatthe change in margins in 2012 did not affect the marketmakers’ provision of market liquidity, since their budgetconstraints were not binding.

The results of the analysis of the structural break inthe time series confirm what we posited in EmpiricalPrediction 3 and allow us to argue that LTRO interven-tion was very effective in severing the strong connectionbetween credit risk and market liquidity. It is interest-ing to observe that both the SMP and LTRO interven-tions generated injections of liquidity into the systemby the ECB. However, the magnitudes were completelydifferent (e103 billion in August 2011 versus e489 bil-lion in December 2011) and so were the mechanisms:in the first case, the ECB bought the sovereign bondsdirectly, while, in the second case, it provided moneyto reduce the funding liquidity constraints of the banks,which perhaps used some of the released liquidity topurchase sovereign bonds.

7. Robustness Checks

7.1. Results for Bonds with Different MaturitiesIn the body of the paper, we report the results based

on the daily bid-ask spread, obtained from MTS data byaveraging the quoted bid-ask spread on a bond-day ba-sis, and then averaging them across bonds. The reader

may wonder about the robustness of our results with re-gard to the data composition. One direction for investi-gating the robustness of the results is that of exploitingthe cross-section of bonds. In fact, the liquidity of bondswith different maturities could relate to the CDS spreadof corresponding maturity in different ways: Prices ofshort-term bonds are less sensitive to changes in creditrisk and, similarly, their relevance for inventory con-cerns and VaR considerations should be mitigated bytheir short time-to-maturity. To characterize the hetero-geneity of the effect of credit risk on market liquiditywith respect to bond maturity, we split the bonds intodifferent maturity groups and investigate whether i) theeffects of credit risk on liquidity are smaller for shortermaturity bonds and ii) our main results hold similarlyfor all maturity groups.26

We consider 11 maturity buckets, based on the classi-fication used by Cassa Compensazione e Garanzia whensetting margins. Bonds are grouped together daily ifthey have the following time-to-maturity: from 0 to 1month, from 1 to 3 months, from 3 to 9 months, from9 months to 1.25 years, from 1.25 to 2 years, from 2to 3.25 years, from 3.25 to 4.75 years, from 4.75 to 7years, from 7 to 10 years, from 10 to 15 years, and fi-nally from 15 to 30 years. We calculate a liquidity mea-sure per group-day by averaging the bid-ask spreads ofthe bonds in each group. For each day, we interpolatethe CDS spread curve provided by Markit for the Italiansovereign entity and extract, per each maturity bucket,the CDS spread for a contract that has maturity equalto the average between the lower and higher maturityboundaries, e.g., we interpolate the CDS curve, obtainthe spread for the 4-year maturity contract and attributeit to the bucket including bonds with 3.25 to 4.75 yearsto maturity. Due to the lack of a CDS spread estimatefor maturities below 3 months, we drop the observationsfor the first two groups. Table 6 reports the average bid-ask spread and CDS spread, together with the correla-tions between changes in the two variables, for eachmaturity group. The illiquidity measure is decreasingin time-to-maturity, with the exception of the 10-yearbenchmark bonds in group 9.

INSERT TABLE 6 HERE

Panel (a) of Figure 10 reports the evolution of the(log-) bid-ask spreads for the nine remaining maturitybuckets from July 1, 2010 to December 2012, whilePanel (b) reports the term structure of (log-) CDS spread

26We thank the anonymous referee for suggesting we pursue thisdirection in our analysis.

18

for the nine corresponding maturities. Figure 11 showsthe margin evolution for each maturity bucket. Panel (a)of Figure 10 shows that the liquidity series for differentmaturities comoved to a very large extent, and so did theCDS spreads in Panel (b). Moreover, when the 5-yearCDS contract reached 500 bp (6.215 on the y-axis), theterm structure became flat, so that all CDS contracts ex-hibited a spread above 500 bp, regardless of their matu-rity. That is exactly the time when the clearing housesraised their margins for all maturities, as shown in Fig-ure 11.

INSERT FIGURES 10 AND 11 HERE

We first perform a pooled OLS panel regression cor-responding to Equation (5), with the changes in the bid-ask spreads for maturity group g on day t, ∆BAg,t, as thedependent variable and changes in CDS contracts formaturity g on day t, ∆CDS g,t, as regressors, allowingthe coefficients to differ across maturities:

∆BAg,t = α +

3∑i=1

αi∆BAg,t−i + β0g∆CDS g,t

+ β1g∆CDS g,t−1 + β2∆CCBS S t

+ β3US AVIXt + εt. (7)

The results for Equation (7) are reported in Table 7Panel A. The table shows that the changes in the bid-ask spread for all the maturities are positively related tochanges in the CDS contracts with one lag, so that theresults for the average of the bid-ask spread reportedabove are confirmed. Moreover, the coefficients are in-creasing with maturities up to the 8th bucket, so that theeffects of credit risk on illiquidity are smaller for shortermaturities. However, the parameters for longer maturi-ties are decreasing. At least for bucket 9, we can at-tribute this effect to the fact that the 10-year bond is themost liquid bond, and has a lower bid-ask spread thanthe other maturities, while instead the term structure ofCDS has a positive slope most of the time.

INSERT TABLE 7 HERE

We investigate whether the result regarding thethreshold level of 500 bp for the 5-year CDS contractCDS t is confirmed, when we allow maturity groups tohave different sensitivities to their corresponding CDS

spread. We thus estimate Equation (8):

∆BAg,t = α +

3∑i=1

αi∆BAg,t−i

+ I[CDS t < γ

] (β0g∆CDS g,t + β1g∆CDS g,t−1

)+ I

[CDS t > γ

] (β0g∆CDS g,t + β1g∆CDS g,t−1

)+ β2∆CCBS S t + β3US AVIXt + εt. (8)

The test statistic for the presence of the threshold hasan estimate of 78.9 and is significant at the 1% level.Figure 12 shows that the results regarding the shift inthe relation between the bid-ask and CDS spread, whenthe CDS spread crosses 500 bp, is confirmed. There-fore, the threshold effect we find for the market-widebid-ask spread measure is the same for all maturities, asexpected given that the term structure of the CDS spreadis flat above 500 bp and all margins change significantlywhen the CDS cross the 500 bp level.27

The results of the panel regression for the subsam-ples in which the 5-year CDS spread is above and be-low 500 bp are reported in Table 7 Panel B. The resultsconfirm those obtained in the previous sections for themarket-wide bid-ask spread measure: below 500 bp, therelation with the lagged changes in the CDS is positiveand significant, while when the CDS spread is abovethe threshold it is the contemporaneous change in creditrisk that is significant. In summary, our main resultshold when we group bonds in maturity buckets, provid-ing robustness to the main results of the paper.

7.2. Results for Different Liquidity Measures

In the main body of the paper, we conducted the anal-yses focusing on a single measure for the (il)liquidity ofthe bond market, the Bid-Ask Spread, since it is both themost familiar and most indicative of market conditions.As a final robustness effort, and since there is no con-sensus in the academic or policy-making literatures re-garding the best metrics for assessing the liquidity of anasset, using a shorter data set, we repeat our regressionsfor the other liquidity measures that have been used ex-tensively in the literature. We establish, in Section Int.8of the internet appendix, that our results are robust tothe choice of liquidity measure.28

27In Section Int.6 of the internet appendix we estimate Equation (8)separately for each maturity group, i.e., we estimate Equation (6) foreach maturity bucket, and we show that the same threshold is presentin all maturity buckets.

28The bid-ask spread is correlated by more than 60% with otherliquidity variables, making it an appropriate representation of market

19

8. Conclusion

The sovereign debt crisis in the Euro-zone has beenthe most important development in the global economyin the past five years. The crisis stemmed from both liq-uidity and credit risk concerns in the market and led toa sharp spike in CDS and sovereign bond yield spreadsin late 2011, particularly in the Euro-zone periphery. Itwas only after the launch of the LTRO program and af-ter Mario Draghi’s “whatever it takes” comment in July2012 that the market’s alarm diminished: CDS spreadsand sovereign bond yields had dropped to sustainablelevels in most Euro-zone countries by late 2012. Hence,there is no doubt, prima facie, that the ECB programswere a crucial factor in, at least partially, abating thecrisis.

These events provide us with an unusual laboratoryin which to study how the interaction between creditrisk and illiquidity played out, in a more comprehen-sive framework than has been used in previous studiesof corporate or other sovereign bond markets, for thereasons we highlighted in the introduction. We investi-gate several hypotheses about the main drivers of the dy-namic relation between credit risk and market liquidity,controlling for global systemic factors and funding liq-uidity. We conclude that credit risk was one of the maindriving forces in determining the liquidity of the bondmarket, based on a Granger-causality analysis aimed atinvestigating whether liquidity risk drives credit risk orvice versa. We verify the robustness of our results bytesting the same hypothesis in a panel-data setting, andby repeating the analysis using other liquidity measures.In addition to the specific Italian sovereign risk, otherglobal factors such as the USVIX and the funding liq-uidity measure CCBSS are relevant to the dynamics ofmarket liquidity.

A second important finding is that, prior to ECB in-tervention, the relation between credit risk and marketliquidity was strong, and depended not simply on thechanges in credit risk, but also on the level of creditrisk. Using an econometric methodology that allows usto identify the threshold above which the relation is al-tered, we estimate that this level corresponds to a CDSspread of 500 bp. This break point of 500 bp is em-ployed in the setting of margin requirements, which fun-damentally alters the relation between changes in creditrisk and market liquidity. We link our findings to thegrowing literature on funding liquidity, providing a fit-ting example of the Brunnermeier and Pedersen (2009)

liquidity. Pelizzon, Subrahmanyam, Tomio, and Uno (2013) studyseveral liquidity proxies in the context of the cross-section of the Ital-ian sovereign bonds.

theoretical prediction on the effect of funding liquidityon market liquidity.

We also examine the improvement in market liquid-ity following the intervention by the ECB. Our analysisindicates that there is a clear structural break followingthe allotment and settlement of the LTRO on December21, 2012. Remarkably, the data show that, following theECB intervention, the improvement in funding liquidityavailable to the banks strongly attenuated the dynamicrelation between credit risk and market liquidity. Al-though the CDS spread breached the 500 bp mark andmargins were raised once again, market liquidity andthe relation between credit risk and market liquidity didnot change significantly between the regimes below andabove this level. Actually, the only variable that still hasan impact on market liquidity after the ECB interventionis the global funding liquidity variable, CCBSS. Thus,the ECB intervention not only vastly improved the fund-ing liquidity of the market, but also substantially loos-ened the link between credit risk and market liquidity.

Our results will be of interest to the Euro-zone na-tional treasuries, helping them to understand the dy-namic nature of the relation between credit risk, fundingliquidity, and market liquidity, which has strong conse-quences for the pricing of their issues in the auctionsas well as in secondary markets. The ECB may alsoderive some insights from our analysis that could helpthem to better understand the impact of the unconven-tional instruments of new monetary policy. Apart fromtargeting both funding and market liquidity, the centralbank ought also to focus on the market’s perceptions ofsovereign credit risk.

20

Appendix A: The Model

In this Appendix, we present our theoretical model indetail and make explicit the steps leading to the resultsreported in Section 3. In our model, the market maker(dealer) has an investment account, holding other secu-rities, and a trading account, holding the bond in whichshe is making a market. At time t, the initial wealth W0is split between the investment account and the tradingaccount, while the remainder, when positive, is investedin the risk free rate.29 If the dealer does not trade duringthe period, at the end of the time interval t to t + 1, theterminal wealth of her initial portfolio will be

WI =W0k (1 + rM) + I (1 + r)

+ (W0 (1 − k) − (1 − MI) I)(1 + BI + r f

),

where k is the fraction of her wealth invested in her pre-ferred portfolio with (expected) return rM (rM), I is thetrue dollar value of current inventory of the stock with(expected) net return r (r) and variance σ2, r f is the(net) risk free rate over the interval. In this appendix,we make use of indicator functions to simplify the ex-position, so that BI = bi(W0 (1 − k) − (1 − MI) I < 0),where i is the indicator function, equals b > 0 (0), whenthe cash position W0(1−k)− (1 − MI) I is negative (pos-itive), due to borrowing costs, and MI = mi(I < 0), dueto margins. All returns are assumed to be normally dis-tributed. The borrowing rate is higher than the lendingrate and equal to rb = r f + b.

To better understand the wealth equation, let us con-sider the following examples (the chosen parameters be-ing rM = 10%, r f = 5%, γ = 1, σ2

M = 1, W0 = 1000,k =

rM−r f

γW0σ2M

= 5%1000 = 0.005%):

Case 1: I = 500 is invested in the inventory. The mar-ket maker is long in the bond, and so no marginshave to be taken into consideration; moreover, hertotal cash position is positive, and hence no bor-rowing is needed.

WI =1000 · k · (1 + rM) + 500 · (1 + r)︸︷︷︸Inventory position

+

(1 − k) 1000 − 500︸︷︷︸Cash paid

to the customer

· (1 + 5%)

29We do not use the time subscript, t, in the following, to avoidclutter in the notation.

Case 2: I = 1500 is invested in the inventory. She islong in the bond, so no margins have to be takeninto consideration, however her total cash positionis negative, so she needs to borrow at the cen-tral bank’s lending facilities, where she pledges thebond as collateral. There, she can borrow the fullamount, but, however, she will have to pay an in-terest rate rb = r f + b > r f

WI =1000 · k · (1 + rM) + 1500 · (1 + r)︸︷︷︸Inventory position

+

(1 − k) 1000 − 1500︸︷︷︸Cash paid

to the customer

· 1 + b + 5%︸︷︷︸

Cost of borrowing

Case 3: I = −500, and thus, she is short 500 worthof the bond. She adds to her cash position(1 − m) 500, because of her short position in thebond (inventory). She borrows the bond at a costthat is a fraction m of the face value.

WI =1000 · k · (1 + rM) − 500 · (1 + r)︸︷︷︸Inventory position

+

(1 − k) 1000 +

Cash receivedfrom the customer︷︸︸︷

500− m500︸︷︷︸

Cost of borrowing the specificbond, paid upfront

· (1 + 5%) .

