The Feedback from Stock Prices to Credit Spreads

Transcription

1 Appled Fnance Projec Ka Fa Law (Keh) The Feedback from Sock Prces o Cred Spreads Maser n Fnancal Engneerng Program BA 3N Appled Fnance Projec Ka Fa Law (Keh)

2 Appled Fnance Projec Ka Fa Law (Keh). Inroducon The curren leraure assumes ha cred spread capures flucuaons n unexpeced and expeced reurns. I s known ha cred spread s a rsk facor (Chen a al. (986)). There s also leraure ha uses he cred spread o proxy for me-varyng expeced reurns (Fama and French (989). However, he nverse effec, he effec of sock prce movemens on he cred spread has no been analyzed. Cred spread analyss s very mporan oday because of he populary of he cred dervaves. Modelng cred spread s also very mporan for prcng a lo of corporae fxed ncome secures and even more complex secury lke he converble bonds. Ths paper wll sudy n deph he cred spread behavor wh respec o nvesmen grade bonds and he non-nvesmen grade bonds. Demonsraon of how o apply hs sudy o prce varous nsrumens wll be brefly dscussed n he las secon. There are wo reasons why changes n prces mgh have an effec on he cred spread.. Lower prce (ex-pos reurns), he equy value of he company decreases, he frm s more levered, probably of defaul ncreases, resulng n changes n he cred spread. Ths channel wll lkely be sronges for companes ha are already n fnancal dsress.. Feedback effec (as n Campbell and Herschel). Dvdng bonds no nvesmen grade and non-nvesmen grade allows us o beer undersand he cred spread responsveness o sock reurns. For nvesmen grade bonds, assumng he company s fnancally healhy, we would expec ha even as he sock prce drops, he marke parcpans wll no lose all confdence. The defaul probably wll no ncrease sgnfcanly and so he cred spread wll no reac srongly. In oher words, he sock prce movemen s no he sole deermnan for he cred spreads for he nvesmen grade bonds. However, for non-nvesmen grade companes, sock prce movemens may be very sensve o he marke parcpans abou her ably o mee he deb oblgaons. We would expec he cred spread s very sensve o he sock prce movemens. Deermnng wheher a company s nvesmen grade or non-nvesmen grade s easly done by lookng a he rang of he bonds by he rang agences, say Sandard & Poor and he Moodys. I wll no furher sub-dvde he bonds no AAA sample, AA sample because here mgh be slgh dfference n he rangs assgned for he same bonds by dfferen agences. Also, furher sub-dvson wll lead o smaller sample and may lead o sample bas.

3 Appled Fnance Projec Ka Fa Law (Keh) Ths paper has hree man fndngs: By classfyng he corporae bonds no nvesmen grade and non-nvesmen grade bonds, he laer one has sgnfcan negave relaonshp beween he cred spread and he sock reurns, and he magnude s huge. Whle for he nvesmen grade bonds, here does no exs a srong negave relaonshp, and even f any, he magnude s small when compared wh he non-nvesmen grade bonds. Ths may be due o he fac ha here exss oher deermnans (oher han movemen of sock prce) for he nvesmen grade bonds. Geske and Delaneds () has suded The Componens of Corporae Cred Spreads: Defaul, Recovery, Tax, Jumps, Lqudy, and Marke facors and found ha he cred rsks and cred spreads are no prmarly explaned by defaul and recovery rsk, bu are manly arbuable o ax, lqudy, and marke rsk facors. Ths may help o explan my fndng abou he weak responsveness of he nvesmen grade bonds o he sock prce. In he long horzon regressons, I also have some evdence abou he lqudy facor n he deermnaon of cred spread for he non-nvesmen grade bonds whle hs facor seems weak for he nvesmen grade bonds. Fnally, he dsrbuon of he bea coeffcens s also surprsng, nearly normal for he nvesmen grade bonds and no specal dsrbuon for he non-nvesmen grade bonds.. Daa 5 (randomly chosen) non-nvesmen grade corporae bonds yeld spreads wh daly frequency are provded by Merrll Lynch Fxed Income dvson daabase. Bu snce 5 of hem are no lsed companes and 7 of hem have less han 4 monhs daa, I can only sudy 38 of hem. 86 benchmark nvesmen grade bonds are randomly chosen from US Corporae Weekly and her daly yelds are colleced from Bloomberg. Bu afer he Frs Sage regresson (Secon 3), when I conduc he long horzon regresson, I can only sudy 77 companes snce 9 of hem have mssng daa ha does no allow he long horzon regresson. Daa span from as early as Jan, 997 (f ha corporae bond was alve already) o December 6, (he dae we sared he research), n daly frequency. I use hgh frequency daa because he response of he cred spread o reurns s hypoheszed mmedae and wll be esed n laer secon. Cred spread s he yeld spread beween a corporae bond and a comparable defaul-free bond solely due o he cred qualy. The proxy for he defaul free bond s he Treasury bond. Therefore, he cred spread s consruced by subracng he Treasury bonds yeld, whch has smlar maury and he coupon rae from he corporae bond yeld. From he ls of he Treasury bonds, I choose he closes maury frs, and hen fnd he closes coupon rae. Then he yeld spread s more or less only due o he cred qualy. Throughou he paper, cred spread s measured n Bass Pons. 3

