Are European Corporate Bond and Default Swap Markets Segmented?

Transcription

1 Are European Corporae Bond and Defaul Swap Markes Segmened? Didier COSSIN IMD Inernaional Hongze LU IMD Inernaional HEC Universiy of Lausanne Research Paper N 33 March 005 FAME - Inernaional Cen er for Financial As se Managemen and Engineering

2 Are European Corporae Bond and Defaul Swap Markes Segmened? Didier Cossin and Hongze Lu This version: Sepember 004 Absrac Marke prices of corporae bond spreads and of credi defaul swap (CDS) raes do no mach each oher. In his paper we argue ha he liquidiy premium he cheapes-o-deliver (CTD) opion and acual marke segmenaion explain he pricing differences. Using he European ransacion daa from Reuers and Bloomberg we esimae a liquidiy premium ha is imevarying and firm-specific. We show ha when ime-dependen liquidiy premiums are considered corporae bond spreads and CDS raes behave in a much closer way han previous sudies have shown. We also find ha high equiy volailiy drives pricing differences ha can be explained by he CTD opion. Keywords: credi defaul swaps corporae bond yields liquidiy premium cheapes-o-deliver opions deb-cds arbirage JEL Classificaion: C3 G G3 IMD Inernaional CH 00 Lausanne Swizerland. Cossin@imd.ch IMD Inernaional and HEC Universié de Lausanne. Hongze.Lu@hec.unil.ch

3 Execuive Summary The valuaion of credi defaul swaps (CDS) requires esimaing he expeced loss in he even ha he reference eniy defauls in he fuure. However corporae bond yields combine differen ypes of risk for which invesors demand compensaion. The mos discussed componen is credi risk which compensaes invesors for he risk of non-repaymen. Anoher componen is ineres rae risk which is sripped ou in he spread bu may noneheless affec i via call feaures or prepayme n opions. Corporae bond yields also conain a liquidiy premium which reflecs he ransacion cos of a paricular bond. In his paper we conduc an empirical examinaion of he pricing of he defaul premium by firs decomposing he bond yield ino differen layers and hen examining how he liquidiy premium and he implied defaul premium behave. This research hus addresses he quesion of wheher he corporae deb marke is inegraed wih he credi proecion marke and of how consisen he pricing of CDS is wih he pricing of corporae bonds in Europe. This paper differs from previous research in ha i decomposes he corporae bond yield spread ino liquidiy and credi risk componens firs. We compare he defaul premium implied from deb markes o he CDS premium quoed in he credi proecion marke before and afer sripping ou liquidiy. Longsaff Mihal and Neis (003) exrac he liquidiy componen by examining he difference beween a pricing model and he marke CDS spread and in his way hey assume ha he deb marke and he credi proecion marke are perfecly inegraed. Our approach seeks o idenify liquidiy as a separae iem. By removing he liquidiy componen we can check o wha exen he deb marke and he credi proecion marke are inegraed. Our approach also differs from hose of Hull Predescu and Whie (003) and Houweling and Vors (00). This aricle ses ou o deermine wheher liquidiy raher han he choice of he risk-free rae can explain he pricing discrepancies of he defaul premium in he corporae deb marke and he credi proecion marke. Houweling and Vors (00) find an average absolue pricing error of 33 basis poins using reasury yields and basis poins when using swap raes. We find a much lower pricing error of.6 basis poins using reasury yields. Afer adusing liquidiy in bond yields he absolue pricing error in cross secion is almos zero. Liquidiy is a difficul concep o define even more so o quanify. In his paper we implemen he limied dependen variable model (hereafer he LDV model) - proposed by Lesmond Ogden and Trzcinka (999) and exended o fixed-income markes by Chen Lesmond and Wei (003) - o separae he liquidiy premium from bond yields and o esimae a ime-varying firm-specific liquidiy premium. In general he LDV model derives he liquidiy premium well. The cross-secional mean of he liquidiy

4 premium is. basis poins which is on he low side of he liquidiy premium found in previous research. Our esimae of he mean liquidiy premium ranges from basis poins o 60 basis poins. Liquidiy is a maor driver of he difference in prices beween he corporae bond marke and he credi proecion marke: When he liquidiy premium is considered spread differences fall and hese differences are no significan anymore for 8 ou of 39 firms. The regression resuls show ha liquidiy is an imporan componen in he bond yield spread. T- saisics of he liquidiy variable are significan for 35 ou of he 39 sample firms. For each firm he roo mean squared error decreases and he adused R² increases by adding liquidiy on op of he credi componen. However he influence of liquidiy and credi varies for differen raing groups (as well as for differen companies of course). As he credi qualiy of he firm declines credi risk becomes he principal explanaory power while liquidiy hough significan decreases in explanaory power. For higher raed firms he maor porion of he yield spread ranging from 60% o 80% can be explained by he combinaion of credi and liquidiy. For a lower raed firm credi risk alone may explain over 95% of he yield spread. Our resuls show ha hough liquidiy adds explaining power an imporan porion of spreads in high-raed bonds ranging from 0% o 40% sill remains unexplained. By ploing he implied bond par yield and CDS quoes we observe ha he divergence period correlaes wih financial disress or periods of high marke uncerainy. We explored he facors driving he pricing differences and found ha he pricing discrepancies are highly correlaed and explained by equiy volailiy. The regression resuls suppor boh he role of he CTD opion in European CDS prices and he marke imperfecion argumen. When paricipans in he wo markes reac differenly o he same credi fundamenals he pricing discrepancies provide arbirage opporuniies o sophisicaed invesors.

