Stock Return Predictability of Cross-Market Deviations in Option Prices and Credit Default Swap Spreads

Transcription

1 P Sock Reurn Predicabiliy of Cross-Marke Deviaions in Opion Prices and Credi Defaul Swap Spreads Georgios Angelopoulos, Daniel GiamouridisP, and Georgios Nikolakakis Curren version: January 2012 (Firs version: April 2011) Absrac Cross-marke deviaions in (deep ou-of-he-money) equiy pu opion prices and credi defaul swap spreads of he same firm are emporary and predic fuure movemens in he pu opions and credi defaul swaps (Carr and Wu, 2011). We documen ha large cross-marke deviaions also srongly relae o fuure equiy prices of he reference firm. The pahs of pu opion and equiy prices are consisen wih he percepions implici in he credi defaul swap hisory. Informed rading in credi defaul swaps parly explains his resul. Our evidence also suggess ha capial srucure arbirage aciviy caers for a legiimae alernaive explanaion. JEL Classificaions: G11, G12, G13, G14, D8 Keywords: credi equiy marke inegraion, equiy reurn predicabiliy, capial srucure arbirage Angelopoulos is a Docoral suden a he Deparmen of Accouning and Finance in he Ahens Universiy of Economics and Business. Giamouridis is an Assisan Professor of Finance a he Deparmen of Accouning and Finance in he Ahens Universiy of Economics and Business. He is also Senior Visiing Fellow a Cass Business School, Ciy Universiy, London, UK, and, Research Associae a EDHEC-Risknsiue, EDHEC Business School, Nice, France. Nikolakakis is a Researcher a he Deparmen of Accouning and Finance in he Ahens Universiy of Economics and Business. We are graefully o Keih Miller and Hong Li for providing us wih impac cos daa and also for helpful discussions. Manolis Liodakis is acknowledged for his consrucive feedback hroughou he course of his work. We appreciae helpful discussions on pracical maers wih David Bieber, Ma King, Helen Krause, Chris Monagu, and Rahul Jalan. Financial suppor from he Laboraory of Accouning Applicaions, he Deparmen of Accouning and Finance, and he Research Cener of he Ahens Universiy of Economics and Business is grealy appreciaed. Daniel Giamouridis grealy acknowledges he financial suppor of he Ahens Universiy of Economics and Business Research Cener (ΕΡ ). Any remaining errors are our own responsibiliy. addresses: gaggelop@aueb.gr (Georgios Angelopoulos), dgiamour@aueb.gr (Daniel Giamouridis, Corresponding Auhor), gnikol85@gmail.com (Georgios Nikolakakis) 1

2 Sock Reurn Predicabiliy of Cross-Marke Deviaions in Opion Prices and Credi Defaul Swap Spreads Absrac Cross-marke deviaions in (deep ou-of-he-money) equiy pu opion prices and credi defaul swap spreads of he same firm are emporary and predic fuure movemens in he pu opions and credi defaul swaps (Carr and Wu, 2011). We documen ha large cross-marke deviaions also srongly relae o fuure equiy prices of he reference firm. The pahs of pu opion and equiy prices are consisen wih he percepions implici in he credi defaul swap hisory. Informed rading in credi defaul swaps parly explains his resul. Our evidence also suggess ha capial srucure arbirage aciviy caers for a legiimae alernaive explanaion. JEL Classificaions: G11, G12, G13, G14, D8 Keywords: credi equiy marke inegraion, equiy reurn predicabiliy, capial srucure arbirage 2

3 1 Inroducion Cross-marke informaion flow is a subjec of widespread ineres. From an academic sandpoin, he sudy of rading on differen venues (e.g. equiies, bonds), or derivaive insrumens (e.g. opions, credi defaul swaps), offers an excellen framework for esing hypoheses peraining o informaion asymmeries. Regulaors are also ineresed in he analysis of cross-marke informaion flow. The analysis may idenify cases where heir inervenion becomes necessary o preven or uncover poenially fraudulen ransacions; or may even simulae discussions for he necessiy of regulaory reforms. Addiionally, invesmen professionals can benefi from idenifying opporuniies ha arise due o emporary informaion delays in he prices of relaed asses. An impressive range of researchers (we review his lieraure below) have empirically invesigaed he links beween differen rading venues, differen derivaive insrumens, as well as cross-marke links. The vas majoriy of hese sudies conclude ha he price or rading in one asse can be informaive for he price or rading in a relaed asse. This finding is consisen wih he predicions of heoreical microsrucure models such as Kyle (1985), and Glosen and Milgrom (1985) which sugges ha he rading process reveals imporan informaion for he asses involved and affecs he fuure pahs of prices. Aricles in his lieraure ypically focus on cross-marke informaion flow beween wo securiies only. One example is he sudy of wheher rading of equiy opions of firm reveal informaion for he price of he firm s equiy (Easley, O Hara, and Srinivas, 1998). Anoher example is he invesigaion of wheher severe changes in credi defaul swap spreads impac he value of he equiy of he reference firm (Acharya and Johnson, 2007). A hird example is he analysis of wheher credi defaul swap spreads predic he defaul probabiliy implici in deep ou of he money pu opions of he same firm and vice versa (Carr and Wu, 2011). Overall, he lieraure on cross-marke informaion flow largely neglecs ha informaion may flow beween more han wo securiies of he same firm. Informaion is expeced o flow beween hree markes for example in he case of credi defaul swap, equiy opions, and he equiy of he same firm, given heir documened pairwise linkages. Sudying he linkages of all poenially relaed securiies of he same firm has imporan implicaions on he inferences regarding fuure prices of hese securiies. More imporanly, 3