4 Appled Fnance Projec Ka Fa Law (Keh) A corporae bond s defned as non-nvesmen grade f s cred rang s below BBB by Moody s and s defned as nvesmen grade f s cred rang s a BBB or above. 3. Mehodology 3. Frs Sage Regresson The frs regresson we frs look a s: CR CR = + β (ln P ln P ) α + ε For dfferen bonds ( ), over me =,,T. The hypohess s ha he change n sock prce over he perod - o wll be correlaed o a correspondng, bu oppose n sgn, change n he cred spread. The resuls of he above regressons for non-nvesmen grade bonds and he nvesmen grade bonds are shown n Table below. Table : Proporon of negave bea coeffcens Proporon of Negave beas Mn. Max. Sandard devaon Non-nvesmen grade 84.% Invesmen grade 6.5% For non-nvesmen grade bonds, ou of 38 companes, 3 have negave beas, or 84.%. Negave bea s he nuon, whch means cred spread decreases wh posve reurn, and ncreases wh negave reurns. Bu for he nvesmen grade bonds, 5 ou of 86 companes (or 6.5%) have negave beas. Compared wh he non-nvesmen grade bonds, we see he dfference beween he proporons. From he resuls of he Frs Sage Regresson, I plo he hsogram of he Bea coeffcens for he Non-nvesmen grade bonds (fgure a) and he nvesmen grade bonds (fgure b) respecvely n Appendx. Two man fndngs are:. The dsperson of he bea coeffcens for he non-nvesmen grade bonds s very large, rangng from 564 o 65, whle he dsperson s small for he nvesmen grade bonds.. Dsrbuons of he bea coeffcens are very dfferen, looks lke normal (bu a lle skewed) for he nvesmen grade bonds whle no specal dsrbuon for he nonnvesmen grade bonds. The economc nuon behnd he fndngs s ha even for he bonds ha are among nonnvesmen grade, he marke percepon abou her fnancal ably can be que 4

5 Appled Fnance Projec Ka Fa Law (Keh) dsperse. Therefore, care should be aken n modelng he cred spread of non-nvesmen grade bonds, snce he dsperson s very large and he non-normaly makes he locaon of confdence nerval mpossble. 3. Second Sage Regresson The dsperson of he bea coeffcens s very large for he non-nvesmen grade bonds. I suspec ha some of he oulers mgh be due o cred spread reacng o reurns n a down swng. So I run he followng regressons for he 38 non-nvesmen grade companes: CR CR = } α + β r { r } + β r { r < + ε where r = ln P ln P { r } s a dummy varable (ndex funcon) ha equals o one f r and zero oherwse. Smlarly, { r < } s an ndex funcon ha equals o one f r < and zero oherwse. The resul of he Second sage regresson s n Table below. Table : Resuls of second sage regresson Bea Bea Number of Negave Bea 5 3 proporon From Table, we see ha 5 ou of 38 companes (or 66%) have negave β, ha s, cred spread decreases wh he posve reurn; Whle 3 ou of 38 companes (or 79%) have negave β, ha s, cred spread ncreases wh he negave reurn. Alhough he change of cred spreads seems o be more sensve o he down swng, suggess no clue o he large dsperson of he bea coeffcens n he Frs Sage regressons for he non-nvesmen grade bonds. I also suggess ha here s no model msspecfcaon for he frs sage regresson. 3.3 Includng he S&P 5 as conrolled varable Snce he marke as a whole can affec he nvesors perspecve abou each frm, I nclude (S&P 5 as a proxy) as a conrolled varable no our regressons and run he followng: CR CR = Re α + β Sock Re urn + β S & P urn + ε The resuls of he above regressons for he non-nvesmen grade bonds and he nvesmen grade bonds are shown n Table 3 below. 5

