Stock Index and Index Futures Markets A Multivaria

TheauthorsacknowledgethefinancialsupportoftheSocialSciencesandHumanitiesResearchCouncilofCanada.TheyalsothankKenGilbertandDarrenMcIlwraithforresearchassistanceandZhuaxinDingandananonymousrefereeforhelpfulcomments.TheviewsexpressedherearethoseoftheauthorsandnotnecessarilythoseoftheFederalReserveBankofAtlantaortheFederalReserveSystem.Anyremainingerrorsaretheauthors’responsibility.PleaseaddressquestionsregardingcontenttoMarieD.Racine,SchoolofBusinessandEconomics,WilfridLaurierUniversity,Waterloo,OntarioN2L3C5,Canada,519/884-0710ext.2776,[e-mail];orLucyF.Ackert,ResearchDepartment,FederalReserveBankofAtlanta,104MariettaStreet,NW,Atlanta,Georgia30303-2713,404/521-8783,[e-mail]iptionstotheFederalReserveBankofAtlantaworkingpaperseriesshouldbeaddressedtothePublicAffairsDepartment,FederalReserveBankofAtlanta,104MariettaStreet,NW,Atlanta,Georgia30303-2713,404/521-8020.Thefulltextofthispapermaybedownloaded(inPDFformat)fromtheAtlantaFed’sWorld-WideWebsiteat:AMultivariateAnalysisMarieD.RacineandLucyF.AckertFederalReserveBankofAtlantaWorkingPaper98-14August1998Abstract:Weuseamultivariategeneralizedautoregressiveheteroskedasticitymodel(M-GARCH)toexaminethreestockindexesandtheirassociatedfuturesprices:theNewYorkStockExchangeComposite,StandardandPoor’s500,andToronto35.TheNorthAmericancontextissignificantbecausemarketsinCanadaandtheUnitedStatessharesimilarstructuresandregulatoryenvironments.Ourmodelallowsexaminationofdependenceinvolatilityasitcapturestimevariationinvolatilityandcross-marketinfluences.Estimatedtime-variationinvolatilityissignificant,andthevolatilitiesarehighlypositivelycorrelated.Yet,wefindthatthecorrelationinNorthAmericanindexandfuturesmarketshasdeclinedovertime.JELclassification:G10,G15Keywords:volatilitydependence,M-GARCHTime-VaryingVolatilityinCanadianandU.S.StockIndexandIndexFuturesMarkets:AMultivariateAnalysisIntroductionFinancialmarketsareinterrelatedandincreasinglyglobal.Whenmakingdecisions,tradersincorporateinformationpertainingtopricemovementsandvolatilityintheassettheyaretrading,includinginformationaboutrelatedassets.Thus,understandinghowmarketsinfluenceoneanotherisimportantforpricing,hedging,andregulatorypolicy.Aplethoraofstudieshaveexaminedhowpricemovementsarecorrelatedacrossassetandderivativesecuritymarketsandinternationalborders,particularlysincethemarketcrashinOctober1987(e.g.,Hamao,Masulis,andNg(1990)andKingandWadhwani(1990)).Therelationbetweenstockindexandstockindexfuturesmarketsisofspecialconcernbecausesomehavesuggestedthattradinginderivativesecuritiescausesinstabilityincashmarkets(StollandWhaley(1990)).However,futuresmarketscanbeanimportantsourceofinformation,particularlyduringperiodsofmarketdistress.Stockandfuturespricevolatilityhavedefinitelycaughttheattentionofresearchers,investors,andpolicymakers.ThepurposeofthispaperistofurtherexaminedependenceinvolatilityforNorthAmericanstockandstockindexfuturesmarkets.WefocusonCanadaandtheUnitedStatesbecausemarketsinthetwocountriessharesimilarstructuresandregulatoryenvironments(Mittoo(1992)andKarolyi(1995)).Inaddition,therearefewcontrolsonthemovementofcapital.Tradingtimesinthecountries’easternmarketsareconcurrent,thoughfuturesmarketsclose15minutesafterstockmarkets.Earlierresearchhasshownthatofthemajormarkets,thesetwoarethemosthighlycorrelated(LonginandSolnik(1995)).Infact,regulationinCanadaand2theU.S.reflectsthisinter-marketcorrelation.Recentlystockandstock-derivativesmarketshaveagainagreedtocoordinatedcircuitbreakers.Thesetradinghaltsareuniformlytriggeredby1largemovementsintheDowJonesIndustrialAverageintheUnitedStatesandCanada.Weadoptthemultivariategeneralizedautoregressiveheteroskedasticitymodel(M-GARCH)developedbyBollerslev(1990)toexaminethreestockindexesandtheirassociatedfuturesprices.PersistenceinvolatilityhasbeendocumentedintheU.S.(Akgiray(1989))andCanada(CalvetandRahman(1995)).Inaddition,volatilitytransmissionandcorrelationhasbeenestimatedforinternationalmarkets(Karolyi(1995)andLonginandSolnik(1995)),aswellascashandfuturesmarkets(Chan,Chan,andKarolyi(1991)).Thispapercontributestoourunderstandingofmarketinterdependenciesbybringingtogethertheliteratureexaminingpersistenceandcorrelationinpricevolatilityacrossstockandfuturesmarkets.Themultivariatemodelcapturestimevariationinvolatilityandcross-marketinfluences.Inaddition,weexaminewhetherthecorrelationacrossmarketsisconstantovertime.Theresultsprovideinsightintodailytimevariationinpricevolatilityaswellascorrelationinvolatilityacrossstockandfuturesmarkets.Theestimatedtime-variationinvolatilityinstockandstockindexfuturesmarketsissignificantandpersistentandthesetime-varyingvolatilitiesarehighlypositivelycorrelated.Furthermore,weprovideevidenceofchangesinvolatilitycorrelationovertime.ConsistentwithresultsreportedbyKarolyi(1995)butinconsistentwithotherstudies,wefindthatvolatilitycorrelationacrossNorthAmericanmarketsdecreasedovertime.Thisf