TheInternationalTransmissionofArbitrageInformationAcross
FuturesMarkets
CHRISBILSON,TIMBRAILSFORD
AND
TWMEVANS*
Abstract:Thispaperexamineswhetherdeviationsfromadomesticspot-futuresrelation,asidentifiedthroughmispricingseriesinstockindexfutures,spilloverinternationalboundaries.Suchspilloverssuggestthatinformationfromamispricingseriesinonemarketconveysasignalofsimilarmispricinginanothermarket.Inthepresenceofarbitragetradersandintheabsenceofmarketfrictions,mispricingseriesshouldbeindependentacrossinternationalboundaries.ThestudyemploysaVARanalysisofstockindexfuturesmispri-cingacrossthreelargefuturesmarkets–Australia,theUKandtheUSA.Usingtimezonedifferences,testsareconductedforthedailytransmissionofarbitrageinformation.Theresultsrevealtherelationshipbetweenmispricingseriesisbi-directional.Basedonthisfinding,atradingstrategyisemployedtoexaminetheeconomicsignificanceofapparentprofits.Theresultsshowthatsomeprofitsarepossibleaftertransactioncostsbutthatalonghorizon,probablybeyondthescopeofmosttraders,isrequiredtoexploitthespilloverinformation.
Keywords:stockindexfutures,futuresmispricing,spillovers,arbitrage,internationalfinancialmarkets
*TheauthorsarerespectivelyfromtheSchoolofFinance&AppliedStatistics,AustralianNationalUniversity;UQBusinessSchool,UniversityofQueensland,Australia;andUniversityofWales(Swansea),UK.(PaperreceivedSeptember2003,revisedandacceptedFebruary2004)
Addressforcorrespondence:TimBrailsford,UQBusinessSchool,UniversityofQueensland,StLucia4069,Australia.e-mail:t.brailsford@business.uq.edu.au
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1.INTRODUCTION
Theexistenceoflinkagesacrossinternationalmarketshasbeenwelldocumented,particularlyinrelationtostockmarketsindevelopedeconomies.Thedeclineininternationalinvestmentbarriersexperiencedoverthepasttwodecades,combinedwiththemarchtowardglobalisation,haveincreasedinternationalcapitalmovementswhichinturnhasacceleratedinter-marketcorrelationsofeconomicactivity.Associatedwiththesechangeshasbeenanapparenthigherdegreeofmarketintegrationandcorrelationofassetpricemovementsacrossmarkets.Asubstan-tialfocusofresearchinthisareahasbeenconcentratedonequitypricemovements,bothinrelationtoreturnco-movementsandvolatilityspillovers.Theevidencefromthesestudiessupportstheexistenceofcontagioneffectsand‘meteorshowers’acrossmarkets(e.g.,Hamaoetal.,1990).
Thedevelopmentofderivativesecuritieshasallowedinves-torstomoreeffectivelymanagetheirexposures.Inthepre-senceofarbitrageforces,thepricesofderivativeinstrumentscangenerallybespecifiedasafunctionofthepricesoftheirunderlyingasset.Hence,totheextentthatinternationalrela-tionsexistbetweenpricemovementsinspotmarketassets,itcanbereasonablyexpectedthatsuchrelationsshouldalsobepresentintheassociatedderivativeassets.Forinstance,iftwoequitymarketsexhibitco-movementthentheirstockindexfuturescontractsshouldalsoexhibitthesamerelation.Ifthiswerenotthecase,arbitrageopportunitieswouldbeapparentbetweenthespotandfuturesinatleastoneofthedomesticmarkets.Thisconceptcanbethoughtofmoreformallyinthecontextofcointegration.Specifically,iftwospotmarketsarecointegratedthenitisreasonabletoexpecttheirfuturesmarketstobesimilarlycointegrated.However,thereisonlylimitedevidenceontheextentofinternationallinkagesbetweenderivativemarkets.
Asanalternativetotestingforinternationalrelationsacrossderivativemarkets,amoredirectandpotentiallyrevealingtestwouldbetoexaminespilloversbetweenmispricingseries.Alargebodyofliteraturehasshownconsistentevidenceofsmallbutpersistentpatternsofmispricingindomesticfuturesmar-kets(e.g.,CornellandFrench,1983).Theaimofthispaperisto
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examinewhetherpotentialarbitrageopportunitiesidentifiedinonemarketcarryinformationsuchthattheycanpredictsub-sequentpotentialarbitrageopportunitiesinanothermarket.Specifically,thestudyfocusesonstockindexfuturesandtheirmispricingseries.Asanexample,thefuturesandspotmarketsbecamedelinkedinOctober1987andthequestionarisesastowhethersuchinstancesarewidespreadandwhethertheyflowovermarketboundaries.1Thereasonforthedeviationinthedomesticspot-futuresrelationisnotimportanthere.Rather,giventhatadeviationexists,thepaperseekstoexaminewhetherthedeviationspillsacrossmarkets.Inasimilarvein,KingandWadhwani(1990)attempttoexplainhowcommonfallsinstockmarketindicesareobservedaroundcrashdates.Despitedifferingeconomicconditions,theyproposethatpricechangesinforeignmarketsmaybesystematicallyinterpretedasrelevantinformationforthelocalmarket,eveniftheforeignmarketpricechangeisinducedbyidiosyncraticevents.
Thestudyhasimplicationsastotheefficiencyofinternationalcapitalmarketsandwhetherinternationalinvestorscanexploitwindowsofarbitrageopportunityidentifiedinonemarketinanothermarket.Thepaperfocusesonthreemarketsonwhichthereisevidenceofexistingcorrelationsinthespotmarket–Australia,theUKandtheUSA.Thesemarketsarelarge,estab-lishedandgenerallyregardedascompetitivelyefficient.Hence,theselectionofthesemarketsshouldbiasagainstfindingevidenceofarbitrageopportunities.Domesticmispricingseriesareconstructedforeachmarketandusingthetimezonediffer-encesbetweenthethreemarkets,aVARisconstructedtoexaminewhetherthedomesticmispricingseriesarerelated.Thepaperisconstructedasfollows.Thenextsectionreviewstheliteratureoninternationalmarketlinkages.Section3dis-cussesknownfeaturesofstockindexfuturespricing.Section4documentsthedatausedinthestudyandtheconstructionoftheVAR.Section5providesadescriptionofthethreemis-pricingseries,whilesection6containstheresultsoftheanalysis.Inshort,allmispricingseriesexhibitautocorrelationandthere
1SeetheBradyCommissionreportforadiscussionoftheCrashofOctober1987(PresidentialTaskForceonMarketMechanisms,ReportofthePresidentialTaskForceonMarketMechanisms,Washington:USGovernmentPrintingOffice,1988).
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isevidenceofbi-directionalspilloversacrossthemarkets.Atradingstrategyisemployedtoexaminetheeconomicsignifi-canceofapparentprofitsaftertransactionscosts.Theresultsshowthatsomeprofitsarepossiblebutthatalonghorizon,probablybeyondthescopeofmosttraders,isrequiredtoexploitthespilloverinformation.Thefinalsectioncontainstheconclusion.