5 . Inroducion The valuaion of credi defaul swaps (CDS) requires esimaing he expeced loss in he even ha he reference eniy defauls in he fuure. The main componen of expeced loss he riskneural defaul probabiliy can be esimaed eiher from equiy (as is he case indirecly in srucural form models 3 ) or from deb markes (as is he case mos ofen in reduced form models). In he laer case he corporae bond spread is he main source of daa for he esimaion. However corporae bond yields combine differen ypes of risk for which invesors demand compensaion. The mos discussed componen is credi risk which compensaes invesors for he risk of non-repaymen. Anoher componen is ineres rae risk which is sripped ou in he spread bu may noneheless affec i via call feaures or prepaymen opions. Corporae bond yields also conain a liquidiy premium which reflecs he ransacion cos of a paricular bond. In his paper we conduc an empirical examinaion of he pricing of he defaul premium by firs decomposing he bond yield ino differen layers and hen examining how he liquidiy premium and he implied defaul premium behave. This research hus addresses he quesion of wheher he corporae deb marke is inegraed wih he credi proecion marke and of how consisen he pricing of CDS is wih he pricing of corporae bonds in Europe 4. Recen empirical lieraure comparing he CDS spread wih he implied defaul premium from corporae bond yields or prices includes Longsaff Mihal and Neis (003) Hull Predescu and Whie (003) Blanco Brennan and Marsh (004) and Houweling and Vors (00). Hull Predescu and Whie (003) firs regress yield agains mauriy of all he bonds issued by he reference eniy o obain a 5-year bond par yield. They es if he difference beween he 5-year bond par yield and he 5-year CDS quoe equals he 5-year risk-free rae. The paper suggess ha he risk-free rae implied from he CDS quoes is beween he Treasury rae and he swap rae wih 6.87 basis poins higher han he Treasury rae and 6.5 basis poins lower han he swap rae. When conrolling he credi qualiy of he reference eniy counerpary defaul risk provides a parial explanaion. They conclude ha he resuls may be influenced by liquidiy risk. Using a reduced-form model Longsaff Mihal and Neis (003) esimae he defaul parameers of he corporae bond model. Subsiuing hese defaul parameers ino he CDS pricing formula gives he CDS spread implied by he corporae bond prices. They find ha he marke CDS quoes are significanly less han he spreads implied by he corporae bonds. They inerpre he difference beween he wo as he liquidiy premium which is suppored by cross-secional 3 See Meron (974) or Cossin and Piroe (000) for deails. 4 As observed by Kwan (00) he separaion of credi risk from liquidiy risk is also imporan for he evaluaion of curren and fuure economic aciviy.

6 regressions. To examine he influence of differen risk-free raes hey repea he analysis by replacing Treasury raes wih swap raes o derive he discoun funcion. This hypohesis can be reeced for 48 of he 68 firms in heir sample meaning ha he use of he swap curve canno explain he large cross-secional differences across firms. The empirical resuls on risk-free rae choice are mixed hough here is a clear consensus ha liquidiy should be a priced iem in he bond prices 5. This paper differs from previous research in ha i decomposes he corporae bond yield spread ino liquidiy and credi risk componens firs. We compare he defaul premium implied from deb markes o he CDS premium quoed in he credi proecion marke before and afer sripping ou liquidiy. Longsaff Mihal and Neis (003) exrac he liquidiy componen by examining he difference beween a pricing model and he marke CDS spread and in his way hey assume ha he deb marke and he credi proecion marke are perfecly inegraed. Our approach seeks o idenify liquidiy as a separae iem. By removing he liquidiy componen we can check o wha exen he deb marke and he credi proecion marke are inegraed. Our approach also differs from hose of Hull Predescu and Whie (003) and Houweling and Vors (00). This aricle ses ou o deermine wheher liquidiy raher han he choice of he risk-free rae can explain he pricing discrepancies of he defaul premium in he corporae deb marke and he credi proecion marke. Houweling and Vors (00) find an average absolue pricing error of 33 basis poins using reasury yields and basis poins when using swap raes. We find a much lower pricing error of.6 basis poins using reasury yields. Afer adusing liquidiy in bond yields he absolue pricing error in cross secion is almos zero. Liquidiy is a difficul concep o define even more so o quanify. Recen empirical lieraure on he liquidiy premium includes Janosi Jarrow and Yildirim (00) Houweling Menink and Vors (003) Chen Lesmond and Wei (003) and Jarrow (00). In his paper we implemen he limied dependen variable model (hereafer he LDV model) - proposed by Lesmond Ogden and Trzcinka (999) and exended o fixed-income markes by Chen Lesmond and Wei (003) - o separae he liquidiy premium from bond yields and o esimae a ime-varying firm-specific liquidiy premium. In general he LDV model derives he liquidiy premium well. The cross-secional mean of he liquidiy premium is. basis poins which is on he low side of he liquidiy premium found in previous research 6. Our esimae of he mean liquidiy 5 See also Brown (00). 6 Houweling Menink and Vors (003) find he liquidiy premium ranges from 9 o 4 basis poins; Chen Lesmond and Wei (003) esimae he mean liquidiy premium is abou 30 basis poins. I is no surprising o have a lower liquidiy premium in our research as he sample firms are he mos liquid