4 insances of invesor disagreemen wih respec o he prices of he relaed securiies serve as a paricularly aracive laboraory for he esing of hypoheses peraining o informed rading. In his sudy we focus on he analysis of he credi defaul swap, he equiy opion, and he equiy of he same firm. The curren lieraure has documened pairwise informaion flow beween hese markes and has provided heoreical explanaions for is exisence. Building on his lieraure allows us o generae our priors for he pah of fuure prices of he relaed securiies, idenify insances of disagreemen, explore wha paern fuure valuaions exhibi and explain why. More specifically, we idenify insances of invesor disagreemen hrough he link beween deep ou of he money pu opions and credi defaul swaps developed in Carr and Wu (2011, CW hereafer). We hypohesize ha when hese wo securiies emporarily rade in opposie direcions, hey poenially reflec differen percepions abou he fundamenals of he firm. These, implici, percepions have been documened o srongly correlae wih fuure equiy reurns when sudied separaely. The purpose of his sudy is o reconcile how his conradicing informaion, joinly revealed in CDS and equiy opions markes, maerializes in he cash equiy marke and explain why. We base our analysis on CDS spreads and deep-ou-of-he-money (DOOM hereafer) pu opions of he same firm. Following CW, we define a sandardized credi conrac o make CDS spreads and DOOM pu opion prices direcly comparable from a heoreical viewpoin. This conrac, ermed a Uni Recovery Claim (URC hereafer), pays off $1 if and only if defaul occurs before expiry. The value of his conrac can be compued from he CDS spread. Since he URC can be replicaed hrough DOOM pu opions, is value can also be compued from he prices of DOOM pu opions. We characerize as large cross-marke deviaions he occurrences of unusually large differences in curren URC values obained from DOOM pu opions and CDS on he same firm s deb. We find ha unusually large differences of URC values are only emporary and rever o heir usual level shorly afer hey occur, on average wihin abou one week. The process of reversion involves changes in he CDS and he equiy opion, and, as we show for he firs ime, also involves largely predicable changes in he equiy values of he reference firm. Unusually large differences of URC values are also srongly economically relaed o fuure equiy reurns. In paricular, our porfolio forming analysis concludes ha spread porfolios of 4

5 socks based on he magniude of cross-marke deviaions of URC values from heir usual level earn on average a risk-adjused reurn of 36.3 basis poins per week (20.73 percen annualized) wih a -saisic of These resuls are confirmed wih cross-secional ess and survive several robusness checks. Our principal finding is ha large cross-marke deviaions in equiy opion prices and CDS spreads of he same firm conain imporan informaion for he firm s fuure equiy price. The predicabiliy we documen is an inegral, ye unaended, componen of he predicabiliy of cross-marke deviaions documened in previous work. We observe ha large deviaions in he relaive pricing of equiy opions and CDS are on average followed by equiy (opion and spo) prices ha are consisen wih he price hisory of he CDS conrac (and are conrary o he price hisory of he opion prices). This is generally consisen wih informed rading in credi markes. However we argue ha informed rading in he CDS markes only parly explains he predicabiliy paern we documen. An alernaive, no muually exclusive explanaion, which suggess ha capial srucure arbirage aciviy dicaes he fuure pah of equiy (opion and spo) prices, canno be ruled ou. 1.1 Relaed Lieraure Cross-marke informaion flow has been he subjec of academic invesigaion from as early as he inroducion of exchange raded opions conracs in he 1970 s. Black (1975) firs argues ha...since an invesor can ge more acion for a given invesmen in opions han he can by invesing direcly in he underlying sock, he may choose o deal in opions when he feels he has an especially imporan piece of informaion. Several sudies have subsequenly esed if his predicion is suppored by acual daa. 1 While he evidence in earlier sudies is mixed, more recen sudies provide sufficien evidence o conclude ha opion prices and rading aciviy in he opions marke predic fuure movemens in he underlying equiy reurns. Ang, Bali, and Cakici (2010) highligh ha he documened 1 Examples include: Manaser and Rendleman (1982), Easley, O Hara, and Srinivas (1998), Cao, Chen, and Griffin (2005), Pan and Poeshman (2006), Roll, Schwarz, and Subrahmanyam, (2010), Xing, Zhang, and Zhao (2010), Cremers and Weinbaum (2010), Yan (2011). See Giamouridis and Skiadopoulos (2012) for a review of he more recen lieraure. 5

6 predicabiliy in he shor-erm is consisen wih he mulimarke rading, sequenial rade model of Easley, O Hara, and Srinivas (1998); while he mid-erm predicabiliy can be economically inerpreed hrough he demand-based opion pricing models of Bollen and Whaley (2004) and Garleanu, Pedersen, and Poeshman (2009). Cross-marke informaion flow has also been sudied beween CDS and cash equiy markes. This lieraure is relaively new given ha sufficienly large cross-secions and imeseries of CDS daa have only become available in recen years. Sudies in his srand include Longsaff, Mihal, and Neis (2003), Acharya and Johnson (2007), Bernd and Osrovnaya (2008), Fore and Pena (2009), Norden and Weber (2009), Qiu and Yu (2012) among ohers. The evidence in hese sudies is raher mixed. Fore and Pena (2009), and Norden and Weber (2009) conclude ha he equiy marke leads he CDS marke more frequenly in he price discovery process, while Longsaff, Mihal, and Neis (2003) do no find a clear leader. Acharya and Johnson (2007) find evidence of informaion flow from he CDS marke o he equiy marke before insances of exreme increases in he CDS spreads, which hey aribue o insider rading. Bernd and Osrovnaya (2008), and Qiu and Yu (2012) also find condiional (on exreme CDS moves) flow of informaion from he CDS o he cash equiy marke. Informaion heerogeneiy is used as an argumen o reconcile he resuls in hese sudies oo. 2 Anoher srand of lieraure ha his paper is relaed o is he lieraure linking CDS and equiy opions markes. Several auhors (e.g. Hull, Nelken, and Whie, 2004; Carr and Wu, 2010) have argued ha due o he common saus of a firm s equiy and is deb as coningen claims on he asses of he firm moivaes why equiy opions and CDS wrien on he same reference company should be valued joinly. Cao, Yu, and Zhong (2010), among ohers linking implied volailiy wih credi risk, find ha individual firms pu opion-implied 2 Relaed, alhough o a lesser exen, o he line of research invesigaing he associaion of equiy and credi are papers ha have been concerned wih he he effec of defaul risk on equiy reurns. Examples include Dichev (1998), Vassalou and Xing (2004), Avramov e al. (2007), Garlappi, Shu, and Yan (2008), Campbell, Hilscher, and Szilagyi (2008), Da and Gao (2010), George and Hwang (2010). A recen paper by Friewald, Wagner, and Zechner (2011) nicely reconciles he inconclusive evidence in his lieraure and suggess ha firms equiy reurns and Sharpe raios increase wih credi risk premia. 6

