The Determinants of Credit Spread Changes

Transcription

1 The Deerminans of Credi Spread Changes PIERRE COLLIN-DUFRESNE, ROBERT S. GOLDSTEIN, and J. SPENCER MARTIN ABSTRACT Using dealer s quoes and ransacions prices on sraigh indusrial bonds, we invesigae he deerminans of credi spread changes. Variables ha should in heory deermine credi spread changes have raher limied explanaory power. Furher, he residuals from his regression are highly crosscorrelaed, and principal componens analysis implies hey are mosly driven by a single common facor. Alhough we consider several macro-economic and financial variables as candidae proxies, we canno explain his common sysemaic componen. Our resuls sugges ha monhly credi spread changes are principally driven by local supply/demand shocks ha are independen of boh credi-risk facors and sandard proxies for liquidiy. Collin-Dufresne is a Carnegie Mellon Universiy. Goldsein is a Washingon Universiy in S. Louis. Marin is a Arizona Sae Universiy. A significan porion of his paper was wrien while Goldsein and Marin were a The Ohio Sae Universiy. We hank Rui Albuquerque, Gurdip Bakshi, Greg Bauer, Dave Brown, Francesca Carrieri, Peer Chrisoffersen, Susan Chrisoffersen, Greg Duffee, Darrell Duffie, Vihang Errunza, Gifford Fong, Mike Gallmeyer, Lauren Gauhier, Rick Green, John Griffin, Jean Helwege, Kris Jacobs, Chris Jones, Andrew Karolyi, Dilip Madan, David Mauer, Erwan Morellec, Federico Nardari, NR Prabhala, Tony Sanders, Sergei Sarkissian, Bill Schwer, Ken Singleon, Cheser Spa, René Sulz (he edior), Suresh Sundaresan, Haluk Unal, Karen Wruck, and an anonymous referee for helpful commens. We hank Ahsan Aijaz, John Puleo, and Laura Tule for research assisance. We are also graeful o seminar paricipans a Arizona Sae Universiy, Universiy of Maryland, McGill Universiy, The Ohio Sae Universiy, Universiy of Rocheser, and Souhern Mehodis Universiy.

2 The relaion beween sock and bond reurns has been widely sudied a he aggregae level (see, for example, Campbell and Ammer (1993), Keim and Sambaugh (1986), Fama and French (1989), and Fama and French (1993)). Recenly, a few sudies have invesigaed ha relaion a boh he individual firm level (see, for example, Kwan (1996)) and porfolio level (see, for example, Blume, Keim and Pael (1991), and Cornell and Green (1991)). These sudies focus on corporae bond reurns, or yield changes. The main conclusions of hese papers are: (1) high-grade bonds behave like Treasury bonds, and (2) low-grade bonds are more sensiive o sock reurns. The implicaions of hese sudies may be limied in many siuaions of ineres, however. For example, hedge funds ofen ake highly levered posiions in corporae bonds while hedging away ineres rae risk by shoring reasuries. As a consequence, heir porfolios become exremely sensiive o changes in credi spreads raher han changes in bond yields. The disincion beween changes in credi spreads and changes in corporae yields is significan: while an adjused R 2 of 60 percen is obained when regressing high-grade bond yield changes on Treasury yield changes and sock reurns (see Kwan (1996)) we find ha he R 2 falls o five percen when he dependen variable is credi spread changes. Hence, while much is known abou yield changes, we have very limied knowledge abou he deerminans of credi spread changes. Below, we invesigae he deerminans of credi spread changes. From a coningen-claims, or noarbirage sandpoin, credi spreads obain for wo fundamenal reasons: 1) here is a risk of defaul, and 2) in he even of defaul, he bondholder receives only a porion of he promised paymens. Thus, we examine how changes in credi spreads respond o proxies for boh changes in he probabiliy of fuure defaul and for changes in he recovery rae. Separaely, recen empirical sudies find ha he corporae bond marke ends o have relaively high ransacions coss and low volume. 1 These findings sugges looking beyond he pure coningen-claims viewpoin when searching for he deerminans of credi spread changes, since one migh expec o observe a liquidiy premium. Thus, we also examine he exen o which credi spread changes can be explained by proxies for liquidiy changes. Our resuls are, in summary: alhough we consider numerous proxies ha should measure boh changes in defaul probabiliy and changes in recovery rae, regression analysis can only explain abou 25 percen of he observed credi spread changes. We find, however, ha he residuals from hese regressions are highly cross-correlaed, and principal componens analysis implies ha hey are mosly driven by a single common facor. An imporan implicaion of his finding is ha if any explanaory variables have been omied, hey are likely no firm-specific. We herefore re-run he regression, bu 1

