Factors affecting the yields on noninvestment grade bond indices: a cointegration analysis

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1 Ž. Journal of Empirical Finance Facors affecing he yields on noninvesmen grade bond indices: a coinegraion analysis Theodore M. Barnhill Jr. a, Frederick L. Jouz b,), William F. Maxwell c a The George Washingon UniÕersiy, Deparmen of Finance, Washingon, DC, USA b The George Washingon UniÕersiy, Deparmen of Economics, 2201 G. Sree NW, Washingon, DC 20052, USA c Texas Tech UniÕersiy, Deparmen of Finance, Lubbock, TX, USA Absrac This sudy examines he long- and shor-run dynamics of he yields on noninvesmen grade indices. Uilizing coinegraion echniques, he radiional yield spread model is found o be inadequae. A revised model finds a long-run relaionship beween noninvesmen grade yields, Treasury securiies, and defaul raes. Error correcion models are formulaed o model he shor-run dynamics of differen segmens of he marke. These models include a long-run equilibrium Ž beween yields, defaul raes, and Treasuries., muual fund flows, minor bond raings, deb subordinaion measures, a sock index, and a January effec. Segmenaion in he noninvesmen grade marke is also demonsraed. q 2000 Elsevier Science B.V. All righs reserved. JEL classificaion: C31; C52; G10 Keywords: Coinegraion; Noninvesmen grade; High yield; Yield spread; Marke segmenaion 1. Inroducion A grea deal of research has focused upon he pricing of corporae deb Žsee Fisher, 1959; Silvers, 1973; and Boardman and McEnally, This research led o he segmenaion of pricing facors ino hree broad caegories: ineres rae risk, defaul risk, and liquidiy risk. However, given he consrains of sample size in comparing he characerisics of specific bonds, a second line of research devel- ) Corresponding auhor. Tel.: q ; fax: q ; bmark@gwu.edu r00r$ - see fron maer q 2000 Elsevier Science B.V. All righs reserved. Ž. PII: S X

2 58 ( ) T.M. Barnhill Jr. e al.rjournal of Empirical Finance oped, which examined he effec of risk facors on bonds grouped by risk caegories Ž comparable o an analysis using panel daa.. This sudy exends he analysis of he risk facors priced in risky deb by uilizing improved esimaion mehodologies, incorporaing and esing he effec of ineres-rae risk, including addiional proxies for defaul and markeabiliy risk, and by segmening he marke by bond raing caegory o improve he differeniaion of risk across bond raing caegories. Fons Ž and Alman and Bencivenga Ž analyzed he marke yield premium for holding risky deb Žhe average yield spread beween risky deb securiies and he risk-free securiy.. This risk neural ype analysis calculaes wheher here is a ne reurn Ž yield premium minus defaul rae. for holding risky bonds over a long period. This research has shown ha as he risk of he bond increases, he marke yield premium also increases, resuling in a posiive risk-adjused reurn. Yield premium models are long-run models, which focus upon he defaul risk of holding a noninvesmen grade securiy. Fridson and Jonsson Ž and Garman and Fridson Ž exend his ype of analysis by focusing upon he shor-run dynamics of he marke by including liquidiy risk measures in he analysis and by more broadly defining defaul risk. The auhors formulaed yield spread models Žyield on he risky deb minus he risk-free rae as he dependen variable., which included boh defaul risk and liquidiy risk measures. The curren sudy exends he yield premium and yield spread models. Firs, he long-run relaionship implied in he yield premium model is esimaed using coinegraion analysis. Second, he models formulaed in his sudy combine boh a long-run relaionship and shor-run dynamic componens o deermine he yield requiremen for holding noninvesmen grade bonds. Third, he yield spread sudies have used a Merrill Lynch aggregae index of he noninvesmen grade marke o assess he effec of defaul and liquidiy risk on he yield of corporae deb. The correlaion analysis in Table 1 demonsraes he inheren problem of relying on a single broad defaul caegory. Risky deb is no homogeneous. Thus, o beer explain he effec of defaul, ineres-rae, and liquidiy risk on corporae bonds, his sudy segmened he marke by bond raing caegory. Raing caegory serves as a proxy for defaul risk, senioriy posiion, securiizaion of he bond, indusry specific risk, and oher facors. To beer differeniae he risks of holding corporae bonds, he sudy has focused upon he riskies segmen of he corporae bond marke, noninvesmen grade deb. CS Firs Boson compiles indices of he high-yield marke. For he curren sudy, CS Firs Boson Indices were used for bonds raed BB and B by boh Moody s and Sandard and Poor s and an aggregae index of high-yield bonds raed Spli BBB and lower. 1 1 Ž. The CS Firs Boson Composie High Yield Index CSFB HYI is composed of approximaely 46% BB, 48% B, and 6% CCC raed bonds.

3 ( ) T.M. Barnhill Jr. e al.rjournal of Empirical Finance Table 1 Descripive analysis of Corporae Bonds and Treasury Bonds Bond Index informaion for Treasury Bond and Invesmen Grade Indices were colleced from Ciibase, which uilizes Moody s bond raings. Noninvesmen Grade Indices were provided by CS Firs Boson. All Index informaion is monhly from 1987Ž. 1 o 1996Ž. 7. Bond index Mean Sd. Correlaion yield deviaion Treasury Bonds T-Bonds Aaa Aa A Baa Spli BBB BB Spli BB B Given he problem of pricing of bonds wih relaively limied rading, monhly daa from January 1987 ill July 1996 was uilized in his sudy. Unforunaely, here is no reliable hisorical daily or weekly daa on he high-yield marke. The paper is organized in he following manner. Secion 2 examines previous empirical and heoreical research suggesing a number of explanaory variables, which could affec he risk of holding high yield securiies. The possible explanaory variables are broken down ino hree broad risk caegories: defaul risk measures, ineres rae risk measures, and liquidiy risk measures. Secion 3 presens he coinegraion analysis, which idenifies long-run equilibrium relaionships. Secion 4 formulaes error correcion models using a general o specific modeling approach. Secion 5 presens he overall conclusions on facors affecing he yields on high-yield bond indices. 2. Previous research on facors affecing he pricing of risky deb 2.1. Defaul risk measures Defaul raes and economic indicaors Fridson and Jonsson Ž found Moody s railing-12-monh defaul rae and an index of lagging economic indicaors o have a saisically significan effec on yield spreads. An index of leading economic indicaors was found o have no saisical significance. A noe should be made abou he defaul rae measure uilized. The marke anicipaes defaul well in advance of he acual defaul Žsee Alman, 1989., and hence some lag occurs beween he marke reacion and he defaul rae. The curren sudy ess he significance of Moody s railing-12-monh defaul raes and Ciibase leading and lagging economic indicaors.