7 premium ranges from basis poins o 60 basis poins. Liquidiy is a maor driver of he difference in prices beween he corporae bond marke and he credi proecion marke: When he liquidiy premium is considered spread differences fall and hese differences are no significan anymore for 8 ou of 39 firms. The bond daa used in he LDV esimaion is downloaded from Reuers and consiss of daily ransacion prices on sraigh corporae bonds from January 00 o July In oal here are 648 daily observaions of 4 bonds issued by 39 European companies. The 5-year CDS daa is aken from Bloomberg. In oal here are 8363 daily observaions issued on he same 39 reference eniies. In he analysis we firs obain zero-coupon yields from sraigh coupon bonds ransform he zero yields ino par yields hen inerpolae he par yields o capure 5-year bond par yields. Following Janosi Jarrow and Yildirim (00) we esimae he liquidiy premium for each bond on each ransacion day using a rolling procedure. We ake he average of he liquidiy premium for all bonds issued by he same firm as a proxy for he liquidiy premium on a 5-year bond as if he firm has one issue each day. The defaul premium implied from deb prices is compared o he CDS premium quoed in he credi proecion marke before and afer sripping ou liquidiy premium. The comparison is o deermine how ime-varying liquidiy plays a role in he pricing of corporae bonds. We hen regress he corporae bond yield spread agains he CDS premium o check how much of he corporae bond yield spread can be explained by credi risk. As an explaining variable he liquidiy premium is also added in he regression o check if i adds explaining power. One resul ha differs from previous research using US daa is ha he average difference beween bond spreads and CDS raes 7 is no always posiive. Blanco Brennan and Marsh (004) repor ha wo facor may lead CDS prices being greaer han he implied yield spread: he CTD opion and he repo cos. They sugges ha CDS is an upper bound on he price of credi risk and he implied yield spreads should form a lower bond. For 5 ou of he 39 firms he average difference before sripping ou liquidiy are significanly negaive meaning ha on average he 5-year bond par yield spread is lower han he CDS premium quoed in he marke for hese 5 firms in he period of he sudy. Afer sripping ou liquidiy he number of firms wih he CDS premium higher han he implied bond par yield increases o 4. I is no conclusive ha CDS prices should always be higher han he implied yield spread due o he liquidiy componen in bond yields. Our resuls sugges ha in peaceful periods boh he repo cos and he CTD opion European names. In choosing hese bonds for analysis issued amoun and oher crieria furher consrain he chosen bonds o be he mos liquid ones. 7 Tha is bond spread minus CDS price. 3

8 value are no significanly high which reflecs he fac ha he pricing differences are small. Only in he volaile period especially when defaul probabiliy increases he combinaion of he increasing repo cos and he CTD opion value may be greaer han he liquidiy componen in bond yields and may lead o CDS prices being greaer han he implied yield spreads. The regression resuls show ha liquidiy is an imporan componen in he bond yield spread. T-saisics of he liquidiy variable are significan for 35 ou of he 39 sample firms. For each firm he roo mean squared error decreases and he adused R² increases by adding liquidiy on op of he credi componen. However he influence of liquidiy and credi varies for differen raing groups (as well as for differen companies of course). As he credi qualiy of he firm declines credi risk becomes he principal explanaory power while liquidiy hough significan decreases in explanaory power. For higher raed firms he maor porion of he yield spread ranging from 60% o 80% can be explained by he combinaion of credi and liquidiy. For a lower raed firm credi risk alone may explain over 95% of he yield spread. These resuls on credi risk are in line wih previous research such as Huang and Huang (00) in which credi risk accouns for a small porion of he yield spreads on high-raed firms bu a large porion of yield spreads on low-raed firms. Our resuls show ha hough liquidiy adds explaining power an imporan porion of spreads in high-raed bonds ranging from 0% o 40% sill remains unexplained. By ploing he implied bond par yield and CDS quoes we observe ha he divergence period correlaes wih financial disress or periods of high marke uncerainy. We explored he facors driving he pricing differences and found ha he pricing discrepancies are highly correlaed and explained by equiy volailiy. The regression resuls suppor boh he role of he CTD opion in European CDS prices and he marke imperfecion argumen. When paricipans in he wo markes reac differenly o he same credi fundamenals he pricing discrepancies provide arbirage opporuniies o sophisicaed invesors. The res of his paper is organized as follows: Secion provides he model ha explains he relaionship beween he bond yield spread he CDS premium and he liquidiy premium; Secion 3 describes he daa for he analysis and he esimaion procedure; Secion 4 examines he maor resuls; and Secion 5 concludes.. Liquidiy Premium Bond Yield Spread and CDS Rae In his secion we firs discuss various approaches o esimaing he liquidiy premium and validae our choice of he LDV model. Then we exend Hull Predescu and Whie (003) o include liquidiy in he non-arbirage relaionship. Furher a simple regression model is proposed o es he explaining power of he differen componens of he corporae bond yield spread. 4

9 . The Liquidiy Model How o measure liquidiy? This research quesion has frequenly been addressed in he finance lieraure. The firs srand of lieraure focuses on he "direc" measures such as bid-ask spreads rade sizes rade frequencies and volume 8. When "direc" measures are no available researchers end o resor o "indirec" measures in he analysis. For example Houweling Menink and Vors (003) examine liquidiy pricing using eigh indirec measures as follows: issued amoun coupon lised age missing prices price volailiy number of conribuors and yield dispersion. The hird srand of lieraure has is roos in he adverse selecion heory. The empirical model sared wih Rose (959). The fricion model was hen inroduced in Maddala (983) as he LDV model. Lesmond Ogden and Trzcinka (999) employ he LDV model in he esimaion of common equiy liquidiy and Chen Lesmond and Wei (003) exend he model o sudy liquidiy in corporae bonds. The LDV model assumes ha an informed invesor will only rade when profis exceed ransacion coss. 9 A securiy wih low ransacion coss will have more frequen price changes han a securiy wih high ransacion coss. The logic is ha high ransacion coss resul in fewer price movemens herefore more zero reurns han low ransacion coss. The significance of he liquidiy effec can be evaluaed by observing he incidence of zero reurns on a securiy. Boh Lesmond Ogden and Trzcinka (999) and Chen Lesmond and Wei (003) find ha liquidiy measures from he LDV model relae o direc liquidiy measures such as he bid-ask spread in boh he equiy and deb markes. LDV liquidiy esimaes are indisinguishable from he underlying bid-ask spreads and compare well wih he rading cos esablished in previous research. The wo successful implemenaions of he LDV model in boh he equiy and deb markes disinguish he LDV model in he liquidiy esimaion. In his research we follow Chen Lesmond and Wei (003) in he esimaion of he bond liquidiy premium on each ransacion day. Though oher models may also be viable approaches we choose he LDV model on he basis of solid heory and daa availabiliy. Chen Lesmond and Wei (003) model he bond reurns as a funcion of he changes in ineres raes and changes in he S&P500 index. They choose he wo facors based on he consensus ha high grade bonds are sensiive o changes in boh ineres raes and general sock prices while low grade bonds are less sensiive o changes in ineres raes bu more sensiive o sock marke changes. Chen Lesmond and Wei (003) scale boh coefficiens by he daily 8 For example Hong and Warga (000) sudy he effecive bid-ask spread using exchange-based bond ransacion daa. However more han 90% of bond rades are carried ou in he OTC marke. 9 The negaive relaionship beween asse illiquidiy coss and rading frequency is he heoreical foundaion of many papers for example Amihud (00). 5