2.LINKAGESACROSSINTERNATIONALMARKETS
Manystudieshavereportedtheexistenceoflinkagesamongfinancialmarkets.Forinstance,AwadandGoodwin(1998)havefoundtheevidenceofdynamiclinkages,particularlyinthelongrun,amongrealinterestratesofthemarketsofG-10countries.Rouwenhorst(1999)reportsadecreaseintheinterestratespreadsamongthetwelveEuropeanMonetaryUnioncountriesfollowingtheMaastrichtTreatyin1992.Inthecontextofstockmarkets,itiswell-knownthatinternationalcorrelationsexist.Internationalassetpricingmodelspredictthatpricespillovereffectswilloccuraspricechangesinforeignmarketsareinter-pretedasrelevanteconomicinformationwhichissubsequentlyincorporatedintopricesonthelocalstockmarket(seeStulz,1981;Solnik,1983;andChoetal.,1986).EunandShim(1989)useaVARmodeltostudylinkagesamongninedevelopedstockmarketsandfindevidenceofmarketinnovationsfromtheUSAflowingtotheothermarkets,withlimitedevidenceofforeignmarketinfluencebacktotheUSA.Similarly,CopelandandCopeland(1998)study29countriesacrosstheAmericas,EuropeandthePacificandreportstatisticallysignificantone-dayleadsoftheUSmarketovertheothermarkets.Insupport,Solniketal.(1996)findthat,onaverage,thecorrelationsbetweennationalstockmarketindicesofindustrialcountrieshaveincreasedovertime.Inpart,developmentsincomputertechnologyhavebeenanimpetusforhigh-speedinformationtransmissionacrossmarkets.
Interactionbetweenfinancialcentreshasalsobeenobservedinpricevolatility.Engleetal.(1990)firstintroducedthe‘heatwave’and‘meteorshower’terminology,inanattempttodistinguishbetweencountry-specificautocorrelationandvolatilityspilloversacrossinternationalborders.Inthecontextofequitymarkets,
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Hamaoetal.(1990)findevidenceofdailyvolatilityspilloversbetweensharepriceindicesontheLondon,NewYorkandTokyoexchanges.Thespillovereffectsareunidirectionalinnature,flowingfromNewYorktoLondon,butnotfromLondontoNewYork(Beckeretal.,1990;andHamaoetal.,1990).KoutmousandBooth(1995)reportastrongmarketinterdepend-enceamongtheUS,UKandJapanesemarketsandalsonoteasymmetryintherelationshipduringgoodandbadnewsperiods.2Spillovereffectsinpricemovementshavenotbeenlimitedtoequitymarkets.KimandSheen(2000)findevidenceofalaggedimpactofUSinterestrateannouncementsonAustralianinterestrates.Similarly,Abhyankar(1995)examinesmeanreturnandvolatilityspilloversbetweentheEurodollarfuturescontractstradedontheSingaporeMonetaryExchange(SIMEX)andChicagoMercantileExchange(CME),andfindsevidenceofbothalaggedspillovereffectinthemeanflowinginaunidirectionalformfromtheCMEtotheSIMEX.SpeightandMcMillan(2001)examinetheforeignexchangerateblackmarketsoffivecentralEuropeancountriesandfindsomeevidenceofvolatilityspillovers.Inthecontextoffuturesmarkets,Boothetal.(1997)studyvolatilityspilloversusingdailydataontheUSA,theUKandJapanesefutures.Insupportofthe‘meteorshower’hypothesis,theyfindsignificantspilloversbetweentheUSAandtheUK.However,Japanesefuturesvolatilitytendstofollowanauto-regressivetrend,assuggestedbytheheat-wavehypothesisandassuchisindependentofUSandUKvolatility.GannonandChoi(1998)reportvolatilityspilloversinstockindexfuturesfromtheUSAtotheHongKongfuturesmarket.Tse(1998),ontheotherhand,findsnoevidenceofvolatilityspilloversbetweentheinterestratefuturesmarketsoftheEurodollarandEuroyen.Insummary,thereissubstantialevidencethatpriceandpricevolatilityspilloversexistacrossalltypesofmarkets.Thestrongevidenceofstockmarketlinkagesmeansthatduetothearbitr-agerelationshipbetweenthespotandfuturesmarkets,linkagesshouldalsoexistbetweenindexfuturesmarkets.Indeed,thelimitedempiricalevidencetendstosupportthisclaim.
2OtherfindingsofvolatilityspilloversacrossequitymarketsaredocumentedbyBaeandKarolyi(1994),Linetal.(1994)andKarolyi(1995).
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3.STOCKINDEXFUTURESPRICING
Thepriceofastockindexfuturescontractcanbegivenbythecost-of-carry,asfollows:3F*t;T¼SteðrÀdÞðTÀtÞ
where:
F*t;T¼thetheoreticalfuturespriceattimetforafutures
contractexpiringatT;
St¼theunderlyingstockindexpriceatt;
r(T-t)¼theyieldattimetofadiscountrisk-freebondmatur-ingattimet;and
d(T-t)¼thecontinuousdividendyieldovertimettoT.Themodelcanbetransformedasin(2)toobtainthemispricingseries:
MPt¼Ft;TÀSteðrÀdÞðTÀtÞ
Ft,T¼
ð2Þð1Þ
theobservedfuturespriceattimetforafuturescontractexpiringatT.
Aprofitablearbitrageopportunityariseswhenthelevelofmispricingexceedsthearbitrageboundaries.Thereissubstantialevidenceonthepricingofindexfutures.ThebulkoftheworkintheUSAhasinvestigatedtheS&P500andreportedsmall,negativemispricing(e.g.,CornellandFrench,1983;Figlewski,1984;andChung,1991).Studiesinothermarketshavealsodocumentedoccurrencesofsmall,negativemispricingsuchasintheUK,Australia,GermanyandSwitzerland(BowersandTwite,1985;BrailsfordandHodgson,1997;Kempf,1998;Stulzetal.,1990;andYadavandPope,1990).PositivemispricingisreportedinJapanandHongKong(BhattandCakici,1990;and
3Thecost-of-carrymodelassumesthatmarketsareperfectandfrictionless,borrowingandlendingcantakeplaceataconstantcontinuouslycompoundedinterestrate,depositandperformancemarginscanbepostedininterestbearingassetsandtheunderlyingbasketofsharespaydividendscontinuously.Relaxationoftheseassumptionsdoesnothaveasubstantialimpactontheevidenceconcerningmispricing(seeSutcliffe,1997).
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Brenneretal.,1989)butoverall,theresultsindicateagreatertendencyofnegativemispricing(underpricing).