3 his ime include several liquidiy, macroeconomic, and financial variables as candidae proxies for his facor. We canno, however, find any se of variables ha can explain he bulk of his common sysemaic facor. Our findings sugges ha he dominan componen of monhly credi spread changes in he corporae bond marke is driven by local supply/demand shocks ha are independen of boh changes in credi-risk and ypical measures of liquidiy. We noe ha a similar, bu significanly smaller effec has been documened in he morgage backed (Ginnie Mae) securiies marke by Boudoukh, Richardson, Sanon, and Whielaw (1997), who find ha a 3-facor model explains over 90 percen of Ginnie Mae yields, bu ha he remaining variaion apparenly canno be explained by he changes in he yield curve. 2 In conras, our muliple-facor model explains only abou one-quarer of he variaion in credi spreads, wih mos of he remainder aribuable o a single sysemaic facor. Similarly, Duffie and Singleon (1999) find ha boh credi-risk and liquidiy facors are necessary o explain innovaions in U.S. swap raes. However, when analyzing he residuals hey are unable o find explanaory facors. They conclude ha swap marke-specific supply/demand shocks drive he unexplained changes in swap raes. Exising lieraure on credi spread changes is limied. 3 Pedrosa and Roll (1998) documen considerable co-movemen of credi spread changes among index porfolios of bonds from various indusry, qualiy, and mauriy groups. Noe ha his resul by iself is no surprising, since heory predics ha all credi spreads should be affeced by aggregae variables such as changes in he ineres rae, changes in business climae, changes in marke volailiy, ec. The paricularly surprising aspec of our resuls is ha, afer conrolling for hese aggregae deerminans, he sysemaic movemen of credi spread changes sill remains, and indeed, is he dominan facor. Brown (2000) invesigaes credi spread innovaions a he porfolio level. Alhough he focus of his paper differs from ours, he also finds considerable evidence ha a large porion of credi spread changes is due o non-credi risk facors. The res of he paper is organized as follows. In Secion I, we examine he heoreical deerminans of credi spread changes from a coningen-claims framework. In Secion II, we discuss he daa and define he proxies used. In Secion III, we analyze our resuls. In Secion IV, we provide evidence for he robusness of our resuls on several frons. Firs, we repea he analysis using ransacions (raher han quoes) daa o obain credi spread changes. Second, we consider a hos of new explanaory variables ha proxy for changes in liquidiy and oher macro-economic effecs. Finally, we perform a regression analysis on simulaed daa o demonsrae ha our empirical findings are no being driven by he economeric echniques used. We conclude in Secion V. 2

4 I. Theoreical Deerminans of Credi Spread Changes So-called srucural models of defaul provide an inuiive framework for idenifying he deerminans of credi spread changes. 4 These models build on he original insighs of Black and Scholes (1973), who demonsrae ha equiy and deb can be valued using coningen-claims analysis. Inroduced by Meron (1974) and furher invesigaed by, among ohers, Black and Cox (1976), Leland (1994), Longsaff and Schwarz (1995), Bryis and de Varenne (1997), and Collin-Dufresne and Goldsein (2000), srucural models posi some firm value process, and assume ha defaul is riggered when he firm value falls below some hreshold. This defaul hreshold is a funcion of he amoun of deb ousanding. In srucural models, holding a deb claim is hus analogous o holding a similar risk-free deb claim and having sold o equiy holders an opion o pu he firm a he value of he risk-free claim. 5 Mahemaically, coningen-claims pricing is mos readily accomplished by pricing derivaives under he so-called risk-neural measure, where all raded securiies have an expeced reurn equal o he risk-free rae (see Cox and Ross (1976) and Harrison and Kreps (1979)). In paricular, he value of he deb claim is deermined by compuing is expeced (under he risk-neural measure) fuure cash flows discouned a he risk-free rae. As he credi spread CS() is uniquely defined hrough: (1) he price of a deb claim, (2) his deb claim s conracual cash flows, and (3) he (appropriae) risk-free rae, we can wrie CS() = CS(V,r, {X }), where V is firm value, r is he spo rae, and {X } represens all of he oher sae variables needed o specify he model. 6 Since credi spreads are uniquely deermined given he curren values of he sae variables, i follows ha credi spread changes are deermined by changes in hese sae variables. Hence, srucural models generae predicions for wha he heoreical deerminans of credi spread changes should be, and moreover offer a predicion for wheher changes in hese variables should be posiively or negaively correlaed wih changes in credi spreads. We discuss hese proposed deerminans individually. 1. Changes in he Spo Rae As poined ou by Longsaff and Schwarz (1995), he saic effec of a higher spo rae is o increase he risk-neural drif of he firm value process. A higher drif reduces he incidence of defaul, and in urn, reduces he credi spreads. This predicion is borne ou in heir daa. Furher evidence is provided by Duffee (1998), who uses a sample resriced o non-callable bonds and 3

5 finds a significan, albei weaker, negaive relaionship beween changes in credi spreads and ineres raes. 2. Changes in Slope of Yield Curve Alhough he spo rae is he only ineres-rae-sensiive facor ha appears in he firm value process, he spo rae process iself may depend upon oher facors as well. 7 For example, Lierman and Scheinkman (1991) find ha he wo mos imporan facors driving he erm srucure of ineres raes are he level and slope of he erm srucure. If an increase in he slope of he Treasury curve increases he expeced fuure shor rae, hen by he same argumen as above, i should also lead o a decrease in credi spreads. From a differen perspecive, a decrease in yield curve slope may imply a weakening economy. I is reasonable o believe ha he expeced recovery rae migh decrease in imes of recession. 8 Once again, heory predics ha an increase in he Treasury yield curve slope will creae a decrease in credi spreads. 3. Changes in Leverage Wihin he srucural framework, defaul is riggered when he leverage raio approaches uniy. Hence, i is clear ha credi spreads are expeced o increase wih leverage. Likewise, credi spreads should be a decreasing funcion of he firm s reurn on equiy, all else equal. 4. Changes in Volailiy The coningen-claims approach implies ha he deb claim has feaures similar o a shor posiion in a pu opion. Since opion values increase wih volailiy, i follows ha his model predics credi spreads should increase wih volailiy. This predicion is inuiive: increased volailiy increases he probabiliy of defaul. 5. Changes in he Probabiliy or Magniude of a Downward Jump in Firm Value Implied volailiy smiles in observed opion prices sugges ha markes accoun for he probabiliy of large negaive jumps in firm value. Thus, increases in eiher he probabiliy or he magniude of a negaive jump should increase credi spreads. 6. Changes in he Business Climae Even if he probabiliy of defaul remains consan for a firm, changes in credi spreads can occur due o changes in he expeced recovery rae. The expeced recovery rae in urn should be 4