7 volailiy dominaes hisorical volailiy in explaining he ime-series variaion in CDS spreads. A novel paper by CW, esablishes a simple robus link beween CDS and DOOM American-syle equiy pu opions. The predicions of heir model are empirically confirmed. Cllecively he analysis in CW concludes ha deviaions in he prices of he wo insurance conracs are emporary and forecas fuure movemens in he pu opions and he CDS. Bernd and Osrovnaya (2008) also conclude ha here is informaion flow from he CDS marke o he opions marke and vice versa. Conrad, Dimar, and Hameed (2011) in anoher recen paper find ha defaul probabiliies esimaed hrough equiy opions and CDS of he same firm presen wih srong correlaion, especially pos he Global Financial Crisis. Finally, his paper also relaes o he capial srucure arbirage 3 lieraure. A key paper in his lieraure is Yu (2006). He provides a horough presenaion and analysis of he capial srucure arbirage sraegy a he level of individual rades ha involve simulaneous posiions in he CDS and he equiy of he same firm. He concludes ha porfolios of capial srucure arbirage rades produce aracive Sharpe raios, similar o hose obained wih oher ypes of fixed-income arbirage sraegies and hedge fund indusry benchmarks. Duare, Longsaff, and Yu (2007) also invesigae he risk and reurn aribues of capial srucure arbirage. CW refer o a rading sraegy ha resembles he characerisics of capial srucure arbirage when hey discuss he concep of selling CDS and buying DOOM pus of he same firm o hedge he credi risk. Kapadia and Pu (2010) is anoher recen paper ha uses he concep of capial srucure arbirage o sudy he inegraion of equiy and credi markes. They conclude ha a convergence rading sraegy - ha involves posiions on he CDS and he equiy of a firm - on he average firm earns an excess reurn of 1.04% over a 1-monh 3 Duare, Longsaff, and Yu (2007) define capial srucure arbirage as a class of fixed-income rading sraegies ha exploi mispricing beween a company s deb and is oher securiies (such as equiy). I is one of he mos popular relaive-value sraegies wihin he hedge fund indusry. Fixed-income arbirage invesed capial amouns for 13.3% of he U.S. $2.48 rillion of hedge fund asses as esimaed by evesmen/hfn and Cii ICG analyics in November Duare, Longsaff, and Yu (2007) poin ou he oal amoun of capial devoed o fixed-income arbirage is likely much larger han ha repored in hedge fund daabases due o heir limied coverage and also due o he fac ha many oher firms direcly engage in proprieary fixed income arbirage rading. 7

8 horizon. Buraschi, Trojani, and Vedolin (2011) also sudy capial srucure arbirage in he conex of invesor disagreemen. Relaive o hese works our main conribuion is o provide a horough and rigorous invesigaion of how he join informaion discovery in he CDS and opion markes maerializes in he cash equiy marke and explain why. We carry ou our analysis wih he enire specrum of cross-marke deviaions no jus negaive evens. We are paricularly concerned wih he economic significance of cross-marke informaion flow beween hese hree markes as well as wih he duraion of economically imporan informaion revelaion. These are issues ha have no been sudied in prior works. Wha addiionally makes our invesigaion more robus and, disinc, from prior analyses is ha we incorporae real-life ransacion cos daa in our analysis. Bernd and Osrovnaya (2008) is he only sudy we know ha invesigaes he informaion flow beween CDS and opions markes, as well as he join conribuion of hese markes o he price discovery in he sock marke in he conex ha we also do. Bernd and Osrovnaya (2008) reach several imporan conclusions ha we reflec on, bu is differen han ours in many repsecs. 4 Tang and Yan (2007) also sudy he hree markes 4 We highligh hree main differences. Firs, in our invesigaion of price discovery in he CDS and opions markes we make use of direcly (or more) comparable prices, i.e. URC values based on CDS spreads and DOOM pus. We believe ha his choice allows us o compare how he wo markes price similar oucomes for he firm s equiy price wihin an as similar as possible ime horizon. In Bernd and Osrovnaya (2008) he opion marke informaion is capured hrough sandardized 60-day a-he-money opions (his pracice is followed in oher sudies oo, e.g. Buraschi, Trojani, and Vedolin, 2011, Cao, Yu, and Zhong, 2010), which are very liquid insrumens and hence more reliable in erms of he informaion hey convey. However we argue ha hese opions are no likely o be used by exremely bearish marke paricipans or by marke paricipans wishing o hedge agains severe negaive price jumps. Hence hey are less likely o impound views similar o hose impounded in CDS spreads. Second, in our analysis he relaionship beween CDS spreads and opion prices is governed by srong heoreical foundaions, i.e. arbirage condiions. Bernd and Osrovnaya (2008) moivae he relaionship beween CDS spreads and opion prices on heoreical grounds; however hey inroduce maerial srucure o his relaionship hrough he economeric specificaion hey esimae o purify he informaion obained in he CDS, opions, or equiy markes. Third, our analysis is carried ou in a period when for a leas 8