Largerlevelsofmispricingaregenerallyobservedundercircumstanceswheretransactionscostsarerelativelyhigh.Forinstance,BrailsfordandHodgson(1997)reportaconsistentnegativemeanpricingerrorinAustralia,wheretransactionscostsarerelativelyhigherthanintheUSA,buttheyreportnosustainablearbitrageprofitsduetothelowfrequencyoflargefuturespricingerrors.FungandDraper(1999)reportthatrelaxingtheshortsalesrestrictionscouldreducethemispricinglevelinHongKong.GayandJung(1999)reportapersistentunderpricingintheKoreanfuturesmarket,causedessentiallybyhightransactioncosts.ButterworthandHolmes(2000)examinemispricingoftheFTSE100andFTSE250contracts.Theyfindasmallmagnitudeofmispricinginbothfuturescontracts,butwithahigherlevelofmispricingintheFTSE250,andreducedarbitrageopportunitiesaftertheintroductionofFTSE250in1994.
Mispricingserieshavebeenfoundtoexhibitsystematicprop-erties.MacKinlayandRamaswamy(1988)notethepresenceofautocorrelationinthemispricingseries.YadavandPope(1992)findamean-revertingprocessinthemispricingseriesoftheUSandUKstockfuturesmarkets.Kempf(1998)documentsasimilarresultintheGermanmarket.VaidyanathanandKrehbiel(1992)explicitlyrecognisethatthemispricingseriesexhibitssystematiclinearandnon-lineartrends,predominantlypositiveinsomeperiodsandnegativeinotherperiods.Non-synchronoustradingintheconstituentstockscaninduceauto-correlationinthestockindexwhich,inturn,canleadtoarbitrageopportunitiesbeingfalselyidentified.Milleretal.(1994)showthatanymispricingseriesconstructedfromhypotheticalarbitragebetweenthespotandfuturescouldbecontaminatedandexhibitspuriousmeanreversion.
Insummary,inthepresenceofarbitragetradersandtheabsenceofmarketfrictions,theexpectedvalueofanymispri-cingseriesiszero.Moreover,amispricingseriesshouldexhibitsmall,randomfluctuations.However,variousfactorsthattendtoberelatedtomarketmicrostructure,inducesomesmallmis-pricing.Asthesefactorsaremarket-specific,anymispricinginonemarketshouldbeindependentofmispricingfromanother
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market.Ifrelationsbetweenmispricingseriesexistacrossmar-ketsthenarbitrageforcesshouldeliminatethem.Thus,nosystematicrelationsshouldexistacrossmispricingseries.
4.DATAANDMETHOD
Thestudyrequiresatimeseriesofmispricingonthethreemarketsunderinvestigation.TheselectedmarketsareAustralia,theUKandtheUSA.Thesemarketsareselectedforseveralreasons.First,thesefuturesmarketsareallrelativelylargeandwelldeveloped.4Theyareamongtheoldestoftheworld’sofficialfuturesexchanges.Eachmarkethasareputationfortransparentandcompetitivetrading.Importantly,eachmarketcontainsarbitragetraderswho,bytheiractions,keepthefuturesandspotmarketrelationshipsefficient.Hence,thesemarketsbiasagainstfindingevidenceofmispricingspilloversandlowerthepotentialforarbitrageopportunitiestobefound.Second,thethreemarketsofAustralia,theUKandtheUSAoperateindifferenttimezones.Forthespotmarkets,thelocaltradingtimesareasfollows:Australiaisopenfrom10amto4pm,Londonfrom8amto4:30pmandtheNYSEfrom8:30amto3:15pm.Forthefuturesmarkets,theAustralianmarketisopenfrom9:50amto4:10pm,Londonisopenfrom8:35amto4:10pmandtheChicagoExchangeisopenfrom9:30amto4pm.5TheopeningtimesareexpressedinGMTinFigure1.6TheAustralianmarketopensfirst,followedbytheUKandthentheUSA.
TheadvantageofselectingthesethreemarketsisthattheyprovidearelativelycleansequenceoftradingGMTtimeswhichfacilitatestheempiricaltestswewishtoconduct.Therearemanypotentialinfluencesonamispricingseries.Ifthebreakbetweentradingtimesacrossmarketsistoolargethenanyinformationtransmissionacrossmispricingseriesmaybelost.Hence,wewishtoreducethetimebetweenvariousmarketopeningsandclosings
4Forinstance,overthepastdecade,thesethreeexchangeshaveconsistentlyrankedinthetoptenintheworldasmeasuredbyturnover.
5TheAustralianandLondonfuturesexchangesoperateanautomatedtradingsystemafterthemainhoursoftheexchange.Inbothcases,tradingvolumeisrelativelylowafterhoursandhenceweconcentrateonthelargevolumedaytrading.
6ThetimesinFigure1donotoperateallyearroundduetotheadventofdaylightsavingsinthethreecountries.However,daylightsavingsdonotalterthebasicmethodastheorderofthemarketsisunchangedandvariationsaresmall.
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Figure1TradingHoursoftheMarkets(inGMT)–SpotandFuturesTimeGMT22002300235000000100020003000400050006000610070008000835090010001100120012301300133014001500160016101630170018001900191520002100220023000000OPENOPENAUSSpotUKUSAUSFuturesUKUSCLOSECLOSEOPENOPENOPENOPENCLOSECLOSECLOSECLOSE#
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butensurethatthereisasufficientnon-overlappingtradingperiodtoallowtraderstoexploitanyapparentprofitabletradingstrategies.Inthissense,theselectionoftheAustralian,UKandUSAmarketsprovidesareasonablebalancebetweenthecompet-ingresearchdesignchoices.
Inordertogeneratethemispricingseries,thecost-of-carryisused,asin(1)and(2).Dailyclosingdataareobtainedforboththespotandfuturesmarketsovera13-yearperiod,2January,1985to30December,1998,yieldingatotalof3,471matchingdailyobservations.However,nodividendsareavailablefortheUKintheyear1985sothesedatesareomitted.Ifanyofthemarketsexperienceaholiday,thedataforthatdayisomittedforallthreemarkets.Aftermakingtheseadjustments,2,996observationsremain.
Morerecentstudiesoffuturesmispricinghaveexaminedtheissuethroughtheuseofintradaydata.However,thesestudieshavebeenlimitedtoasinglemarket.Wechoosetoworkwithdailydataforfourreasons.First,asthethreeselectedmarketsoperateindifferenttimezones,thereisalmostnosimultaneityintradingandhencetradedataprovidenoadvantage.Thematchingoftradedatawouldnecessitateadifferentselectionofmarketsandbelimitedtothosetradingatthesametime.Forinstance,agroupofmarketsinAsiacouldbechosen.However,thiswouldlimittheadvantagesofthethreeselectedmarketsasoutlinedearlier,andwouldalsonarrowthepotentialglobalinterestinthestudy.Second,wewishtocoveralongtime-seriestoexaminethepersistenceofanyfindingsandavoidcriticismthatanyresultsaresamplespecific.Unfortunately,tradedataarenotavailableoverasufficientlylongperiod.Third,dailydataallowforaconsistentpointintimetobeusedasareference,asopposedtotradedatathatoccuratvarioustimesthroughouttheday.Finally,dailydataarelikelytobiasagainstanyfindingofspillovers.Evenifspilloversexist,weexpectanytradinginforma-tiontobeexploitedquicklyandwashedoutofclosingprices.Inordertoimplementthecost-of-carry,dividendandinter-estrateseriesarealsorequired.Thedividendseriesistakenastheyieldontheunderlyingindexineachmarket.Fortherisk-freeproxy,thefollowingareused–13-weekTreasurybillrateforAustralia;3-monthTreasurybillratefortheUKandthe3-monthTreasurybillratefortheUSA.
