Returns to defaulted corporate bonds

Transcription

1 Invesmen Managemen and Financial Innovaions, Volume 8, Issue 1, 011 Hekan Thorsell (Sweden) eurns o deauled corporae bonds Absrac The paper sudies he reurn paerns or deauled bonds a deaul ime and nine monhs aer. The auhor ideniies and describes an srong overshooing eec, where he large negaive reurn a deaul is ollowed by srong posiive reurns or a number o ime periods. The aricle ess saisically or shor-erm excess reurn in a sample o 374 deauled U.S. corporae bonds. There is a robus overshooing eec also aer he auhor has conrolled or marke and liquidiy risk. The average expeced recovery rae during he ime period o is esimaed o be seven percenage poins lower a he irs monh aer deaul han he presen value o he recovery rae nine monhs laer. Keywords: bond pricing, recovery rae. JEL Classiicaion: G1, G33. Inroducion The pricing o deauled bonds have become a ho opic in he aermah o he inancial crisis. From being a marginal phenomenon, i has become a very real aspec o owning a corporae bond porolio. Some aspecs o sandard bond pricing, such as, or example, inluence rom liquidiy risk can also be valid or deauled bonds. However, very lile is known apar rom schedules o shor-erm recovery raes. I ill he gap in he lieraure, by suding reurn paerns or deauled bonds using ime series ess. I also show ha he excess reurn I have ound canno be eliminaed by he risk acors used by oher sudies o bond pricing. There are reasons o believe ha here is biased pricing or deauled bonds and subsequenly ha recovery raes migh be depressed. Firs, deauled bonds migh have he same acors inluence heir pricing as non-deauled bonds (liquidiy, deaul risk, and ineres rae risk). Second, he marke or deauled securiies can exhibi inormaion asymmeries, where buyers and sellers have dieren inormaion on he value o he bonds. There could also be oher risks hen ones I conroll or when esing or mispricing. I here exiss oher risks ha are no properly conrolled or in he ess, hey could give a resul ha suggeses ha bonds are mispriced. The pricing o non-deauled corporae bonds is inluenced by liquidiy risk. Ericsson and eneby (003) ind ha bond spreads incorporae a subsanial liquidiy componen in addiion o he deaul risk. The less liquid a bond is in he sudy o Chen, Lesmond and Wei (005) he higher he yield spread, and de Jong and Driessen (005) ind ha liquidiy is a priced acor in a muli-acor model. I Hekan Thorsell, 011. Financial suppor rom he Torsen and agnar Söderberg Foundaions is graeully acknowledged. I wan o hank Henrik Andersson, Magnus Dahlquis, Kaerina Hellsröm, Tomas Hjelsröm, Peer Jennergren, Hanna Seerberg, Kenh Skogsvik, and Johan Södersröm or helpul commens. All errors are my own. 168 corporae bond prices are sensiive o liquidiy beore deaul, here is no reason o hink ha hey are less sensiive aer deaul. The sysemaic par o he deaul risk is priced according o Weinsein (1981), Bernd and Lookman (006), and Thorsell (008). I expec he marke bea o increase aer deaul due o he ac ha he bond owners have he possibiliy o conver heir bond ino equiy. This means ha he uure pay os rom he deauled bond can be he residual paymens rom he issuer, raher han he coupons. For a deauled bond here is uncerainy abou i he bond will become equiy or no, so he bond marke bea should be somewhere in beween a bond bea and an equiy bea. The ineres rae risk is ignored here, since i is no likely a major conribuor o he risk o a deauled corporae bond. In a deaul siuaion or a company here are also new reasons or rading is securiies. Some invesors, such as pension unds and insurance companies, are no allowed o hold high risk asses, creaing an increase in he supply o he deauled bond in he marke. Oher invesors specialize in his ype o high risk asses. This specializaion could poenially creae a siuaion o inormaion asymmery 1. The exisence o vulure unds indicaes here migh be opporuniies o earn good reurns on disressed or deauled asses. The holders o deauled corporae bonds have o ind some means o knowing ha heir bonds are worh. A naural choice is o look a wha has been recovered in earlier deauls, making he hisoric recovery raes he norm also or uure recovery raes. The cross-secional sudies o recovery raes sared wih Alman and Kishore (1996). ecovery raes are now sudied by he raing agencies as a maer o rouine (Moody, 010). Alman and Kishore (1996) shows ha indusry and he senioriy 1 Financial organizaions ha specialize in disressed securiies, such as near deaul or deauled bonds or shares, are commonly reerred o as vulure unds.

2 Invesmen Managemen and Financial Innovaions, Volume 8, Issue 1, 011 o a bond maers or he recovery rae in he crosssecion. They canno show ha invesmen grade saus, size o issue, or longeviy beore deaul has any impac on he recovery rae. The requen sudies o he cross-secion can be sel-ulilling, bu should no inluence a possible bias. Tha is, any pre-exising bias can be srenghened by he success o he cross-secional sudies since i is he only inormaion available on recovery raes. There are hree ways o deining he recovery rae o deauled bonds in he lieraure: recovery o he ace value o he bond; recovery o marke value preceding he deaul; or ranormaion ino an equivalen, bu deaulree bond. These hree mehods are all based on an insan change ino a sae asse. I here are unlimied rading opporuniies, he hree mehods are equivalen. I i is no possible o immediaely sell he bond a is inrinsic value, hen he variaion in he recovery rae o he deauled bond is imporan or he value. The recovery rae o ace value is ypically calculaed as he marke price one monh aer deaul o he bond divided by he ace value. The recovery rae o marke value is he marke price one monh aer deaul o he bond divided by he marke price one monh beore deaul. There are issues ha can generae bias in he recovery rae; pos deaul risk and inormaion asymmery beween invesors. Alman and Pompeii (003) show ha he marke value divided by he ace value o deauled bonds varies rom 0.15 o 0.74 and diers rom year o year. The bonds in heir sample are he deauled bonds ha are included in he Alman- NYU Salomon Cener Deauled Bond Index. To measure he poenial bias in he cross-secional deaul raes here are a ew possible mehods: he repaymens rom deauled bonds could be summed and discouned or a ne presen value; he reurns rom vulure unds could be esed or excess reurns; or he reurn on bonds o deauled issuers could be esed or excess reurns. The repaymens rom deauled irms are diicul o sudy since he daa is no public and i oen akes a long ime unil he deaul is resolved and/or bankrupcy is inalized. This means ha i is no only hard o ind he daa, bu many hings can happened during he long ime period ha elapsed since deaul. The main problem wih sudying vulure unds is ha here is a collecion o asses in he unds a any ime. Some o hese asses migh be recenly deauled bonds, bu here can be many oher asses as well. Furher, he vulure und managers may add value o he deauled securiies aer deaul and such a sudy can be biased o increase he value o he asses a deaul. I use he hird mehod and sudy he reurn on bonds o companies ha have deauled on heir securiies. I use daa rom a limied number o monhs. The reasons or sudying a shor ime period aer deaul are ha i akes ime o do value enhancing resrucurings, so he shor ime period does no include oo much o value enhancing measures by he company, and i is possible ha he recovery rae is depressed by a larger han usual supply jus aer deaul due o a supply eec. The underlying claim ha is esed in his sudy is; Claim 1. The marke price o a recenly deauled bond is biased. Muliple regression analysis is used o es he claim. The es is operaionalized as a es i he one monh recovery rae esimaion is biased. I calculae he cross-secional recovery rae (as can be compared o or insance Moody s (010)), and inroduce ime-series ess on deauled corporae bond reurns. The bond acors used o explain he excess reurns do no in ac explain he reurns. The common liquidiy have no srong bearing on he excess reurn aer deaul. However, he equiy risk acors are dieren rom zero and signiican. This suggess ha here is mispricing or deauled bond reurns. In unabulaed ess using only he ime period, neiher liquidiy nor equiy acors are signiican 1. This indicaes ha he crisis in he end o he period he bonds behave more like equiy. The esimaed recovery raes ares seven percenage poins oo low on average o make he excess reurn go away during he period o In he nex Secion, he model or bond values are described. In Secion he ess and calculaions ha deviae rom sandard asse pricing ess are presened. The summary saisics o he sample and how he sample selecion was done is described in Secion 3. The resuls are presened and discussed in Secion 4. Concluding remarks are presened in he las Secion. 1. Model or corporae bond value The purpose o his Secion is o explain how he deaul value o he bond relaes o he beore deaul value and o describe how he bond recovery value can be compared over ime periods aer 1 I have run all ess in his paper using he shorer pre-crisis ime period o , and he excess reurns are similar o he ones presened, i.e., he main resuls do no depend on he inancial crisis. 169