9 joinly focusing on poenial liquidiy spillovers from he equiy and he equiy opion markes o he CDS marke. Our second conribuion is ha we furher sudy he link beween equiy opion and CDS and, more imporanly, provide new insighs for he process of reversion of he wo securiies afer he occurrence of large cross-marke deviaions. We exend he analysis of CW o a broader cross-secion of firms and a longer period of ime ha also includes he Global Financial Crisis. We documen for he firs ime ha i akes on average abou one week for he cross-marke deviaion o rever from eiher exreme back in he range defined by roughly he 25 h and he 75 h perceniles. This conclusion provides addiional empirical suppor for he link developed in CW; cross-marke deviaions characerized hrough heir link consiue mispricing and are only emporary. Kapadia and Pu (2010) also reach he conclusion ha equiy and credi marke disinegraion is due o mispricing. Our evidence finally also complemens ha of Bernd and Osrovnaya (2008), and Conrad, Dimar, and Hameed (2011), who also invesigae he linkages of he CDS and he equiy opions markes. Our hird conribuion relaes o he lieraure on informaion discovery in opions markes. The overall conclusion in his lieraure suggess ha abnormal increases in pu implied volailiies (e.g. Ang, Bali, and Cakici, 2010) or pu rading (e.g. Easley, O Hara, and Srinivas, 1998; Pan and Poeshman, 2006; Roll, Schwarz, and Subrahmanyam, 2010) are negaive predicors of he fuure move of equiy prices. Our conribuion over he exising lieraure is o show ha in he presence of a raded CDS on he firm s deb, and in insances of CDS and DOOM pu opion prices disagreemen, hese predciions are no confirmed ex pos. In parciular, we documen ha large deviaions in he relaive pricing of he wo securiies are on average followed by equiy prices ha are consisen wih he price hisory of he CDS conrac (and are conrary o he price hisory of he pu opion conrac). Finally, we conribue o he capial srucure arbirage lieraure and also provide useful clues o invesmen professionals engaging in capial srucure arbirage or equiy marke he second half of i neiher CDS spreads nor opion price changes have been moderae. Bernd and Osrovnaya (2008) recognize ha one disadvanage in heir framework is ha moderae move in raes as hose observe in heir sudy period - will be recognized as adverse credi evens for he firm even hough he change in spreads mos likely did no signal a drasic deerioraion of is credi qualiy. 9

10 neural sreegies. Our empirical analysis suggess ha he measure we use for cross-marke deviaions is sufficien o idenify insances of poenially profiable capial srucure arbirage rades. This measure may serve as an alernaive o he measures used in Kapadia and Pu (2010) or Yu (2006). Moreover, our analysis suggess ha such opporuniies, which may simply occur because he equiy price reacs oo slowly o new informaion (Yu, 2006), can be exploied in he equiy marke alone. The ransacion cos analysis wih real-life daa we carry ou is he firs o our knowledge in his conex. The res of his aricle is organized as follows. Secion 2 demonsraes he link beween equiy opion prices and CDS spreads. Secion 3 provides he deails of our sample and he selecion process we follow. Secion 4 conducs exploraory analysis o ge qualiaive insighs on he poenial informaion flow from he CDS and opion markes o he cash equiy markes. Secion 5 presens he resuls of he cross-secion and ime-series analyses ha invesigae he economical and saisical significance of he informaion conen of equiy opion prices and CDS spread deviaions. Secion 6 repors he resuls of a number of robusness checks. Secion 7 presens an inerpreaion of he resuls, and Secion 8 concludes. 2 The link beween DOOM Pus and CDS In order o link American-syle DOOM pus and CDS we implemen he CW approach. CW proposed a simple and robus link beween equiy American-syle DOOM pu opions and a credi insurance conrac on he same reference company. In heir seing, he sock price is bounded below by a sricly posiive barrier B > 0 before defaul, bu drops below a lower barrier A<B a defaul, and says below A hereafer. The range [A, B] defines a defaul corridor in which he sock price can never reside. Given he exisence of he defaul corridor, hey showed ha a spread beween any wo American-syle DOOM pu opions of he same mauriy and wih srike prices falling wihin he defaul corridor, i.e. a long posiion in he high srike pu opion combined wih a shor posiion in he low srike pu opion, replicaes a pure credi insurance conrac ha pays off when and only when he company defauls prior o he opion expiry. Should his spread be scaled hrough he difference in he srike prices, he payoff becomes one uni hence i is ermed a URC. The URC price is: ( 2, ) ( 1, ) UR p (, T) = PK T PK T (1) K K

11 where he superscrip p denoes he informaion source as American pu opions on he underlying sock, and T denoe he ime he URC price is compued and he mauriy of he pu opion respecively, P(K 2,T), P(K 1,T) are he pu opion prices for he conracs replicaing he credi insurance conrac wih srike prices K 2 >K 1. Alernaively, credi insurance can be bough hrough CDS. Assuming fixed and known bond recovery rae (R), consan ineres rae (r) and fixed defaul arrival rae ( λ ) as in CW, we can compue he URC value from a single CDS spread as: [ ξ ] r(, T) + k ( T ) c 1 e UR (, T ) = ξk, ξ = 1(1 R) rt (, ) + ξk (2) where he superscrip c denoes he informaion source as CDS wrien on he corporae bond of a firm and k is he CDS spread which according o he earlier assumpions is known o have a fla erm srucure, proporional o he defaul rae, i.e. k = λ(1 R). rt (, ) denoes he ime coninuously compounding spo ineres rae for he period o T. For simpliciy we p c refer o UR (, T ) and UR (, ) T as p c UR and UR respecively hereafer. 3 Sample selecion and Daa consrucion The sample period of our sudy is January 2004 o Sepember We source opions daa from OpionMerics and CDS daa from CMA. 5,6 Equiy reurns daa and company fundamenal daa are obained hrough CRSP and Compusa respecively. 5 The OTC naure of CDS may cas skepicism on wheher CMA provides he mos accurae CDS informaion for our analysis. A recen paper by Mayordomo, Pena, and Schwarz (2010), argues ha CMA quoes lead he price discovery process in comparison wih he quoes provided by oher daabases, such as GFI, Fenics, Reuers EOD, Marki and JP Morgan. 6 CMA receives CDS spreads from a range of marke conribuors. These conribuors consis of boh buy and sell side insiuions acive in he fixed income markes such as asse managers, hedge funds and banks. These acive marke paricipans provide CMA wih boh real-ime and delayed prices of execued rades, firm or indicaive bid/offers on specific eniies (e.g. company or emerging marke), enors, senioriies (ranking of he deb receiving moneys in case of defaul) and resrucuring ypes (definiion of wha consiues a defaul, ISDA agreemen ypes). To ensure he highes level of accuracy, CMA checks hese prices agains previous quoes and validaes hose using relaed securiies and news. For less liquid eniies where marke aciviy is infrequen, 11

