The Sensitivity of Corporate Bond Volatility to Macroeconomic Announcements. by Nikolay Kosturov* and Duane Stock**

Transcription

1 The Sensiiviy of Corporae Bond Volailiy o Macroeconomic nnouncemens by Nikolay Kosurov* and Duane Sock** * Michael F.Price College of Business, Universiy of Oklahoma, 307 Wes Brooks, H 205, Norman, OK 73072, US. phone #: (405) nkosurov@ou.edu ** Michael F.Price College of Business, Universiy of Oklahoma, 307 Wes Brooks, H 205, Norman, OK 73072, US. phone #: (405) dsock@ou.edu

2 The Sensiiviy of Corporae Bond Volailiy o Macroeconomic nnouncemens bsrac The paper examines excess reurns and volailiy of Treasury bonds, and boh corporae invesmen grade (CIG) bonds and high yield (HY) bonds of differen mauriies on days wih scheduled macroeconomic announcemens. We find ha all bonds earn posiive announcemen-day excess reurns which increase monoonically wih mauriy. Treasury and CIG bond excess reurns exhibi srong GRCH effecs wih highly persisen shocks. Volailiy is abou 100% higher on announcemen days for CIG s and Treasuries, where he effec decreases wih mauriy. Unlike general shocks, announcemen day shocks do no persis and only affec announcemen-day condiional variance. HY bonds behave quie differenly around macroeconomic announcemens han CIG and Treasuries of corresponding mauriy. Mainly, we find evidence ha HY bond general shocks do no persis and do no affec condiional variance forecass. We also find ha differen macroeconomic announcemen ypes affec bond excess reurns in dissimilar fashion.

3 Inroducion Many sudies have analyzed he impac of macroeconomic announcemens upon he value of financial insrumens including equiies, derivaive insrumens and Treasury bonds. 1 None, however, have analyzed he reacion of corporae bond prices of various credi qualiies and mauriies o regularly scheduled monhly macroeconomic announcemens as done here. The corporae bond marke is a vial par of he financial sysem where approximaely $1.4 rillion of corporae deb is ousanding, (see Fabozzi, 2000). In he recen pas he imporance of he corporae bond marke has grown in ha many companies ha once borrowed from banks have been able o ap he high yield bond marke insead. Our purpose is o answer imporan ses of quesions relaed o corporae bond pricing on announcemen days. The firs se of quesions concerns wheher corporae bond reurns are more volaile on announcemen days. Does he answer depend on credi qualiy? If reurns are more volaile on announcemen days, imporan subsequen quesions wihin his se include how much more volaile are reurns on announcemen days compared o oher days, and is greaer volailiy rewarded wih greaer reurn on announcemen days? relaed quesion is wheher volailiy is rewarded wih greaer reurn on nonannouncemen days. The second se of quesions concerns wheher he volailiy persiss for a number of days afer he announcemen day. If no, i suggess ha he marke digess he informaion very quickly and efficienly wihin one day. Reasons will be given for expecing he volailiy o persis as will reasons for expecing he volailiy o no persis. Relaed o hese quesions, if he higher volailiy persiss beyond he announcemen day, is volailiy rewarded wih greaer reurns beyond he announcemen day? lso, for compleeness, does volailiy of nonannouncemen days persis? hird se of quesions concerns wheher announcemen-day volailiy is relaed o credi qualiy and mauriy. re corporae bond reurns more or less volaile han equal mauriy U. S. Treasury bonds? Reasons o expec boh greaer and lesser volailiy for corporae bonds will be briefly given below. Relaed o his, does he answer depend on 1 For examples see McQueen and Roley (1993), Ederingon and Lee (1993) and Huberman and Schwer (1985).

4 he credi qualiy and mauriy of he corporae bonds? For example, does a Treasury bond or a op grade bond exhibi more or less announcemen-day volailiy han a high yield bond? For compleeness, he same series of quesions also applies o nonannouncemen days. The fourh se of quesions concerns he poenially diverse reacions o he six differen ypes of macroeconomic announcemens we analyze. Do some announcemens evoke lile reacion in erms of reurn and volailiy while ohers evoke a srong reacion? Do some announcemens resul in increased reurns bu no increased volailiy for some ypes of bonds? If so, invesing in hese bonds prior o an announcemen would be a superior invesmen. The answers o his fourh se have obviously imporan invesmen sraegy implicaions. The answers o hese ses of quesions are quie imporan given he size of he corporae bond marke and he obvious fac ha invesors need o know how risky (volaile) corporae bonds are. Bond marke professionals who hedge volailiy of corporae bond posiions need o be aware of he special challenge of hedging heir bonds on announcemen days. Collin-Dufresne, Goldsein and Marin (2001) noe ha hedge funds are exposed o considerable credi risk when hey use Treasury fuures o hedge corporae bond porfolios. Large hedging errors could occur if volailiy is no modeled correcly. Pedrosa and Roll (1998) mainain ha hedging corporae bond porfolios is very difficul as much of he volailiy is sysemaic risk which is a leas largely aribuable o macroeconomic announcemens. The growh in credi derivaives, which aemp o hedge corporae bonds (and oher deb), has been srong in recen years. The San Francisco Federal Reserve Bank (2001) esimaes ha he volume of credi derivaives raded grew from $600 billion in 1999 o $800 billion in Furhermore, he resuls will be useful o hose aemping o value opions embedded in corporae bonds and hose aemping o incorporae GRCH ime series resuls ino GRCH opion pricing of deb. See Richken and Trevor (1999). The nex secion describes he heory of bond marke reacion o macroeconomic announcemens. Then we describe he daa sources and compue mean reurns and 2 The Wall Sree Journal (December 3, 2001) esimaed 2001 volume as $1 rillion. Models o use and value credi derivaives should incorporae informaion abou frequen and regular announcemens which affec corporae bond marke volailiy.