4 60 ( ) T.M. Barnhill Jr. e al.rjournal of Empirical Finance Equiy index A number of auhors have demonsraed he correlaion of reurns on high-yield bonds o equiy indices Žsee Booksaber and Jacob, 1986; Ramaswami, 1991; and Shane, Such a relaionship is consisen wih he Black and Scholes model Ž Black and Scholes, of firm capial srucure which, is someimes ermed a coningen claims analysis Ž CCA.. The bondholders payoff is he value of he bonds Ž on he upside. or he value of he firm on he downside. In his framework, he closer he value of he bonds is o he oal firm value Ž high leverage., he more highly correlaed changes in bond value and changes in equiy value will become. The greaer he posiive difference in he value of he firm compared o he value of he bonds Ž low leverage., he more highly correlaed changes in bond value and changes in risk free bond values will become. This heory is suppored by he observed correlaion srucure of reurns on invesmen and non-invesmen grade deb. Unforunaely, an equiy index is no available for firms, which have noninvesmen grade deb ousanding. Insead, a correlaion analysis was performed on a number of sock indices o deermine he bes index o uilize in he curren sudy. 2 The Russell 2000 Index had he highes correlaion across he noninvesmen grade indices, and hence, was uilized in he sudy. In addiion, he pricerearnings raio was also uilized in he sudy as a proxy for he cos of equiy minus he growh rae. The pricerearnings raio of he Russell 2000 Index was unavailable for he hisorical ime frame examined, so he Sandard and Poor pricerearnings raio was uilized. Finally, a dummy variable Ž d.v.. was added o reflec he Ocober 1987, marke crash o deermine is effec on he yield requiremen of high-yield bonds. The sock marke crash would be expeced o have a posiive effec on yield Subordinaed deb Black and Cox Ž and Smih and Warner Ž used a coningen claims analysis o heoreically prove ha senior deb should be priced higher Žlower yield. han similar subordinaed deb. Cary and Lieberman Ž demonsraed ha he senioriy of a bond has a significan impac on he bond s recovery raes in defaul. However, Fridson Ž found ha senior deb yields more han like-raed subordinaed deb. Fridson s finding a firs seems anomalous, bu raing agencies facor ino accoun a bond s poenial recovery rae, which is a funcion of senioriy, when assigning a raing. Hence, Fridson s finding suggess ha bondholders, as compared o he raing agencies, place more emphasis on he poenial of defaul as compared o he poenial recovery in he case of defaul. Given he heoreical and empirical work in he area, i is hypohesized ha a change in he 2 We ran correlaion analyses on he yields on he BB, B and CSFB Composie Indices and reurns on a he S&P 500, S&P MidCap, NASDAQ Composie, Russell 1000, Russell 2000, and Russell 3000.

5 ( ) T.M. Barnhill Jr. e al.rjournal of Empirical Finance percenage of securiies in an index, which are subordinaed could have an effec on is yield. The percenage of subordinaed bonds ousanding could also serve as a proxy for he average credi qualiy of he marke. The curren sudy uses COMPUSTAT o deermine he monhly percenage of subordinaed BB and B raed bonds Minor raing classificaion Previous research has found bond raings significanly lag marke changes in value Žsee Heenhouse and Saroris, 1976; Wansley and Terrence, 1985; and Ederingon e al., However, he informaion conen of minor raing classificaion Ž q or y for S&P s and 1, 2, or 3 for Moody s. has no been analyzed. If he minor raing classificaions are significan, a change in he percenage of he major raing caegory which is made up of he lowes credi qualiy Ž BBy and By. would have an effec on he index s yield. COMPUS- TAT 4 was used o deermine he percenage of he major raing caegory segmened ino he hree differen minor raing caegories. If minor raing caegories provide informaion, a posiive correlaion beween he percenage of bonds in he lowes credi qualiy and yield would be expeced Kuwai inõasion When Iraq invaded Kuwai, Augus of 1990, he effec on he world s oil supply, and hus, on he financial markes was unknown. To reflec a possible srucural break caused by he Iraq invasion, a dummy variable was included for Augus of 1990, and lagged one period o encompass an effec in Sepember of An addiional dummy variable was included o sudy he effec he liberaion of Kuwai had on he high-yield marke Ineres rae risk measures Ineres rae risk is he dominan facor affecing he value of invesmen grade bonds. However, as credi qualiy decreases defaul risk begins o dominae ineres rae risk in bond valuaion. By analyzing yield as compared o yield spread, he srengh and significance of changes in Treasury raes on he yield of noninvesmen grade bonds can be sudied. Unforunaely, he hisorical average duraion of he high-yield indices was unavailable, and hence, some of he emporal variance in each index and cross-secional variance across indices may be due o changes in average duraion as well as simple changes in Treasury raes, which canno be conrolled for in his sudy. 3 The percenage of subordinaed bonds in he lowes raing caegory was unavailable on a monhly basis for he indices uilized in his sudy. As a proxy, COMPUSTAT daa was uilized o measure hese vaiables. 4 Ibid.

