Information Asymmetry in Corporate Bond Trading, Credit Risk, and Yield Spread. Song Han Division of Research & Statistics Federal Reserve Board

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1 Informaion Asymmery in Corporae Bond Trading, Credi Risk, and Yield Spread Song Han Division of Research & Saisics Federal Reserve Board Xing Zhou Deparmen of Finance & Economics Rugers Business School Rugers Universiy ABSTRACT Taking advanage of recenly augmened corporae bond ransacion daa, we examine he pricing implicaions of informed rading in corporae bonds, as well as is abiliy in predicing corporae defauls. We find ha microsrucure measures of informaion asymmery seem o capure adverse selecion in corporae bond rading reasonably well. We demonsrae ha informaion asymmery in bond rading has explanaory power for corporae bond yield spreads, and his resul holds afer conrolling for he ransacion coss of liquidiy, credi risk and oher radiional bond pricing facors. Furher, informaion asymmery can help forecas corporae defauls afer condiioning on oher defaul predicion variables. Such forecasing abiliy of bond informed rading is especially useful for privae firms as he bond marke consiues he only venue for informed raders o exploi heir informaion advanages. Keywords: Corporae Bond Yield Spread, Informaion Asymmery, Informaion Risk Premium JEL Classificaions: G12, G14 For heir helpful commens and discussions, we hank Hazem Daouk, David Easley, Yongmiao Hong, Rober Jarrow, Francis Longsaff, David Ng, Maureen O Hara, David Weinbaum, Xiaoyan Zhang, and seminar paricipans a Cornersone Research, Cornell Universiy, Rugers Universiy, San Francisco Sae Universiy, Universiy of Souh Carolina, Universiy of Torono, and he American Economic Associaion Annual Meeings. The views expressed herein are compleely our own and do no necessarily reflec he views of he Federal Reserve Board or is saff.

2 Informaion Asymmery in Corporae Bond Trading, Credi Risk, and Yield Spreads ABSTRACT Taking advanage of recenly augmened corporae bond ransacion daa, we examine he pricing implicaions of informed rading in corporae bonds, as well as is abiliy in predicing corporae defauls. We find ha microsrucure measures of informaion asymmery seem o capure adverse selecion in corporae bond rading reasonably well. We demonsrae ha informaion asymmery in bond rading has explanaory power for corporae bond yield spreads, and his resul holds afer conrolling for he ransacion coss of liquidiy, credi risk and oher radiional bond pricing facors. Furher, informaion asymmery can help forecas corporae defauls afer condiioning on oher defaul predicion variables. Such forecasing abiliy of bond informed rading is especially useful for privae firms as he bond marke consiues he only venue for informed raders o exploi heir informaion advanages. 0

3 I. Inroducion One salien feaure of he U.S. corporae bond marke is he predominance of insiuional rading. 1 Recen work suggess ha rading by sophisicaed insiuions ends o be informaion based. 2 According o marke microsrucure heory, he presence of such informed rading can affec bond prices. As uninformed raders face he risks of losing o informed ones, given a bond s conracual cash flow, lower prices, or equivalenly, higher yields are required o hold bonds wih more informed rading. Based on his raionale, we examine he degree of informaion asymmery in corporae bond rading and is effec on corporae yield spreads. We also examine wheher informaion asymmery in bond rading can help predic corporae defauls. If rading aciviies by informed bond invesors carry imporan informaion on he issuer s credi condiions, hey should be useful for forecasing defauls. The possibiliy of informed rading in he corporae bond marke may sem from is insiuional naure. Firs of all, insiuional invesors differ significanly in heir sophisicaion levels. Some insiuions are beer able o inerpre he value relevance public informaion han ohers (see for example Kandel and Pearson (1995)). Secondly, informaion advanages of some insiuions can also arise due o heir privileged access o informaion. For example, mos insiuional invesors who rade corporae bonds, such as hedge funds and muual funds, ofen paricipae in syndicaed loans for he same issuer. As large crediors are eniled o send represenaives o regular meeings wih he borrowing company s managemen, hey have access o confidenial informaion, such as updaed growh projecions, covenan negoiaions, and merger/acquisiion or divesiure plans. 3 Moreover, a single rader a a hedge fund ofen deals in all of a company's deb insrumens. In a siuaion of his naure, precluding improper use of privae informaion and mainaining confidenialiy are a challenge. 4 In fac, boh anecdoal evidence and empirical sudies indicae ha informed rading akes place in he corporae bond marke. Following insider rading and price manipulaion scandals in corporae 1 Insiuional invesors accoun for he majoriy of he ownership and mos of he rading volume of corporae bonds. According o he Flow of Funds Accouns of he Unied Saes, ousanding corporae bonds issued by U.S. firms oaled abou $7 rillion a he end of 2009, he bulk of which were owned by insiuional invesors. Edwards, Harris, and Piwowar (2007) repor ha insiuional sized rades (hose greaer han $100,000 in par value), accoun for mos of he dollar volume of corporae bonds. 2 See, for example, Ke and Peroni (2004), Bushee and Goodman (2007), Barber, Lee, Liu and Odean (2009), Ivashina and Sun (2010), and Boulaov, Hendersho, and Livdan (2010) for evidence on insiuional rading in he equiy markes. 3 Ivashina and Sun (2010) provide some evidence ha insiuional invesors rade socks based on privae informaion acquired from he loan marke. There has also been anecdoal evidence of such channel of informaion leakage. For example, Movie Gallery's sock dropped by 25 percen over he wo days following a privae conference call wih lenders, mos of whom are hedge funds, despie he fac ha he firm did no release any news o he public. See, As Lenders, Hedge Funds Draw Insider Scruiny, New York Times, Ocober 16, You can' pu a Chinese wall hrough someone's head," commened by Michael Kaplan a Davis Polk & Wardwell LLP. For furher discussions of poenial insider rading in he bond marke, see The New Insider Trading? Invesmen Dealers Diges, Ocober 31,

