Index arbitrage and the pricing relationship between Australian stock index futures and their underlying shares

Transcription

1 Idex arbirage ad he pricig relaioship bewee Ausralia sock idex fuures ad heir uderlyig shares James Richard Cummigs Uiversiy of Sydey Alex Frio Uiversiy of Sydey Absrac This paper coducs a empirical aalysis of he mispricig of Ausralia sock idex fuures. Exogeous ad edogeous price volailiy is cofirmed o have a posiive impac o he mispricig spread, afer filerig ou predicable ime series compoes. More accurae pricig associaed wih surprise radig volume i he uderlyig socks is cosise wih arbirageurs acig o arrow price dispariies relaive o he fuures marke. Ex-ae ieres rae volailiy is he primary source of risk faced by arbirageurs ad flucuaios i he marke impac cos of opeig idex arbirage posiios ifluece he exe o which hey drive prices owards heoreical fair values. JEL classificaio: G13, G14 Keywords: Sock idex fuures, Arbirage, Marke efficiecy This research was fuded by he Sydey Fuures Exchage uder Corporaios Regulaio (2). The auhors graefully ackowledge commes by David Cambridge, David Socke, George Wag ad Rober Webb, as well as semiar paricipas a he Ausralia Securiies Exchage, CPA Ausralia Ivesme Sraegy Discussio Group, Europea Fiacial Maageme Associaio 2008 Aual Meeig (forhcomig), Fiacial Maageme Associaio Ieraioal 2008 Aual Meeig (forhcomig) ad he Uiversiy of Sydey. Address correspodece o Alex Frio, Fiace Disciplie, Faculy of Ecoomics ad Busiess, Uiversiy of Sydey NSW 2006; elephoe ; fax ; [email protected]. 1

2 1. Iroducio The price likage bewee Ausralia sock idex fuures ad he replicaig porfolio of uderlyig shares is examied. I is geerally acceped ha his likage is maiaied by arbirageurs. The purpose of his paper is o updae ad exed Brailsford ad Hodgso s (1997) aalysis of sock idex fuures pricig based o he former Ausralia All Ordiaries Share Price Idex corac. The updaed aalysis for SFE SPI 200 Idex fuures ha are currely he mos acively raded equiy derivaive i Ausralia provides furher evidece abou he efficiecy of iformaio rasmissio bewee he spo ad fuures markes. The aalysis is exeded o icorporae he impac of uexpeced volume i he uderlyig socks, i addiio o price volailiy ad uexpeced volume i he fuures marke. Expadig upo previous research, his sudy akes accou of specific risks ad rasacio coss faced by arbirageurs acig o arrow price dispariies bewee he spo ad fuures markes. I paricular, he relaive imporace of divided yield uceraiy ad exae ieres rae volailiy i obsrucig he exe o which arbirageurs ca drive prices owards heoreical levels furher ou from mauriy are assessed. The ifluece of iraday variaios i he rasacio coss represeed by bid-ask spreads i he spo ad fuures markes ad securiies borrowig are also esimaed whereas previous mispricig sudies have relied upo cosa oal rasacio coss of idex arbirage rades. These exesios eable a more comprehesive examiaio of sock idex fuures pricig icorporaig uexpeced iformaio arrival i cojucio wih he relaive effeciveess of he arbirage mechaism. 1.1 Iformaio rasfer This paper furher explores he impac o he mispricig series of he possibiliy ha he sock ad fuures markes reac o differe iformaio ses (he differeial iformaio hypohesis ). I his coex, he sregh of he arbirage pricig relaioship for idex fuures reflecs he efficiecy wih which he iformaio ses are rasferred bewee he sock ad fuures markes followig heir arrival i he mos recepive marke o each occasio. Hodgso, Masih ad Masih (2006) provide evidece ha subsaial macroecoomic iformaio flows i from Ausralia sock idex fuures price chages ad predics subseque movemes i sock prices. I is likely ha marke-wide iformaio is icorporaed wih greaer speed i he fuures marke relaive o he uderlyig sock marke, if rasacios coss are subsaially lower ad execuio delays are shorer i he fuures marke. Cosise wih he relaive domiace of he fuures marke compared o he cash marke i he price discovery process, Brailsford ad Hodgso (1997) fid ha uexpeced radig volume ad he volailiy of fuures prices have a posiive impac o he mispricig spread of Ausralia sock idex fuures 1. Coversely, idividual socks radig i he 1 Garbade ad Silber (1993) demosrae ha he price discovery fucio of fuures markes higes o wheher price chages i fuures markes lead price chages i cash markes more ofe ha he reverse. I paricular, if he fuures marke domiaes he cash marke, ay deviaios from he carryig cos relaioship bewee cash ad fuures prices will be arrowed by cash prices movig furher owards fuures prices ha fuures prices move owards cash prices. Usig daily daa for cash ad sock idex fuures markes i he Uied Saes, Merrick (1987) fids evidece of a srog causal flow from volailiy o he cash/fuures mispricig spread ad Hill, Jai ad Wood (1988) describe a posiive, coemporaeous relaioship bewee mispricig chages ad larger absolue idex reurs. Usig execuable prices for he idex baske every hiry secods i Hog Kog, Draper ad Fug 2

3 cash marke are more likely o reac o firm specific iformaio. This sudy ess wheher he arrival of uique iformaio i he cash marke represeed by surprise urover i he uderlyig baske of socks domiaes he presece of arbirageurs acig o arrow price discrepacies relaive o he fuures marke 2. By esimaig is impac o he mispricig spread, evidece is provided abou he source of iformaio arrival i he cash marke. The radig hours of he Ausralia sock marke do o overlap wih he Uied Saes sock marke, which allows he effec of overigh public iformaio arrival o be observed. Brailsford ad Hodgso (1997) fid ha volailiy of he overigh Uied Saes sock marke has a cosise sigifica impac o he absolue pricig errors of Ausralia sock idex fuures a he opeig of he local sock marke. Higher mispricig a he opeig is likely o be compouded by a microsrucural feaure; he opeig price seig mechaism i he sock marke eails saggered opeig imes for groups of socks over he firs ie miues. 1.2 Risks faced by idex arbirageurs Greaer absolue magiudes of mispricig for loger imes o mauriy which have bee observed i sock idex fuures markes are cosise wih arbirage beig more risky furher ou from mauriy (MacKilay ad Ramaswamy, 1988 i he Uied Saes; Yadav ad Pope, 1990; 1994 i he Uied Kigdom). Arbirageurs require greaer compesaio o ac upo deviaios from heoreical pricig levels whe he risks hey face are higher, permiig larger deviaios o be susaied early i he fuures expiry cycle. MacKilay ad Ramaswamy (1988) ideify hree of he risks ha are greaer wih loger imes uil expiraio: (i) he risk of uaicipaed icreases or decreases i divideds; (ii) uaicipaed ieres earigs or coss from fiacig he markig-o-marke flows from fuures posiios; ad (iii) aemps a arbirage moivaed radig ha employ less ha he full baske of socks i he idex mus allow for a greaer margi of error wih loger imes o expiraio. Focusig o he parameers of he cos-of-carry valuaio model ha provides fair values, he divided yield ad ieres rae o mauriy, his paper edeavours o diseagle which of he risks associaed wih idex arbirage aciviies have he mos sigifica impac o absolue mispricig. Exisig research does o explicily quaify he risk premium required by arbirageurs o accou of divided yield uceraiy, excep by cosiderig wors case scearios (Yadav ad Pope, 1994). This sudy measures he uceraiy abou he magiude of divideds based o he dispersio of aalyss forecass for idex cosiue socks 3. The likelihood of icorrecly predicig ex-divided daes is also (2003) show greaer mispricig of idex fuures occurs wih icreased marke volailiy (caused by he arrival of sigifica iformaio). 2 Kumar ad Seppi (1994) develop a iformaio-based model of arbirage, where he order flow iself is iformaive abou iermarke price discrepacies. A empirical implicaio of heir model is ha idex arbirage is associaed wih permae price revisios. Providig suppor for he model, Neal (1996) fids arbirage rades arrow he deviaio from fair value ad mos rades ivolve a simulaeous submissio of he sock ad fuures porios of he rade. 3 Typically, marke paricipas esimae fuure divideds by applyig a perceage growh facor o pas divideds ad use correspodig ex-divided daes from previous years. Aalys forecass for he sizes of divideds spaig he period o fuures expiry are less reliable furher ou, depede upo 3