3 Invesmen Managemen and Financial Innovaions, Volume 8, Issue 1, 011 deaul. The value o he bond (V ) a ime is equal o he discouned presen value o he expeced value o he bond value a dae r = e E V 1 C 1 V. (1) For simpliciy assume ha he coupon is zero ( C = 0 ). Deining he deaul probabiliy beween 1 and 1 as, 1 I assume i is exogenous. d Deine he value o he bond a ime 1 as V 1 s or he deaul sae and V 1 in he survival sae. The value o he deaul sae is he recovery value. The survival value o he bond is ulimaely he promised paymen. The saes o deaul or survival are muually exclusive, so equaion (1) can be decomposed ino: d s V E(1 V r V = e E, 1 1, 1) 1. () The deaul probabiliy o a sae bond is by deiniion,t = 0 and he sae bond value a mauriy (T ) is hus equal o is ace value V T = 1. The paymen in deaul is he objec o ineres, so deine he paymen in deaul uncion as d : 1 V 1. The se o acors 1 conain all inormaion necessary o deermine he paymen in d deaul ( V 1 ). can be seen as he ime-varying exchange rae beween he promised paymen and s he paymen a deaul, so 1 V 1. Assuming a consan probabiliy o deaul ( ) gives he valuaion ormula a ime beore deaul a ime ( < ) : s ( ) (1 e r EV r V = e E 1 ) 1, (3) and aer deaul r = 1 > : V e E ( ). (4) Assuming ha crediors ake over when a company deauls on is deb paymens. This implies ha he company is hen ree o all deb and here canno be any addiional deauls. Since I sudy only a shor ime aer deaul, his assumpion should no inluence he resuls. The hree sandard ways o deine he deaul paymen uncion can be described as: recovery o ace value o he bond ( 1 ) = k1, recovery o marke value ( 1 ) = kv, and recovery in a sae s bond ( 1 ) = k3v 1, where k 1, k and k 3 are consans. In he recovery o a sae bond an invesor receives a racion ( k 3 ) o a sae bond ha oherwise has he same characerisics as he deauled bond. All hree mehods are poin esimaes. I here are risk adjused excess reurns aer deaul i is no possible o rade he deauled bond and ge an economic value ha corresponds o any o he he hree mehods. This ransacion problem can make empirical esimaes or deaul paymens using he hree mehods invalid. I liquidiy is poor aer deaul, a bond owner is exposed o he variabiliy o he asse price and an unknown holding period. This can resul in changing values o he recovery rae and a simple model o his is: ( q ) 1) = q, (5) (1 ) q ( 1 i= 1 i where q is he number o ime periods aer deaul, and i he discoun rae. I use he risk adjused discoun rae in a capial asse pricing model (CAPM) seing. The value o he bond a deaul depends on he reurn on he asse ( 1) uncion and he lengh o he holding period q.. Tes mehod To es he recovery raes variabiliy over ime some iniial calculaions have o be made. I deine he he deaul ime no as when he bond issuer ormally deauled on he obligaion, bu he ime when he marke adaped he bond price o include he uure deaul o he irm on he ineres or principal 1. In pracice his means ha he larges negaive price adjusmen or each ime series is deined as he deaul period. The exreme price decreases in 008 or almos all asses makes he deauls ha ook place in 007 o be ascribed o 008. In unrepored ess ha exlcudes he inancial crisis yields similar resuls as he ess in he sudy. The sysemaic underpricing a deaul is smaller (our percenage poins insead o seven). All reurns are measured excluding he accrued ineres. Only in cases where he bond is repaid in 1 The price adjusmen occurs when invesors realize ha he company will no be able o service he deb. The acual deaul dae is he dae he service is due. Even i invesors claims on principal or ineres are equivalen rom an economic perspecive, hey migh be reaed dierenly in he prescripion clauses o he bonds. There are insances o dieren prescripion imes or principal and ineres. In addiion o smaller dierences in conracual reamen, Asquih and ober Gerner and David Scharsein (1994) ind ha banks almos never orgive principal as par o any comprehensive deb resrucuring ha include subordinaed public crediors.

4 Invesmen Managemen and Financial Innovaions, Volume 8, Issue 1, 011 ull his exclusion maer. This is no common or deauled bonds, so he impac on my resuls should be minimal. All ess have also been done also wih reurns including he accrued ineres. The dierence in resuls are minimal and i anyhing he inclusion o he accrued ineres increases he excess reurn and risk-adjused discouned recovery rae..1. Cross-secion. The cross-secional recovery raes are presened as averages, bu calculaed using OLS, since his aciliaes calculaing measures on variabiliy such as he explained variaion ( )... Time-series. To es i he marke price o a deauled bond is biased, he reurns are esed or excess reurns. The idea is o ind ou i he deauled bonds have reurns ha exceed heir risk compensaion. A deauled bond can be seen as somehing ha is beween deb or equiy, since he rue saus ypically is unknown a he ime o deaul. I he deb is serviced in he uure, i migh reurn o being a normal bond, bu here can also be conversion ino equiy. This unknown saus implies ha eiher acors imporan or corporae bond pricing or equiy pricing migh be useul in risk-adjusing he deauled bond reurns. Facors ha have been ound o inluence corporae bond pricing in earlier sudies are esed or my sample o deauled bonds. This means ha I es CAPM marke risk acor and liquidiy risk acors on reurns rom deauled bonds. The marke risk acor can be expeced o increase in size aer he deaul simply rom he bond aking on a more equiy like pay-o proile. The earlier ess are complemened wih ess or liquidiy risk in deauled bonds. I consruc bond liquidiy acor series in Secion 3.1. In addiion o he es o bond acors I es he Fama and French acors as designed by Krizman (010), which have been successul in explaining equiy reurns. The saisical models used o es or signiicance o acors are sandard porolio ess, wih porolio ormaion dependen on indusry and senioriy. The esimaion equaion can be seen in equaion (6): F, (6) = where is he simple reurn o a bond a ime, is he risk ree reurn, F is a vecor o acors, and is he error erm. All esed acors are no zero cos porolios. This implies ha or he nonzero cos porolios he average value o he acors can inluence he esimaed inercep, and hence he esimaed excess reurn. As i urns ou, his is no a problem since he inerceps are abou he same size when he non-zero cos porolios are included as when hey are no included. Sudies on equiy porolio reurns ypically use value-weighed porolios. My porolios are equally weighed, since he marke capializaion canno be deermined rom my daa se. I is also unclear wha a value weighing would resul in when equiy values are very low, and bond values are reduced. The choice o equally weighed porolios can give smaller issue bonds a relaive large impac on he resuls..3. Presen value o recovery raes. To esimae he economic signiicance o he pos deaul variaions in he recovery rae, I calculae he presen value o he recovery rae o ace value (marke price o he bonds divided by heir ace value) aer deaul. I adjus he ineres rae or marke risk o see i he esimae or over ime n diers rom he a deaul recovery raes or boh book and marke values. The discouning is presened below in equaion (8). Deauled bonds are asses which need o generae risk-adjused reurns or invesors o hold hem. There should hus be an insigniican excess reurn (alpha) and insigniican beas i he use o a risk ree asse as a proxy or he recovery value is a good assessmen. The variabiliy in price o he sae asse is by naure small, and he deaul probabiliy is also small (empirically racions o a percen per monh). I he value in deaul is oo depressed, hen here should be excess reurns in he monhs ollowing he deaul. These excess reurns are he ingerprins o he oo low recovery rae. The sample is randomly divided ino wo groups o avoid discouning wih in-sample beas. The irs group is used o calculae beas or indusry and senioriy: j F, (7) = j j j is he reurn on bond j a ime, F is a vecor o acors, and where he risk ree reurn, is is he error erm. Time ( ) runs rom he ime o deaul ( ) or k periods. The coeicien esimaes are used or calculaing he discoun rae in he nex equaion. The second group is used o calculae he ou-osample presen value o he equivalen recovery rae CleanPrice o ace value ( = ). This operaion is FaceValue done o make he recovery raes comparable over ime. Noe ha he excess reurn es is suicien o answer he quesion o bias in he recovery rae a deaul. The presen value o he recovery raes is calculaed as: 171