6 62 ( ) T.M. Barnhill Jr. e al.rjournal of Empirical Finance A he end of 1995, he CS Firs Boson Aggregae Index had an average mauriy of 7.85 years and duraion of 4.35 years. 5 However, since he majoriy of he bonds have call feaures he effecive mauriy and duraion are less. To assess he appropriae Treasury yield o uilize in his sudy, a correlaion analysis was done on 5-, 7-, and 10-year noes. The resuls indicae ha he appropriae Treasury yield o uilize is he 10-year Treasury noe Liquidiy risk measures Supply and demand facors Warher Ž found ha muual fund invesmen flow influenced sock and bond reurns. The Invesmen Insiue Ž ICI. racks muual funds by invesmen caegory including one labeled high-yield. The ICI repors daa on he asse value and percenage of asses held in liquid invesmens on a monhly basis. Since muual funds make up a large segmen of he marke, 6 he change in muual fund flow and liquidiy posiion of he muual funds could have a significan effec on marke yield. Fridson and Jonsson Ž found increased fund flow ino high-yield muual funds, as a percenage, o be associaed wih a narrowing of he yield spread and an increase in he price of noninvesmen grade securiies. Furher, an increase in he amoun of asses held as liquid securiies, as percenage of high-yield asses, was associaed wih an increase in yield spread and a decrease in he price of noninvesmen grade securiies. ICI provided muual fund daa for he curren sudy January effec There is a well documened January effec in bond reurns Žsee Chang and Pinegar, 1986, 1988; Chang and Huang, 1990; Fama and French, 1993; Cooper and Shulman, 1994; and Maxwell, Chang and Pinegar Ž concluded he evidence regarding a January effec was consisen wih a ax-loss selling sraegy. On he oher hand, Cooper and Shulman Ž offered a conjecure ha a January effec was he resul of year-end selling by porfolio managers o preven high-yield deb from appearing on he fund s financial repor. This year end selling is commonly referred o as window dressing Ž see Lakonishok e al., DeRosa-Farag Ž suggesed he January effec was he resul of supply and demand consideraions. Bond coupon paymens are no evenly disribued hroughou he year. Coupon paymens are a heir highes in December and lowes in January, and hence, DeRosa-Farag suggesed he January price increase was due o an increase in fund flow in December and a decrease in fund flow in January. Fridson and Garman Ž found no supporing evidence for a coupon-paymen heory. 5 Ž. High Yield Handbook, 1996, CS Firs Boson, New York. 6 Chase Securiies esimaes high-yield muual funds comprise 22% of he marke in Ž. DeRosa-Farag, 1996.

7 ( ) T.M. Barnhill Jr. e al.rjournal of Empirical Finance The year-end based heories and he coupon-paymen heory provide esable hypoheses. The year-end heories and demand based heories sugges yields should be a heir highes in December and lowes in January. DeRosa-Farag s demand-based heory has an addiional esable hypohesis. Mos coupon-bond paymens are made semi-annually, and hence, he coupon-paymen heory suggess ha a similar effec on yields should be found in June and July. The curren sudy ess for he significance of a January effec as well as he compeing hypoheses for he causes of he anomaly Drexel Burnham bankrupcy Drexel Burnham was he larges underwrier and marke maker in high-yield bonds when i declared bankrupcy in February of Cornell Ž found he Drexel Burnham bankrupcy had an effec on he overall markeabiliy of high-yield bonds. To es for he significance of he markeabiliy crisis, a Drexel Bankrupcy dummy variable was included. If he bankrupcy caused a liquidiy crisis a posiive effec on yield would be expeced around he ime of he bankrupcy. To accoun for he marke anicipaing he bankrupcy, he dummy variable was also examined over wo lags. 3. Analysis of long-run equilibrium yield relaionships In his secion, he variables saionariy and order of inegraion are esed. The coinegraion ess for long-run relaionships beween he simple yield spread model and our defaul risk adjused yield spread model are hen presened. The sample period under invesigaion is January 1987 o July Saionariy and inegraion analysis To avoid a poenial spurious regression problem ŽGranger and Newbold, 1974 and Phillips, 1986., he firs sep in analyzing he daa was o deermine he saionariy or nonsaionariy of he variables. The variables were ploed, he auocorrelaion funcions were examined, and augmened Dickey-Fuller Ž ADF. saisics were evaluaed on he levels and he firs differences of he variables. 7 As expeced, mos of he variables were found o be nonsaionary, IŽ. 1, bu he firs differences of all were saionary, IŽ Coinegraion analysis and esing long-run relaionships Given he nonsaionariy of a number of he variables, he radiional approach is o model a process in differences. While his is common pracice, i resuls in a 7 Tes resuls are available from he auhors upon reques.

8 64 ( ) T.M. Barnhill Jr. e al.rjournal of Empirical Finance poenial loss of informaion on he long-run ineracion of variables. So insead of direcly moving o a model uilizing differences, an analysis was performed o deermine if here is a coinegraing vecor. The implicaion of a coinegraing vecor is ha while he variables may be individually nonsaionary a linear combinaion of variables is saionary Ž see Enders, Hence, a coinegraing vecor indicaes a long-run relaionship beween he variables. This sudy considers wo models o explain he long-run relaionship of noninvesmen grade bond yields and Treasury yields. The firs model examines a yield spread model in which here is a long-erm equilibrium beween Treasury yields and noninvesmen grade bond yields. The second model examines he more complex relaionship of he defaul adjused yield-premium models beween Treasury yields, noninvesmen grade bond yields, and defaul raes. Figs. 1 and 2 show graphs of he variables. Two mehodologies have been developed for esing for coinegraion. The firs approach was a single-equaion approach developed by Engle and Granger Ž aply called he Engle Granger Mehodology. This approach is valid in bivariae analysis, bu inadequae in a mulivariae framework and sysems approach. A second and more powerful sysem mehodology was developed by Johansen Ž 1988; The Johansen maximum likelihood procedure for a finie-order vecor auoregressions Ž VARs. was uilized in he curren sudy. The firs sep in he Johansen mehodology is o deermine he appropriae lag srucure o use in he VARs. The VARs include he BB, B, and CSFB bond yields, T-Bond yields, and Moody s defaul raes. In addiion, variables, which Ž. Fig. 1. Ten-year reasury, BB and B indices yields January 1987 December 1996.