5 volailiy for bonds of various credi qualiies and mauriies for announcemen and nonannouncemen daes. Nex, we uilize simple OLS regressions o calculae expeced reurns and variance and follow up wih more sophisicaed GRCH models which recognize he auocorrelaion of reurns and volailiy. Finally, we summarize he research in he las secion. Theory and Hypoheses The firs se of quesions revolve around measuring he volailiy on an announcemen day and comparing i o volailiy on oher days. Why would one expec greaer volailiy on announcemen days? One reason is relaed o he resuls of Elon, Gruber, grawal and Mann (2001) where hey aemp o explain he rae spread for corporae bonds. They find ha expeced defaul explains relaively lile of he spread bu he spread is more explained by he sysemaic risk facors ha we commonly accep as explaining risk premiums for common socks. Furhermore, Collin-Dufresne, Goldsein and Marin (2001) find ha firm specific facors explain lile of he spread and macroeconomic facors are much more imporan in explaining spreads. We mainain ha macroeconomic announcemens represen a good deal of he sysemaic risk of corporae bonds (and oher financial insrumens). For example, if he consumer price index (CPI) repors a dramaic increase in inflaion, he value of all corporae bonds is likely significanly affeced. Numerous sudies have examined volailiy in he U. S. Treasury bond marke. Jones, Lamon and Lumsdaine, hereafer JLL, (1998) noe ha he source of auocorrelaed volailiy commonly found in financial insrumens is elusive and hen examine he impac of macroeconomic announcemens upon volailiy in he U. S. Treasury bond marke. Given ha macroeconomic announcemens are no auocorrelaed, such announcemens enable one o es wheher characerisics of he rading process give rise o auocorrelaion. They find ha volailiy is considerably greaer on announcemen days. Fleming and Remolona (1997) find ha he weny five larges price shocks in Treasury bonds were aribuable o macroeconomic announcemens. In a laer sudy (1999), Fleming and Remolona analyze minue by minue Treasury bond price changes

6 and find ha prices adjus sharply o announcemens in he firs few minues afer an announcemen. Given hese sudies one migh hink ha corporae bond prices should also exhibi high volailiy on announcemen days. However, his expecaion is moderaed by he relaively weak evidence ha macroeconomic announcemens have a clear impac on equiy prices. See, for example McQueen and Roley (1993). Corporae bonds may be described as a mix of risk free deb and equiy where he equiy componen rises as credi qualiy declines. Blume, Keim and Pael (1991) mainain ha low grade bonds exhibi characerisics of boh high grade bonds and equiy and Weinsein (1983, 1985) mainains ha high yield bonds have a srong equiy componen. s discussed below, i may be ha corporae bonds of cerain credi qualilies are more volaile on announcemen days han nonannoucemen days bu less volaile han Treasury bonds on announcemen days. lso, i may be ha lower grade bonds, wih a greaer equiy componen ha may no be responsive o announcemens, have lile or no reacion o announcemens. n obviously imporan quesion is wheher volailiy is rewarded wih greaer reurns. If no, he moivaion for holding corporae bonds on announcemen days is very weak. JLL (1998) find ha greaer announcemen-day Treasury bond volailiy is rewarded on announcemen days. However, Li Li and Engle (1998, working paper) find ha Treasury fuures volailiy is no rewarded. The second se of quesions revolve around he persisence of announcemen-day volailiy. The evidence on Treasury markes is mixed. JLL find lile or no evidence ha announcemen-day volailiy persiss for he cash marke in Treasury bonds bu Li Li and Engle, aking ino accoun asymmery for posiive and negaive news, find persisence in Treasury fuures markes. Corporae bond volailiy could be more persisen han for Treasury bonds due o he greaer complexiy of corporae bond valuaion. Diebold and Nerlove (1989) mainain ha volailiy should reflec he ime i akes for marke paricipans o process informaion fully. Cerain ypes of new informaion may involve more disagreemen and lack of clariy concerning is relevance. Relaed o his, Kandel and Pearson (1995) mainain ha no all marke paricipans inerpre public informaion in he same way. Learning models as suggesed by Brock and LeBaron (1996) mainain

7 ha he more precise he informaion, he less he likelihood of profiable rading (due o privae informaion). Furhermore, a new equilibrium is reached more quickly he more precise he informaion. In our sudy, alhough macroeconomic news is received wih high precision, 3 he implicaions a ime of disclosure are no immediaely clear. s Li Li and Engle (1998) sugges, he news impac may no dominae all beliefs. For example, if a subsanial change in reail sales is announced, he meaning for he corporae bond marke is complex. lhough we elaborae more on his immediaely below, suffice o say ha a decrease in reail sales may raise he sysemaic risk of corporae bonds and perhaps raise doubs abou he abiliy of all firms o mee deb service requiremens in a imely fashion and raise defaul risk premia. On he oher hand, a decrease in reail sales may also reduce inflaion expecaions hus reducing bond yields. Thus he ne effec is complex and unclear. Relaed o his las poin, he hird se of quesions concerns wheher announcemen-day volailiy is relaed o credi qualiy and mauriy. Wih respec o variaion due o credi qualiy, Fleming and Remolona (1997) and ohers have noed ha he impac of macroeconomic announcemens on equiies is complex in ha an announcemen causes revisions in boh he esimaes of cash flows generaed by he firm and, also, he appropriae discoun rae o apply o hese expeced cash flows. Of course he same applies o corporae bonds and especially o high yield bonds. The price of a corporae bond responds o an announcemen in a leas wo inerrelaed ways. To explain his, consider ha he required yield of a corporae bond consiss of he risk free yield for he given mauriy plus a risk premium o compensae he purchaser for poenial defaul and oher hings such as sysemaic risk sressed by Elon, Gruber, e. al.(2001). Tha is, i c = i f + i d where i c is he corporae bond yield, i f is he risk free yield, and i d is he premium. n announcemen could have a complex impac on he sum of hese componens. Consider he impac of an announcemen ha he unemploymen rae has increased. Here i f may well decline as inflaionary expecaions decline wih a weaker economy represened by higher unemploymen. lso, noe ha he Federal Reserve may be expeced o ake 3 The auhors noe ha macroeconomic announcemens are someimes revised afer he iniial release.