5 Invesmen Managemen and Financial Innovaions, Volume 8, Issue 1, 011 he Daasream sample, rade volume is regisered in n PV ( n) =, (8) n he ISMA TAX sysem in 11 percen o all monhs. (1 i ˆF i) Daasream does no only rely on he TAX sysem i= or price inormaion, bu mainly source heir where alpha is assumed o be zero and bea ( ˆ ) is corporae bond daa rom FT Ineracive Daa (FTID). he mean esimaed parameer rom he irs group 1 FTID uses marke ransacions and calculaes prices esimaed in accordance wih equaion (7). Equaion using, amongs oher hings, bid inormaion rom heir (8) is used o calculae he presen value up o nine und cliens. According o FTID, prices are calculaed monhs aer deaul ( n ). The reason or his o relec veriiable inormaion o he exen ha i is relaively shor period is ha he ess are i he ormaive or he good aih opinion o FTID as o recovery rae migh be depressed a he ime o wha a buyer would pay or he bond in a curren sale. deaul, no i here is a dri in he asse value. The price inormaion has a endency o go sale 3. Daa aer he deaul, i.e., he same price is repeaed The sample consiss o 47 companies wih 374 during several ime periods in he daa se. I here is deauled bond price series. No company has issued a problem wih sale prices, he inerceps in he more han 3.5 percen o he bonds in he sample. The CAPM ess are negaive since here is a inancing sample is colleced rom he Thomson/Daasream cos ( ), bu no income rom he bond. The daabase. All bonds in he sample have ixed coupons. deaul even seems o creae rading volume. The The sample period covers almos en years rom average urn-over ive monhs aer deaul is 4 January 001 o Augus 010. The bond reurns have percen higher han he average urnover ive monhs been winzorized a he one percen level. The beore deaul, measured in erms o ace value. winsorizaion decreases he number o high posiive Summary reurn saisics or he sample o deauled reurns. bond are presened in Table 1. The reurn saisics are A problem wih corporae bond daa is ypically hin calculaed using reurns rom en monhs beore and rading and rade reporing. For he average bond in en monhs aer deaul or each bond. Table 1. Monhly sample reurns or deauled bonds 1 Asse Observaions Mean Sd. dev. Skewness Kurosis Min Max Enire sample Senior secured Senior unsecured Senior subordinaed Subordinaed Junior subordinaed Unknown Oil & gas Basic maerial Indusrials Consumer goods Healh care Consumer services Telecommunicaions Uiliies Financial Technology Noe: This Table presens reurns rom a sample o 79 deauled corporae bonds. The bonds are colleced rom Thomson/Daasream. The reurn or each bond-monh is he clean price reurn P P 1. The senioriy o he bonds has been ideniied rom he EDGA daabase. Bonds where he senioriy has been unclear are classiied as unknown. The classiicaion ino indus- P 1 ries ollows he ICB sandard. 1 Each bond is assigned a pos-deaul bea in accordance wih wha grouping i belongs o. ISMA (he Inernaional Securiies Marke Associaion) is he sel-regulaory organizaion and rade associaion or he inernaional securiies marke (including he Eurobond marke). ISMA TAX is he ISMA rade maching and regulaory reporing sysem or he OTC markes. 17

6 There is a large negaive reurn in each bond reurn series (he deaul) and his inluences all momens o he reurn series. The maximum reurns are all he same due o he winzorinzing. The mean reurn or he enire sample is negaive, as well as or all groups in he sample. The sandard deviaions are high compared o he mean reurns. The implicaion rom he high sandard deviaion is ha here is subsanial dierences beween bond reurns wihin he sample, as well as wihin each segmenaion. The skewness is negaive and he kurosis is high, so Invesmen Managemen and Financial Innovaions, Volume 8, Issue 1, 011 he sample ha include beore and aer he deaul is non-normal. Table. Bounce back and drop dead bonds aer deaul The sample characerisics or he deauled bonds can be expeced o be dieren rom a random sample o corporae bonds. The reason is ha a random sample conains ew deauls compared o his sample. I presen he number o bonds wih values exceeding heir ace value and he bonds wih value less han wo percen o he ace value aer deaul in Table. Caegory/monh Acive bonds Value > ace value Value < percen ace value Noe: This Table presens he number o bonds ha recover aer deaul and he number o bonds ha are valued a less han percen o ace value up o nine monhs aer he deaul even. Few bonds bounce back o becoming priced as normal bonds aer a deaul even. In my sample only 6.1 percen have values ha exceed heir ace value aer a deaul even. On he oher side o he specrum 14.1 percen o bond are worh less han wo percen o heir ace value nine monhs aer deaul. The number o highes priced bonds and he number o lowes priced bonds remain a abou he same magniude during he ime period I sudy Liquidiy measures. The liquidiy risk is imporan or he pricing o corporae bonds, as i is menioned beore. There are many ways o operaionalize he liquidiy measure; hree ways are measures o raded volume, marke impac o a large ransacion, and he size o he dierence beween he bid-and-ask spreads. The available bond daa has low requency (monhly) and conains only prices and raded volumes, so he reurn and volume based liquidiy measures are used. In addioion o he bond based measures, I also use wo acors based on share prices. The idea wih he share price based acors is ha hey capure general sensiiviy o asse prices agains sysemaic liquidiy risk. The wo share based series are calculaed according o Pásor and Sambaugh (003) and Sadka (006). The Pásor and Sambaugh se o series are available rom 001 hrough 008. The Sadka series are available rom 001 hrough 005. The Pásor and Sambaugh series are based on a volume reversal coeicien. They ind ha heir marke wide liquidiy acor is priced. To complemen he share price based liquidiy measures, measures or liquidiy risk are calculaed rom a sample o 10,74 U.S. corporae bond price series. From he sample o corporae bond price series innovaions are calculaed in line wih wha Pásor and Sambaugh (003) do or he sock marke. Monhly daa give a limied number o daa poins. The idea is o calculae he reurn response o rading volume. The response coeicien or each bond (i ) is calculaed using he OLS regression: e r v, e ri, 1 = i iri, i sign i, i, i, (9) where sign () is a uncion ha akes on -1 or 1 depending on he sign o he inpu, and he variables are deined as in Pásor and Sambaugh (003). r i, e r i, v i, i, Table 3. Deined variables he clean price reurn on bond i in monh r i rm, r,,, 0 where is he average clean price reurn on all m he bonds in he sample during monh. he nominal raded volume repored in he TAX sysem or bond i in monh. he residual. The gamma ( ) coeicien is he excess reurn response o rading volume. The sign () uncion eliminaes he dierence beween posiive and negaive excess reurns, making he coeicien linear in absolue volume. The underlying economic idea is ha an increase in rading volume inlaes he reurn in he irs ime period and when he rading volume decreases in he nex ime period he reurns decrease, i.e., a reurn reversal. I his idea is correc he gamma can be expeced o be negaive on average. High rading volumes should be associaed wih negaive excess reurns in he nex ime period 1. Only bond monh observaions where here is rade volume 1 This is rue, he mean or all bonds in he sample is negaive -.0e- 009 wih a sandard deviaion o 1.3e