6 a funcion of he overall business climae. 9 II. Daa Our firs objecive is o invesigae how well he variables idenified above explain observed changes in credi spreads. Here, we discuss he daa used for esimaing boh credi spreads and proxies for he explanaory variables. 1. Credi Spreads The corporae bond daa are obained from Lehman Brohers via he Fixed Income (or Warga) Daabase. We use only quoes on non-callable, non-puable deb of indusrial firms; quoes are discarded whenever a bond has less han four years o mauriy. Monhly observaions are used for he period July 1988 hrough December Only observaions wih acual quoes are used, since i has been shown by Sarig and Warga (1989) ha marix prices are problemaic. 10 To deermine he credi spread, CS i, for bond i a monh, we use he Benchmark Treasury raes from Daasream for mauriies of 3, 5, 7, 10, and 30 years, and hen use a linear inerpolaion scheme o esimae he enire yield curve. Credi spreads are hen defined as he difference beween he yield of bond-i and he associaed yield of he Treasury curve a he same mauriy. 2. Treasury Rae Level We use Daasream s monhly series of 10-year Benchmark Treasury raes, r 10. To capure poenial non-linear effecs due o convexiy, we also include he squared level of he erm srucure, (r 10 ) Slope of Yield Curve We define he slope of he yield curve as he difference beween Daasream s 10-year and 2-year Benchmark Treasury yields, slope ( r 10 r 2 ). We inerpre his proxy as boh an indicaion of expecaions of fuure shor raes, and as an indicaion of overall economic healh. 4. Firm Leverage For each bond i, marke values of firm equiy from CRSP and book values of firm deb from COMPUSTAT are used o obain leverage raios, lev i, which we define as Book Value of Deb Marke Value of Equiy + Book Value of Deb. 5

7 Since deb levels are repored quarerly, linear inerpolaion is used o esimae monhly deb figures. We noe ha previous sudies of yield changes have ofen used he firm s equiy reurn o proxy for changes in he firm s healh, raher han changes in leverage. For robusness, we also use each firm s monhly equiy reurn, re i, obained from CRSP, as an explanaory variable. 5. Volailiy In heory, changes in a firm s fuure volailiy can be exraced from changes in implied volailiies of is publicly raded opions. Unforunaely, mos of he firms we invesigae lack publicly raded opions. 11 Thus, we are forced o use he bes available subsiue: changes in he VIX index, VIX, which corresponds o a weighed average of eigh implied volailiies of near-he-money opions on he OEX (S&P 100) index. 12 These daa are provided by he Chicago Board Opions Exchange. While use of VIX in place of firm-specific volailiy assumes a srong posiive correlaion beween he wo, his assumpion does no seem o affec our resuls significanly. Indeed, one of our main findings is ha mos of he credi spread innovaion is unexplained, and ha he residuals are highly correlaed cross-secionally. Noe ha if changes in individual firm volailiy and marke volailiy are no highly correlaed, hen our proxy should bias our resuls away from finding residuals which are so sysemaic. 6. Jump Magniudes and Probabiliies Changes in he probabiliy and magniude of a large negaive jump in firm value should have a significan effec on credi spreads. This facor is raher difficul o proxy because hisorical occurrences of such jumps are rare enough o be of lile value in predicing fuure probabiliies and magniude of such jumps. Therefore, we approach he problem using a forward-looking measure. In paricular, we employ changes in he slope of he smirk of implied volailiies of opions on S&P 500 fuures o deermine perceived changes in he probabiliy of such jumps. Opions and fuures prices were obained from Bridge. Our proxy is consruced from a- and ou-of-he money pus, and a- and in-he-money calls wih he shores mauriy on he nearby S&P 500 fuures conrac. We firs compue implied volailiies for each srike K using he sandard Black and Scholes (1973) model. We hen fi he linear-quadraic regression σ(k) = a + bk + ck 2, where K is he srike price. Our esimae of his slope, jump,isdefined via jump =[σ(0.9f ) σ(f )], where F is he a-he money srike price, which equals he curren fuures price. We choose o look a he implied volailiy a K =.9F because we do no wan 6