4 bonds in he lae 1980s, 5 he opaqueness of his marke has become a major concern for regulaors. Daa and Iskandar-Daa (1996) argue ha in he absence of any reporing requiremens for insider bond ransacions, insiders have an enhanced opporuniy o exploi privae informaion and ake advanage of uninformed raders. Consisen wih his view, former SEC chairman Arhur Levi saed in 1998 ha he SEC had found anecdoal evidence of he possible misuse of inside informaion in he high-yield (deb) marke. 6 Recenly, here have also been a few high profile cases, such as Delphi and Six Flags deb resrucurings, wih alleged insider rading in corporae bonds. 7 Furher, several recen empirical sudies have explored poenial informed rading in corporae bonds. For example, Kedia and Zhou (2009) provide evidence consisen wih he occurrence of informed bond rading prior o corporae akeover announcemens. Massa and Manconi (2009) show ha balanced muual funds end o inves in bonds issued by firms in which hey already hold an equiy sake o reduce he cos of informaion collecion. Marke microsrucure heory suggess ha informaion asymmery affecs asse prices. Easley and O Hara (2004) show ha during he process of incorporaing new informaion ino prices, he informaional advanage of informed raders creaes addiional risks for uninformed ones. Uninformed raders have differen beliefs han informed ones regarding an asse s risk and price profiles, and always end up wih porfolios ha inves oo much in bad asses and oo lile in good ones. Furher, in a world wih asymmeric informaion, he uninformed are unable o diversify his risk of losing o he informed. Therefore, in a non-revealing equilibrium, lower price is required in order for invesors o hold securiies abou which hey are uninformed. Several empirical sudies have examined his heoreical predicion by esing wheher more informed rading leads o lower prices, and hence higher reurns, using equiy marke daa. For example, Easley, Hvidkjaer and O Hara (2002) show ha, all else being equal, socks wih relaively more privae informaion earn a higher excess reurn. Easley, Hvidkjaer, and O Hara (2010) find ha zero-invesmen porfolios formed by soring on informaion measures earn significan excess reurns which canno be explained by he Fama-French or momenum facors. Using an alernaive informaion measure, Burlacu e. al. (2008) also conclude ha sock prices embed an informaion risk premium. However, Duare and Young (2009) find ha liquidiy, raher han informaion asymmery, is priced in he cross-secion of sock reurns. 5 In a well-known case in 1989, James Dahl, an employee of Michael Milken s junk bond deparmen, swore before a grand jury ha Milken advised him o buy up Caesar s World s bonds from is own cusomers on he day when Milken made a presenaion o Caesar s World on how o handle is finance. 6 See The Imporance of Transparency in America s Deb Marke, a speech delivered by Auhur Levi a he Media Sudies Cener in New York on Sepember 9, In 2008, Delphi Corporaion accused invesors of insider rading, alleging ha a leas one of is seveneen insiuional invesors shored is bonds afer receiving confidenial informaion on he firm s bankrupcy exi financing. See Jeffrey McCracken (2008), Delphi Recovery His Snag -- Bankrupcy-Cour Exi Sideracked by Dispues wih Invesor Groups, he Wall Sree Journal (WSJ) 03/13/2008. In 2009, a hedge fund allegedly dumped he low-raed bonds of Six Flags Incorporaion afer obaining informaion in he process of negoiaing he firm s reorganizaion plan. See Mike Specor and Tom McGiny (2010), Bankrupcy Cour Is Laes Baleground for Traders, WSJ 09/07/

5 In his paper, we explore he relevance of informaion asymmery for corporae bonds by examining he pricing implicaions of informed bond rading and is power in predicing corporae defauls. Firs, given he coupon rae and principal amoun, he value of a corporae bond is largely deermined by he erm srucure of ineres raes and he risk of defaul. When some invesors have superior informaion on a firm s cash-flow prospecs, hey can beer assess he credi risks of is bonds. The exisence of such informaion asymmery creaes addiional risks for uninformed invesors, since informed raders always gain on wha he uninformed lose. Therefore, all else being equal, bonds wih a higher degree of informaion asymmery should have lower prices, or equivalenly, higher yields in equilibrium o compensae bond invesors for aking such informaion risk. Second, corporae bonds are very sensiive o downside risks. When he issuer s financial condiion deerioraes, credi risk relaed informaion become especially valuable, since such informaion can poenially generae significan reurns for informed raders before he issuer defaul on is deb obligaions. Therefore, we expec informed rading o increase when he issuer ges close o defaul. Informaion conveyed by informed rading prior o corporae defaul can hus be used o enhance he predicive power of radiional defaul forecasing models. To his end, we uilize an augmened TRACE daa o esimae wo alernaive measures of informaion asymmery in bond rading, measures based on Madhavan, Richardson, and Roomans (1997) and Glosen and Harris (1988) (hereafer MRR and GH, respecively). The augmened TRACE daa include ransacion daa used in previous sudies, such as he execuion dae and ime, price, and quaniy for each rade, as well as addiional informaion on he rading direcion, an indicaor for he side of a rade ha he reporing pary (a dealer) akes. 8 In he absence of qualiy dealer quoe daa, knowing he direcion of he rades allows us o esimae informaion-based microsrucure measures, a ask ha was no feasible before. Our key findings are he following: Firs, microsrucure measures of informaion asymmery, even hough originally developed for he equiy marke, seem o capure adverse selecion in corporae bond rading reasonably well. In paricular, boh of our measures show ha informaion asymmery is higher in larger sized rades, consisen wih he noion ha, due o larger ransacion coss for smaller bond rades, bond raders do no break orders o minimize price impac, in conras o he common pracice in he equiy marke. Second, we find srong evidence ha informaion asymmery in bond rading has significan power in explaining corporae yield spreads even afer accouning for he ransacion coss of liquidiy and oher bond pricing facors. Specifically, a one-basis-poin increase in he MRR and he GH measures 8 The TRACE daa analyzed by Edwards, Harris and Piwowar (2007) also included informaion on rade direcion, bu his informaion was no made available o he public unil very recenly. 3

