An empirical analysis of the dynamic relationship between investment-grade bonds and credit default swaps

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1 An emprcal analyss of he dynamc relaonshp beween nvesmen-grade bonds and cred defaul swaps Robero Blanco * Smon Brennan ** Ian W Marsh *** Workng Paper no. 211 * ** *** Banco de España. E-mal: rblanco@bde.es Bank of England. E-mal: smon.brennan@bankofengland.co.uk Bank of England and CEPR. E-mal: an.marsh@bankofengland.co.uk Ths paper represens he vews and analyss of he auhors and should no be hough o represen hose of he Bank of England, Moneary Polcy Commee members or he Banco de España. Any errors and omssons are he responsbly of he auhors. The auhors would lke o hank Bll Allen, Eva Caarneu, Charles Goodhar, Andrew Haldane, Smon Hayes, Kevn James, Davd Rule, Hyun Shn, Mchela Vecch, Geoffrey Wood and semnar parcpans a he Bank of England and Banco de España for useful commens. Karen Goff and Andrew Paerson provded very able research asssance. CredTrade and J.P. Morgan Secures kndly allowed us o use her cred defaul swap daa. Numerous people a Banc of Amerca Secures, Bloomberg, BNP Parbas, CredTrade, Deusche Bank and J.P. Morgan answered our quesons and correced our msundersandngs. They know who hey are and ha we are very graeful. Copes of workng papers may be obaned from Publcaons Group, Bank of England, Threadneedle Sree, London EC2R 8AH; elephone , fax , e-mal mapublcaons@bankofengland.co.uk Workng papers are also avalable a The Bank of England s workng paper seres s exernally refereed. Bank of England 2003 ISSN

2 Conens Absrac 5 Summary 7 1 Inroducon 9 2 Cred defaul swaps and cred spreads The cred defaul swap marke Prcng of cred rsk 12 3 Daa descrpon Cred defaul swap daa Rsky bond yeld daa Reference rae yeld daa 16 4 The emprcal relaonshp beween cred defaul swaps and cred spreads Average prcng of cred rsk Prce dscovery 25 5 The deermnans of changes n cred defaul swap prces and cred spreads Theorecal deermnans of cred spread and CDS prce changes Resuls 32 6 Concludng commens 40 References 42 3

3 Absrac Ths paper analyses he behavour of cred defaul swaps (CDS) for a sample of frms and fnds suppor for he heorecal equvalence of CDS prces and cred spreads. When hs s volaed, he CDS prce can be vewed as an upper bound on he prce of cred rsk, whle he spread provdes a lower bound. The paper shows ha he CDS marke s he man forum for cred rsk prce dscovery and ha CDS prces are beer negraed wh frm-specfc varables n he shor run. Boh markes equally reflec hese facors n he long run, and hs s prmarly brough abou by bond marke adjusmen. Key words: Cred defaul swaps, cred spreads, prce dscovery. 5

4 Summary Rsky corporae and soveregn bonds are among he mos recen secures o benef from he radng of assocaed dervave conracs. Cred dervaves are fnancal nsrumens ha can be used o ransfer cred rsk from he nvesor exposed o he rsk (he proecon buyer) o an nvesor wllng o assume ha rsk (he proecon seller). Sngle-name cred defaul swaps (CDS) are he mos lqud of he several cred dervaves currenly raded and form he basc buldng blocks for more complex srucured cred producs. A sngle-name CDS s a conrac ha provdes proecon agans he rsk of a cred even by a parcular company or counry. The buyer of proecon makes perodc paymens o he proecon seller unl he occurrence of a cred even or he maury dae of he conrac, whchever s frs. If a cred even occurs he buyer s compensaed for he loss (possbly hypohecally) ncurred as a resul of he cred even, whch s equal o he dfference beween he par value of he bond or loan and s marke value afer defaul. Ths paper addresses he valdy and mplcaons of a heorecal relaonshp equang cred defaul swap prces and cred spreads usng daa for a small cross-secon of US and European frms for whch hgh-qualy daa are avalable. For hs sample of nvesmen-grade frms, he heorecal arbrage relaonshp lnkng cred spreads over he rsk-free rae o CDS prces holds reasonably well on average for mos of he companes (bu especally for US frms), when he rsk-free rae s proxed by he swap rae. Where he relaonshp does no hold, mperfecons n he CDS marke or measuremen errors n he cred spread may be responsble. Due o conrac specfcaons n cred defaul swaps, parcularly n Europe, a cheapes-o-delver opon may also be ncluded n he CDS prce makng an upper bound on he rue prce of cred rsk. We are unable o ncorporae he repo cos of corporae bonds n our analyss due o a lack of relable daa. As a resul, he measured cred spread may underesmae he rue cred spread, and so forms a lower bound on he rue prce of cred rsk. Subjec o hese caveas, for mos reference enes, boh he cash bond and cred defaul swap markes appear o prce cred rsk equally on average. We demonsrae, however, ha prce dscovery akes place prmarly n he CDS marke. We speculae ha prce dscovery occurs n he CDS marke because of (mcro)srucural facors ha make he mos convenen locaon for he radng of cred rsk, and because here are dfferen parcpans n he cash and dervave marke who rade for dfferen reasons. 7

5 The second par of he paper examnes he deermnans of changes n he wo measures of he prce of cred rsk. Varables suggesed by he srucural leraure on cred rsk are capable of explanng around one quarer of he weekly changes n cred defaul swap prces. The same varables are less successful n capurng changes n cred spreads. Frm-specfc equy reurns and mpled volales are sascally more sgnfcan and of greaer economc mporance for CDS prces han for cred spreads. The prcng dscrepancy beween CDS prces and cred spreads s closed prmarly hrough changes n he cred spread, reflecng he CDS marke s lead n prce dscovery. I s hrough hs error correcon mechansm ha boh CDS and cred spreads prce cred rsk equally n he long run. We argue ha hese fndngs are supporve of he srucural models of cred rsk. 8