8 acions o lower ineres raes which may also reduce i f. However, i d may increase as corporae bonds become more risky as firms deb servicing prospecs diminish wih he weakening economy. lernaively, consider he impac of an announcemen ha he consumer price index has dramaically increased when he economy and earnings are growing rapidly. Here, i f may increase as inflaionary expecaions increase bu i d may decline due o a decline in perceived defaul risk. Volailiy in i c depends on he volailiy in each componen as well as he correlaion beween he componens. negaive correlaion beween componens reduces volailiy everyhing else consan. Consisen wih he above scenarios, researchers such as Collin-Dufresne and Goldsein (2001); Collin-Dufresne, Goldsein and Marin (2001); and Longsaff and Schwarz (1995) have found a negaive correlaion beween risk premia (spreads) and risk free raes which could moderae corporae bond volailiy. Collin-Dufresne, Goldsein and Marin (2001) find ha his negaive relaion grows sronger wih greaer leverage and lower raings, hence he moderaing effec may be sronger for high yield bonds. Similarly, Duffee (1999) finds a negaive correlaion beween he likelihood of defaul and risk free raes which is sronger for lower bond raings. Longsaff and Schwarz (1995) sugges he negaive correlaion beween risk premia (spreads) and risk free raes is consisen wih heir heory of corporae bond valuaion where higher risk free ineres raes increase he growh rae of firm asse values. In his conex, Blume, Keim and Pael (1991) and Sock (1992) find lower grade bonds are less volaile han higher grade alhough hey did no have he heory of Longsaff and Schwarz (1995) and ohers o help explain such behavior. Thus, here are solid reasons o expec lower grade bonds may have less volailiy han higher grade where his includes he possibiliy ha Treasury bonds may be more volaile on announcemen days han corporae bonds of varying credi qualiy. Of course his does no prove ha lower credi qualiy bonds are necessarily less volaile on announcemen days; lower grade bonds could be more volaile han high grade if, for example, he defaul componen (i d ) is very large and volaile and if he negaive correlaion is small or posiive. We mainain ha his is an imporan empirical issue for us o resolve.

9 Daa and reurn compuaions descripion We gahered macroeconomic announcemen days for six macroeconomic announcemens: CPI, PPI, unemploymen, employmen cos, durable goods, and reail sales for he period December 30, 1994 o February 11, We also colleced daily Salomon Brohers corporae bond index values for raings,, BBB, and a pooled allraing series. These are compiled for mauriies 1 o 3 years, 1 o 5 years, 3 o 7 years, 1 o 10 years, 7 o 10 years, and 10 plus years. Similarly, we colleced Goldman Sachs indices for Treasuries of mauriies 1 o 3, 3 o 5, 5 o 7, 7 o 10, and 10 plus years. Since all of our Salomon Brohers indices are invesmen grade, we colleced ne asse values (NV) for Vanguard s high yield (HY), inermediae mauriy (average mauriy of 6.8 years), and Fideliy s high yield, inermediae mauriy (average mauriy of 5.3 years) corporae bond funds, boh of which are largely composed of below invesmen grade bonds. We were unable o find daily HY indices of differen mauriy and credi raing. The icker symbols for he wo are VWEHX and SPHIX respecively. We used he indices and he NVs (as in Cornell and Green, 1991) o compue he daily corporae and Treasury bond reurns. We adjused he HY corporae bond NVs for coupon disribuions 4. Excess reurn is compued as realized daily reurn minus he daily reurn on 30-day T-bills. We hus obain daily excess reurn series for hree credi qualiies of bond indices: Treasuries, corporae invesmen grade (CIG), and corporae HY for he ime-span of our macroeconomic announcemen sample of December 30, 1994 o February 11, Our sample s relaively shor ime span is due o he unavailabiliy of longer CIG bond index series. Descripive saisics of daily excess reurns and preliminary resuls In Table 1 we provide descripive saisics for he daily excess reurns of our bond index series. We hen compare he characerisics of reurns on announcemen versus nonannouncemen days. s in JLL we also repor he squared excess reurns and absolue excess reurns as well, since hese approximaely represen he volailiy of he index reurns. For he sake of breviy, we don lis resuls for CIGs wih mauriies 1-5, 3-7, 1-10, and 7-10 years. 4 The wo funds disribue he bond coupon income as dividends in an uninerruped monhly fashion over our sample ime period. Daes and amouns of all dividend disribuions were obained and spread evenly over he previous monh o approximae he coninuous process of he underlying ineres.

10 Full Sample of announcemen and nonannouncemen days Treasury mean daily excess reurns are monoonically increasing wih mauriy, ranging from 0.005% o 0.017%, which suggess annualized excess reurns of 1.8% and 6.4%, respecively. Maximum daily excess reurn is 1.77% and minimum is -2.5%, boh in he longes mauriy series. Excess reurns are slighly negaively skewed and lepokuric. The resul is dissimilar o JLL s sample of Treasuries which displayed posiively skewed excess reurns. Jarque-Bera ess rejec he null hypohesis of normally disribued excess reurns. Firs order auocorrelaion is significan and ranges beween and 0.1. Wih he excepion of inermediae mauriies, squared excess reurns and absolue excess reurns also exhibi a posiive firs order correlaion, srongly suggesing excess reurn variance migh be auocorrelaed. We nex urn our aenion o CIGs. Mean daily excess reurns of he CIG indices range from o 0.015% per rading day, which ranslaes ino annualized excess reurns of 2.2% and 5.6%, respecively. Maximum daily excess reurn is 1.66%, and he minimum is 3.3%. Firs order auocorrelaion is posiive and significan, ypically abou Wih he excepion of he shores mauriy which has posiively skewed excess reurns across all raings, excess reurns are negaively skewed and significanly faailed. Jarque-Bera saisics soundly rejec he null hypohesis of normally disribued excess reurns. The posiive significan firs order auocorrelaion of he squared and absolue CIG excess reurns (from 0.02 o 0.18) jusifies our laer use of GRCH models. Daily corporae HY mean excess reurns are 0.015% for Fideliy and % for Vanguard. Maximum daily excess reurns are abou 0.9%, and he minimum is 2%. Thus, mean excess reurns for junk bonds are predicably higher. Skewness is negaive, and ails are faer han hose of invesmen grade reurns, hining of a non-normal disribuion. Excess reurn firs order auocorrelaion is significanly higher for junk bonds (around 0.33) compared o CIG and Treasuries counerpars. Thus, our invesigaion of he descripive saisics of excess daily reurns over he whole sample finds ha mean excess reurns increase wih mauriy and decrease as credi qualiy declines. In addiion, firs order auocorrelaion in boh reurns and variances is posiive and significan.