12 We apply a number of filers o minimize he impac of recording errors. Following CW, on each day we look hrough he opions daa o selec a lis of companies wih pu opions ha saisfy he following crieria: (1) he bid price is greaer han zero; (2) he open ineres is greaer han zero; (3) he mid price is lower han he srike price of he opion, K; (4) he mid price is no lower han K S, where S is he curren spo price of he opion s underlying equiy; (5) The ask price is greaer han or equal o he bid price; (6) The bid-ask spread is greaer han or equal o $0.05 for mid price less han $3, and he bid-ask spread is greaer han or equal o $0.1 for mid price greaer han or equal o $3 (following Goyal and Sarreo, 2009); (7) he ime-o-mauriy is greaer han or equal o 360 days; and (8) he absolue value of he pu opion Dela is no greaer han For companies wih muliple pu opions ha saisfy he above crieria, we choose he pu opion wih he highes open ineres. If wo or more opions have he same open ineres we selec he opion wih he lowes moneyness. We define moneyness as K/S. Following CW we idenify he defaul corridor [A, B] ex-ane by assuming ha he sock price drops o zero upon defaul, i.e., A = 0. Thus, we se he lower of he wo srikes in he pu spread o zero so ha we only need a single pu o creae he desired payoff. To locae he srike of his pu opion and o ensure ha he chosen srike is below he upper barrier B, in addiion o he low (absolue) Dela crierion, we require he opion o have low moneyness. 7 Following he characerizaion of ou-of-he money opions in several sudies (e.g. Xing, CMA calculaes he fair CDS spread using a proprieary issuer/secor curve model ha derives an appropriae curve using known liquid CDS spreads, bond spreads and raings daa. Illiquid reference eniies are considered hose for which CMA parses fewer han hree quoes. See he CMA documenaion for addiional informaion. 7 CW require ha he opion has a low srike, i.e. below $5, insead of he opion having low moneyness. Our approach o locae he upper barrier B increases our cross-secion of observaions dramaically wihou maerially changing he srong ime-series co-movemens of he wo ses of URC values. In paricular, he low Dela/low srike crieria (CW) sources 44,210 opion conracs for analysis. The low Dela crierion alone, qualifies 111,982 opion conracs for furher analysis which are reduced o 111,907 when we apply he low moneyness filer. In erms of he ime-series co-movemens of he wo ses of URC values, when opions are obained wih he low Dela/low srike crieria he full sample correlaion of he URC values is (p-value=0.000) and i is (p-value=0.000) when opions are obained wih he low Dela/low moneyness crieria (CW, repor a cross-correlaion of in heir sample). 12

13 Zhang, and Zhao, 2010; Doran and Krieger, 2010), we se he moneyness hreshold equal o We repea he above procedure every rading day and for every company in order o selec he pu opion ha saisfies our crieria. Once he pu opion is seleced we compue he values of URC from boh American pus on a company s sock and 5-year CDS spreads on he same company s corporae bonds according o equaions (1) and (2). This choice implies a fla erm srucure of CDS spreads which may inroduce bias. We invesigae he poenial impac of his bias in subsecion 6.1. We assume a fixed and known bond recovery rae of 40% as in CW. 8 rt (, ) is compued wih he assumpion ha i is piecewise consan, echnically, hrough inerpolaion of US dollar LIBOR and swap raes which we obain from Bloomberg. We use senior unsecured USD-denominaed CDS. To address liquidiy concerns and monior he qualiy of he informaion we obain from he CDS marke, we exclude CDS spread observaions ha have remained unchanged for five or more days. Addiional filers are applied once URC values are obained as in CW. When we apply he full range of he above filers, we obain a sample of 258 companies wih broad secor coverage. 9 The number of companies on a rading day, deermined by he number of companies for which we can compue URC values from boh CDS and pu opion conracs, ranges from 5 (which occurs in wo rading days in he enire sample) o 138, wih an average of 60 companies per rading day. Table 1 repors summary saisics for our sample. Panel A repors summary saisics for he sample firms characerisics, Panel B 8 The 40% recovery rae assumpion is based on long-erm hisorical averages; see for insance he discussion in Guo, Jarrow and Lin (2009). Using shorer esimaion horizons, Elkamhi, Jacobs, and Pan (2010) find ha he average recovery rae is around 50%. Conrad, Dimar, and Hameed (2011) repor a much higher recovery rae of 65.8% on average (wih 27% sandard deviaion), which hey compue use he join informaion in opionimplied defaul probabiliies and CDS-implied defaul probabiliies. We carry ou our analysis wih he 40% recovery rae assumpion o allow comparisons of our resuls wih CW when possible. We also provide baseline resuls for analysis based on a 50% recovery rae assumpion. 9 The indusry spli of our sample based on he Fama and French classificaion of 10 indusrial secors is as follows: Consumer Non-Durables 10 firms, Consumer Durables 3 firms, Manufacuring 37 firms, Energy 23 firms, HiTec Business Equipmen 17 firms, Telecoms 19 firms, Shops 33 firms, Healh 13 firms, Uiliies 19 firms, and Oher 92 firms. 13

14 repors he sample firms opions conracs characerisics, and Panel C repors he sample firms CDS conracs characerisics. [Table 1 abou here] The median marke capializaion is U.S. $4.90 billion, he median book value of deb is U.S. $3.36 billion, and he median raio of oal deb o book value of equiy is 97% (he median raio of oal deb o marke value of equiy is 78%). Mos firms in our sample are large and hence rading in heir equiy marke is quie liquid, i.e. he median urnover is 1.43% of he ousanding shares per day. The median (annualized) sock reurn idiosyncraic volailiy based on daily sock reurns is 27.3% wih a 90 h percenile of 56.9% and a 10 h percenile of 14.5%. The median sock implied volailiy is 56.3% when i is obained from DOOM pu opions, while i is 43% when we use a-he-money pu opions wih he same mauriy o imply i. The opions we use in our analysis are opions wih median moneyness of and a 90 h percenile moneyness of suggesing ha he vas majoriy of pu opions we use are far ou-of-he money opions. The median CDS level is 256 basis poins wih a 90 h percenile of abou 707 basis poins and a 10 h percenile of 133 basis poins. The disribuion of CDS levels indicaes ha he median firm has been rading in reasonable CDS levels for corporaes in he period we examine. The median S&P credi raing of he firms in sample is BB. 4 The predicabiliy of cross-marke deviaions: pu opions and CDS We sar our empirical analysis wih he invesigaion of he relaionship beween crossmarke deviaions and fuure CDS spreads, and pu opion prices. Our objecive is o improve our undersanding of he join informaion/price discovery in he CDS and opion markes and explore he naure of he relaive mispricing idenified by he cross-marke deviaion measure. We sar by defining our basic measure of cross-marke deviaions and discuss is empirical properies. Nex, we sudy is predicabiliy over fuure price movemens in he corresponding pu and CDS conracs as in CW. We exend heir analysis, however, in wo imporan ways. Firs, we accoun for he fac ha cross-marke deviaions may addiionally depend on 14