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Asnotedearlier,evidencehasshownthatmispricingseriescanexhibittime-seriespropertiessuchasautocorrelation.Assuch,themispricingseriesforeachmarketisassumedtobeinfluencedbothfromitspriorown-marketmispricinginadditiontothevariablesofinterest,thatis,themispricingseriesfromtheothermarkets.AVARmodelisusedtotesttheserelationships.Asdiscussedearlier,thethreemarketsoperateindifferenttimezones.GiventhesequencingofmarketopeningsasdescribedinFigure1,theVARmodelsin(3)onlyuseobservationsfromothermarketsthatareavailableatthetime(i.e.close-to-closeprices).Themodelisestimatedusingequalinformationlags,asfollows:
MPAU;t¼AUþ
þ
nXi¼1
nÀ1Xi¼0
nXi¼1
nXi¼1
iAUMPAU;tÀi
þ
nXi¼1
iAUMPUK;tÀi
ð3aÞ
AUiMPUS;tÀiþeAU;t
MPUK;t¼UKþ
þ
nXi¼1
iUKMPAU;tÀi
þ
iUKMPUK;tÀi
ð3bÞ
UKiMPUS;tÀiþeUK;t
nÀ1Xi¼0
nÀ1Xi¼0
MPUS;t¼USþ
þ
nXi¼1
iUSMPAU;tÀi
þ
iUSMPUK;tÀi
ð3cÞ
USiMPUS;tÀiþeUS;t
whereMPAU,MPUKandMPUSarethemispricingseriesfrom
theAustralian,UKandUSfuturesmarketsrespectivelygener-atedfrom(2).
5.MISPRICINGSERIES
Table1reportsdescriptivestatisticsonthemispricingseries.Thetableincludesinformationonascaledserieswherethemispricingisscaledbythespotseriestoaccountfordifferencesinindexvalues
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Table1DescriptiveStatisticsofMispricingSeriesAcrossMarketsMeanÀ3.660À0.003140.00854À0.405À0.000310.003900.2560.000080.0029013.8810.005480.00387À0.390À0.000200.0052420.3400.013150.01048MedianStd.Dev.Min.À249.614À0.161120.00000À118.525À0.057750.00000Max.76.8550.037280.1611263.2000.021990.05775BILSON,BRAILSFORDANDEVANS
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AustraliaMispricingMispricingScaledbyStAbsoluteMispricingScaledbyStUKMispricingMispricingScaledbyStAbsoluteMispricingScaledbyStUSAMispricingMispricingScaledbyStAbsoluteMispricingScaledbySt0.9640.001650.003130.3780.000890.001702.5850.005150.00441À24.777À0.110130.0000014.7690.028100.11013BlackwellPublishingLtd2005
Notes:ThedataaredrawnfromindexfuturesontheAustralianSPIcontract,UKFTSE100contractandtheUSS&P500contract.ThesamplecoversJanuary1986toDecember1998.Themispricingseriesiscalculatedfromthecost-of-carrymodelasin(2)usingdailyclosingvalues.Thenumberofobservationsis2,996.INTERNATIONALTRANSMISSIONOFARBITRAGEINFORMATION
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acrossthemarkets.ThemispricingseriesforAustraliaandtheUKarenegativeonaverage,whereastheUSAexhibitspositiveaveragemispricing.ThemediansoftheUKandUSseriesarepositive,whereastheAustralianmispricingmedianisnegative.Australiahasthelargestlevelofmispricing,aresultwhichremainsaftertheseriesarescaled.However,allseriesaresmallwiththemeanscaledmispricinglessthan0.5%inallthreemarkets,consistentwiththepresenceofcompetitiveandefficientmarkets.ThelargerabsolutemispricinginAustraliaprobablyreflectsgreaterarbitrageboundsinthismarket.Thatis,thesmallerlevelsofmispricingintheUKandUSmarketsmayreflectlowertransactionscostsandhigherliquiditycomparedwiththeAustralianmarket.Moreover,thedominanceofnegativemispricingmaybeexplainablebygreaterrestrictionsonshortsalesintheAustralianmarket.Ofnote,graphs(notshown)ofthethreemispricingseriesshowthattheextremevaluesacrossthemarketstendtoclusterintime.
Beforeexaminingtherelationsbetweenthemispricingseries,weconductAugmentedDickey-Fullerunitroottestsonthevariablesusedincalculatingthecost-of-carryusing:
ÁYt¼0þ1YtÀ1þ2tþ
pXj¼1
jÁYtÀjþ\"t:
ð4Þ
ThelagordersinthetestingequationsaredeterminedbyAIC,
suchthattheerrorsarerenderedwhitenoise.7Theresults(notreported)showevidenceofaunitrootinthefuturespriceandspotpriceseries.Theratioofthefuturesclosingpricetothespotpriceandthemispricingserieswerebothfoundtobestationary.TheseresultsareconsistentacrosstheAustralian,UKandUSmarkets.Table2containstheresultsofcointegrationtestsonthecost-of-carryvariables.Thecomparisonofvariablesacrossmarketsisundertakenbearinginmindtimezonedifferencessothatmarketsarecomparedatcommontimes(asperFigure1).TheapproachusedtotestforacointegratingrelationfollowsthatofDickeyandFuller.8Thetestfornocointegrationisobtainedbytestingforaunitrootintheresidualsofequation(4),viz:
7Examinationofhigherlagordersyieldssimilarresults.
8Notimetrendisfittedfortheresidualregression,andthelagorderisthatdescribedfortheADFtests.
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pXj¼1
Á\"t¼1\"tÀ1þjÁ\"tÀjþut:
ð5Þ
Table2
CointegrationTestsAcrossMarkets
AUSt/UKtÀ1Futures
Spot
À3.77*À3.54*
UKt/UStÀ1À2.78À3.03
UStÀ1/AUStÀ3.38*À3.35*
Notes:
ThedataaredrawnfromindexfuturesontheAustralianSPIcontract,UKFTSE100contractandtheUSS&P500contract.ThesamplecoversJanuary1986toDecember1998.Thenumberofobservationsis2,996.ThenullhypothesisoftheADFtestisH0:I(1)orunitrootandisbasedonthefollowingregressions:
ÁYt¼0þ1YtÀ1þ2tþ
pXj¼1
jÁYtÀjþ\"tð4Þ
Á\"t¼1\"tÀ1þ
pXj¼1
jÁ\"tÀjþutð5Þ
withnullhypothesisthat1¼0.ADFtestsarerunwithtime-trendincludedwithlag
orderdeterminedbyAIC.