11 nnouncemen vs. Nonannouncemen days Excess reurns on announcemen days are quie differen from heir nonannouncemen counerpars. nnouncemen-day Treasury mean excess reurns are posiive and abou 5 o 6 imes higher han on an average day for he full sample. Volailiy is also much higher on announcemen days. nnouncemen-day excess reurns are negaively skewed bu wih hinner ails han full sample reurns. Unlike JLL s findings for Treasuries, firs order auocorrelaion (day o +1) of squared and absolue excess reurns is consisenly negaive, hining of lower volailiy on days afer announcemen. Mean excess reurns of Treasuries on nonannouncemen days are no only lower han heir announcemen day counerpar, bu are ofen negaive, especially for he longer mauriies. The resul is no oally unexpeced, since boh Campbell (1995) and JLL also claim ha ex ane excess reurns are no necessarily posiive for Treasuries. nnouncemen day reurns are also negaively skewed, and hin ailed. uocorrelaion (day o +1) is generally posiive for excess reurns, jus like i is for reurns of he full sample. For CIGs, announcemen-day resuls are quie similar o Treasuries. Mean excess reurns are abou 5 o 6 imes higher han on a normal day, and squared excess reurns are slighly higher. Excess reurns are non normal, and squared and absolue excess reurns exhibi a negaive auocorrelaion, again hining ha announcemen-day volailiy is no perpeuaed. On nonannouncemen days, mean excess reurn is much lower and ofen even negaive, jus like for Treasuries. Squared and absolue excess reurn firs order auocorrelaion coefficien is negaive, confirming ha he variance behaves differenly on announcemen days. HY bonds also exhibi higher mean excess reurns on announcemen days of up o wice hose on a normal, full sample day. Excess reurn volailiy on announcemen days is however smaller in erms of sandard deviaion and range compared o full sample days. nnouncemen-day firs order auocorrelaion (day o +1) of excess reurns and squared and absolue excess reurns is posiive, hining ha announcemen-day volailiy migh permeae o days afer announcemens. Mean nonannouncemen excess reurns for HY bonds are almos idenical o he full sample resuls. To summarize, boh CIG and HY bonds earn significanly higher excess reurn (abou 16% annualized on average) on announcemen days, which appears o be monoonically

12 increasing wih mauriy and relaively sable across credi raings. Wih he excepion of HY bonds, volailiy on announcemen days is higher, and negaively correlaed wih volailiy on he day-afer announcemen. From he six announcemens we use, employmen cos, unemploymen, reail sales, and CPI have he larges impac. Durable goods announcemens end o have he smalles impac on bond excess reurns. PPI announcemens seem o have an almos idenical effec as CPI. These resuls are no shown in ables for he sake of breviy. OLS Regressions. Volailiy Measures Coninuing our preliminary inspecion of excess reurn variance, we run simple OLS regressions of corporae and Treasury absolue, R, and squared excess reurns,, on a full se of weekday dummies, an announcemen day indicaor (equal o one on days wih any ype of macro announcemens), and he one day lag and lead of he announcemen, (day afer and day before announcemen respecively.) The adjusmen for he day afer and before announcemen is necessary in ligh of he fac ha announcemen day is a dummy variable equal o 1 on days wih a macro announcemen and 0 oherwise. When his dummy is lagged by one day, equivalen o shifing he series down by one observaion, he day afer announcemen dummy variable obains. Similar logic applies o he day before announcemen variable. The regression equaion is hus: R M Tu W Th F = Mon + κ Tues + κ Wed + κ Thur + κ Fri + θ 1I θi + θ + 1I 1 κ + ε Due o suspeced heeroskedasiciy, we repor Whie s (1980) heeroskedasiciyconsisen sandard errors. This OLS regression does no aemp o model condiional volailiy, bu merely analyzes poenial day-of-week effecs and announcemen volailiy paerns. We firs repor resuls for CIG s and hen compare hose resuls o Treasury and HY bonds. Table 2a presens he resuls for absolue excess reurns. For CIG bonds, we find evidence of srong weekday effecs. Volailiy of corporae bond excess reurns is low on Mondays, hen rises on Tuesday, falls on Wednesday, and rises hrough Friday. This is somewha similar o he U-shaped paern deeced by JLL in Treasury bond daa. Weekday volailiy coefficiens increase sharply wih mauriy. There does no seem o be a significan difference among invesmen grade credi raings. Even hough mos of our 2 R