6 of a corporae bond causes he bond s yield spread o increase 0.37 and 0.30 basis poin, respecively. 9 This resul is robus afer conrolling for he ransacion cos of liquidiy, alernaive measures of credi risk, firm and ime fixed effecs, indusry effecs, as well as afer using an insrumenal variable approach o miigae he poenial influence of endogeneiy and unobservable credi risks. We also find sronger informaion effecs for lower raed and shorer erm bonds, and bonds issued by privaely-held firms. Finally, he degree of informed rading in bonds can help predic corporae defauls. The predicive power of our asymmeric informaion measures remains significan, albei weaker, afer we condiion on oher firm-specific and macroeconomic defaul predicion variables as used in Duffie, Saia, and Wang (2007). Furher, informaion asymmery in corporae bond rading seems o be especially useful in forecasing defauls for privae firms. This is consisen wih he noion ha for hese firms, corporae bond marke consiues he only venue for informed raders o exploi heir informaion advanages. Our main conribuions o he lieraure are he following: Firs, o he bes of our knowledge, his sudy is he firs o examine he implicaions of informaion asymmery in bond rading for corporae bond pricing, which sheds ligh on he widely documened credi spread puzzle. Boh srucural and reduced-form models have had limied success in explaining he observed corporae yield spreads, 10 and empirical applicaions of hese models find ha credi risk accouns for only a par of yield spreads. 11 A recen srand of he lieraure has sared o look beyond he radiional bond pricing framework for beer explanaions of he credi spread puzzle. Odders-Whie and Ready (2004) show ha microsrucure measures of adverse selecion in equiies are larger when credi raings of he issuer s bonds are poor. Duffie and Lando (2001) argue ha incomplee accouning informaion in beween a firm s periodical financial repors may help explain he seemingly-high shor-erm yield spreads. Consisen wih his, Yu (2005) finds empirical evidence ha firms wih higher accouning ransparency end o have lower credi spreads. Furher, several sudies have explored he role of liquidiy in he pricing of corporae bonds. Since illiquidiy increases ransacion coss and prevens invesors from coninuously hedging heir risks, lower prices, or equivalenly higher yields, are required for holding bonds wih lower liquidiy. See, for example, Longsaff, Mihal and Neis (2005), Nashikkar and Subrahmanyam (2006), Chen, Lesmond and 9 This magniude is comparable o he liquidiy effec documened in Chen, Lesmond, and Wei (2007), who find an increase of 0.21 and 0.82 basis poins in he yield spread for a one-basis-poin increase in heir esimaed liquidiy cos for invesmen-grade and high-yield bonds, respecively. 10 For srucural models, see Meron (1974); Black and Cox (1976); Geske (1977); Ingersoll (1977); Kim, Ramaswamy, and Sundaresan (1993); Leland (1994, 1998); Longsaff and Schwarz (1995); Anderson and Sundaresan (1996); Leland and Tof (1996); Mella-Barral and Perraudin (1997); Collin-Dufresne and Goldsein (2001); and Duffie and Lando (2001). For reducedform models, see Jarrow and Turnbull (1995); Das and Tufano (1996); Duffie and Singleon (1997, 1999); Jarrow, Lando, and Turnbull (1997); Lando (1997); Madan and Unal (1998, 2000); Duffee (1999); and Elon, Gruber, Agrawal, and Mann (2001). 11 See for example Collin-Dufresne, Goldsein, and Marin (2001); and Huang and Huang (2003). 4

7 Wei (2007), and Bao, Pan and Wang (2009). Liquidiy has also been examined as a risk facor in deermining expeced bond reurns (see De Jong and Driessen (2006)). 12 This paper conribues o he lieraure on he credi spread puzzle by showing ha in addiion o he ransacion coss of liquidiy, informaion asymmery among bond raders plays an imporan role in deermining yield spreads. O Hara (2003) argues ha liquidiy and price discovery are wo main bu differen funcions of markes and ha boh of hem are imporan for asse pricing. Liquidiy refers o he ease of maching buys and sells. When buy and sell orders follow independen sochasic processes wihou being informaive abou fuure price movemens, a spread can emerge beween buying and selling prices as compensaion for providing liquidiy. 13 Therefore, sricly speaking, liquidiy is no necessarily relaed o how informaion ges incorporaed ino prices, nor o he degree of informaion asymmery. This liquidiy cos dimension of he bond marke has been addressed in he aforemenioned sudies. However, he price discovery dimension of he bond marke ha underlies he asymmery informaion risk has no ye been explicily explored in he lieraure. By decomposing oal rading cos ino a liquidiy cos componen and an asymmeric informaion componen based on wheher he price impac of a rade is ransiory or permanen, we highligh he role of adverse selecion risks in deermining corporae yield spreads. 14 Our finding suggess ha in addiion o compensaion for liquidiy coss, corporae yield spreads may conain an informaion premium ha has no been considered in radiional bond pricing models. I confirms he argumen by O Hara (2003) ha asse pricing models need o be recas in broader erms o incorporae he ransacion coss of liquidiy and he risks of price discovery. Second, our paper represens he firs aemp o measure he degree of informaion asymmery in corporae bond rading. Since boh socks and bonds represen claims on he same underlying asses of a firm, invesors wih superior informaion on he firm s asses can poenially benefi from rading wih hose relaively uninformed in eiher marke. While a large body of lieraure has examined adverse selecion in he equiy marke and is implicaions for corporae decisions, firm valuaions, and regulaory policies, surprisingly lile aenion has been devoed o poenial informed rading in he bond marke. We no only show ha microsrucure models on esimaing informaion asymmery using ransacion level daa can be generalized o asse classes oher han socks, bu also highligh he implicaions of informaion asymmery for a firm s cos of borrowing. Our sudy hus complemens Cai, Helwege and 12 While lower bond price implies higher yields or higher expeced reurns, yield spreads and expeced reurns are no idenical. Expeced reurns can be measured by yield spreads correced for defaul losses. See De Jong and Driessen (2006), and Campello, Chen and Zhang (2008). We hank an anonymous referee for poining his ou. 13 A srand of microsrucure lieraure has been focused on he noion of liquidiy. See, for example, Demsez (1968), Garman (1976), Soll (1978), Ho and Soll (1981), Amihud and Mendelson (1986, 1991), O Hara and Oldfield (1986), Grossman and Miller (1988), Biais (1993), and Madhavan and Smid (1993). O Hara (1995) provides an excellen exbook reamen of liquidiy issues in microsrucure heory. 14 The liquidiy effec documened by previous sudies migh also include some of he influence from informaion risks ha we are focusing on here. Since he liquidiy measures used in hese sudies are broadly defined, hey may capure some of impac of adverse selecion under asymmeric informaion (see O Hara (2003)). Analysis in Secion IV.C below confirms his predicion. 5

8 Warga (2007) who find informaion asymmery beween managers and bondholders drives underpricing in he corporae bond marke. Third, our sudy shed some ligh on he decision of public equiy lising by examining he effec of being privae on funding coss. While early sudies have explored he effec of informaion environmen on a firm s equiy or overall values, he direc effec of public saus on he cos of deb has received lile aenion. 15 Furher, limied daa on privae firms render i very difficul o empirically evaluae he coss and benefis of being privae. 16 Because corporae bonds are publicly raded for boh public and privae firms, we no only circumven he daa challenge, bu also provide addiional insighs ino he benefis of being public. Thus, our sudy complimens he discussions on he moivaion for being public and he relaive coss of capial in he public versus privae markes. 17 Finally, our sudy conribues o he lieraure on corporae defaul predicion. Several sudies have explored he predicive power of some firm-specific and macroeconomics variables, including he firm s disance o defaul and sock reurn, sock marke reurn and risk-free ineres rae (see for example, Duffie, Saia, and Wang (2007), and Bharah and Shumway (2008)). However, lile aenion has been devoed o he role played by he corporae bond marke. During he price discovery process of credi risk, some informaion is revealed hrough informed rading by bond invesors. As bond invesors incur subsanial losses following a defaul even, heir rading aciviies can be especially informaive prior o acual defauls. Indeed, we find ha microsrucure measures of informaion asymmery exhibi addiional power in forecasing corporae defauls afer condiioning on radiional defaul predicion variables. Furher, since equiy rade informaion and Compusa liabiliy daa do no exis for privae held firms, i is no feasible o esimae some of he key predicors of defaul, such as a firm s disance o defaul measure and sock reurn. Our resuls highligh he value of informaion conveyed by rading aciviies in an issuer s bonds when he firm has no publicly raded equiy. II. Measuring Informaion Asymmery, Liquidiy, and Yield Spreads for Corporae Bonds A. Daa and Sampling Compared wih he abundan lieraure on he pricing of equiy securiies, research on corporae bond pricing is much sparser due in par o he lack of high-qualiy bond ransacion daa. Unlike he sock marke, he corporae bond marke is an opaque dealer marke where mos securiies are raded over 15 See, for example, Leland and Pyle (1977), Chemmanur and Fulghieri (1999), and Subrahmanyam and Timan (1999). 16 See, for example, Pagano, Panea, and Zingales (1998); Boehmer and Ljungvis (2004); Helwege and Packer (2004); Kim and Weisbach (2008); and Bharah and Dimar (2010). 17 See Modigliani and Miller (1963) and Sco (1976). 6