*Significantat10%(criticalvalueisÀ3.12).
ThefuturesclosingpricesarecointegratedacrossAustraliaandtheUK,andacrosstheUSAandAustraliabuttheUK-USApairingismildlyinsignificant.Asimilarresultholdsforthespotseries.Theseresultsconfirmpriorstudiesofcloselyrelatedmarketmovements.Whilethestationarypropertiesofthemis-pricingseriesprecludeslookingatcointegrationinmispricingacrossmarkets,thecauseofanycross-marketdependenceinthemispricingcouldbeattributabletocointegrationbetweenothervariablesinthecostofcarryrelation.96.MISPRICINGANALYSISACROSSMARKETS
Table3,PanelA,reportsontherelationsbetweenthemispri-cingseriesineachmarket.AnOLSregressionisrunforeach
9Recallthatthemispricingseriesshouldprimafaciebeindependent.
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marketwherethescaledmispricingseriesisregressedagainstitsownlaggedseriesandthelaggedseriesfromthetwoforeignmarkets.Thatis,themodelassumesthateachmispricingseriesisafunctionofafirst-orderautoregressiveprocessandbythemostrecentavailableinformationfromtheforeignmarkets.Themispricingseriesisscaledbythespotseriestoavoiddis-tortionsfromdifferingindexvalues.Atthisstageoftheanalysisonlyone(daily)informationlagisused.10Theregressionsare:
AUAU
MPAU;t¼AUþ1MPAU;tÀ1þ1MPUK;tÀ1þAU1MPUS;tÀ1þeAU;tUKUKMPUK;t¼UKþ1MPUK;tÀ1þ1MPAU;tþUK1MPUS;tÀ1þeUK;tUSUSMPUS;t¼USþUS1MPUS;tÀ1þ1MPAU;tþ1MPUK;tþeUS;t:
FromPanelAofTable3,themodelappearstoexplaintherelationshipwell,withalladjustedR-squaredvaluesinexcessof45%,withtheAustralianmispricingregressionexhibitingthehighestvalueof72%.Theexplanatorypowerofthemodelineachmarketappearstobedrivenmainlybyanownmarketinfluence,thatis,mispricingappearstobepersistentandpositivelyrelatedtoitslevelinthepreviousperiod,consistentwithpriorevidence(e.g.,MacKinlayandRamaswamy,1988).Thisresultisconsistentacrossallmarkets.Despitethepresenceofthisstrongautoregressiverelationship,mispricingfromtheforeignmarketsalsohasanimpact.Thecoefficientsonthecross-marketlaggedmispricingseriesaregenerallysignificant.Theseresultssuggestthatinnovationsinthemispricingseriesinonemarketspillovertothemispricingseriesinanothermarket.Primafacie,theseresultsareanomalousandinconsistentwiththeconceptofintegratedandcompetitiveinternationalcapitalmarkets.Ofnote,theinterceptsareconsistentwiththeresultsinTable1,withAustraliabeingnegative,USpositiveandUKbeingsmallandslightlynegative.Atthisstageoftheanalysis,transactioncostshavenotbeenconsidered.Presumablyifsometradingstrategywereusedtotakeadvantageofthecorrelationininformationacrossmarkets,thentheprofitfromthisstrategywouldberelatedtothedegreeofmispricing.11Wethereforere-estimatetheregressionin(3a),
10Thepossibilityofhigherorderrelationshipsisinvestigatedatalaterstage.
11Theauthorswishtothankananonymousrefereeforbringingthisissuetoourattention.
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Table3
AnalysisofMispricingSeriesandCross-MarketRelations
MPAU,tMPUK,tMPUS,tPanelA:MispricingSeriesandCross-marketRelationsWithoutTransactionCostsConstantÀ0.00107**À0.000020.00065**
(À3.42)(À0.25)(4.52)
MPAU,t0.02920**0.01266*
(2.80)(1.77)
MPAU,tÀ10.80884**
(31.07)
MPUK,t0.07912
(1.21)
MPUK,tÀ10.064500.70176**
(1.21)(34.07)
MPUS,tÀ10.27746*0.004040.64413**
(1.84)(0.12)(8.99)
2AdjustedR0.7200.5240.455PanelB:MispricingSeriesandCross-marketRelationsIncorporatingTransactionCostsObservations791203220ConstantÀ0.00293**À0.000110.00595**
(À6.31)(À0.15)(7.08)
MPAU,t0.05613*0.04372
(1.86)(1.01)
MPAU,tÀ10.83314**
(40.33)
MPUK,t0.72873**
(9.08)
MPUK,tÀ10.070650.93592**
(1.26)(16.62)
MPUS,tÀ10.37243**À0.14967**0.57059**
(6.06)(À2.30)(8.53)
AdjustedR20.7360.6310.680
Notes:
ThedataaredrawnfromindexfuturesontheAustralianSPIcontract,UKFTSE100contractandtheUSS&P500contract.ThesamplecoversJanuary1986toDecember1998.Themispricingseriesiscalculatedfromthecost-of-carrymodelasin(2)usingdailyclosingvaluesandscaledusingspotvalues.Onlythoseobservationsforeachmarketareincludedwherethemispricingseriesexceeds1.0%,whichproxiesfortransactioncosts.Thetablereportsonthefollowingregressions.StandarderrorshavebeenadjustedforheteroscedasticityandautocorrelationusingtheNewey-Westprocedure.T-statisticsarepresentedinparentheses:
AUAU
MPAU;t¼AUþ1MPAU;tÀ1þ1MPUK;tÀ1þAU1MPUS;tÀ1þeAU;t
UKUKMPUK;t¼UKþ1MPUK;tÀ1þ1MPAU;tþUK1MPUS;tÀ1þeUK;tUSUSMPUS;t¼USþUS1MPUS;tÀ1þ1MPAU;tþ1MPUK;tþeUS;t:
*Significantat10%.