13 announcemens occur on Fridays, we conrol for weekdays, herefore separaing he Friday effec from he announcemen effec. The posiive and highly significan coefficien of he announcemen dummies confirms ha, conrolling for day-of-week effecs, announcemen days have significanly higher volailiy. Volailiy (absolue excess reurns) increases by a lile more han one-hird on announcemen days, a resul perfecly consisen wih Treasury bond daa in JLL. The increase is clearly saisically significan. The coefficien of he day before announcemen indicaor allows us o es he calm before he sorm effec repored by JLL. We find he coefficien o be generally negaive bu saisically insignifican. Therefore, days before announcemen generally do no unambiguously exhibi lower volailiy. Day afer announcemen coefficiens are also negaive, and saisically insignifican. The only excepion is he coefficiens for he longes mauriies, which are negaive and significan, hining of a calm-afer he sorm effec. The resul suggess ha he higher volailiy on announcemen days does no generally persis, and ha volailiy seems o go back o normal, nonannouncemen levels on he day afer announcemen. nnouncemen shocks don seem o generae persisen volailiy. Furhermore, he finding suppors he claim ha he rading process iself does no generae auocorrelaed volailiy, and ha new informaion is impounded quickly ino bond prices. For he Treasury sample, he regression resuls were quie similar. ll week-day dummies are significan, increasing hrough Tuesday, hen falling on Wednesday, and rising hrough Friday, which is he highes volailiy day. This is precisely he excess reurn variance paern JLL found. Variance is significanly higher (by abou 30 o 50%) on announcemen days, regardless of mauriy. The announcemen-day coefficien θ is slighly higher for Treasuries han CIG. Day-before (θ -1 ) and day-afer(θ +1 ) coefficiens are once again insignifican. For HY corporaes, we observe almos he same weekday paern, wih he excepion ha volailiy sars somewha higher on Monday and falls on Tuesday before i sars increasing hroughou he res of he week. nnouncemen day dummies have posiive coefficiens, bu are only significan for he Vanguard fund. Boh day before and dayafer coefficiens are negaive bu insignifican. We hus fail o deec any calm before he sorm effecs or announcemen-day volailiy persisence. There is only limied

14 evidence of increased volailiy on announcemen days. The claim ha informaion ges quickly impounded ino prices, and ha he rading process is no o blame for generaing auocorrelaed volailiy is once again suppored. The resuls for Treasuries, CIG, and HY corporaes are virually idenical o he above when using he alernaive specificaion of squared excess reurns o represen volailiy (Table 2b.) To summarize, volailiy of all corporae grades and Treasuries displays a similar paern across days of he week. Excess reurn volailiy on announcemen days is ypically abou 30% higher han volailiy on a normal day, wih he excepion of he Fideliy fund which displays an insignifican announcemen effec. Excess announcemen-day volailiy seems o dissipae quickly, he quickes adjusmen being for he longes mauriies of CIGs. OLS Regressions B: Excess Reurns Nex, in Table 3, we run an OLS regression wih he same se of independen variables, bu his ime using excess reurns as he dependen variable. We repor CIG resuls and hen compare o Treasury and HY bonds. For CIGs, he firs noable resul is ha excess reurn is consisenly negaive on Mondays, Wednesdays, and ofen Fridays, however Monday is he only significan one. The observaion for Mondays and Wednesdays is consisen wih he lower volailiy (Table 2a) on hese wo days. We hus find some evidence ha excess reurns and volailiy are posiively relaed across days of he week. We will explicily es for he excess reurn-volailiy relaion in our GRCH models secion. The relaion also lends some empirical suppor for a GRCH-in-mean specificaion. The coefficien for he announcemen-day dummy is posiive, and monoonically increasing wih mauriy. s an example, he longes mauriy raed index excess reurn is % higher on announcemen days han on non announcemen days. The higher reurn is marginally significan across he indices, wih p-values beween 6% and 7%. The coefficiens for he day before and afer announcemen are consisenly posiive bu insignifican. Therefore, afer accouning for day-of-week effecs, we find no evidence of excess reurns on he days before and afer announcemen. We have reasons o believe, however, ha he daa

15 exhibis heeroskedasiciy. Ljung-Box Pormaneu saisics for he Table 3 regressions fail o rejec he null hypohesis of no auocorrelaion in he residuals. In addiion, he descripive saisics in Table 1 also confirm significan firs order auocorrelaion of volailiy. Wih heeroskedasiciy presen, our OLS esimaes are inefficien. Treasuries exhibi resuls very much similar o hose for CIGs. Low volailiy days end o ranslae ino lower excess reurns bu he coefficiens are no significan. nnouncemens end o increase excess reurns. Days before and afer effecs are indisinguishable from zero. The regressions for HY bonds are similar o he Treasury and CIG wih he following differences. mong day of he week coefficiens, Tuesday is he larges and he only significan one. In ligh of our finding ha Tuesdays were he lowes volailiy days, our hypohesized volailiy-excess reurn relaion is reversed (negaive) for junk bonds. The announcemen-day coefficien was posiive and significan only for he Fideliy HY fund, and he day-afer announcemen coefficien was significan only for Fideliy. Generally, our resuls suppor he hypohesis ha bonds earn excess reurns on announcemen days due o he higher exposure o macroeconomic risk. lso, he exposure o macroeconomic risk ranslaes ino higher volailiy on announcemen day. This announcemen-induced volailiy does no persis ino he following day, consisen wih he JLL resul ha he rading process iself does no generae auocorrelaed volailiy. Longer mauriy bonds reurn and volailiy are more sensiive o macroeconomic news, probably due o heir greaer exposure o ineres rae risk. The HY bonds however, display a differen behavior. Of he wo HY bond funds, only Fideliy seems o earn posiive announcemen and pos announcemen excess reurns. The only significan weekday coefficien (Fideliy) for boh HY funds indicaes ha HY bonds end o only earn a posiive excess reurn on he lowes volailiy day. Condiional Variance Models Since Ljung-Box ess confirm he presence of heeroskedasiciy, we devoe he remainder of our examinaion of announcemen-day volailiy o modeling he condiional variance of he excess reurn process and delving ino he persisence of differen shock ypes. The saring poin in our analysis of condiional variance is he sandard GRCH(1,1) model developed by Bollerslev (1986). In paricular, we will use a quasi-