8 o exrapolae he quadraic regression beyond he region where acual opion prices are mos ypically observed. Noe ha if here is a non-negligible probabiliy of large negaive jumps in firm value, hen he appropriae hedging ool for corporae deb may no be he firm s equiy, bu raher deep ou-of-he-money pus on he firm s equiy. Assuming large negaive jumps in firm value are highly correlaed wih marke crashes, we hope o capure sysemaic changes in he marke s expecaion of such evens wih his proxy. We expec ha a seepening in he slope of he smirk will rigger an increase in credi spreads. 7. Changes in Business Climae We use monhly S&P 500 reurns, S&P, as a proxy for he overall sae of he economy. The daa are obained from CRSP. Table 1 summarizes he prediced sign of he correlaion beween changes in credi spreads and changes in he underlying variable. INSERT TABLE I ABOUT HERE III. The Empirical Tes A. Mehodology In addiion o being non-callable and non-puable, for an indusrial bond i o ener our sample, i mus have a leas 25 monhly rader quoes CS i over he period July 1988 hrough December These resricions generae a final sample of 688 bonds from 261 differen issuers. The average number of quoes per bond is 56. We define CS i as he difference in credi spreads beween wo consecuive quoes. Of he resuling observaions CS i, 99.8 percen are from differences in credi spread quoes from consecuive monhs. For each sample bond i a dae wih credi spread CS i we esimae he following regression: CS i = α + β i 1 levi + βi 2 r10 + β i 3 ( r10 ) 2 + β i slope 4 +β i 5 VIX + β i 6 S&P + β i 7 jump + ɛi. (1) For ease of analysis, each bond is assigned o a leverage group based on he firm s average leverage raio for hose monhs where he bond has quoes available. These groups have been chosen o broadly 7

9 replicae he boom four quiniles and op wo deciles of he sample: under 15 percen, 15 up o 25 percen, 25 up o 35 percen, 35 up o 45 percen, 45 up o 55 percen, and 55 percen or more. In Table II, summary saisics of he disribuion of coefficien esimaes are presened. 13 In Panels II and III of Table II we presen our findings for shor- and long-mauriy subsamples. In he shor subsample, quoes are discarded whenever a bond has more han nine years o mauriy, and in he long subsample, quoes are discarded whenever a bond has less han 12 years o mauriy. Then, in each subsample and for each bond i sill having a leas 25 monhly quoes CS i over he period July 1988 o December 1997, we re-esimae he regression of equaion (1). INSERT TABLE II ABOUT HERE Previous sudies of corporae bonds have ofen used sock reurns re i raher han changes in leverage o proxy for changes in he firm s healh. Furher, hese sudies have grouped bonds by raing raher han firm leverage. For robusness, we also invesigae credi spread changes using his approach. We hus esimae he following regression: CS i = α + β i 1 rei + βi 2 r10 + β i 3 ( r10 ) 2 + β i slope 4 +β i 5 VIX + β i 6 S&P + β i 7 jump + ɛi (2) In Table III, summary saisics of he disribuion of coefficien esimaes are presened. Each bond is assigned o a raing group based on he firm s average raing in monhs where he bond has quoes available. The bond raing is aken as he weaker of Moody s or S&P raings whenever boh are available. Mauriy subsample resuls are also presened in Panels II and III of Table III. INSERT TABLE III ABOUT HERE The resuls of he regressions of equaions (1) and (2) are very similar. The adjused R 2 ranges from 19 percen o 25 percen when he sample is divided only by leverage raios (or raings). When he sample is furher divided ino bins based on mauriy, a wider range of adjused R 2, 17 percen o 34 percen, is observed. The model performs wors when explaining variaion in long-erm, high-leverage bonds. This resul urns ou o be a general feaure for all of he regressions we perform. B. Resuls Mos of he variables invesigaed in he regressions (1) and (2) have some abiliy o explain changes in credi spreads. Furher, he signs of he esimaed coefficiens generally agree wih heory. We summarize some of he major findings below. 8

10 1. From Tables II and III respecively, boh he change in leverage lev i and he firm equiy reurn re i are saisically significan, wih prediced sign, for mos groups in he mulivariae analyses. The economic significance, however, is raher weak. Indeed, he facor loading on he S&P 500 reurn is ypically several imes larger han he loading on he firm s own equiy reurn. This is he firs indicaion ha monhly changes in firm-specific aribues are no he driving force in credi spread changes. Sensiiviy o changes in leverage also ends o increase as leverage does, bu ha resul is more apparen in a univariae regression framework, shown in Tables IV and V. Tables IV and V also demonsrae ha he apparenly weak explanaory power of firm-specific variables is no due o poenial collineariy wih he marke reurn S&P. INSERT TABLE IV ABOUT HERE 2. Consisen wih he empirical findings of Longsaff and Schwarz (1995) and Duffee (1998), we find ha an increase in he risk-free rae lowers he credi spread for all bonds. Furhermore, he sensiiviy o ineres raes increases monoonically across boh leverage and raing groups. Once again, his finding can be explained by noing ha an increase in drif decreases he risk-neural probabiliy of defaul, and ha he closer firms are o he defaul hreshold, he more sensiive hey are o his change. INSERT TABLE V ABOUT HERE 3. Overall, convexiy and slope of he erm srucure are no very significan eiher saisically or economically. Ineresingly, in he shor- and long-mauriy subsamples, he coefficiens on convexiy and slope end o be of opposie sign. 4. The change in VIX is saisically significan. As seen in Panel II of Tables II and III, i appears o have is greaes economic impac for shor mauriy bonds credi spreads. However, some of hese resuls are clouded by collineariy beween S&P 500 reurns and changes in he VIX index (sample correlaion.52). To invesigae furher, we perform univariae regressions of credi spread changes on changes in VIX, and find srong economic significance hroughou. Exploring his relaion more closely, 9