**Significantat5%.
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(3b)and(3c)usingonlythoseobservationswherethemagni-tudeofthemispricingseriesforthemarketofinterestexceedssomepre-specifiedlevel.Thislevelrepresentsthevalueoftransactionscosts.PanelBofTable3reportstheresultsfromre-runningtheanalysisonthoseobservationswherethemispricingvalueexceeds1.0%,andtherebyimplicitlyassumingthattransactionscostsaresetatthislevel.12TheresultsaremarkedlysimilartothosereportedinPanelAthatassumezerotransactionscosts.Theinterpretationoftheresults,whilenotusefulasatradingstrategyinitself,suggeststhatwhenmispricingofalargemagnitudeoccursforamarket,itistypi-callyassociatedwithmispricingofalargemagnitudeinothermarkets.13Todate,onlyfirst-ordereffectshavebeenconsidered,suchthatitwasassumedthatonlyinformationcontainedintheperiodimmediatelyproceedingtheperiodofinterest.Further,Table3reportsonseparateregressionsforeachmar-ket.Wenowconsideralessrestrictivemodel,wherebyhigherorderimpactsandcross-correlationsareconsideredwithinasingleestimation.Theframeworkofequations(3a),(3b)and(3c)isemployed,againusingscaledmispricing.Consistentwithmoststudiesincorporatingdailydata,fivelagsareusedfortheVAR.Thespecificationtakesintoaccounttimezonedifferencesbetweenthemarketssuchthatonlyinformationthatisknownisincluded.Forinstance,intheUKregression,thecontempora-neousAustralianmispricingvariableisincludedasanadditionalexplanatoryvariable.IntheUSregression,contemporaneousvariablesforAustraliaandtheUKareincluded.TheresultsarepresentedinTable4.14TheresultsinTable4confirmthoseinTable3.First,own-countryeffectsdominatewherebythelaggedmispricingseries
12WhilePanelBofTable3reportstheresultsfromrunningthefilterat1.0%,wealsoexaminedresultsvaryingthelevelofthefilterrangingfrom0.1%to1.0%.Acrossallfilterlevels,theresultsarequitesimilartothosereportedhereanddonotalterthegeneralconclusions.
13Theinvestigationofanarbitrage-basedtradingstrategyusingconditionedinforma-tionfromothermarketsisconsideredinalatersectionofthepaper.
14ConsistentwiththeearlierresultsreportedinTable3,theregressionsinTable4werealsoestimatedusingonlythoseobservationswherethelevelofmispricingexceedsafilterthatproxiesfortheleveloftransactionscosts.Again,usingarangeoffiltersfrom0.1%to1.0%,theresultswerehighlyconsistentwiththosereportedinTable4.
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Table4
VARAnalysisofCross-marketRelationsinMispricing
ConstantMPAUS,tMPAUS,tÀ1MPAUS,tÀ2MPAUS,tÀ3MPAUS,tÀ4MPAUS,tÀ5FMP-testUK,tMPUK,tÀ1MPUK,tÀ2MPUK,tÀ3MPUK,tÀ4MPUK,tÀ5FMP-testMPUS,tUS,tÀ1MPUS,tÀ2MPUS,tÀ3MPUS,tÀ4MPUS,tÀ5FAdjusted-test
R2MPAUS,t(ÀÀ0.001**4.02)(32.46)0.607**(5.04)0.110**(2.26)0.050**0.148**À(6.72)0.018(À1.01)
[0.000]0.221**À(6.32)0.204**(ÀÀ5.42)0.041(ÀÀ1.08)0.023(À0.60)10.88(1.74)
0.060*[0.000](13.89)0.464**À0.171**(À4.41)0.118**À(3.04)0.064*(ÀÀ1.65)0.209**(À49.226.17)
0.751
[0.000]MPUK,tMPUS,t(ÀÀ0.0000.81)0.074**(4.73)0.000**0.042**(À(7.59)À0.038**(À(4.06)À0.089**7.37)(À3.28)À0.0070.58)0.007(3.17)0.039**(0.97)0.012(À(0.59)À0.009À0.74)0.021**(ÀÀ0.0080.64)0.007(À10.782.17)
[0.000](0.66)
9.29(8.22)0.156**[0.000](22.13)0.415**0.0140.178**À(0.68)0.097**(8.85)0.125**(ÀÀ4.61)0.056**(6.19)0.041**(ÀÀ2.66)0.022(2.03)(À1.04)0.009751.53(5.16)
0.096**[0.000]15.81(0.47)
[0.000]À(1.34)0.0250.048**(28.09)0.535**0.014(À2.31)0.111**(0.65)À(5.40)0.013(7.23)0.155**0.029(ÀÀ0.60)0.061**(1.36)0.054**(À3.33)
8.390.593
[0.000]483.48(2.88)
0.505
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Table4(Continued)
Notes:
ThedataaredrawnfromindexfuturesontheAustralianSPIcontract,UKFTSE100contractandtheUSS&P500contract.ThesamplecoversJanuary1986toDecember1998.Themispricingseriesiscalculatedfromthecost-of-carrymodelasin(2)usingdailyclosingvaluesandscaledusingspotvalues.Thenumberofobservationsis2,996.Thetablereportsonthefollowingregressions.StandarderrorshavebeenadjustedforheteroscedasticityandautocorrelationusingtheNewey-Westprocedure.T-statisticsarepresentedinparentheses.TheF-testisforthejointsignificanceofthemispricingcoefficientsforeachmarketineachregressionunderthenullhypothesisthatthecoefficientsarejointlyequaltozero.P-valuesfortheF-testarepresentedinsquarebrackets:
MPAU;t¼AUþ
nXi¼1
iAUMPAU;tÀiþ
nXi¼1
iAUMPUK;tÀiþ
nXi¼1
AUiMPUS;tÀiþeAU;t
ð3aÞ
MPUK;t¼UKþ
nÀ1Xi¼0
iUKMPAU;tÀi
þ
nXi¼1
iUKMPUK;tÀi
þ
nXi¼1
UKiMPUS;tÀiþeUK;t
ð3bÞ
MPUS;t¼USþ
nÀ1Xi¼0
iUSMPAU;tÀi
þ
nÀ1Xi¼0
iUSMPUK;tÀi
þ
nXi¼1
USiMPUS;tÀiþeUS;t:
ð3cÞ
*Significantat10%.
**Significantat5%.
ineachmarketisgenerallysignificant.Thecoefficientsonthefirstlagarelargeforeachofthethreemarketsandgenerallymostlagsaresignificant.Second,laggedforeignmispricingagainexertsasignificantinfluenceondomesticmispricing,withlargepositivecoefficientsonthemostrecentlag.TheonlyexceptionistheimpactoflaggedUSmispricingontheUKseries.Thereissomeevidenceofreversalswiththetrendofapositiverelationtothemostrecentmispricingandanegativerelationtomispricingfrompriorperiods.
InaVAR,relianceonindividualcoefficientscanbemisleadinggiventhelargenumberofparametersthatareestimated.Hence,anF-testisconductedfortherestrictionthatthemispricingcoefficientsforeachmarketineachregressionarejointlyequaltozero.TheF-valuesinTable4indicatethatthenullhypothesisthatthecoefficientsarejointlyequaltozerocanberejectedforeachmarketineachregression.Thatis,themispricingcoeffi-cientsineachmarketarejointlysignificant.Thisresultconfirmstheinfluenceofcross-marketcorrelationsinthemispricingseriesoneachdomesticmarket’smispricingseries.