16 maximum likelihood esimaion, and repor Bollerslev-Wooldridge (1992) robus sandard errors. The model has been widely used in he finance lieraure, and provides a good approximaion of condiional variance for a wide variey of volailiy processes (Nelson 1990). We begin wih a univariae GRCH(1,1) model of daily corporae bond excess reurns wih an inercep, an R(1) erm, and an announcemen dummy in he mean (excess reurn) equaion, as in JLL. In he variance equaion, we include he exogenous announcemen dummy as well as is lead and lag. Thus we model he conemporaneous impac of announcemens on boh condiional mean excess reurn and condiional volailiy. In addiion, we allow days before and afer announcemen o have a differen condiional variance inercep. The model is described below, where h is he condiional variance and ε is he residual. 1) R = µ + φr 1 + θi + ε 2) 2 h = ω + αε 1 + βh 1 + ρ 1I ρ0i + ρ + 1I 1 In he model above, R is he realized percenage excess reurn on day, and I is he announcemen dummy indicaor. The residual ε Φ -1 is assumed disribued N(0, h ). Noe ha in he condiional variance equaion, he lag of he announcemen dummy indicaes he day afer announcemen and he lead indicaes he day before announcemen. The coefficien θ measures changes in mean reurns on announcemen days. Because of he significan posiive auocorrelaion found in excess reurns, we allow for he R(1) erm in he firs momen. JLL claim such auocorrelaion could be due o microsrucure effecs in measuring prices or equilibrium parial adjusmen. Our announcemen dummy incorporaes all announcemen ypes and resuls are repored in Table 4. Individual announcemen effecs have also been compued and will be briefly discussed as well. We firs repor CIG resuls and hen compare o reasury and HY bonds. For CIG bonds, he coefficien for he R(1) erm in he mean equaion φ is posiive, and consisenly significan excep for he lower mauriies. I also seems o be humped wih regard o mauriies, peaking in he inermediae 3-7 year mauriy range. The I + 1 I 1

17 announcemen-day dummy coefficien θ is posiive, significan and increasing wih mauriy, confirming he hypohesis ha corporae bonds earn significan risk premia on announcemen days. I does no appear o be significanly differen among invesmen grade raings. In he condiional variance equaion, α and β are boh significan. Their sum is abou 0.96, providing evidence ha he effec of shocks persiss, and yielding a half-life 5 of abou 17 rading days. The day before announcemen coefficien ρ -1 is small, negaive and usually insignifican hus lending only weak suppor for he calm before he sorm effec. The mos noable resuls are for he ρ 0 and ρ +1 coefficiens, represening he day of he announcemen and day afer in he condiional variance equaion. The announcemen-day coefficien ρ 0 is posiive, significan, and increases wih mauriy. Therefore, corporae bonds volailiy rises on announcemen days. On he day afer announcemen, however, volailiy is back o normal. The coefficien for he day-afer announcemen is negaive, significan, and of he same absolue value as he announcemen coefficien. For example, for he raed 3-7 year index, ρ 0 is and ρ +1 is The resul is no o be inerpreed as lower volailiy afer announcemens. Raher, i means ha volailiy revers back o normal. We can no rejec he null ha he sum of he wo coefficiens is zero, wih p-values of The finding is very similar o Engle and Li (1998) and he JLL conclusion: shocks o variance persis, bu shocks from announcemens do no, even hough hey significanly raise announcemen-day volailiy and excess reurn. These resuls do no differ significanly among differen CIG credi qualiies. The model performs well in erms of purging he residuals from auocorrelaion, as refleced by he low Q-saisics. Using he model on he Treasury reurn series, he resuls are remarkably similar o CIGs. In he mean equaion, he inercep is insignifican, he R(1) erm is posiive, significan and humped wih respec o mauriy, peaking a he 7-10 year mauriy. The announcemen dummy is posiive and significan, and monoonically increasing wih mauriy, indicaing ha Treasuries earn a posiive excess reurn on announcemen days. In he variance equaion, we ge srong shock persisence, where α and β sum o abou 5 Half-life is compued as ln(0.5) ln( α + β )

18 0.96 again. nnouncemens increase condiional variance, bu i does no persis since he increase is exacly offse on he day afer; for example, in he 5-7 year index, ρ 0 is and ρ +1 is Wih respec o HY bonds, we firs presen mean equaion resuls for Vanguard and hen Fideliy. The inercep in he mean equaion is posiive and significan for he Vanguard fund providing some suppor ha HY bonds earn a consisenly posiive average excess reurn (µ is ), perhaps as a consequence of heir higher defaul risk. The R(1) erm in he mean equaion is also posiive (φ is 0.474) and saisically significan, bu he announcemen coefficien (θ) is no significan. For Fideliy, he coefficiens are µ = and φ = , respecively and only he laer is significan. The announcemen dummy in he mean equaion is posiive and significan for he Fideliy fund (θ is ) We herefore find some limied evidence ha junk bonds earn posiive excess reurns on announcemen days. The coefficiens in our condiional variance esimaion for HY bonds display ineresingly differen behavior compared o he oher ypes of bonds. The α coefficiens for boh Vanguard and Fideliy are posiive ( abou 0.5 and 0.3 respecively) and clearly significan, indicaing ha he lagged shocks have quie an impac on condiional variance. In conras, he β coefficiens are small (0.267 for Fideliy and for Vanguard), and significan only for Fideliy. The sum of α and β is he same (0.56) for boh he HY funds, which ranslaes ino a half-life of only 1.19 days. Shocks o HY excess reurns do no seem o persis and permeae ino fuure condiional variance. The coefficien for he announcemen dummy and is leads and lags in he variance equaion are insignifican, wih he excepion of he Fideliy day-afer which is negaive and significan. We herefore find very lile evidence ha macro announcemens have an effec upon condiional variance of HY excess reurns. There are no announcemen day, or calm-before he sorm effecs, and limied calm-afer effecs. Even hough he model cleans residuals of auocorrelaion, i seems ha for HY bonds, very simple RCH model migh be beer suied o describe excess reurn condiional variance. We find ha he six ypes of macro announcemens have quie differen effecs on excess reurns and condiional variance.