6 Appled Fnance Projec Ka Fa Law (Keh) Table 3: Includng S&P 5 reurns as conrolled varable Proporon of negave β Proporon of neg. β Non-nvesmen grade 77% 79% Invesmen grade 6% 67.5% We see ha even when I nclude he S&P 5 reurn as a conrol varable n he regressons, he proporon of negave beas assocaed wh he sock reurn remans more or less he same, 77% for he non-nvesmen grade bonds and around 6% for he nvesmen grade bonds. Bu one neresng pon s ha he S&P reurns have a larger negave bea proporon han he sock reurns for boh he non-nvesmen grade bonds and he nvesmen grade bonds. The reason for hs may be mulcollneary, ha he sock reurns and he S&P reurns have correlaons so ha he S&P reurns draw he sock reurn effecs away. Anoher neresng resul can be found when we look a he hsogram of boh bea coeffcens (sock reurn) and he bea coeffcens (S&P reurn), Fgure 3 n Appendx. Even we nclude he S&P 5 reurns, our former resuls do no change. The dsrbuon of he bea coeffcens (sock reurn) s more or less he same for he case whou he S&P 5, looks lke a bell shape for he nvesmen grade bonds, whle very dspersed for he non-nvesmen grade bonds. (Fgure 3a and fgure 3c). The proporon of he negave bea coeffcens s much hgher for he non-nvesmen grade bonds han ha of he nvesmen grade bonds. Bu when we look a he dsrbuon of he bea coeffcens assocaed wh S&P reurn, he dsrbuon s even more dspersed, lookng unform for he non-nvesmen grade bonds (fg 3b), whle sll akng a bell shape for he nvesmen grade bonds. The economc nuon behnd he above fndngs s ha S&P reurn seems o be a very mporan facor n deermnng he cred spread for boh he nvesmen grade bonds and he non-nvesmen grade bonds. The large proporon of negave beas s evdence. Also, he more dspersed beas for he non-nvesmen grade bonds sugges ha parcular care should be aken n modelng he cred spread for hem Long Horzon Regressons whou S&P reurns as conrolled varable So far, I have been runnng he regresson: CR CR = + β (ln P ln P ) α + ε () The hypohess was ha he change n he sock prce over he perod - o wll be correlaed wh a correspondng, bu oppose n sgn, change n he cred spread. 6

7 Appled Fnance Projec Ka Fa Law (Keh) Bu prces canno adjus whn a sngle day. For nsance, f here s a jump (a bg even), prces mgh frs reac, bu gven ha he bonds marke s no very lqud, mgh ake several days before prces reach equlbrum. Suppose ha I can also wre equaon () for perod + CR α () + CR = + β (ln P + ln P ) + ε + Therefore, pung he wo equaons ogeher, we have: CR + CR + CR CR = + β (ln P + ln P + ln P ln P ) + ε + α + ε CR + CR = α + β (ln P + ln P ) + u+ where he subscrps below he coeffcens denoe he perod over whch we are runnng he regresson. In fac, we wan o run he -day change n he cred spread on he -day reurn. The above mehod can be generalzed o CR α (3) + k CR = k + β k (ln P + k ln P ) + u+ where we analyze he k-day change n he cred spread o movemens n he k-day reurn. Ths mehod wll allow us o see wheher s rue ha β k = β, as expeced from he equaons above. If urns ou ha β k > β, hen he long-horzon adjusmen s bgger han he one-me adjusmen. If urns ou ha β k < β, hen he long-horzon adjusmen s no as mporan as he mmedae one. Anoher neresng exenson of he long-horzon regressons s relaed o lqudy. If we fnd ha β k β, hs mgh mply ha here were lqudy problems ha prevened he prces from adjusng mmedaely. If here are no oher facors, we mus have β = β. In hs secon, I wll conduc long horzon regressons for k = (as before) as well as for k =, 3, 4, 5 (week),, (monh). The resuls for non-nvesmen grade bonds and nvesmen grade bonds are shown n Table 4 below: k Table 4: Long Horzon regresson Proporon of neg. β K= K= K=3 K=4 K=5 K= K= 7