7 Invesmen Managemen and Financial Innovaions, Volume 8, Issue 1, 011 repored in TAX are included in he regression. Monhly reurn observaions wih abnormally high (+10%) and low (-10%) reurns are excluded. This gives 3,174 coeicien esimaes or he enire period. For each ime period he average gamma esimae is calculaed: The rescaling by 100 is done according o Pásor and Sambaugh (003), bu is no necessary or he bond series, since he raded volumes ypically are large in comparison o he reurns. The eec o no rescaling means ha he acor values are very small and ha here will be some very large liquidiy bea esimaes. In addiion o he share-based series and he above bond liquidiy measure, a second bond liquidiy measure, AILLIQ, is calculaed in line wih Amihud (00). More precisely, he AILLIQ measure is deined here as: N 1 ˆ = ˆ i,. N (10) i=1 The average reurn response coeicien is a measure o how large he average reurn reversal is in he nex ime period. Pásor and Sambaugh (003) have a problem wih an upwards rend in Nj rk, heir sample o NYSE and AMEX bonds. My AILLIQ = 1/ N j, (13) shorer sample period does no exhibi his problem, k = 1 vk, and i does no have signiican serial correlaion 1, so where N he innovaion is calculaed in a similar manner, bu j is he number o bond observaions in exclude he dollar value scaling quoa: monh, r k, is he clean price ne reurn or bond k ˆ ˆ = a b 1 cˆ 1 u. (11) during period, and v k, y is he repored daily average The regression in equaion (11) produces serially nominal volume in he TAX sysem. AILLIQ is uncorrelaed residuals. The residuals are he par o hus he average quoa beween absolue clean price he changes in reurn response coeiciens ha does reurn and repored ransacion volume. In he irs no depend on earlier changes or levels o reurn monh included (February 001) here are 7 quoes. response coeiciens. The idea is o clean he reurn This is he smalles number o quoes in he sample response innovaions rom ime series dependencies. and he maximum is 1,066. I calculae he innovaion ( L ) in liquidiy rom he The measures or liquidiy risk are all based on residuals ( u ): changes in reurn in relaion o rading volumes. The pair wise correlaion beween he liquidiy series is 1 L = û. (1) calculaed, o see i here are similariies beween 100 he dieren liquidiy series. Table 4. Pairwise correlaion beween liquidiy measures 1 ˆ L PS Level PS Innov Sadka TF Sadka PV AILLIQ ˆ 0.47 (0.00) (0.00) (0.00) (0.01) (0.44) (0.00) (0.8) (0.0) (0.01) (0.00) L PS level PS innov. Sadka TF Sadka PV (0.48) (0.11) (0.86) (0.90) (0.4) (0.16) (0.09) (0.88) (0.78) (0.49) (0.05) Noe: This Table presens he pair wise correlaions beween he dieren measures o liquidiy or he maximum available ime periods or each measure. The measures are he AILLIQ measure, as calculaed in equaion (13), and he ˆ, as calculaed in equaion (10). The L measure is he innovaions in liquidiy in he bond marke, as calculaed in equaion (1). The wo PS series (Level and Innov) are he level and innovaions or he sock marke in accordance wih Pásor and Sambaugh (003). The wo Sadka series are ixed (TF) and variable (PV) price eecs, calculaed according o Sadka (006). In parenhesis below each pair wise correlaion is he p-value. 1 The irs order serial correlaion is 0.0, slighly below Pasor and Sambaugh s 0., bu no signiican. Boh bond series are calculaed rom February 001 hrough 010. Amihud sums over days when here has been rading, while here only he monhs when he TAX sysem has repored rading volume is used in he cross-secional calculaions. Amihud calculaes he absolue mean average daily reurn and here he absolue monhly reurn is calculaed rom clean prices, ignoring he possible eec o he accrued coupon. 174

8 The bond-based series (AILLIQ, ˆ, and L ) have low correlaions wih he share-based series. Only a ew o he correlaions beween bond and share series are signiicanly dieren rom zero. This is unexpeced, since all series are expeced o measure liquidiy risk. The liquidiy series seems o measure dieren aspecs o liquidiy since hey are dieren rom each oher. The implicaion is ha more han one liquidiy measure needs o be used in he laer ess. 3.. Insiuional seing. A company eners ino deaul i: i ails o pay ineres on he due dae, i ails o pay he principal on he due dae, i breaches any oher covenans or warranies conneced o he securiies and he ailure coninues, or i declares isel in bankrupcy, insolvency or reorganizaion. Firms in inancial disress have a number o opions or how o avoid bankrupcy. The wo main opions are o do an inormal resrucuring wih he crediors or o ile or bankrupcy proecion under Chaper 11 o he U.S. bankrupcy code. Asquih and Gerner and Scharsein (1994) ind ha only 4 o heir 10 inancially disressed irms ile or bankrupcy. The irms ry o avoid going ino Chaper 11 since he process is cosly. The way irms handle heir disress siuaion helps o deermine he value o he deauled bonds. Invesmen Managemen and Financial Innovaions, Volume 8, Issue 1, 011 Invesors can purchase corporae bonds a issue or in he secondary marke. On he secondary marke corporae bonds are eiher raded over-he-couner or on an exchange. Only some o he corporae bonds ha are raded hrough an exchange are ormally lised. All bonds in he sample are quoed and raded a he New York Sock Exchange (NYSE). Mos o he bonds in he sample (a leas 80 percen) have or have had equiies lised on one o he U.S. exchanges. The companies ha have lised equiy are required o ollow sandard disclosure and reporing regulaions. There is no lising agreemen or a deb issuer on NYSE, bu he regulaions or lised companies sae ha he issuer mus release all relevan inormaion immediaely upon deermining ha he ineres or principal will no be paid in ull. 4. esuls 4.1. Cross-secion. The cross-secional recovery raes are in line wih he daa o oher sudies, or insance by Alman and Kishore (1996) or he yearly Moody s repor. Moody has a larger sample since hey include bonds rom several counries. The igures here include only US corporae bonds, so he parameers dier somewha rom Moody s. In Tables 5 hrough 7 he recovery rae based on marke value grouped by senioriy and indusry is calculaed. Table 5. Average marke value recovery rae on deauled corporae bonds per year by senioriy Senior sec. Senior unsec. Senior subo. Subordinaed Junior sub. Unknown Year ae Number ae Number ae Number ae Number ae Number ae Number Average Book rae Median Sd. dev Noes: This Table presens he average recovery rae or deauled bonds. The recovery rae is calculaed rom clean prices as P P 1 1. P 1 The book rae is he average clean price on he monh aer deaul divided by he par value. Each esimae is ollowed by he number o observaions used o calculae i. The senioriy o a corporae bond is an indicaor or he level o he recovery rae. There is a paern where boh he average marke and he book recovery rae are higher or he senior bonds and he junior subordinaed bonds. There is a smile paern in he average recovery rae. This is a bi unexpeced, bu could be caused by only less risky irms or irms wih ixed asses being able o issue junior deb. The book recovery raes are lower han he recovery raes o marke values. There are wo reasons or his. Firs, he book recovery rae incorporaes all price adjusmens beore he deaul and he recovery rae o marke 175