19 nnouncemen ype Effec on Excess Reurn Effec on Condiional Variance PPI + on announcemen day No effec CPI No effec + on announcemen day Durable Goods No Effec No Effec Unemploymen No effec + on announcemen day Employmen Cos + on announcemen day No effec Reail Sales + on announcemen day + on announcemen day Producer Price Index announcemens seem o only increase excess reurn on announcemen day bu have no effec on condiional variance of Treasuries and CIGs. For he HY bonds, PPI announcemens give rise o some calm before he sorm effec. CPI announcemens end o increase condiional volailiy on announcemen days and are associaed wih boh calm before and calm afer effecs for CIG bonds and Treasuries. The mean equaion coefficien is however insignifican for hese raings, suggesing ha CPI effec is complimenary o PPI effec: he former only affecs he mean equaion, and he laer affecs he variance equaion. Resuls are mixed for he HY bonds. There is a remarkable similariy o he effecs of employmen cos and unemploymen announcemens on CIG and Treasury bonds excess reurns. Jus like he CPI and PPI effecs, one announcemen ype only affecs excess reurn, and he oher affecs only condiional variance. Our resuls sugges unemploymen announcemens only posiively affec condiional variance and also sugges some limied calm afer effec, bu have no effec on excess reurn. Employmen cos announcemens, on he oher hand, generae consisenly posiive and significan excess reurns, bu have no effec on condiional variance. For HY bonds, neiher employmen cos nor unemploymen seem o affec excess reurn or variance. Reail sales seem o be he only announcemen ha affecs boh excess reurns and condiional variance for boh CIG s and Treasuries. The resuls sugges boh invesmen grade corporae bonds and Treasury bonds realize a significan posiive excess reurn on days wih reail sales announcemens. Furhermore, condiional variance is significanly higher on reail sales announcemen days, and goes back o normal on he day afer. Reail sales announcemens seem o have no effec on HY excess reurns and variances.

20 Durable goods announcemens seem o have no effec on eiher excess reurn or condiional variance across all credi raings. To summarize, he effecs of he join macroeconomic announcemen dummy invesigaed by he res of he models are mos likely due o he effec of reail sales and he complimenary forces exered by PPI and CPI, and unemploymen and employmen cos. The paerns of he individual announcemen effecs remain invarian wih he GRCH specificaions presened nex, and will no be repored for he sake of breviy. In he simple GRCH framework above, we also esed for GRCH-M and asymmeric effecs; however, no such effecs were found. lernaive GRCH Models Componen GRCH The conclusion above ha general shocks o variance persis, bu announcemen-day shocks do no, fis Engle and Lee s (1993) componen GRCH model which separaes ransiory and permanen componens of variance. Specifically, he above resuls sugges a specificaion ha includes announcemen dummies (-1 o 1) in he ransiory equaion, and no exogenous variable in he permanen equaion. 1') R µ φr + θi + ε = + 1 2') 2 h q = ω + α( ε 1 ω ) + β ( h 1 ω ) + ρ 1I ρ 0I + ρ + 1I 1 2 3') q ω + τ q ω) + υ( ε h ) = ( Here h is sill he condiional volailiy, while q akes he place of ω and is he ime varying long run volailiy. Equaion 2' describes he ransiory componen, which converges o zero wih powers of (α + β). Equaion 3' describes he long run componen q, which converges o ω wih powers of τ. Typically τ is beween 0.99 and 1 so ha q approaches ω very slowly. The announcemen dummies in he ransiory equaion will have an impac on he shor run movemens in volailiy, while he variables in he permanen equaion will affec he long run levels of volailiy. Oupu from he model is presened in Table 5. Resuls for CIG s confirm ha announcemen and pos announcemen-day shocks have marginally significan coefficiens of he same magniude and differen signs, boh having a ransiory effec on condiional volailiy (equaion 2'). The resul is mos

21 pronounced for longes (10 plus years) mauriy bonds and he coefficiens in he ransiory equaion are marginally significan, a bes. lso, he permanen equaion (3') τ is significan, and close o uniy, meaning ha variance slowly revers o a long run mean. In erms of he value of he maximized log-likelihood funcion, he model slighly improves on he simpler GRCH model wih exogenous variables in he variance equaion. The model s resuls for Treasury bond excess reurns are remarkably similar o hose for CIG. In he mean equaion, he inercep is insignifican for all mauriies, he R(1) erm is posiive, significan, and humped across mauriies, peaking a he 3-5 year mauriy. The announcemen dummy is posiive, significan, and monoonically increasing wih mauriy. The permanen variance equaion slowly converges o a long run mean of ω, as evidenced by he τ coefficiens of abou The ransiory equaion announcemen-day dummies are significan and posiive. Only he 1-3 year mauriy series displays an offse in condiional variance on he day afer. For HY bonds, he model does no perform so well. In he mean equaion, only he R(1) erm is posiive and consisenly significan. The inercep is posiive and significan for Vanguard only, and he announcemen dummy is posiive and significan only for Fideliy. We herefore, again find limied suppor ha junk bonds earn excess reurns on announcemen days. In he variance equaion, he τ coefficien is smaller han invesmen grades, suggesing ha variance is quicker o rever o is long run mean, and ha shocks probably do no persis as much as wih invesmen grade bonds. Transiory equaion coefficiens are mosly insignifican, deracing from he model s appeal. The relaively weak resuls of he componen GRCH model lead us o search for alernaive volailiy models. Filer GRCHs The models mos exensively used in he lieraure employ a volailiy seasonal filer which allows volailiy o be differen on announcemen days, while reaining he underlying volailiy process. Compared o he simpler GRCH wih exogenous variables discussed in he previous secion which, in effec allowed for a simple shif in he inercep in he variance equaion on announcemen days, he new model allows for a regime swich on announcemen days. Namely, i models a muliplicaive seasonal