11 Table VI demonsraes ha credi spreads respond asymmerically o changes in implied volailiy: increases in implied volailiy dramaically impac credi spreads, whereas decreases do no. This asymmery is reminiscen of he findings of Bekaer and Wu (2000) for sock reurns. INSERT TABLE VI ABOUT HERE 5. The reurn of he S&P 500 is exremely significan boh economically and saisically. Esimaed coefficiens have abou he same magniude for all groups. As expeced, i has a negaive impac. A reurn of one percen for he S&P 500 is associaed wih a credi spread decrease of abou 1.6 basis poins. 6. The change in he seepness of he S&P 500 smirk, jump, is saisically and economically significan. The sign, as expeced, indicaes ha an increase in he marke s expeced probabiliy of a negaive jump (as revealed by an increase in ou-of-he-money pu prices) riggers an increase in credi spreads. The laer behavior is relaively homogeneous across all bond groups The average RMSE is 14 basis poins across all bonds. The average serial correlaion of residuals is -0.2, and he average Durbin Wason saisic is 2.36, suggesing serial correlaion is no affecing our resuls. C. Principal Componens Analysis of Residuals Overall, he variables suggesed by heory are significan boh economically and saisically in explaining variaions in individual firms credi spreads. However, a mos hey capure only around 25 percen of he variaion as measured by adjused R 2. To beer undersand he naure of he remaining variaion, we underake principal componens analysis on he residuals. We assign each monh s residuals o one of fifeen bins, deermined by hree mauriy groups (< 12 years, years, > 18 years), and five leverage groups: under 15 percen, 15 up o 25 percen, 25 up o 35 percen, 35 up o 45 percen, and 45 percen or over. 15 For each bin, we compue an average residual, and hen exrac he principal componens of he covariance marix of hese residuals. The resuls reveal ha over 75 percen of he variaion is due o he firs componen. Noe ha his firs componen is approximaely an equally-weighed porfolio across qualiy and mauriy groups. This resul indicaes ha credi spread changes conain a large sysemaic componen ha lies ouside 10

12 of he srucural model framework. Furher, i implies ha he low average adjused R 2 is likely no due o noisy daa, bu raher o a sysemaic effec. The second principal componen explains an addiional six percen of he remaining variaion. The weighs of he eigenvecor are shor in high-leverage deb and long in low-leverage deb. The firs wo principal componens are displayed in Columns 3 and 4 of Table VII. Similar (unrepored) resuls obain when he analysis is repeaed using mauriy and raing bins. INSERT TABLE VII ABOUT HERE IV. Robusness So far, we have only considered as regressors hose facors suggesed by radiional models of credi risk. If his lis of facors were comprehensive, hen our findings would sugges ha o a large exen he corporae bond marke is segmened from he equiy and Treasury markes. Tha is, hese markes would seem o be driven by differen aggregae risk facors. If his conclusion holds, hen using radiional models of credi risk o price and, especially, o hedge risky deb is bound o be unsuccessful. Of course, anoher possibiliy is ha we have omied imporan sysemaic explanaory variables. In his secion, we invesigae he robusness of our resuls along several dimensions. Firs, we rerun he analysis of Secion III.A. using ransacions daa. Second, we include numerous addiional explanaory variables. Finally, we address he possible concern ha our regression generally presumes he independen variables affec credi spread changes in a linear fashion, whereas heory predics a non-linear relaion. We perform a simulaion o demonsrae ha he enforced lineariy of our regressions does no spuriously generae he resuls. A. Transacion Prices versus Bids Our findings in he previous secion are based on dealer quoes raher han acual ransacion prices. I is conceivable ha he limied explanaory power ha we observe, especially for he firm-specific regressors, is due o he way hese bid quoes are updaed by raders. In paricular, hese bid quoes may be slow o respond o changes in firm sock price or leverage, and hus our resuls may be an arifac of a bid facor or a Lehman facor. 16 There are several reasons o believe his is no he case. Firs, in a previous even sudy, Warga and Welch (1993) find ha he Lehman dealer-quoes reac immediaely o leveraged buyous. We also noe ha Lehman Brohers bears a fiduciary responsibiliy for he accuracy of heir quoes on bonds 11

13 having membership in one heir bond marke indices. Thus, following Elon e al. (1999), we re-run he regression (1) using only he sub-sample of quoes from bonds belonging o a Lehman index a he ime of he quoe. Nearly idenical (unrepored) resuls are obained. We furher bolser suppor for our findings by repeaing he above regressions using credi spread changes obained from acual ransacions daa. Bond yields were hand-colleced from he Mergen (formerly Moody s) Bond Record from January 1991 o December Of he 40 bonds so colleced, 29 bonds remained afer resricing he sample o hose bonds having a leas 25 monhly quoes and a leas four years o mauriy a he ime of each quoe. Of he bond quoes remaining in he sample, 77 percen were from acual rades (i.e., specifically labeled sale raher han bid ). The resuls of esimaing (2) on his sample are shown in Table VIII. I is ineresing o noe ha, alhough he average adjused R 2 increases somewha, he explanaory power of he firm-specific proxy remains insignifican. INSERT TABLE VIII ABOUT HERE B. Addiional Variables To furher subsaniae our claim ha a significan porion of corporae bond price innovaions is driven by local supply/demand shocks ha canno be hedged using insrumens from oher markes, we would like o show here are no obvious sysemaic facors ha have been omied from he righ-hand side of our regressions. While here can be no complee refuaion of an omied-variables argumen, we can bolser confidence in he robusness of our findings by showing hey are unchanged even afer including a hos of addiional explanaory variables in he regressions. B.1. Mehodology To invesigae he robusness of our resuls, we expand our regression model in equaion (1) o include addiional explanaory variables. Furher, we es for nonlineariies by inroducing quadraic and cross-erms ino he regression. In addiion o he seven previous variables, we include he following independen variables: 1. Measures of Changes in Liquidiy We consruc hree measures of changes in liquidiy: 12