4 higher for loger imes uil mauriy. The risk peraiig o he ukow imig of ex-divided daes is especially releva o he pricig of he fuures corac, i cases whe eiher divideds are delayed ha were expeced o have ex-divided daes before he expiraio of he corac or divideds are brough forward ha were expeced o be deferred uil afer he expiraio of he corac. Despie he presece of hese forms of divided uceraiy, Yadav ad Pope (1994) are uable o aribue he magiude of mispricig hey observe i FTSE 100 fuures o divided forecas errors. Their measure of he uceraiy surroudig he imig of fuure divideds focuses o he differece bewee he ex-divided dae ad he acual divided payme dae, which does o capure he pricig cosequeces of firms reschedulig ex-divided daes relaive o previous years. This issue is addressed i our sudy by cosrucig a aleraive measure of he ime o expiraio based o gross divideds ha remai udisclosed i relaio o heir magiude ad imig. Ieres rae risk arises from fuures posiios because he markig o marke feaure ecessiaes he daily reivesme or borrowig of cash 4. Wih he cos of fiacig he se of shares of he uderlyig idex deermied a he ime of eerig io a fuures corac, idex arbirageurs are furher exposed o ieres rae risk if he borrowig or ledig hey uderake o suppor he cash leg of heir rasacios does o mach he mauriy of he fuures 5. The cos of coiually rebalacig he mauriies of cash ad fuures posiios o euralise his ieres rae exposure may be prohibiive. Uaicipaed chages i ieres raes spaig he period o fuures expiry are more likely o occur whe sarig furher ou. This paper ivesigaes he depedece of absolue mispricig o he ex-ae esimae of ieres rae volailiy implied i ieres rae opio prices. Furher, aoher aleraive measure of he ime o expiraio is cosruced based o he frequecy of ecoomic releases ha ifluece ieres rae expecaios over he period o fuures expiry. MacKilay ad Ramaswamy (1988) provide evidece of couervailig forces ha serve o esablish a arrower radig bad for idex fuures prices. Arbirageurs opio o uwid heir posiios premaurely iroduces pah depedece io he mispricig series (refer also o Kempf, 1998). I paricular, MacKilay ad Ramaswamy show ha codiioal o he mispricig of S&P 500 fuures coracs havig crossed oe arbirage boud, i is less likely o cross he opposie boud. This pheomeo is cosise wih arbirageurs uwidig posiios esablished whe he early guidace from a greaer umber of firms. Addiioally, special divideds ca cosiue a subsaial fracio of oal divideds ad are difficul o predic. 4 The applicaio of he cos-of-carry model for forward prices o he pricig of fuures coracs relies upo he assumpio of o-sochasic ieres raes (Cox, Igersoll ad Ross, 1981). As a aleraive, Ramaswamy ad Sudaresa (1985) develop a coiuous ime model i which he sock idex follows a logormal diffusio process ad he ieres rae follows a mea-reverig process. Cakici ad Chaerjee (1991) compare he pricig models wih sochasic ad o-sochasic ieres raes for S&P 500 fuures ad coclude ha he sochasic model gives sigificaly beer resuls whe he spo ieres rae is far away from he log-erm mea or whe he parameer accouig for he speed of adjusme oward his log-erm mea is very high. However, simulaio aalysis used by Modes (1984) suggess ha sochasic ieres raes ad markig o marke are likely o have a miimal effec o equilibrium prices. Bailey (1989) ad Brailsford ad Hodgso (1997) examie he empirical performace of he Ramaswamy-Sudaresa model i he Japaese ad Ausralia markes respecively ad fid ha he pricig errors are o subsaially differe from hose for he simpler cos-of-carry model. These fidigs do o preclude ieres rae volailiy resulig i a wideig of he arbirage bad for idex fuures prices. 5 I pracice arbirage firms ypically fiace heir aciviy o a overigh basis. 4

5 mispricig was ouside oe boud before i reaches he oher boud. I is opimal o close ou hese posiios before puig o ew arbirage rades i he reverse direcio 6. The early uwid opio poeially miigaes he greaer risks ivolved i arbirage sraegies furher ou from mauriy 7. Arbirageurs also obai he opio o roll heir fuures posiios forward io he ex available mauriy 8. Brailsford ad Hodgso (1997) argue ha he risk faced by arbirageurs i a small volaile marke like Ausralia may be lower ha i larger ad more liquid markes because he implici opio compoe of a arbirage posiio icreases i value wih he volailiy of he mispricig. 1.3 Trasacio coss Eve before he risks faced by arbirageurs are ake io accou, he exisece of rasacio coss implies ha he price of he idex fuures ca flucuae wihi a bad aroud is heoreical value wihou represeig a profi opporuiy for eve he mos favourably siuaed arbirageurs (Modes ad Sudaresa, 1983; Modes, 1984; Gould, 1988; Kawaller, 1987; 1991). Usig miue-by-miue daa, Dwyer, Locke ad Yu (1996) esimae a error correcio mechaism for he S&P 500 fuures ad cash idexes ha allows for he o-lieariy suggesed by arbirage wih rasacio coss. I respose o shocks from he fuures marke, heir resuls idicae he basis coverges o he cos of carry as much i five o seve miues whe arbirage is profiable as i coverges i fifee miues whe arbirage is uprofiable 9. The widh of he bad is deermied by explici coss such as fees paid o brokers, exchage levies ad shor sellig coss ad from implici coss icludig he bid-ask spreads ad price impac coss of opeig up posiios i boh he sock ad fuures markes. This sudy furher exeds he mispricig aalysis performed by Brailsford ad Hodgso (1997) by deermiig he ifluece o he mispricig series of he miimum implici roud-rip rasacio coss associaed wih bid-ask spreads i he sock ad fuures markes. I his way, he pricig relaioship bewee he spo ad fuures markes is examied while corollig for flucuaios i he widh of he arbirage bouds due o 6 The opio o close ou early may also make i opimal o ope a ew arbirage posiio eve whe he simple arbirage profi is less ha he cos icurred i opeig ad closig he posiio a mauriy (Brea ad Schwarz, 1990). Empirical evidece provided by Fiery ad Park (1988) idicaes ha mos program raders are beer off o o hold heir posiios ad uwid hem a he expiraio of he fuures corac bu isead o keep radig heir posiios uil expiraio. Neal (1996) fids arbirage posiios are ypically liquidaed early ad very few are held o expiraio. 7 I his regard, greaer divided yield uceraiy ad ieres rae volailiy may icrease he value of he early uwid opio by icreasig he volailiy of he mispricig series. 8 Merrick (1989) ad Yadav ad Pope (1990; 1994) reveal early uwidig ad rollovers are impora deermias of arbirage profis ad explai why he arbirage marke ca be acive eve hough prices are wihi coveioally-measured rasacio cos bouds. 9 Also i he Uied Saes, Chug (1991) shows he frequecy of ex ae pricig violaios declies sigificaly wih he assumed level of rasacio coss ad legh of execuio lags ad he size of ex ae arbirage profi is subsaially smaller ha he riggerig ex pos mispricig sigal. I he Uied Saes ad Korea respecively, Klemkosky ad Lee (1991) ad Gay ad Jug (1999) fid ha member firms have more opporuiy o egage i profiable idex arbirage ha isiuioal ivesors who icur higher rasacio coss. I Japa, Lim (1992) fids ha arbirage opporuiies are very limied; accouig for rasacio coss o arbirage profi could be made by hose ouside of he brokerage busiess. I he Uied Kigdom, Buerworh ad Holmes (2000) fid ha alhough mispricigs ed o be larger ad more persise for he mid 250 corac ha for he FTSE 100 corac, his is cosise wih he larger rasacio coss ad difficulies associaed wih radig he illiquid cosiues of he mid 250 idex. 5