9 he couner (OTC). 18 Unil recenly, informaion abou rading aciviy, such as ransacion price and quaniy, was no widely available o he public. Under pressure from regulaory agencies and invesors, he Financial Indusry Regulaory Auhoriy (FINRA, formerly Naional Associaion of Securiies Dealers) now requires is members o repor all of heir secondary corporae bond ransacions hrough is Trade Reporing and Compliance Engine (TRACE). FINRA has also phased in real-ime reporing of his informaion o he public. The iniial public disseminaion ook place on July 1 s, 2002, for a small number of seleced corporae bonds, including he bonds ha were rolled over from he Fixed Income Pricing Sysem (FIPS). 19 The disseminaion expanded over ime, and on February 7, 2005, i began o cover OTC rades of all bu Rule 144A corporae bonds. The augmened TRACE daa used in his sudy include deailed informaion for each rade, including he execuion dae and ime (recorded o he second), price, quaniy, rade direcion indicor, as well as oher informaion ha can be used o purge invalid ransacion repors. Trades are of hree ypes: cusomer rade in which he dealer bough from a cusomer, cusomer rade in which he dealer sold o a cusomer, and inerdealer rade (only sell-side repors). We use all bu inerdealer rades. Following he pracice of previous sudies using he TRACE daa, we removed observaions wih daa errors observaions wih missing price or quaniy values, price ouside he range of 10 and 500, and price reversals over 20 percen in adjacen rades. 20 In addiion, o limi esimaion errors, we excluded bondquarers wih fewer han 60 rades in he quarer. We sared wih a sample consising of bonds issued by publicly-raded firms over he period Informaion on bond characerisics, such as offering dae and amoun, mauriy, hisorical credi raings and coupon rae, was obained from he Fixed Income Securiies Daabase (FISD). Issuer accouning informaion was rerieved from he COMPUSTAT Annual Indusrial Daabase, while rade informaion on issuer equiy and macroeconomic daa were obained from he Cener for Research in Securiy Prices (CRSP) daa files. 21 We excluded bond-quarers when eiher he ime since issuance or remaining mauriy was shorer han a full quarer. 22 Also, excep in Secion IV.C where we provide deailed analysis on bonds wih credi raing changes, we use only bondquarers wih no raing changes o beer idenify he effecs of informaion asymmery. Applying hese filers resuled in a sample of 2,514 bonds by 522 firms. B. Microsrucure Measures of Informaion Asymmery 18 Some corporae bonds are also raded on he NYSE s Auomaed Bond Sysem. However, he rading volume is raher small compared wih ha on he OTC marke. 19 For more informaion abou FIPS, please see he NASD Noice o Members (NM) 94-23, Alexander, Edwards, and Ferri (2000), and Hochkiss and Ronen (2002). 20 See for example Edwards, Harris and Piwowar (2007), and Goldsein, Hochkiss, and Sirri (2007). 21 For bonds issued by subsidiaries, we use he paren company s accouning and equiy informaion. 22 We excluded bonds ha were newly issued or close o mauriy because rading in hese bonds ends o be unusual. See, for example, Goldsein and Hochkiss (2007), and Cai, Helwege, and Warga (2007). Our resuls hold when using wo quarers or one year as he cuoff poin. 7

10 We use microsrucure models o esimae he degree of informaion asymmery. A key insigh of he marke microsrucure lieraure is ha rading by invesors possessing superior informaion of asse values creaes an adverse selecion risk o marke makers. In equilibrium, marke makers require exra bid-ask spreads o compensae for aking on such informaional risk (see, e.g., Kyle (1985)). Imporanly, he effec of adverse selecion on asse prices is permanen, as opposed o he ransiory effec of he liquidiy provision coss coss normally associaed wih order processing and invenory risk. A number of sudies, including MRR and GH, exploi such disincion and design models o decompose bid-ask spreads ino adverse selecion or informaion asymmery componen and liquidiy provision componen. Here we implemen GH and MRR models using he augmened TRACE daa. 23 Specifically, he GH model consiss of following assumpions: m m 1 Q Z e (1a); P m Q C (1b); Z z 0 z1v (1c); C c 0 c1v (1d). The changes in he unobserved rue price ( m ) can be caused by eiher he arrival of public informaion ( e ), or privae informaion embedded in he order flow ( Q Z ) (Eq. (1a)), where Q is a rade direcion indicaor which is +1 if he rade is buyer iniiaed and -1 if he rade is seller iniiaed, and Z is he adverse selecion componen of he spread (Eq. (1c)). The observed price, P, is he summaion of he unobserved rue price and he ransiory componen of rading coss ( QC ) (Eq. (1b)), where C is he liquidiy cos componen of he spread (Eq. (1d)). Boh componens are assumed o be a linear funcion of he size of he order ( V ). Equaions (1a)-(1d) are hen combined o obain he following model on observed price changes ( ): P P z Q z QV c Q c QV e. (1) We use he above model o esimae parameers ( z 0, z 1, c 0, c 1 ) and hen compue he asymmeric informaion and ransacion cos componens as in equaions (1c) and (1d). The MRR model differs from he GH model in ha MRR assume only he surprise in he order flow has an impac on he expeced fundamenal value of he asse. Tha is, using he same noaions as above, MRR differeniae he ransiory effec of liquidiy provision coss from he permanen effec of informaion asymmery as follows: m m 1z Q EQ Q 1 e, (2a) 23 See Van Ness, Van Ness, and Warr (2001) for a review of alernaive measures of informaion asymmery. Due o he lack of qualiy bond quoe daa, models which rely on quoe prices canno be esimaed for corporae bonds. 8