10 6 duraion of he bonds. We find ha scaling changes by daily duraion has no significan impac on he esimaion and he reurn process is hus modified o he following equaion: () where R is he daily unobserved "rue" bond reurn for bond a ime ß and ß are he coefficiens of bond a ime?r is he daily change of he 0-year risk-free ineres rae?sockindex is he daily reurn on he sock index. 0 The relaionship beween he observed bond reurn he unobserved "rue" bond reurn and he liquidiy cos can be saed as R = R - a i i = or wih a as he effecive buy side cos and a as he effecive sell side cos for bond. The LDV model imposes he liquidiy consrain on he obecive funcion: () where a <0 and a >0. The loglikelihood funcion for his model is: (3) The sum is over he ses 0 of observaions for which a =R = a R < a and R > a. The difference a = a - a represens he round-rip ransacion coss on bond reurns normalized by price. In he implemenaion he liquidiy coefficiens a and a are consrained o make heir difference posiive.. The Non-Arbirage Relaionship Wihou considering liquidiy risk corporae bond yield spreads and CDS raes should be closely relaed as boh conain a defaul and risk premium on he same reference eniy. For example Hull and Whie (000) sae he relaionship as follows: Value of Treasury Bond - Value of Corporae Bond = Presen Value of Cos of Defaul if we assume ha he defaul risk is he only difference beween a corporae bond and a similar Treasury bond. If we denoe he bond yield as y he yield on a similar risk-free bond as r and he CDS spread as s he relaionship y r = s should hold approximaely. If he bond yield spread y r is higher han he CDS spread s deb marke paricipans assume a higher credi risk 0 We use sock indices o represen he European counries involved in he analysis and he subscrip has been omied for simplificaion. R R SockIndex ε β β + + = R R R R R R R R R R if if 0 if SockIndex α α α α α α ε β β > = = < = + + = Φ Φ = 0 / / ) ln( ) ( ln ) ( ln ) SockIndex ( ) SockIndex ( ) SockIndex ( ln R R R R R R L πσ πσ β β α σ β β α σ σ β β α α

11 han paricipans in he credi proecion marke and buying depressed corporae bonds using proceeds from shoring Treasury is profiable. The posiion can be covered by buying he CDS o aain risk-free arbirage profis. Oherwise he arbirage by buying Treasury shoring bond and CDS is profiable. Pricing discrepancies would give rise o arbirage opporuniies. One issue ha complicaes he arbirage is he fac ha in pracice he real payoff of CDS is differen from he idealized. To correc for he difference Hull and Whie (000) and Hull Predescu and Whie (003) refine he relaionship as: Rˆ ARˆ s = (y r) ( R)( ˆ + A (4) ) where Rˆ is he expeced recovery rae A is he expeced accrued ineres on he reference bond a he ime of defaul and A is he expeced accrued ineres on he par yield bond a he ime of defaul. In he even of a defaul he bond delivered is usually he one wih he lowes accrued ineres herefore A migh be assumed o be zero. Furher A can be assumed o be equal o y/4 in Hull Predescu and Whie (003). This assumpion is based on he fac ha mos of he corporae bonds in heir analysis pay coupons wice a year. The expeced accrued ineres a he ime of defaul is 5% of he par yield. The arbirage relaionship is hen simplified o: ( y r) s = (5) ( + y / 4) This relaionship holds approximaely under many srong assumpions: a fla Treasury yield curve consan ineres raes and he independence of ineres raes defaul probabiliies and recovery raes. More significanly when defaul happens he expeced accrued ineres on he reference bond is assumed o be zero and he expeced accrued ineres on he par yield bond is assumed o be 5% of he par yield. Building on his largely simplified model we inroduce liquidiy risk as his componen is widely recognized. For example in Collin-Dufresne Goldsein and Marin (00) only 5% of he observed credi spread changes can be explained by he numerous credi risk proxies. They assume ha liquidiy migh be he single common facor ha drives he residuals. As liquidiy is an indispensable componen in he bond yield if i is ignored he defaul premium derived from he corporae bond yield is an upward biased measure of he acual risk of defaul. This noion is based on he assumpion ha liquidiy is a posiive componen in he bond yields. A firs sigh he credi marke is no liquid as many CDS prices do no change over ime. Though here migh This arbirage works exacly if he CDS allows he buyer o sell a par yield bond for is face value plus accrued ineres. See Chen Lesmond and Wei (003) Hong and Warga (000) and Schulz (00). 7