The dealer trades so that her expected utility from main-taining the time-0 portfolio, or trading the dollar quan-tity Q, are equal, with the post trading wealth being

WI+Q =W0k (1 + rM) + (I + Q) (1 + r)

+(W0 (1 − k) −

(1 − MI+Q

)(I + Q)

)·(1 + BI+Q + r f

)+ C

(1 + r f

),

where C is the dollar cost of entering into this trans-action, and the last term includes the cost of carry-ing the inventory (profit from borrowing out) in caseof a buy (sell) trade. These costs can be positive ornegative, depending on whether the trade in the stockraises or lowers the dealer’s inventory holding costs, andessentially capture the dealer’s exposure cost of hold-ing a non-optimal portfolio. The indicator functionsBI+Q = bi(W0 − kW0 −

(1 − MI+Q

)(I + Q) < 0) and

MI+Q = mi(I + Q < 0) serve the same purpose of BI and

21

MI . She will trade if

E [U (WI)] = E[U

(WI+Q

)]. (9)

The market maker is assumed to have a constant abso-lute risk-aversion utility function U(x) = −e−γx. Themarginal condition in Equation (9) implies that the rel-ative cost of trading for a quantity Q is

CQ

Q=γ(

Q2 + I

)σ2 − (1 + r) + γkW0σiM

1 + r f

+IQ

(1 − MI+Q

) 1+BI+Q+r f

1+r f

− (1 − MI)1+BI+r f

1+r f

+

W0

Q(1 − k)

BI − BI+Q

1 + r f

+(1 − MI+Q

) 1 + BI+Q + r f

1 + r f,

where σiM = COV [rM , r] is the covariance between thebond and the market returns. We add the subscript inCQ to highlight the dependence of C on Q. The dealerchooses k optimally so that, when I = 0, ∂WI

∂k = 0, or

k =rM−r f

γW0σ2M.30 The choice of k, together with the mean-

variance capital asset pricing model (CAPM) portfolioequilibrium condition r − r f =

(rM − r f

)σiM

σ2M

, allows us

to rewrite CQ

Q as

CQ

Q=γ(

Q2 + I

)σ2 −

(1 + r f

)1 + r f

+IQ

(1 − MI+Q

) 1+BI+Q+r f

1+r f

− (1 − MI)1+BI+r f

1+r f

+

W0

Q(1 − k)

BI − BI+Q

1 + r f

+(1 − MI+Q

) 1 + BI+Q + r f

1 + r f.

The relative bid ask spread for a dollar quantity |Q| >0 is the summation (since they are signed quantities) be-tween buying a stock from the market maker at the askprice −|Q| + C−|Q| (i.e., the price at which the marketmaker sells |Q|), and selling it at the bid price |Q|+C+|Q|,

30We follow Stoll (1978) and assume that the market maker choosesthe fraction of her wealth invested in the market portfolio before build-ing an inventory.

so that the relative bid-ask spread becomes

−|Q| + C−|Q| + |Q| + C+|Q|

|Q|

=C+|Q| + C−|Q|

|Q|=

C+|Q|

|Q|−

C−|Q|−|Q|

.

We restrict our attention to the case when the marketmaker incurs costs both when she accumulates a longand a short position, i.e., BI+|Q| = b, BI−|Q| = BI = 0 andMI−|Q| = m, MI+|Q| = MI = 0. Moreover, we assumethat I = 0, and the two components of the relative bid-ask spread for a quantity |Q| become

C+|Q|

|Q|=

γ |Q|2 σ2 −

(1 + r f

)−

W0|Q| (1 − k) b + 1 + b + r f

1 + r f

=γ |Q|2 σ

2

1 + r f+

b1 + r f

|Q| −W0 (1 − k)|Q|

C−|Q|− |Q|

=

γ−|Q|2 σ2 −(1 + r f

)+ (1 − m)

(1 + r f

) 1 + r f

= −γ |Q|2 σ

2

1 + r f− m.

Finally, the absolute bid-ask, calculated as the relativebid-ask spread for purchasing a quantity Q = p0 multi-plied by the price of the bond p0, is

BA =γp2

0σ2

1 + r f+ mp0 + b

p0 −W0 (1 − k)1 + r f

. (10)

The Option

Since the default of a sovereign is, at least partly, apolitical decision, we take the approach of looking atthe underlying process as merely that, rather than an en-dogenous choice of the “equity holders”. We can thinkof a CDS contract as sort of an event-triggered put op-tion written on the sovereign bond.31 Brennan (1979)and Stapleton and Subrahmanyam (1984) show that asufficient condition for a risk-neutral valuation of a con-tingent claim when the price of the underlying assetis assumed to be normally distributed is that the util-ity function of the representative investor be exponen-tial (Theorem 6). Therefore, the price of a put optionwith strike k at time t, if the price of the underlying pis normally distributed N(p, σ2

p), with p = p0(1 + r),

31This is not literally correct, given that the CDS is triggered byan event, rather than by exercise at expiration, but is useful here as asimplification, to avoid the need to model the default intensity process

22

p = p0(1 + r), and σ2p = p2

0σ2, would be

CDS =1

1 + r f

+x∫−∞

(x − p)1

σp√

2π

· exp− 1

2σ2p

(p −

(1 + r f

)(1 − m) p0

)2 dp

and, with a change of variable to z =p−(1+r f )(1−m)p0

σp

CDS =

x −(1 + r f

)(1 − m) p0

1 + r f

· N

x −(1 + r f

)(1 − m) p0

σp

+

σp

1 + r fn

x −(1 + r f

)(1 − m) p0

σp

,where N and n are the cumulative and standard normaldistribution functions, respectively.

If we consider a margin-adjusted at-the-money putoption, i.e., one such that x =

(1 + r f

)(1 − m) p0, the

CDS price formula simplifies to CDS =σp01+r f

n (0), sothat the market maker extracts the volatility from theCDS market according to a simple linear approach:

σ =(1 + r f

) CDSp0n (0)

. (11)

Empirical PredictionsRe-writing the absolute bid ask spread in Equation

(10) as a function of the CDS price, and plugging Equa-tion (11) into 10, we obtain the relation between the de-pending variable of interest, the bid-ask spread, and itsdeterminants, the CDS spread, and the policy quantitiesset by clearing houses and the central bank:

BA(CDS ) = δCDS 2 + m (b,CDS ) p0 + bη, (12)

where γ(1+r f )n(0)2 = δ > 0 and p0−W0(1−k)

1+r f= η > 0 and,

where, realistically, we allow the margin setting deci-sion by the clearing house to depend on both the level ofthe CDS spread and the borrowing rate set by the centralbank.32,33 From Equation (12), we obtain the followingempirical predictions, which we discuss in Section 3.1:

32We refer to CDS price, in the theoretical section, and CDS spread,in the rest of the paper, interchangeably.

33The second inequality follows from the assumption that the mar-ket maker borrows the funds necessary to buy a bond by pledging

Empirical Prediction 1. The illiquidity of the bondmarket increases with credit risk.



An Implicit Formulation

Similar implications can be derived from Equation(10) even without the assumption that the market makeruses the simple linear approach in Equation (11). Indi-cating the relation between the CDS price and the returnvolatility that is extracted from it byσ2(CDS ), Equation(10) becomes

BA =γp2

0

1 + r fσ2 (CDS ) + m (b,CDS ) p0 + bη

and the same empirical predictions follow.

the latter at the central bank. That is, BI+|Q| = b, meaning that(1 − k)W0 − (1 − MI+|Q|)(I + |Q|)) < 0, which corresponds to theinequality, when we assume that I = MI+|Q| = 0, and that the tradeoccurs for a quantity |Q| = p0.

23

Appendix B: Methodological Appendix

Threshold AnalysisIn empirical settings, a regression such as the OLS

specification yi = β′xi + ei, where yi is the dependentvariable that is regressed on the independent variable xi,is often repeated for subsamples, either as a robustnesscheck or to verify whether the same relation applies toappropriately grouped observations. The sample split isoften conducted in an exogenous fashion, thus dividingthe data according to the distribution of a key variable,such as size and book-to-market quantile portfolios ina Fama-French (1993) setting. Hansen (1996, 2000)develops the asymptotic approximation of the distribu-tion of the estimated threshold value γ, when the samplesplit, based on the values of an independent variable qi,can be rewritten as

Y = Xθ + Xγδ + e where Xγ = XI(q ≤ γ)

or yi = θ′xi + δI(qi ≤ γ)xi + ei, where I(qi ≤ γ) equals 1if qi ≤ γ, and 0 otherwise. He shows that, under a set ofregularity conditions, which exclude time-trending andintegrated variables, the model can be estimated by leastsquares, minimizing S S Rn(θ, δ, γ) = (Y−Xθ−Xγδ)′(Y−Xθ − Xγδ).34 Concentrating out all parameters but γ,i.e. expressing them as functions of γ, yields S n(γ) =

S S Rn(θ(γ), δ(γ), γ) = Y ′Y − Y ′X∗γ(′X∗γ′X∗γ)−1X∗γ

′Y withX∗γ =

[X Xγ

]. The parameters θ and δ are formulated

as functions of γ, and the sum of squared residuals de-pends exclusively on the observed variables and on γ.Thus, the value of γ that minimizes S n(γ) is its leastsquares estimator γ, and the estimators of the remainingparameters θ(γ) and δ(γ) can be calculated.

When there are N observations, there are at most Nvalues of the threshold variable qi, or equivalently Nvalues that the S S R(γ) (step-)function can take. Afterre-ordering the values qi in (q(1), q(2), ...q(N)), such thatq( j) ≤ q( j+1), the method is implemented by

1. estimating by OLS yi = θ′2xi + δI(q ≤ q( j))xi + ei

(or equivalently, when all parameters are allowed todepend on the threshold, estimating separately yi =

θ′1xi + e1i where qi ≤ q( j) and yi = θ′2xi + e2i whereqi > q( j)),

2. calculating the sum of squared residuals,S S R(q( j)) =

∑ei (or =

∑e1i +

∑e2i),

3. repeating 1 and 2 with q( j+1),

34A theory for the latter case was developed in Caner and Hansen(2001).

4. finding the least squares estimate of γ as γ =

arg minq( j)S (q( j)), and

5. repeating the estimation of the equations on thesubsamples defined by the γ threshold, calculatingheteroskedasticity-consistent standard errors for theparameters.

As suggested by Hansen (1999), we allow each equa-tion to contain at least 20% of the observations, and,to minimize computing time, we search only through0.5%-quantiles. Although Hansen (1999) presents anextension of the procedure to several thresholds, we fo-cus in this paper on a single sample split.

To test the presence of the threshold, thus testingwhether θ1 = θ2, the usual tests cannot be used, sinceγ is not identified under the null hypothesis. This isknown as the “Davies’ Problem”, as analyzed by Davies(1977, 1987). Hansen (1996) provides a test whoseasymptotic properties can be approximated by bootstraptechniques.

To provide confidence intervals for the threshold esti-mate γ, Hansen (2000) argues that no-rejection regionsshould be used. To test γ = γ0, the likelihood ratio testcan be used such that LR(γ) = (S S R(γ) − S S R(γ))/σ2,where σ2 = S S R(γ)/N is the estimated error variance,will be rejected if γ is sufficiently far from γ, i.e., the teststatistic is large enough. In its homoskedastic version,the test has a non-standard pivotal distribution, such thatthe test is rejected at an α-confidence level if LR(γ) >−2 ln(1 −

√α). In this paper, we choose α = 0.95, con-

sistent with Hansen (2000); thus, the null hypothesis isconsidered rejected if LR(γ) >= −2 ln(1 −

√0.95) =

7.35. This level is plotted as a horizontal line in theplots of the test. The confidence interval for the thresh-old will be [γL, γU], such that LR(γ |γ < γU ) > 7.35,and LR(γ |γ > γU ) > 7.35, or, graphically, the portionof the x-axis in which the plot of the test is below the7.35 horizontal line.

Structural Break Tests

The Chow test is a standard break point analysisused widely in the economics literature. Based on twonested regressions, it follows an fk,T−2k-distribution andits statistic is

F =(S S R0 − S S R1)/k

S S R1/(T − 2k).

where S S R0 and S S R1 are the sum of squared resid-uals of the restricted regression, yt = x′tβ + εt (witht = 1, ...,T ), and the unrestricted regression, yt =

24

x′tβ + gt x′tγ + εt , respectively. In the unrestricted re-gressions, the observations following the break point t∗,selected by the dummy variable gt (such that gt = 1 ift < t∗ ≤ T and 0 otherwise), are allowed to depend onxt through the composite parameters β + γ, while theprevious observations depend on xt through β only. Therestriction γ = 0 thus imposes the condition that all yt

depend on xt in a homogeneous fashion.35

A drawback of the Chow test is that the breakpointhas to be specified exogeneously. The Chow test hasa null hypothesis, which is that the parameters after aspecific date are equal to those that generated the databefore the break date. The alternative hypothesis is thatthe two sets of parameters are indeed different. How-ever, a test statistic can be calculated from the statisticsresulting from the Chow test, the Fs, to test whethera structural break took place at an unknown date. Af-ter the F-statistics have been computed for a subset ofdates, e.g., all the dates in the sample except for the firstand last i%, several test statistics can be calculated fromthem.

Andrews (1993) and Andrews and Ploberger (1994)show that the supremum and the average, respectively,of the F-statistics converge to a pivotal non-standarddistribution, depending on the number of parameterstested and the relative number of dates tested. The teststatistics that we calculate to test for a structural breakat an unknown date are therefore

supF = supt

Ft

aveF =

∑t Ft

T,

where the Ft are found using the Chow test estimation.We then compare the supF and aveF test statistics withthe corresponding confidence levels, that can be foundin Andrews (2003), which rectified those tabulated inAndrews (1993), and Andrews and Ploberger (1994).

35We exclude the first and last 10% of the observations, in order toestimate meaningful regressions.

25

References

Acharya, V. V., Steffen, S., 2015. The greatest carry trade ever? Un-derstanding Eurozone bank risks. Journal of Financial Economics115 (2), 215–236.

Andrews, D. W., 1993. Tests for parameter instability and structuralchange with unknown change point. Econometrica 61 (4), 821–856.

Andrews, D. W., 2003. Tests for parameter instability and structuralchange with unknown change point: A corrigendum. Economet-rica 71 (1), 395–397.

Andrews, D. W., Ploberger, W., 1994. Optimal tests when a nui-sance parameter is present only under the alternative. Economet-rica 62 (6), 1383–1414.