6 1 Inroducon Rsky corporae and soveregn bonds are among he mos recen secures o benef from he radng of assocaed dervave conracs. Cred dervaves are fnancal nsrumens ha can be used o ransfer cred rsk from he nvesor exposed o he rsk (he proecon buyer) o an nvesor wllng o assume ha rsk (he proecon seller). The payoffs o a cred dervave are condonal on he occurrence of a cred even. The cred even s defned wh respec o one or more reference enes and one or more reference asses ssued by he reference eny. Sngle-name cred defaul swaps (CDS) are he mos lqud of he several cred dervaves currenly raded and form he basc buldng blocks for more complex srucured cred producs. (1) A sngle-name CDS s a conrac ha provdes proecon agans he rsk of a cred even by a parcular company or counry. The buyer of proecon makes perodc paymens o he proecon seller unl he occurrence of a cred even or he maury dae of he conrac, whchever s frs. If a cred even occurs he buyer s compensaed for he loss (possbly hypohecally) ncurred as a resul of he cred even, whch s equal o he dfference beween he par value of he bond or loan and s marke value afer defaul. The economc effec of a cred defaul swap s smlar o ha of an nsurance conrac. The legal dsncon comes from he fac ha s no necessary o hold an nsured asse (eg he underlyng bond or loan) n order o clam compensaon under a CDS. Speculaors can ake long (shor) posons n cred rsk by sellng (buyng) proecon whou needng o rade he cash nsrumen. Cred dervaves are almos exclusvely over-he-couner ransacons ha can be desgned o mee he specfc needs of he counerpares o he conrac. However, recognsng ha he sandardsaon of a conrac can ac as a major spur o he growh of a marke, he Inernaonal Swaps and Dervaves Assocaon (ISDA) released ses of Cred Dervaves Defnons n 1999 (whch were amended n 2001) and The majory of cred dervaves ransacons are documened accordng o ISDA defnons. Accordngly, havng only been nroduced n 1992, he Brsh Bankers Assocaon (BBA) esmaed he oal noonal value of ousandng cred dervaves (excludng asse swaps) o be US$1.19 rllon a he end of (2) (1) Oher basc cred dervaves nclude oal reurn swaps, where he reurn from one asse or group of asses s swapped for he reurn on anoher, and cred spread opons, whch are opons on he spread beween he yeld earned on wo asses. (2) The rapd growh rae should no dsguse he fac ha he cred dervaves marke s sll relavely small. The oal noonal ousandng value of neres rae swaps was esmaed o be US$49 rllon a he end of 2000 (Bank for Inernaonal Selemens (2000)), or around wo o hree mes he value of he underlyng cash nsrumen. Ousandng cred dervaves only amoun o some 2%-3% of he value of underlyng asses. 9

7 Sngle-name cred defaul swaps accouned for 45% of hs oal (BBA (2002)). Cred defaul swaps arguably provde he eases way o rade cred rsk. Many corporae bonds are bough by nvesors who smply hold hem o maury (Alexander, Edwards and Ferr (1998)). Secondary marke lqudy s herefore ofen poor makng he purchase of large amouns of cred rsk n he secondary cash marke dffcul and cosly (Schulz (1998)). Shorng cred rsk s even more dffcul n he cash marke. The repurchase agreemen (repo) marke for rsky bonds s ofen llqud, and even f a bond can be shored on repo he enor of he agreemen s usually very shor, leavng he nvesor lookng o shor a bond for a long perod of me exposed o changes n he repo rae. Cred dervaves, especally cred defaul swaps allow nvesors o shor cred rsk over a long perod of me a a known cos by buyng proecon. We hnk ha cred defaul swaps warran sudy for wo reasons. The frs relaes o he ssue of prce dscovery. As we dscuss furher below, here are approxmae arbrage relaonshps ha mean bond spreads and CDS prces should normally be closely lnked. For oher asse classes where an arbrage relaonshp exss beween he dervave and underlyng nsrumen, prce dscovery can ake place n eher marke. I s neresng o see wheher he new, small bu dynamc cred dervaves marke s a beer source of nformaon on he prce of cred rsk han he much larger and more esablshed cash bond marke. Damond and Verreccha (1987) argue ha, n he presence of shor-sales consrans, good and parcularly bad news s mpounded no he prce more slowly han n he absence of consrans. The less consraned dervaves marke mgh hen concevably be he forum whn whch he majory of prce dscovery akes place. Indeed, hs s wha we demonsrae below. Second, recen emprcal work has suggesed ha he yeld offered by defaulable secures n excess of he rsk-free rae s only parly relaed o cred rsk. Elon, Gruber, Agrawal and Mann (2001) fnd ha axaon and rsk prema compensang for sysemac rsk on corporae bonds ogeher accoun for wo-hrds of he spread beween en-year US corporae bonds and reasures. The expeced loss from defaul accouns for only 18%. Colln-Dufresne, Goldsen and Marn (2001) show ha he facors suggesed by radonal models of defaul rsk explan only one quarer of he varaon n cred spreads, and ha he majory of he remanng varance s capured by a sngle prncpal componen. They hypohesse ha aggregae shocks are he source of he common facor. Whle cred dervaves prces are usually closely relaed o cred spreads, we show ha a hgher proporon of he varaon n CDS prces can be explaned by defaul-rsk relaed facors. 10

8 The emprcal leraure on cred defaul swaps s que small. Cossn, Hrcko, Aunon-Nern and Huang (2002) consder he facors ha deermne he level of CDS prces usng a cross-secon of ransacons prces, and sugges ha he negraon beween equy and cred markes was less han perfec, a leas unl Sepember 2000 when her daa end. Houwelng and Vors (2002) f a reduced-form model o CDS quoaons wh parameers exraced from he bond markes. They conclude ha cross-seconally he CDS and cash bond marke prce cred rsk equally for nvesmen-grade bonds. Fnally, Sknner and Townend (2002) nerpre cred defaul swaps as pu opons and regress CDS prces on facors ha should nfluence her prce n hs framework wh modes success. In hs paper we add o hs leraure by examnng he me seres properes of cred defaul swap prces n conjuncon wh machng cred spread daa. The paper addresses hree man ssues. Frs, quesons wheher bond and cred defaul swap markes prce defaul rsk equally. Second, examnes wheher cred rsk prce dscovery akes place predomnanly n he cash bond or cred dervave marke. Thrd, examnes he facors ha nfluence shor-run changes n CDS prces and cred spreads. The paper s organsed as follows. Secon 2 descrbes he cred defaul swap marke and he relaonshp beween CDS prces and cred spreads. Secon 3 descrbes he daa used. Secon 4 nvesgaes emprcally he shor and long-erm relaonshps beween CDS prces and spreads. Secon 5 consders he deermnans of changes n cred spreads and CDS prces. Secon 6 conans concludng commens. 2 Cred defaul swaps and cred spreads 2.1 The cred defaul swap marke In a cred defaul swap, he proecon seller agrees o pay he defaul paymen o he proecon buyer f a defaul even has happened before maury of he conrac. If here s no defaul even before maury, he proecon seller pays nohng. The proecon seller charges a fee for he proecon. Ths s ypcally a consan quarerly fee pad unl defaul or maury, whchever s frs. Should a defaul even happen, he accrued fee s also pad. We refer o he annualsed fee as he cred defaul swap prce. The defaul paymen s eher repaymen a par agans physcal delvery of a reference asse (physcal selemen) or he noonal amoun mnus he pos-defaul marke value of he reference asse deermned by a dealer poll (cash selemen). Physcal delvery s he domnan form of selemen n he marke. A broad se of deb oblgaons s delverable as long as hey rank par passu wh he senor unsecured ndebedness of he 11