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Thekeyresulttodateisthattheanalysisconsistentlyindicatesthatmispricingfromforeignmarketsisrelatedtocurrentmis-pricingineachmarket.Thisevidenceisconsistentwithpoten-tialarbitrageprofits.Wehavebeencarefultouseonlyknowninformationsothereisnolook-aheadbias.Onereasonastowhythepotentialarbitrageprofitsarenotrealisedistheremaybebarrierstoinvestmentacrossborders.However,giventhedevelopednatureofthesemarkets,itisdifficulttobelievethatsuchbarriersexistforsophisticatedinvestors.Analternativeexplanationisthatwhilestatisticalsignificanceisachieved,thepotentialprofitsarenoteconomicallysignificanteitherbecausetransactionscostsaresufficientlylargetopreventexploitationofthearbitragewindoworthefrequencyofoccurrenceisrare.Toinvestigatethisissuefurther,atradingstrategyisdevelopedbelow.
Inordertoexploitthecross-marketcorrelation,atradershouldexecuteatradewhentheinformationfromtheforeignmarketscarriespredictiveability.InTable4,thelargestcoeffi-cientsontheforeignmispricingseriesareobservedonthemostrecentinformationandinallcasesthesecoefficientswereposi-tive.Thisobservationtranslatesintoatradertakingthefollow-ingposition.Consideringeachmarketinturn,ifboththeforeignmarketsexhibitpositive(negative)mispricinginthemostrecentperiod,thenthisinformationdrivesexpectationsofpositive(negative)mispricinginthedomesticmarket.
Dependingontheexpectedvalueofthemispricingseriesfromthetradingrule,thetraderwouldtaketheappropriatearbitragepositionandholdituntileitherthemispricingseriesrevertedtozeroandorexpiry.Undereitherapproach,thegainsfromthestrategyarethedollarvalueofthemispricing.Inordertoinvestigatethepotentialreturnsthatsuchastrat-egywoulddeliver,wefirstcountthenumberoftimesthatthetradingstrategywouldbeexecuted.15However,notethatthemeansofthemispricingseriesarenon-zero(asperTable1)andhencethedistributionsoftheserieswillnotbesymmetricalaroundzero.Withthispriorknowledge,wecanestimatethenumberoftimesthatthetradingstrategywouldbe
15TheanalysisisrepeatedexcludingthosedayswhereaholidayoccurredinoneoftheforeignmarketsandtheresultsareremarkablysimilartothoseinTables5and6.
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implementedifthecross-marketcorrelationsinthemispricingseriesarezero.Thatis,ifweassumethatthethreemispricingseriesareindependent,thentheincidenceobservingtwoimme-diatelypriorpositive(negative)observationsinthetwoforeignmarketsfollowedbyapositive(negative)observationinthemarketofinterestcanbeexpressedasaproportionofthetotalnumberofobservations.ThisnumberisreportedinTable5inthecolumnlabelledas‘naı¨ve’andrepresentsabenchmark.
However,inthepresenceofcross-marketcorrelationsinthemispricingseries,theproportionofobservationsthatresultinexecutionofthetradingstrategy(labelledas‘actual’inTable5)willdifferfromthenaı¨veproportion.Thisdifferencewillbeattributabletotheextentofcross-marketcorrelationsintheseriesandcanbetestedusingaz-test.Table5reportsonsuchatest.Moreover,implementationofthetradingstrategyinrealitywouldincurtransactionscosts.Toaccountforthesecosts,severalfiltersareappliedsuchthatthetradingstrategyisexecutedonlywhenthemispricingseriesfromtheconditionedforeignmarketsexceedthefilter.16Thesefiltersrangefrom0.1%to1.0%.Giventhepositivecorrelationdocumentedbetweenthethreemispricingseriesusingthemostrecentinformation,thenincreasesinthe(absolute)magnitudeofmispricingintheforeignmarketsshouldtranslatetoaproportionateincreaseinthe(absolute)magnitudeofmispricinginthedomesticmarket.
TheresultsinTable5arerevealing.First,foreverymarket,thetradingstrategyissignificantwhenthereisnofilter.Primafacie,thisindicatesalargenumberofpotentialarbitrageoppor-tunities.Second,asthefilterincreasesinsize,thedifferencebetweentheactualandnaı¨veproportionsdiminishes,andinmostcasesreversessuchthattheproportionofactualtradesislessthanthatexpectedundertheassumptionofindependencebetweenthemispricingseries.Thesecasesarehighlightedbyanegativevalueonthez-statisticsinthetable.17Hence,thereare
16Recallthatthemispricingseriesisscaledbythespotassetandtransactionscostswillbeafunctionofthevalueofthespotmarket.Tothisextent,atransactionscostfiltercanbeappliedtothescaledmispricingseries.
17TheexceptionsaretheUSAandUKseriesusinga1%filter.However,therearerespectivelyonly85and20instancesofthetradingstrategybeingexecutedoutofa13-yearsetofpotentialtradingdays.
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ComparisonofTradingStrategiesUsingConditionedMispricingInformationDescription14270.476310770.35966130.20451860.0621480.0163À7.52**À17.17**À12.78**À10.41**14810.494311330.37857620.25433370.11275.27**Naı¨veActual15710.52448890.29673220.1075760.0254120.0040Filter(%)PanelA:AustralianMispricingConditionedontheUSandtheUK0#TradesProportionZ-test0.1#TradesProportionZ-test0.25#TradesProportionZ-test0.5#TradesProportionZ-test1.0#TradesProportionZ-testBILSON,BRAILSFORDANDEVANS
#
6.65**À3.10**À11.45**16620.554710520.35115240.17491930.0644BlackwellPublishingLtd2005
PanelB:UKMispricingConditionedonAustraliaandUK0#TradesProportionZ-test0.1#TradesProportionZ-test0.25#TradesProportionZ-test0.5#TradesProportion1.03.14**16930.565112540.41868430.28143700.1235À1.335.39**850.0284À10.72**200.0007#
Z-test#TradesProportionZ-test60.002015110.504312180.40678410.28063940.1316360.01190.081.336.70**BlackwellPublishingLtd2005
PanelC:USAMispricingConditionedonUKandAustralia0#TradesProportionZ-test0.1#TradesProportionZ-test0.25#TradesProportionZ-test0.5#TradesProportionZ-test1.0#TradesProportionZ-testINTERNATIONALTRANSMISSIONOFARBITRAGEINFORMATION
Notes:Thistablereportsonatradingstrategythatassumestakinganarbitragepositionineachmarketifthemostrecentmispricingfromthetwoforeignmarketsarebothpositive(negative).Eachmarketisanalysedseparatelyusingconditionalinformationfromthetwoforeignmarkets.Thenaı¨vestrategyassumesindependencebetweenthemispricingseriesacrossmarketsbutusesthesamplemeansandstandarddeviationstoestimatethenumberandproportionoftrades,whereastheactualstrategyusestheobservedcorrelationsbetweenthemispricingseries.ThedataaredrawnfromindexfuturesontheAustralianSPIcontract,UKFTSE100contractandtheUSS&P500contract.ThesamplecoversJanuary1986toDecember1998.Themispricingseriesiscalculatedfromthecost-of-carrymodelasin(2)usingdailyclosingvaluesandscaledusingspotvalues.Thez-testisatestofthenullhypothesisthatthereisnodifferencebetweentheactualandnaı¨veproportions,calculatedas:pÀpZ¼qffiffiffi:pqn0995
**Significantat5%.996
BILSON,BRAILSFORDANDEVANS
few,ifany,arbitrageopportunitiesonceafilterisimposed.Theimplicationofthesefindingsisthatwhilethereappearstobemanypotentialarbitrageopportunities,theseareprobablyinsufficientlylargetocovertransactionscosts.Attheextremeend,thereappearstobeafewpotentiallylargearbitrageprofitopportunities(giventhefilter)buttheseareveryinfrequent.Asafinalinvestigation,themagnitudeofthepotentialdollarprofitsfromthetradingstrategyisexamined.Table6reportstheaveragedollarprofitinindexpointsfromthetradingstrat-egy.Toillustrate,ifweexpectthemispricingseriesonaparti-cularmarketatdayttobepositive(negative)anditindeedispositive(negative)ondaytthenthevalueofthemispricingisagain.Conversely,ifweexpectthemispricingseriesinaparti-cularmarketatdayttobepositive(negative)anditisnegative(positive)ondaytthenthevalueofthemispricingisaloss.ThefiguresinTable6aretheaverageofthegainsandlossespertrade(andonlyfromdayswhenatradeoccurs).Thedollarvalueoftheprofitisthenthenumberofcontractsbythedollarvalueperindexpoint(whichdiffersacrosscontracts)multipliedbytheaveragemispricingfigureinTable6.