12 a possibiliy ha CDS may be even less liquid han bonds 3 we follow Longsaff Mihal and Neis (003) and assume ha he CDS is conracual in naure and ha he CDS spreads reflec he defaul risk componen. The CDS price also includes a CTD opion and repo coss which enails ha he marke CDS price is an upward esimae of defaul risk. However he size and scope of his opion is hard o esimae and we do no have reliable daa on repo cos. We herefore assume ha he corporae bond yield he risk-free rae bond liquidiy and he CDS spreads are relaed hrough he following equaion: n ( y r ) n α s = (6) ( + y / ) where s is he 5-year CDS spread quoed in he credi proecion marke a ime y is he implied 5-year bond par yield a ime r is he 5-year risk-free Euro ineres rae a ime n is he number of bonds used in he esimaion a is he round-rip liquidiy premium for a par bond a ime. In his paper s has a 5-year mauriy which is he mos common one in he CDS marke hough i is up o he conracual paries o decide he mauriies of he CDS. However we do no see corporae bonds wih a fixed mauriy of 5 years everyday. The corporae bond par yield y used in he analysis has o be esimaed wih a se of bonds wih mauriies ha bracke he mauriy of he CDS. The esimaion of he 5-year bond par yield y follows hree seps: Sripping ou coupons o obain zero-coupon bond yields ransforming he zero-coupon bonds yield ino bond par yields and inerpolaing he bond par yield curve o obain he 5-year bond par yields. The risk-free Euro curve could be eiher he Treasury curve or he swap curve. Hull Predescu and Whie (003) argue ha he swap curve can bridge he difference beween he deb and credi markes ciing ha he yields on US Treasury bonds end o be lower compared wih he yields on oher low risk bonds. In his paper we use he Euro Treasury curve for wo reasons: Firs he deb marke regards he corporae yield spread as he spread of he corporae bond yield over he yield of a governmen bond; second here is no consensus wheher he facors leading o a depressed US Treasury curve would have he same effec on he Euro Treasury curve. For each firm he number of bonds used in he esimaion varies ranging from o 7 wih an average of 3. We allow he liquidiy premium o be a ime-varying variable o reflec he changing ransacion cos of a paricular bond. The average liquidiy premium for all bonds issued by he same firm is a proxy for he ransacion cos of he implied 5-year bond. The expeced accrued ineres on he par yield bond a he ime of defaul is approximaed by y / 3 he LDV model does no work well wih quoes and we do no have ransacion daa on CDS ransacion prices. 8

13 as mos of he European bonds in he analysis pay coupons once a year. Though in realiy he accrued ineres could be any porion of y we ake he yearly average of 50% for simplificaion. By sripping ou he liquidiy componen in he bond yield spread we expec ha he credi componen implied from he bond marke should be more closely relaed o he CDS spread quoed in he credi marke. We hen consider o wha exen he corporae bond spread as deermined by he bond markes correlaes o he CDS rae deermined by he credi proecion marke. The firs regression we esimae is: y r = a + b s +ε (7) where y is he implied 5-year bond par yield a ime r is he 5-year risk-free Euro rae a ime and s is he 5-year CDS spread quoed in he credi proecion marke a ime. Furher for robusness we invesigae wheher adding he liquidiy componen increases he explaining power. We hus esimae he following regression: n r = a + b s + c α + y ε (8) n For ease of inerpreaion we group firms by raings. Summary saisics of he disribuion of coefficien esimaes are presened in Table 3. The S&P raings (AA A BBB BB B) are chosen o replicae he credi qualiy of each borrower in he period of he sudy. We expec ha by adding he liquidiy componen he second regression should increase he overall explaining power. We also expec ha he wo componens play specific roles in differen raing groups. The pricing of credi risk in he wo markes is no expeced o be perfec all ime. A meaningful research resul is o know he rue driver of he pricing differences. For example if he CTD opion is priced in CDS prices hen he driver of he CTD opion value he riskiness of a company - should be able o explain he pricing difference. We consider he regression: n ( y r α ) n S = a3 + b3 σ + ε 3 (9) ( + y / ) We expec o know if high equiy volailiy - ha is a high CTD opion value in CDS prices - would consequenly drive up s above 3. Daa and Esimaion ( y n r ) n α he implied bond par yield. ( + y / ) In his secion we discuss he daa used. We also deail he implemenaion procedure and some preliminary saisical resuls. Credi Defaul Swaps 9

14 We download he daily 5-year CDS las prices for 80 liquid European reference eniies from Bloomberg for he period saring on January 00 and ending on July Bloomberg uses Morgan Sanley as a daa source for CDS prices. Each quoe conains informaion such as he ransacion dae he reference eniy and he price. The CDS price is he midpoin of bid-ask quoaions. As poined ou by Hull Predescu and Whie (003) a confirmed quoe from a dealer is a firm commimen o rade a minimum noional of US$ 0 million. Thus he CDS las price represens he marke price for he credi risk of he borrower. When downloading he daa we choose no o carry over he price if here was no rading or quoaion on ha day. In his way he non-rading days are excluded from he analysis. We double check he reference names wih he names included in he JECI-00 index linked noes which are issued by BNP Paribas and JPMorgan Chase on he credi exposure of he 00 mos liquid and diversified European eniies. From hese wo samples we idenify 39 reference names 4 ha have issued a sufficien number of Euro-denominaed bonds. The daily CDS quoes were scanned for daa errors. We do observe abnormaliy in he daa se hough overall he daa was reliable. On February he CDS price for Ahold was 000 basis poins and he nex day he price dropped o 35 basis poins. Furher on May he CDS price rose from 7 basis poins wo days earlier o 550 basis poins. In such cases he CDS prices for he abnormal period were deleed. The sudy period saw he mos dramaic urbulence in he European credi proecion marke. Many reference eniies experienced credi decline especially auos and elecoms. In our finding resuls he maoriy of quoes lay beween 0 and 700 basis poins wih he wo big movers Ahold and KPN reaching 000 basis poins. The average of he CDS quoes for all reference eniies is 06 basis poins. The summary saisics of he CDS are given in Table. Table 3 shows he summary saisics for he CDS premium which varies across raings. Corporae Bonds The bond daa are crucial in he esimaion of he defaul premium as well as of he liquidiy premium. For each of he 80 reference eniies we download he bond characerisics of each issue from Reuers 3000Xra. The Reuers search crieria are sricly moniored. Firs here have o be a leas wo issues denominaed in Euro; Second here have be a leas one bond wih mauriy lying beween January 004 and July and anoher wih mauriy lying beween July and December 30 0; In his way he inerpolaion of wo issues could bracke he enor of he 5-year CDS in he sample; Third bonds are sraigh bonds wih fixed 4 Regarding he number of reference names Longsaff Mihal and Neis (003) sudy 68 names Hull Predescu and Whie (003) examine 34 names and Janosi Jarrow and Yildirim (00) analyze 5 names all firms are US based. Our sample size is comparable wih previous research. 0