11 where ˆ Q EQ Q 1 P m cq, (2b) Q measures he surprise in order flows which may carry privae informaion abou he fundamenal asse value. The parameer z capures he permanen impac of order flow innovaions and hence is used o measure he degree of informaion asymmery, while c capures he emporary effec of order flow on prices and herefore is used o measure he liquidiy provision coss. Similar o he GH model, he changes in ransacion prices can be expressed as: P zqˆ cq E. (2) Following MRR, we assume E Q Q 1 Q Thus, Qˆ Q Q 1 in our esimaions. One limiaion wih he TRACE daa is ha he rade size informaion ha is disseminaed o he public is capped for very large rades. Specifically, he caps for invesmen- and speculaive-grade bonds are $5 million and $1 million, respecively. Because we do no observe he acual rade sizes for hese large rades, we excluded hem in implemening he GH model. 25 However, we included all rades in esimaing he MRR model because his model uses only informaion on rade price and direcion. We esimaed boh he GH and MRR models for each bond-quarer pair. The esimaed GH and MRR measures are highly correlaed wih each oher, wih a correlaion coefficien of Their respecive correlaion wih oal number of rades wihin he quarer is and C. Esimaing Corporae Bond Yield Spreads The yield spread of a corporae bond is defined as he spread of he yield on he corporae bond over he yield on a defaul-free bond wih exacly he same mauriy and coupon. To sar, we esimaed he daily risk-free zero-coupon yield curve using he exended Nelson-Siegel model, as oulined in Appendix 1 (see also Bliss (1997)). Then, for each corporae bond, we discouned is conracual cash flow a he esimaed risk-free yield curve o compue he price of a corresponding risk-free bond. Finally, yield on his hypoheic risk-free bond was calculaed and subraced from ha on he original corporae bond o obain is yield spread. We firs used his procedure o esimae each bond s daily yield spread, and hen averaged he daily yield spreads wihin a quarer o ge he bond s yield spread for ha quarer. III. Assessing Measures of Informaion Asymmery in Corporae Bond Trading 24 If rade direcion changes follow a Markov process wih he probabiliy of swiching direcion from buyer iniiaed o seller iniiaed, or vice versa, being he same, hen = We also re-esimae he GH model by reaing rades wih 5MM+ / 1MM+ codes as if heir rade sizes were $5,000,000/$1,000,000. The resuls are qualiaively he same as hose repored here, as shown in Table VI and discussed in Secion IV.C. 9

12 Since informaion measures, including hose derived from GH and MRR models, were originally developed for he equiy marke, a naural quesion is how well hey capure he underlying informaion asymmery in corporae bond rading. Admiedly, direc assessmen of he validiy of hese measures is exremely difficul, even for equiy rading, simply because informaion asymmery is never precisely observable. In his secion, we ry o address he model validaion issues indirecly by formulaing and esing wo hypoheses on he behavior of he asymmeric informaion measures. If hese measures are indeed able o capure a leas some of he informaion asymmery in bond rading, hey should exhibi cerain paerns consisen wih our expecaions. A. Informaion Asymmery Measures across Credi Raings Our firs hypohesis relaes he risk of adverse selecion in bond rading o he bond s credi risk. 26 According o Meron (1974), corporae deb can be valued as a porfolio comprised of similar risk-free deb and a shor posiion in a pu opion on he issuer s asses. Therefore, any informaion relaed o he firm s underlying asses should affec is bond values. However, he relevance of he informaion for bond raders depends on he moneyness of he opion. When he pu is deep ou of he money (i.e., when he underlying asse value is way above he srike price (face value of bonds)), he issuer has a low probabiliy of defaul, and hus, informaion on asse values is of lile relevance. The relevance of he informaion ends o increase for bond raders when he issuer s credi risk rises. Thus, our hypohesis is ha he degree of informed rading in bonds should be posiively relaed wih he bond s credi risk. Table I provides summary saisics on he informaion asymmery measures esimaed using he GH and MRR models across differen credi raings. Panel A shows ha, as expeced, informaion asymmery ends o be higher for lower raed bonds. The mean values of informaion asymmery esimaes, using eiher he GH or he MRR model, increase by over 200 percen when we move from high qualiy invesmen-grade bonds (raed AAA or AA) o high-yield bonds (raed BB and lower). Panel B presens he resuls of -es and Wilcoxon sign rank es on he differences in he mean and in he median of he informaion asymmery measures beween wo broad raing caegories, invesmen-grade and highyield bonds. The mean (median) of he MRR informaion asymmery measure is (7.23) for highyield bonds, while i is only 5.55 (4.70) for invesmen-grade bonds. These differences are all saisically significan a he 1 percen level. Similar resuls hold for he GH informaion asymmery measure. B. Informaion Asymmery Measures and Trade Size 26 Several sudies have examined he relaionship beween liquidiy and bond credi risks. Ericsson and Renaul (2006) argue ha illiquidiy and credi risk are posiively correlaed. He and Xiong (2011) show ha deerioraing marke liquidiy and shorer deb mauriy can lead o excessive credi risk. 10

13 Our second hypohesis relaes informaion asymmery in bond rading o rade size. Microsrucure heory suggess ha informed raders prefer o make large rades o fully exploi heir informaion advanages (e.g., Easley and O Hara (1987)). Therefore, prices for large rades reflec such increased probabiliy of informed rading. However, empirical sudies in equiy rading do no always suppor such a predicion. For example, Huang and Soll (1997) find ha he adverse selecion componen of he bid-ask spread is acually smaller for large rades han for medium and small rades. Barclay and Warner (1993) show ha informed rading in he arge socks of ender offers during pre-announcemen periods is concenraed in medium sized rades, a conclusion also reached by Chakravary (2001). These findings are consisen wih he noion ha large rades end o be broken up and spread over ime o reduce price impac and ransacion coss (Kyle (1985)). However, such incenive o break large rades ino small pieces o reduce ransacion coss migh no exis for bond raders. A number of empirical sudies have shown ha ransacion coss in corporae bond rading are acually larger for smaller sized rades. 27 Therefore, as prediced by Easley and O Hara (1987), adverse selecion risks should be more severe in large rades of corporae bonds. If he informaion asymmery measures derived from GH and MRR models capure he degree of informed rading, we would expec hem o be posiively correlaed wih rade size. GH explicily model he informaion asymmery componen of he bid-ask spread as a funcion of rade size (see Eq. (1c)). Therefore, if larger rades are more likely o be iniiaed by informed raders, we would expec o see a posiive z 1. Panel A of Table II provides supporing evidence for his predicion. The esimae of z 1 is a posiive wih a p-value of when large rades subjec o TRACE cap are excluded. This esimae is lile changed when we rea large rades wih 5MM+ / 1MM+ codes as if heir sizes were $5,000,000/$1,000,000, and in his case, he p-value drops o In he original MRR model, he informaion asymmery measure does no depend on rade size. To es our hypohesis, we exend heir model o explicily accoun for poenial rade size effecs. Specifically, we replace he consan effecs of informaion and liquidiy, as capured by he coefficiens z and c in equaions (2a) and (2b), wih wo general funcions f V and h V, respecively. Firs, we assume ha, as in GH, boh informaion and liquidiy impacs are linear in rade size: f h V 0 1V ; V V. Therefore, replacing z and c wih f V and V (2 a) (2 b) 0 1 h in equaion (2c) yields: 27 See Hong and Warga (2000), Schulz (2001), Chakravary and Sarker (2003), Warga (2004), Bessembinder, Maxwell and Venkaaraman (2006), Edwards, Harris and Piwowar (2007), and Goldsein, Hochkiss, and Sirri (2007). 11

