Information Asymmetry, Bid-Ask Spreads and Option Returns

Transcription

1 Informaion Asymmery, Bid-Ask Spreads and Opion Reurns Fredrik Berchold and Lars Nordén * Deparmen of Corporae Finance, School of Business, Sockholm Universiy, S Sockholm, Sweden. Absrac This sudy analyses wo differen ypes of informaion in he sock marke. The firs ype represens changes in informaion where informed invesors know if he sock price will increase or decrease. The second ype is less specific he direcion is unknown, bu informed invesors know ha he sock price eiher will increase or decrease. The differen flows of informaion are esimaed wihin a GARCH framework, using shocks in Swedish OMX index reurns and opions srangle reurns respecively. The resuls show significan condiional sock index and opions srangle variance, alhough wih noable differences. The sock index reurns exhibi a high level of variance persisence and an asymmeric iniial impac of shocks o variance. Opions srangle reurns have a relaively low variance persisence, bu a higher (and more symmeric) iniial impac of shocks. A ime series regression of call and pu opion bid-ask spreads is performed, relaing spreads o hese wo ypes of informaion, as well as oher explanaory variables. The resuls show ha opion spreads are relaed o shocks in index and opions srangle reurns, as well as he condiional variance of he sock reurns. Marke makers appear o aler opion bid-ask spreads primarily in response o unexpeced shocks in sock index and opions srangle reurns and o changes in he expeced variance level of sock reurns. Keywords: Informaion asymmery; opion bid-ask spreads; ime series; sock and opions srangle shocks. JEL classificaion: G10; G13; G14 * This sudy has benefied from commens and suggesions from Parik Sandås. We have also received valuable inpu from seminar paricipans a he 2003 meeing of European Finance Associaion. Send correspondence o Lars Nordén, address: ln@fek.su.se.

2 1. Inroducion In he marke microsrucure lieraure, here is exensive evidence of ime varying bid-ask spreads in he sock marke. Invenory models (see Soll, 1978; Amihud and Mendelson, 1980, 1982; Ho and Soll, 1981) moivae spreads as compensaion o marke makers for bearing he risk of an undesired invenory. Hence, if he invenory risk is ime varying and varies across securiies, spreads should flucuae accordingly. In asymmeric informaion models (see Copeland and Galai, 1983; Glosen and Milgrom, 1985; Kyle, 1983; Easley and O Hara, 1987; Back, 1993; Foser and Viswanahan, 1994), marke makers have an informaional disadvanage relaive o informed invesors. Therefore hey have o quoe spreads wide enough o compensae for losses arising from rading wih informed invesors. When informed invesors are acive spreads increase. Mos models are developed o explain he bid-ask spreads of socks, bu are relevan for derivaives as well. In addiion o invenory and informaion asymmery models, Cho and Engle (1999) propose a derivaive hedge heory, where bid-ask spreads of opions are relaed o he bid-ask spreads of he underlying securiies, e.g. socks or fuures. If marke makers can hedge opions perfecly in he underlying securiy, hey are no exposed o invenory or informaion asymmery risk in he opions marke. Hence, opion spreads should reflec invenory and informaion asymmery coss in he underlying securiy. According o invenory and asymmeric informaion models, he volailiy of he underlying securiy deermines opions bid-ask spreads. Firs, higher volailiy of he underlying securiy increases he risk of unhedged invenory opions, and is herefore expeced o resul in wider opion spreads. Second, following Copeland and Galai (1983), higher volailiy in he underlying securiy may be he resul of informed rading. If his is he case, informed invesors migh also be presen in he opions marke, widening opions spreads. The second argumen is consisen wih he derivaive hedge heory. If informed rading causes higher volailiy in he sock, i will produce wider sock spreads. Consequenly, as he underlying sock marke becomes less liquid, so does he opions marke, since i hereby is more cosly o hedge he opion posiions. 2

3 Here informaion is divided ino wo caegories. Firs, an informed invesor may know wheher he underlying securiy will increase or decrease omorrow. The second caegory is less specific; he direcion is unknown, bu an informed invesor knows ha he underlying securiy eiher will increase or decrease. According o Cox and Rubinsein (1985), hese wo ypes of informaion can exis independenly a he same ime, causing informaion asymmery. As recognised by Cherian and Jarrow (1998) and Nandi (1999), one ype of invesor may know wheher he sock price will increase or decrease (ofen called a direcional invesor) and anoher ype of invesor migh have informaion abou he fuure volailiy of he sock (volailiy or un-direcional invesor). Supposedly, he firs ype of invesor would rade socks and he second opions. 1 This sudy decomposes he informaion ino wo ypes empirically. The firs ype represens unexpeced direcional informaion and is measured as sock index shocks, whereas he second ype is measured as opions srangle shocks. An opions srangle posiion uilises undirecional informaion, i.e. informaion abou he volailiy of he underlying securiy unil expiraion. The wo ypes of informaion shocks are esimaed wihin an asymmeric GARCH(1,1) framework, allowing a dynamic formulaion of he condiional sock index and opions srangle variance. Following Engle and Ng (1993), news impac curves are presened for measuring he response of he condiional variance o new informaion, i.e. lagged shocks. Noably, he condiional opions srangle variance can be viewed as a measure of volailiy of volailiy, as formulaed by Nandi (1999). The main purpose of his sudy is o perform a ime series regression of opion bid-ask spreads and o sudy he dynamic relaionship beween he spreads and he informaion shocks. In doing so, i is possible o invesigae he relaive imporance of he wo ypes of informaion, measured as shocks in index and srangle reurns respecively, for deermining he size of opion spreads. Furhermore, i is also convenien o analyse wheher opion spreads are relaed o condiional variance in he GARCH framework or unexpeced shocks. 1 More specifically, when an invesor is in possession of direcional informaion, he/she can use he sock marke, where he sock posiion has a posiive or negaive dela, depending on he informaion conen. If he rader has un-direcional informaion, he/she wishes o have a dela neural posiion, bu wih a non-zero gamma or vega, which is exacly wha an opions srangle posiion consiues. 3