9 reference eny. Defaul evens for CDS mgh nclude some or all of he followng: A. Bankrupcy B. Falure o pay C. Oblgaon defaul or acceleraon D. Repudaon or moraorum (for soveregn enes) E. Resrucurng The frs four are no conenous, alhough he evolvng ISDA documenaon has dropped evens C and D n some jursdcons snce hey have been deemed subsumed by evens A and B. Resrucurng has been and remans a source of conroversy n he CDS marke. The 1999 ISDA documenaon defnes resrucurng o consue a defaul even f eher he neres rae or prncpal pad a maury are reduced or delayed, f an oblgaon s rankng n paymen prory s lowered or f here s a change n currency or composon of any paymen (excludng adopon of he euro by a member sae of he European Unon). The key problem s ha no all delverable asses necessarly become due and payable should resrucurng occur and s concevable ha some delverable oblgaons wll be cheaper han ohers. Ths s lkely o be parcularly acue where delverable asses nclude very long-daed or converble bonds ha ofen rade a a dscoun o shorer-daed sragh bonds. Ths means ha where here s a non-neglgble probably of a resrucurng ha falls shor of makng all deb due and payable and where some oblgaons rade a a subsanal dscoun o ohers, hen a physcally-seled CDS prce also conans a cheapes-o-delver (CTD) opon and s no a pure measure of cred rsk. European CDS raded on he bass of hs defnon hroughou our daa sample. US CDS have been subjec o a Modfed Resrucurng defnon snce 11 May 2001 ha, among oher aspecs, resrced he scope of delverable asses and specfcally prevens he delvery of very long-daed bonds. Ths reduces he value of he delvery opon n US defaul swaps. 2.2 Prcng of cred rsk There s a large and growng leraure on he prcng of cred rsk, whn whch wo approaches domnae. Srucural models are based on he value of he frm and are usually derved from Meron (1974). In hs class of models defaul occurs when he process descrbng he value of he frm hs a gven boundary. Black and Cox (1976), Geske (1977) and Longsaff and Schwarz 12

10 (1995) are hree of many mporan references. Das (1995) and Perdes (1997) apply srucural models o he prcng of cred dervaves. The second approach, usually ermed reduced-form or nensy-based models, nsead assume ha he mng of defaul s specfed n erms of a hazard rae. Leadng reduced-form frameworks would nclude Jarrow and Turnbull (1995), Jarrow, Lando and Turnbull (1997) and Duffe and Sngleon (1999). Das and Sundaram (1998), Duffe (1999) and Hull and Whe (2000a, 2000b) apply reduced-form models o cred dervave prcng ssues. Boh srucural and reduced-form approaches are very comprehensvely surveyed n Lando (1997) and Schonbucher (2000). Ths paper does no conrbue o he leraure on cred rsk prcng. Insead wll make use of he approxmae arbrage relaonshp ha exss beween cred defaul swap prces and cred spreads for a gven reference eny dscussed n Duffe (1999) and Hull and Whe (2000a). Begn wh a loose approxmae arbrage relaonshp. Suppose an nvesor buys a T-year par bond wh yeld o maury of y ssued by he reference eny, and buys cred proecon on ha eny for T-years n he cred defaul swap marke a a cos of p CDS. The nvesor has elmnaed mos of he defaul rsk assocaed wh he bond. If p CDS s expressed as an annual paymen as a percenage of he noonal prncpal hen he nvesor s ne annual reurn s y p CDS. By arbrage, hs ne reurn should approxmaely equal he T-year rsk-free rae, denoed by x. For y p CDS less han x, shorng he rsky bond, wrng proecon n he CDS marke and buyng he rsk-free nsrumen would be a profable arbrage opporuny. Smlarly, for y p CDS greaer han x, buyng he rsky bond, buyng proecon and shorng he rsk-free bond s profable. Ths suggess ha he prce of he CDS, p CDS, should equal he cred spread, y x. Ths s he relaonshp used n he emprcal analyss ha follows, alhough we recognse ha he arbrage s only perfec n some nsances. Duffe (1999) shows ha he spread on a par rsky floang-rae noe over a rsk-free floang-rae noe exacly equals he CDS prce. Unforunaely, floang-rae noes are rare. The spread on par fxed-coupon rsky bond over he par fxed-coupon rsk-free bond exacly equals he CDS prce f he paymen daes on he CDS and bond concde and recovery on defaul s a consan fracon of face value (Houwelng and Vors (2002)). Alernavely, wh a fla rsk-free curve and consan neres raes, he arbrage s perfec f he payou from a CDS on defaul s he sum of he prncpal amoun plus accrued neres on a rsky par yeld bond mes one mnus he recovery rae (Hull and Whe (2000a)). As noed above, however, he payou from a CDS usually equals he prncpal amoun mnus he recovery rae mes he sum of prncpal and accrued neres on he reference oblgaon. Neverheless he 13