6 medium-erm, seasoal ad iraday variaios i rasacio coss icurred whe layig o idex arbirage rades. This sudy ivesigaes wheher here is ay mauriy effec o he magiude of mispricig of he fuures corac relaed o he cos of borrowig sock. Borrowig coss are icurred by arbirageurs who do o have capial i he form of reasury bills (for buy programs whe he fuures corac is overvalued relaive o he uderlyig socks) ad idex socks (for sell programs whe he fuures corac is udervalued relaive o he uderlyig socks) 10. Shor-sellers have o locae a willig sock leder ad pay a sock borrowig fee 11. The cos rages from zero for hose already owig he sock o a poeially high level. A dyamic equilibrium model developed by Kempf (1998) predics ha he absolue level of egaive mispricig icreases wih ime o mauriy, sice he holdig coss associaed wih shor arbirage posiios icrease wih ime o mauriy. If arbirageurs have o borrow socks o exploi egaive idex fuures mispricig, he pricig of he ear corac could deviae from is heoreical level more frequely whe sock borrowig is relaively expesive. To es his expecaio, i is deermied wheher borrowig coss i he Ausralia marke have ay icremeal impac o he volailiy of he mispricig series. The remaider of his paper is srucured as follows. Secio 2 describes he isiuioal seig ad daa used i he empirical ess. The empirical resuls are repored i secio 3 ad he paper is cocluded i secio Isiuioal seig ad daa Iroduced i April 2000, he S&P/ASX 200 idex measures he performace of he 200 larges socks lised o he Ausralia Sock Exchage (ASX). The idex is floaadjused ad represes approximaely 80 perce of he Ausralia equiies marke capialisaio 12. The socks comprisig he idex are raded o he ASX s compuerised radig sysem, kow as he Sock Exchage Auomaed Tradig Sysem (SEATS) uil Ocober The level of he S&P/ASX 200 is calculaed by Sadard & Poor s ad is repored o he marke every 30 secods as cosiue prices chage. SFE SPI 200 Idex Fuures are wrie over he S&P/ASX 200 idex wih a corac ui of 25 Ausralia dollars per idex poi. The coracs follow a March- Jue-Sepember-December quarerly mauriy cycle ad are cash seled a a price 10 I Ausralia, he borrower pays he leder a fee for he use of he borrowed securiies ragig aywhere bewee 25 ad 400 basis pois per aum for ASX 200 equiies ad bewee 5 ad 50 basis pois per aum for Commowealh Goverme securiies (refer o Kig, 2005a). Pricig ypically akes io accou facors such as demad ad supply for paricular securiies, he size of ay maufacured divided ad he likelihood of he leder recallig he securiies early (Kig, 2005a; b). There is o auomaed elecroic plaform for egoiaig securiies ledig rasacios i use i Ausralia ad all rasacios are eered io bewee he couerparies. Thus, whereas bid-ask spreads i boh he sock ad fuures markes are able o be gauged, rasacio coss associaed wih securiies ledig ad repo rasacios are o repored i Ausralia. 11 Modes ad Sudaresa (1983) demosrae ha if par of he proceeds from shor sales i he spo marke is uavailable o raders for earig ieres, he radig bad dicaed by rasacio coss ca be asymmeric aroud he heoreical fair value ad he fuures price ca be below he spo idex especially whe he cos of shorig he spo idex is large. 12 The idex was covered from a marke capialisaio weighed idex o a free floa based idex o 1 Ocober

7 calculaed usig he firs raded price of each compoe sock i he idex o he las radig day (deoed day 0 i his aricle). From he Jue 2003 expiry owards, he las radig day is he hird Thursday of he seleme moh. Earlier coracs expired o he las busiess day of he seleme moh 13. Tradig of SFE SPI 200 fuures i he dayime sessio commeces a 9:50 a.m. ad fiishes a 4:30 p.m. o he Sydey Fuures Exchage (SFE). I coras, he socks from which he idex is cosruced are raded o he ASX from 10:00 a.m. o 4:00 p.m.. Socks o he ASX do o ope simulaeously. Raher, hey are grouped accordig o he sarig leer of heir ASX code ad each group is opeed radomly up o fifee secods o eiher side of differe imes bewee a.m. ad a.m Daa descripio Reuers rade ad quoe daa for SFE SPI 200 TM fuures were provided by he Securiies Idusry Research Cere of Asia-Pacific (SIRCA). The daa covers he period 1 Jauary 2002 o 15 December 2005, which provides a srucural break free daa se of sixee corac mauriies for aalysis 14. Though up o six mauriies are lised a ay paricular ime, our aalysis is cofied o he eares-o-mauriy corac which has by far he mos sigifica radig volume. Hece, each corac is followed from he expiry dae of he previous corac uil is expiraio. Expiraio day observaios are o icluded 15. The daa describes he ime (o he eares secod), price ad volume of each rade ad he prices of he bes available bids ad offers. Ed-of-day ope ieres figures were obaied from Bloomberg. S&P/ASX 200 sock idex values, ime-samped approximaely 30 secods apar, ad Reuers rade ad quoe daa for he idex cosiues were also provided by SIRCA. The idex cosiues were ideified usig a daily lis from Bloomberg. The lis coais he floa-adjused idex weighs, umbers of shares ousadig ha are icluded i he idex calculaio ad closig prices for socks i he idex. The Reuers rasacio file records all rades ad quoes o he ASX. I coais he ime o he eares secod, he price ad volume for each rade ad he ime ad bid/ask prices for each quoaio. Daily series for he overigh cash, 30, 90 ad 180 day bak acceped bills raes were obaied from he Reserve Bak of Ausralia. The ieres rae for loas maurig a he expiraio dae of he fuures was esimaed usig liear ierpolaio bewee hese four referece ieres raes. A daily divided series was obaied from Bloomberg. The divided series coais he oal acual cash divideds ad gross divideds (cash divideds plus impuaio credis) paid each ex-divided day by 13 A excepio is he December 2002 corac which expired o 9 December Observaios for 11 Jauary 2002 ad 2 May 2003 wih average iraday mispricig give by equaio 3 of perce idicaig he fuures corac was uusually expesive ad perce idicaig he corac was uusually cheap respecively are excluded from he sample. 15 Soll ad Whaley (1987) provide evidece of price effecs associaed wih S&P 500 fuures corac expiraios. The cash seleme feaure of idex fuures coracs requires arbirageurs o uwid posiios i he sock marke. Abormal sock price movemes may arise if may arbirage programs are beig uwoud i he same direcio a he opeig call aucio o he expiraio day. 7

8 socks i he S&P/ASX Our mispricig esimaes are based o he assumpio ha he divided amous ad frakig perceages are kow from he expiry dae of he previous corac. The discree ad seasoal divided paymes of he S&P/ASX 200 idex porfolio are ake io accou by usig he acual ex-pos daily divided iflows for he baske socks, which Harvey ad Whaley (1992) show reduces pricig errors ha occur whe cosa divided yields are assumed. I calculaig he differeces bewee acual ad heoreical idex fuures prices, fuures price quoes ad idex values ha are approximaely five miues apar ad ha are he laes available before he ed of each five miue mark are used. The bidask midpoi price prevailig a he ed of each five miue ierval is ake o represe he acual fuures price 17. I he same way, he mos rece idex value repored o he marke before he ed of he five miue ierval is ake o represe he acual spo marke price 18. While raders have access o he updaed idex level hroughou he course of he day, he idex calculaio uilises o-sychroous or sale prices especially for hily raded socks, so ha he ruly radeable price of he replicaig porfolio ca diverge emporarily from he isaaeously repored value 19. These price series are cosruced for every five miue ierval from 10:00 a.m. o 4:00 p.m. Sydey ime, which is he segme of he radig day whe boh he fuures ad cash markes are ope simulaeously i coiuous aucio mode. Observaios for which here were zero fuures radig volume are excluded o provide resuls comparable wih hose repored by Brailsford ad Hodgso (1997) 20. The fial sample cosiss of 66,040 observaios. The levels of auocorrelaio i he price chages for boh SFE SPI 200 TM fuures ad he S&P/ASX 200 spo price series are show i able 1. The auocorrelaios of he fuures price chages are close o zero a all e lags, alhough are slighly egaive a he firs ad secod lags cosise wih raders pickig off liquidiy usig marke orders whe i becomes available a improved quoe prices. More oiceably, he idex series is posiively auo-correlaed a he firs lag wih a firs order auocorrelaio coefficie of 0.19 similar o ha repored by Brailsford ad Hodgso (1997) for he Ausralia All Ordiaries idex (0.20). This behaviour is cosise wih he presece of sale prices i he available idex values (described by Fisher, 1966). 16 Daily divided paymes of baske socks are uavailable for oher sudies. For example, Brailsford ad Hodgso (1997) rely upo published Ausralia All Ordiaries idex divided yields ha were oly available o a mohly basis i order o form ex-ae expecaios abou divided yields. 17 Quoe midpoi prices are used o miimise he effec o he mispricig series of bid-ask bouce i he fuures marke. Similarly, Bühler ad Kempf (1995) use he mea of he curre bid-ask quoes for fuures coracs ad ieres raes o calculae he relaive mispricig of Germa sock idex fuures. 18 As he sock idex values are clocked approximaely hiry secods apar, hey will be updaed o average fifee secods before he five miue mark. The deviaios from heoreical pricig levels compued from hese values may be slighly upward biased due o he momeary delay uil he ed of he each ierval. 19 The idex is updaed usig rasacio prices ad does o use he bid ad offer quoes for he compoe socks. This problem may be exacerbaed i he relaively hily raded Ausralia sock marke because o all socks i he idex rade every five miues. The problem of o-sychroous radig i he fuures marke is overcome by usig he bid-ask midpoi price prevailig a he ed of each ierval. 20 As a resul, 730 observaios were removed represeig 1.1 perce of he origial sample. 8