4 This sudy conribues o previous research in several ways. Firs, he empirical decomposiion of informaion ino wo differen ypes, using GARCH specificaions of sock and srangle reurns, consiues a new idea. Second, a ime series regression analysis relaing opion spreads o hese wo ypes of informaion has never been conduced before. 2 Third, previous sudies have concluded, heoreically and empirically, ha he condiional sock index variance is imporan for opions spreads. This sudy, however, is he firs o invesigae wheher opion spreads are more sensiive o he condiional sock index variance or corresponding shocks. Furhermore, he empirical analysis is conduced wih daa from he Swedish OMX sock index opions marke, presenly one of he en larges sock index opions markes in he world. This daa has never been used in a similar sudy before. The resuls show significan condiional variance, according o he GARCH esimaions, in OMX sock index reurns and opions srangle reurns, alhough wih noable differences. The index reurns exhibi a high level of variance persisence, as observed in previous sudies. 3 Also, here is significan evidence of asymmery; negaive sock index shocks have a larger impac on condiional sock index variance han posiive shocks. The srangle reurns appear o have relaively lower persisence in condiional variance, bu a considerably higher iniial impac of shocks o variance. Furhermore, here is no significan asymmery; posiive and negaive opions srangle shocks have a similar impac on condiional variance. The ime series regressions wih call and pu bid-ask spreads as dependen variables indicae significan relaionships beween he spreads and he index and opions srangle shocks. For boh calls and pus, he bid-ask spread is posiively relaed o opion srangle shocks. This is consisen wih he idea ha opion spreads become wider (narrower) on days when here is a large unexpeced increase (decrease) in volailiy when un-direcional informaion is revealed hrough rading. Also, opion bid-ask spreads are no significanly influenced by he condiional opions srangle variance. Evidenly, opion spreads are relaed o unexpeced srangle shocks, and no o he expeced, condiional, variance. Using he alernaive 2 George and Longsaff (1993) as well as Cho and Engle (1999) examine he cross-secional disribuion of bidask spreads in he S&P 100 index opions marke. Chan e al. (1995), compare he inraday behaviour of spreads of CBOE equiy opions and NYSE socks. Fahlenbrach and Sandås (2003) use panel daa mehods o analyse wheher invenory risk can raionalise he bid-ask spreads for FTSE 100 sock index opions. 3 See e.g. Bollerslev (1987) for some early US evidence, and Hansson and Hördahl (1997) for evidence from he Swedish sock marke. 4

5 definiion of condiional opions srangle variance, he volailiy of he volailiy of sock index reurns does no appear o be an imporan deerminan of he opion bid-ask spreads. Call and pu spreads are differenly relaed o sock index shocks. In he regression model for he call spread, sock index shocks have a significanly posiive resul on he spread, whereas in he pu spread model, he relaionship is significanly negaive. This is quie obvious, since he value of a call (pu) increases (decreases) as he sock index increases. Also, posiive sock index shocks may cause marke makers o increase he call ask quoe relaively more han he bid, and decrease he pu ask quoe more han he corresponding bid. As posiive informaion is revealed hrough rading, he marke maker is more exposed o increases in he sock index. Hence, here could be a endency owards increasing (decreasing) call (pu) spreads. However, he mos direc inerpreaion of hese empirical resuls is ha opion spreads are relaed o he size of he opion premium. Finally, opion bid-ask spreads are posiively relaed o he condiional sock index variance. Evidenly, marke makers appear o aler opion spreads in response o changes in he variance of sock reurns as well as o sock index shocks. The remainder of he sudy is organised as follows. Secion 2 describes he Swedish marke for OMX sock index opions, secion 3 presens he daa and mehodology and secion 4 he empirical resuls. Secion 5 ends he sudy wih some concluding remarks. 2. The Swedish marke for OMX-sock index opions and fuures In Sepember 1986 he Swedish exchange for opions and oher derivaives, OM, inroduced he OMX sock index. OMX is a value-weighed sock index based on he 30 mos acively raded socks a he Sockholm Sock Exchange (SSE), since 1998 acquired by OM. The purpose of he inroducion was o use he index as an underlying asse for rading in sandardised European index opions and fuures. A OM, all derivaives are raded wihin a compuerised sysem. The rading sysem consiss of an elecronic limi order book, managed by OM. If possible, incoming orders are auomaically mached agains orders already in he limi order book. If no maching orders 5