11 referenced papers show ha he arbrage s reasonably accurae for asses radng close o par when neres raes are no hgh and yeld curves are relavely fla. Three oher consderaons are relevan. Frs, physcally-seled CDS prces, especally for European enes, may conan CTD opons as noed above. Oher hngs equal, hs wll lead CDS prces o be greaer han he cred spread. Unforunaely, s mpossble o value hs opon analycally snce here s no benchmark for he pos-defaul behavour of delverable bonds, and hence we canno smply subrac s value from he CDS prce. Second, he arbrage relaonshp ha should keep he wo prces ogeher can rely on shor sellng he cash bond. Ths s no always cosless and ndeed s no always even possble n llqud corporae bond markes. If he repo cos of shorng he cash bond s sgnfcan hen he cred spread we have compued (bond yeld mnus he rsk-free rae) underesmaes he rue cred spread (bond yeld mnus rsk-free rae plus he repo cos). Agan, he CDS prce wll end o be greaer han he measured cred spread (Duffe (1999)). Alhough boh he CTD opon and non-zero repo coss can occur ndependenly, when a frm s cred rsk ncreases he demand o shor sell he bond rses, drvng up he repo cos, and he value of he CTD opon rses. Neher marke hen provdes a pure measure of cred rsk. Quanfyng hese wo facors s dffcul n he absence of relable repo cos daa or a valuaon model for he opon. However, snce boh he repo cos and he opon value are bounded a zero, we can say ha he CDS prce s an upper lm on he prce of cred rsk whle he cred spread provdes a lower lm. Thrd, lqudy prema exs n boh he cash bond and CDS markes. The cash bond marke s ofen descrbed as relavely llqud, parcularly ousde he Uned Saes. Movemens n lqudy prema may explan a large proporon of he oal varaon n cred spreads (Colln-Dufresne, Goldsen and Marn (2001)). The CDS marke s sll relavely small despe s rapd recen growh and so demand-supply mbalances can ofen cause shor-erm prce movemens unrelaed o defaul expecaons. We make srenuous effors o reduce he mporance of CDS and bond marke lqudy prema for he reference enes we examne, as dealed n he followng secon. 14

12 3 Daa descrpon 3.1 Cred defaul swap daa Cred defaul swaps are over-he-couner dervaves raded manly n London and New York. We use daly ndcave bd and ask prces from CredTrade, a CDS broker, for sngle-name CDS ha hey deem o be lqud. The daa run from 2 January 2001 hrough 20 June The prces are for a noonal value of $10 mllon and are based on ISDA benchmark conracs for physcal selemen. All prces are for fve years, whch s by far he mos lqud maury n he CDS marke. The prces hold a close of busness (approxmaely 5pm local me) n London for European reference enes, or New York for US names. Some me seres have mssng or, very occasonally, suspcous values. We use md-marke daa suppled by J.P. Morgan, one of he leadng players n he CDS marke, o fll n mssng values, check suspcous enres and for general confrmaon of he CredTrade daa. (3) J.P. Morgan s md-marke prces are only rarely ousde he bd-ask quoes from CredTrade. We rean all US and European companes for whch we can compue a conssen seres of md-marke quoes for a leas 250 days by combnng daa sources. 3.2 Rsky bond yeld daa In order o mach he consan fve-year maury of he CDS conracs we need fve-year bond yelds. For each reference eny wh suable CDS daa we search Bloomberg for a bond wh beween hree and fve years lef o maury a he sar of our sample perod, and anoher bond wh more han sx and a half years o maury a he sar of he sample. By lnearly nerpolang hese yelds we are able o esmae a fve-year yeld o maury for he full sample whou exrapolang. We exclude floang-rae secures and all bonds ha have embedded opons, sep-up coupons, snkng funds or any specal feaure ha would resul n dfferenal prcng. We are also concerned o mnmse he possble mpac of llqudy ha appears problemac n prevous sudes usng corporae bonds and only use yelds calculaed from so-called generc Bloomberg md-marke bond prces. These are a weghed average of frm and ndcave quoes submed by a leas fve brokers or dealers. The exac weghng mehod s propreary bu frm quoes receve a hgher wegh han merely ndcave quoes. The rsky bond daa are also a close of busness bu hs ends o be slghly laer han he close n he CDS marke (eg 5:50pm New York me for US corporae bonds). (3) J.P. Morgan was he mos acve rader n he Cossn, Hrcko, Aunon-Nern and Huang (2002) CDS ransacons daabase. 15

13 Where a choce of lqud bond yelds s avalable we use bonds radng relavely close o par and, f a choce remans, whose maury more closely corresponds wh our needs. We prefer par bonds due o he mperfec arbrage consderaons menoned above. We prefer o mnmse he dfference beween maures o reduce he errors caused by our choce of lnear nerpolaon. 3.3 Reference rae yeld daa The reference rae s used o proxy he rsk-free neres rae when cred spreads are calculaed. Governmen bond yelds are he obvous choce, and we use fve-year governmen bond md-marke yelds. The curves are consruced usng Treasures for US reference enes and German governmen bonds for European enes. However, s well known ha governmen bonds are no longer an deal proxy for he unobservable rsk-free rae. Taxaon reamen, repo specals, scarcy prema and benchmark saus ssues are usually ced. As an alernave proxy we also collec fve-year swaps raes for dollars and euros. Swaps, beng synhec, are avalable n vrually unlmed quanes so ha lqudy s no an ssue, and hey have he furher advanage of beng quoed on a consan maury bass. McCauley (2002) conans a dscusson of he swap rae s role as a benchmark. However, swaps conan cred prema because () he floang leg s ndexed o LIBOR, whch s self a defaul-rsky neres rae (Sundaresan (1991)), and () he presence of counerpary rsk (alhough Duffe and Huang (1996) show hs accouns for jus 1-2 bass pons). Hull, Predescu and Whe (2003) noe ha he n-year swap rae should be hough of as he rae of neres on an n-year loan ha s srucured such ha he oblgor s ceran o have an accepable cred rang a he begnnng of each accrual perod. Ths accrual perod s sx monhs for plan vanlla swaps n he Uned Saes bu may be as hgh as welve monhs n oher markes. Snce one-year defaul probables of AA-raed nsuons s very low s clear ha swap raes are very low bu no que rsk-free raes. Duffe (1999) and Houwelng and Vors (2002) recommend usng general collaeral or repo raes n preference o swaps, argung ha hese are lqud and vrually rsk free. Accordngly, hey le below maury mached swap raes. Unforunaely, general collaeral raes are only avalable for maures up o one year, and snce he erm srucure s ypcally upward slopng durng our daa perod we prefer o use swaps raes. The 33 reference enes for whch we can fnd boh CDS and nerpolaed bond yelds are lsed n Table A ogeher wh some basc descrpon. Ths s a small cross-secon of he 157 US and European reference enes n he CredTrade CDS daabase. Of hese, 38 have been dropped due o nsuffcen CDS daa and 86 due o a lack of bond daa. In many cases marx bond prces are avalable bu we are relucan o use hese due o problems relang o he accuracy, relably 16