9 ( ) T.M. Barnhill Jr. e al.rjournal of Empirical Finance Fig. 2. BB and B indices yields and Moody s railing-12-monh defaul rae ŽJanuary 1987 December will be esed for significance bu no considered in he coinegraing vecor, were allowed o ener unresriced. 8 To deermine he appropriae lag srucure he log-likelihood, Schwarz crierion, Hannan Quinn, and he F-saisic for model comparison were uilized. The es saisics suggesed ha a lag srucure of wo periods was appropriae. Table 2 repors he summarized resuls of he Johansen procedure for he firs model beween he bond indices and he Treasury yields. The Johansen maximal eigenvalue Ž l. max for he BB Index for rs0 is 8.83 and he 95% criical value is The maximal and race eigenvalues indicae ha he null hypohesis of no coinegraing vecor Ž r s 0. canno be rejeced for any of he sysems. The resuls in Table 2 along wih he correlaion analysis above demonsraes he danger of viewing a consan and insananeous change in yields on very-risky deb o changes in he risk-free securiy. 9 8 The unresriced variables were an index of lagging economic indicaors, an index ofleading economic indicaors, a Russell 2000 Index, he % subordinaed deb in raing class, he % of lowes credi qualiy in raing class, a Iraq Invasion d.v., a 1987 Marke Crash d.v., he % of high-yield muual fund asses held in liquid securiies, he change in high-yield muual fund flow, seasonal d.vž. s., and a Drexel Bankrupcy d.v. 9 Coinegraing vecors beween invesmen grade indices yields and Treasury yields were found for all invesmen grade indices, which implies he legiimacy of a yield spread model as applied o invesmen grade indices.

10 66 ( ) T.M. Barnhill Jr. e al.rjournal of Empirical Finance Table 2 Coinegraion analysis of high-yield indices and reasury bond yield lmax and lmax a are Johansen s maximal eigenvalue saisics, and lrace and lrace a are Johansen s race eigenvalue saisics. An a signifies he saisic is adjused for degrees of freedom. Index BB B CSFB Coinegraion saisics Eigenvalue Null hypohesis r s0 r s0 r s0 lmax a lmax % criical value lrace a lrace % criical value X Sandardized eigenvecors b T-Bond yield y1.397 y2.082 y2.605 Sandardized adjusmen coefficien a y y y The es of a long-erm relaionship beween Treasury yields, defaul raes, and yields on very-risky deb are repored in Table 3. Variables, which will be used laer o help describe he shor-erm dynamics of he marke, were allowed o ener he VARs unresriced. The null hypohesis of rs0 is ha here is no coinegraing vecor. The Johansen maximal eigenvalue Ž l. max for he BB Index for rs0 is and he 95% criical value is All he maximal and race eigenvalue saisics srongly rejec he null hypohesis ha here is no coinegraing vecor for all he differen high-yield indices implying a leas one coinegraing vecor exiss for each of he indices. The null hypohesis of rf1 is ha here is one or more coinegraing vecor. The Johansen maximal eigenvalue Ž l. max for he BB Index for rf1 is 7.98 and he criical value is All he maximal and race eigenvalue saisics sugges lile evidence of more han one coinegraing vecor, and i was concluded ha here was one coinegraing vecor for each of he indices. Table 3 includes Chi-square Žx 2 Ž df.. es saisics for he significance of Treasury Bond yields and defaul raes in he coinegraing vecor for he differen noninvesmen grade bond indices. For example, he x 2 Ž. 1 for Treasury Bond Yield s significance on he BB Index is indicaing ha he variable adds explanaory power a 1% o he model. The Chi-square es saisics sugges ha boh Treasury Bond yields and defaul raes are saisically significan in deermining he coinegraing relaionship for all he indices Coinegraing vecors were esimaed for invesmen grade indices, Treasury yields, and defaul raes. The coinegraing vecors were saisically significan. However, he defaul rae was found o be nonsignifican in he coinegraing vecor.

11 ( ) T.M. Barnhill Jr. e al.rjournal of Empirical Finance Table 3 Tes of inegraed model coinegraion analysis of high-yield indices, reasury bond yields and Moody s 12-monh railing defaul rae Index BB B CSFB Coinegraion saisics Eigenvalue Null hypohesis r s0 r s0 r s0 UU lmax a UU lmax % criical value UU lrace a UU lrace % criical value Null hypohesis r F1 r F1 r F1 lmax a lmax % criical value lrace a lrace % criical value X Sandardized eigenõecors b T-Bond yield y y y Moody s defaul rae y y y Sandardized adjusmen Coefficien a y y y Tes saisic for he significance of he variable in coinegraing vecor 2Ž. 2Ž. 2 Variable x 1 x 1 x Ž. 1 T-Bond yield Moody s defaul rae lmax and lmax a are Johansen s maximal eigenvalue saisics, and lrace and lrace a are Johansen s race eigenvalue saisics. An a signifies he saisic is adjused for degrees of freedom. The following variables enered unresriced: Consan, Seasonal d.vž. s., Drexel d.v., Iraq d.v., Mk. Crash d.v., %MF Liq. Asses, DFund Asses, S&P Index, Lead Index, Lag Index, %Sub BBrB, %ybbryb. Aserisks will be used in ables o represen saisical significance in he following manner: represens a saisically significan resul a he 99% confidence level, UU a he 95% confidence level, and U a he 90% confidence level. The sandardized eigenvecors b X in Table 3 are he esimaed coinegraing vecors for he differen indices long-erm marke equilibrium. The coinegraing vecors for he differen indices can be wrien as: BB Index Yields T-Bond Yieldq Moody X s Defaul Rae qž a coefficiensy Ž 1.