22 (1+δI ) which adjuss he magniude of condiional volailiy on announcemen days, raher han jus he inercep erm ω. The model is oulined by ndersen and Bollerslev (1997), and can be presened as 1'') R µ φr θi = s 1/ 2 2'') s = 1+ δ I )(1 + δi )(1 δ I ) ( ε 2 3'') h = + + ω αε 1 βh 1 where I is announcemen indicaor dummy variable, s is he volailiy seasonal, and ε is a random variable wih condiional mean zero, and condiional variance h, independen of s. Even hough he volailiy seasonal is defined muliplicaively, he announcemen and pre and pos announcemen dummies can never ake a common realizaion. In oher words, he volailiy seasonal hus allows o differeniae beween announcemen and pre and pos announcemen volailiy, while on all oher days i is equal o uniy. We use an announcemen dummy for any of our six ypes of macroeconomic announcemens. In summary, he above specificaion allows announcemen days and pre and pos announcemen days o have differen volailiy han nonannouncemen days. Parameer esimaes are obained using quasi-maximum likelihood esimaion wih a normal likelihood funcion. Resuls are repored in Table 6. Saring values for h are se o uncondiional variance obained from a basic GRCH model as suggesed by JLL. Robus Bollerslev-Wooldridge (1992) sandard errors are repored. The models perform well in general, ridding he residuals of auocorrelaion and slighly improving he loglikelihood funcion compared o he simple GRCH(1,1) model wih announcemen dummies in he variance equaion. lso, he kaike and Schwarz informaion crieria improve. Firs, we examine he model on CIG bond indices. Resuls confirm ha volailiy on announcemen days is from 90% o 135% greaer han volailiy on a normal day. The δ coefficien is srongly significan, and ineresingly decreases wih mauriy across corporae bonds. Thus, bonds wih more ime o mauriy end o exhibi a smaller increase in condiional volailiy on days wih a scheduled macroeconomic announcemen. There seems o be no significan difference among he coefficiens for he differen raings, even hough he raed bonds coefficiens are slighly lower han he

23 coefficiens for similar mauriy raed bonds, which in urn are higher han he BBB raed. Variance is consisenly abou 12% lower on days before announcemen han on a normal day. The coefficiens δ -1 are however only marginally significan a bes, herefore evidence of a calm before he sorm effec is limied. On he oher hand, here is a srongly significan decrease of abou 15% on days afer announcemens, equivalen o a calm afer he sorm effec. The effec ends o be negaively relaed o mauriy, hus bonds wih highes mauriy end o exhibi lowes day-afer announcemen variance. ll variance coefficiens are significan, and he sum of α and β is abou.97, yielding a halflife of approximaely 22.7 days. General volailiy shocks herefore persis. There is a sligh decrease in he sum of α and β as mauriy increases, hining a slighly lower volailiy persisence for longer erm bonds. The ω coefficien is insignifican again. The R(1) erm in he mean equaion is posiive and significan, and so is he announcemen dummy in he mean equaion, again confirming he resul ha corporae bonds earn higher reurns on announcemen days. This announcemen excess reurn is again monoonically increasing wih mauriy. We nex run he model wih Treasury daa, and he resuls are remarkably similar. Volailiy on announcemen days increases by as much as 123% for he lowes mauriy Treasuries (1 o 3 years), and declines wih mauriy. There seem o be neiher calm before nor calm afer effecs. Wih CIG s, volailiy on he day afer announcemen was lower han Treasuries, possibly indicaing ha relevan macro informaion has very quickly been priced ou. Treasury bonds earn posiive excess reurns on announcemen days, which increases wih mauriy, supporing he exposure o sysemaic risk hypohesis. This excess reurn is commensurae o ha for he corporae bonds wih similar mauriy. Boh α and β are significan and he sum is close o heir CIG counerpar. Thus, shocks o excess reurns persis. For corporae HY bonds, our resuls are no so unambiguous. The announcemen-day volailiy coefficien δ is significan and 41% larger han normal day volailiy for Vanguard s HY fund bu insignifican for Fideliy. Therefore, here is no clearcu evidence ha condiional variance on announcemen days is higher. The day before coefficien is also significan and posiive for Vanguard only. Day-afer volailiy is only significan (negaive) for Vanguard. Variance coefficiens are significan, bu he sum of

24 α and β for junk bonds is quie low, 0.52 for Vanguard, and 0.58 for Fideliy, ranslaing ino half-lives of 0.94 and 1.27 days respecively. The evidence suggess ha boh announcemen and nonannouncemen shocks o junk bonds excess reurns do no persis. Mean equaion coefficiens for Fideliy suppor he claim ha bonds earn a posiive excess reurn on announcemen days. The Vanguard bond fund once again seems o earn a posiive mean excess reurn. Modified Filer GRCH We generally find suppor ha full sample volailiy persiss wih invesmen grade corporae and Treasury bonds. However, we are ineresed in he persisence of announcemen shocks and announcemen volailiy in paricular. We would like o es he hypohesis ha macroeconomic news ges quickly incorporaed ino corporae bond prices, and ha news effecs do no linger. Thus we employ an alernaive specificaion of he filer GRCH(1,1) ha accommodaes such a es. The model is represened as: 1''') R µ φr θi = s 1/ 2 2''') s = 1+ δ I )(1 + δi )(1 δ I ) ( ε 2 3''') h = ω + [ α0 + α I 1] ε 1 + [ β0 + β I 1] h 1 where announcemen day shocks are allowed o feed differenly ino condiional volailiy via α. lso, on days afer announcemen, he imporance of lagged condiional volailiy also varies hrough β. Thus he specificaion allows announcemen and nonannouncemen shocks and volailiy o have differen effecs on condiional volailiy. I is noeworhy ha if α =β =0 he model reduces o he simple filer model above. Thus, his regime swiching model ness he benchmark model. lso, he model ness he specificaion in which announcemen shocks do no persis a all, i.e. α = -α 0, and β = δ 1 =0, in which case volailiy evolves by compleely disregarding announcemen-day shocks. Firs, for he CIGs and he Treasuries, we compue Wald coefficien saisics o es he benchmark filer model in favor of he regime-swiching filer. Coefficien values and resuls are repored in Table 7. We are able o rejec he null of α =β =0, in favor of he regime swiching model. Besides, he model leads o improvemens in he log-likelihood