15 liquidiy in he markes involved; 10 and second we carry ou he analysis wih a much richer, boh in he cross-secion and in he ime-series, daase. Finally, for he firs ime, we explore he ime-series of he URC values obained from he opions and he CDS marke before and afer he observaion of large cross-marke deviaions (even sudy). 4.1 A simple measure for cross-marke deviaions Cross-marke deviaions may occur for several reasons. Kapadia and Pu (2010) for example find ha equiy marke illiquidiy conribues o equiy and CDS markes disinegraion. They argue ha exising or poenial funding consrains (and liquidiy), and oher coss associaed wih cross-marke rading may preven equiy and CDS markes from resoring heir usual pariy (e.g. Gromb and Vayanos, 2002; Brunnermeier and Pedersen, 2009; Poniff, 1996, 2006). Buraschi, Trojani, and Vedolin (2011) documen also ha larger belief heerogeneiy increases credi spreads and heir volailiy, and conribues o he disinegraion of he equiy and CDS markes. To ake hese consideraions ino accoun, we propose he following measure: p c p c URCS _ DEV = ( UR UR ) mean( UR UR ) (3) p c where mean( UR UR ) is measured over a wo-monh period. We argue ha a shor-erm hisorical average value incorporaes relevan curren informaion hus deermining a usual level of cross-marke deviaion under he prevailing marke condiions. Wih his choice we believe we minimize he impac of limis o arbirage and measuremen errors associaed wih he valuaion of URCs on he characerizaion of cross-marke deviaions as usual or unusual. Our analysis in subsecions 4.2 and 4.3 confirms his conjecure. Measures of unusual marke condiions in he spiri of ours have been used in oher sudies oo. Bernd and Osrovnaya (2008), and Qiu and Yu (2012) for example characerize a 10 For example, if an invesor wans o build her porfolio wih he equiy opions and he CDS conracs, she may no rade he CDS conrac a all if her sock opion posiion is oo cosly o build due o illiquidiy. Tang and Yan (2007) find significan liquidiy spillover from bond, sock, and opion markes o he CDS marke. Qiu and Yu (2012) find ha CDS liquidiy is a key deerminan of he amoun of informaion flow from he CDS o he equiy marke. 15

16 change in he CDS ha exceeds is mean plus four sandard deviaions as a credi even. Yu (2006) defines a variable ha measures mispricing beween equiy and CDS markes. He considers levels beyond wo sandard deviaions in excess of is hisorical mean sufficien o rigger a capial srucure arbirage sraegy. Finally, Kapadia and Pu (2010) invesigae he predicabiliy of a cross-marke disinegraion measure during days of exreme as classified by an in-sample average - equiy marke movemens. Relaive o hese measures, ours is simple, has sound heoreical underpinnings and does no suffer from look-ahead bias. URCS _ DEV exhibis ineresing empirical properies. The average (cross-secional) mean URCS _ DEV is and he average (cross-secional) median value is The 5%, 25%, 75%, and 95% perceniles are , , , and respecively. The median URCS _ DEV has a minimum value of and a maximum value of The disribuion of URCS _ DEV exhibis slighly posiive skew due o a small number of exreme (large) values observed during he Fall of Figure 1 plos he ime series of URCS _ DEV over he sudy period. 4.2 Pooled regressions [Figure 1 abou here] We proceed wih he invesigaion of he predicabiliy of cross-marke deviaions over fuure price movemens in he corresponding pu and CDS conrac. We define p c D = ( UR UR ) and orhogonalize i wih respec o various company, opion, CDS, and liquidiy 11 characerisics X hrough he following ime-series regression: 12 D = a+ bx + δ (4) 11 Our measures for sock and opion liquidiy are raher sandard. To measure CDS liquidiy we use he bid-ask over he mid quoe which has been used in some sudies (e.g. Acharya and Johnson, 2007; Tang and Yan, 2007). More recen works use insead he number of quoe providers (Friewald, Wagner, and Zechner, 2011; Qiu and Yu, 2012). Friewald, Wagner, and Zechner (2011) find however ha he wo measures are empirically similar. 12 Unrepored analysis of he cross-marke deviaion of he URC value esimaes rejecs he null of nonsaionariy. 16

17 This analysis uses daily daa over he pas wo-monh period o calculae he residualδ. Noe ha URCS _ DEV, he measure we define in equaion (3), is equivalen o δ when we se X = 1 in equaion (4). Nex, we perform pooled (cross-secional and ime-series) regressions where he regression residual δ is used o predic fuure uni recovery claim value movemens, as follows: UR UR = α + β δ + e (5) p p p p +Δ +Δ and UR UR = α + β δ + η (6) c c c c +Δ +Δ p c We conjecure ha he null β = β = 0 is consisen wih he hypohesis ha he residualδ conveys no informaion. [Table 2 abou here] Table 2 repors esimaes of he coefficiens in equaions (5) and (6). Our analysis focuses on he predicabiliy of cross-marke deviaions over one- and four-week forecasing horizons. The conclusions from his analysis can be summarised as follows. When he wo markes deviae from each oher, he deviaion predics fuure movemens in boh markes o he direcion of heir fuure convergence. The resuls indicae ha URC values sourced from equiy pu opions are more sensiive o he deviaion of he wo markes han URC values obained hrough CDS spreads. For example for URCS _ DEV (op row), we observe ha over a one-week forecas horizon, he p β = (se=0.007) and he c β = (se=0.005). This paern prevails in he enire Table and conforms o he argumen of Bernd and Osrovnaya (2008) ha changes in opion prices are much more sudden han changes in he CDS spreads due o more ofen rading of he former on unsubsaniaed rumours. The predicabiliy of cross-markes deviaions is no explained away by firm, equiy opion, CDS or liquidiy characerisics. Overall, our analysis conludes ha he resuls in CW hold in he exended sample as well as afer we accoun for liquidiy. Moreover, he measure of crossmarke deviaions we propose is qualiaively as effecive in predicing fuure moves in CDS and equiy opions as oher measures ha accoun also for various company, opion, CDS, and liquidiy characerisics. 17