6 can be found, he orders are added o he book. Only members of he exchange can rade direcly a OM. 4 Members are eiher ordinary dealers or marke makers. The rading environmen hus consiues a combinaion of an elecronic maching sysem and a marke making sysem. 5 Marke makers supply liquidiy o he marke by posing bid-ask spreads on a coninuous basis. Trading based only on a limi order book could exhibi problems wih liquidiy since he high degree of ransparency may adversely affec he willingness of invesors o place limi orders o he marke. The rading sysem a SSE is also based on a limi order book. However, here are no marke makers a he Swedish sock marke. The Swedish OMX index opion marke consiss of European calls and pus, as well as fuures conracs, wih differen ime o expiraion. 6 A any ime hroughou a calendar year, rading is possible in a leas hree opion conracs series, wih up o one, wo and hree monhs o expiraion respecively. On he fourh Friday each monh, if he exchange is open, one series expires and anoher wih hree monhs o expiraion is iniiaed. For insance, owards he end of Sepember, he Sepember conracs expire and are replaced wih he December conracs. A ha ime, he Ocober conracs (wih ime o expiraion of one monh) and he November conracs (wih ime o expiraion of wo monhs) are also lised. In addiion o his basic mauriy cycle, opions and fuures wih up o wo years mauriy exis. These long conracs always expire in January and are included in he basic mauriy cycle when hey have less han hree monhs o expiraion. The same cycle applies for OMX sock index calls and pus. Furhermore, for every opions series, a range of srikes is available. Before November 28, 1997, srikes are se a 20 index poin inervals. Thereafer, saring wih he conracs expiring in February 1998, new rules apply, where srikes are se a 40 index poin inervals. Furhermore, on April 27, 1998, OM decided o spli he OMX sock index wih a facor 4:1. 7 Afer he spli, srikes below 1,000 4 The OM is he sole owner of he London Securiies and Derivaive Exchange (OMLX). The wo exchanges are linked o each oher in real ime. This means ha a rader a he OMLX has access o he same limi order book as a rader a he OM. In 1995, 35 members were regisered a he OM and 50 a he OMLX. 5 Compare e.g. he rading sysem a he CBOE, which is a coninuous open-oucry aucion among compeiive raders; floor brokers and marke makers. 6 The opions and fuures are all seled in cash a expiraion, where one opion conrac is worh an amoun of 100 imes he index. For valuaion purposes, he index fuures conracs are commonly considered as he underlying securiy for he index call and pu opions wih he idenical mauriy. For insance, he OM uses opion valuaion formulas according o Black (1976) for assessing margin requiremens. 7 The spli reduced he opion conrac size o a fourh of is previous value. The index muliplier is 100 before as well as afer he spli. 6

7 poins are se a 10 poin inervals, whereas srikes above 1,000 poins are se a 20 poin inervals. When new opions series are inroduced srike prices are cenred round he value of he OMX index. Furher, as he sock index value increases or decreases wih a considerable amoun during he ime o expiraion, new srikes are inroduced. Thus, he prevailing srike price range depends on he developmen of he index during he ime o expiraion. 3. Mehodology 3.1 Two differen ypes of informaion shocks Two daily ime series are consruced; one for OMX sock index reurns and anoher for reurns from a rolling opions srangle posiion. The sock index reurn a day is calculaed as he difference beween he naural logarihm of he sock index value a day (I ) and he corresponding value a day 1 ( I 1): (1) Rs, = ln I ln I 1 The opions srangle posiion is iniiaed a day 1 by buying one call opion, wih a srike jus above he sock index value a day 1, and one pu opion, wih a srike jus below he sock index value. The posiion is held unil day, when i is closed and he opions srangle reurn is calculaed as: (2) R o, = ln( C + P ) ln( C 1 + P 1) where C is he mid-quoe of he call opion a day, i.e. he average of he bid-ask quoes, and P he corresponding mid-quoe of he pu. To obain a ime series for opions srangle reurn, a new opions srangle posiion is iniiaed each rading day, using he closes o ouof-he-money opions available. The opion series closes o expiraion is always used, excep during expiraion weeks. Each Thursday before he expiraion week, he opion series is rolled over ino he nex conracs. For insance, on Thursday he week prior o he January expiraion week, January opions held from Wednesday o Thursday close are sold a he 7

8 prevailing mid-quoes. Then, an opions srangle posiion is iniiaed a he Thursday s midquoes of he February conracs. This posiion is held unil Friday s close. Thereafer, February opions are used unil he nex rollover. If he Friday before he expiraion week is a holiday, he rollover is iniiaed a he close of he corresponding Wednesday. To obain he informaion shocks, unexpeced changes in he reurns, sock index and opions srangle reurns are modelled as AR(1) processes wih GARCH(1,1) errors, allowing for asymmery in he condiional variance. Hence, he condiional variance can respond differenly o posiive and negaive shocks, in accordance wih Glosen e al. (1993): 5 (3) R s, = µ s, i Di, + ρs, i Di, Rs, 1 + ε s, i= 1 5 i= 1 h 2 2 s, = δs+ θsεs, 1 + αsεs, 1Qs, 1+ γ sh s, 1 5 (4) R o, = µ o, i Di, + ρo, i Di, Ro, 1 + εo, i= 1 5 i= 1 h 2 2 o, = δo+ θoεo, 1 + αoεo, 1Qo, 1+ γoh o, 1 Here, he s are dummy variables for days of he week ( equals one on Mondays and D i, D 1, zero oher vice, D2, one on Tuesdays, and so forh), ε s, ( ε o, ) is he sock index (opions srangle) reurn residual, or shock, assumed o be IID wih he condiional opions srangle (sock index) variance h (h ). In he condiional variance equaions (Q ) is a s, o, Q s, o, dummy variable which is equal o one if ε s, < 0 ( ε o, < 0) and zero oherwise. Furhermore µ s,i, o, i µ, ρ s, i, and ρ o, i are coefficiens in he mean equaions, whereas δ s, δ o, θ s, θ o, α s, α o, γ s and γ o are coefficiens in he variance equaions. The shocks from equaion (1) and (2) represen wo ypes of informaion. The sock index reurn on day is he gain (loss) from holding he index socks from he close of he earlier 8