12 68 ( ) T.M. Barnhill Jr. e al.rjournal of Empirical Finance B Index Yields T-Bond Yieldq Moody X s Defaul Rae qž a coefficiensy Ž 2. CSFB Index Yields T-Bond Yieldq Moody X s Defaul Rae qž a coefficiensy Ž 3. The noninvesmen grade indices long-run equilibrium is essenially he risk-free rae plus a premium o reflec he increased rae of defaul. The relaionship of he defaul rae o he differen indices is as expeced, as he bond credi qualiy decreases, signified by bond raing, defaul rae has a larger effec on yield. This resul is consisen wih heory. The a coefficiens in Table 3 Žalso found under Eqs. Ž 1. Ž 3.. represen he speed of adjusmen o disequilibrium comparable o a mean-reversion rae. The a coefficiens ranged from y o y The signs are as expeced Ža negaive sign indicaes as he variables move away from equilibrium here is an adjusmen back owards he equilibrium relaionship.. The alphas sugges a slow adjusmen o disequilibrium in he more volaile B and CSFB Indices. 4. Error correcion models and shor-run dynamics Afer esing for a coinegraing vecor in a sysem of equaions, he models are hen esimaed as a single-equaion error correcion model Ž ECM. Žfor furher discussion of ECMs see Enders, 1995; and Hendry, Error correcion models combine he informaion from he shor-run dynamics of he high-yield indices wih he long-run relaionship found in he coinegraion analysis Reparameerizing an auoregressiõe disribued lag model o an ECM The VAR suggesed a wo-period lag was he appropriae srucure. Hence, a single-equaion auoregressive disribued lag model for he BB Index is: Ý Ý Ý BB s a q a BB q a T-Bond q a DefaulRae 0 1i yi 2 i yi 3i yi is1 is0 is0 qa LeadIndex qa LagIndex qa DRussell qa DS&PPrEqa D%Subordinaed qa D%BB qa Iraq y 10 q a KuwaiLiberaion q a 1987Crash q a %MFLiqAsses q a %MFFlows q a Seasonals 4 Ž

13 ( ) T.M. Barnhill Jr. e al.rjournal of Empirical Finance Ž. Eq. 4 can be reparameerized ino an ECM wihou a loss of generaliy as: 1 1 Ý DBB s a q b DBB q b DT-Bond q b DDefaulRae 0 1 y1 2i yi 3i yi is0 is0 qc1bby1qc2t-bond y1qc3defaulraey1 qa4leadindex qa5lagindex qa6 DRussell2000 qa7ds&ppreqa8d%subordinaed qa9d%bby q a Iraq q a KuwaiLiberaion q a 1987Crash Ý q a %MFLiqAsses q a %MFFlows q a Seasonals Ž Ž. Eq. 5 can hen be manipulaed algebraically o direcly incorporae he long-run soluion: 1 1 Ý DBB s a q b DBB q b DT-Bond q b DDefaulRae i yi 3i yi is0 is0 qc Ž BBq T-Bondqd DefaulRae. y1 qa LeadIndex 1 4 qa LagIndex qa DRussell2000 qa DS&PPrE qa D%Subordinaed qa D%BB qa Iraq 8 9 y 10 q a KuwaiLiberaion q a 1987Crash q a %MFLiqAsses q a %MFFlows q a Seasonals Ž The reparameerized general ECM formulaion found in Eq. Ž. 6 will be used as he model o discuss he single-equaion resuls. c1 is he feedback coefficien reflecing a long-run adjusmen o disequilibrium and is comparable o he a coefficien found in Eqs. Ž.Ž. 1 3 from he coinegraion analysis. The and d coefficiens are yc rc and yc rc from Eq. Ž Therefore, he error correcion variables can be represened from he coinegraion resuls as: ECM s BB y Ž T-Bond. y Ž DefaulRae. Ž 7. BB ECM s B y Ž T-Bond. y Ž DefaulRae. Ž 8. B ECM s CSFBy Ž T-Bond. y Ž DefaulRae. Ž 9. CSFB 4.2. General o specific modeling General ECMs are esimaed, which include boh he long-run soluion and he variables heorized as possibly affecing he shor-run dynamics of he indices. A wo-period lag was found significan on he levels in he VARs. Thus, he appropriae lag srucure is wo periods for saionary variables. For differenced variables he appropriae lag srucure is a single period. Tables 4 6 are he resuling general models for he BB, B, and CSFB High-Yield Indices. Ý y1 y1 y1

14 70 ( ) T.M. Barnhill Jr. e al.rjournal of Empirical Finance Table 4 General error correcion model for DBB index The VAR suggesed a wo period lag for he coinegraion analysis. Thus, he appropriae lag srucure for differenced Ž D. variable is one lag and for saionary variables he appropriae lag srucure is wo periods. R-squared s 0.747, Sandard Deviaion s 0.225, Durbin Wason s 2.25, ARCH Ž df:7,59. s 0.890w0.520 x, Normaliy x 2 Ž. 2 s9.119 w0.011 x UU. Variable Coefficien Sandard -value -prob. Parial error R 2 Long-run soluion ECM Ž Lag 1. y y Ineres rae risk DT-Bonds Monh Lag Defaul rae risk DMoody s Defaul Rae y y Monh Lag DRussell 2000 sock index Ž ln Monh Lag y y DS&P PricerEarnings Raio y y Monh Lag DLagging Economic Indicaor U Monh Lag y y DLeading Economic Indicaor Monh Lag D%BB class subordinaed Monh Lag y y D%BB class raed minus Ž y Monh Lag UU Iraq Invasion y y Monh Lag y y Kuwai Liberaion y y Marke Crash Liquidiy risk Drexel Bankrupcy y y1.891 U Monh Lag y y Monh Lag UU %Muual Fund Liquid Asses y y Monh Lag Monh Lag y y %New Muual Fund Flow y y Monh Lag y y Monh Lag UU January y y June y y July y y December