9 Invesmen Managemen and Financial Innovaions, Volume 8, Issue 1, 011 value only wha is los during he monh o deaul. Second, he recovery rae o marke value is calculaed wih a smaller denominaor, due o he parial adjusmen in price aking place beore deaul. The lower recovery rae o book value indicaes ha he marke, o some exen, has no anicipaed he deauls. I divide he sample ino he en ICB secor code indusries and presen he average recovery rae o marke value in Table 6. Table 6. Average marke value recovery rae on deauled corporae bonds per year by indusry Oil & gas Basic maerial Indus. Consumer goods Healh care Consumer services Telecom Uiliies Financial Tech Year ae Nr ae Nr ae Nr ae Nr ae Nr ae Nr ae Nr ae Nr ae Nr ae Nr Average Median Sd. dev Noes: This Table presens he average recovery rae or deauled corporae bonds. The recovery rae is calculaed rom clean prices as P P 1 1. Each esimae is ollowed by he number o observaions used o calculae i. P 1 In general, each year has only a ew daa poins, so i is no possible o draw any srong conclusions on he ime variaion rom his grouping. From a risk perspecive he Telecom, Financial and Technology secors show he lowes averages and he lowes medians. The sandard deviaions are in he same magniude or all segmenaions indicaing a subsan- ial spread in all segmens. For example, he sandard deviaion or he oil & gas indusry is 48.4 percen o he mean. Firms in dieren indusries ypically have dieren composiions o asses. The recovery raes grouped by senioriy and indusry are presened in Table 7. Table 7. Average marke recovery rae on deauled corporae bonds by senioriy and indusry Senior Sec. Senior Unsec. Senior Subo. Subordinaed Junior sub. Unknown Indusry ae Nr ae Nr ae Nr ae Nr ae Nr ae Nr Oil & gas Basic maerial Indusrials Consumer goods Healh care Consumer services Telecomm Uiliies Financial Technology Noe: This Table presens he average recovery rae or deauled bonds. The recovery rae is calculaed rom clean prices as P P 1 P The cross-secional recovery raes are in line wih earlier resuls. This is o course given rom he ac ha he use he same daa, bu i seems like he smile paern ideniied in Secion 4.1 is presen in he indusry and concumer services 1 indisries. From Tables 5 and Table 6 i is clear ha here is ime variaion in he recovery raes. A dieren ype o ime variaion is he heme o he nex Secion, he aer deaul ime reurn variaion

10 Invesmen Managemen and Financial Innovaions, Volume 8, Issue 1, Time-series. Time-series o deauled bond reurns are problemaic, since hey conain boh sale prices and dead ca bounces 1. Sale prices will in his seup give zero reurns on he bond and make i harder o ind excess reurns. In laer periods when he poenially sale price adjuss, i is easier o ind excess reurns. Cross-secional smoohing should alleviae his problem. For a schemaic overview o wha happened o he mean reurns o deauled corporae bonds I include Figure 1. The mean excess reurn in Figure 1 is calculaed as: 1 = (, )) i=1... N i, where N is he number o bonds, is he ime period,, i reurn on N bond i, and he risk ree rae. The cumulaive mean excess reurn is he cumulaive sum o he presened mean excess reurns. Fig. 1. Mean excess reurn on deauled corporae bonds The mean excess reurn rom corporae bonds is negaive beore he deaul occurs, implying ha invesors adjus heir pricing beore he deaul. This adjusmen can also have happened or many bonds no enering ino he deaul sae, so i does no necessarily carry any inormaion. More ineresing is ha, as can be seen in Figure 1, he mean excess reurn is consisenly posiive aer he deaul. The airly sharp rise in reurns in he monhs aer he deaul implies ha here migh be an overshooing eec, a leas or he mean excess reurn. The posiive mean excess reurn aer deaul raises he quesion o wha bonds perorm well aer he deaul. Is i he same bonds ha consisenly do well in a urnaround siuaion? To ry and answer his quesion I rank he sample ino deciles depending on heir reurn one monh aer he deaul. Table 8. Average excess reurn in decile porolios aer deaul 1 Porolio/monh Mean Porolio Porolio Porolio Porolio Porolio Porolio Porolio Porolio Porolio Porolio Mean Noes: This Table presens he average clean price excess reurn or decile porolios ranked on log excess reurn he monh aer deaul. The average log excess reurn or each decile porolio is presened or en monhs ollowing he deaul. is he irs order auocorrelaion coeicien or he mean excess reurns in each porolio. 1 A dead ca bounce is when a moderae rise in he price o a sock ollows a specacular all, wih he connoaion ha he rise does no indicae improving circumsances. 177

11 Invesmen Managemen and Financial Innovaions, Volume 8, Issue 1, 011 From he mean excess reurns per porolio in Table 8 i is no eviden ha some bonds will recover more han ohers, or ha here is any paern rom he reurn ranking. Longer ranking periods have been esed, bu he resuls are similar wih no clear paern in he cross secion. The median variabiliy or he porolio reurns is 0.01, wih wo ouliers (Porolios 1 and 8). The poenial urn around in excess reurns aer deaul is presen in all en porolios. The srong excess reurns could however be explained by risk. The correlaions are airly large, bu no signiican isk explanaions. Two risks or corporae bonds can be expeced o survive a deaul: he marke and he liquidiy risks. The marke risk could even be expeced o increase since he bond aer deaul has a pay-o proile more resembling ha o a share. Predicing how he liquidiy risk should change is no as clear cu. The increase in volume aer deaul decreases he risk associaed wih selling he bonds, bu rading on asymmeric inormaion could increase he risk. The iniial es on he enire sample o deauled corporae bonds is presened in Table 9 below. I es or excess reurns beore and aer he deaul even. All he liquidiy acors calculaed in Secion 3.1 are used, bu only our o hem are presened in Table 8. The excluded ones are no signiican and he inercep and marke bea are no dieren han he ones presened in Table 9. The risk acors deined by Fama and French (199) are also used as addiional conrols, and repored in Table 1 in Appendix. The resuls are similar o he ones in Table 9, where he SMB and HML coeiciens are signiican beore deaul. Aer deaul HML is signiican i no combined wih any o he liquidiy acors. SMB is signiican in wo ess. The inercep and marke bea are only marginally dieren when he SMB and HML acors are included. Table 9. eurn bea represenaion or he one-acor model and he liquidiy acor Panel A. Bond beas beore deaul Inercep (-7.6) (-.19) (-7.70) (-8.8) (-7.73) Marke 0.60 (9.85) 0.43 ( (9.31) 0.57 (9.06) 0.9 (4.45) AILLIQ -11,538 (-5.87) P&SBond -758,884 (-0.79) P&SSock 0.13 (.16) Sadka.07 (.51) Obs. 3,188 3,188 3,148 3,033, Panel B. Bond beas aer deaul Inercep 0.09 (5.4) 0.07 (.4) 0.09 (5.9) 0.05 (4.) 0.05 (3.69) Marke 0.98 (.46) 1.00 (.43) 0.98 (1.99) 0.53 (4.98) 0.49 (4.06) AILLIQ 11,697 (0.85) P&SBond 190,417 (0.03) P&SSock 0.0 (0.16) Sadka (-0.03) Obs. 3,591 3,591 3,591,89, e = F Noes: In his Table he one-acor model, and wo-acor liquidiy models, are esed on a sample o deauled bonds, measured in deaul ime. Panel A consiss o he esimaed coeiciens beore he deaul even and Panel B consiss o he esimaed coeiciens aer he deaul. The daa is pooled or en monhs beore deaul (Panel A) and en monhs aer deaul (Panel B). The marke bea ( Marke ) uses he marke acor by Fama and French (199). The liquidiy measures are based on he sudies o Amihud (00), Pásor and Sambaugh (003) and Sadka (006). The speciicaions o he liquidiy measures are described in Secion 3.1, equaions (1) and (13). The -saisics are presened wihin parenhesis and calculaed using robus sandard errors. 178