14 Table A Descrpve sascs Ths able lss he reference enes n our sample, ogeher wh basc descrpve nformaon and he number of observaons n he cred defaul swap and cred spread seres. See Secon 2 of he paper for deals on he crera for ncluson n he sample. Observaons Counry Secor Rang CDS Bond yeld AOL US Inerne BBB Bank of Amerca US Bankng A Bank One US Bankng A Bear Searns US Bankng A Cgroup US Bankng AA FleeBoson US Bankng A Ford Moor Cred Corp US Auomoble/Fnance BBB GE Capal Corp US Fnance AAA General Moors Cred Corp US Auomoble/Fnance BBB Goldman Sachs US Bankng A J.P. Morgan Chase US Bankng AA Lehman Brohers US Bankng A Merrll Lynch US Bankng AA Morgan Sanley US Bankng AA Wal-Mar US Real AA Wells Fargo US Bankng A Barclays UK Bankng AA Brsh Telecom UK Telecommuncaons A Commerzbank Germany Bankng A DamlerChrysler Germany Auomoble BBB Deusche Telecom Germany Telecommuncaons BBB Dresdner Bank Germany Bankng AA Endesa Span Ules A Fa Ialy Auomoble A France Telecom France Telecommuncaons BBB Iberdrola Span Ules A Mero AG Germany Real BBB Semens Germany Telecommuncaons AA Telefonca Span Telecommuncaons A Toal Fna Elf France Ol AA Uned Ules UK Ules A Vodafone UK Telecommuncaons A Volvo Sweden Auomoble A and melness of such daa. The daa we use are no deal. For example, we would have preferred o use ransacons prces raher han quoes. Cossn, Hrcko, Aunon-Nern and Huang (2002) consder CDS ransacons daa bu do no have enough observaons on parcular reference enes o perform me seres analyss. Monh-end corporae bond ransacons daa 17

15 are avalable from Capal Access Inernaonal (used by Schulz (1998), Hong and Warga (2000) and Blume, Lm and MacKnlay (1998)) bu we need a daly frequency o mach he CDS daa. The daa we use are hen he bes we hnk avalable for our purpose. 4 The emprcal relaonshp beween cred defaul swaps and cred spreads 4.1 Average prcng of cred rsk If boh CDS and cash bonds prce defaul rsk equally hen, subjec o he arbrage mperfecons noed above, he spread on he rsky bond over a rsk-free reference rae should equal he CDS prce of he same maury. Defne he bass o be he dfference beween he me CDS prce, p CDS,, and he cred spread, p CS, : bass bass swaps gov = = p p CDS, CDS, p p swaps CS, gov CS, = p = p CDS, CDS, swaps ( yˆ x ) gov ( yˆ x ) (1) where ŷ denoes he nerpolaed fve-year yeld on he rsky bond, x swaps denoes he fve-year swap rae, and x gov s he fve-year governmen bond yeld. In he frs panel of Table B we gve he average bass and he average absolue bass for each of our reference enes usng boh swap raes and governmen bond yelds as canddae reference raes. Char 1 gves a represenave plo of daly CDS prces and cred spreads over swaps for Ford. The cross-seconal mean of he me seres average bases s -41 bass pons usng fve-year governmen bond yelds as a proxy for he reference rae. The mean average bass s jus 6 bass pons f fve-year swap raes are used. Smlarly he mean average absolue bass falls from 46 bass pons over governmen bonds o 15 bass pons over swaps. Usng medan values does no aler he sory. These resuls are conssen wh Houwelng and Vors (2002) who found an average absolue prcng error of around 11 bass pons when usng swap raes and of around 33 bass pons when usng reasury yelds for bonds raed A and AA. The second panel of Table B gves mean average bass and mean average absolue bass wh he daa spl by cred rang and locaon. The mean average absolue bass over swaps rses as cred qualy (proxed by rang) declnes, a fndng also emphassed by Houwelng and Vors (2002). Smlarly, he bass over swaps s hgher for European corporaes (parly because he average rang of he European corporaes s lower). Gven hese resuls we compue cred spreads usng swap raes as he proxy for defaul-free neres raes n our subsequen analyss. 18

16 Char 1 Cred defaul swap prce and cred spread over swaps for Ford /01/ /02/ /03/2001 bass pons 25/04/ /05/ /06/ /07/ /08/ /09/ /10/ /11/ /12/ /01/ /02/ /03/ /04/ /05/2002 CDS CREDIT SPREAD The prevous resuls sugges ha he heorecal relaonshp lnkng cred spreads over he rsk-free rae o CDS prces holds reasonably well on average for mos reference enes (and especally for US frms). However, for some reference enes he average bass over swaps s meanngfully greaer han zero. The wo exreme cases are France Telecom (64 bass pons) and Fa (45 bass pons), wh he former ploed n Char 2. Traders ndcae ha large and perssen posve bases such as hese are due o he presence of he wo mperfecons noed above non-zero repo coss n he bond marke mean we have underesmaed he rue cred spread and he cheapes-o-delver opon nflaes he CDS prce. J.P. Morgan (2002) llusraes he mporance of ncludng repo coss for a cross-secon of 19 bonds wh he larges bass from her unverse of prced bonds on 16 Augus 2002 (unforunaely jus afer our sample ends). A France Telecom egh-year bond had he hghes bass on ha day (186 bass pons) bu was mpossble o borrow hs bond on repo makng he rue cred spread mpossble o calculae. 19

17 Table B Dscrepances n he average prcng of cred rsk n cred defaul swap and cash bond markes Panel A provdes descrpve sascs of he bass, defned o be he dfference beween he cred defaul swap prce and he cred spread, for each reference eny and expressed n bass pons. The cred spread s calculaed as he dfference beween he nerpolaed fve-year yeld on he rsky bonds and eher he fve-year reasury bond rae or he fve-year swap rae. Panel B provdes summary sascs for groups of bonds accordng o rang and naonaly. Panel A: Treasury raes Swap raes Average absolue Average absolue Average bass bass Average bass bass AOL Bank of Amerca Bank One Bear Searns Cgroup FleeBoson Ford Moor Cred Corp GE Capal Corp General Moors Cred Corp Goldman Sachs J.P. Morgan Chase Lehman Brohers Merrll Lynch Morgan Sanley Wal-Mar Wells Fargo Barclays Brsh Telecom Commerzbank DamlerChrysler Deusche Telecom Dresdner Bank Endesa Fa France Telecom Iberdrola Mero AG Semens Telefonca Toal Fna Elf Uned Ules Vodafone Volvo Mean Medan Panel B: Treasury raes Swap raes Average absolue Average absolue Means Average bass bass Average bass bass AAA-AA A BBB US Europe