8 Appled Fnance Projec Ka Fa Law (Keh) Non-nv Inv The long horzon regressons gve us very rch resuls:. For non-nvesmen grade bonds, wh larger K, n fac when K=, all 38 bonds have negave beas assocaed wh he sock reurns. I suppors he lqudy argumen; wh more me o adjus o equlbrum, cred spreads move oppose wh he sock reurns.. The proporon of negave beas for he nvesmen grade bonds seems o no ncrease wh he ncrease n K, he economc nuon s: here exss no lqudy problem and he proporon says around 6% o 7%. 3. The proporon of negave beas say around 6% and 7% for nvesmen grade bonds hrough me whle nearly % for he non-nvesmen grade bonds, suggesng ha he cred spread s less sensve o sock reurns for he nvesmen grade bonds whle very sensve for he non-nvesmen grade bonds. 4. We can say ha sock reurns are very mporan n he change of he cred spread for he non-nvesmen grade bonds. Ths s because for he non-nvesmen grade companes, he probably of fnancal dsress s very hgh and so sock prce movemen s very sensve o he defaul probably. Whle for he nvesmen grade companes, we do no know he movemen of cred spread from he sock reurns because hey are fnancally healhy and he movemen of cred spread s no very sensve o sock prce movemens. There are oher facors a work, lke axaon, capal srucure and oher dosyncrac facors. More resuls can be found from he hsogram wh dfferen K, see he 3D graphs for he non-nvesmen grade (fgure 4) bonds and fgures 5 for he nvesmen grade bonds. Wh larger K, he dsrbuon of he bea coeffcens for he non-nvesmen grade bonds does no change, bu s shfng lefwards, wh more and more negave magnude wh he ncrease n K, ha s, more prce adjusmen hrough me, supporng our lqudy argumen. For nvesmen grade bonds, he dsrbuon and he magnude of he bea coeffcens do no seem o change wh dfferen K levels, suggesng no lqudy facor nvolved n he prce adjusmen Long Horzon Regressons wh S&P reurns as conrolled varable 8

9 Appled Fnance Projec Ka Fa Law (Keh) In order o see boh he effecs of he sock reurns and he S&P reurns on he change of he cred spread hrough me, I run he long horzon regressons ncludng he S&P reurns as ndependen varables: + k CR = α k + β k Sock urnkperod + β k S & P Re urnkperod + CR Re u + The resuls for he above regressons a K=, 3, 4, 5,. for non-nvesmen grade bonds and nvesmen grade bonds are shown n Table 5. Table 5: Long horzon regresson wh S&P 5 reurn as conrolled varable Proporon K= K= K=3 K=4 K=5 K= K= of neg. β Non-nv Inv Proporon K= K= K=3 K=4 K=5 K= K= of neg. β Non-nv Inv Resuls from Table 5:. A all horzons, he number of negave beas assocaed wh sock reurns s larger han he number of negave beas assocaed wh S&P reurns for he non-nvesmen grade bonds. The oppose s rue for he nvesmen grade bonds; ha s, a all horzons, he number of negave beas assocaed wh S&P reurns s hgher.. For non-nvesmen grade bonds: Wh larger K, he number of negave beas assocaed wh sock reurns s ncreasng whle he number of negave beas assocaed wh S&P reurns says around he same. Ths suggess ha akes me for he cred spread o adjus from sock prce change only bu no he S&P movemen. 3. For nvesmen grade bonds: Wh larger K, he number of negave beas assocaed wh sock reurns and he number of negave beas assocaed wh S&P reurns say around he same a all horzons, suggesng no me adjusmen from sock prce change and S&P level changes. 4. The above rend can bes be vsualzed by he 3D graph n he appendx, Fgure 6 o Fgure 9. For non-nvesmen grade bonds, he bea assocaed wh he sock reurn s more and more negave wh he ncrease n K; whle for bea (S&P reurn), here s no rend wh he ncrease n K. For nvesmen grade bonds, here are no rends for boh bea coeffcens wh ncreasng K. 9