Table6
ReturnsfromTradingStrategiesUsingConditionedMispricing
Information
Filter(%)00.10.250.51.0
Australia4.96(1571)6.39(889)10.04(322)17.30(76)70.36(12)
UK2.873.684.955.8422.79
(1662)(1052)(524)(193)(20)
USA0.290.370.350.420.96
(1693)(1254)(843)(370)(85)
Notes:
Thistablereportsonatradingstrategythatassumestakinganarbitragepositionineachmarketifthemostrecentmispricingfromthetwoforeignmarketsarebothpositive(negative).Eachmarketisanalysedseparatelyusingconditionalinformationfromthetwoforeignmarkets.Thetablereportsontheaveragegainpertradeinindexpoints.Thenumberoftimesthetradingstrategyisexecutedispresentedinparentheses.ThedataaredrawnfromindexfuturesontheAustralianSPIcontract,UKFTSE100contractandtheUSS&P500contract.ThesamplecoversJanuary1986toDecember1998.Themispricingseriesiscalculatedfromthecost-of-carrymodelasin(2)usingdailyclosingvaluesandscaledusingspotvalues.
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First,notethatineverymarketandineverycase,thegainispositiveimplyingthatthetradingstrategyappearstowork.Focusingonthenofiltercase,weobservearelativelylargenumberofinstanceswherethetradingruleisinvoked(asperTable5)ofsomewherebetween1,500and2,000times,orabouthalfofthetradingdaysinthesample.Ignoringtransactionscosts,theaverageprofitinindexpointsperdayrangesfromalmost5inAustraliato0.29intheUSA.Toputthisinperspec-tive,thistranslatestoadollarvaluepercontractof$72intheUSAand$62inAustralia.18Webelievethesegainsaremodestandprobablynotsufficientlylargeenoughtoexceedtransac-tionsandexecutioncosts.Moreover,onayear-by-yearanalysis,thereisconsiderablevariabilityinthegains.Hence,aninvestorwouldhavetohaveexercisedadealofpatienceoveralonghorizontohaverealisedthesepotentialprofits.
Ofnote,theaveragegainsarenegativelyassociatedwiththedollarvalueperindexpoint.Asthefilterincreases,sothenumberofdaysonwhichthetradingruleisinvokeddecreases.However,thereisasimultaneousriseintheaveragegain.Thereisamonotonicriseinthedollargainpercontractasthefilterisincreased.Usinga1%filter,thereappeartobepotentiallylargegainstoberealised.Again,toputtheseinperspective,thegainstranslatetoadollarvaluepercontractof$240intheUSAand$880inAustralia.ButrecallthatthereportednumbersareaveragesandarenotrealisedoneveryoccasionMoreover,thereareveryfewinstanceswhenthetrad-ingruleisinvoked.InthecaseofAustralia,thetradingruleisexercisedusingthe1%filterjust12timesin13years.Theoccasionswhenthetradingrulesareexecutedtendtobeclus-tered,especiallyforthehigherfilters.Forexample,againusingthecaseofAustraliawitha1%filter,outofthe12timesthetradingruleisexecuted,7ofthesedatesareclusteredinOctober1987and4ofthesedatesareclusteredinJune1990.Again,oursummaryisthatwhilepositivereturnsappeartobepresent,averylonginvestmenthorizonwouldhavebeenrequiredtorealisethem.
18ThedollarprofitsareexpressedinUSdollars(usinganexchangerateofUSD$0.50¼AUD$1)andusethedollarvalueperindexpointinthe2001contractspecifications.Thesevalueshavechangedovertimeduetocontractredenominationandhencethedollarfiguresareindicativeonly.
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7.SUMMARY
Thereisconsiderableevidencethatinformationfromonemarketspillsoverintoothermarkets,especiallyinrelationtodevelopedmarkets.However,thisevidenceisgenerallylimitedtospotmarkets.Thispaperextendstheliteraturebyinvestigatingspilloversinderivativeinstrumentsacrossinternationalmarkets.Moreover,thepaperfocusesonwhetherthereisinformationinamispricingseriesfromadomesticindexfuturescontractthatisrelevanttoamispricingseriesinanothermarket.Intheory,eveniftheunderlyingmarketsarecorrelated,thereisnoapriorireasonastowhymispricingseriesshouldalsoberelated.Toinvestigatethisquestion,threewell-knownindexfuturescontractsareexaminedintheAustralian,UKandUSAmarkets.
Thestudyfirstconstructsamispricingseriesforeachmarketusingdailydata.Then,afterallowingfortime-zonedifferences,thestudyexaminescorrelationacrossthethreemispricingser-ies.Thefindingsfirstrevealthateachmispricingserieshasstrongautocorrelationproperties,consistentwithpriorlitera-ture.Second,usingaVARframework,evidenceisfoundofbi-directionalspilloversbetweenthethreemispricingseries.Theseresultssuggestthatamispricingseriesinonemarketispredictable.Inordertoexaminewhetherthestatisticalsignifi-cantresultstranslateintoeconomicallysignificantprofits,atradingruleistestedthatusesconditionalinformationfrommarketsoverthepreviousday.Wefindthatthetradingrulegeneratesalargenumberofsmallprofitabletrades,howevertheseprofitsquicklydisappearwhenafilterisappliedthatproxiesfortransactionscosts.Insummary,theresultsshowthatsomeprofitsarepossiblebutthatalonghorizon,probablybeyondthescopeofmosttraders,isrequiredtoexploitthespilloverinformation.
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