Augustin, P., Subrahmanyam, M. G., Tang, D. Y., Wang, S. Q., 2014.Credit default swaps: a survey. Foundations and Trends in Finance9.

Baba, N., 2009. Dynamic spillover of money market turmoil from FXswap to cross-currency swap markets: evidence from the 2007–2008 turmoil. The Journal of Fixed Income 18 (4), 24–38.

Baba, N., Packer, F., Nagano, T., March 2008. The spillover of moneymarket turbulence to FX swap and cross-currency swap markets,BIS Quarterly Review.

Bai, J., Julliard, C., Yuan, K., 2012. Eurozone sovereign bond crisis:liquidity or fundamental contagion, Federal Reserve Bank of NewYork Working Paper.

Bank of Italy, 2012. Financial stability report, 3.Bao, J., Pan, J., Wang, J., 2011. The illiquidity of corporate bonds.

The Journal of Finance 66 (3), 911–946.Beber, A., Brandt, M. W., Kavajecz, K. A., 2009. Flight-to-quality

or flight-to-liquidity? Evidence from the euro-area bond market.Review of Financial Studies 22 (3), 925–957.

Bessembinder, H., Maxwell, W., 2008. Transparency and the corpo-rate bond market. The Journal of Economic Perspectives 22 (2),217–234.

Boissel, C., Derrien, F., Ors, E., Thesmar, D., 2014. Systemic risk inclearing houses: evidence from the European repo market, HECParis Working Paper.

Brennan, M. J., 1979. The pricing of contingent claims in discretetime models. The Journal of Finance 34 (1), 53–68.

Brenner, M., Subrahmanyan, M. G., 1988. A simple formula to com-pute the implied standard deviation. Financial Analysts Journal44 (5), 80–83.

Brunnermeier, M. K., 2009. Deciphering the liquidity and creditcrunch 2007–2008. The Journal of Economic Perspectives 23 (1),77–100.

Brunnermeier, M. K., Nagel, S., Pedersen, L. H., 2008. Carry tradesand currency crashes, National Bureau of Economic ResearchWorking Paper.

Brunnermeier, M. K., Pedersen, L. H., 2009. Market liquidity andfunding liquidity. Review of Financial studies 22 (6), 2201–2238.

Caner, M., Hansen, B. E., 2001. Threshold autoregression with a unitroot. Econometrica 69 (6), 1555–1596.

Chakravarty, S., Sarkar, A., 1999. Liquidity in US fixed income mar-kets: a comparison of the bid-ask spread in corporate, governmentand municipal bond markets. Federal Reserve of New York Staff

Report (73).Chow, G. C., 1960. Tests of equality between sets of coefficients in

two linear regressions. Econometrica 28 (3), 591–605.Coluzzi, C., Ginebri, S., Turco, M., 2008. Measuring and analyzing

the liquidity of the Italian treasury security wholesale secondarymarket, Universita degli Studi del Molise Working Paper.

Corradin, S., Maddaloni, A., 2015. The importance of being special:repo markets during the crisis, European Central Bank WorkingPaper.

Corradin, S., Rodriguez-Moreno, M., 2014. Limits to arbitrage: em-pirical evidence from Euro area sovereign bond markets, EuropeanCentral Bank Working Paper.

Darbha, M., Dufour, A., 2013. Measuring Euro area government bondmarket liquidity and its asset pricing implications, University ofReading Working Paper.

Davies, R. B., 1977. Hypothesis testing when a nuisance parameter ispresent only under the alternative. Biometrika 64 (2), 247–254.

Davies, R. B., 1987. Hypothesis testing when a nuisance parameter ispresent only under the alternative. Biometrika 74 (1), 33–43.

Dick-Nielsen, J., Feldhutter, P., Lando, D., 2012. Corporate bond liq-uidity before and after the onset of the subprime crisis. Journal ofFinancial Economics 103 (3), 471–492.

Dufour, A., Nguyen, M., 2012. Permanent trading impacts and bondyields. The European Journal of Finance 18 (9), 841–864.

Dufour, A., Skinner, F., 2004. MTS time series: market and data de-scription for the European bond and repo database, University ofReading Working Paper.

Edwards, A. K., Harris, L. E., Piwowar, M. S., 2007. Corporate bondmarket transaction costs and transparency. The Journal of Finance62 (3), 1421–1451.

Engle, R., Fleming, M. J., Ghysels, E., Nguyen, G., 2011. Liquidityand volatility in the US treasury market: Evidence from a new classof dynamic order book models, Federal Reserve Bank of New YorkWorking Paper.

Ericsson, J., Renault, O., 2006. Liquidity and credit risk. The Journalof Finance 61 (5), 2219–2250.

Eser, F., Schwaab, B., 2013. Assessing asset purchases within theECB’s securities markets programme, European Central BankWorking Paper.

Fama, E. F., French, K. R., 1993. Common risk factors in the returnson stocks and bonds. Journal of Financial economics 33 (1), 3–56.

Favero, C., Pagano, M., von Thadden, E.-L., 2010. How does liquidityaffect government bond yields? Journal of Financial and Quantita-tive Analysis 45, 107–134.

Feldhutter, P., 2012. The same bond at different prices: identifyingsearch frictions and selling pressures. Review of Financial Studies25 (4), 1155–1206.

Fleming, M. J., 2003. Measuring treasury market liquidity. Economicpolicy review 9 (3).

Fleming, M. J., Mizrach, B., 2009. The microstructure of a US trea-sury ECN: the BrokerTec platform, Federal Reserve Bank of NewYork Staff Report.

Fleming, M. J., Remolona, E. M., 1999. Price formation and liquidityin the US treasury market: The response to public information. TheJournal of Finance 54 (5), 1901–1915.

Friewald, N., Jankowitsch, R., Subrahmanyam, M. G., 2012a. Illiq-uidity or credit deterioration: A study of liquidity in the us cor-porate bond market during financial crises. Journal of FinancialEconomics 105 (1), 18–36.

Friewald, N., Jankowitsch, R., Subrahmanyam, M. G., 2012b. Liquid-ity, transparency and disclosure in the securitized product market,New York University Working Paper.

Ghysels, E., Idier, J., Manganelli, S., Vergote, O., 2014. A high fre-quency assessment of the ECB securities markets programme, Uni-versity of North Carolina Working Paper.

Goyenko, R., Subrahmanyam, A., Ukhov, A., 2011. The term struc-ture of bond market liquidity and its implications for expected bondreturns. Journal of Financial and Quantitative Analysis 46 (01),111–139.

Hansen, B. E., 1996. Inference when a nuisance parameter is not iden-tified under the null hypothesis. Econometrica 64 (2), 413–430.

Hansen, B. E., 1997. Approximate asymptotic p values for structural-change tests. Journal of Business & Economic Statistics 15 (1),60–67.

26

Hansen, B. E., 1999. Threshold effects in non-dynamic panels: Es-timation, testing, and inference. Journal of Econometrics 93 (2),345–368.

Hansen, B. E., 2000. Sample splitting and threshold estimation.Econometrica 68 (3), 575–603.

He, Z., Milbradt, K., 2014. Endogenous liquidity and defaultablebonds. Econometrica 82 (4), 1443–1508.

International Monetary Fund, 2013. Italy, technical note on financialrisk management and supervision of Cassa di Compensazione eGaranzia S.p.A., Country Report No. 13/351.

Ivashina, V., Scharfstein, D. S., Stein, J. C., 2012. Dollar fundingand the lending behavior of global banks, National Bureau of Eco-nomic Research Working Paper 18528.

Jankowitsch, R., Nagler, F., Subrahmanyam, M. G., 2014. The deter-minants of recovery rates in the US corporate bond market. Journalof Financial Economics 114 (1), 155–177.

Jankowitsch, R., Nashikkar, A., Subrahmanyam, M. G., 2011. Pricedispersion in OTC markets: A new measure of liquidity. Journal ofBanking & Finance 35 (2), 343–357.

LCH.Clearnet, 2011. LCH.Clearnet margining ap-proach. http://www.ecb.europa.eu/paym/

groups/pdf/mmcg/Item_1_LCH_Margining.pdf?

0fe79f1cef93461dc22566a4e165db44.Lin, H., Wang, J., Wu, C., 2011. Liquidity risk and expected corporate

bond returns. Journal of Financial Economics 99 (3), 628–650.Lutkepohl, H., 1993. Introduction to Multiple Time Series Analysis,

Second Edition. Springer-Verlag.Mahanti, S., Nashikkar, A., Subrahmanyam, M., Chacko, G., Mallik,

G., 2008. Latent liquidity: A new measure of liquidity, with anapplication to corporate bonds. Journal of Financial Economics88 (2), 272–298.

Mancini, L., Ranaldo, A., Wrampelmeyer, J., 2014. The Euro inter-bank repo market, University of St. Gallen Working Paper.

Mesters, G., Schwaab, B., Koopman, S. J., 2014. A dynamic yieldcurve model with stochastic volatility and non-gaussian interac-tions: an empirical study of non-standard monetary policy in theEuro area, Tinbergen Institute Working Paper.

Nashikkar, A., Subrahmanyam, M. G., Mahanti, S., 2011. Liquidityand arbitrage in the market for credit risk. Journal of Financial andQuantitative Analysis 46 (3), 627–656.

Pasquariello, P., Roush, J., Vega, C., 2011. Government interven-tion and strategic trading in the US treasury market. University ofMichigan Working Paper.

Pasquariello, P., Vega, C., 2007. Informed and strategic order flow inthe bond markets. Review of Financial Studies 20 (6), 1975–2019.

Pelizzon, L., Subrahmanyam, M. G., Tomio, D., Uno, J., 2013. Themicrostructure of the European sovereign bond market: a study ofthe Euro-zone crisis, New York University Working Paper.

Stapleton, R. C., Subrahmanyam, M. G., 1984. The valuation of mul-tivariate contingent claims in discrete time models. The Journal ofFinance 39 (1), 207–228.

Stoll, H. R., 1978. The supply of dealer services in securities markets.The Journal of Finance 33 (4), 1133–1151.

Vickery, J. I., Wright, J., 2010. TBA trading and liquidity in theagency MBS market, Federal Reserve Bank of New York Work-ing Paper.

Zhou, X., Ronen, T., 2009. Where did all the information go? Tradein the corporate bond market, Rutgers University Working Paper.

27

http://www.ecb.europa.eu/paym/groups/pdf/mmcg/Item_1_LCH_Margining.pdf?0fe79f1cef93461dc22566a4e165db44



Tables

Table 1: Maturity and Coupon Rate by Maturity Group and Bond Type. This tablepresents the distribution of the bonds in the sample in terms of Maturity and Coupon Rate,by maturity group (Panel A) and bond type (Panel B). Maturity groups were determined bythe time distance between bond maturities and the closest whole year. Our data set, obtainedfrom the Mercato dei Titoli di Stato (MTS), consists of transactions, quotes, and orders forall 189 fixed-rate and floating Italian sovereign bonds (Buoni Ordinari del Tesoro (BOT) orTreasury bills, Certificato del Tesoro Zero-coupon (CTZ) or zero-coupon bonds, Certificatidi Credito del Tesoro (CCT) or floating notes, and Buoni del Tesoro Poliennali (BTP) orfixed-income Treasury bonds) from July 1, 2010 to December 31, 2012.

Panel A

Maturity Group # Bonds Coupon Rate Maturity MinMaturity MaxMaturity

0.25 11 a 0.26 0.21 0.270.50 38 a 0.50 0.36 0.521.00 44 a 1.00 0.81 1.022.00 13 b 2.02 2.01 2.093.00 14 3.38 2.98 2.93 3.025.00 16 3.86 5.02 4.92 5.256.00 15 c 6.71 5.21 7.01

10.00 21 4.54 10.44 10.10 10.5215.00 7 4.59 15.71 15.44 16.0030.00 10 5.88 30.88 30.00 31.79

Panel B

Bond Type N Coupon Rate Maturity MinMaturity MaxMaturity

BOT 93 ZCB 0.71 0.21 1.02BTP 68 4.34 11.12 2.93 31.80CCT 15 Floating 6.71 5.21 7.01CTZ 13 ZCB 2.02 2.00 2.09

a All bonds in this group are BOT, Buoni Ordinari del Tesoro (Treasury bills)b All bonds in this group are CTZ, Certificati del Tesoro Zero-coupon (zero-coupon

bonds)c All bonds in this group are CCT, Certificati di Credito del Tesoro (floating bonds)

1

Table 2: Time-series Descriptive Statistics of the Variables. This table shows the time-series and cross-sectional distribution of various variables defined in Section 4.1, and their correlations. The sample consistsof the quotes and trades from 641 days in our sample for bond market data and end-of-day quotes for theother measures. Quoted Bonds is the number of bonds actually quoted on each day, Trades is the total numberof trades on the day, and Volume is the daily amount traded in e billion on the whole market. The liquiditymeasure Bid-Ask Spread is the difference between the best bid and the best ask. The global systemic variablesare the spread between three-month Euribor and three-month German sovereign yield, the USVIX, and theCross-Currency Basis Swap Spread CCBSS. Our bond-based data, obtained from the Mercato dei Titoli diStato (MTS), consist of transactions, quotes, and orders for all 189 fixed-rate and floating Italian sovereignbonds (Buoni Ordinari del Tesoro (BOT) or Treasury bills, Certificato del Tesoro Zero-coupon (CTZ) or zero-coupon bonds, Certificati di Credito del Tesoro (CCT) or floating notes, and Buoni del Tesoro Poliennali (BTP)or fixed-income Treasury bonds) from July 1, 2010 to December 31, 2012. All other data were obtained fromBloomberg.