9 Table 1 Auocorrelaios for chages of he logarihm of price i SFE SPI 200 TM fuures ad he S&P/ASX 200 idex Log of price raios SFE SPI 200 TM S&P/ASX 200 fuures idex Auocorrelaio coefficies ρ * * ρ * * ρ ρ ρ ρ ρ ρ ρ ρ Auocorrelaios are based o five miue observaio iervals. *Deoes sigificace a he 1% level. 2.2 Variable measureme Published empirical work o sock idex fuures pricig has implicily assumed ha ivesors face he same margial ax rae o all forms of icome ad employ oly he cash value of divideds. These assumpios ca lead o sigificaly biased esimaes of fuures mispricig i a marke like Ausralia, where ieres ad divided icome are axed more harshly ha capial gais o socks ad a impuaio sysem provides ivesors wih a ax credi o fraked divideds (see Cummigs ad Frio, 2008). Assumig he followig ivesors do o defaul o ay corac; o moey chages hads hrough markig o marke durig he lifeime of he corac, oly o he mauriy dae; all ivesors ca borrow ad led a he same o-sochasic ieres rae; he cash divided yield ad impuaio credi yield of he idex over he remaiig life of he ear fuures corac are kow i advace; o rasacio coss; ad o resricios o shor sales he heoreical price of a fuures corac uder he ax-adjused cos-of-carry model developed by Cummigs ad Frio (2008) is: f T r( T ) r( T s), T p) = S + (1 1) S (e 1) γ 1 Dse s= + 1 ( τ γ IC (1) T 2 s= + 1 s 9

10 where f,t (p) = he fair value a ime of a idex fuures corac wih parially valued carry compoes maurig a ime T; S = he spo idex value a ime ; r = he aualised risk-free ieres rae a ime for repayme a ime T; D s = he aggregae divided cash flows o he idex associaed wih a exdivided dae s; IC s = he aggregae impuaio credis for he baske socks i he idex associaed wih a ex-divided dae s; τ 1 = he reducio i he fiacig cos achieved hrough he ax deducibiliy of oe dollar of ieres o loas; γ 1 = he value of oe dollar of accumulaed cash divideds allowig for he harsher ax reame of divided icome relaive o capial gais o socks; ad γ 2 = he value of oe dollar of impuaio credis. The accumulaed value of cash divideds o he uderlyig socks over he remaiig life of he corac are calculaed o he assumpio ha he forward ieres rae a ime for loas made a ime s o be repaid a ime T is ideical o he spo ieres rae a ime s for loas maurig a ime T. Subsiuig he values of he parameers τ 1 = 0.066, γ 1 = ad γ 2 = esimaed by Cummigs ad Frio (2008) for SFE SPI 200 fuures over he same sample period, he heoreical fair price of a fuures corac a ime wih mauriy dae T is give by: f, T ( p) = S S (e T s= + 1 IC s r( T ) 1) T s= + 1 D e s r( T s) (2) The ax-adjused mispricig series is defied as: M ( p) = log F log f, ( p) (3) T where F is he acual fuures bid-ask midpoi price ad f,t (p) is he heoreical fuures price a ime for a corac expirig a ime T usig he ax-adjused cos-ofcarry model. 10

11 3. Empirical resuls Secio 3.1 repors o he behaviour of he mispricig series. I secio 3.2 a ime series ad regressio based approach is ake o explai he mispricig series. 3.1 Behaviour of he mispricig series Table 2 provides descripive saisics for he mispricig series. The overall mea pricig error is close o zero ( perce) wih a sadard deviaio of perce 21. The average mispricig is lowes for he Jue 2002 corac ( perce) ad highes for he Sepember 2003 corac (0.060 perce). These esimaes are closer o zero ha he esimae of perce provided by Brailsford ad Hodgso (1997) for average mispricig of he former Ausralia All Ordiaries Share Price Idex fuures corac employig oly he cash value of he divided. The resuls are cosise wih he hypohesis ha he adjused cos-of-carry pricig model allowig for he differe ax reame of ieres ad divideds versus capial gais o socks ad he marke value of impuaio ax credis produces a ubiased esimae for he fuures price 22. Slighly more ha half of he observaios (51.8 perce) are egaively mispriced. This resul could be due o he relaively higher coss of shor sellig whe he arbirage sraegy calls for shorig raher ha buyig socks (also oed by Modes ad Sudaresa, 1983 i he Uied Saes; Fug ad Draper, 1999; 2003 i Hog Kog; Breer, Subrahmayam ad Uo, 1989a i Japa; Gay ad Jug, 1999 i Korea; Vipul, 2005 i Idia; Kempf, 1998 i Germay; Puoe ad Marikaie, 1991; ad Puoe, 1993 i Filad; ad Brailsford ad Hodgso, 1997 i Ausralia). Mispricig is predomialy posiive i some periods ad egaive i oher periods, as show i previous empirical work (for example, Figlewski, 1984b; Klemkosky ad Lee, 1991 i he Uied Saes; Breer, Subrahmayam ad Uo, 1989a; 1989b; 1990 i Japa; Yadav ad Pope, 1994; Buerworh ad Holmes, 2000 i he Uied Kigdom; ad Bowers ad Twie, 1985 i Ausralia). 21 Whe measured as he simple differece bewee he acual ad heoreical idex fuures corac price, he average mispricig over he eire sample is pois ad he sadard deviaio is 3.85 pois, where each idex poi is valued a AUD Similarly for he S&P 500 fuures corac, Klemkosky ad Lee (1991) fid ha he frequecy of pricig violaios oably decreases whe axes are cosidered i he aalysis. 11

12 Table 2 Summary saisics o he levels of mispricig i SFE SPI 200 TM Idex Fuures coracs employig he ax-adjused cos-of-carry model, by expiraio (5-miue quoe sapsho daa, mispricig i perce of heoreical fuures price) M (p ) Mea Sd. dev. % % Number posiive Number egaive Corac Mar ,903 1,981 3,884 Ju ,048 3,072 4,120 Sep ,747 2,580 4,327 Dec ,726 1,098 3,824 Mar ,538 1,821 4,359 Ju ,138 1,245 3,383 Sep , ,376 Dec ,413 2,863 4,276 Mar ,539 2,336 3,875 Ju ,352 1,744 4,096 Sep ,710 1,572 4,282 Dec ,419 1,775 4,194 Mar ,780 2,327 4,107 Ju ,786 2,325 4,111 Sep ,056 3,329 4,385 Dec ,295 3,146 4,441 Overall ,843 34,197 66,040 N Noe: M (p ) = log F - log f,t (p ) where F is he fuures bid-ask midpoi price ad f,t (p ) is he heoreical fuures price employig he ax-adjused cosof-carry model. 3.2 Modellig mispricig I his secio, he ime series ad regressio based approach o explaiig he mispricig series adoped by Brailsford ad Hodgso (1997) is exeded o icorporae he impac of uexpeced iformaio arrival i boh he cash ad fuures markes ad risks ad rasacio coss faced by arbirageurs. The modellig process is uderake i wo sages. Firs, he dyamic ad saic ime series compoes are filered ou by applyig he followig model o raw mispricig. M 25 = β jm j + β 26M d + β 27M 2d j= + β 28D1 + β 29D2 1 (4) + β D β D β D ε The depede variable M is defied as he differece i logarihms bewee he marke fuures price ad is heoreical price, ha is M = log F log f,t, β 1 o β 27 are dyamic auoregressive parameers where is he five-miue sample ierval ad d is oe radig day, D 1, D 2,, D 5 are zero-oe dummy variables o es wheher here are sysemaic ad fixed mispricig paers relaed o each day of he week where D 1 = Moday,, D 5 = Friday 23. This model allows a compariso o previous 23 Garbade ad Silber (1983) specify a model which describes he ierrelaioship bewee cash marke prices ad fuures prices of sorable commodiies as a firs-order auoregressive process. The 12