18 4.3 Even sudy To shed ligh on he pahs of CDS and equiy opion prices before and afer observing a large cross-marke deviaion in he URC values obained from he wo markes we conduc an even sudy. We argue ha if large cross-marke deviaions are due o informaion delays or heerogeneous beliefs, URC values obained from he wo markes should diverge (converge) prior o (pos) he occurrence of he large cross-marke deviaion. If on he oher hand deviaions are eiher due o violaions of he model and/or implemenaion assumpions, we do no expec o observe any disinc paern. We focus on large cross-marke deviaions. In our baseline invesigaion, we characerize an observed deviaion as large if i falls in he op/boom one hird of he cross-secion disribuion of URCS_DEV. Firms are grouped in ercile porfolios based on heir ranking wih respec o heir URCS_DEV. We hen monior he evoluion of URC value changes, i.e. he cross-secional average URC value change in he porfolio, in he period preceding he reference poin of ime by up o one monh unil one monh pos he reference dae. We do ha for URC values obained hrough equiy pu opions as well as for URC values obained hrough CDS spreads and repor he resuls for a weekly rebalance in Figure 2. Panel A repors he average cumulaive change in URC values for porfolios of socks wih low URCS_DEV (boom one hird) and Panel B repors he average cumulaive change in URC values for porfolios of socks wih high URCS_DEV (op one hird). [Figure 2 abou here] Panel A and Panel B provide very ineresing insighs. In he pre-even period, we observe ha URC values obained from CDS and DOOM pu opions move in he opposie direcions. Therefore, if he CDS and opions markes are examined independen of each oher, hey reveal differen percepions. For example, in Panel A, we observe ha over he days ha precede a large cross-marke deviaion occurrence, URC values obained hrough CDS increase (cumulaively). The curren lieraure (e.g. Acharya and Johnson, 2007; Bernd and Osrovnaya, 2008; Qiu and Yu, 2012) suggess ha CDS increases are genearlly negaively correlaed wih fuure equiy reurns. Over he same period, URC values obained hrough DOOM pu opions decrease (cumulaively). Decreasing pu opion prices are associaed wih posiive fuure reurns (e.g. Ang, Bali, and Cakici, 2010). 18

19 The pos-even paerns of URC value changes are opposie o heir respecive pre-even paerns and hence also opposie o each oher. The only excepion is he paern of CDS changes afer he occurrence of large negaive cross-marke deviaions. The resuls from he even-sudy are consisen wih he predicions of he pooled regression model. There are wo imporan new findings hough. Firs, URC values rever o heir usual relaive levels hrough a process ha is relaively smooh and is no dicaed on average by large jumps. Second, and more imporan, he process of reversion is differen in he wo exreme cross-marke deviaion porfolios. This is a paern ha we documen for he firs ime and is raher criical in our explanaion of he predicabiliy of cross-marke deviaions over fuure equiy reurns ha we discuss below. We observe he same pre- and pos-even paerns when we repea he analysis wih δ obained hrough all alernaive specificaion of equaion (4). Collecively, his secion finds ha discrepancies of he curren cross-marke deviaion of URC values and heir usual level are significan predicors of fuure URC values. This predicabiliy is no explained away by firm, equiy opion, CDS or liquidiy characerisics. Our even sudy analysis suggess ha prior o he observaion of large cross-marke devaions, CDS and pu opion prices move on average in opposie direcions. Pos he even, CDS and pu opion prices move in order o resore heir fair relaive valuaions. These findings are robus o he measure of cross-marke deviaion we use. Hence we mainain our basic measure, ha is URCS _ DEV in equaion (3), for he res of he paper. 5 The predicabiliy of cross-marke deviaions: equiy reurns The earlier analysis indicaes ha he occurrence of large cross-marke deviaions is he resul of significan price changes in he CDS and he equiy opions markes and ha hose deviaions predic fuure movemens in boh markes due o he fuure convergence. CDS, equiy opions, and he equiy of he same firm are however relaed securiies. Provided ha pairwise linkages have been documened in he liarure, we expec ha cross-marke deviaions predic fuure movemens in cash equiy markes oo. To invesigae his conjecure we perform sandard cross-secional and porfolio forming analysis in subsecions 5.1 and 5.2 respecively. In subsecion 5.3, we examine he decay of he predicabiliy of cross-marke deviaions. 19