9 rading day. If an informed invesor has informaion on day 1 abou he direcion of he sock index on day, profis can be maerialised by aking a posiion in he underlying index socks on day 1. Here he residual ε s, from equaion (3) is inerpreed as he unexpeced sock index reurn due o direcional informaion during day. For example, his informaion can be unexpeced macro daa, or any oher informaion affecing all index socks or firmspecific informaion for a subse of he socks. When he informaion becomes common knowledge on day, he sock index adjuss accordingly. Consequenly, if an invesor on day 1 is informed abou he sock index volailiy on day, i.e. o wha exen he index is expeced o move unil he close of day or no, upwards or downwards, he invesor can uilise he informaion by buying or selling an opions srangle posiion on day 1. If he informed invesor knows ha he volailiy will increase (decrease), or alernaively ha he index is (no) going o move a lo, a long (shor) opions srangle posiion is iniiaed on day 1 and closed on day. A posiive (negaive) residual ε o, measures he unexpeced par of he opions srangle reurn, no known o, in a saisical sense, uninformed invesors. In his conex, he opions srangle residual ε o, is inerpreed as he unexpeced opions srangle reurn due o un-direcional informaion. Previous research repors asymmery in condiional sock and sock index variance; see e.g. Black (1976), Glosen e al. (1993) and Hansson and Hördahl (1997). Hence, he condiional sock index variance migh be relaed differenly o posiive and negaive index shocks ( ε ). This poenial so-called leverage effec, as labelled by Black (1976), is accouned for in equaion (3). For example, if α s > 0 a negaive shock increases he condiional variance more han a posiive shock. For opions srangle reurns, here is no prior evidence of asymmery in he condiional variance, since his sudy is he firs o invesigae srangle reurns in a GARCH framework. Neverheless, he coefficien α o is included in equaion (4) o analyse a poenial leverage effec in he condiional variance for srangle reurns as well. s, 3.2 Opion bid-ask spreads, condiional variance and informaion shocks 9

10 This sudy invesigaes he ime series properies of opion bid-ask spreads. The main prupose is o analyse he dynamic relaionship beween call and pu spreads and he wo ypes of informaion shocks and condiional variance. The call and pu spreads are regressed agains sock index and opions srangle shocks, as well as condiional sock index and opions srangle variance and some oher variables, in he following ime series regressions: (5) β + β ε + β ε + β h + β h + Vol + S c, = c,0 c,1 o, c,2 s, c,3 o, c,4 s, βc,5 f, 5 β c,6volc, + βc,7c 1 + βc,8s f, + βc,9time + ξc, φc, iξc, i i= 1 (6) S β + β ε + β ε + β h + β h + Vol + p, = p,0 p,1 o, p,2 s, p,3 o, p,4 s, β p,5 f, β p,6 Vol p, + β P p,7 1 + β p,8 S f, + β p,9 Time + ξ p, 5 i= 1 φ p, i ξ p, i where S c, (S p, ) is he call (pu) opions bid-ask spread on day, ε o, ( ε s, ) is he opions srangle (sock index) shock, h (h ) is he condiional opions srangle (sock index) o, s, variance, Vol f,, Volc, and Vol p, are rading volume of sock index fuures, calls and pus, S f, is he corresponding fuures bid-ask spread, and Time is ime o expiraion of he opion, on an annual basis. Also, β k,0,, k, 9 β and φ k, i, i = 1,, 5, are regression coefficiens, where he lag-lengh in he moving average formulaion for call and pu spreads is se o five, k = c, p represen calls and pus, whereas ξ and ξ p, are residuals. The calls and pus are he same conracs as in he opions srangle posiions in equaion (2). For example, when he opions srangle posiion is sold a he close on a day, he prevailing call and pu spreads are used in he spread regressions. c, Opions spreads are expeced o be posiively relaed o opions srangle shocks ( ε large posiive (negaive) shock can be inerpreed as an unexpeced volailiy increase o, ). A 10

11 (decrease), and would cause a marke maker o increase (decrease) he quoed opion spreads. This supposed behaviour of marke makers is in line wih an increase in invenory risk and asymmeric informaion risk. In oher words, ceeris paribus, an unexpeced increase (decrease) in volailiy would cause marke makers, or limi order raders, o pos lower (higher) opion bid quoes and higher (lower) ask quoes. Hence, in equaions (5) and (6), he coefficiens β c,1 and β p,1 are expeced o be posiive. Sock index shocks ( ε s, ), on he oher hand, ough o affec call and pu spreads differenly. For example, an increase in he sock index would imply an increase (decrease) in he value of call (pu) opions and he bid-ask spread would be expeced o increase (decrease) accordingly. Also, posiive sock index shocks may cause marke makers o increase he call ask quoe relaively more han he bid, and decrease he pu ask quoe more han he corresponding bid. As posiive informaion is revealed hrough rading, he marke maker is more exposed o increases in he sock index. Hence, here could be an addiional endency owards increasing (decreasing) call (pu) spreads. As a resul, he coefficien for sock index shocks (, β c 2 ) is expeced o be posiive, whereas he coefficien for opions srangles ( p, 2 is expeced o be negaive. β ) The condiional opions srangle and sock index variance ( and ) are also included as explanaory variables in equaions (5) and (6). This is o invesigae wheher he opion spreads are dependen on he variance levels in addiion o he shocks. In oher words, when marke makers quoe opion bid-ask spreads; do hey ake ino accoun he simulaneously observed variance levels and/or he shocks? h o, h s, Trading volumes for he fuures and each opion conrac are variables in equaion (5) and (6) measuring rading aciviy. Previous research has found opion volume o be imporan for opion bid-ask spreads. According o Cho and Engle (1999), marke makers find i more difficul o hedge invenory if rading aciviy is low. Marke makers are averse o holding unhedged posiions, so he spread is expeced o widen (narrow) when he opion is less (more) acively raded. In oher words, he β k,6 -coefficiens are expeced o be negaive. 11