13 domesic ad overseas sudies which have ideified srog firs order auocorrelaio ad day of he week effecs i he mispricig series. Selec resuls for he ime series aalysis usig equaio 4 o he ax-adjused mispricig series are show i able 3. For he auoregressive parameers, oly he sigifica esimaes are repored. Table 3 Dyamic ad fixed ime series compoes of he ax-adjused mispricig series Esimae Variable Coefficie β * Mispricig lag 1 ierval β * Mispricig lag 2 iervals β * Mispricig lag 3 iervals β * Mispricig lag 4 iervals β * Mispricig lag 5 iervals β * Mispricig lag 6 iervals β * Mispricig lag 7 iervals β * Mispricig lag 8 iervals β * Mispricig lag 9 iervals β * Mispricig lag 10 iervals β * Mispricig lag 11 iervals β * Mispricig lag 12 iervals β * Mispricig lag 15 iervals β * Mispricig lag 25 iervals β * Mispricig lag 2 days β * Moday dummy β Tuesday dummy β * Wedesday dummy β Thursday dummy β Friday dummy adj R F 6,427.55* N 66,040 *Deoes sigificace a he 1% level. Coefficies are muliplied by The resuls i able 3 cofirm ha he mispricig of SFE SPI 200 fuures is highly predicable; cosecuive auoregressive coefficies are uiformly posiive ad sigifica ou o welve iervals as well as 144 iervals, equivale o wo radig days. The sigificace of he cosecuive auoregressive coefficies idicaes a high degree of persisece i he mispricig series, cosise wih ifreque radig i he uderlyig socks (Miller, Muhuswamy ad Whaley, 1994) 24. I combiaio wih he auoregressive effecs, mispricig is sigificaly higher o Moday ad sigificaly lower o Wedesday ha o oher days of he week. Afer pre-filerig usig he model specified i equaio 4, he absolue values of he residuals are obaied. The mea absolue residual is perce wih a sadard auoregressive parameer δ i heir model measures he (iverse of) he elasiciy of supply of arbirage services. Furhermore, Wag ad Yau (1994) show ha he esimaed firs-order auoregressive coefficie of he mispricig series ca measure he degree of marke likage if i is saisically differe from oe. 24 The persisece i he mispricig series is cosise wih Klemkosky ad Lee (1991), who fid ha a arbirage posiio is sill profiable e miues afer i is iiially ideified as profiable. 13

14 deviaio of perce as show i able 4 pael A. The relaioship bewee ime o mauriy ad he absolue residuals is illusraed i figure 1. The absolue residuals are greaer i he firs half of he expiry cycle. Sice he residuals represe he upredicable iovaios i fuures corac mispricig, his is cosise wih idex arbirage beig more risky furher ou from mauriy. Figure 1 Time-o-expiry paer i he absolue value of he pre-filered mispricig series employig he ax-adjused cos-of-carry model ε (p ) (%) Tradig days The impac of explaaory variables is esimaed usig he followig model. ε = α + β Opeig β UVolume 4 + β UDivided 8 + β UVolume US 5 + β Opeig c + β IVIeres 9 + β Close 6 US + β MICos 10 + β Volailiy + β TExpiry β BCos 11 + ε (5) A umber of possible explaaory variables are cosidered before cosrucig he above model. Descripive saisics (pael A) ad correlaios bewee he variables represeig he risks ad rasacio coss faced by arbirageurs (pael B) are preseed i able 4. The explaaory variables are defied as follows. Opeig1 ad Opeig2 are zero-oe dummy variables for he firs wo iervals a he opeig of sock radig edig a a.m. ad a.m. respecively, icluded o assess he possible impac of opeig procedures i he sock marke. US is he absolue value of he overigh Uied Saes reur o he S&P 500 sock idex which is oly acivaed a a.m. ad a.m.. This variable is icluded o es wheher he volailiy from he Uied Saes marke, which acs as a proxy for overigh public iformaio arrival, has a impac o he mispricig series i he smaller depede Ausralia marke. Volailiy is he price volailiy of SFE SPI 200 fuures where volailiy is measured i accordace wih Bessembider ad Segui (1992) as: 14

15 Volailiy log( F ) log( F 1) π 2 (6) = This variable is used o verify wheher iraday price movemes i he fuures marke have a sigifica impac o he mispricig series. Fuures prices are more variable ha for he idex, cosise wih previous research by Hill, Jai ad Wood (1988), MacKilay ad Ramaswamy (1988) ad Yadav ad Pope (1990). This suggess ha ew iformaio is icorporaed wih greaer speed i he fuures marke. There does o appear o be ay ime o expiraio paer i he volailiy of spo ad fuures prices, ploed i figure Figure 2 Time-o-fuures-expiry paers i price volailiy ad bid-ask spreads Volailiy (x 100) Tradig days Bid-ask spread (%) Fuures volailiy Sock idex volailiy Fuures bid-ask spread Uderlyig socks bid-ask spread UVolume ad UVolume c are uexpeced radig volume of SFE SPI 200 fuures ad heir uderlyig socks respecively. The measure of radig volume for he fuures marke i a give ierval is simply he umber of ear mauriy coracs raded. The sock marke urover raio is used o proxy for he radig volume of he uderlyig socks. I is calculaed as he value of oal shares raded divided by he aggregae floa-adjused marke capialisaio of he idex cosiues. Followig Bessembider ad Segui (1993), ARIMA models are used o decompose volume io is expeced ad uexpeced compoes 26. Repeaed ess o he sample do o give ay firm evidece of improveme whe movig beyod ARMA(1,2) for he fuures mauriies ad ARMA(1,1) for he cash marke volume series 27. To he ARMA 25 This is cosise wih prior research by Grammaikos ad Sauders (1986) based o five differe foreig currecy fuures raded o he Ieraioal Moeary Marke, which fids ha while mauriy has a srog effec o volume of radig, o such relaio could be foud for price volailiy. Likewise i he spo equiy marke, Bessembider ad Segui (1992) fid o evidece ha S&P 500 volailiy varies sysemaically wih he ime uil mauriy of equiy idex fuures coracs. Figure 2 appears o cofirm ha iformaio arrival i he spo ad fuures markes is radom across corac mauriy. 26 The saioariy of each ime series was assessed usig augmeed Dickey-Fuller ess. The exisece of a ui roo is rejeced for all sixee fuures mauriies ad he cash marke volume series. 27 Schwarz s Bayesia crierio is used o deermie he orders of he auoregressive ad movig average pars i he ARIMA models. Regressios are ru usig a umber of differe ARIMA specificaios ad hese do o seem o ifluece he resuls. 15

16 models dummy variables are added for he opeig ad close of sock radig 28. Deoig he raw radig volume as V, uexpeced volume is expressed as: UVolume = log( V ) log E( V ) (7) The level of radig aciviy i boh he fuures ad sock markes varies cyclically, wih he highes levels of aciviy occurrig ear corac expiraio. Mea spo ad fuures radig volume for each of he sixy days o expiraio are show i figure 3. Fuures radig volume is relaively sable, he icreases rapidly ad peaks o he hird las radig day as raders close ou posiios i he ear corac. Spo radig volume is ypically higher a he ed of caledar mohs ad o fuures expiraio days 29. Figure 3 Time-o-fuures-expiry paers i radig aciviy Volume ('000) Relaive volume (%) Fuures volume Fuures ope ieres Uderlyig socks volume Tradig days 0.0 Close is a zero-oe dummy variable for he close of sock radig a 4.00 p.m. o capure possible effecs from raders exiig he marke before closig i order o avoid he risk of holdig posiios overigh. TExpiry is ime-o-expiry expressed as a fracio of a year, icluded o es for he ime-depede risks of idex arbirage ha simulaeously improve he implici opio compoe i a arbirage posiio. UDivided represes he uceraiy abou he magiude of divideds paid ou by uderlyig socks. Aalys-by-aalys fiscal year 1 divided forecass for all covered socks are exraced from he I/B/E/S Daily Deail Earigs Esimaes Hisory 28 The cash marke volume series is also augmeed wih a dummy variable correspodig o exraordiarily high sock marke urover of AUD 11.8 billio (1.48 perce of marke capialisaio) bewee 11:05 ad 11:10 a.m. o 5 July A weekly paer evide i figure 3 suggess ha spo radig volume is lowes o Modays (usually day 3, 8, 13 ad so forh before he hird Thursday of he expiry moh), possibly due o he lack of a immediae lead from he New York Sock Exchage i resolvig he implicaio of ew iformaio for equiy prices. 16