Time Series Unit Root Test

Panel A: Market Measures

Variable Mean STD 5th Pct Median 95th Pct Level Difference

Quoted Bonds 88.583 2.430 85.000 88.000 93vTrades 352.158 149.394 145.000 331.000 614.000Volume 2.874 1.465 0.951 2.555 5.647

Panel B: System Variables

Bid-Ask Spread 0.389 0.340 0.128 0.298 1.092 -8.200*** -32.597***Italian CDS 320.748 137.834 149.356 302.026 540.147 -1.469 -19.922***

USVIX 21.212 6.302 15.070 18.970 34.770 -3.951*** -26.790***CCBSS 44.003 18.915 21.100 39.900 79.400 -1.613 -25.969***

Euribor-DeTBill 0.729 0.357 0.264 0.629 1.474 -1.750 -31.843***

Panel C: Correlations

Differences\Levels Bid-Ask Italian USVIX CCBSS EuriborSpread CDS -DeTBill

Bid-Ask Spread 1 0.628 0.440 0.659 0.676Italian CDS 0.224 1 0.318 0.788 0.589

USVIX 0.151 0.334 1 0.511 0.660CCBSS 0.182 0.367 0.233 1 0.842

Euribor-DeTBill 0.049 0.088 0.050 0.054 1

2

Table 3: Results for the Granger-Causality Analysis of the Italian CDS Spread and Bid-Ask Spread. This table presents the results for the regressions of the day t changes in Bid-Ask Spread, ∆BAt, and Italian CDS spread ∆CDS t, on the lagged terms of both variables andon contemporaneous macro variable changes, in a VARX(3,0) setting as shown in Equation(4). The data have a daily frequency. The significance refers to heteroskedasticity-robustt-tests. Heteroskedasticity-robust F-test statistics and their significance are reported for the

null hypothesis of ∆BAt = ∆BAt−1... = 0 ( BAGC−−→ CDS ), and ∆CDS t = ∆CDS t−1... = 0

(CDSGC−−→ BA) respectively. We also report the contemporaneous correlation in the model

residuals. Our data set consists of 641 days of trading in Italian sovereign bonds, from July1, 2010 to December 31, 2012, and was obtained from the MTS (Mercato dei Titoli di Stato)Global Market bond trading system. The CDS spread refers to a USD-denominated, five-yearCDS spread. The CDS spread and the macro variables were obtained from Bloomberg.

Variable ∆BAt ∆CDS t

∆BAt−1 -0.357*** -0.011∆CDS t−1 0.917*** 0.212***∆BAt−2 -0.224*** -0.007∆CDS t−2 -0.069 -0.091*∆BAt−3 -0.174*** -0.004∆CDS t−3 0.117 0.024∆EuriborDeT Billt 0.027 0.035∆CCBS S t 0.545*** 0.213***∆US VIXt 0.334** 0.154***Intercept -0.001 0.001

Adj R2 0.180 0.236

Granger-Causality Tests

BAGC−−→ CDS . 0.476

CDSGC−−→ BA 6.007*** .

Residuals Correlation

∆BAt 1.000 0.107∆CDS t 0.107 1.000

* Significant at a 10% level. ** Significant at a 5% level. *** Significant at a 1% level.

3

Table 4: Results for the Regression of the Bid-Ask Spread on the CDSSpread and Macro Variables. This table presents the results for the regres-sion of the change in the Bid-Ask Spread (the change in the quoted bid-askspread) on day t, ∆BAt, on its lagged terms, and the change in the CDSspread on day t, ∆CDSt, and its lagged terms and on macro variables, us-ing daily data. The regressions are presented in Equations 5 and 6, forPanels A and B, respectively. Parameters multiplying the identity operator[CDS ≤ (>)500] are reported under the [CDS ≤ (>)500] column. The statis-tical significance refers to heteroskedasticity-robust t-tests. The Test columnreports the heteroskedasticity-robust test for the two parameters above andbelow the threshold being equal and distributed as chi-square (1). Our dataset consists of 641 days of trading in Italian sovereign bonds, from July 1,2010 to December 31, 2012, and was obtained from the Mercato dei Titoli diStato (MTS) Global Market bond trading system. The CDS spread refers to aUSD-denominated, five-year CDS spread and macro variables were obtainedfrom Bloomberg.

Variable Panel A Panel BWhole Sample I[CDS≤500] I[CDS>500] Test

∆CDSt 0.541 ** 0.319 2.845*** 11.33***∆CDSt−1 0.794 *** 0.983*** -0.854* 10.75***∆BAt−1 -0.352 *** -0.332***∆BAt−2 -0.216 *** -0.199***∆BAt−3 -0.167 *** -0.164***∆CCBSSt 0.429 *** 0.402***∆USVIXt 0.251 * 0.208*Intercept -0.002 -0.002

Adj R2 0.191 0.219N 637 637

* Significant at a 10% level. ** Significant at a 5% level. *** Significant at a1% level.

4

Table 5: Results for the Regression of the Bid-Ask Spread on the CDSSpread and Macro Variables for Subsamples Based on the StructuralBreak. This table presents the results for the regression of the change in theBid-Ask Spread (the change in the quoted bid-ask spread) on day t, ∆BAt, onits lagged terms, and the change in the CDS spread on day t, ∆CDSt, and itslagged terms, using daily data for the Bid-Ask Spread and the CDS spread.The regressions are presented for Equations 6 and 5 in Panels A and B re-spectively. Parameters multiplying the identity operator [CDS ≤ (>)500]are reported under the [CDS ≤ (>)500] column. The statistical signifi-cance refers to heteroskedasticity-robust t-tests. The Test column reports theheteroskedasticity-robust test results for the two parameters above and belowthe threshold being equal and distributed as chi-square (1). Panel A (B) isbased on the pre-(post-)structural-break sample. Our data set consists of 641days of trading in Italian sovereign bonds, from July 1, 2010 to December 31,2012, and was obtained from the Mercato dei Titoli di Stato (MTS) GlobalMarket bond trading system. The CDS spread refers to a USD-denominated,five-year CDS spread and macro variables were obtained from Bloomberg.

Variable Panel A: 2011 Panel B: 2012I[CDS≤500] I[CDS>500] Test

∆CDSt 0.493 3.877*** 16.21*** 0.064∆CDSt−1 1.028*** -1.491** 11.77*** 0.566**∆BAt−1 -0.261*** -0.501***∆BAt−2 -0.183*** -0.295***∆BAt−3 -0.162*** -0.188***∆CCBSSt 0.310* 0.858***∆USVIXt 0.320** -0.105Intercept 0.002 -0.006

Adj R2 0.233 0.237N 377 260

* Significant at a 10% level. ** Significant at a 5% level. *** Significant at a1% level.

5

Table 6: Descriptive Statics for Bonds Grouped by Maturity. This tablepresents the time-series average of the bid-ask spread for bonds grouped bytheir time to maturity, the time-series average of the CDS spread with match-ing maturity, and the correlation between daily changes in the bid-ask andCDS spreads (contemporaneous, and with a lag). Our data set consists of 641days of trading in Italian sovereign bonds, from July 1, 2010 to December 31,2012, and was obtained from the Mercato dei Titoli di Stato (MTS) GlobalMarket bond trading system. The CDS spread refers to a USD-denominatedCDS spread with maturity matching the average maturity of the bond groupand was obtained from the term structure of the CDS spread provided byMarkit.

Maturity Bid-Ask CDS Contemporaneous LaggedGroup Spread Spread Correlation Correlation

03:3-9m 0.142 201.883 0.108 0.09004:0.75-1.25y 0.198 230.540 0.136 0.13705:1.25-2y 0.282 255.422 0.148 0.16306:2-3.25y 0.337 286.799 0.214 0.15007:3.25-4.75y 0.469 308.557 0.207 0.15508:4.75-7y 0.519 317.945 0.196 0.16709:7-10y 0.495 317.701 0.130 0.14210:10-15y 0.757 315.404 0.121 0.10011:15-30y 0.958 311.923 0.073 0.093

6

Table 7: Results for the Regression of the Bid-Ask Spread on the CDS spread and MacroVariables with Maturity-Specific Coefficients. This table presents the results for the regres-sion of the change in the Bid-Ask Spread for maturity group g on day t, ∆BAg,t, on its laggedterms, and the change in the CDS spread with maturity matching that of group g on day t,∆CDSg,t, and its lagged term and on macro variables, using daily data. The regressions pre-sented in Equations 7 and 8 are used for Panels A and C, and for Panel B, respectively. Parame-ters multiplying the identity operator [CDS ≤ (>)500] are reported under the [CDS ≤ (>)500]column. The statistical significance refers to heteroskedasticity-robust t-tests. The Test columnreports the heteroskedasticity-robust test for the two parameters above and below the thresholdbeing equal and distributed as chi-square (1). Our data set consists of 641 days of trading inItalian sovereign bonds, from July 1, 2010 to December 31, 2012, and was obtained from theMercato dei Titoli di Stato (MTS) Global Market bond trading system. The CDS spread refersto a USD-denominated CDS spread with maturity matching the average maturity of the bondgroup and was obtained from the term structure of the CDS spread provided by Markit.

Variable Panel A Panel B:2011 Panel C:2012Whole Sample I[CDS≤500] I[CDS>500] Test

∆CDS3,t 0.247 0.397* 3.776*** 17.62*** -0.043∆CDS4,t 0.301 0.403* 3.751*** 10.29*** -0.077∆CDS5,t 0.196 0.360 4.085*** 21.32*** -0.443*∆CDS6,t 0.372* 0.422 2.763*** 7.00*** -0.052∆CDS7,t 0.356 0.501 2.344*** 3.85** -0.292∆CDS8,t 0.275 0.288 2.784*** 6.73*** -0.339∆CDS9,t -0.014 -0.146 2.757*** 9.51*** -0.421∆CDS10,t 0.091 0.131 2.827*** 5.57** -0.630*∆CDS11,t -0.106 -0.147 2.374** 4.61** -0.624∆CDS3,t−1 0.437*** 0.745*** -0.227 2.13 0.032∆CDS4,t−1 0.75*** 1.099*** 0.349 0.83 0.169∆CDS5,t−1 0.941*** 1.144*** -0.277 3.61* 0.594***∆CDS6,t−1 0.944*** 1.071*** 0.078 2.53 0.745**∆CDS7,t−1 1.066*** 1.178*** 0.069 2.45 0.939***∆CDS8,t−1 1.197*** 1.521*** -0.004 4.6** 0.711**∆CDS9,t−1 0.954*** 1.225*** 0.291 1.85 0.395∆CDS10,t−1 0.672*** 1.092*** -1.554* 9.06*** 0.351∆CDS11,t−1 0.624** 0.932** -1.221 6.21** 0.486∆BAg,t−1 -0.429*** -0.400*** -0.490***∆BAg,t−2 -0.25*** -0.234*** -0.286***∆BAg,t−3 -0.159*** -0.168*** -0.140***∆CCBSSt 0.652*** 0.515*** 1.026***∆USVIXt 0.315*** 0.302*** 0.142Intercept 0.001 0.003 -0.004

Adj R2 0.190 0.199 0.209N 7007 4147 2860


7

Figures

Inventory Risk

Borrowing Costs

Clearing House

Credit Risk

Funding Rate Margin Framework

Margins

Margin Setting

Central Bank

Market Maker’s Liquidity Provision

Figure 1: The Dynamics of the Theoretical Model. This figure shows the channels through which the players inthe model are affected by credit risk and by each other.

8

Figure 2: Time-Series of Bond Yield, Bond Yield Spread, CDS Spread, and Bid-Ask Spread. The bond yieldspread (dotdash line, left-hand axis) is calculated between the Italian (dotted, left-hand axis) and German bonds withten years to maturity. The CDS Spread (solid, left-hand axis) is the spread for a five-year US-denominated CDScontract. This MTS bid-ask spread (dashed, right-hand axis) is a market-wide illiquidity measure. Our data setconsists of transactions, quotes, and orders for all 189 fixed-rate and floating Italian sovereign bonds (Buoni Ordinaridel Tesoro (BOT) or Treasury bills, Certificato del Tesoro Zero-coupon (CTZ) or zero-coupon bonds, Certificati diCredito del Tesoro (CCT) or floating notes, and Buoni del Tesoro Poliennali (BTP) or fixed-income Treasury bonds)from July 1, 2010 to December 31, 2012. Data for the bond yield, yield spread, and CDS spread were obtained fromBloomberg.

9

(a) 3-Month Euribor-German T-Bill Spreads

(b) USVIX Index

(c) Cross-Currency Basis Swap Spread

Figure 3: Time-Series of Macro variables. The time-series evolution of the global variables: the spread betweenthe three-month Euribor and the three-month yield of the German TBill, the USVIX, and the Cross-Currency BasisSwap Spread are shown in Panels (a), (b), and (c), respectively. Global variables are described in detail in Section4.1. Our data set was obtained from Bloomberg and covers the period from July 1, 2010 to December 31, 2012.

Bid

Ask

Spr

ead

0.0

0.2

0.4

0.6

0.8

1.0

CD

S

0.0

0.2

0.4

0.6

0.8

1.0

0 1 2 3 4 5 6 7 8 9 10

Impulse Response from CDS Spread

95 % Bootstrap CI, 5000 runs

(a) Shock to CDS spread

Bid

Ask

Spr

ead

0.0

0.5

1.0

CD

S

0.0

0.5

1.0

0 1 2 3 4 5 6 7 8 9 10

Impulse Response from Bid Ask Spread


(b) Shock to the bond market liquidity

Figure 4: Impulse Response Functions for the VARX(3,0) System. This graph shows the evolution of the impulseresponse functions (IRFs) following a shock in the CDS spread and the bond market liquidity, as measured by theBid-Ask Spread, in Panels (a) and (b) respectively. The VARX(3,0) system that produces these IRFs is presentedin Equation (4) and discussed in Section 6.1. Our data set consists of transactions, quotes, and orders for all 189fixed-rate and floating Italian sovereign bonds from July 1, 2010 to December 31, 2012.

11

Figure 5: Sum of Squared Residuals as γ Changes. The evolution of the sum of squared residuals (SSR) fromEquation (6) is plotted as the threshold value γ changes. The γ that minimizes SSR (γ) is the estimate for thethreshold. The point at γ = 0 is the SSR for Equation (5), namely the regression with no threshold. Our data setconsists of transactions, quotes, and orders for all 189 fixed-rate and floating Italian sovereign bonds, from July 1,2010 to December 31, 2012.

12

Figure 6: Test to Determine Confidence Bands around the CDS Threshold. The test statistic described inAppendix B is plotted here for Equation (6). The test statistic is normalized at 0 at the threshold that minimizes thesum of squared residuals. The horizontal line at 7.35 marks the 5% confidence values for the threshold. Our data setconsists of transactions, quotes, and orders for all 189 fixed-rate and floating Italian sovereign bonds, from July 1,2010 to December 31, 2012.