14 V Qˆ Q V Q E. P Qˆ (2 ) Panel A of Table II shows ha he informaion componen esimaed using he modified MRR model is again posiively correlaed wih rade size, wih 1 being and significan a he 1 percen level. Second, we employ a semi-parameric approach o allow for poenial nonlinear effecs of rade s m l size in he MRR model. Specifically, we creae hree size dummy variables, D, D, and D, for small, medium and large rades, respecively. We classify rades wih par values less han $100,000 as small rades, hose wih par values of a leas $1 million as large rades, and hose in beween as medium size rades. Noice ha his classificaion also allows us o include all large rades ha are subjec o TRACE cap wihou assigning any fixed number ($5 million or $1 million). Thus, he informaion and liquidiy effecs can be expressed as: Replacing z and c wih f V and V P f h k k V z D, (2 a) k s, m, l k k V c D. k s, m, l (2 b) h in equaion (2c) now gives: z k s, m, l k k ˆ k k D Q c D Q E. k s, m, l As shown in Panel B, for each size group, boh he mean and he median values of he informaion effec (as capured by z ) are posiive and significan a he 1 percen level. More imporanly, he -es and he Wilcoxon es indicae ha he z esimae for he large rades is greaer han ha for he medium and he small rades, while here is no significan difference in he z esimaes beween medium and small rades. This resul again confirms ha larger bond rades end o be more informaive in he bond marke, a finding ha is in conras o ha in he equiy marke documened by Huang and Soll (1997). (2 ) IV. Informaion Asymmery and Corporae Yield Spreads We now examine wheher our esimaed informaion asymmery measures possess any explanaory power for corporae yield spreads afer conrolling for facors considered in radiional corporae bond pricing models. As discussed previously, marke microsrucure heory suggess ha invesors would require higher yields o hold hose bonds exhibiing more asymmeric informaion risk, above and beyond he compensaion for credi risk and he cos of providing liquidiy. Therefore, our hypohesis is ha corporae yield spreads are posiively relaed o informaion asymmery measures. A. The Effec of Informaion Asymmery on Corporae Yield Spreads 12

15 Our sraegy is o incorporae our informaion asymmery measures ino exising empirical models for corporae yield spreads (e.g., Campbell and Taksler (2003) and Chen, Lesmond, and Wei (2007)). These models are ofen moivaed by a srucural view of corporae defaul, which holds ha a firm s credi risk, in erms of boh he probabiliy of defaul and recovery rae given defaul, depends on is capial srucure and he firm value. Various firm accouning variables and macroeconomic variables have been used as proxies for a firm s credi risk. In addiion, bond-specific characerisics and proxies for liquidiy condiions have also been used as deerminans of bond yield spreads. Consisen wih his lieraure, we specify our empirical model as follows: YieldSpread 6 EuroDollar LongermDeb / ToalAsses 10 OperaingIncome/ sales i, IssueSize i, AsymInfo IssuerSockReurn 1 Coupon i, i, 17 1yr. TreasuryRae i, i, 8 Liquidiy 14 2 i, Raing i, PreaxIneresCoverage 3 (10yr. 2 yr. TreasuryRae ) 9 ToalDeb / Capializaion SockMarkeVolailiy SockMarkeReurn, i, i, Mauriy 15 4 i, Age 5 i, i, i, IssuerSockVolailiy i, (3) where AsymInfo i, and Liquidiy i, refer o, respecively, he asymmeric informaion and liquidiy cos componens of he bid-ask spreads esimaed by eiher MRR or GH model for bond i in quarer. The res of he conrol variables include bond-specific characerisics: credi raing (Raing), ime o mauriy (Mauriy), ime since issuance (age), coupon rae (coupon), and (log) issue size (IssueSize); firm-specific characerisics: long-erm deb/oal asse, oal deb/oal capializaion, operaing income/sales, and preax ineres coverage; and macroeconomic variables: one-year Treasury rae (1yrTreasuryRae), he difference beween en-year and wo-year Treasury raes (10yr.-2yr.Treasuryrae), and he difference beween he 30-day Eurodollar and Treasury yields (EuroDollar). 28 Furher, following Campbell and Taksler (2003), we include he mean and he sandard deviaion of he daily excess reurn of he issuer equiy relaive o he CRSP value-weighed index (IssuerSockReurn and IssuerSockVolailiy), as well as he mean and he sandard deviaion of he daily sock marke reurns (measured using CRSP valueweighed index reurns) wihin each quarer (SockMarkeReurn and SockMarkeVolailiy). Table III presens regression resuls based on wo specificaions of model (3) for each informaion asymmery measure. Because our sample conains muliple bonds issued by he same firm over muliple periods, we correc he sandard errors following Thomson (2009) o accoun for poenial correlaions across bonds and over ime. The regression resuls are presened in Columns I and III for MRR and GH 28 We follow he exising lieraure in defining our conrol variables. For credi raing, we assign a numeric value o each S&P raing leer, wih 1, 2,..., 10 denoing AAA, AA,, D, respecively. Firm-specific variables are calculaed using COMPUSTAT daa as of he end of he previous calendar year excep for when compuing oal deb/oal capializaion raio, where we use he marke value of he equiy from CRSP and he book value of deb from COMPUSTAT o calculae oal firm capializaion. See Blume, Lim and MacKinlay (1998), Collin-Dufresne, Goldsein and Marin (2001), Elon, Gruber, Agrawal and Mann (2001), Campbell and Taksler (2003), Nashikkar and Subrahmanyam (2006), and Chen, Lesmond and Wei (2007). 13