18 Char 2 Cred defaul swap prce and cred spread over swaps for France Telecom /01/ /02/ /03/ /04/2001 bass pons 02/05/ /06/ /07/ /08/ /09/ /10/ /11/ /12/ /01/ /02/ /03/ /04/ /05/ /06/2002 CDS CREDIT SPREAD The average bass for he remanng 18 bonds was 103 bass pons bu once he repo cos was added o he cred spread over swaps he average repo-adjused bass fell o 13 bass pons. Hgh bass levels reman for some bonds even afer ncludng repo coss. For example, he egh European reference enes on he ls had an average bass of 96 bass pons and an average repo-adjused bass of 29 bass pons. (4) Ths raher large resdual s, we argue, prmarly due o he cheapes-o-delver opon. A naural expermen llusraes he poenal value of such opons. On 11 December 2001, Fa ssued a bond converble no he sock of General Moors. Ths bond raded a a subsanal dscoun o exsng sragh Fa bonds. If resrucurng was hough possble for Fa (and press repors around he me sugges was) hs would ncrease he value of he CTD opon snce under ISDA documenaon hs was a delverable bond. Char (4) The US enes had an average bass of 109 bass pons and an average repo-adjused bass of 0.5 bass pons, conssen wh he hypohess ha CTD opons are less mporan n hs jursdcon. 21

19 Char 3 Fa s converble bond ssue and he value of he cheapes-o-delver opon 200 Bass pons Bass pons CDS 180 Cred Spread Bass (RHS) /10/01 08/10/01 15/10/01 22/10/01 29/10/01 05/11/01 12/11/01 19/11/01 26/11/01 03/12/01 10/12/01 17/12/01 24/12/01 31/12/01 07/01/02 14/01/02 21/01/02 28/01/02 3 llusraes he behavour of he CDS prce, cred spread and bass around hs me. The average bass for Fa from he sar of he sample o 10 December 2001 was jus 8.8 bass pons. In he perod mmedaely before he ssue he bass flucuaed around hs level, suggesng no large repo coss or valuable CTD opon. Immedaely followng he ssue, he bass jumped o 50 bass pons, due almos enrely o he ncrease n he CDS prce snce he cred spread was relavely sable over he ssue. Snce we have no evdence ha Fa s exan sragh bonds wen specal afer he ssue, we ascrbe hs jump n he bass o he newly emerged CTD opon value. (5) These cases of large average bass levels are he excepon raher han he rule n our sample. A more formal es of he equvalence of he prce of cred rsk across he wo markes can be movaed n erms of ransory and permanen prce movemens. Suppose ha he unobservable effcen prce of cred rsk, m, follows a random walk: m m u = 1 (2) (5) The bass also jumped n subsequen monhs when Fa was affeced by rang agency acons and equy ssuance lkely o have alered he valuaon of he opon. 22

20 where u s..d. wh zero mean and consan varance. The observed prce n each marke j a me, p j,, s equal o hs effcen prce plus a componen conanng mcrosrucural nose, s j,, assumed o be ransen, plus a componen reflecng oher possbly non-ransen facors ncluded n he observed prce, c j, : p = m s c j CDS CS (3) j, j, j, =, If he wo markes prce cred rsk equally n he long run, hen her prces should be conegraed wh conegrang vecor [1, -1, c], suggesng a saonary bass, and deally he consan n he conegrang space, c, should equal zero. Snce we know our proxy for he rsk-free rae s mperfec, however, we do no requre ha he consan equal zero. If he prces do no conegrae wh he [1, -1, c] resrcon mposed hen eher () he wo markes prce rsk dfferenly (n excess of a consan amoun), () a leas one marke prce conans me-varyng non-ransen facors ha reflec somehng oher han cred rsk or () a leas one marke prce conans me-varyng non-ransen measuremen error. From our dscusson of CDS conrac specfcaons n Secon 2.1, we suspec a pror ha some CDS prces may conan a cheapes-o-delver opon relaed o resrucurng lkely o resul n a case () falure of he conegraon ess. Furher, from Secon 2.2 we know ha he cred spread as measured gnores he repo cos of he bond. If hs cos s sgnfcan and no purely a shor-erm phenomenon we mgh expec a case () falure of he conegraon ess. We repor Johansen conegraon es resuls for each reference eny n Table C. There s evdence of conegraon under he mposed resrcon of a saonary bass for each US reference eny examned. (6) For hese frms, he CDS and bond marke appear o prce rsk equally on average, a leas up o a consan erm ha possbly reflecs msmeasuremen of he rsk-free rae. Furher, we canno rejec he addonal resrcon ha he consan s zero n he conegrang vecor for 11 of he 16 US enes a he 1% level, suggesng for hese names ha he cred spread over swaps equals he CDS prce over he long run. We fnd suppor for conegraon for only 10 of he 17 European enes, alhough a saonary bass canno be rejeced a he 1% level for any of hese. The usual suspecs France Telecom and Fa are ncluded n he ls of frms ha rejec conegraon, ogeher wh Vodafone, anoher frm wh a large average bass over swaps from Table B. As we have noed, Fa clearly suffers from he sudden emergence of a CTD opon and we canno rejec he null of a saonary (6) The presence of a conegrang vecor s suggesed for all 16 US companes. Of hese, hree rejec he resrcon of a saonary bass a he 5% level bu none rejec a he 1% level. 23