13

Figure 7: Time-Series of Margins, CDS Spread, and Bid-Ask Spread. This graph shows the time-series of theaverage of the margins (dotdashed, left axis) set by Cassa Compensazione e Garanzia, a clearing house, on Italianbonds, the spread of a five-year CDS contract (solid, left axis), and the liquidity of the bond market (dashed, rightaxis), as measured by the market-wide bid-ask spread. Our data set consists of transactions, quotes, and orders forall 189 fixed-rate and floating Italian sovereign bonds, from July 1, 2010 to December 31, 2012.

14

Figure 8: Structural Break Test. This figure shows the F-test results for the Chow test performed for Equation

(6) for each day in our sample, excluding the first and last 20% of observations. The horizontal line marks the 10%

level of significance for the largest of the F-test values. Our data set consists of transactions, quotes, and orders for

all 189 fixed-rate and floating Italian sovereign bonds, from July 1, 2010 to December 31, 2012. The CDS data were

obtained from Bloomberg.

15

(a) Threshold Confidence Bands Determination: 2011 Sample

(b) Threshold Confidence Bands Determination: 2012 Sample

Figure 9: Confidence Bands Determination for Two Subsamples. The test statistic described in Appendix

B is plotted here for Equation (6) in Panels (a) and (b) for the subsamples before and after the structural break,

respectively. The test statistic is normalized at 0 at the threshold that minimizes the sum of squared residuals. The

horizontal line at 7.35 marks the 5% confidence values for the threshold.

16

(a) Bid-Ask Spread Evolution and Maturity.

(b) CDS Spread and Maturity.

Figure 10: Bid-Ask Spread, CDS Spread, and Maturity. This figure shows time-series of the log of the average

bid-ask spread for bonds as a function of maturity and the time-series of the log of the CDS spread for 9 maturities

of the contract, in Panels (a) and (b), respectively. Our data set consists of transactions, quotes, and orders for all 189

fixed-rate and floating Italian sovereign bonds, from July 1, 2010 to December 31, 2012.

17

Figure 11: CDS Spread and Margins for the Cross-Section of Italian Bonds. This figure shows time-series of

the CDS spread for a 5-year contract and the margins applied to different maturity bonds by Cassa Compensazione e

Garanzia.

18

Figure 12: Confidence Bands Determination for the Panel Analysis. The test statistic described in Appendix

B is plotted here for Equation (8). The test statistic is normalized at 0 at the threshold that minimizes the sum of

squared residuals. The horizontal line at 7.35 marks the 5% confidence values for the threshold.

19

Internet Appendix

Int.I Instrumental Variable Analysis

In Section VI, we focused on the bid-ask spread equation of the VAR system, augmenting it with the

contemporaneous changes in the CDS spread. In order to test whether the causality runs one way

or both ways, i.e., whether the variables suffer from contemporaneity, we re-estimate Equation 3 and

test for the endogeneity of ∆CDSt by instrumenting it with several cohorts of variables.

Conditional on the instruments being valid—i.e., strong, exogenous, and relevant—if the Hausman-

Wu test cannot reject the null hypothesis of the ordinary least squares (OLS) and IV estimators being

the same (under the null hypothesis both are consistent), we can conclude that the OLS estimate is to

be preferred in virtue of having a smaller estimator variance. On the other hand, if the Hausman-Wu

test rejects the null hypothesis, only the IV estimator is consistent and hence preferred, regardless of

its larger estimator variance. In this appendix, we will describe our cohorts of instruments, establish

their exogeneity, show that they are strong and relevant, and finally present the IV results, together

with the Hausman-Wu test results.

We have three cohorts of instruments:

• Other European sovereign CDS/bond yields:

– Germany: The German 10-year yield is likely to be correlated with the Italian CDS, presum-

ing that the German sovereign has very little credit risk. In the case of a flight-to-quality,

as the Italian CDS rises, the German yield could plummet due to investors switching from

holding Italian bonds to German bonds. If the change in German yield were perfectly cor-

related with the change in Italian CDS, however, the German yield should not be correlated

with the residuals from Equation 3, since the CDS is on the right-hand side, and hence, it

would constitute a good instrument. If, however, a flight to liquidity depended also on the

relative change in the CDS compared to the yield and the two were not perfectly correlated,

then the instrument would not be exogenous. Nevertheless, we repeat the analysis using the

lagged value of the change in the German bond yield, in order to account for this possible

endogeneity.

– Finland: The flight-to-quality argument applies less stringently for a relatively safer country

with a small bond market. The Finnish sovereign debt amounted to e90 billion during the

period of our study, a small fraction of both the Italian and German outstanding sovereign

debt. Bai, Julliard and Yuan (2012) report that the Finnish bond market has a similar

bid-ask spread to the German and Italian ones, while the trading volume is an order of

magnitude smaller. Moreover, in our sample, the changes in Italian and Finnish CDS

spreads are correlated at the 70% level, while those of Germany and Italy are correlated

at -57%. Hence, the data hardly support a flight-to-quality from Italian to Finnish bonds.

Hence, the change in the Finnish CDS spread qualifies as a valid instrument.

• The CDS of Italian-government-owned/controlled companies significantly comove with the sovereign

CDS (with correlations above 56% in the changes), and moreover, would not constitute a safer

Int 1

security, since a government-owned company would be hit hard if the central government were

to fail, thus disqualifying it from a flight-to-quality or other asset substitution perspective. We

consider all government-owned companies that had a traded CDS spread during our sample

period, namely

– ENI: the national oil and gas company,

– ENEL: the national electricity company,

– Finmeccanica: a large industrial group, specializing in aerospace, defence, and security.

• The European stock market index Euro50 is highly correlated with the Italian CDS spread (-

61%); so, when the crisis mounted for the sovereign, it also pushed the stock market down,

partially due to the presence of some Italian companies in the index. In order for Euro50

to be correlated with the regression residuals – that is partially correlated with bond-market

liquidity, after controlling for the overall worsening of the crisis through the Italian CDS, for

investor sentiment with the VIX, and for the funding liquidity with the CCBSS, there should be

a substitution effect between Italian bonds and Euro50-included companies. We are not aware

of any academic study showing this phenomenon.

Table Int.1 presents the results from the IV estimation, for both the first and the second-stage

regression, in Panels A and B, respectively. First of all, all our instruments are strong, with F -test

results well above 10, the level recommended in Greene (2012), among others. The F -test IV row

presents the F -test results regarding whether the added exogenous variables are contemporaneously

zero. As one might expect, the weakest instrument is the lagged German yield change. However, even

for Model 3, the F -statistic is 29.09 (although only 6.44 for the instrument alone). The adjusted R2

of all the models is very high, supporting our claims of strong instruments.

As shown in Panel B, which presents the results of the second-stage estimations, the Hausmann-Wu

test is not statistically significant for any of the specifications (only marginally so for model 6), thus

supporting the exogeneity of ∆CDSt in Equation 3. Indeed, the parameter estimates are very similar

to those in Table 4 Panel A. The specification with the highest difference in the ∆CDSt parameter (and

thus one of the highest Hausman-Wu tests) is that using only ∆Y ieldDEt−1 as an additional instrument,

which we attribute to the poor predictive power provided by the additional instrument in the first-stage

regression.

Using different sets of IVs, we have shown that ∆CDSt is not endogenous (implying contempo-

raneous feedback effects) in Equation 3. Therefore, we have justified the use of a single equation in

explaining the dynamics of the CDS/bid-ask spread system in the remainder of the paper.

Int 2

Table Int.1: Results for the Instrumental Variable Analysis. This table presents the results for the instrumentalvariable (IV) analysis. The first-stage regressions are presented in Panel A, where ∆CDSt is regressed on the second-stage right-hand-side variables and several combinations of variables exogenous to Equation 3. The significance of theparameters refers to heteroskedasticity-robust t-tests. The F -test row reports the (standard) F -test for the hypothesisthat all regression parameters are contemporaneously 0, while F Test IV reports the F -test for the hypothesis that onlythe parameters of the exogenous variables added to the second-stage variables are contemporaneously equal to 0. PanelB reports the IV estimators of Equation 3 when using different combinations of exogenous variables in the first stage.The Hausmann-Wu test verifies whether the OLS and the IV estimates are significantly different under the assumptionthat both are consistent against the alternative that only the IV set is. Our dataset consists of 640 days of trading inItalian sovereign bonds, from July 1, 2010 to December 31, 2012, and was obtained from the Mercato dei Titoli di Stato(MTS) Global Market bond trading system. The CDS spread refers to a USD-denominated, five-year CDS spread andwas obtained, together with the instrumental and exogenous variables, from Bloomberg.

Panel A: First-Stage Regression

Variable MODEL1 MODEL2 MODEL3 MODEL 4 MODEL5 MODEL6 MODEL7

Intercept 0.000 0.000 0.001 0.000 0.001 0.001 0.000

∆CDSt−1 0.203 *** 0.206 *** 0.138 *** 0.209 *** 0.025 0.179 *** 0.033

∆BAt−1 -0.009 -0.01 -0.015 -0.012 -0.01 -0.009 -0.008

∆BAt−2 -0.004 -0.006 -0.011 -0.009 0.000 -0.007 0.002

∆BAt−3 0.002 0.000 -0.004 -0.003 0.001 0.000 0.003

∆CCBSSt 0.156 *** 0.158 *** 0.211 *** 0.172 *** 0.055 ** 0.129 *** 0.046 **

∆USV IXt 0.055 ** 0.058 ** 0.16 *** 0.085 *** 0.046 ** 0.002 0.000

∆Y ieldDEt -0.996 *** -0.636 *** . . . . -0.448 ***

∆Y ieldFIt 0.482 *** . . -0.653 *** . . 0.155

∆Y ieldDEt−1 . . -0.148 ** . . . -0.065

∆CDSENELt . . . . 0.563 *** . 0.483 ***

∆CDSENIt . . . . 0.101 ** . 0.053

∆CDSFINMECCt . . . . 0.229 *** . 0.214 ***

∆Euro50t . . . . . -1.371 *** -0.091

Adj R-Sq 0.400 0.392 0.236 0.342 0.592 0.387 0.634

F Test 54.016*** 59.555*** 29.09*** 48.144*** 103.557*** 58.268*** 85.694***

F Test IV 90.53*** 169.19*** 6.44** 108.23*** 187.60*** 162.32*** 100.38***

Panel B: Second-Stage Regression

Variable MODEL1 MODEL2 MODEL3 MODEL 4 MODEL5 MODEL6 MODEL7

Intercept -0.007 -0.002 -0.005 -0.002 -0.003 -0.003 -0.003

∆CDSt 0.722* 0.629 3.723 0.436 0.719** 1.299*** 0.748**

∆CDSt−1 0.759*** 0.777*** 0.178 0.814*** 0.759*** 1.647*** 0.754***

∆BAt−1 -0.349*** -0.350*** -0.306*** -0.353*** -0.349*** -0.341*** -0.349***

∆BAt−2 -0.214*** -0.215*** -0.179*** -0.218*** -0.214*** -0.207*** -0.214***

∆BAt−3 -0.166*** -0.166*** -0.156*** -0.167*** -0.166*** -0.164*** -0.166***

∆CCBSSt 0.390** 0.410** -0.244 0.450*** 0.391*** 0.268 0.385***

∆USV IXt 0.222* 0.237* -0.258 0.268* 0.222* 0.130 0.218*

Hausmann-Wu 0.24 0.05 2.65 0.05 0.72 3.79* 1.23


Int 3

Int.II The MTS Datasets and Market Structure

The MTS Datasets

There are four types of database currently offered by MTS. At the highest level, “daily summaries”

including aggregate price and volume information regarding the trading of European bonds are pub-

lished. At the second level, the “trade-by-trade” data including all transactions, stamped at the

millisecond level, are available. However, neither of the two aggregate databases has any information

on the price quotations of the instruments at the dealer, or even the market-wide, level. The pub-

licly available dataset at the third level includes the three best bid and ask prices and the aggregate

quantities offered at those levels. Prior studies, not using the dataset at the third level, are unable

to describe the market in its entirety, as the two dimensions indicating willingness to trade, quotes,

and orders, for primary dealers and dealers respectively, were not available previously. Only actual

trading events are observable in the second-level dataset, and trading intent as a pre-trade measure

cannot be measured. Thus, it is not possible to study liquidity provision, as measured by the dealers’

willingness to trade, as evidenced by their bid and offer quotations, based on this dataset. We use the

third-level dataset from July 2010 to June 2011.

In contrast, the dataset we analyze between June 2011 and December 2012 is at the fourth level

and is by far the most complete representation of the market available, and has been released only

recently. It covers all trades, quotes, and orders that took place on the MTS market between June

1, 2011 and December 31, 2012. Every event is stamped at the millisecond level, and the order IDs

permit us to link each order to the trade that was eventually consummated from it. Every quote, or

“proposal”, in this market can be followed in the database in terms of their “revisions” over time,

thanks to a “single proposal” identifier. We take advantage of the higher detail available in this dataset

in Section Int.VIII of the internet appendix, where we repeat our analysis using alternative liquidity

measures.

Despite the difference in the details contained in the third- and fourth-level databases, calculating a

market-wide bid-ask spread measure leads to very similar values, regardless of the dataset that is used.

We measure the bid-ask spread at a five-minute frequency for each bond, then average it throughout

the day for each bond and then across bonds, to obtain a market-wide measure, separately, for the two

databases. Figure Int.1 shows the bid-ask spread series calculated with the third-level (fourth-level)

dataset in red (blue), for the seven months of overlap of the two datasets. While the two series are

almost always indistinguishable from each other (their correlation is 0.975), differences between them

appear largely when the largest spikes are present in the time series. These spikes, however, were

winsorized in our analysis, after taking first differences.

Int 4

Figure Int.1: Market-Wide Bid-Ask Spread from the High-Frequency and the Three-Best-QuotesDatasets. This figure plots the evolution of the market-wide bid-ask spread obtained from two different datasets(the high-frequency and three-best-quotes datasets) for the overlapping period between June and December 2011. Ourdataset consists of seven months of trading in Italian sovereign bonds, from June 1, 2011 to December 31, 2011, and wasobtained from the Mercato dei Titoli di Stato (MTS) Global Market bond trading system.