10 Appled Fnance Projec Ka Fa Law (Keh) 4. Adjusmen for auocorrelaon due o overlappng daa for he Long Horzon Regressons The Long horzon regresson above uses overlappng daa whch wll nroduce seral correlaon. Seral correlaon wll no have an effec on he value of he bea coeffcens, bu noneheless he sascs mus adjused. Even when he sascs are adjused, he man resuls of he above analyss do no change. The sgnfcan negave beas assocaed wh he non-nvesmen grade bonds are sll sgnfcan hough he sascs reduce n magnude. The resul for he nvesmen grade bonds s also unchanged. 5. Concluson The man resul n hs paper s he dfferen responsveness of he change n cred spread o he sock reurns and he S&P reurns for he non-nvesmen grade bonds and he nvesmen grade bonds. For non-nvesmen grade bonds, he movemen s negave whle he resul s que mxed for he nvesmen grade bonds. The above fndng s useful for prcng a Fxed Income nsrumen, especally n he consrucon of prcng models. I has he mplcaon of usng dfferen models for prcng nsrumens wh dfferen cred rangs. For nsance, he S&P 5 reurn seems o be more negavely correlaed wh he cred spread han he sock reurn for he nvesmen grade bonds whle he reverse s rue for he non-nvesmen grade bonds. Take he example of prcng a more complcaed nsrumen: converble bonds usng he ree mehod. A converble bond has he dual feaure of equy and bonds: a hgher prce level, s prced as equy; whle a lower prce level, s prced as bonds. When he cash flow s dscouned backward usng a ree, a rsk free dscoun rae should be used a he very upper nodes where he sock prce s hgh, snce s for sure o be convered. Dfferen sock prce levels means dfferen frm values and possble dfferen rangs, whch s he case for non-nvesmen grade and nvesmen grade. As found n hs paper, he responsveness of he cred spreads s dfferen o non-nvesmen grade bonds and nvesmen grade bonds. Thus, he dscoun rae used (rsky rae = rsk free rae + cred spread) should be dfferen for prcng purposes. See Goldman Sachs research Paper (994). However, he resuls n hs paper subjec o wo lmaons:. Possble small sample effecs: I have red my bes o ge as many samples as possble, bu unforunaely was only able o ge 5 (38 vald) samples for he nonnvesmen grade bonds. Ths may enal small sample bas.

11 Appled Fnance Projec Ka Fa Law (Keh). Possble ncluson of Marx Prce. I was no able o conac Merrll Lynch for he mehod of how he daabase ses he prce of he corporae bonds when hey are no raded on some days. All I know s ha nvesmen banks always use some knd of marx o prce a bond on a day when s no raded. As has been shown by Sarg and Warga (989) ha marx prces are problemac. I beleve ha he above wo problems poenally cause bas, bu wll no dsor he man resuls I found. I have also found ha here exss lqudy problem for he non-nvesmen grade bonds by he long horzon regressons. Thus, par of he yeld spread for he non-nvesmen grade bonds may be due o compensaon for lqudy. Ths problem seems no exs for nvesmen grade bonds and hs wll be our ongong research opc. Fnally, he dsrbuons of non-nvesmen grade bonds and he nvesmen grade bonds also seem dfferen, bu I canno draw a srong concluson on ha because of my small sample. Bu hs wll be suded n fuure effors.