16 measures, respecively. There is srong evidence ha corporae bond yield spreads reflec informaion risk. Afer conrolling for liquidiy coss, bond- and firm-specific characerisics, and macroeconomic facors, he coefficiens of our informaion asymmery measures (based on boh MRR and GH models) are posiive and saisically significan a he 1 percen level. The poin esimae using he MRR (GH) model implies ha a one-basis-poin increase in he informaion asymmery measure leads o a widening of he yield spread by 0.37 (0.30) basis poin. These resuls coninue o hold when we add firm fixed effecs in our model, as shown in Columns II and IV. Conrolling for firm fixed effecs is desirable because bond issues may be concenraed in a small se of firms. The fixed effec model also miigaes he effec of poenial unobservable firm heerogeneiy on our esimaion, effecively allowing us o idenify he informaional risk effec by comparing bonds issued by he same firm. As we can see, he coefficiens of informaion asymmery measures coninue o be posiive and saisically significan, and heir magniudes are only slighly lower. Consisen wih findings in previous sudies on liquidiy effecs, he coefficiens for liquidiy provision coss are also posiive and significan a he 1 percen level. 29 Noe ha some bond specific characerisics, such as issue size, coupon rae, and age, have also been used exensively in he lieraure as proxies for bond liquidiy, especially before he TRACE daa became available. 30 Our resuls on hese variables are also largely consisen wih findings in exising sudies. Furher, he coefficiens of oher conrol variables carry expeced signs and are generally consisen wih previous sudies. The level of erm srucure, measured by he one-year Treasury rae, is negaive and saisically significan, supporing he argumen by Longsaff and Schwarz (1995) ha an increase in he risk-free ineres rae implies an upward drif in he risk-neural process for he firm value, and hence a reducion in he risk-neural probabiliy of defaul and in urn a lower corporae yield spread. The slope of he erm srucure, measured by he difference beween en- and wo-year Treasury raes, has a significan negaive effec on yield spreads, consisen wih he reasoning pu forh by Collin-Dufresne, Goldsein, and Marin (2001) ha a larger slope implies an expecaion of higher fuure shor raes and a sronger economy. The coefficien for Eurodollar, which measures marke liquidiy effecs on corporae bonds relaive o Treasury bonds, is posiive and saisically significan, as expeced. In addiion, lower oal deb raios and higher pre-ax ineres coverage are associaed wih lower yield spreads, suggesing ha financially healhy firms incur lower coss of deb. The coefficiens for long-erm deb raio and operaing margin are no saisically significan. Finally, informaion conveyed by sock marke rading 29 See, for example, Nashikkar and Subrahmanyam (2006), Chen, Lesmond, and Wei (2007), and Bao, Pan, and Wang (2008). 30 See, for example, Gehr and Marell (1992), Alexander, Edwards and Ferri (2000), and Hong and Warga (2000). Elon, Gruber, Agrawal and Mann (2004) argue ha higher coupon bonds should have higher yield spreads as ineres paymens on corporae bonds are axed a he sae level. 14

17 has also a srong effec on he value of bonds. For example, an increase in he volailiy of he issuer s equiy excess reurns increases corporae yield spreads, as documened by Campbell and Taksler (2003). B. Alernaive Conrols for Credi Risks In his secion, we ake wo alernaive approaches o conrol for he poenial confounding effecs from credi risks. The inerpreaion of our resuls relies imporanly on appropriae conrol for credi risk, because, o he exen ha unobserved credi risk may be posiively correlaed wih informaion asymmery in bond rading, inadequae conrol for credi risk may resul in a bias favoring finding posiive informaion effecs. Our firs approach is o experimen wih alernaive specificaions on he credi raings of bonds, and o include some srucurally generaed nonlinear variables, in addiion o radiional accouning and marke-based raios. We presen he resuls from using he MRR informaion asymmery measure in Table IV. Using GH measure yields similar resuls which, for breviy, are no repored bu available upon reques. Firs, we refine he credi raing variable by using noch-level raings (compared o leer-level raings above) from Sandard and Poor s. 31 A more graduaed raing variable may conrol for more variaion in he credi risk. As shown in Column I of Table IV, he coefficien of he informaion asymmery measures is posiive and saisically significan a 1% level. In fac, is magniude barely changes from when using he leer-level raings (See Column II of Table III). To accoun for poenial non-linear effec from credi raing, we also replace he linear raing variable wih six caegorical dummy variables for he following raing classes: AAA, AA, A, BBB, BB, and B. No surprisingly, higher raed bonds end o have lower yield spreads (see Column II). More imporanly, using raing dummies o conrol for nonlineariies imposes lile influence on he esimae of he coefficien of informaion asymmery. Second, we esimae a disance o defaul (DoD) measure and combine i wih raing dummies o conrol for credi risk. Roughly speaking, he disance o defaul is he number of sandard deviaions of quarerly asse growh by which asse values exceed he firm s liabiliies. In sandard srucural models, models ha assume a firm defauls when is asses drop o a sufficienly low level relaive o is liabiliies, he condiional defaul probabiliy depends heavily (or compleely for some models) on he disance o defaul (e.g., Black and Scholes (1973), Meron (1974)). Empirically, he relevance of disance o defaul in predicing defauls has also been well esablished in he lieraure (e.g, Bharah and Shumway (2008), 31 A numeric value is assigned o each noch of S&P s credi raing, wih 1, 2, 3, denoing AAA+, AAA, AAA-, respecively. Noice ha he sample for his es shrank a bi since we excluded any bond-quarer when a bond experienced even a single noch of credi raing change. 15

18 Campbell, Hilscher, and Szilagyi (2011)). Besides is srucural and nonlinear naure, disance o defaul incorporaes curren marke informaion more imely han possibly sale credi raings. Following Duffie, Saia, and Wang (2009), we consruc our disance o defaul measure based on he Black-Scholes-Meron specificaion and use an ieraive mehod o esimae he measure based on marke equiy daa and Compusa balance shee daa. Since he disance o defaul measure is essenially a volailiy-adjused leverage measure, we exclude firm leverage measures and sock volailiy measures as conrol variables in esimaing Model (3). Column III in Table IV shows ha he coefficien of informaion asymmery measure remains posiive and saisically significan. The coefficien of Meron DoD measure is negaive and highly significan, consisen wih our expecaion ha bonds issued by firms far from defaul ends o have lower yield spreads. The Black-Scholes-Meron specificaion implies ha he condiional defaul probabiliy is simply he cumulaive sandard normal disribuion funcion valued a he negaive disance o defaul (see, e.g., Crosbie and Bohn (2002) and Vassalou and Xing (2004)). So we also use hese esimaed condiional defaul probabiliy as an alernaive conrol for credi risk. As shown in Column IV of Table IV, he coefficien of defaul probabiliy is posiive and significan, suggesing ha yield spreads end o be wider when he defaul probabiliy of he issuer increases. Again, informaion asymmery coninues o exhibi significan explanaory power for corporae yield spreads afer conrolling for credi risks. Lasly, we use a firm s 5-year credi defaul swap (CDS) spread, in addiion o credi raing dummies, o conrol for credi risk. CDS are insurance conracs o proec invesors agains he issuer s defaul risk. Thus, CDS spreads are generally viewed as a direc measure for credi risk (see, e.g., Longsaff, Mihal, and Neis (2005)). 32 Because CDS spreads are marke based, hey reflec invesors expecaions on a firm s credi risk in more imely han do credi raings, as raings are commonly viewed as lagging behind he acual changes in a firm s credi risk. We obained he daa on CDS spreads from Marki. The resuls presened in Column V once again confirm he robusness of our resuls o alernaive credi risk conrols. Our second approach is o use an insrumenal variables (IV) mehod o conrol for poenial endogeneiy beween informaion asymmery and credi risks as well as for unobservable credi risk. A valid IV has o mee he exclusiviy condiion ha he IV is correlaed wih he measures of informaion asymmery bu no direcly wih a bond s credi risk. Our candidae for he IV is he degree of concenraion in insiuional ownership of corporae bonds mees such requiremen. Several sudies have used insiuional ownership as a proxy for privae informaion (see for example Brennan and 32 CDS spreads may also be affeced by heir own liquidiy issues. Bongaers, de Jong, and Driessen (2011) find ha he effec of liquidiy is saisically significan in he CDS marke bu ha he magniude of he effec is raher small. This small economic effec is consisen wih he view of Longsaff, Mihal, and Neis (2005) ha liquidiy concerns migh be less severe in he CDS marke due o he conracual naure of CDS. See also Tang and Yan (2007). 16