17 daabase 30. All esimaes ha are curre o a paricular day (idicaed by he esimae dae ad review dae) are used o calculae he sadard deviaio of divided per share (DPS) forecass for a idividual sock. Two assumpios are made i proceedig o cosruc a measure of divided uceraiy for he idex as a whole from he sadard deviaios for idividual socks: (i) he spread of (equally weighed) aalyss forecass represes he probabiliy disribuio for fuure divideds; ad (ii) he DPS forecass for idividual socks are ucorrelaed. O he basis of hese assumpios, divided yield uceraiy for he idex is give by he weighed average sadard deviaio of aalyss forecass for cosiue socks: 200 ( Sharesi, SdDev( FDPSi, )) i= 1 = 200 UDivided (8) ( Sharesi, Pi, ) i= 1 where FDPS i, are aalyss fiscal year 1 divided per share forecass for sock i, Shares i, is he umber of shares of sock i icluded i he idex calculaio ad P i, is he closig price of sock i o day. This variable is icluded o capure possible effecs relaed o he dispersio of aalyss divided forecass. The mea divided yield uceraiy as idicaed by his measure is 0.07 o 0.08 perce hroughou he corac life cycle as show i figure 4. ADivided is a aleraive measure of he ime-o-expiry, defied as he proporio of oal gross divideds paid by uderlyig socks wih ex-divided daes fallig wihi he curre fuures corac life cycle (from he expiry dae of he previous corac uil he expiry dae of he curre ear corac) ha are aouced over he remaiig life of he ear corac 31 : 200 T1 ( Sharesi, DPSi, a ) i= 1 a= + 1 T1 ( Sharesi, DPSi, w ) ADivided (9) = 200 i= 1 w= T0 + 1 where DPS i,a is he gross divided aouced for sock i o day a wih he releva ex-divided dae scheduled o occur before he ear corac expires o day T 1 ad DPS i,w is he gross divided for sock i wih a ex-divided dae w fallig bewee he expiraio of he previous fuures corac o day T 0 ad he expiraio of he curre ear fuures corac o day T 1. The aouceme of divided amous ad ex-divided daes resolves uceraiy relaig o boh he magiude ad imig of divideds 32. The schedulig of ex-divided daes ha accompaies divided 2 30 Each divided forecas record coais broker ad aalys codes, he forecas period ed dae, he esimaed divided i ces per share, he dae he esimae was eered io he daabase (esimae dae) ad he mos rece dae ha he esimae was cofirmed as accurae (review dae). 31 A daily divided series for idividual socks obaied from Bloomberg ideifies he aouceme daes, ex-divided daes ad payme daes associaed wih e ad gross divideds per share paid by socks i he S&P/ASX Peers (1985) shows ha he icreasig efficiecy of idex fuures markes hrough ime appears o be due o beer esimaio of he divided sream for each idex ad is ueve characerisics. 17

18 aoucemes could subsaially reduce uceraiy, if i was upredicable wheher some divideds would be assiged ex-divided daes before or afer fuures corac expiraio relyig upo he imig of correspodig divideds i previous years. Figure 5 shows he proporio of oal gross divideds ha remai uaouced agais he ime o mauriy of he corac. The frequecy of divided aoucemes (refleced i he slope of he curve) icreases aroud he middle of he fuures corac life cycle, ogeher wih he periodic reporig of Ausralia compay resuls. Almos all compaies goig ex-divided before fuures mauriy have declared heir divideds by hree weeks ou from mauriy. IVIeres is he volailiy implied i ieres rae opio prices, expressed as a aualised perceage. Ieres rae opio coracs based o 90 Day Bak Acceped Bills Fuures are raded o he Sydey Fuures Exchage ad expire o he firs Friday of he delivery moh for he uderlyig fuures corac. Up o six mauriies correspodig o he bak bill fuures quarerly mauriy cycle ad several exercise prices were available a ay oe ime. The implied volailiy esimaes used i his sudy are hose provided by marke paricipas ad used by he Sydey Fuures Exchage o deermie daily closig prices for eares-o-expiry pu ad call opios which are closes o beig a-he-moey. Ex-ae volailiy is relaively greaer i ieres raes (0.12 perce) ha divided yields (0.08 perce) ad may play a impora role i deermiig he mispricig series. From figure 4, he implied volailiy of ieres rae opios furher ou from mauriy is higher ha ha close o mauriy (akig io cosideraio ha opios o bak bill fuures expire earlier i he delivery moh ha SFE SPI 200 fuures) 33. REcoomic is aoher aleraive measure of he ime-o-expiry, defied as he proporio of ecoomic releases fallig wihi he curre fuures corac life cycle ha are scheduled o occur over he remaiig life of he ear corac: T 1 EIRr r= + 1 REcoomic = T (10) EIR 1 r = T0 + 1 r where EIR r is he umber of separae ypes of ecoomic releases o day r bewee he expiraio of he previous fuures corac o day T 0 ad he expiraio of he curre ear fuures corac o day T 1. Daa for macroecoomic ews releases were obaied from Bloomberg s Ecoomic Caledar. The releases seleced were hose foud by Coolly ad Kohler (2004) o have a sigifica effec o ieres rae expecaios for Ausralia: he cosumer price idex, employme, he uemployme rae, gross domesic produc, buildig approvals, he rade balace, iveories, 33 I compariso, Ami ad Moro (1994) deermie a daily ime series of forward rae volailiies mos cosise wih Eurodollar fuures opios prices o he Chicago Mercaile Exchage (CME). They fid ha he volailiy of loger-erm forward raes is higher ha ha of shor-erm raes. Similarly, Neely (2005) observes ha log-horizo implied volailiies ed o be larger ha shorhorizo implied volailiies of opios o Eurodollar fuures. 18

19 ivesme ad reail sales 34. These ypes of ecoomic releases resolve ieres rae uceraiy because hey provide iformaio which eables marke paricipas o reassess he likely oucome of subseque Reserve Bak decisios o ieres raes 35. Figure 5 shows hey are relaively evely spread over he fuures corac life cycle, excep icrease i frequecy i he hird las radig week ad are ever scheduled i he las week before expiraio. Figure 4 Time-o-fuures-expiry paers i divided yield uceraiy ad ieres rae volailiy Sadard deviaio (%) Ieres rae opios Divided yield forecas Tradig days Figure 5 Time-o-fuures-expiry paers i divided aoucemes ad ecoomic releases Aoucemes (%) Ecoomic releases Divided aoucemes Tradig days 34 Alhough we cofie ourselves o domesic ecoomic releases i his sudy, Coolly ad Kohler (2004) fid ha foreig marke movemes modelled as chages i Uied Saes ieres rae fuures prices are also impora i explaiig chages i ieres rae expecaios for Ausralia. 35 The Reserve Bak Board formulaes moeary policy wih regard o developmes i he Ausralia ad ieraioal ecoomies. 19

20 MICos is he marke impac cos ivolved i opeig a idex arbirage posiio, measured as he sum of oe-half he bid-ask spread i he sock marke ad oe-half he bid-ask spread i he fuures marke 36. A perceage bid-ask spread (BAS) is compued for every quoaio as: BAS = [(ask - bid)/(ask + bid)/2]. Followig McIish ad Wood (1992), ime-weighed bid-ask spreads for boh fuures ad idividual socks i each ime ierval are calculaed as follows: BASpread j= 1 = BAS j= 1 j w w j j (11) where BAS j = he perceage quoed bid-ask spread; w j = he legh of ime ha spread j is ousadig; ad = he umber of differe bid-ask spreads ha occur durig ierval. I he case of he cosiue socks i he idex, he perceage bid-ask spreads for idividual socks are furher weighed accordig o he floa-adjused weigh of each sock i he idex, such ha he bid-ask spreads of socks wih he greaes weigh i he idex have he greaes weigh i he composie measure of idex perceage bidask spread. The mea bid-ask spreads are approximaely 0.03 perce i he fuures marke ad 0.18 perce i he sock marke hroughou he corac life cycle as show i figure 2. The subsaially wider bid-ask spread for he uderlyig socks ha for he fuures suggess i has a greaer ifluece o he widh of he radig bad for fuures prices. Bid-ask spreads are also more variable i he sock marke ha i he fuures marke. BCos is he miimum idicaive fees for he use of borrowed securiies repored by Kig (2005a) of 25 basis pois per aum for ASX 200 idex socks ad 5 basis pois per aum for bak acceped bills. The sock borrowig fee for sell programs is applied whe he mispricig is egaive ad he lower bak acceped bills borrowig fee for buy programs is applied whe he mispricig is posiive. Ieres is he logarihm of he ed-of-day ope ieres i SFE SPI 200 fuures measured i umber of coracs. Ope ieres accumulaes seadily across he corac life cycle ad he dissipaes rapidly from he hird las radig day, as show i figure 3. The correlaio bewee he ope ieres ad he ime-o-expiry is (see able 4, pael B). 36 The bid-ask spreads ad price impac coss of closig ou boh he sock ad fuures posiios ca be avoided by holdig he posiios uil he las radig day ad employig marke-o-ope orders i he sock marke. 20