15 ( ) T.M. Barnhill Jr. e al.rjournal of Empirical Finance Table 5 General error correcion model for DB index The VAR suggesed a wo period lag for he coinegraion analysis. Thus, he appropriae lag srucure for differenced Ž D. variable is one lag and for saionary variables he appropriae lag srucure is wo periods. R-squared s 0.816, Sandard Deviaion s 0.240, Durbin Wason s 1.64, ARCH Ž df:7,59. s 0.265w0.965 x, Normaliy x 2 Ž. 2 s30.912w0.000 x. Variable Coefficien Sandard -value -prob. Parial error R 2 Long-run soluion ECM Ž Lag 1. y y Ineres rae risk DT-Bonds Monh Lag Defaul rae risk DMoody s Defaul Rae Monh Lag DRussell 2000 Sock Index Ž ln. y y Monh Lag DS&P PricerEarnings Raio y y Monh Lag DLagging Economic Indicaor Monh Lag DLeading Economic Indicaor Monh Lag y y D%B class subordinaed y y Monh Lag D%B class raed minus Ž y. y y Monh Lag y y Iraq Invasion Monh Lag y y1.670 U Kuwai Liberaion y y Marke Crash y y Liquidiy risk Drexel Bankrupcy y y Monh Lag y y Monh Lag y y %Muual Fund Liquid Asses y y Monh Lag Monh Lag y y %New Muual Fund Flow y y Monh Lag y y Monh Lag UU January y y June y y July y y December

16 72 ( ) T.M. Barnhill Jr. e al.rjournal of Empirical Finance Table 6 General error correcion model for DCSFB index The VAR suggesed a wo-period lag for he coinegraion analysis. Thus, he appropriae lag srucure for differenced Ž D. variable is one lag and for saionary variables he appropriae lag srucure is wo periods. R-squareds0.808, Sandard Deviaions0.233, Durbin Wasons1.41, ARCH Ž df:7, 59. s0.300 w0.951 x, Normaliy x 2 Ž. 2 s w0.000 x. Variable Coefficien Sandard -value -prob. Parial error R 2 Long-run soluion ECM Ž Lag 1. y y1.959 U Ineres rae risk DT-Bonds Monh Lag Defaul rae risk DMoody s Defaul Rae Monh Lag DRussell 2000 Sock Index Ž ln. y y Monh Lag DS&P Pricerearnings Raio y y Monh Lag DLagging economic indicaor Monh Lag DLeading Economic Indicaor Monh Lag y y Iraq Invasion Monh Lag y y Kuwai Liberaion y y UU Marke Crash y y Liquidiy risk Drexel Bankrupcy Monh Lag y y Monh Lag %Muual Fund Liquid Asses y y Monh Lag Monh Lag y y %New Muual Fund Flow y y Monh Lag y y Monh Lag UU January y y June y y July y y December The general models were hen reduced o more parsimonious models. The decision crieria used o deermine he final specific model was wofold. Firs, all

17 ( ) T.M. Barnhill Jr. e al.rjournal of Empirical Finance variables, which were saisically significan a he 90% confidence level, were included. Second, F-ess were performed on he models o deermine he significance of he loss of informaion from removing a variable. The differences in he saisical significance in he general and parsimonious models are in par due o he correlaion of a number of he dummy variables o he oher independen variables. For example, he significance of he 1987 marke crash is higher if he sock index, S&P pricerearnings raio, and muual fund flow are removed from he model. The same argumen can be made abou he dummy variables accouning for he Kuwai invasion and subsequen liberaion. 11 The dummy variables in effec cach he addiional variaion. 12 Table 7 shows he resuling parsimonious models for he BB, B, and CSFB Indices respecively. The specific models include summary es saisics o examine he properies of he models Saisical properies of he models Tables 4 7 conain summary es saisics a he boom of he ables. The es saisics examine he fi of he model, he auocorrelaion, heeroscedasiciy, and normaliy of he errors. Overall he models prediced values fi well wih he acual values. The specific models had R 2 of 0.62 o 0.82 and sandard errors of 0.20 o The sandard error equaes o 20 o 25 basis poins error. The auocorrelaion and heeroscedasiciy measures for a six-period lag indicae no saisically significan problem. However, here was an indicaion of heeroscedasiciy for a single lag. An ARCH Ž. 1 model was esed bu was found o add lile o he model. The bigges saisical problem was he nonnormaliy of he errors. To assess he exen and cause of he normaliy problem he acual versus fied values were examined. The problem wih he normaliy of he errors appears o be relaed o exernal shocks during he 1990 o 1992 ime frame raher han a problem wih he overall fi of he model. The exernal shocks in he 1989 o 1992 ime frame included a 11 To deermine if he dummy variables were influencing our conclusions he specific models for he BB, B and CSFB Indices were reesimaed excluding he dummy variables. The only change in he reesimaed models was ha he percenage of subordinaed deb in he BB index slipped slighly below he 90% confidence level. 12 A problem wih he collineariy of he lagged change in he dependen variable was also found in he general models. To correc for his, he lagged change was dropped from he model wih no loss of informaion. 13 An invesmen grade index Ž A raed bonds. was also modeled. The coinegraing vecor only included he A yield and he Treasury yield. 8,9 The resuling specific model for he index A included he ECM variable, he change in Treasury yields, and he change in muual fund flow ino invesmen grade bond funds. The change in Treasury yield was he mos significan facor wih a parial R 2 s0.833 and he models R 2 s0.870.