12 Following he derivaive hedge heory by Cho and Engle (1999), he coefficiens for he volume of he sock index fuures ( β k,5 ) are expeced o be negaive, and he coefficiens for he spread of he sock index fuures ( β k,8 ) are expeced o be posiive. If marke makers can hedge opion posiions in he fuures marke, hen hey are no exposed o invenory risk or he presence of informed invesors in he opions marke. Therefore, opion spreads are expeced o reflec informed rading and invenory risk in he underlying fuures marke. George and Longsaff (1993), as well as Cho and Engle (1999), find ha opion spreads are funcions of opion-specific variables as e.g. moneyness and ime o expiraion. Since his sudy analyses he spreads of calls and pus in a srangle posiion, aken a-he-money, moneyness is no an issue. However, ime o expiraion is included as an explanaory variable for he spreads. Based on resuls from previous sudies, ha opions wih longer ime o mauriy have wider spreads, he regression coefficiens ( β k, 9 ) are expeced o be posiive. 4. Daa and empirical resuls 4.1 The daa The daa se consiss of daily OMX opions and fuures closing prices obained from OM for all conracs beween Ocober 24, 1994, and June 29, In addiion, he se of daa includes closing bid and ask quoes, high and low prices, rading volume (number of conracs and ransaced amoun in SEK) and open ineres for all available conracs. The closing bidask spread represens he bes bid and ask quoed in he limi order book a he close of he exchange. Daily OMX sock index values are also obained from OM, calculaed from daily closing sock prices. The daa are subjec o a screening process. If an opion spread is unreasonably wide, i.e. wider han 10 SEK, he observaion is deleed and assigned a missing value in he subsequen spread regressions. 8 Furhermore, he ime period is spli ino wo sub-periods, before and afer April 27, 1998, when he spli in he OMX index occurred. As argued in Bollen e al. 8 The screening process resuls in he deleion of 38 call and 38 pu spread observaions, ou of a oal of 1,675 daily observaions during he sample period. 12

13 (2003), he primary argumen for reducing he derivaives conrac size is o enhance invesor accessibiliy. However, he auhors also claim ha a spli increases rading coss. They suppor heir claim wih anecdoal evidence from he spli in S&P 500 index suggesing ha brokerage fees, per conrac, for index fuures did no change afer he spli. Consequenly, an invesor rading he same nominal amoun of fuures afer, as before he spli, experience doubled ransacions coss. A OM, rading coss per conrac were reduced wih he same facor as he spli, boh for marke makers and brokers. Hence, he spli in he OMX index should no increase opions rading coss. Neverheless, he empirical analysis in his sudy is performed using daa from he wo sub-samples, pre and pos spli, accouning for he possibiliy ha marke makers did no aler opion spreads in accordance wih he spli. 4.2 Summary saisics Table 1 presens summary saisics for he dependen and primary explanaory variables in equaion (5) and (6). Panel A and B of Table 1 conains summary saisics of he pre and pos spli daa respecively. The mean of he dependen call spread ( ) is 2.13 SEK before he spli and 2.74 SEK afer. Pu opions have almos exacly he same mean spread as he calls; 2.03 SEK before he spli and 2.70 SEK afer. Comparing mean relaive spreads, i.e. relaing absolue mean spreads o average opion premium, yields an average relaive call (pu) spread of abou 7.0% (7.6%) before and 11.1% (11.3%) afer he spli. Hence, on average, here is an increase in opions spreads. The sandard deviaions of he opion spreads are abou he same before and afer he spli; 1.87 and 1.83 for calls and 1.79 and 1.76 for pus respecively. S c The mean sock index fuures spread ( S f ) is 2.02 SEK pre spli and 1.40 pos, i.e. well below he corresponding mean call and pu spreads. In conras o he opions spreads, he fuures spread has decreased on average afer he spli. Hence, here appears o be a shif in liquidiy from he opions o he fuures marke. As expeced, he mean sock index shock ( ε s ) is almos exacly zero, as is he mean opions srangle shock ( ε o ). More ineresingly, he daily sandard deviaion of sock index shocks is abou 1.11% (1.87%) before (afer) he spli, while he corresponding sandard deviaion of opions srangle shocks is roughly 10% (10.9%). Also, he mean condiional sock index 13