15 annual coupons and an amoun ousanding over 00 million Euros; Fourh bonds have o be raed by recognized raing agencies lised on an exchange and no be a privae placemen; Fifh bonds could no be included in a sinking fund indexed parially paid wih muliple seps or currencies; Sixh bonds could no embed any call or pu opion or be converible. The screening significanly reduces he number of suiable bonds and borrowers. Furher each issue was scanned using Reuers Bond Credi model and subordinaed debs were herefore idenified and excluded from he sample. We hen use Reuers Excel Add-in PowerPlus Pro o download ime series daa for all he bond issues. Bond issues wihou a recognizable RIC code are excluded from he sample. We choose o download he "Las Trade" close price 5 for each ransacion day. The bond prices were also scanned for errors. In our research he LDV model requires a sufficien number of non-zero reurns o esimae he liquidiy parameers. If here are oo many missing daa poins or he number of zero reurns is oo high he bond issue is deleed from he sample. Afer all he screening procedures we have a sample of 4 qualified bonds issued by 39 corporaions. For comparison as well as o es he srengh of he bond ransacion daa we also download bond daa from Daasream. The bond prices from Daasream are he daily clean price. We use boh bond daa ses o check if ransacion daa provides more accurae esimaes. Risk-Free Rae Sock Marke Indices and Implied Pu Volailiy Euro governmen curves are provided by Pice. The governmen bonds used in he boosrapping procedure are hose included in he JPMorgan EMU governmen bond index. The bonds are sraigh bonds wih fixed coupon raes. Following a sandard boosrapping and inerpolaion procedure on each ransacion day we observe boh 5-year and 0-year risk-free Euro raes. The 5-year governmen curve is used as a proxy for he risk-free rae and changes in he 0-year curve are used in he LDV model and maximum likelihood esimaion. We record MSCI counry indices for he European sock markes from Daasream. Like he 0-year risk-free curve changes in sock marke indices are used for maximum likelihood esimaion. Implied pu volailiy daa are aken from Bloomberg for 9 firms. The volailiy daa are used in he analysis of he pricing differences beween deb and credi markes. The period of risk-free raes sock indices and implied pu volailiy corresponds o he period of he CDS sample. Esimaion of Corporae Bond Par Yield For each ransacion day we firs obain zero-coupon bond yields from sraigh coupon bonds issued by he same firm using a boosrapping procedure. We hen ransform he zero yields 5 In a conversaion wih Reuers people hey confirmed ha las rade close prices are he las ransacion prices of he day verified by dealers.

16 obained ino bond par yields. By regressing agains mauriy along he bond par yield curve we obain a 5-year bond par yield y implied from raded deb prices. Esimaion of Liquidiy Premium To esimae he liquidiy premium for each bond on each ransacion day we follow Janosi Jarrow and Yildirim (00) using a rolling procedure. For each day in he bond observaion period we calculae bond daily reurns from bond prices. The corresponding daily changes in he 0-year ineres rae and sock index are also calculaed. For each CDS rading day we go back daa poins in he bond reurn sample and esimae he ransacion cos parameers a and a for ha bond on ha paricular day. Thus each liquidiy esimae incorporaes informaion from he pas ransacion prices. The esimaion requires maximizing he loglikelihood funcion of equaion (3) using bond reurns changes in ineres raes and sock index as inpus. The round-rip ransacion coss can be calculaed as a = a a which is normalized by price. In he esimaion if boh inercep coefficiens are negaive we add he wo ogeher and ake he absolue value. If boh coefficiens are posiive we add he wo. If a is negaive and a posiive we ake he liquidiy esimae as a a. The liquidiy esimae is hen consrained o be posiive. We rescale he ransacion coss by he bond's par value o represen he liquidiy premium of a par yield bond. Afer esimaing and normalizing ransacion coss for each bond issued by he same firm we ake he average of ransacion cos n n α as a proxy for he liquidiy premium on a 5-year bond as if he firm has one issue each day. The summary saisics for he liquidiy premium are provided in Table. The maoriy of liquidiy premiums lay beween 0.3 and 70 basis poins wih he wo big excepions of Ahold and KPN again exceeding 00 basis poins. The average of he liquidiy premium for all reference eniies is. basis poins. An ineresing correlaion beween he marke CDS premium and he liquidiy premium can be viewed in Table 3. For AA firms he CDS price is negaively correlaed wih he liquidiy premium; a decreasing CDS price or increasing credi qualiy couples wih increasing liquidiy premium. We find he same negaive relaionship exiss for he 5 A-raed firms hough he correlaion coefficien increases from -0.3 o The correlaion beween credi and liquidiy reverses saring wih BBB-raed firms. For hese 8 firms he average correlaion is 0.06 meaning ha decreasing credi qualiy leads o a higher liquidiy premium. The effec is more pronounced when credi qualiy declines furher wih BB-raed firms having a correlaion of and B-raed firms one of This phenomenon agrees wih he heoreical predicions ha ransacion coss are significanly higher a he wo ends. High-raed bonds end o fall ino he hands of insiuional invesors who