21 Table 4 Summary saisics for eire daase Pael A: Descripive saisics Absolue ax-adjused residual ε (p ) Overigh reur o S&P 500 idex US Fuures five-miue volailiy S&P/ASX 200 idex five-miue volailiy Fuures five-miue volume Uderlyig socks five-miue volume Divided yield uceraiy Ieres rae opios implied volailiy Marke impac cos Borrowig cos Fuures ope ieres Ui Mea Media Sd dev N % ,040 % ,239 % x π / ,040 % x π / ,040 Los ,040 % ,032 % p.a ,040 % p.a ,685 % ,032 % ,040 Los 159, ,755 22,933 65,627 Pael B: Correlaio marix TExpiry UDivided ADivided IVIeres REcoomic UDivided ADivided IVIeres REcoomic MICos BCos Ieres MICos BCos The explaaory variables which ac as proxies for he uexpeced arrival of iformaio i he fuures ad sock markes ad he close of radig i he sock marke, while corollig for specific risks ad rasacio coss faced by arbirageurs, are cosidered usig equaio 5. Whie s procedure is used o obai heeroskedasiciy-correced sadard errors of he parameer esimaes (Whie, 1980). All -saisics are adjused accordigly. The resuls are preseed i able 5. Table 5 Esimaio of he explaaory coefficies for he absolue value of he pre-filered mispricig series employig he ax-adjused cos-of-carry model Esimae Variable Coefficie α Iercep β * Impac of overigh US reur a a.m. β * Impac of overigh US reur a a.m. β * Volailiy of SFE SPI 200 fuures β * SFE SPI 200 fuures uexpeced volume β * Uderlyig socks uexpeced volume β * S&P/ASX 200 close a 4.00 p.m. β * Time-o-expiry β Divided yield uceraiy β * Ieres rae opios implied volailiy β * Marke impac cos β Borrowig cos adj R N 63,871 *Deoes sigificace a he 1% level. Coefficies are muliplied by The coefficies o he variables desiged o capure he impac of volailiy from he Uied Saes sock marke (β 1 ad β 2 ) are posiive ad sigifica. A overigh price 21

22 moveme of oe perce i he Uied Saes sock marke is associaed wih icreases i he absolue residual mispricig of 0.07 perce a a.m. ad 0.06 perce a a.m. immediaely afer he opeig of he local sock marke. The icreased mispricig spread a a.m. is cosise wih he impac of opeig procedures i he sock marke lasig ie miues. Beyod he firs ierval, he persisely higher mispricig spread a a.m. suppors he proposiio ha foreig marke movemes sigal icreased radig risk, which i ur dampes opeig arbirage aciviy. The impac of volailiy i SFE SPI 200 fuures prices is posiive ad highly saisically sigifica 37. A price moveme of oe perce i he fuures marke is associaed wih a icrease i he mispricig spread of / π/2 = 0.26 perce. This resul is cosise wih he hypohesis ha marke-wide iformaio is icorporaed wih greaer speed i he fuures marke relaive o he uderlyig sock marke. The impac of surprise radig volume i he fuures is also posiive ad saisically sigifica. I coras, surprise radig volume i he uderlyig socks is egaive ad saisically sigifica 38. This suggess ha radig aciviy i execuig he cash leg of arbirage rasacios domiaes radig aciviy based o firm specific iformaio i movig spo prices. Surprise volume i he uderlyig socks more ofe sigifies he presece of arbirageurs acig o arrow price discrepacies relaive o he fuures marke 39. Alhough he coefficie which accous for he close of radig (β 6 ) is saisically sigifica, he icrease i he mispricig spread a he close of he sock marke is icosequeial i magiude. The coefficies o he volailiy implied i ieres rae opio prices (β 9 ) ad he ime-o-expiry (β 7 ) are posiive ad sigifica, implyig ha he higher he ex-ae ieres rae volailiy ad he loger he ime-o-expiry, he higher is he mispricig spread. The fidig wih respec o ime-o-expiry is robus o he hree differe ime measures (TExpiry, ADivided ad REcoomic ). The variable which proxies for divided yield uceraiy is saisically isigifica. These resuls idicae ha exae ieres rae volailiy is he primary source of risk faced by arbirageurs whe hey ac upo deviaios from heoreical pricig levels for loger imes o mauriy. As he absolue residual mispricig measures he volailiy of he irregular compoe of he mispricig series, hese resuls also imply ha ex-ae ieres rae volailiy i combiaio wih he ime uil corac expiraio are he source of he implici opio value i arbirage posiios. Through is ifluece o ieres rae volailiy, 37 The coemporaeous relaioship documeed here poreds he iraday emporal relaioship characerised by Cha ad Chug (1993) i he Uied Saes: higher iraday volailiy is followed by a sigifica decrease i he arbirage spread, probably because higher marke volailiy ivies more arbirage services or eables faser price adjusmes which, i ur, arrow he spread. 38 Regardig he relaioship bewee explaaory variables, Merrick (1987) provides srog evidece ha cash idex reur volailiy causes aggregae cash marke volume. Therefore, i aempig o discer he relaioship bewee he iraday mispricig spread ad surprise radig volume i he uderlyig socks, i is appropriae o have employed a measure of iraday price volailiy o help corol for volume surprises urelaed o arbirage moives or firm specific iformaio. 39 This fidig is cosise wih he evidece provided by Furbush (1989) ha idex arbirage respods o basis error ad has he effec of elimiaig i, hus aligig cash ad fuures prices. I also complemes he evidece of a sigifica uidirecioal relaioship ruig from he fuures corac mispricig spread o cash marke volume foud by Merrick (1987), usig daily daa for he New York Sock Exchage Composie idex marke. 22

23 public iformaio arrival has a more lasig effec o he mispricig spread ha from he faser speed of adjusme of iraday fuures prices relaive o sock prices. The coefficie o he marke impac cos ivolved i opeig up idex arbirage posiios (β 10 ) is posiive ad sigifica. A icrease of oe perce i he marke impac cos is associaed wih a icrease i he absolue residual mispricig of 0.10 perce. This resul wih respec o implici rasacio coss demosraes ha flucuaios i he cos of immediacy i he sock ad fuures markes have he mos impora ifluece o he widh of he arbirage bouds for idex fuures. I coras, he securiies borrowig cos coefficie (β 11 ) is posiive ad isigifica. While he posiive coefficie o he borrowig cos implies ha shor arbirage posiios are more expesive o maiai over loger holdig periods, here is oly weak evidece ha he pricig of he ear corac deviaes from is heoreical level more frequely as a cosequece of he cos of borrowig idex socks. 3.3 Robusess ess Addiioal regressio aalysis is repored i his secio o provide resuls ha are direcly comparable wih Brailsford ad Hodgo s (1997) examiaio of sock idex fuures pricig usig he former Ausralia All Ordiaries Share Price Idex fuures corac. I paricular, Brailsford ad Hodgso implicily assume ha ivesors face he same margial ax rae o all forms of icome; hey do o obai ay reducio i he cos of fiacig he se of shares of he uderlyig idex hrough he ax deducibiliy of ieres o loas (τ 1 = 0), he full cash value of he divided is employed (γ 1 = 1) ad he impuaio ax credis are o priced i idex fuures (γ 2 = 0). Based o hose assumpios, equaio 1 for he heoreical price of a fuures corac ca be reduced as follows: f T r( T ) r( T s), T c) = S e Dse s= + 1 ( (12) where f,t (c) is he fair value a ime of a idex fuures corac wih cash divideds. The uadjused mispricig series is defied as: M ( c) = log F log f, ( c) (13) T where F is he acual fuures bid-ask midpoi price ad f,t (c) is he heoreical fuures price a ime for a corac expirig a ime T usig he uadjused cos-ofcarry model. For he uadjused series, he overall mea pricig error is egaive ( perce) wih a sadard deviaio of perce as show i able 6 pael A. This resul is cosise wih he hypohesis ha he uadjused forward pricig model gives a upward biased esimae for he fuures price 40. Selec resuls for he ime series 40 Several overseas sudies fid evidece of subsaial ad susaied mispricig usig he cos-of-carry pricig model wihou adjusme for he axaio reame of ieres ad divideds relaive o capial gais o socks. I he Uied Saes, Corell ad Frech (1983), Figlewski (1984a) ad Ardii, Ayaydi, Mau ad Rigsbee (1986) repor ha sock idex fuures were priced a a discou o he levels prediced by he carryig cos relaioship, while Bha ad Cakici (1990) ad Chug (1991) 23