14 variance ( h s ), recalculaed o annual figures, is 0.18 (0.28) pre (pos) spli, whereas he corresponding mean opions srangle variance ( h ) is 1.63 (1.65). One inerpreaion of hese figures is ha he dispersion or he risk of he opions srangle posiion is a lo higher han for he porfolio of index socks. Also, he condiional sock index variance is higher in he second sub-sample, whereas he condiional opions srangle variance is unchanged. o Among oher explanaory variables, he mean call rading volume is 1,308 conracs per day before he spli and 206 afer, where pos spli volume figures are divided by he spli facor 4 for comparison. Pus are abou as acively raded as calls, wih a mean pre (pos) spli daily volume of 1,114 (169) conracs. Evidenly, here is a subsanial decline in opion rading volume, which could explain he increase of he opions spreads. As a comparison, he average daily sock index fuures volume is 4,814 before he spli and 7,088 afer. Consequenly, he underlying fuures conracs are more acively raded han he opions, and increasingly so in he second sub-sample. 4.2 GARCH regression resuls Table 2 presens he resuls from he GARCH(1,1) esimaions for sock index and opions srangle reurns in equaion (3) and (4). In he sock index mean equaion, he coefficiens for Mondays and Fridays ( µ s, 1 and µ s, 5 ) are posiive and significan a he 1% level, suggesing a weekend effec. The sock index has a significan auocorrelaion coefficien for Mondays ( ρ s, 1), also indicaing a weekend effec. In he opions srangle equaion, he dummy coefficien for Fridays ( µ o, 5 ) is negaive and significan a he 5% level. Also, he auocorrelaion coefficien for Fridays ( ρ o, 5 ) is significan and posiive. Hence, here is a differen day-of-he-week paern for opions srangle reurns. Esimaed GARCH coefficiens for equaion (3) and (4) are also provided in Table 2. There is srong evidence of condiional heeroskedasiciy in sock index and opions srangle reurns. The condiional sock index variance exhibis a high level of persisence (as measured by he sum θs + γ s = 0.93 for posiive shocks, and θs + γ s +αs = 0.98 for negaive shocks). Figure 1 illusraes he effec of a posiive and negaive one uni sock index shock on he condiional 14

15 sock index variance a differen lags. A lag one, he impac of a posiive shock corresponds o he coefficien θ = 0. 06, whereas he impac of a negaive shock is θ + α = s Thereafer, each shock diminishes a a rae of γ s = for lags k > 1. k k s s. The GARCH(1,1) model for opions srangle reurns exhibis considerably lower variance persisence, θo + γ o = 0.50 for a posiive shock and θ o + γ o + αo = for a negaive shock. Furhermore, for opions srangle reurns here is no evidence of asymmery in he variance equaion. The αo -coefficien is no significanly differen from zero. From Figure 2, i can be seen ha he iniial impac of opions srangle shocks is higher ( θ = 0.21) for posiive shocks han for negaive shocks ( θ o + α o = ) and ha shock diminishes faser ( γ o = ) relaive o sock index shocks. The GARCH(1,1) specificaions capure he condiional variance quie well. The Ljung-Box Q-es indicaes no remaining auocorrelaion in sock index or opions srangle residuals a he 5% level. 9 o k k Engle and Ng (1993) presen news impac curves, a mehod for measuring he condiional variance response o new informaion. Their curve shows he implied relaion beween lagged shocks ( news ) and curren condiional variance holding earlier informaion consan. In his sudy, he condiional sock index and opions srangle variance is evaluaed a he level of he uncondiional variance. Hence, news impac curves for equaion (3) and (4) are given by: 2 2 s, = δs+ ( θs+ αs s, 1) εs, 1+γsσs (7) h Q 2 2 o, = δo+ ( θo+ αo o, 1) εo, 1+γoσo (8) h Q 2 ε s, 1 = 2 o, 1 = which are quadraic funcions wih minimum a 0 and ε 0 respecively. Here, σ s 2 is he uncondiional sock index variance and σ o 2 he uncondiional opions srangle variance. Figure 3 and 4 display news impac curves for he condiional sock index and opions srangle variance. The condiional opions srangle variance is more sensiive o 15

16 shocks han he condiional sock index variance. The asymmeric response is clearly demonsraed in Figure 3, whereas in Figure 4 he response is virually symmeric. 4.3 Spread regression resuls Table 3 provides resuls of he ime series regressions for he call spread, according o equaion (5), whereas Table 4 conains corresponding resuls for he pu spread regressions formulaed in equaion (6). Each Table is divided ino Panel A and B, which conain regression resuls for he period before and afer he index spli respecively. All coefficiens for opions srangle shocks ( β c, 1 and β p, 1 in boh panels) are posiive and saisically significan a he 5% level for call spreads and a he 1% level for pu spreads. Call and pu spreads are similarly relaed o opions srangle shocks. Posiive (negaive) shocks give wider (narrower) spreads. The magniudes are roughly he same. However, afer he spli, pu spreads are considerably more sensiive o opion srangle shocks han call spreads and also more sensiive han before he spli. Call and pu spreads are differenly relaed o sock index shocks. In he call spread equaion, he coefficien for sock index shocks ( β c, 2 ) is posiive in boh panels, so posiive (negaive) sock index shocks increases (decreases) call spreads in boh sub-periods. The corresponding coefficien for sock index shocks ( β p, 2 ) is negaive, meaning ha posiive (negaive) sock index shocks decreases (increases) pu spreads. These resuls are in line wih he expecaions formulaed in secion 3. Noably, no coefficien for he condiional opions srangle variance ( β c, 3 or β p, 3 ) is significan. The condiional opions srangle variance ( ) does no influence call or pu spreads significanly. Evidenly, opions spreads are relaed o opions srangle shocks, bu no o condiional opion srangle variance. In conras, he condiional sock index variance ( ) affecs bid-ask spreads wih posiive coefficiens ( β c,4 and β p, 4 ). Ineresingly, he effec on h o, h s, 9 The Ljung-Box Q(12)-saisic equals (18.71), wih a p-value of (0.0960), in he sock index 16