14 Firs, we examine he relaive frequency of quoes vs. marix prices in he Warga daabase, quoe. Tha is, for each monh, wedefine quoe as he log-change in he raio of he number of quoes, q, o he oal number of repored prices, n, which includes marix prices. We inerpre a higher raio of quoes as indicaive of more liquidiy. Hence, he expeced sign of he facor loading is negaive. We noe, however, ha his indicaor is somewha noisy because he overall scope of he daabase ends o increase over ime. The second liquidiy index is more general: an esimae of changes in on-he-run minus offhe-run 30-year Treasury yields, on off. If liquidiy worsens and he gap beween hese wo widens, his measure decreases. Hence, we expec he facor loading o be negaive. The hird index is derived from anoher marke of corporae ransacions: an esimae of changes in he difference beween yields on he 10-year swap index and 10-year Treasuries, swap. The swap index yields were obained from Daasream. If liquidiy in he swap marke dries up, i seems plausible ha liquidiy in he corporae bond marke will dry up as well. Thus, we expec he facor loading o be posiive. 2. Proxy for Firm Value Process For robusness we include boh he individual firm s equiy reurn re i and he change in leverage lev i as independen variables. Alhough hey are highly correlaed, i is conceivable ha hey provide non-redundan informaion. 3. Nonlinear Effecs In he previous secion we included as a regressor he squared-changes in he spo rae o accoun for convexiy issues. More generally, srucural models of defaul predic ha changes in credi spreads should be nonlinear funcions of changes in leverage, ineres raes, ec. 17 We herefore invesigae several nonlinear erms as regressors, such as squared and cubed changes in leverage, and various cross-erms of regressors, such as (lev i 1 (rei )2 ). However, we only repor he resuls for hose variables found o have saisical significance, namely, ( r 10 ) 2 and ( r 10 ) SMB and HML Facors Since he S&P 500 reurn was found o be an imporan deerminan of credi spread changes, we also examine oher equiy reurn sysemaic facors, such as he Fama and French (1996) Small-Minus-Big, smb, and High-Minus-Low, hml, facors. 13

15 5. Economic Sae Variables If here is mean-revering behavior in spo raes, leverage, volailiy, or credi spreads, hen he beginning-of-monh levels of hose variables should conain informaion abou he curren monh s change in credi spreads. We hus include he dae-( 1) levels of: spo rae, r 10, firm 1 leverage, lev i, VIX index, VIX, and he defaul premium, Spread 1 1 o represen he sae 1 of he corporae bond marke. The laer is measured as Daasream s BBB Index Yield minus 10-year Treasury yield. 6. Leading Effecs of Socks on Bonds Since lagged values of equiy reurn have been documened o have impac on changes in bond yields (e.g., Kwan (1996)), we include he one-monh lagged S&P 500 reurn r SP as a 1 regressor. B.2. Resuls and Analysis Incorporaing he exra variables yields he following regression: CS i = α + β i 1 levi + βi 2 r10 + β i 3 ( r10 ) 2 + β i slope + 4 βi VIX 5 + β i S&P 6 + β i jump + 7 βi quoe + 8 βi on off + 9 βi swap + 10 βi 11 rei + βi 12 ( r10 ) 3 + β i smb 13 + β i 14 hml + β i 15 r βi 16 levi 1 + βi 17 VIX 1 + βi 18 Spread 1 + βi 19 rsp 1 + ɛi. (3) Due o he addiional regressors, we increase o 36 he minimum number of rader quoe observaions a bond mus have in order o qualify for he sample. As in he prior analyses, we esimae his regression on each individual corporae bond credi spread ime series. We repor in Table IX (Table X) he average facor loadings and associaed -saisics when he bonds are divided only by leverage (raings). Similar resuls are obained when we furher divide he bins up by mauriy and are omied for conciseness. INSERT TABLE IX ABOUT HERE The main finding of hese kichen-sink regressions is ha, even hough he added variables do conribue somewha o our undersanding of credi spread movemens, hey have no explained he sysemaic facor which was so prominen in he earlier residuals. Indeed, alhough he average adjused R 2 from equaion (3) has increased o approximaely 34 percen, a repeiion of our principal componens analysis shows ha he residuals are sill highly cross-correlaed. The firs principal componen explains abou 59 percen of he (now smaller) remaining variaion, and he corresponding eigenvecor 14