17 hold he posiion unil mauriy. When credi qualiy declines o he speculaive level sellers canno liquidae heir posiions simply because hey canno find buyers of disressed bonds in he marke. Boh ends lead o high ransacion coss which is suppored by he liquidiy premium derived from he LDV model. 4. Resuls We compare he defaul premium implied from deb prices o he CDS premium quoed in he credi proecion marke before and afer sripping ou he liquidiy premium. Since he CDS prices are no carried over non-rading days we clean he bond par yields implied liquidiy and he 5-year risk-free rae o make he hree ime series correspond o he CDS in calendar daes. Using equaion (6) we srip ou risk-free and liquidiy componens from he implied bond par yield y rescale i o remove he influence of accrued ineres and obain a 5-year defaul premium implied from he deb marke. The implied defaul premium series is herefore compared wih he CDS quoes in he credi proecion marke and he differences are given in he analysis. We regress corporae bond yield spread agains he CDS premium o see how much of he corporae-treasury spread could be explained by credi risk. We add liquidiy as an explaining variable o see if by doing so he overall explaining power improved. We also explore he changes of he CTD opion value in driving he pricing differences in a volaile marke. The resuls are deailed in his secion. 4. How Are Deb Markes and Credi Markes Relaed When Sripping ou Liquidiy? The differences beween he defaul premium implied from deb prices and he marke CDS premium ( y ( + r y / ) s ) are repored in Table 4. The saisics include he indusry raings mean of he difference associaed -saisics he minimum and maximum values of he difference and he correlaion of he wo series. The hypohesis esing for he difference in means of he wo samples is also given in he able. If he resul is we can reec he null hypohesis of zero mean a he 0.0 significance level. Unlike previous research using US daa we find ha he average difference is no all posiive for he 39 firms. The defaul premium implied from deb prices is no always greaer han he marke CDS premium. In heory here is always a posiive liquidiy componen in he corporae bond yield which leads o higher yield lower price and higher defaul premium implied from deb prices han oherwise. However our sudy of European daa shows his is no he case for all firms which leads o he role of he CTD opion imbedded in he conrac o be discussed in Secion 4.3. The average differences beween deb and credi markes range from -48 basis poins o 5 basis poins. The mean of he average differences is.6 basis poins. These resuls show ha 3

18 on average he CDS price is less han he defaul premium implied from bond prices; he differences vary significanly across all firms. The same conclusion can be seen from he maximum and minimum differences - on average he minimum value is -55. and he maximum value is 54.. The European resul shows smaller differences compared wih Longsaff Mihal and Neis (003) in which he cross-secional mean of he average differences is 60.8 basis poins. We also es he differences in means of he wo series. A 0.0 significance level we can reec he null hypohesis of zero mean for 8 ou of he 39 firms. The implied defaul premium ( y r ) is also highly correlaed wih he CDS premium s. The lowes ( + y / ) correlaion beween he wo series is 0.9 and he highes 0.99 wih an average correlaion of 0.8. Then we es if sripping ou liquidiy componen would cause he average differences o change. The comparison is o deermine how ime-varying liquidiy plays a role in he pricing of corporae bonds. The difference beween he wo marke s becomes ( y n r ) n α s and he summary saisics are presened in Table 5. 6 The mean of he ( + y / ) average differences is 0.7 basis poins. In he es of he differences in means he null hypohesis ha he mean is zero can be reeced for ou of he 39 firms. The average of - saisics decreases from 7.7 o 3.3 and he maoriy of he firms 7 have -saisics smaller han en in absolue value. Ineresingly enough wihou using a differen risk-free curve we show ha he average differences can be reduced by adusing he liquidiy componen. Noe ha he cross-secional variaion in differences across firms canno be eliminaed compleely by adusing liquidiy. The variaion is likely o be firm-specific due o he CTD opion imbedded in he CDS prices. In Figure we observe clearly from he Akzo Nobel graph ha he defaul premium implied is higher han he CDS premium bu afer adusing liquidiy he difference beween he defaul premium implied and he CDS premium is almos indisinguishable from Sepember o March on a daily basis. 4. How Much of he Corporae -Treasury Yield Spread Can Be Explained by Credi Risk and Liquidiy Risk? To es he significance of he credi componen in bond spreads we regress he spreads on CDS raes. In Table 7 we presen he regression resuls following he equaion y r = a + b s +ε. As shown he CDS premium is significanly posiively relaed o he yield spread meaning ha as he CDS premium increases he bond yield spread increases as 6 A summary of he pricing differences by raings is given in Table of he 39 firms in he samp le. 4

19 well. We also group he esimaed coefficiens by raings in Table 9. From Table 9 b increases from for AA-raed firms o.39 for B-raed firms and he associaed -saisics also increase from 6. o 9. The rend along he raings is almos linear for boh he coefficiens and he -saisics. As credi qualiy declines he credi componen increases is significance which can also be observed hrough he increases in R². The R² for AA-raed firms is 0.53 increasing o for B-raed firm. This means ha he credi componen alone explains almos 00% of he yield spread for low-raed firms. To es he liquidiy componen as a priced iem in he bond yields we regress he CDS premium and liquidiy premium on he bond yield spread wih his equaion y n r = a + b s + c α + n ε. The resuls are presened in Table 8. Of all 39 firms only 4 show ha he liquidiy componen is no significan which confirms he noion ha our esimae of liquidiy is a priced iem in corporae bond yields. In erms of adused R² adding he liquidiy componen always adds explaining power hough he improvemen varies. In Table 9 we show ha for invesmen grade bonds liquidiy adds more explaining power. For AA-raed firms he adused R² increases from 0.5 o 0.57; for A-raed firms he adused R² increases from 0.65 o 0.7; for BBB-raed firms he adused R² increases from 0.78 o Various previous research 8 use indirec credi variables in he regression and heir resuls show ha credi risk accouns for a small porion of corporae bond yield spread. Using he direc credi variable of CDS prices 9 in he regression we confirm ha credi risk migh accoun for a larger porion of yield spread for low-raed firms. For high-raed firms we find ha he explained porion by credi risk is higher han 50%. The unexplained porion for AA firms is 49% for A firms i is 35% and for BBB firms 3%. Though Collin-Dufresne Goldsein and Marin (00) predic ha liquidiy has he poenial o be he common facor driving he unexplained porion i is no eviden in our analysis. The fac is ha liquidiy does improve he explaining power bu he unexplained porion of 0% o 40% sill remains. We can explain his finding wih he segmenaion of he credi and he deb markes and he exisence of he CTD opion in he CDS prices. When grea credi uncerainy cass a shadow over he fuure of a company invesors in differen markes end o rade on incomplee informaion. In he case of France Telecom he fear of defaul drives up boh he CDS price and he CTD opion value and deb prices - hough more volaile - follow sui bu no all bond prices decline o he same level. 8 For example Collin-Dufresne Goldsein and Marin (00) Huang and Kong (003) and Eom Helwege and Huang (003). 9 The CDS price is no a pure measure of credi risk because he CTD opion and he repo rae are included in he pricing. 5