17 he call spread is significan in boh sub-samples, whereas he pu spread is significanly relaed o he condiional sock index variance only in he second sub-sample. Hence, marke makers change opion spreads no only in response o opion srangle and sock index shocks, bu also in response o he condiional sock index variance. Afer he spli, he laer response is more significan. In Table 3, he coefficien for he volume of sock index fuures ( β c, 5 ) is posiive in boh subsamples, bu i is only significan a he 5% level in he firs period. Hence, afer he spli he fuures volume has no effec on call spreads, which is inconsisen wih he derivaive hedge heory. On he oher hand, he coefficien for he spread of he sock index fuures ( β c, 8 ) is significan and have he expeced sign in boh sub-samples. This suppors he derivaive hedge heory. Also, he coefficien for he call opion volume ( β c, 6 ) is significan and negaive in boh sub-samples, supporing invenory models. The corresponding resuls for he pu spread, which are presened in Table 4, show no significan influence from he fuures volume ( β p, 5 ), a significanly negaive influence from he pu volume ( β p, 6 ) and a significanly posiive effec from he fuures spread ( β p, 8 ). Comparing he resuls before and afer he spli, shows more pronounced effecs of he fuures spread and pu rading volume on he opion spreads, in paricular for he pus, in he second sub-sample. Each coefficien for lagged opion price ( β c, 7 and β p, 7 respecively) is also significan, bu only in he second sub-sample. In he second sub-sample, he coefficien for ime o expiraion ( β c, 9 and β p, 9 ) is significan in boh equaions. Furhermore, moving average erms are included o correc for auocorrelaion in each opion spread, up o five lags. 4.4 Economic significance of he resuls As an illusraion of he economic significance of he imes series regressions, prediced call and pu opion spreads from he regression models are presened in Table 5. The predicion equaions can be wrien as: (srangle) reurn model. 17

18 (9) ˆ ˆ β + ˆ β ~ ε + ˆ β ~ ε + ˆ β h + ˆ β h + S c, = c,0 c,1 o, c,2 s, c,3 o, c,4 s, ˆ β Vol ˆ ˆ + Tim~ e c, 5 f, + βc,6volc, + βc,7c 1 + βc,8s f, βc,9 (10) ˆ ˆ β + ˆ β ~ ε + ˆ β ~ ε + ˆ β h + ˆ β h + S p, = p,0 p,1 o, p,2 s, p,3 o, p,4 s, ˆ β Vol ˆ ˆ + Tim~ e p, 5 f, + β p,6vol p, + β p,7c 1 + β p,8s f, β p,9 where ˆ ( ˆ ) is he prediced call (pu) spread, ~ ε, = ( ~ ε, = 0. 01) is an example of S c, S p, o s an opions srangle (sock index) shock, h o, ( h s, ) is he average condiional srangle (sock index) variance, Vol f,, Vol c, and Vol p, is he average rading volume for fuures, calls and pus respecively, C ( P ) is he average call (pu) mid-quoe, S, is he average fuures f spread, Ti me ~ = , i.e. wo weeks on an annual basis, and ˆk,0 β,, βˆk, 9 (k = c, p for calls and pus respecively) are he esimaed regression coefficiens from Table 3 (for calls) and Table 4 (for pus). The resuls in Table 5 should be inerpreed as wo examples, fixing he explanaory variables a reasonable values from each period, before and afer he spli, o illusrae he impac on he spread in SEK. The choice of ~ ε, = 0.10 and ~ ε, = 0.01 corresponds o roughly one o sandard deviaion of each informaion shock, according o he summary saisics in Table 1. The choice of wo weeks o expiraion is arbirary. s For he period before he spli, Panel A in Table 5, he prediced average call spread is 2.03 SEK, including a consan of 0.82 SEK. Ceeris paribus, a 10% opions srangle shock adds 0.12 SEK o he spread, whereas a 1% sock index shock adds abou 0.11 SEK. Evidenly, boh shocks affec he call spread wih economically significan amouns. Decomposing he call spread furher, he average condiional opions srangle variance reduces he spread wih 0.41 SEK while he average condiional sock index variance adds 0.94 SEK. This confirms he resul ha he condiional sock index variance is significan, boh saisically and 18

19 economically, whereas he condiional opions srangle variance is less imporan. Furhermore, rading aciviy clearly maers economically, as he average fuures rading volume adds 0.29 SEK o he call spread, whereas he average rading volume of he call opion reduces he spread wih 0.28 SEK. Finally, he average spread of he underlying fuures conrac has an economic effec on he call spread of abou 0.26 SEK and ime o expiraion, abou wo weeks, an addiional 0.26 SEK. For he firs period, he prediced pu spread is 1.44 SEK, wih a quie high consan erm equal o 1.26 SEK. A similar decomposiion of he prediced pu spread shows ha a 10% opions srangle shock adds 0.12 SEK, and a 1% sock index shock reduces he spread wih 0.36 SEK. Surprisingly, he average condiional opions srangle variance removes 0.11 SEK, bu his relaively small number is saisically insignifican. On he oher hand, he average condiional sock index variance adds 0.29 SEK, considerably less han for he call spread. As is he case of calls, rading aciviy maers for pu spreads. The average fuures volume adds 0.10 SEK o he pu spread, less han he corresponding figure for he call spread. The pu opion volume decreases he spread, as expeced, and as in he case of call opions. The average pu opion volume reduces he pu spread wih 0.19 SEK. Also, he average sock index fuures spread adds 0.20 SEK and a ime o expiraion of wo weeks anoher 0.10 SEK. In Panel B of Table 5, he economic inerpreaion of he imes series regressions for he daa beween April 28, 1998, and June 29, 2001, is presened. For he second period, he prediced average call spread is 2.83 SEK, including a consan of only 0.32 SEK, much higher average call spread han during he firs period. Here, ceeris paribus, a 10% opions srangle shock adds 0.12 SEK o he spread, exacly he same amoun as in Panel A. A 1% sock index shock adds 0.23 SEK. Evidenly, shocks do affec he call spread wih economically significan amouns in Panel B as well. The average condiional opions srangle variance now increases he spread wih 0.33 SEK while he average condiional sock index variance adds 1.11 SEK. Again, he condiional opions srangle and sock index variances are economically imporan, alhough he condiional opions srangle variance is less imporan. As in Panel A, rading aciviy maers economically, alhough he average fuures rading volume now only adds 0.09 SEK, whereas he average call opion rading volume reduces he spread wih 0.32 SEK. 19