12 Invesmen Managemen and Financial Innovaions, Volume 8, Issue 1, 011 Three o he liquidiy risk acors are signiican beore he deaul even. None o he liquidiy acors are signiican aer deaul. Eiher he measures o liquidiy risk do no inluence pricing or bond in deaul, or he measures are inadequae or capuring he liquidiy risk. The AILLIQ and P&S bond beas are very large, as anicipaed 1. However, hey do no seem o inluence he size o he inercep much and are insigniican, so he poenial problem wih bias in he inercep is mos likely minor. The inerceps in Panel A are negaive, indicaing ha bonds have poor reurns beore a possible deaul. The esimaed beas are high or corporae bonds ( ) compared o beas or going concerns esimaed by Weinsein (1981) (mean beas agains sock marke during he period o ) or Thorsell (008) (0.06 during he period o ). Now, hese bonds are par o a choice-based sample, and do deaul, bu his paern could be presen in oher bonds as well, so i is no a cerain indicaor o imminen deaul. The risk measures in he es do no do a good job a capuring he variabiliy, as measured by he (1 percen). The inerceps and he marke beas are all signiicanly dieren rom zero, bu some o he liquidiy coeiciens are no. The low signiicance o he liquidiy coeiciens is puzzling, considering ha rading volumes ends o increase boh beore and aer deaul, and ha liquidiy risk is a common explanaion or corporae bond reurns. The liquidiy acors have only slighly higher signiicance i he marke bea is le ou o he regressions. Hence i is no he marke bea ha crowds ou he liquidiy acors. Aer he deaul even, in Panel B, he sample can be considered o be a random selecion o deauled bonds. The inerceps urn posiive ( ) and are signiican. Considering ha he inerceps are he average monhly unexplained excess reurn, hey are very high. The median unexplained excess reurn is abou 0.0 percen per monh. This dierence beween mean and median indicaes ha he disribuion is non-normal. The robus sandard errors deined by Whie (1980) are used o decrease he problem wih non-normaliy. The marke bea o he deauled bonds increase o , as could be expeced rom he bond becoming more equiy-like. The variance in he clean price reurns increases rom a mean o 0.04 beore deaul o a mean o 1.03 aer deaul. As could be expeced rom he signiican inercep and insigniican parameer esimaes he is zero. The perormance o he esed risk acors and he large posiive inercep rom Table 8 indicaes ha a 1 This is a resul rom he choice no o rescale he liquidiy measures. porolio o deauled bonds acquired a deaul generaes excess reurns. The spread o reurns in Table 7 is airly even, and i looks like mos deauled bonds have an expeced posiive reurn. The conclusion is ha he average bond is underpriced in he deaul monh, and ha a leas he risks I have esed are no he sole reason or his underpricing. Marke risk, and o some exen liquidiy risk, seems o be imporan or he pricing o deauled bonds. The large variaion in pos deaul reurns and earlier crosssecional resuls on indusries and senioriy give cause o invesigae i he risk proile diers in hese dimensions Senioriy. The deb prioriy order in bankrupcy deermines in wha order bonds value is recovered in bankrupcy. The dieren prioriy bonds ypically ge paid in dieren racions (see Table 5 or he markes esimaes a deaul). The sandard deviaion also diers beween he dieren prioriies. I could hus be expeced ha boh he inercep and he marke bea varies depending on prioriy ranking. The daa on he prioriy ranked porolios is presened below in Table 10. Table 10. eurn bea represenaion or senioriy ranked porolios Panel A. Bond beas beore deaul Senior secured Prioriy Inercep Marke Obs. Senior unsecured Senior subordinaed -0.0 (-1.69) 0.4 (.50) (-5.16) 0.60 (6.01) (-4.3) 0.84 (6.) Subordinaed (-3.0) 0.6 (.60) Junior subordinaed (-5.16) 0.59 (4.3) Unknown (-0.0) 0.45 (1.74) Panel B. Bond beas aer deaul Senior secured Senior unsecured Senior subordinaed 0.10 (1.17).91 (1.79) (3.54) 0.81 (1.0) (.95) (-0.13) Subordinaed 0.10 (.56) 1.57 (1.90) Junior subordinaed 0.05 (.45) 1.16 (.6) Unknown 0.04 (3.98) 1.14 (5.98) e = F Noes: In his Table he one-acor model is esed on a sample o deauled bonds, measured in deaul ime. Panel A consiss o he esimaed coeiciens beore he deaul even and Panel B consiss o he esimaed coeiciens aer he deaul. The daa is pooled or en monhs beore deaul (Panel A) and en monhs aer deaul (Panel B). The marke bea ( ) uses he marke acor deined Marke by Fama and French (199). The -saisics are presened in parenheses and calculaed using robus sandard errors. 179

13 Invesmen Managemen and Financial Innovaions, Volume 8, Issue 1, 011 The ess or he prioriy ranked sample in Table 9 have similar resuls as he enire sample in Table 9. The explained variaion ( and ) is sill low, indicaing ha he risk, as measured by he esed acors, has lile o do wih he reurns pos deaul. The inerceps or he senioriy groups are negaively correlaed beore and aer deaul. This is shown or he senioriy grouped sample in Figure below. Fig.. Inerceps beore and aer deaul or senioriy grouped sample The negaive correlaion beore and aer deaul is valid or he enire sample, and o a lesser degree or he indusry and reurn ranked groups. The alphas beore deaul and he alphas aer deaul have a negaive correlaion coeicien o The alphas aer deaul are posiive, so eiher he negaive correlaion is a sign o an overshooing eec (mispricing) or here are unknown risks ha are no conrolled or. To he exen ha he risks in Table 8 and Table 1 (in Appendix) are conrolled or he inercep is sill signiican and posiive. I he Prioriy explanaion is mispricing, hen he size o he overshooing is dieren or dieren senioriies Indusry. The sample is divided ino indusry porolios and es are presened or marke risk in Table 10 below. The idea is ha he asses and leverages are similar wihin indusries bu dier beween indusries. The indusry sample should help o give an indicaion i here are speciic indusry risks ha generae he resuls in Table 8. Table 10. eurn bea represenaion or indusry ranked porolios Inercep Marke Obs. Panel A. Bond beas beore deaul. Oil & gas (-3.00) 1.10 (6.93) Basic maerial (-4.06) 0.5 (4.0) Indusrials -0.0 (-.19) 0.44 (.78) Consumer goods -0.0 (-1.45) 0.7 (3.10) Healh care (-0.53) 0.37 (1.8) Consume services -0.0 (-.44) 0.85 (5.18) Telecommunicaions (-4.71) 0.57 (3.45) Uiliies -0.0 (-4.57) 0.1 (1.6) Financial (-.75) 0.19 (0.45) Technology (-4.7) 0.56 (.4) Panel B. Bond beas aer deaul. Oil & gas 0.07 (.09) 1.50 (.86) Basic maerial 0.17 (.80) (-1.4) Indusrials 0.04 (.6) 0.59 (.15) Consumer goods 0.3 (.6) 3.49 (1.67) Healh care 0.1 (1.33) 1.98 (0.64)