Int 5

The MTS Market Structure

Market participants can decide whether they want to trade a sovereign bond on the European

market or on that country’s domestic market. While every Euro-zone bond is quoted on the domestic

markets, only bonds that are issued for an amount higher than a certain threshold can be traded on the

EuroMTS platform. Even though the two markets are not formally linked, most dealers participate

in both venues. The previous literature (Cheung, de Jong and Rindi (2005), Caporale and Girardi

(2011)) has shown that the two markets essentially constitute a single venue.1 Thus, in our analysis,

we consider trading in both markets. The liquidity measures used in this paper do not depend on

where the order placement and trading activity take place.

There are two kinds of trader in the sovereign bond markets, primary dealers and other dealers.

Primary dealers are authorized market-making members of the market. That is, they issue standing

quotes, which can either be single-sided or double-sided, on the bonds they have been assigned. They

indicate the quantity they are willing to trade and the non-negative fraction of that quantity they are

willing to “show” to the market. Primary dealers can be on the passive side, when their proposals are

“hit” or “lifted,” and/or on the active side of the market, when they submit orders aimed at “hitting”

or “lifting” another primary dealer’s standing quote. Primary dealers have market-making obligations

that, in spite of some relaxations that were made after 2007, still require each primary dealer not to

diverge from the average quoted times and spreads calculated among all market makers. In this market,

the event of crossed quotes is guaranteed not to occur, except by chance, since, when the opposite

sides of two proposals cross, a trade takes place for the smaller of the two quoted quantities.2 Other

dealers with no market-making responsibilities can originate a trade only by “hitting” or “lifting”

the primary dealers’ standing quotes with market orders. However, it should be noted that primary

dealers are also on the active side of 96% of the trades present in our database.

1By this we mean that a sell or buy order could “trade-through” a better price if the trader sent the order to themarket with the worse of the bid or ask prices, respectively. However, MTS assures market participants that their tradingplatforms always show quotations from both the domestic and the European market, when available.

2While this is one way for the primary dealers to trade, it seldom happens. Hence, we do not include trades originatingin this manner in our sample.

Int 6

Int.III Yield Spread - CDS Dynamics

In this section, we address the concern that between the CDS spread and the BTP yield spread with

the German sovereign bond counterpart, two alternative measures of credit risk, there exists a lead-lag

relationship or, alternatively, that the credit risk discovery happens first in one of the markets and is

then transmitted to the other. Figure Int.2 shows that the two measures are very highly correlated in

the changes (75%), confirming that the two measures do indeed comove to a very high extent.

Figure Int.2: Each dot in this scatterplot represents a daily observation of the changes in the bond yield spread andthe CDS spread, for an Italian underlying bond. The bond yield spread is calculated between the Italian and Germanbonds with five years to maturity. The CDS spread is the spread for a five-year US-denominated CDS contract. All datawere obtained from Bloomberg and span our data sample of 641 trading days from July 1, 2010 to December 31, 2012.

To address the goal of determining the dynamics between the two measures, we perform a VARX(1,0)

analysis of the measures ∆CDSt, the change in the CDS spread, and ∆Y St, the change in the yield

spread to the German Bund, augmented with the exogenous variables ∆CCBSSt and ∆USV IXt.

Table Int.2 shows the results of the analysis: There exists no lead-lag relationship between the CDS

spread and the yield spread, as the Granger-causality panel shows. The correlation between the

contemporaneous residuals, however, is very high (72%), suggesting that, if credit risk is indeed incor-

porated in one market first and then transmitted to the other, the credit risk transmission takes place

within the same day. These results suggest that, when performing an analysis using daily data, the

credit risk discovery dynamics should not be a concern, for example when determining the dynamics

of credit risk and liquidity, as in the case of this study.

Int 7

Table Int.2: Results for the Granger-Causality Analysis ofthe Italian CDS Spread and Yield Spread. This table presentsthe results for the regressions of the day-t changes in the CDS Spread,∆CDSt, and the Italian yield spread, ∆Y St, on the lagged terms ofboth variables. The data have a daily frequency. The significance refersto heteroskedasticity-robust t-tests. Heteroskedasticity-robust F -teststatistics and their significance are reported for the null hypothesis ofeach variable Granger-causing the other. We also report the contempo-raneous correlation in the model residuals. Our dataset consists of 640days of trading in Italian sovereign bonds, from July 1, 2010 to December31, 2012. The CDS spread refers to a USD-denominated, five-year CDSspread and the yield spread refers to the spread between the five-yearnotch of the Italian term structure and its German counterpart. Bothvariables were obtained from Bloomberg.

Variable ∆CDSt ∆Y St

∆CDSt−1 0.085 0.001

∆Y St−1 0.087 0.081

∆CCBSSt 1.700*** 1.414***

∆USVIXt 1.714** 2.029**

Intercept 0.167 0.240


Y SGC−−→ CDS 1.69 .

CDSGC−−→ Y S . 0.00

Residuals’ Correlation

∆BAt 1.000 0.715

∆CDSt 0.715 1.000

* Significant at a 10% level. ** Significant at a 5% level. *** Significantat a 1% level.

Int 8

Int.IV Price Volatility and CDS Liquidity

Price Volatility

A variable that we have not included in the analysis of Section VI is the intraday price volatility

of the bonds. Microstructure models (e.g., Glosten and Milgrom (1985), among others) suggest that

an increase in price volatility should decrease the amount of liquidity offered to the market by mar-

ket makers because of concerns about the risk of the inventory they carry. Moreover, the effect of

heightened credit risk could affect liquidity only through price volatility, and not necessarily directly.

For example, a worsened public finance situation could accentuate the uncertainty regarding the true

value of the sovereign bond and the informativeness of its price, and hence affect its market liquidity.

As a matter of fact, the price volatility, σ2t , (measured as the intraday variance of the five-minute

mid-quote changes for each bond, averaged into a market-wide daily measure) and the Bid-Ask Spread

are highly correlated in our sample, even in differences (59%).

We thus need to test the effect of a change in credit risk, after controlling for the effect of volatility

on the liquidity measure. We therefore estimate a VAR, as in Equation 2, with the changes in the

CDS Spread, Bid-Ask Spread, and bond price volatility, σ2t . The lag structure selected by the modified

Akaike criterion is 6, due to the stickiness of the volatility measure. Table Int.3 reports the results for

the Granger-causality test, while Figure Int.3 shows the IRFs for the VARX(6,0) system. The Granger-

causality test shows that we cannot reject the hypotheses that any variable is Granger-causing the

other two. However, Figure Int.3 shows that the bid-ask spread significantly leads the volatility of

returns (and not the CDS spread), while a shock to volatility seems not to significantly affect the

illiquidity measure, at least not in an economically significant fashion. It is clear from Panel (b) that

the main driver of the illiquidity variable dynamics is the CDS spread, as we posited in the main body

of the paper.

Finally, we repeat the threshold estimation from Equation 4, adding ∆σ2 as an explanatory vari-

able. The test for the presence of the threshold is significant at the 1% level and confidence intervals

around the threshold estimate can be seen in Figure Int.4. The estimates of Equation 4, with the

addition of the bond market volatility, are shown in Table Int.4. The contemporaneous bond price

volatility is indeed significant at the 1% level and it increases the R2 by 20%. However, the estimates

of the parameters related to the CDS Spread dynamics are remarkably similar to those of Table 4

Panel B.

Int 9

Table Int.3: Results for Granger-Causality with Variance ofReturns. We regress changes in the liquidity measure, changes in creditrisk, and changes in the volatility of the returns, on their own lags andthe lags of the other two variables, and on contemporaneous changes inmacro variables in a VARX(6,0) setting. Heteroskedasticity-robust F -test statistics and their significance are reported for the null hypothesisof no Granger-causality from one variable to the other two. Our datasetconsists of 640 days of trading in the sovereign bonds, from July 1, 2010to December 31, 2012, and was obtained from the MTS (Mercato deiTitoli di Stato) Global Market bond trading system. The CDS spreadrefers to a USD-denominated, five-year CDS spread. The CDS spreadand the macro variables were obtained from Bloomberg.


BAGC−−→ CDS + σ2 5.071***

CDSGC−−→ BA+ σ2 4.282***

σ2 GC−−→ CDS +BA 3.483***


∆BAt ∆CDSt ∆σ2t

∆BA 1.000 0.113 0.631

∆CDS 0.113 1.000 0.031

∆σ2 0.631 0.031 1.000


Table Int.4: Results for the Regression of the Bid-Ask Spread on the CDS spread and Macro Variablesand Bond Return Volatility. This table presents the results for the regression of the change in the Bid-Ask Spread(the change in the quoted bid-ask spread) on day t, ∆BAt, on its lagged terms, and on the change in the CDS spread onday t, ∆CDSt, and its lagged terms, and the bond return volatility, using daily data. The statistical significance refersto heteroskedasticity-robust t-tests. The Test column reports the heteroskedasticity-robust test result for whether thetwo parameters above and below the threshold are equal and distributed as chi-square(1). Our dataset consists of 640days of trading in Italian sovereign bonds, from July 1, 2010 to December 31, 2012, and was obtained from the Mercatodei Titoli di Stato (MTS) Global Market bond trading system. The CDS spread refers to a USD-denominated, five-yearCDS spread. The CDS spread and the macro variables were obtained from Bloomberg.

Variable I[CDS≤500] I[CDS>500] Test

∆CDSt 0.420** 1.874*** 8.44***

∆CDSt−1 0.840*** -0.738** 13.89***

∆BAt−1 -0.201***

∆BAt−2 -0.116***

∆BAt−3 -0.125***

∆CCBSSt 0.287**

∆USVIXt 0.105

∆σ2t 0.092***

Intercept -0.001

Adj R2 0.449

N 637


Int 10

Bid

Ask

Spr

ead

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00.

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Impulse Response from Volatility


(c) Shock to the bond market volatility

Figure Int.3: Impulse Response Functions for the VARX(6,0) System for Bid-Ask Spread, CDS Spread,and Volatility. This graph shows the evolution of the impulse response functions to a shock in the bond marketliquidity, as measured by the bid-ask spread, the CDS spread, and the bond market return volatility, in Panels (a), (b),and (c) respectively. Our dataset consists of transactions, quotes, and orders for all 189 fixed-rate and floating Italiansovereign bonds and quotes for the CDS spread, from July 1, 2010 to December 31, 2012.

Int 11

Figure Int.4: Test to Determine Confidence Bands around the CDS Threshold with the Addition of BondReturn Volatility. The test statistic described in Appendix B is plotted here for Equation 4, with the addition of bondreturn volatility. The test statistic is normalized at 0 at the threshold that minimizes the sum of squared residuals. Thehorizontal line at 7.35 marks the 5% confidence values for the threshold. Our dataset consists of transactions, quotes,and orders for all 189 fixed-rate and floating Italian sovereign bonds, from July 1, 2010 to December 31, 2012.

Int 12

CDS Market Liquidity

Another variable that could affect the dynamics of the system we analyze is the market liquidity

of the CDS contract itself: If the CDS spread is affected by the demand and supply of credit-event

insurance, measured by its own bid-ask spread, and we do not include this liquidity variable in our

system, we could be ignoring a significant determinant of the system’s dynamics. We investigate this

issue in detail. We replicate the analysis from Section VI.I by adding a third endogenous variable,

∆CDSBAt, the change in the daily bid-ask spread for a CDS contract. We construct this measure by

averaging bid-ask spread observations sampled at a five-minute frequency from high-frequency CDS

quotes obtained from CMA. Figure Int.5 shows the time-series of CDS liquidity, Table Int.5 shows the

Granger-causality results for the VARX(6,0), and Figure Int.6 shows the IRFs for the system (after

standardizing the variables).

While the Granger-causality from the CDS spread to the other two variables is the most significant,

the causation from the liquidity of the CDS market to the other two variables is also significant.

However, the IRFs show that the prior finding that a change in the CDS spread significantly affects

the bond market bid-ask spread is unchanged. A change in CDS liquidity has only a marginally

statistically significant effect on the liquidity of the bond market seven days after the shock. The

inclusion of the CDS spread in the VAR system does not, thus, affect our conclusion regarding the

dynamic relationship between credit risk and market liquidity.

On the other hand, Table Int.5 shows that the residual correlation is high between the liquidity

of the bond and CDS markets, and one might be concerned that the CDS level was capturing the

CDS liquidity, although the residual correlation of the latter two is low. In Table Int.6 we repeat

the analysis of Table 4 Panel B, including the liquidity of the CDS market as one of the explanatory

variables. Figure Int.7 reports the threshold confidence band. The threshold selected by the procedure

is very close to that selected the first time we performed the analysis (496.55 vs. 488.04), although

the confidence band around it is rather large. However, Table Int.6 shows that the parameters related

to the CDS Spread dynamics are remarkably similar to those of Table 4 Panel B. We thus conclude

that, although the liquidity of the CDS market is significantly partially correlated with the liquidity

of the bond market (as the literature on commonality in liquidity would suggest), the inclusion of the

CDS liquidity does not invalidate the results in the main part of the study regarding the relationship

between credit risk and market liquidity.

Int 13

Figure Int.5: The daily average absolute bid-ask spread for the CDS contract was obtained from the CMA data, andspans our sample period of July 1, 2010 to December 31, 2012.

Table Int.5: Results for the Granger-Causality Analysis of theItalian CDS Spread, Bond Liquidity, and CDS Liquidity. Thistable presents the results for the regressions of the day-t changes in CDSSpread ∆CDSt, the Italian bond market bid-ask spread ∆BAt, and theItalian CDS bid-ask spread ∆BACDSt on their lagged terms and thecontemporaneous changes in CCBSS and USVIX. The data have a dailyfrequency. Heteroskedasticity-robust F -test statistics and their signifi-cance levels are reported for the null hypothesis of each variable Granger-causing the others. We also report the contemporaneous correlation inthe model residuals. Our dataset consists of 640 days of trading in Ital-ian sovereign bonds, between July 1, 2010 and December 31, 2012. TheCDS spread and bid-ask spread refer to a USD-denominated, five-yearCDS spread. The CDS spread was obtained from Bloomberg, the CDSbid-ask spread from CMA, and the bond market bid-ask spread fromMTS data.