16 is sill roughly equally weighed in all mauriy and leverage (or raings) groups. These are repored in Columns 5 and 6 of Table VII. Thus, he addiional welve variables have raher limied explanaory power for he sysemaic facor ha drives credi spreads changes. Our major conclusion sill holds: i appears ha credi spread changes of individual bonds are mosly driven by an aggregae facor ha is capured neiher in exising heoreical lieraure, nor by he kichen sink regression in equaion (3). Sill, several of he regression resuls provide ineresing insighs abou he deerminans of credi spreads. We summarize hese below: INSERT TABLE X ABOUT HERE 1. Measures of Liquidiy Changes The facor loadings for boh quoe and on off have a negaive sign, as prediced. However, he difference beween on- and off-he-run Treasury yields is boh economically and saisically more significan. The facor-loading indicaes ha a widening of en basis poins in on off is associaed wih an increase of abou wo basis poins in credi spreads. This would be consisen wih posied fligh o qualiy effecs. As prediced, he facor loading on he swap spread swap is posiive and saisically significan. This measure of liquidiy also seems o have superior explanaory power over our oher wo proxies for liquidiy. Sill, swap provides raher limied explanaory power for credi spread changes. As an example of he implicaions of hese resuls, we performed a simple ou of sample experimen. We gahered daa on credi spreads, swap raes, and on-minus-off-he-run Treasury raes for lae summer 1998, when he Long-Term Capial crisis severely disruped he bond markes. During Augus 1998, credi spreads increased by abou 34 bp for AAA and 38 bp for BBB bonds. Using our esimaed coefficiens on liquidiy variables (swap spread and on-he-run minus off-he-run), our model can race only abou 25 percen of his variaion back o changes in liquidiy, mosly o he change in swap spread (which increased by 24 bp during ha same monh). These findings are consisen wih hose of Duffie and Singleon (1997), who also noe ha he corporae bond marke is affeced by forces differen from hose affecing he swap marke. 2. Nonlinear Effecs The cubic erm in he change in ineres rae is ypically posiive, bu lacking in economic 15

17 significance. 3. SMB and HML Facors The facor loadings on boh he smb and hml facors are saisically significan for every bin, and are negaive hroughou. The loadings become more negaive for he higher leverage bins. 4. Economic Sae Variables The coefficien on defaul premium levels Spread 1 reflecs mean-reversion in credi spreads. The coefficien on he level of he risk-free rae r 10 is negaive and significan hroughou, bu his is a marginal effec. In a univariae conex, repored in Table XI, he relaion beween 1 changes in credi spreads and ineres rae levels is uniformly posiive, bu here is almos no explanaory power. Finally, he coefficiens on levels of leverage (lev i ) and VIX (VIX ) have 1 1 limied saisical significance. INSERT TABLE XI ABOUT HERE 5. Leading Effecs of Socks on Bonds The coefficiens on lagged S&P 500 reurns are negaive and are saisically significan excep for higher leverage (lower raed) bonds. In erms of economic significance, he effec is smaller, roughly 30 percen of he size of he curren S&P 500 reurn. B.3. Addiional Evidence To furher check ha our observaion of a sysemaic facor is no spurious, we repea regression (3) wih he addiion of a single explanaory variable: Spread,a marke facor for he corporae bond marke which we define as he monh change in: (Daasream s BBB Index Yield minus en-year Treasury yield). Since we have documened above a large sysemaic movemen in credi spreads, we expec he addiion of his explanaory variable o generae a very high R 2. To no surprise, he resuls show adjused R 2 of over 60 percen (no repored) for he invesmen grade groups, and 55 percen overall. Having included Spread in he regression, we once again underake principal componens analysis of he residuals using he same mehods as before. The resuls are elling, and are repored in Columns 7 and 8 of Table VII. The firs componen now accouns for only 40 percen of he (now 16

18 much smaller) remaining variaion, and is no longer a all equally weighed across groups. Indeed, over 63 percen of he weighing falls ino a single bin. Overall, hese ess reinforce he conclusions of he previous secion. In paricular, here seems o exis a sysemaic risk facor in he corporae bond marke ha is independen of equiy markes, swap markes, and he Treasury marke and ha seems o drive mos of he changes in credi spreads. C. Simulaion If he srucural models of credi spreads are correc, hen he change in credi spreads should be a nonlinear funcion of changes in mauriy, leverage, and ineres raes. Alhough our kichensink regression srongly suggess ha hese nonlinear erms are no he cause of he relaively low R 2 obained, here we give addiional suppor o his claim. Furher, we show ha he heoreical model predics mos of he explanaory power should come from changes in firm value, in direc conflic wih our findings. Below, we consruc a simulaed economy generaed by recenly-proposed srucural models of defaul and demonsrae ha even a wo-facor linear regression on his daa produces a very high R 2 ; indeed, around 90 percen. C.1. The Economy The simulaed economy has he following dynamics. Firs, under he hisorical measure he spo rae r follows he Vasicek dynamics: dr = κ(θ P r ) d + σdz 1 (), (4) where κ =0.3, θ =0.06, σ =0.015, r 0 =0.06. In addiion, o compue credi spreads we need he spo rae dynamics under he risk-neural measure. We assume he following form: dr = κ(θ Q r ) d + σdz Q (), (5) 1 where θ Q =.09. We also assume firm value follows he process: dv V = (µ δ) d + νdz 2 () (6) = (r δ) d + νdz Q (), 2 (7) 17

19 Defining he log-leverage raio as 18 l k y, (11) where µ = r +0.05, δ =.03, ν =.2, and ρ = 0.2,whereρ is defined hrough dz 1 () dz 2 () =ρd. Given he srucure above, he log-firm value y log V has he dynamics: dy = (µ δ ν2 2 ) d + νdz 2 () (8) = (r δ ν2 2 ) d + νdzq (). (9) 2 This model is consisen wih boh he LS model, proposed by Longsaff and Schwarz (1995), and he CG model of Collin-Dufresne and Goldsein (2000). We noe, however, ha he LS model assumes a consan defaul hreshold. If his hreshold is monoonic in leverage, hen he LS model predics ha he expeced leverage raio decreases exponenially over ime. In conras, he CG model assumes ha he log-defaul boundary for firm i follows he process dk = λ(y ν k ) d. (10) is dynamics follow: ) dl = λ (l l d νdz 2 () (12) = λ (l Q ) l d νdz Q (), (13) 2 where l ν + δ+ σ 2. Tha is, his model generaes saionary leverage raios. The parameers are chosen o be λ =.15, l 0 = 1, l = 1, andl Q ν + δ+ σ 2 2 r =.6. 2 µ λ C.2. Daa and Resuls Assuming he log-leverage raio follows his process, we firs simulae 100-monh sample pahs for leverage and ineres raes. Then, monhly credi spreads for boh he LS and CG models are deermined. 19 Finally, we hen esimae he following regression: λ CS i = α + β i 1 levi + βi 2 r10 + ɛ i. (14) The resuls are repored in Table XII. Several poins are noable. Firs, he regressions from he 100-monh simulaions imply ha he nonlinear relaionship beween changes in credi spreads and changes in boh ineres raes and leverage raios is no he cause of he low R 2 obained when running regressions on acual daa. Indeed, he wo-facor linear regression obains an R 2 on he order of 90 percen for boh models. 18