21 Table C The long-run relaonshp beween he prce of cred rsk n CDS and bond markes The frs wo columns of Panel A presen Johansen race es sascs for he number of conegrang relaonshps beween he cred defaul swap prce and he cred spread over swap raes. A consan s ncluded n he long-erm relaonshp, and he number of lags n he underlyng vecor auoregresson s opmsed usng he AIC for each eny. The hrd and fourh columns gve es sascs for resrcons on he conegrang space for hose enes where a conegrang vecor appears o be presen. The frs resrcon s ha he cred defaul swap prce mnus he cred spread over swaps s consan, and s dsrbued as ch-squared wh one degree of freedom. The second resrcon s ha he cred defaul swap prce equals he cred spread over swaps, and s dsrbued as ch-squared wh wo degrees of freedom. Panel B repors smlar ess for Fa over a resrced sample perod. Rejecon of he null a 1, 5 or 10% level s ndcaed by a superscrp A, B or C respecvely. Panel A: Number of conegrang vecors Resrcons on vecor None A mos 1 [1, -1, c] [1, -1, 0] AOL A C A Bank of Amerca B B 5.84 C Bank One C B Bear Searns A B Cgroup B 8.63 C 3.53 C 8.57 B FleeBoson B 8.28 C Ford Moor Cred Corp B GE Capal Corp B B A General Moors Cred Corp A A Goldman Sachs A C 6.79 B J.P. Morgan Chase A C 4.12 Lehman Brohers A A Merrll Lynch B Morgan Sanley B B 6.59 B Wal-Mar A A Wells Fargo A C 6.62 B Barclays Bank NA NA Brsh Telecom C Commerzbank B B A DamlerChrysler B C Deusche Telekom C B 9.09 B Dresdner Bank C NA NA Endesa NA NA Fa NA NA France Telecom NA NA Iberdrola B C A Mero AG B C A Semens C B Telefonca B C 9.26 A Toal Fna Elf NA NA Uned Ules C B Vodafone NA NA Volvo B A Panel B: Number of conegrang vecors Resrcons on vecor None A mos 1 [1, -1, c] [1, -1, 0] Fa (Jan 2001 Nov 2001) A A 24

22 bass usng daa up o he emergence of he delvery opon (see panel B). Surprsngly, four enes wh small average bases also rejec conegraon. We suspec ha hs s because bd-ask spreads are proporonaely so wde ha he CDS prce and cred spread have moved n seemngly unrelaed ways whou arbrage forces comng no effec. 4.2 Prce dscovery One of he mos mporan funcons of fnancal markes s prce dscovery, defned by Lehmann (2002) o be he effcen and mely ncorporaon of he nformaon mplc n nvesor radng no marke prces. When here s only one locaon for radng an asse, by defnon all prce dscovery akes place n ha marke place. When closely relaed asses rade n dfferen locaons, order flow s fragmened and prce dscovery s spl beween markes. We have demonsraed ha boh he cash bond and he cred defaul swap markes usually appear o prce cred rsk equally on average. CDS prces and cred spreads are conegraed I(1) varables for mos of our sample of companes and he common facor can be vewed as he mplc effcen prce of cred rsk. Whch of he wo markes conrbues mos o he cred rsk prce dscovery process s a queson ha we aemp o resolve n hs secon. The approprae mehod o nvesgae he mechancs of prce dscovery s no clear. The wo popular common facor models due o Hasbrouck (1995) and Gonzalo and Granger (1995) boh rely on vecor error correcon models of marke prces. Hasbrouck s model of nformaon shares assumes ha prce volaly reflecs new nformaon, and so he marke ha conrbues mos o he varance of he nnovaons o he common facor s presumed o also conrbue mos o prce dscovery. Gonzalo and Granger s approach decomposes he common facor self and gnorng he correlaon beween he markes arbues superor prce dscovery o he marke ha adjuss leas o prce movemens n he oher marke. When prce change nnovaons are correlaed, Hasbrouck s approach can only provde upper and lower bounds on he nformaon shares of each marke. However, Balle, Booh, Tse and Zabona (2002) argue ha he average of hese bounds provdes a sensble esmae of he markes roles n he dscovery of he effcen prce. Snce neher mehod s consdered unversally superor we repor boh. To compue he measures of he conrbuons o prce dscovery s necessary frs o esmae he followng vecor error correcon model (VECM): p p p ( pcds, 1 α 0 α1 pcs, 1 ) β1 j pcds, j CDS, = 1 δ 1 j pcs, j ε1 j= 1 j= 1 λ (4a) 25

23 p p p ( pcds, 1 α 0 α 1 pcs, 1 ) β 2 j pcds, j CS, = 2 δ 2 j pcs, j ε 2 j= 1 j= 1 λ (4b) where ε 1 and ε 2 are..d. shocks. If he cash bond marke s conrbung sgnfcanly o he dscovery of he prce of cred rsk, hen λ 1 wll be negave and sascally sgnfcan as he CDS marke adjuss o ncorporae hs nformaon. Smlarly, f he CDS marke s an mporan venue for prce dscovery, hen λ 2 wll be posve and sascally sgnfcan. If boh coeffcens are sgnfcan, hen boh markes conrbue o prce dscovery. The exsence of conegraon means ha a leas one marke has o adjus by he Granger represenaon heorem (Engle and Granger (1987)). Tha marke s neffcen snce he prce reacs o publcly avalable nformaon. Manpulaons of he relave magnudes of he λ coeffcens reveal whch of he wo markes leads n erms of prce dscovery. The conrbuons of marke 1 (he CDS marke) o prce dscovery are defned by he followng expressons: σ 12 λ 2 σ σ σ λ2σ 1 λ1 HAS 2 σ 1 1 = HAS = λ2 σ 1 2λ1λ2σ 12 λ1 σ 2 2 λ2 σ 1 2λ1λ2σ 12 λ1 σ 2 λ2 GG = λ λ 2 1 where HAS 1 and HAS 2 gve he wo bounds of Hasbrouck s measures and GG sands for he Gonzalo and Granger measure. The covarance marx of ε 1 and ε 2 s represened by he erms σ 2 1, σ 12, σ 2 2. The prce dscovery sascs are repored n panel A of Table D for hose enes where conegraon s presen beween CDS prces and cred spreads. Where approprae, he resrcons ha α 1 equals uny and α 0 equals zero are mposed. In 25 of he 27 cases λ 2 s sgnfcanly posve, ndcang ha he CDS marke conrbues o prce dscovery. The cash bond marke appears o have a sgnfcan role o play n only egh cases. Of hese egh, he cash marke s he source of all nformaon n only one (Uned Ules). In fve cases, whle boh cash and dervaves marke conrbue sgnfcanly he CDS marke s domnan (defned as boh he Hasbrouck lower bound and he Gonzalo-Granger measure suggesng more han 50% of he dscovery occurrng n he CDS marke), and n he 26