20 5.1 Fama-MacBeh Regression We conduc cross-secional reurn predicabiliy ess (Fama and McBeh, 1973) by means of hree differen specificaions, all based on he following generic specificaion: RET = b + b URCS _ DEV + b CONTROLS + e (7) i, 0, 1, i, 1 i, i, 1 i, i= 2 n where RET is firm i s reurn for week 13, i, URCS _ DEVi, is he normalized cross-marke 1 deviaion for firm i on week -1 defined in equaion (3) wih averaging over he pas wo monhs, and CONTROLS i,-1 are he n-1 conrol variables for firm i observed a week -1. The hree differen specificaions we consider involve an implemenaion of equaion (7): i) wihou any conrol variables (specificaion [1]); ii) wih conrols for firm size, book-omarke raio, and previous 1-monh reurn, (specificaion [2]); and iii) wih conrols for firm size, book-o-marke raio, he previous 1-monh reurn, Chang, Chrisoffersen, and Jacobs (2010) skewness measure, and Amihud s (2002) illiquidiy measure (specificaion [3]). Firm size and book-o-marke conrols are ypical conrols in he lieraure. We choose o conrol for shor-erm momenum as opposed o a longer-erm momenum variable given he naure of cross-marke deviaions, i.e. emporary, expeced o reverse in he shor-erm. We use he skewness measure proposed by Chang, Chrisoffersen, and Jacobs (2010) which is based on he opion marke o capure he marke skewness risk premium, documened in Harvey and Siddique (2000), Conrad, Dimar, and Ghysels (2009), and Chang, Chrisoffersen, and Jacobs (2010). Chang, Chrisoffersen, and Jacobs (2010) show ha his measure is more effecive han ohers based on he sock marke. Finally, we use Amihud s (2002) facor which has been shown in he lieraure o be predicive of he fuure crosssecion of equiy reurns. [Table 3 abou here] 13 Like Hou and Moskowiz (2005), Cremers and Weinbaum (2010), and CW among ohers, we compue reurns beween adjacen Wednesdays raher han Mondays or Fridays. Friday-o-Friday reurns have high auocorrelaions, while Monday-o-Monday reurns have low auocorrelaions (e.g. Chordia and Swaminahan, 2000). 20

21 Table 3 repors coefficien esimaes, i.e. averages of weekly esimaes, along wih - saisics obained wih he Newey-Wes (1987) adjusmen. The coefficien (saisic=3.71) in he firs column of Table 3 suggess ha a one-sandard deviaion change in URCS_DEV is associaed wih a weekly reurn of 24 basis poins (13.28 percen annualized). The resuls repored in he second column of Table 3 sugges ha he predicabiliy of URCS_DEV is independen of he predicabiliy of oher well-known facors predicing he cross-secion of equiy reurns. The coefficien (-saisic=3.20) suggess ha even afer conrolling for size, book-o-marke, and shor-erm momenum effecs, he predicabiliy of URCS_DEV remains economically and saisically significan. The alernaive riskadjusmen approach of specificaion [3] also indicaes ha he predicabiliy of URCS_DEV over he subsequen week reurns is significan, i.e. he coefficien is (-saisic=2.93). 14 We now ake a closer look a he coefficiens in he conrol variables as esimaed hrough specificaion [2]. The size variable carries a negaive and only marginally significan coefficien, i.e (-saisic=-1.63). The sign of he coefficien is consisen wih he size effec. The large capializaion of he firms in our sample, he relaively poor performance of he size facor over our specific sample period of 2004 o 2010, and he shor-erm naure of he invesigaion of predicabiliy could possibly explain why he size effec is no sronger. The coefficiens of he BM and MOM variables are boh insignifican. In specificaion [3], he coefficien of SKEW is negaive bu insignifican, i.e (-saisic=-0.88), consisen wih a negaive correlaion beween reurn and skewness. The coefficien of illiquidiy is posiive bu insignifican, i.e (-saisic=0.74). A possible concern for he genuine drivers of he cross-marke deviaion predicabiliy is non-synchroniciy. Evidence ha deviaions in URC values conain informaion no ye incorporaed in he prices of he underlying securiies could simply reflec he fac ha CDS, opion, and sock price quoes are no observed a he same poin of ime. Opion markes close a 4:02 PM Easern Sandard Time (EST), sock exchanges close a 4:00 PM EST, and 14 These resuls are obained wih a 40% recovery rae assumpion. Wih a 50% recovery rae assumpion we obain qualiaively similar resuls. In paricular one-sandard deviaion change in URCS_DEV is associaed wih a weekly reurn of 21 basis poins (-saisic=3.68), 21 basis poins (-saisic=3.68), and 21 basis poins (saisic=3.68) as specificaions [1], [2], and [3] indicae respecively. 21

22 CDS quoes are snapshos obained a 5:00 PM EST. Xing, Zhang, and Zhao (2010), and Cremers and Weinbaum (2010) among ohers raise his issue in heir analysis ha involves opions and underlying equiies and conduc heir ess also by assuming ha: (a) purchases and sales of socks ake place a he opening of rading on he day afer he signal is observed, hus ignoring he firs overnigh reurn (Cremers and Weinbaum, 2010), and (b) purchases and sales of socks ake place a he close of rading on he day afer he signal is observed, hus ignoring he firs day reurn (Xing, Zhang, and Zhao, 2010). 15 When we conduc analysis (available on reques) o examine he impac of nonsynchroniciy of he quoes on our resuls we find ha he predicabiliy of URCS_DEV deerioraes, however i remains highly economically and saisically significan. In paricular, when we assume ha he sales and purchases of socks ake place a he opening of rading on he day afer he signal is observed, he facor coefficiens for specificaions [1], [2], and [3] are (-sa=3.60), (-sa=3.09), and (-sa=2.86) respecively. When we assume ha purchases and sales of socks ake place a he close of rading on he day afer he signal is observed he facor coefficiens for specificaions [1], [2], and [3] are (-sa=3.04), (-sa=1.98), and (-sa=1.67) respecively. These resuls sugges ha he non-synchroniciy of he price quoes does no explain he predicabiliy of cross-marke deviaions. Summarizing, he cross-secional evidence, we find ha cross-marke deviaions in CDS spreads and equiy pu opion prices are srongly relaed o fuure equiy reurns. The predicabiliy holds even afer conrolling for firm and marke characerisics and for he nonsynchroniciy of equiy, opions, and CDS prices. This evidence complemens Bernd and Osrovnaya (2008) who find informaion flow however only condiional on adverse credi evens. The addiional conribuion over he exising lieraure is ha we documen ha he 15 We argue ha boh approaches are raher conservaive. Barclay, Hendersho, and Jones (2008) for example sress ha he opening price mus be deermined wih lile or no rading a a ime when uncerainy abou fundamenal values is high and hence opening a financial marke creaes unusual sress. They also argue ha his sress is compounded when here are large order imbalances a he open, even if hese order imbalances are unrelaed o changes in fundamenal values. Ignoring he firs day reurn on he oher hand may also be criical given he naure of he phenomenon we sudy and he shor horizon we expec i o las for. 22