20 Second, unrepored one-facor regressions demonsrae ha almos all of his explanaory power comes from he change-in-leverage facor. This resul is in sark conras o he empirical findings. 20 Finally, he CG model exhibis less sensiiviy of credi spreads o changes in firm leverage. This effec arises because in he CG model, increases in firm value are parially offse by fuure increases in issuances of pari-passu deb. This may parially explain why observed credi spreads are so insensiive o changes in leverage. Bond prices may simply reflec he fac ha increases in firm value will lead o an increase in fuure deb issuances, and ha decreases in firm value will lead o a decrease in fuure deb issuances. V. Conclusion We invesigae changes in credi spreads on individual bond yields. Several surprising resuls are obained. Firs, we find he facors suggesed by radiional models of defaul risk explain only abou onequarer of he variaion in credi spreads as measured by he adjused R 2. Given ha he srucural framework models risky deb as a derivaive securiy which in heory can be perfecly hedged, his adjused R 2 seems exremely low. Furhermore, principal componens analysis indicaes ha he residuals are highly correlaed, wih he firs principal componen (which is nearly equally-weighed across all bins of bonds) capuring abou 76 percen of he remaining variaion. We aemp o explain his sysemic facor by inroducing a hos of oher variables as regressors. However, he added financial and economic variables provide only limied addiional explanaory power. Second, in conras o he predicions of srucural models of defaul, aggregae facors appear much more imporan han firm-specific facors in deermining credi spread changes. Furhermore, changes in credi spreads are o a grea exen driven by facors no associaed wih eiher he equiy or Treasury markes. This has imporan implicaions for he risk-managemen of corporae bond porfolios. I seems difficul o reconcile our findings wih he exising models of defaul risk, and, in paricular, wih he so-called srucural models, based on coningen claims analysis iniiaed by Meron (1974). The laer predics a relaion beween credi spreads and leverage, volailiy, and ineres raes. Alhough early empirical ess of hese models proved disappoining (see Jones, Mason and Rosenfeld (1984), Kim, Ramaswamy, and Sundaresan (1993)), recen exensions (e.g., Goldsein, Ju, and Leland (1998), Mella-Barral and Perraudin (1997), and Anderson and Sundaresan (1996)) have shown ha inroducing agency heory or dynamic capial srucure decisions can help improve he fi ofhelevel of he credi spread. However i seems unlikely ha hese exensions can generae he kind of correlaion in changes 19

21 in credi spread uncovered in our analysis. A naural explanaion for our findings is segmenaion of bond and equiy markes. Clearly if markes are segmened and differen invesors rade in bonds and socks, hen prices in hose markes could be driven by independen demand/supply shocks in boh markes. Nowihsanding, in ha case one needs o explain why hese markes are segmened, and if hey are, why equiy and bonds do no reac o he same aggregae facors. Could imperfecions in he bond marke daa explain our findings? The possibiliy canno be precluded compleely: Alhough we use wo independen sources of daa in his sudy, neiher one reaches he sandards of qualiy ha prevail in CRSP daa for he sock markes. However, our resuls are qualiaively consisen wih hose obained from oher sources, such as he high frequency FIPS daa invesigaed by Hochkiss and Ronen (1999). Could imperfecions in bond marke insiuions e.g., ransacion coss, liquidiy explain our findings? Recen sudies by Schulz (1998), Chakravary and Sarkar (1999), and Hochkiss and Ronen (1999) conclude ha he sock and bond markes are equally adep a efficienly incorporaing new informaion ino prices (i.e., pricing efficiency ). A he same ime, hey also show ha liquidiy (as measured by rading volume and bid-ask spread) can have major effecs on bond prices. So, poenially, an aggregae facor driving liquidiy in he bond marke could explain he common facor we are deecing. Our measures of liquidiy (he spread beween on- and off-he-run Treasuries, swap spreads, and he frequency of quoes vs. marix prices in he Warga daabase) may simply be inadequae a capuring his facor. Our findings appear o highligh a shorcoming of exising heoreical models of defaul risk. Besides ineres raes, srucural models of defaul predic ha i is firm-specific facors ha drive credi spreads. Tha is, hey uniformly predic ha he explanaory power of firm-specific measures (e.g., equiy reurn, firm leverage) should swamp hose of aggregae measures (e.g., marke reurn). 21 However, we find empirically ha mos of he variaion in credi spreads of individual bonds is explained by an aggregae facor common o all corporae bonds. Thus, our paper suggess he need for furher work on he ineracion beween marke risk and credi risk i.e., general equilibrium models embedding defaul risk

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