20 4.3 Wha Drives CDS Prices Higher han he Bond Premium? In pracice he marke price of a bond immediaely afer defaul is usually lower han he amoun o be recovered. Because of he lack of a fair marke price CDS raders favor a physical selemen in which one pus he reference bond or a pari passu bond o he seller and ges par. The choice of available bonds for physical delivery afer defaul gives he proecion buyer a CTD opion. The opion should be priced in he CDS price. Thus when some of he qualified bonds are much cheaper han he res he CTD opion becomes more valuable which drives up he CDS prices. Anoher facor ha drives up he CDS price is he repo cos. In a perfec marke selling proecion and shoring he bond form an arbirage posiion. Wihou he convenience of owning he bond he arbirage has o be carried ou by borrowing he bond which incurs he repo cos. The repo cos is hen ransferred in he proecion price quoed. In ha sense he sum of he credi componen he CTD opion and he repo cos in he CDS prices migh exceed he sum of he liquidiy premium and he credi componen implied from he raded bonds. A closer examinaion of he 5 firms wih CDS prices higher han he implied bond par yield shows ha 3 firms were downgraded in his period and he oher firms were on he verge of being downgraded. In Figure he daily series graph of France Telecom shows ha he wo series closely resemble each oher before and afer he credi urmoil. Only in he period of severe disress and speculaion he CTD opion is deeply in he money. However when he scope of deliverable asses is resriced by he conrac he CTD opion value is grealy reduced. European CDS conracs are less resriced and we observe 5 firms whose CDS prices are higher han he corresponding bond par yield spread. On he oher hand he US CDS prevens he delivery of very long-daed bonds which migh parially explain why none of he CDS prices are higher in previous research using US daa. The CTD argumen is no easy o prove because of he difficuly in esimaing he size of he individual opion value. Inspired by he ploing of he marke CDS quoes and he par bond yield series we end o believe ha he pricing differences are closely linked o he uncerainy in he firm's financial performance which is naurally linked o he CTD value. If here is huge uncerainy in he firm's crediworhiness he expeced recovery rae ends o be very low for cerain bonds qualifiable for delivery hus he CTD opion becomes valuable given he pricing divergences across bonds. When a direc es is no possible due o he lack of he necessary daa o derive he CTD value we op for an indirec es of he CTD opion impac on he pricing differences. In his secion we es if marke uncerainy as approximaed by he implied equiy volailiy is significan in explaining he pricing differences wih he equaion 6

21 ( y r n ( + y n / ) α ) S = a 3 + b 3 σ + ε 3. s is he implied pu volailiy series corresponding o he implied bond par yields and CDS quoes. The resuls are presened in Table 0. Of he 9 firms for which we have implied pu volailiy daa 7 show a negaive relaionship meaning ha he higher he volailiy he higher he CDS quoe over he implied bond par yield. Of he 7 negaive coefficien firms 0 show ha volailiy is significan in explaining he credi risk pricing differences in he wo markes wih -saisics average of R² varies across he firms wih he lowes near zero and he highes over 60%. The relaionship beween marke uncerainy and he pricing difference is ploed in Figure 3 using France Telecom as an example. Throughou he whole observaion period he equaion ( y n r α n (+ y / ) ) S is negaively correlaed o he marke uncerainy. In he previous secion we found ha he unexplained porion of he pricing differences remains afer considering he liquidiy premium in bond prices and credi risk. To explore he facor driving he pricing differences we consider he exisence of he CTD opion embedded in he CDS quoes and is impac on he pricing differences. Using he implied volailiy as a proxy for he CTD opion value we found ha he CTD opion is a significan facor driving he pricing differences. As implied volailiy increases he CDS price becomes higher han he implied bond par yield. The relaionship also confirms he role of he CTD opion in he CDS prices. Given he near linear relaionship beween he credi deb and equiy markes he quesion will be: Can money be made on his hree-way relaionship? 4.4 Is Arbirage Possible? The credi proecion marke differs from he corporae deb marke in many ways. Firs he CDS is conracual which allows hedge funds o ener margin rading and leverage up. The same group of invesors do no necessarily rade bonds in he cash marke. Second he proecion buyer can choose from a se of bonds or loans o deliver in he case of a physical selemen while he exac CTD opion value is unknown. Third he bond invesors wih a large invesmen end o buy and hold which makes he marke less liquid. Fourh in he even of defaul he CDS pays par minus a recovery rae while a bond may pay he marke price less he recovery rae. Wih all hese differences are here arbirage opporuniies o be exploied? The answer lies in he ransacion coss. For example o exploi he pricing discrepancies beween he CDS and bond yields in he case of France Telecom he mos possible acion is o shor boh CDS and corporae bonds when he wo markes diverge. Shoring disressed corporae bonds involves significan ransacion coss. Firs of all he arbirage posiion can 7