14 Prioriy Panel B. Bond beas aer deaul. Invesmen Managemen and Financial Innovaions, Volume 8, Issue 1, 011 Table 10 (con.). eurn bea represenaion or indusry ranked porolios Inercep Marke Obs. Prioriy Inercep Consumer services 0.04 (.69) 1.1 (3.69) Telecommunicaions 0.0 (1.36) 0.91 (4.5) Uiliies 0.05 (.11) 0.17 (0.38) Financial 0.3 (1.41) -.9 (-0.53) Technology 0.10 (.95) 1.57 (.77) e = F Noes: In his Table he one-acor model is esed on a sample o deauled bonds, measured in deaul ime. Panel A consiss o he esimaed coeiciens beore he deaul even and Panel B consiss o he esimaed coeiciens aer he deaul. The daa is pooled or en monhs beore deaul (Panel A) and en monhs aer deaul (Panel B). The marke bea ( Marke ) uses he marke acor deined by Fama and French (199). The -saisics are presened in parenheses and calculaed using robus sandard errors. The paern or inerceps and beas are similar o Table 9 and Table 10. Indusry segmenaions aer deaul reveals beas in excess o one or a ew indusries. This is slighly surpricing since ha would indicae ha he deauled bonds in hese indusries have higher risk han an invesmen in he marke. I he es is run on a pre-crisis sample o , only one bea value is in excess o one. This indicaes ha he inancial crisis has increased he percieved riskyness o he deauled bonds eurn ranked porolios. As an addiional robusness es, he reurn ranked porolios rom Table 8 are esed or marke risk. The deaul and ranking monhs are no included in he ess. The es agains he marke risk is presened in Table 1. Table 11. eurn bea represenaion or reurn ranked porolios Panel A. Bond beas beore deaul Prioriy Inercep Marke Obs. Porolio (-3.97) 1.31 (8.4) Porolio (-4.54) 0.46 (3.56) Porolio (-0.45) 0.4 (0.79) Porolio (-1.0) 0.45 (3.6) Porolio (-3.19) 0.18 (0.91) Porolio (-.4) 0.63 (.71) Porolio (-.48) 0.1 (1.61) Porolio (-.3) 0.33 (.89) Porolio (-4.7) 0.66 (4.80) Porolio (-.47) 0.73 (.43) Panel B. Bond beas aer deaul Porolio (1.90) 3.60 (1.63) Porolio 0.08 (6.91) 0.51 (.48) Porolio (.89) 0.85 (4.7) Porolio (3.13) 0.71 (3.33) Porolio (1.76) (-0.49) Porolio (1.53) 0.75 (0.3) Porolio (4.19) 0.3 (.87) Porolio (.13) 0.86 (4.65) Porolio (.97) 1.3 (5.03) Porolio (1.47) 1.30 (3.80) e = F Noe: In his Table he one-acor model is esed on a sample o deauled bonds, measured in deaul ime. Panel A consiss o he esimaed coeiciens beore he deaul even and Panel B consiss o he esimaed coeiciens aer he deaul. The daa is pooled or en monhs beore deaul (Panel A) and en monhs aer deaul (Panel B). The marke bea ( ) uses Marke he marke acor deined by Fama and French (199). The - saisics are presened in parenheses and calculaed using robus sandard errors. The resuls or he inerceps and beas and heir signiicance levels beore he deaul even are similar o he earlier ess (in Tables 9, 10, and 11). The inerceps are, like in he oher ess, posiive and oen signiican. The resuls rom his secions shows ha he overshooing eec a deaul ime canno be aribued o he proxies or marke risk or liquidiy risk. Furher, i is also no possible o segmen ou which bonds have he overshooing eec. I is presen across he line when segmenaions are done on senioriy, indusry and reurn ranking. This indicaed ha he reason or he mispricing a deaul is mispricing Presen value o recovery raes. The excess reurns ha ollow he deaul even canno be explained by he esed risk acors (marke risk, SMB, HML and seven dieren liquidiy acors). The inerceps are signiican and large (in he range o ) aer deaul. The high reurns and he low impac o he esed risk acors indicae ha he recovery rae migh be biased (oo low) one monh aer deaul. Anoher way o looking a he excess reurns pos deaul is o discoun he uure recovery raes o he deaul dae. I he presen values deviae rom he recovery rae a deaul here is a bias. The quesion is 181

15 Invesmen Managemen and Financial Innovaions, Volume 8, Issue 1, 011 how large he bias is, and i i is economically signiican. For his purpose, he recovery rae o marke value in column (1), he recovery rae o ace value (3) and he presen value o he recovery raes o ace value (4)-(11) are calculaed during nine monhs aer deaul in Table 1. The average marke bea is 18 Table 13. isk-adjused discouned recovery raes used o calculae discoun rae. The marke bea increases rom 0.4 o 0.63 beween he irs and second hal o he sample. This change in marke bea means ha he earlier discouned recovery raes are discouned using a oo low discoun rae, bu ha laer periods have a more correc discoun rae. Asse/recovery rae Marke Book Obs. (1) () (3) (4) (5) (6) (7) (8) (9) (10) (11) (1) Enire sample Senior secured Senior unsecured Senior subordinaed Subordinaed Junior subordinaed Unknown Oil & gas Basic maerial Indusrials Consumer goods Healh care Consumer services Telecomm Uiliies Financial Technology i= i i Noe: This Table presens he ne presen value o he uure book recovery raes discouned wih a risk-adjused ineres rae. n PV ( n) =. is he recovery rae a deaul ime n, he risk ree ineres rae, n is he num- (1 r ˆF ) ber o periods aer deaul, ˆ is he esimaed sandardized covariance or he asse, and F is he marke reurn. The resuls in Table 1 are conclusive in he sense ha recovery value increases as he monhs go by (4)- (11). For he enire sample he average mean discouned recovery value nine monhs ou (11) is seven percenage poins higher han he recovery value one monh aer deaul (3). The sandard mehod or calculaing he recovery rae ha uses one monh aer deaul seems o underesimae he recovery value by abou 17.5 percen. The crosssecional variaion is here, boh in erms o senioriy and indusry, bu he resul wih increasing recovery rae over ime is robus. Invesors ha sell corporae bonds one monh aer deaul receive, on average, a lower risk-adjused price or heir bonds han invesors ha wai. Furher, using he biased measure o deaul value will bias price and reurn esimaes. This resul could be expeced since i is he same resul as ound in Secion 4., even i he magniude in erms o recovery raes was unknown. In addiion o he calculaions or Table 13 I have done in-sample ess using he generalized mehod o momens mehod (GMM) rom work o Hansen (198). When here are soluions o he momen condiions 1 he esimaes deviae rom he esimaes in Table 13, bu he paern o increasing recovery raes over ime is as srong as in Table 13. I have applied he eicien weighing marix in he calculaions. The use o GMM allows or calculaions o -saisics on he discouned presen value o he uure recovery raes in parallel o he esimaes in Table 13. The esimaes o discouned recovery raes are signiicanly dieren rom zero. In he enire sample he deaul recovery rae is 0.35 and he nine monh ou recovery rae is The dierence beween he deaul recovery rae and he nine monhs ou presen value o he recovery rae has a robus -saisic o abou 0.57 and is no saisically signiican. 1 g T ˆ i, n ˆ n (1 ˆ j i j ) = j =1 n i k k ˆ, ik k =1, where ˆ and ˆ are he esimaed parameers, i is he bond, n is he number o ime periods he recovery rae is discouned, is he risk ree rae, is he marke risk acor, and i,k is he bond reurn on bond i in period k.