19 Subrahmanyam (1995)). Thus, if a bond s ownership is highly concenraed in a few insiuions, he informaion asymmery beween a few large block holders and oher invesors may be greaer. We use informaion on he fund-level insiuional holdings of corporae bonds from Lipper s emaxx fixed income daabase o esimae he degree of concenraion in insiuional ownership. This daabase provides quarerly bond ownership informaion by all insurance companies, over 95 percen muual funds, and he op 250 public pension funds in he Unied Saes. 33 Because insurance companies and pension funds generally face regulaory limiaions or invesor mandaes on heir invesmens in highyield bonds, we focus on holdings by muual funds so ha our bond ownership measure is no direcly relaed o credi risks. For each bond/quarer, we calculae he Herfindahl index in muual fund holding, which is he sum of squared share of holding by each insiuion, and use i as a proxy for concenraion. On average, our sample bonds are held by 28 muual funds. The Herfindahl index has a mean value of 0.37, bu exhibi high variaions across bonds (wih a sandard deviaion of 0.24). Imporanly, Henfindahl index is no higher for lower raed bonds. In fac, he mean and median values of he Herfindahl index are and for high-yield bonds, which are smaller han he and for heir invesmen-grade counerpars. This finding alleviaes he concern ha our insrumen simply capures some unobserved credi risk informaion. Table V presens he resuls from he wo-sage leas squares regressions. In he firs sage, we regress he measures of informaion asymmery from he MRR and he GH models on he Herfindahl index in bond holding and all oher conrol variables used in model (3). Panel A shows ha he coefficien of Herfindahl index is posiive and highly significan. This resul is consisen wih our expecaion ha bonds held by compeiive insiuions have less informaion asymmery. The resuls of he second sage regressions, in which we replace he measures of informaion asymmery wih heir prediced values from he corresponding firs sage regressions, are presened in Panel B. Consisen wih our previous analysis, he coefficiens of he informaion asymmery measure are all posiive and saisically significan a he 1 percen level. C. Addiional Robusness Checks We conduc a number of ess o check he robusness of our resuls and presen hem in Table VI. Firs, we examine wheher our resuls hold when we re-esimae our model (3) using alernaive esimaes of he informaion and liquidiy componens. We consider he following hree alernaive esimaes: (a) esimaes based on he GH model by reaing large rades wih 5MM+ / 1MM+ codes as if heir rade sizes were $5,000,000/$1,000,000; (b) esimaes based on a modified MRR model allowing he rade 33 This daase has been examined in a few recen sudies. See for example, Manconi and Massa (2009), and Massa, Yasuda, and Zhang (2008). 17

20 effecs o be linear in rade size (i.e., model (2 ) shown above); and (c) esimaes based on a modified MRR model allowing he rade effecs o be nonlinear in rade size (i.e., model (2 ) shown above). As shown in Panel A, in all hree cases, he coefficiens of he informaion asymmery measures coninue o be posiive and saisically significan a he 1 percen level. Second, we check wheher our resuls are robus o alernaive measures of liquidiy coss. For his purpose, we re-esimae model (3) by replacing he liquidiy cos componens from he MRR and GH models wih several general liquidiy measures esimaed from unsigned bond ransacion daa, such as urnover (rade volume normalized by issue size), price impac (lower Amihud (2002) measure), and rading frequency (boh in erms of he number of days raded and he number of rades). 34,35 As an addiional measure, we consider inraday price range, which is he difference beween he highes and he lowes ransacion prices wihin a day. As a liquidiy proxy, inraday price range is in he same spiri as boh he realized bid-ask spread proposed by Chakravary and Sarkar (1999) and he volailiy measure proposed by Alexander, Edwards and Ferri (2000) and Hong and Warga (2000). 36 The resuls using he informaion asymmery measure based on he original MRR model are presened in Panel B. 37 Resuls from using he GH measure yields similar resuls and are no repored here. All liquidiy measures exhibi expeced signs and are saisically significan a he 1 percen level. Specifically, yield spreads are negaively associaed wih volume-based liquidiy measures, including urnover, number of days raded, and oal number of rades, bu posiively associaed wih illiquidiy measures, including he Amihud measure and he inraday price range measure. 38 Imporanly, regardless of which liquidiy measure is used, he coefficiens of he informaion asymmery measures are all posiive and saisically significan a he 1 percen level. Noe ha he magniude of hese coefficiens does drop somewha. The weaker informaional effecs are no surprising because hese convenional liquidiy measures end o be broadly-defined and may capure par of he effecs from informaion asymmery. For example, he Amihud measure, which esimaes he impac of order flow on price based on Kyle s (1985) coefficien, may reflec boh adverse selecion coss and invenory coss. Also, Goldsein, Hochkiss and Sirri (2007) aribue he cos differences beween large and small bond rades o eiher a high level of fixed coss for small rades or a ren exraced by dealers in rading wih relaively 34 Oher sudies have also esimaed bond liquidiy measures using lower frequency daa. For example, Chen, Lesmond and Wei (2007) esimae a liquidiy measure from Lesmond, Ogden and Trzcinka (1999) using daily prices repored by a large bond dealer. 35 To esimae he Amihud liquidiy measure for each bond-quarer, we firs calculae he price impac for each bond-day by dividing he absolue daily price changes by daily rade volume, whenever prices for wo consecuive rading days are available. We hen average he daily price impac over days wihin each quarer for each bond o obain a bond-quarer level esimae. 36 The realized bid-ask spread is defined as he difference beween average buying and selling prices per bond per day in Chakravary and Sarkar (1999). 37 Resuls using he informaion asymmery measures based on he GH model, no shown bu available upon reques, are similar o wha we repored here. 38 We also use he inraday price volailiy of a bond, a measure very similar o inraday price range, o conrol for liquidiy and found similar resuls. 18