BAGC−−→ CDS&BACDS 1.56*

CDSGC−−→ BA&BACDS 2.51***

BACDSGC−−→ BA&BACDS 2.43***


∆BAt ∆CDSt ∆BACDSt

∆BAt 1.000 0.119 0.312

∆CDSt 0.119 1.000 0.132

∆BACDSt 0.312 0.132 1.000


Int 14

Bid

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Impulse Response from CDS Bid−Ask Spread


(c) Shock to the CDS market liquidity

Figure Int.6: Impulse Response Functions for the VARX(6,0) System for the Bid-Ask Spread, CDSSpread, and CDS Liquidity. This graph shows the evolution of the impulse response functions to a shock in the bondmarket liquidity, as measured by the bid-ask spread, the CDS spread, and the CDS bid-ask spread, in Panels (a), (b),and (c) respectively. Our dataset consists of transactions, quotes, and orders for all 152 fixed-rate and floating Italiansovereign bonds and quotes for the CDS spread, from July 1, 2010 to December 31, 2012.

Int 15

Table Int.6: Results for the Regression of the Bid-Ask Spread on the CDS Spread, Macro Variables andCDS Liquidity. This table presents the results for the regression of the change in the bid-ask spread (the change inthe quoted bid-ask spread) on day t, ∆BAt, on its lagged terms, and on the change in the CDS spread on day t, ∆CDSt,and its lagged terms, using daily data for the bid-ask spread and the CDS spread. The statistical significance refers toheteroskedasticity-robust t-tests. The Test column reports the heteroskedasticity-robust test result for whether the twoparameters above and below the threshold are equal and distributed as chi-square(1). Our dataset consists of 624 daysof trading in Italian sovereign bonds, from July 1, 2010 to December 31, 2012, and was obtained from the Mercato deiTitoli di Stato (MTS) Global Market bond trading system. The CDS spread refers to a USD-denominated, five-yearCDS spread and the macro variables were obtained from Bloomberg.

Variable I[CDS≤500] I[CDS>500] Test

∆CDSt 0.209 2.008*** 7.84***

∆CDSt−1 0.884*** -0.588 8.40***

∆BAt−1 -0.338***

∆BAt−2 -0.194***

∆BAt−3 -0.176***

∆CCBSSt 0.329**

∆USVIXt 0.118

∆BACDSt 0.428***

Intercept -0.001

Adj R2 0.276

N 624


Figure Int.7: Test to Determine Confidence Bands around the CDS Threshold with the Addition of CDSLiquidity. The test statistic described in Appendix C is plotted here for Equation 4, with the addition of CDS liquidity.The test statistic is normalized at 0 at the threshold that minimizes the sum of squared residuals. The horizontal line at7.35 marks the 5% confidence values for the threshold. Our dataset consists of transactions, quotes, and orders for all152 fixed-rate and floating Italian sovereign bonds, from June 1, 2011 to December 31, 2012.

Int 16

Int.V Higher Winsorization Level

In this section, we replicate Table 5, after winsorizing the data at the 5% level, rather than the 1%

level, and report the estimates in Table Int.7. The parameters related to the CDS spread dynamics

when the CDS spread level is above the threshold are smaller, which was expected since we winsorized

observations belonging to that part of the sample. The main results, however, are qualitatively

unchanged from the analysis in the main part of the paper.

Table Int.7: Results for the Regression of the Bid-Ask Spreadon the CDS Spread and Macro Variables after a 5% Winsoriza-tion. This table presents the results for the regression of the change inthe bid-ask spread (the change in the quoted bid-ask spread) on day t,∆BAt, on its lagged terms, and the change in the CDS spread on dayt, ∆CDSt, and its lagged terms, using daily data for the bid-ask spreadand the CDS spread. The regressions are presented for Equations 4and 3 in Panels A and B respectively. Parameters multiplying the iden-tity operator [CDS ≤ (>)500] are reported under the [CDS ≤ (>)500]column. The statistical significance refers to heteroskedasticity-robustt-tests. The Test column reports the heteroskedasticity-robust test re-sults for the two parameters above and below the threshold being equaland distributed as chi-square (1). Panel A (B) is based on the pre-(post-)structural-break sample. Our dataset consists of 641 days oftrading in Italian sovereign bonds, from July 1, 2010 to December 31,2012, and was obtained from the Mercato dei Titoli di Stato (MTS)Global Market bond trading system. The CDS spread refers to a USD-denominated, five-year CDS spread and the macro variables were ob-tained from Bloomberg.

Variable Panel A: 2011 Panel B: 2012

I[CDS≤500] I[CDS>500] Test

∆CDSt 0.478 2.867*** 9.36*** 0.161

∆CDSt−1 0.808*** -1.326** 9.66*** 0.582**

∆BAt−1 -0.255*** -0.488***

∆BAt−2 -0.177*** -0.265***

∆BAt−3 -0.132** -0.155***

∆CCBSSt 0.355** 0.788***

∆USVIXt 0.309* -0.105

Intercept 0.003 -0.004

Adj R2 0.233 0.237

N 377 260


Int 17

Int.VI Additional Results on Threshold Regressions

The Bootstrapped Test Distributions

In Section VI.II and VII.I we reported the test statistic and its significance for the test of the

presence of the threshold in Equations 4 and 6. The distribution of the test, bootstrapped according

to Hansen (1996), is reported in Figures Int.8, Int.9, and Int.10 for the thresholds shown in Figures

6, 9, and 12, respectively.

Figure Int.8: Bootstrapped Distribution for the Test for Threshold Presence for Equation 4 and Ob-served Test Value We bootstrapped the distribution of the test for the presence of a threshold and plot it here. Thecurve superimposed on the empirical distribution is a chi-square distribution with as many degrees of freedom as thereare parameters that are allowed to change in the specification, for reference. The observed test statistic was 25.05. Ourdataset consists of transactions, quotes, and orders for all 189 fixed-rate and floating Italian government bonds, fromJuly 1, 2010 to December 31, 2012.

Int 18

(a) Threshold Confidence Bands Determination: 2011 Sample

(b) Threshold Confidence Bands Determination: 2012 Sample

Figure Int.9: Bootstrapped Distribution for the Test for Threshold Presence for Equation 4 and Ob-served Test Value for Two Subsamples We bootstrapped the distribution of the test for the presence of a thresholdseparately for the subsamples before and after December 21, 2011, and plot those distributions in Panels (a) and (b),respectively. The vertical red line marks the observed test value (23.73 and 6.06, respectively), while the curve superim-posed on the empirical distribution is a chi-square distribution with as many degrees of freedom as there are parametersthat are allowed to change in the specification, for reference. Our dataset consists of transactions, quotes, and orders forall 189 fixed-rate and floating Italian government bonds, from July 1, 2010 to December 31, 2012.

Int 19

Figure Int.10: Bootstrapped Distribution for the Test for Threshold Presence for Equation 6 andObserved Test Value We bootstrapped the distribution of the test for the presence of a threshold and plot it here.The observed test statistic is 78.9. The curve superimposed on the empirical distribution is a chi-square distributionwith as many degrees of freedom as there are parameters that are allowed to change in the specification, for reference.Our dataset consists of transactions, quotes, and orders for all 189 fixed-rate and floating Italian government bonds,from July 1, 2010 to December 31, 2012.

Int 20

Maturity Bucket Specific Thresholds

In Section VII.I, we estimated Equation 6 as a pooled OLS panel regression, and showed that the

threshold result was robust to this alternative specification. Alternatively, to test the robustness of

our results, we can estimate Equation 6 separately for each maturity bucket. We therefore estimate

∆BAt =α0 +3∑i=1

αi∆BAt−i + I [CDS ≤ γ]

1∑j=0

βj∆CDSt−j

(11)

+ I [CDS > γ]

1∑j=0

βj∆CDSt−j

+ β2USV IXt + β3CCBSS + εt

for each maturity group. The CDS spread level that is used as a discontinuity variable is the CDS

spread for the five-year maturity, since this is the reference maturity and it is explicitly mentioned in

the “Sovereign Risk Framework” (LCH.Clearnet, 2011). Figure Int.11 shows the threshold confidence

band determination for each of the nine maturity buckets for which we can estimate Equation 11.

For each group the threshold is found for a CDS spread of 497 or 502, with 500 always contained

within the confidence bands, with the exception of the group with the shortest maturity. We interpret

the finding that the relationship between market liquidity and credit risk shows a structural break

regardless of the maturity of the bonds, when the five-year CDS is 500 bp, as supporting and showing

the robustness of the results contained in the main body of the paper.

Int 21

(a) Group 3: 3 to 9 months (b) Group 4: 0.75 to 1.25 years

(c) Group 5: 1.25 to 2 years (d) Group 6: 2 to 3.25 years

(e) Group 7: 3.25 to 4.75 years (f) Group 8: 4.75 to 7 years

Figure Int.11: Test to Determine Confidence Bands around the CDS Threshold for each Maturity Group.The test statistic described in Appendix B is plotted here for Equation 11, estimated for each maturity group. The teststatistic is normalized at 0 at the threshold that minimizes the sum of squared residuals. The horizontal line at 7.35marks the 5% confidence values for the threshold. Our dataset consists of transactions, quotes, and orders for all 189fixed-rate and floating Italian sovereign bonds, divided into 11 maturity groups, from July 1, 2010 to December 31, 2012.[Continued]

Int 22

(g) Group 9: 7 to 10 years

(h) Group 10: 10 t0 15 years

(i) Group 11: 15 to 30 years

Int 23

Int.VII Granger-Causality Below and Above the CDS Threshold

We repeat the VAR analysis, while only using the dates when the CDS is below and above the

threshold, separately, and report the results in Table Int.8, in Panels A and B, respectively. Regarding

the lead-lag relationship between CDS and market liquidity, even above 500 bp, the CDS spread leads

the bid-ask spread. However, given that the contemporaneous correlation between the CDS spread and

the bid-ask spread is very high, when the CDS spread is above 500 bp, and that both the CDS spread

and the bid-ask spread are subject to mean reversion, excluding the contemporaneous changes in the

VAR analysis induces a negative relationship between the bid-ask spread and the CDS spread at lag 3.

Nevertheless, the analysis including the contemporaneous CDS changes shows that there is indeed a

positive relation between the CDS spread and the bid-ask spread, where the CDS spread is the driver,

as confirmed by the instrumental variable analysis. Repeating the analysis for the subsample below

500 bp leads to results similar to those for the whole sample reported in Table 3.

Int 24

Table Int.8: Results for the Granger-Causality Analysis ofthe Italian CDS Spread and Bond Liquidity when below theThreshold. This table presents the results for the regressions of the day-t changes in the CDS spread ∆CDSt, and the Italian bond market bid-askspread ∆BAt, on the lagged terms of both variables. The data have adaily frequency. The significance refers to heteroskedasticity-robust t-tests. Heteroskedasticity-robust F -test statistics and their significancelevels are reported for the null hypothesis of each variable Granger-causing the other. Our dataset consists of 541 and 96 days of trading inItalian sovereign bonds, between July 1, 2010 and December 31, 2012,when the CDS level is below and above the threshold found in SectionVI.II, in Panels A and B, respectively. The CDS spread refers to a USD-denominated, five-year CDS spread and was obtained from Bloomberg.

Panel A: CDS < 500bp

Variable ∆BAt ∆CDSt

∆CDSt−1 1.035*** 0.200***

∆BAt−1 -0.342*** -0.011

∆CDSt−2 0.032 -0.087*

∆BAt−2 -0.229*** -0.007

∆CDSt−3 0.262 0.047

∆BAt−3 -0.177*** -0.004

∆Euribor −DeTBillt 0.007 0.034

∆CCBSSt 0.533*** 0.204***

∆USVIXt 0.189 0.153***



CDSGC−−→ BA 7.263*** .

BAGC−−→ CDS . 0.377

Panel B: CDS > 500bp

Variable ∆BAt ∆CDSt

∆CDSt−1 0.067 0.233***

∆BAt−1 -0.427*** -0.025

∆CDSt−2 -0.881 -0.106

∆BAt−2 -0.172 -0.020

∆CDSt−3 -1.196* -0.198

∆BAt−3 -0.111 0.001

∆EuriborDeTBillt 0.112 0.061

∆CCBSSt 0.620 0.236***

∆USV IXt 0.985*** 0.163***



CDSGC−−→ BA 3.68** .

BAGC−−→ CDS . 1.237


Int 25

Int.VIII Results for Other Liquidity Measures

In the main body of the paper we conducted the analyses focusing on a single measure for the

(il)liquidity of the bond market, the Bid-Ask Spread, since it is both the most familiar and most

indicative of market conditions. Nonetheless, in order to validate the results presented in the prior

sections, we employ a cohort of other liquidity measures and show that they are all highly correlated

with the Bid-ask Spread. Even so, we repeat most of the analysis from the earlier sections, using these

measures. Due to dataset limitations, however, we repeat the analysis with other liquidity measures

only for the subsample covering 152 bonds and 406 trading days between June 2011 and December

2012, for which the tick-by-tick data are available.3

The proxies we use can be divided into two main categories: quote-based and trade-based mea-

sures. Quote-based measures include the total quoted quantity (Quoted Quantity), and the market

depth measure, Lambda, while the Effective Spread constitutes our trade-based measure. The Ef-

fective Spread measures the actual spread experienced by traders, while Quoted Quantity measures

the largest amount a trader could buy or sell at any point in time, if she were not concerned with

execution costs. The depth measure Lambda attempts to combine the bid-ask spread and the quoted

quantity by measuring by how much a trader would move the best bid (ask) if she were to trade

e15 million of a given bond.4 Mathematically, the Lambda on the ask side would be defined as

λa = E[(P at − P at−1)(Qt) |Qt = 15M

]= E [∆P at (Qt) |Qt = 15M ], where P at is the time t ask price

following a buy trade of quantity Qt = 15M , and λb would be defined similarly. In order to represent

both sides of the market, we consider the mean, λ = λa+λb

2 , in our empirical estimations, as a market

depth measure. As for the trade-based measures, the effective bid-ask spread Effective Spread is cal-

culated as Q · (AP −M) · 2, where Q = 1 if it is a buy order, Q = −1 if it is a sell order, AP is the

face-value-weighted trade price, and M is the mid-quote in place at the time the order arrives.5

All quote-based measures are calculated at a five-minute frequency for each bond, and then aver-

aged across bonds to calculate a daily market-wide measure.6 The Effective Spread is calculated for

our sample of the whole market, with volume-weighting of the trades of all bonds. Figure Int.11 shows

the time-series evolution of the liquidity variables and Table Int.9 shows the correlations between

3The differences between the two datasets we use are presented in Section Int.II of this internet appendix.4This amount was chosen since it is at the 90th percentile of the overall market in terms of trade size. As traders

might split up large amounts over several subsequent trades, Lambda captures the price movement caused by a relativelylarge trade requiring immediacy. It is conceptually equivalent to the concept of market depth defined by Kyle (1985).