18 74 Table 7 Specific error correcion model for DBB, B, and CSFB indices The VAR suggesed a wo period lag for he coinegraion analysis. Thus, he appropriae Lag srucure for differenced Ž D. variable is one lag and for saionary variables he appropriae Lag srucure is wo periods. Variable Coefficien Sd. error -value -prob. Parial R 2 BB index long-run soluion ECM Ž Lag 1. y y Ineres rae risk DT-Bonds Defaul rae risk DMoody s Defaul Rae 1-Monh Lag D% BB Class Subordinaed U D% BB Class Raed Minus Ž y U Liquidiy risk Drexel Bankrupcy 2-Monh Lag UU %New Muual Fund Flow 2-Monh Lag y y BB Model es saisics: R s0.622, Sandard Deviaions0.235, Durbin Wasons2.11, ARCH Ž df:7, 97. s0.673w0.694 x, Normaliy x 2 Ž. 2 s17.231w0.000x B index long-run soluion ECM Ž Lag 1. y y T.M. Barnhill Jr. e al.rjournal of Empirical Finance 7 ( 2000 ) Ineres rae risk DT-Bonds

19 Defaul rae risk DMoody s Defaul Rae DS&P PricerEarnings Raio y y2.325 UU Iraq Invasion 1-Monh Lag Liquidiy Risk %New Muual Fund Flow y y January y y1.897 U B Model es saisics: R s0.818, Sandard Deviaions0.201, Durbin Wasons1.77, ARCH Ž df:7,89. s1.433w0.202 x, 2 Normaliy x Ž. 2 s12.994w0.001x CSFB HYI long-run soluion ECM Ž Lag 1. y y Ineres rae risk DT-Bonds Defaul rae risk DMoody s Defaul Rae Iraq Invasion 1-Monh Lag Kuwai Liberaion y y2.089 UU Liquidiy risk %New muual fund flow y y Monh Lag U CSFB Model es saisics: R s0.734, Sandard Deviaions0.252, Durbin Wasons1.95, ARCH Ž df:7,88. s1.128 w0.267 x, Normaliy x 2 Ž. 2 s23.182w0.000x T.M. Barnhill Jr. e al.rjournal of Empirical Finance 7 ( 2000 )

20 76 ( ) T.M. Barnhill Jr. e al.rjournal of Empirical Finance large number of bankrupcies, increased regulaion of Savings and Loans porfolios, he bankrupcy of he larges underwrier and marke maker ŽDrexel-Burn- ham., he failed UAL buyou, and he Gulf War. Given hese exernal shocks o he marke i is no surprising he model has large errors during ha ime period Formulaion of specific models The following is he formulaion of he parsimonious error correcion models Ž.Ž. derived from Eqs. 4 6 and Table 7: DBB s y0.26 ŽBB y 0.99Ž T-Bond. y 0.12Ž DefaulRae. q 0.32Ž DT-Bond. q 0.13Ž DDefaulRae. y1 q 0.05Ž D%Subordinaed. q 0.05Ž D%BBy. q 0.55Ž Drexel. y 0.05 Ž %MuualFundFlow. y2 q 0.02 Ž %MuualFundFlow. y2 Ž 10. DBsy0.15 By0.79 Ž TyBond. y0.29ž DefaulRae. q 0.15Ž DT-Bond. q 0.17Ž DDefaulRae. y 0.06Ž DPrE Raio. q 1.24Ž IraqInvasion. y 0.08 Ž %MuualFundFlow. y 0.14Ž January. Ž 11. DCSFBs y0.11 CSFBy 0.83Ž T-Bond. y 0.35Ž DefaulRae. y1 q 0.31Ž DT-Bond. q 0.14Ž DDefaulRae. y1 y1 q 0.98Ž IraqInvasion. y 0.58Ž KuwaiLiberaion. y1 y 0.09 Ž %MuualFundFlows. q 0.01 Ž %MuualFundFlows. y2 Ž 12. y1 y1 5. Empirical findings In his secion, conclusions are drawn from he empirical findings abou he long-run properies of he model, he effec of removing muual fund flow from he models on our conclusions, he effec of dynamic liquidiy, defaul and ineres rae measures on he indices yields, and he segmenaion of he high-yield marke Long-run properies of he models The error correcion componen was saisically significan in all he models. These resuls in conjuncion wih he coinegraion analysis clearly demonsrae

21 ( ) T.M. Barnhill Jr. e al.rjournal of Empirical Finance he imporance of he long-run relaionship beween noninvesmen grade yields, Treasury yields, and defaul raes. The speed of adjusmen response was highes for he BB Index and lowes for he CSFB Index. The value of he coefficien in he BB Index was y0.261 Ž -saisicsy This represens a relaively rapid reversion owards he long-run relaionship beween he variables. The lower credi qualiy B Index had a lower coefficien Žy0.082 wih a -saisic of Ž y suggesing a slower reversion owards he equilibrium over ime. Is he long-run relaionship sable or flucuaing over ime? One way o assess his is o analyze he consisency of he ECM coefficien esimae over ime using recursive esimaion. To do his he ECM variable is esimaed using hree years of daa and he change in he coefficien is hen racked over ime as each addiional ime period is added o he model. Fig. 3 shows he bea esimaes of he error correcion coefficien over ime wih dashed lines represening wo sandard errors. Fig. 3. Sabiliy of Bea Esimae of he Error Correcion Coefficien in he specific BB, B, and CSFB Ž. index models he Bea Esimae is Bounded"Two Sandard Errors.

22 78 ( ) T.M. Barnhill Jr. e al.rjournal of Empirical Finance Table 8 Correlaion analysis beween muual fund flow and oher variables Correlaion o muual fund flow Defaul rae measures DMoody s Defaul Rae y0.19 DLeading Economic Indicaors Ž naural logarihm DLagging Economic Indicaors Ž naural logarihm. y0.01 DRussell 2000 Sock Index Ž naural logarihm DS&P PricerEarnings Raio 0.24 Ineres rae measure DT-Bond y0.23 Liquidiy measure %MF liquid asses y0.21 The resuls indicae a sable and consisen relaionship for each of he indices. The primary excepion o his conclusion is he 1990 ime period when he ECM coefficien for B and CSFB Indices had large sandard errors. This is no unexpeced given he high volailiy during ha period. However, he upper recursive sandard error bound is always negaive. Also he recursive coefficien esimaes for he full sample say wihin he confidence inerval a he end of he sample Reesimaion of models excluding muual fund flows Given he dominance of muual fund flow in explaining he yield on noninvesmen grade indices, he significance of a number of oher correlaed variables may be los. For example, muual fund flow ino he high-yield marke decreased 8% in Ocober of 1987, which coincides wih he 1987 marke crash. Similarly muual fund flow decreased 9% and 10% respecively in Augus and Sepember of 1990 Ž Iraq invaded Kuwai in 8r90., and increased by 8% in February and 7% in March when he coaliion liberaed Kuwai. Table 8 conains he resuls of a correlaion analysis beween muual fund flows and oher explanaory variables esed in he models. Given he correlaion srucure of muual fund flows o he oher explanaory variables, he models were reesimaed wihou muual fund flows in he models Ž Table 9.. The following are he formulaions of he parsimonious error correcion models from Table 9: DBBs y0.23 ŽBB y 0.99Ž T-Bond. y 0.12Ž DefaulRae. y1 q 0.54Ž DT-Bond. q 0.20Ž DDefaulRae. y1 y 1.85Ž DRussell2000. q 0.08Ž D%Subordinaed. q 0.05Ž D%BBy. y 0.21Ž January. Ž 13.