16 The reurn ess in Table 9 hrough Table 1 measure he same eec as he es o dierence in recovery raes. The reason he ormer ess have signiican resuls and he laer es no is ha hey are based on many more observaions. For each enire sample esimae o reurns here are over wo housand observaions (Table 9) and or he discouned recovery rae here are only 360 (Table 13). The excess simple reurn or he enire sample is per monh. The dierence beween recovery raes (0.40 agains 0.47) is only 17.5 percen over nine monhs. A irs glance he monhly reurns and he oal dierence in recovery rae seems unreconcilable. The reason or his apparen discrepancy is ha he probabiliy ha an invesor will receive he expeced reurn or more is less han 50 percen 1. Compounding over ime means ha he expeced reurn is going o be higher han he median reurn, i.e., large reurns wih low probabiliy increase he expeced reurn. Conclusions The descripive daa on he cross-secion or deauled bonds aligns wih previous indings on how deauled bonds are priced. The indings in he pos-deaul ime-series daa are new. The claim on he bias in recovery rae esimaions is validaed by he increases in he average discouned recovery rae. My ess or excess reurns in deauled corporae bond reurns give signiican excess reurns. The eerences 1 Invesmen Managemen and Financial Innovaions, Volume 8, Issue 1, 011 explained variaion in excess reurn is low wih values. The risks acors I use o explain he reurns does no eliminae he excess reurn, as measured by alpha. The marke acor inluences he pos deaul reurn or he majoriy o porolios (as can be seen in Tables 10-1). The oher acors give some help in explaining he reurns. Perhaps mos ineresing is he weak perormance o he liquidiy acors, since hey are imporan or pricing o corporae bonds or non deauled bonds. The remaining excess reurn, when risk acors are conrolled or, is posiive and signiican in my sample, and in he robusness checks (senioriy and indusry). The dispersion o he reurns increases aer deaul, as can be (indirecly) seen in Table 8. I can no ind a suiable risk explanaion or he posiive inerceps, so perhaps asymmeric inormaion and invesor specializaion is he key o undersanding he apparen mispricing. I i is mispricing, he owner o a deaul bond need no adjus he price when selling he bond as much has been done in my sample. The holder o a deauled bond canno regain he loss ha was incurred a deaul, bu here is no reason o absain rom he high unexplained reurns ollowing deaul. The high excess reurns could also poenially spill over o bond prices beore deaul, bu he size o he dierence beween a deaul and uure discouned recovery raes is small (17.5 percen), making his poin less imporan. 1. Edward I. Alman and Vellore M. Kishore (1996). Almos Everyhing You Waned o Know Abou ecoveries on Deauled Bonds, Financial Analyss Journal, Edward I. Alman and Jason Pompeii (003). Marke Size and Invesmen Perormance o Deauled Bonds and Bank Loans: Economic Noes by Banca Mone dei Paschi de Siena SpA, 3 (): Yakov Amihud (00). Illiquidiy and sock reurns: cross-secion and ime-series eecs, Journal o Financial Markes, 5 (1): Paul Asquih and ober Gerner and David Scharsein (1994). Anaomy o Financial Disress: an Examinaion o Junk-Bond Issuers. The Quarerly Journal o Economics, 109 (3): Anje Bernd, Aziz A. Lookman and Iulian Obreja (006). Deaul isk Premia and Asse eurns. SSN elibrary. 6. Long Chen and David A. Lesmond and Jason Wei (005). Corporae Yield Spreads and Bond Liquidiy, Journal o Finance (orhcoming). 7. Frank de Jong and Joos Driessen (005). Liquidiy isk Premia in Corporae Bond Markes. SSN elibrary. 8. Jan Ericsson and Joel eneby (003). The Valuaion o Corporae Liabiliies: Theory and Tess, SSE/EFI Working Paper Series in Economics and Finance, Eugene F. Fama and Kenneh. French (199). The Cross-Secion o Expeced Sock eurns, The Journal o Finance, 47 (): Lars Peer Hansen (198). Large Sample Properies o Generalized Mehod o Momens Esimaors, Economerica, 50 (4): Mark P. Krizman. Puzzles o Finance. John Wiley & Sons, Inc, 605 Third Avenue New York, NY , Unied Saes o America, Moody (010). Corporae Deaul and ecovery aes, Luboš Pásor and ober S. Sambaugh (003). Liquidiy isk and Expeced Sock eurn, Journal o Poliical Economy, 111 (3): Krizman (000) provides an inuiive explanaion or his in Chaper 4 Why he Expeced eurn Is No o Be Expeced. 183

17 Invesmen Managemen and Financial Innovaions, Volume 8, Issue 1, onnie Sadka (006). Momenum and Pos-Earnings-Announcemen Dri Anomalies: he ole o Liquidiy isk, Journal o Financial Economics, 80 (): Hekan Thorsell. The Pricing o Corporae Bonds and Deerminans o Financial Srucure. Ph.D. hesis, Sockholm School o Economics, Mark Weinsein (1981). The Sysemaic isk o Corporae Bonds, The Journal o Financial and Quaniaive Analysis, 16 (3): Halber Whie (1980). A Heeroskedasiciy-Consisen Covariance Marix Esimaor and a Direc Tes or Heeroskedasiciy, Economerica, 48 (4): Appendix Panel A. Bond beas beore deaul Table 1. eurn bea represenaion or he hree-acor model and he liquidiy acor Inercep (-8.49) -0.0 (-.98) (-8.37) (10.06) (-8.54) Marke 0.57 (8.39) 0.4 (5.59) 0.56 (7.79) 0.57 (8.49) 0.9 (3.5) SMB 0.40 (8.76) 0.9 (6.07) 0.39 (8.68) 0.4 (10.99) 0.46 (7.3) 0.48 (4.01) 0.0 (3.1) 0.43 (11.54) 0.63 (14.69) 0.37 (3.83) HML AILLIQ -9,397 (-3.97) P&SBond -387,883 (-0.40) P&SSock 0.15 (.5) Sadka (-0.74) Obs. 3,154 3,188 3,148 3,033, Panel B. Bond beas aer deaul Inercep 0.09 (4.7) 0.06 (1.77) 0.09 (4.67) 0.04 (3.61) 0.06 (3.68) Marke 0.78 (.07) 0.78 (1.74) 0.74 (1.9) 0.61 (4.71) 0.56 (3.94) SMB 0.8 (1.90) 0.78 (.37) 0.84 (.44) 0.11 (0.75) 0.17 (0.69) 0.71 (0.7) 0.94 (5.1) 0.73 (4.39) 0.66 (6.51) 0.93 (3.44) HML AILLIQ 14,815 (1.04) P&SBond -1,789,445 (-0.5) P&SSock (-0.63) Sadka (-1.08) Obs. 3,591 3,591 3,591,89, e, i = F, i, i Noes: In This able he hree-acor model is esed on a sample o deauled bonds, measured in deaul ime. Panel A consiss o he esimaed coeiciens beore he deaul even and Panel B consiss o he esimaed coeiciens aer he deaul. The daa is pooled or en monhs beore deaul (Panel A) and en monhs aer deaul (Panel B). The marke, he SMB and HML beas (, Marke, SMB ) uses he marke acor deined by Fama and French (199). The liquidiy measures are based on Amihud HML (00), Pásor and Sambaugh (003) and Sadka (006). The speciicaions o he liquidiy measures are described in Secion 4.1. The -saisics are presened wihin parenheses and calculaed using robus sandard errors. 184

18 Invesmen Managemen and Financial Innovaions, Volume 8, Issue 1, 011 Fig. 3. Liquidiy measures 185