5We do not include two widely known trade-based liquidity metrics, the Amihud illiquidity measure and the Rollmeasure, in the list of alternative liquidity measures. The MTS market is characterized by high-frequency quote updates,but not high-frequency transactions. However, the MTS database provides detailed order book information, enabling usto compute a liquidity measure, the hypothetical market impact, for buy and sell orders separately (Lambda). Thus, dueto the large number of quotes relative to trades, Lambda is a far better and more granular measure for this market thanthe Amihud measure. Additionally, market makers in the MTS market post firm quotes that are executable immediately,so that the difference between best ask and best bid (quoted bid-ask spread) indicates the market-making risk perceivedby professional market makers at any point in time. Therefore, there is no need to rely on alternative estimations of thebid-ask spread, such as the Roll measure, since the actual measure is itself available.

6It is common in the sovereign bond literature to separate the bonds into on-the-run and off-the-run issues, or to onlyconsider the former, reckoning that the former are more liquid and more sought after by investors. The Italian sovereignissuer, the Tesoro, often reissues existing bonds, thus enhancing their liquidity, and causing the on-the-run/off-the-rundichotomy to lose its relevance. In any event, we checked whether there were differences in the quoted or effective bid-askspread for “new” issues compared to the prior issues and did not find any significant differences. For this reason, weaverage our liquidity measures across all bonds without sorting them by remaining maturity or age since issue.

Int 26

them. The measures tend to comove and clearly follow the same evolution. The Bid-Ask Spread is

the liquidity measure that most highly correlates with the others; all absolute correlations between

it and the other variables exceed 59% (44%) in levels (differences), with λt being the least correlated

with it.

To check the robustness of the results in Section VI, we repeat the analysis in which we estimated

Equation 3, the threshold test in Equation 4 for the sample up to December 21, 2011, and the structural

break of Section VI.III, using the other liquidity variables described in this subsection, namely the

Quoted Quantity, the Effective Spread, and Lambda. The number of lags for each variable and the

CDS Spread are determined using the same methodology as for the Bid-Ask Spread. The results are

reported in Table Int.10, while Figure Int.12 shows the plots of the identification of the threshold in

the relationship between changes in liquidity and changes in the Italian CDS Spread level for the 2011

subsample, and the structural break test, as performed in Section VI.III for the Bid-Ask Spread.

Figure Int.12 shows that the structural break around the LTRO settlement (Panels e, f, and i) is

also a feature of the Quoted Quantity and Effective Spread, as is the 500 bp threshold in the regression

of the changes in the liquidity measure on its lags and the changes in the Italian CDS spread and

its lag and the macro variables, for the 2011 subsample (Panels c, d, and h) for the Quoted Quantity

and Lambda. A 10% change in the Italian CDS Spread is contemporaneously associated with a 14%

decrease in Quoted Quantity, a 33% increase in the Effective Spread, and a 52% increase in Lambda,

when the CDS spread for Italian bonds is above 500 bp, compared to a 7% decrease, a 10% increase, and

a 28% increase when the Italian CDS Spread is below the same threshold. After the ECB intervention,

a change in the Italian CDS Spread has no significant effect on any liquidity measure. The sensitivity

of the Effective Spread is lower than that of the Bid-Ask Spread because of the endogeneity of the

trading decision: traders will choose to trade when the Bid-Ask Spread is comparatively low, thus

dampening the sensitivity of the Effective Spread to changes in market conditions. The dynamics

of the relationship between credit risk and liquidity are confirmed by the analysis of the alternative

liquidity measures, so that the lagged change in credit risk is significant when the market is relatively

quiet, while, in a stressed market, when the Italian CDS Spread is above 500 bp, the liquidity changes

contemporaneously with the credit risk.

An alternative measure of liquidity used in the previous literature for markets with few quotes and

trades is the volume traded on the market, or, alternatively, the number of daily transactions. Figure

Int.13 shows the total number of Trades and the trading Volume (in billions of euros) exchanged on

the MTS. It is evident that these two variables share a strong commonality in movement and a clear

cyclical pattern. We reckon that the peaks coincide with auctions of new bonds, the reopening of

previous issues, and the releases of relevant economic variables and events, over time. In contrast to

the previous literature, we find a very low correlation between changes in Trades (Volume) and the

Bid-Ask Spread of about -11% (-13%). Since the Bid-Ask Spread correlates highly with other market

liquidity measures and not with the Volume, we conclude that Trades and the trading Volume in the

Italian sovereign bond market are mostly driven by factors other than market liquidity and, therefore,

act as a poor proxy for it.

Int 27

Table Int.9: Time-series Correlations of Trade- and Quote-based LiquidityMeasures. This table shows the time-series correlations between the bid-ask spread andthe liquidity measures defined in Section Int.VIII in levels (differences) above (below) thediagonal. The sample consists of the quotes and trades from 406 days in our sample. Bid-Ask Spread is the difference between the best bid and the best ask, Effective Spread isthe effective bid-ask spread paid by the traders, Quoted Quantity is the face value quan-tity offered on average per bond on the bid and ask side in millions of euros, Lambda isa measure of depth. Our bond-based data, obtained from the Mercato dei Titoli di Stato(MTS), consist of transactions, quotes, and orders for all 152 fixed-rate and floating Ital-ian sovereign bonds (Buoni Ordinari del Tesoro (BOT) or Treasury bills, Certificato delTesoro Zero-coupon (CTZ) or zero-coupon bonds, Certificati di Credito del Tesoro (CCT)or floating notes, and Buoni del Tesoro Poliennali (BTP) or fixed-income Treasury bonds)from June 1, 2011 to December 31, 2012.

Differences\Levels Bid-Ask Spread Quoted Quantity Lambda Effective Spread

Bid-Ask Spread 1.000 -0.591 0.904 0.890

Quoted Quantity -0.600 1.000 -0.496 -0.557

Lambda 0.437 -0.402 1.000 0.789

Effective Spread 0.512 -0.508 0.240 1.000

Int 28

(a) Quoted and Effective Bid-Ask Spread

(b) Quoted Quantity and Lambda

Figure Int.11: Time-Series of Liquidity Measures. Panel (a) shows the time-series evolution of the Quoted

(in blue) and Effective (in red) Bid-Ask Spread, while Panel (b) shows the depth measure Lambda (in red) and Quoted

Quantity (in blue). Our liquidity measures are described in detail in Section Int.VIII. Our dataset consists of transactions,

quotes, and orders for all 152 fixed-rate and floating Italian sovereign bonds (Buoni Ordinari del Tesoro (BOT) or Treasury

bills, Certificato del Tesoro Zero-coupon (CTZ) or zero-coupon bonds, Certificati di Credito del Tesoro (CCT) or floating

notes, and Buoni del Tesoro Poliennali (BTP) or fixed-income Treasury bonds) from June 1, 2011 to December 31, 2012.

Int 29

Table Int.10: Other Liquidity Variables: Results for Subsamples Basedon Time and CDS Level. This table presents the results for the regression of thechanges in several liquidity measures on their lagged terms, and the change in theCDS spread on day t, ∆CDSt, and its lagged terms, and contemporaneous changesin macro variables, using daily data. Panel A(C) reports the regressions as specifiedin Equation 3 for the whole (post-structural-break) sample and Panel B reports theregressions as specified in Equation 4. The alternative liquidity measures employedhere are Quoted Quantity ∆QQt, Effective Spread ∆ESt, and Lambda ∆λt, describedin Section Int.VIII. Parameters multiplying the identity operator [CDS ≤ (>)500]are reported under the [CDS ≤ (>)500] column. The statistical significance refersto heteroskedasticity-robust t-tests. The Test column reports the heteroskedasticity-robust test results for the two parameters above and below the threshold being equaland distributed as chi-square (1). The subsamples are based on our dataset, whichconsists of 406 days of trading in Italian sovereign bonds, from July 1, 2010 to December31, 2012, and was obtained from the MTS (Mercato dei Titoli di Stato) Global Marketbond trading system. The CDS spread refers to a USD-denominated, five-year CDSspread and macro variables were obtained from Bloomberg.

Variable Panel A Panel B: 2011 Panel C: 2012

All Sample I[CDS ≤ γ] I[CDS > γ] Test

Dependent Variable: Quoted Quantity, QQt

∆CDSt -0.077 0.245 -1.367*** 9.06*** -0.203

∆CDSt−1 -0.265 -0.676** 0.709* 7.31*** -0.036

∆QQt−1 -0.330*** -0.232* -0.393***

∆QQt−2 -0.309*** -0.125 -0.479***

∆QQt−3 -0.201*** -0.131* -0.289***

∆CCBSSt -0.098 0.002 -0.270*

∆USV IXt -0.280*** -0.438*** 0.022

Intercept -0.000 0.001 -0.004

Adj. R2 0.191 0.279 0.255

Dependent Variable: Effective Spread, ESt

∆CDSt 0.851** 0.679 3.291*** 5.19** 0.649

∆CDSt−1 0.526 0.973* 0.528 0.13 -0.287

∆ESt−1 -0.427*** -0.219*** -0.598***

∆ESt−2 -0.320*** -0.217*** -0.458***

∆ESt−3 -0.224*** -0.218*** -0.283***

∆CCBSSt 0.393 -0.002 0.719

∆USV IXt 0.383* 0.521** 0.142

Intercept -0.002 0.001 -0.008

Adj. R2 0.221 0.204 0.302

Dependent Variable: Lambda, λt

∆CDSt 0.120 -0.254 5.207*** 8.58*** -0.352

∆CDSt−1 1.276** 2.781** -0.871 6.42** 0.157

∆λt−1 -0.535*** -0.453*** -0.574***

∆λt−2 -0.285*** -0.125* -0.357***

∆λt−3 -0.241*** -0.181** -0.303***

∆CCBSSt 0.673* 0.160 1.473**

∆USV IXt 0.228 0.318 -0.303

Intercept 0.000 0.003 -0.003

Adj. R2 0.257 0.307 0.272

* Significant at a 10% level. ** Significant at a 5% level. *** Significant at a 1% level.Int 30

(a) Quoted Quantity: Threshold Presence Test (b) Effective Spread: Threshold Presence Test

(c) Quoted Quantity: Threshold Confidence Bands Determi-nation

(d) Effective Spread: Threshold Confidence Bands Determi-nation

(e) Quoted Quantity: Structural Break (f) Effective Spread: Structural Break

Figure Int.12: Bootstrapped Threshold Significance Test Distribution and Confidence Bands Deter-

mination for the 2011 Subsample and Structural Break Test for Alternative Liquidity Measures. We

bootstrapped the distribution of the test for the presence of a threshold and plot it in Panels (a), (b), and (g) for the

2011 subsamples, for Equation 4 performed using Quoted Quantity, Effective Spread, and Lambda, respectively, instead

of Quoted Spread as the liquidity measure. The vertical red lines mark the observed test values, while the curve superim-

posed on the empirical distribution is a chi-square distribution with as many degrees of freedom as there are parameters

that are allowed to change in the specification, for reference. [Continued]

Int 31

(g) Lambda: Threshold Presence Test

(h) Lambda: Threshold Confidence Bands Determination

(i) Lambda: Structural Break

Figure Int.12: Bootstrapped Threshold Significance Test Distribution and Confidence Bands Determi-

nation for the 2011 Subsample and Structural Break Test for Alternative Liquidity Measures. [Continued]

The test statistic described in Appendix B is plotted here in Panels (c), (d), and (h) for the 2011 subsamples for Equa-

tion 4 performed using Quoted Quantity, Effective Spread, and Lambda, respectively, instead of Bid-Ask Spread as the

liquidity measure. The test statistic is normalized at 0 at the threshold that minimizes the sum of squared residuals. The

horizontal line at 7.35 marks the 5% confidence values for the threshold. Panels (e), (f), and (i) present the structural

break for Equation 4 performed using Quoted Quantity, Effective Spread, and Lambda, respectively, instead of Bid-Ask

Spread as the liquidity measure. The horizontal lines mark the 10%, 5%, and 1% significance levels for the largest of the

Chow F -values.

Int 32

Figure Int.13: Time-Series of Trades and Volume. The time-series evolution of the overall market volume, right-

hand axis (in red), in billions of euro, and the overall number of trades, left-hand axis (in blue). Our dataset consists

of transactions, quotes, and orders for all 189 fixed-rate and floating Italian sovereign bonds (Buoni Ordinari del Tesoro

(BOT) or Treasury bills, Certificato del Tesoro Zero-coupon (CTZ) or zero-coupon bonds, Certificati di Credito del

Tesoro (CCT) or floating notes, and Buoni del Tesoro Poliennali (BTP) or fixed-income Treasury bonds) from July 1,

2010 to December 31, 2012.

Int 33

References

Bai, J., Julliard, C., and Yuan, K., 2012, Eurozone Sovereign Bond Crisis: Liquidity or Fundamental

Contagion. Federal Reserve Bank of New York Working Paper.

Caporale, G. M., and Girardi, A., 2011, Price formation on the EuroMTS platform. Applied Economics

Letters, 18(3), 229-223.

Cheung, Y. C., de Jong, F., and Rindi, B., 2005, Trading European Sovereign Bonds: The Microstruc-

ture of the MTS Trading Platforms. European Central Bank Working Paper.

Glosten, L. R., and Milgrom, P. R., 1985, Bid, ask and transaction prices in a specialist market with

heterogeneously informed traders. Journal of Financial Economics, 14(1), 71-100.

Greene, W. H., 2012, Econometric Analysis, Seventh Edition, Pearson.

Hansen, B., 1996, Inference when a nuisance parameter is not identified under the null hypothesis.

Econometrica, 64(2), 413-430.

Kyle, A. S., 1985, Continuous auctions and insider trading. Econometrica, 1315-1335.

LCH.Clearnet, 2011, LCH.Clearnet Margining Approach, http://www.ecb.europa.eu/paym/

groups/pdf/mmcg/Item_1_LCH_Margining.pdf?0fe79f1cef93461dc22566a4e165db44

Int 34



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