23 ( ) T.M. Barnhill Jr. e al.rjournal of Empirical Finance DB sy0.07 ŽB y 0.79Ž T-Bond. y 0.29Ž DefaulRae. y1 q 0.59Ž DT-Bond. q 0.23Ž DDefaulRae. y 2.26Ž DRussell2000. y 0.21Ž DLeadIndicaors. q 1.71Ž IraqInvasion. y1y 0.87Ž KuwaiLiberaion. y 0.27Ž January. Ž 14. DCSFBs y0.02 CSFBy 0.83Ž T-Bond. y 0.35Ž DefaulRae. y1 q 0.61Ž DT y Bond. q 0.19Ž DDefaulRae. y 2.23Ž DRussell2000. q 1.44Ž IraqInvasion. y1 y 1.32Ž KuwaiLiberaion. y 0.30Ž January. Ž 15. The resuls were consisen wih he specific models found in Table 7 bu some variables previously found no o be saisically significan enered ino he new models. The change in he Russell 2000 Index enered ino he BB, B, and CSFB Indices wih a p-value a 1%. This is consisen wih he srong correlaion beween muual fund flow and changes in he sock index found in Table 9. The change in he leading economic indicaor was found o have a negaive effec on yield a he 90% confidence level for he B Index. However, he sandard error is considerably higher for hese models which have excluded muual fund flow. This is especially rue for he lower credi qualiy B index Ž see Table Dynamic liquidiy risk measures affecing he yield of high-yield indices The Percenage of Muual Fund Flow had a saisically significan negaive effec on all he indices. In fac, muual fund flow had he highes parial R 2 of any variable in all of he models. The resuls also sugges he lower qualiy indices, B and CSFB, are more suscepible o price flucuaions as a resul of fund flow. This is exemplified by he large -saisics and parial R 2 of he fund flow coefficien in he B and CSFB Indices. The srengh of he relaionship of yield o fund flow could be he explanaion for he seemingly conradicory finding of a higher R 2 for he more volaile B and CSFB Indices as compared o he BB Index. Curiously, fund flow lagged 2 monhs had a posiive impac on all he indices and was saisically significan for he BB and CSFB Indices. This could indicae a seasonal componen o fund flow. The resuls are consisen wih a January effec for all he indices. The January coefficien was negaive as expeced in all he general models and was saisically significan a he 10% level in he specific model of he B Index. The December coefficien was posiive in all he general models. When muual fund flow was removed from he models, a posiive effec of beween 21 and 30 basis poins was found a he 5% level in January for all he indices. Overall, he resuls regarding he January and December variables are consisen wih eiher a ax-loss selling effec, porfolio window dressing andror coupon paymen flows. However, here was no corresponding seasonal variaion during June and July which calls ino quesion he validiy of he coupon paymen flow

24 80 Table 9 Specific error correcion model for DBB, B, and CSFB indices excluding muual fund flow The VAR suggesed a wo period lag for he coinegraion analysis. Thus, he appropriae lag srucure for differenced Ž D. variable is one lag and for saionary variables he appropriae lag srucure is wo periods. Variable Coefficien Sd. error -value -prob. Parial R 2 BB index long-run soluion ECM Ž Lag 1. y y Ineres rae risk DT-Bonds Defaul rae risk DMoody s Defaul Rae 1-Monh Lag DRussell 2000 Sock Index Ž ln. y y D%BB class subordinaed UU D%BB class raed minus Ž y U Liquidiy risk January y y2.163 UU BB Model es saisics: R s0.499, Sandard Deviaions0.270, Durbin Wasons2.14, ARCH Ž df:7,94. s2.472w0.023 x UU, Normaliy x 2 Ž. 2 s10.031w0.007x B index long-run soluion ECM Ž Lag 1. y y1.766 U T.M. Barnhill Jr. e al.rjournal of Empirical Finance 7 ( 2000 ) Ineres rae risk DT-Bonds

25 Defaul rae risk DMoody s Defaul Rae DRussell 2000 sock index Ž ln. y y DLeading Economic Indicaor y y1.740 U Iraq Invasion 1-Monh Lag Kuwai Liberaion y y Liquidiy Risk January y y2.388 UU B Model es saisics: R s0.557, Sandard Deviaions0.318, Durbin Wasons1.92, ARCH Ž df:7,85. s0.654w0.709 x, Normaliy x 2 Ž. 2 s5.339w0.069x U CSFB HYI long-run soluion ECM Ž Lag 1. y y Ineres rae risk DT-Bonds Defaul rae risk DMoody s Defaul Rae DRussell 2000 sock index Ž ln. y y Iraq Invasion 1-Monh Lag Kuwai Liberaion y y Liquidiy risk January y y CSFB Model es saisics: R s0.584, Sandard Deviaions0. 303, Durbin Wasons1.85, ARCH Ž df:7,85. s0.410 w0.893 x, Normaliy x 2 Ž. 2 s6.715w0.035x UU T.M. Barnhill Jr. e al.rjournal of Empirical Finance 7 ( 2000 )