20 The average spread of he underlying sock index fuure increases he call spread wih 0.26 SEK and ime o expiraion, adds an addiional 0.32 SEK. In Panel B, he prediced pu spread is 2.45 SEK, much higher han in Panel A. The decomposiion of he pos spli pu spread shows ha a 10% opions srangle shock adds 0.22 SEK, and a 1% sock index shock reduces he spread wih 0.25 SEK. The average condiional opions srangle variance adds 0.23 SEK, bu he coefficien is saisically insignifican. The coefficien for he condiional sock index variance is significan, and he average variance adds 0.83 SEK, considerably more han in Panel A, and more in line wih call opion resuls. The average sock index fuure volume adds 0.01 SEK o he pu spread, much less han he corresponding figure for he call spread and also less han he corresponding figure in Panel A. The pu opion volume reduces he spread wih 0.26 SEK. Also, he average sock index fuures spread adds 0.60 SEK and ime o expiraion anoher 0.34 SEK. 5. Concluding remarks This sudy analyses informaion asymmery a he sock marke, and is implicaions for bidask spreads of call and pu opions. The asymmery is based on wo ypes of informaion. The firs ype is where informed invesors know if omorrow s sock price will increase or decrease when he informaion becomes public. The second ype represens informaion where an informed invesor knows ha he sock prices eiher will increase or decrease. Evidenly, he firs ype of invesor, ofen called direcional invesor, profi from rading socks, whereas he second ype, called un-direcional rader, would profi from rading opions. These wo ypes of informaion are modelled wihin a GARCH framework, using a daa se from OM, of all conracs beween Ocober 24, 1994, and June 29, The GARCH model decomposes he informaion ino unexpeced opions srangle and sock index shocks and condiional variance. Here, opions srangle shocks represen un-direcional informaion and sock index shocks represen direcional informaion, only available o informed undirecional invesors and direcional invesors respecively. 20

21 Boh opions srangle and sock index shocks as well as he condiional opions srangle and sock index variance, are explanaory variables in wo ime series regressions, where he dependen variables are he call and pu spreads respecively. In hese regressions, oher explanaory variables are he volume and spread of he sock index fuure, he volume of he opion and he lagged opion premium and ime o expiraion. The resul is significan relaionships beween opion spreads and sock index and opions srangle shocks. For call and pu opion spreads, he spreads are posiively relaed o opions srangle shocks, so opion spreads become wider (narrower) when un-direcional informaion is revealed hrough rading. Furhermore, call and pu spreads are differenly linked o sock index shocks. Sock index shocks have a significanly posiive influence on he call spreads, whereas he relaionship is negaive for pu spreads. Evidenly, posiive (negaive) sock index shocks bring larger (smaller) call spreads, and smaller (larger) pu spreads. This is quie obvious, since absolue spreads are analysed. An increase in he sock index increases (decreases) he call (pu) opion premium and hereby he absolue spread. Moreover, direcional shocks migh change bid and ask quoes differenly. For example, a posiive sock index may cause marke makers o increase (decrease) he ask quoe of calls (pus) relaively more han he bid quoe. As direcional informaion is revealed hrough rading, he exposure o he sock index increases, and hence a endency owards increased (decreased) call (pu) spreads is possible. Also, call and pu spreads are posiively relaed o he condiional sock index variance, bu no o he condiional opion srangle variance, apar from unexpeced opions srangle and sock index shocks. Hence, marke makers adjus opion bid-ask quoes as unexpeced informaion in revealed rough he rading process, in suppor of asymmeric informaion models. Furhermore, he condiional sock index variance deermines he evoluion of opion bid-ask spreads. The economic inerpreaion is ha afer he spli, he condiional sock index variance explains he larges par of he observed spreads. The impacs of opions srangle and sock index shocks are imporan as well. In he second period, afer he spli, he impacs are more 21

22 similar han before he spli. Also, he volume of he opion conrac is imporan for he size of he spreads, as is ime o expiraion. 22

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27 Table 1: Summary saisics Panel A: Daa beween Ocober 24, 1994, and April 27, 1998 Saisics S c, S p, ε o, ε s, h o, h s, Vol f, Vol, c Vol p, C 1 P 1 S f, Mean ,814 1,308 1, Median , Sandard deviaion ,168 1,451 1, Observaions Panel B: Daa beween April 28, 1998, and June 29, 2001 Saisics S c, S p, ε o, ε s, h o, h s, Vol f, Vol c, Vol p, C 1 P 1 S f, Mean , Median , Sandard deviaion , Observaions Table 1 conains summary saisics for call ( S ) and pu ( S ) spreads, opions srangle shocks ( ε o ), sock index shocks ( ε s ), condiional opions srangle variance ( h o ), c p condiional sock index variance ( hs ), fuures rading volume ( Vol ), call and pu opions rading volume ( Volc and Vol p ), lagged call and pu prices ( C 1 and P 1), as well as he fuures spread ( S ). f f