24 Table D Conrbuons o prce dscovery Panel A repors varous measures of he conrbuon o he cred prce dscovery process made by cred defaul swap prces for hose reference enes where he resuls n Table C ndcae a long-run relaonshp beween cred defaul swap prces and cred spreads exs. The measures are based on he wo regressons: p p p 1( pcds, 1 α 0 α 1 pcs, 1 ) β j 1 j pcds, j p ( pcds, 1 α 0 α1 pcs, 1 ) β 2 j pcds, j p CDS, = λ δ = = j j p CS, j ε 1 p CS, = λ 2 δ = = j j j p CS, j ε 2 Where approprae accordng o he resuls n Table C, he resrcon ha α 0 equals zero and/or α 1 equals uny are mposed. The Hasbrouck measure provdes upper and lower bounds o he prce dscovery conrbuon made n he cred defaul swap marke. The able also repors he mdpon of hs range. The fnal column repors he Granger- Gonzalo measure. Panel B repors Granger causaly es resuls for hose reference enes where he resuls n Table C sugges no long-erm relaonshp beween cred defaul swap prces and cred spreads. Panel A: Hasbrouck GG λ 1 -sa λ 2 -sa Lower Upper Md AOL Bank of Amerca Bank One Bear Searns Cgroup FleeBoson Ford Moor Cred Corp GE Capal Corp General Moors Cred Co Goldman Sachs J.P. Morgan Chase Lehman Brohers Merrll Lynch Morgan Sanley Wal-Mar Wells Fargo Brsh Telecom Commerzbank DamlerChrysler Deusche Telecom Fa (Jan 01 Nov 01) Iberdrola Mero AG Semens Telefonca Uned Ules Volvo AB Mean Medan

25 Table D Connued Panel B: Ho: CDS causes CS Ho: CS causes CDS Sum of sgnfcan coeffcens F-sa p-value Sum of sgnfcan coeffcens F-sa p-value Barclays Dresdner Endesa France Telecom Toal Fna Elf Vodafone remanng wo cases he prce dscovery measures gve conflcng sgnals. On average, he CDS marke conrbues around 80% of prce dscovery. (7) Snce he prces are measured asynchronously n he bond and CDS markes we re-compue he prce dscovery measures wh he CDS prces lagged by one day o delberaely favour he bond marke. Whle obvously he CDS marke s conrbuon o prce dscovery s lower n hs case, remans he man forum for prce dscovery. For a small subse of our reference enes conegraon s rejeced and hence he VECM represenaon s no vald. We beleve ha rejecon s due o he presence of a subsanal cheapes-o-delver opon n he CDS prce and/or bndng shor sales consrans n he cash bond marke meanng ha we are markedly msmeasurng he cred spread. Snce we canno prce he opon or more accuraely measure he spread, we rely on he smpler concep of Granger causaly n a smple VAR n dfferences o es for prce leadershp n hese cases. These resuls are gven n panel B of Table D. CDS prces Granger-cause cred spreads for four of he sx enes. For he oher wo enes here s no causaon n eher drecon, whle cred spreads cause CDS prces for hree enes (ndcang b-dreconal causaly). Wh he excepon of France Telecom, he sum of he coeffcens on lagged CDS prces s noceably greaer han for lagged spreads suggesng ha he economc mporance of CDS prces s greaer. Why do we fnd such srong evdence ha cred defaul swap prces lead cred spreads? Prce dscovery wll occur n he marke where nformed raders rade mos. The CDS marke, as we noed above, benefs from beng arguably he eases place n whch o rade cred rsk. Is synhec naure means ha does no suffer from he shor-sales consrans seen n he cash bond marke, and buyng (or sellng) relavely large quanes of cred rsk s possble. The (7) In hree cases he Gonzalo-Granger measure produces a sasc greaer han one, whch s dffcul o nerpre. In compung he average value, we replaced hese numbers by uny. 28

26 sandard CDS conrac sze s $10 mllon whle Schulz (1998) repors he average cash marke rade sze o be of $1.5 mllon. Addonally, he parcpans n he cash and cred dervaves markes are lkely o be dfferen. There s no counerpary rsk (beyond selemen rsk) when radng a cash bond. CDS radng does enal akng on counerpary rsk and for hs reason s usually resrced o nsuons of relavely hgh cred rang. Perhaps more mporanly, he CDS marke s he forum for radng cred rsk, whereas he cash marke rades bond cred rsk. Parcpans hedgng loan and counerpary exposures are able o do so n he CDS marke. I s hs concenraon of lqudy from dfferen pools ha means he CDS marke leads he bond marke accordng o some marke parcpans. Gven ha CDS prces and cred spreads are lnked by an arbrage relaonshp, how can he markes perss n prcng cred rsk dfferenly? Our answer s n several pars. Frs, n he absence of ransacons coss daa we canno be sure ha he dscrepances are large enough o be profable o arbrageurs. Second, he arbrage relaonshp s only approxmae as noed above and we are usng a synhec fve-year bond spread ha s no raded n he marke. Thrd, we do no measure he repo coss of shorng he bond. I s possble ha when he cred qualy of an eny declnes, he repo marke prce ncreases such ha he arbrage gap s closed. I could be argued ha we have only parally capured he prce conrbuon from he cash marke by gnorng he repo cos. However, snce repos are no raded for erms n excess of one year, le alone he fve years necessary n our consruc, he repo marke canno conrbue owards he dscovery of he prce of fve-year cred rsk. Furhermore, even f he holder of a bond sees msprcng n he CDS marke here are wo reasons why he canno arbrage he dscrepancy fund managers are ofen no permed o rade CDS conracs eher by naonal law or mandae, and he noonal sze of he CDS conrac s so large ha he cash bond holdng s unlkely o be large enough (see Dhllon (2002)). 5 The deermnans of changes n cred defaul swap prces and cred spreads 5.1 Theorecal deermnans of cred spread and CDS prce changes From he conngen-clams approach, cred spreads on corporae bonds occur for wo reasons. Frs, here s he possbly of defaul. Second, should defaul occur he bondholder receves only a proporon of conraced paymens. Facors relaed o changes n he probably of a bond defaulng or changes n he lkely amoun recovered should help explan cred spread and CDS prce changes snce he laer are nmaely relaed wh he former. However, Table E shows 29

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