24 aalysis usig equaio 4 o he uadjused mispricig series are show i able 6 pael B. The esimaed coefficies are similar o hose obaied usig he axadjused cos-of-carry model ad also cofirm Brailsford ad Hodgso s (1997) fidig ha he mispricig series i Ausralia is highly predicable 41. The iraday mispricig series evolves more gradually; higher auoregressive coefficies a subseque lags compesae for a lower coefficie a he firs lag of ha repored by Brailsford ad Hodgso for All Ordiaries Share Price Idex fuures (0.689). Negaive mispricig of All Ordiaries Share Price Idex fuures o Friday documeed by Brailsford ad Hodgso is prevale hroughou he laer par of he week (from Wedesday o Friday) i our sudy of SFE SPI 200 fuures 42. Excep for Wedesday, he day of he week effecs are sesiive o wheher he uadjused or ax-adjused model is used. The R 2 saisic of 0.81 is higher ha for he ime series compoes of he ax-adjused mispricig series. This implies ha he excess variaio i he uadjused mispricig series is explaied by ime series effecs; ay misspecificaio of he fiacig charge ad divided flow is serially correlaed a cosecuive pois across he corac life cycle. Resuls of esimaig equaio 5 wih he absolue residuals afer pre-filerig he uadjused mispricig series are repored i able 7. The resuls are o maerially differe from hose based o he ax-adjused series. Brailsford ad Hodgso s (1997) fidigs for All Ordiaries Share Price Idex fuures are verified for SFE SPI 200 fuures. I paricular, he impora role of boh exogeous ad edogeous fuures price volailiy i icreasig he mispricig spread is cofirmed for SFE SPI 200 fuures: he impac of volailiy from he overigh Uied Saes sock marke ad he volailiy of Ausralia fuures prices are boh posiive ad saisically sigifica. Moreover, uexpeced fuures radig volume is sigifica. The posiive coefficie o he ime-o-expiry documeed by Brailsford ad Hodgso is smaller ad saisically isigifica i our sample. This resul suggess ha he ihere opio value i he mispricig series has decreased as he pricig efficiecy of he Ausralia marke has improved i rece years. Wih he iclusio i he model of risks ad rasacio coss faced by arbirageurs, he iercep of perce is smaller ha observed by Brailsford ad Hodgso (0.030 perce). repor hey are priced a a premium. I Caada, Hog Kog, Korea, Idia, he Uied Kigdom, Germay ad Filad respecively, Chamberlai, Cheug ad Kwa (1989), Draper ad Fug (2003), Gay ad Jug (1999), Vipul (2005), Yadav ad Pope (1990), Bühler ad Kempf (1995) ad Kempf (1998), Puoe ad Marikaie (1991) ad Puoe (1993) provide evidece ha fuures ed o be priced a discous o heoreical values. 41 I compariso, MacKilay ad Ramaswamy (1988), Lim (1992) ad Bühler ad Kempf (1995) fid ha mispricig levels are highly posiively auocorrelaed for S&P 500 fuures across fifee-miue ime iervals, Nikkei 225 fuures across five-miue iervals ad DAX fuures across oe-miue iervals respecively. 42 This resul coradics he divergece bewee cash ad fuures marke behaviour o Friday repored by Yadav ad Pope (1992) i he Uied Kigdom. 24

25 Table 6 Dyamic ad fixed ime series compoes of he uadjused mispricig series M (c ) Variable Pael A: Descripive saisics Mea Media s. dev N 66,040 Pael B: Dyamic ad fixed ime series compoes β * Mispricig lag 1 ierval β * Mispricig lag 2 iervals β * Mispricig lag 3 iervals β * Mispricig lag 4 iervals β * Mispricig lag 5 iervals β * Mispricig lag 6 iervals β * Mispricig lag 7 iervals β * Mispricig lag 8 iervals β * Mispricig lag 9 iervals β * Mispricig lag 10 iervals β * Mispricig lag 11 iervals β * Mispricig lag 12 iervals β * Mispricig lag 15 iervals β * Mispricig lag 25 iervals β * Mispricig lag 2 days β Moday dummy β Tuesday dummy β * Wedesday dummy β * Thursday dummy β * Friday dummy adj R F 8,635.52* *Deoes sigificace a he 1% level. Coefficies are muliplied by Table 7 Esimaio of he explaaory coefficies for he absolue value of he pre-filered mispricig series employig he uadjused cos-of-carry model Esimae Variable Coefficie α Iercep β * Impac of overigh US reur a a.m. β * Impac of overigh US reur a a.m. β * Volailiy of SFE SPI 200 fuures β * SFE SPI 200 fuures uexpeced volume β * Uderlyig socks uexpeced volume β * S&P/ASX 200 close a 4.00 p.m. β Time-o-expiry β Divided yield uceraiy β * Ieres rae opios implied volailiy β * Marke impac cos β Borrowig cos adj R N 63,871 *Deoes sigificace a he 1% level. Coefficies are muliplied by

26 4. Coclusio A mispricig series usig five-miue coemporaeous observaios from he Ausralia S&P/ASX 200 spo idex ad SFE SPI 200 fuures marke over a period of four years is cosruced ad aalysed, usig he ime series ad regressio based approach of Brailsford ad Hodgso (1997). A ax-adjused cos-of-carry model, which accous for he discree ad seasoal divided paymes of he uderlyig socks, as well as he differe axaio reame of he fiacig charge ad divided flow relaive o capial gais o socks ad he pricig of he impuaio ax credis o fraked divideds, is used as he valuaio mehod for he fuures corac. Overall, he resuls idicae ha he mea pricig error is close o zero ad oiceably less volaile ha i oher sudies, cofirmig ha he ax-adjused marke valuaio model produces a relaively ubiased esimae for he fuures price. Slighly more ha half of he observaios are egaively mispriced, cosise wih he higher rasacio coss ivolved i shor sellig sock. Time series aalysis cofirms ha he raw mispricig exhibis a high degree of auocorrelaio ad predicabiliy. Mispricig based o he ax-adjused series is sigificaly higher o Moday ad sigificaly lower o Wedesday. Afer filerig ou he dyamic ad saic ime series compoes, a umber of explaaory variables are sigificaly associaed wih he absolue residual mispricig. Overigh public iformaio arrival modelled as volailiy from he Uied Saes sock marke ad marke-wide iformaio arrival modelled as uexpeced radig volume ad he volailiy of SFE SPI 200 fuures are cofirmed o have a posiive ad sigifica impac o he mispricig spread. I addiio, he egaive impac of uexpeced radig volume i he uderlyig socks is cosise wih he presece of idex arbirageurs acig o arrow price dispariies relaive o he fuures marke. I suppor of he differeial iformaio hypohesis, his fidig highlighs ha he adjusme of he uderlyig sock marke o macroecoomic iformaio is faciliaed by price discovery i he fuures marke. Idicaed by is impac o he mispricig spread, ex-ae ieres rae volailiy is he primary source of risk faced by arbirageurs whe hey ac upo deviaios from heoreical pricig levels furher ou from mauriy. From he sadpoi of he ceral bak herefore, he efficiecy of he arbirage mechaism is improved by smoohig shor-erm ieres raes. I coras, he impac o he ear corac of divided yield uceraiy based o he dispersio of aalyss forecass for idex cosiue socks is saisically isigifica ad appears o be rivial. The implici rasacio cos represeed i bid-ask spreads ivolved i opeig up sock ad fuures posiios have he mos impora ifluece o he widh of he arbirage bouds for idex fuures. Arbirageurs require greaer compesaio o sep io he marke whe bidask spreads for he idex cosiues are large. This follows because bid-ask spreads for he uderlyig socks are wider ad more variable ha i he fuures marke. There is lile evidece ha he pricig of he ear corac deviaes from is heoreical level more frequely due o he cos of borrowig socks. From he sadpoi of securiies exchages ad regulaors herefore, he efficiecy of he arbirage mechaism is improved by icreasig he level of liquidiy i he sock marke; hereby sregheig he mos vulerable poi relied upo o maiai he price likage bewee sock idex fuures ad heir uderlyig shares. 26

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