12 Appled Fnance Projec Ka Fa Law (Keh) Appendx Table : Proporon of negave bea coeffcens for Frs sage regresson Proporon of Negave beas Mn. Max. Sandard devaon Non-nvesmen grade 84.% Invesmen grade 6.5% Table : Resuls of second sage regresson Bea Bea Number of Negave Bea 5 3 proporon Table 3: Regresson ncludng S&P 5 reurns as conrolled varable Proporon of negave β Proporon of neg. β Non-nvesmen grade 77% 79% Invesmen grade 6% 67.5% Table 4: Long Horzon regresson wh S&P as conrolled varable Proporon K= K= K=3 K=4 K=5 K= K= of neg. β Non-nv Inv Table 5: Long horzon regresson wh S&P 5 reurn as conrolled varable Proporon K= K= K=3 K=4 K=5 K= K= of neg. β Non-nv Inv Proporon K= K= K=3 K=4 K=5 K= K= of neg. β Non-nv Inv

13 Appled Fnance Projec Ka Fa Law (Keh) Fg a Hsogram of 38 Bea Coeffcens for non- Invesmen grade companes Bea Fg.b Hsogram of 86 bea coeffcens for he Invesmen grade companes Bea 3

14 Appled Fnance Projec Ka Fa Law (Keh) Frequency Fg 3a: Hsogram of Bea coeffcens (sock) for Non-nvesmen grade bonds Bea 6 4 More Fg 3b: Hsogram of Bea coeffcens (S&P) for Invesmen grade bonds bea 4

15 Appled Fnance Projec Ka Fa Law (Keh) Fg 3c: Hsogram of Bea coeffcens (sock) for Invesmen grade bonds Frequency bea 8 6 Fg 3d: Hsogram of bea coeffcens (S&P reurn) for Invesmen grade bonds Frequency bea 8 6 5

16 Appled Fnance Projec Ka Fa Law (Keh) Fgure 4: Hsogram of bea coeffcens wh dfferen K for Non-nvesmen grade bonds 3D graph of he bea coeffcens a dfferen K Bea coeffcens Frequences 8 K 6

17 Appled Fnance Projec Ka Fa Law (Keh) Fgure 5: Hsogram of bea coeffcens wh dfferen K for Invesmen grade bonds 3D graph of bea coeffcens a dfferen K bea Frequency K= K=4 K= K 7

18 Appled Fnance Projec Ka Fa Law (Keh) Fgure 6. Bea coeffcens (sock reurns) for he non-nvesmen grade bonds 3 D g r a p h o f b e a c o e f f c e n ( s o c k r e u r n ) f r e q u e n c y b e a K= K= K=3 K=4 K=5 K= K= K Fgure 7. Bea coeffcens (S&P 5 reurns) for he non-nvesmen grade bonds 3 D g r a p h o f b e a c o e f f c e n (S & P r e u r n ) fr e q u e n c y b e a K= K= K=3 K=4 K=5 K= K= K 8

19 Appled Fnance Projec Ka Fa Law (Keh) Fgure 8. Bea coeffcens (sock reurn) for he nvesmen grade bonds 3 D g r a p h o f b e a c o e f f c e n ( s o c k r e u r n ) f r e q u e n c y b e a K= K= K=3 K=4 K=5 K= K K= Fgure 9. Bea coeffcens (S&P 5 reurn) for he nvesmen grade bonds 3 D g r a p h o f b e a c o e f f c e n ( S & P r e u r n ) b e a F r e q u e n c y K= K= K=3 K=4 K=5 K= K K= 9

20 Appled Fnance Projec Ka Fa Law (Keh) References Geske and Delaneds,, The Componens of Corporae Cred Spreads: Defaul, Recovery, Tax, Jumps, Lqudy, and Marke facors Goldman Sachs research Paper (994), Prcng Converble bonds. George Pan,, Equy o cred prcng, Rsk KMV, The Defaul Predcon Power of he Meron Approach, Relave o Deb Rangs and Accounng Varables. Rober Jarrow,, Defaul Parameer Esmaon Usng Marke Prces.