A Markov regime switching approach for hedging energy commodities.docx
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A Markov regime switching approach for hedging energy commodities.docx
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AMarkovregimeswitchingapproachforhedgingenergycommodities
AMarkovregimeswitchingapproachforhedgingenergycommodities☆
AmirH.Alizadeh
NikosK.Nomikos
PanosK.Pouliasis
FacultyofFinance,CassBusinessSchool,106BunhillRow,LondonEC1Y8TZ,UnitedKingdom
Received6April2007.Accepted18December2007.Availableonline1January2008.
http:
//dx.doi.org/10.1016/j.jbankfin.2007.12.020,HowtoCiteorLinkUsingDOI
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Abstract
ThispaperestimatesconstantanddynamichedgeratiosintheNewYorkMercantileExchangeoilfuturesmarketsandexaminestheirhedgingperformance.WealsointroduceaMarkovregimeswitchingvectorerrorcorrectionmodelwithGARCHerrorstructure.Thisspecificationlinkstheconceptofdisequilibriumwiththatofuncertainty(asmeasuredbytheconditionalsecondmoments)acrosshighandlowvolatilityregimes.Overall,inandout-of-sampletestsindicatethatstatedependenthedgeratiosareabletoprovidesignificantreductioninportfoliorisk.
JELclassification
G13
Keywords
Commoditymarkets;
Futuresmarketshedging;
Dynamichedging;
Markovregimeswitchingmodels
1.Introduction
Derivativemarketsallowmarketagentstoreducetheirpriceriskexposure.Oneparameterwhichiscriticalforthedevelopmentofeffectivehedgingstrategiesisthehedgeratiowhichprovidesthenumberoffuturescontractstobuyorsellforeachunitoftheunderlyingassetonwhichthehedgerbearsrisk.Ederington(1979)deriveshedgeratiosthatminimizethevarianceofthehedgedportfolio,basedonportfoliotheory.LetΔStandΔFtrepresentthepricechangesinspotandfuturesprices,respectively.Then,theminimum-variancehedgeratioistheratiooftheunconditionalcovariancebetweencashandfuturespricechangesoverthevarianceoffuturespricechanges;thisisequivalenttotheslopecoefficient,γ1,inthefollowingregression:
(1)
TheestimatedR2ofEq.
(1)representsthehedgingeffectivenessoftheminimum-variancehedge.However,thefactthatmanyassetpricesfollowtime-varyingdistributionssuggeststhattheminimumvariancehedgeratioshouldbetime-varying(KronerandSultan,1993)whichinturnraisesconcernsregardingtheriskreductionpropertiesofhedgeratiosbasedonEq.
(1).Toaddressthisissue,anumberofstudiesapplymultivariategeneralisedautoregressiveconditionalheteroscedasticity(GARCH)(EngleandKroner,1995)modelsandderivetime-varyinghedgeratiosdirectlyfromtheestimatedsecondmoments(seeforinstance,[KronerandSultan,1993] and [KavussanosandNomikos,2000]).TheconsensusfromthesestudiesisthatGARCHhedgeratioschangeasnewinformationarrivesand,onaverage,tendtooutperform,intermsofriskreduction,constanthedgeratiosderivedfromEq.
(1).However,thesegainsaremarketspecificandvaryacrossdifferentcontractswhile,occasionally,thebenefitsintermsofriskreductionseemtobeminimal(LienandTse,2002).
Empirically,acommonfeatureofGARCHmodelsisthattheytendtoimputeahighdegreeofpersistencetotheconditionalvolatilityi.e.shockstotheconditionalvariancethatoccurredinthedistantpastcontinuetohaveanontrivialimpactinthecurrentestimateofvolatility.LamoureuxandLastrapes(1990)associatethesehighlevelsofvolatilitypersistencewithstructuralbreaksinthevolatilityprocess.AnotherstudybyWilsonetal.(1996)showsevidenceofsuddenchangesintheunconditionalvolatilityofoilfuturescontracts.Duringtheperiod1984–1992,threemajorshiftsinvolatilityaredetectedandareattributedtothenatureandmagnitudeofexogenousshocks(OPECpolicychanges,Iran-Iraqconflict,GulfWarandextremeweatherconditions).[FongandSee,2002] and [FongandSee,2003]alsoreportsignificantregimeshiftsintheconditionalvolatilityofcrudeoilfuturescontracts,whichtendtodominatetheGARCHeffects.Inaddition,theyfindthatinahighvarianceregimeanegativebasisismorelikelytoincreasetheregimepersistencethanapositivebasisandassociatevolatilityregimeswithspecificmarketevents.SarnoandValente(2000)provideafurtherdimensiontotheliteratureusingamultivariateextensionofthemarkovregimeswitching(MRS)modelproposedby[Hamilton,1989] and [Krolzig,1999].TheyfindthattherelationshipbetweenspotandfuturesisregimedependentandMRSmodelscanexplainthisrelationshipbetterthansimplelinearmodels.
Theevidencepresentedabovesuggeststhatbyallowingthevolatilitytoswitchstochasticallybetweendifferentprocessesunderdifferentmarketconditions,onemayobtainmorerobustestimatesoftheconditionalsecondmomentsand,asaresult,moreefficienthedgeratioscomparedtoothermethodssuchasGARCHmodelsorOLS.Forinstance,AlizadehandNomikos(2004)examinedthehedgingeffectivenessofFTSE-100andS&P500stockindexfuturescontracts,usingMRSmodelsfortheestimationofdynamichedgeratios.AllowingEq.
(1)toswitchbetweentwostateprocesses,theyprovidedevidenceinfavourofthosemodelsintermsofvariancereductionandincreaseinutilitybothin-andout-of-sample.Similarly,LeeandYoder(2007a)extendtheunivariateMRS–GARCHmodelofGray(1996),toastatedependentmultivariateGARCHmodel.Theyapplytheirmodeltothecornandnickelfuturesmarketsandtheyreporthigher,yetinsignificant,variancereductioncomparedtoOLSandsingleregimeGARCHhedgingstrategies.SimilarresultsareobtainedfromtheLeeandYoder(2007b)MRSmodeloftime-varyingcorrelation(MR–TVC–GARCH)asappliedtotheNikkei225andHangSengindexfutures.
ThispaperinvestigatesthehedgingeffectivenessoftheMRSmodelsfortheWTIcrudeoil,unleadedgasolineandheatingoilfuturescontractstradedonNYMEX.Indoingso,itcontributestotheexistingliteratureinanumberofways.First,weextendtheunivariateMRSmodelinthehedgingliteraturebyintroducing,forthefirsttime,aregimeswitchingvectorerrorcorrectionmodel(VECM)withGARCHerrorstructure,whichincludesinthemeanequationthecointegratingrelationshipbetweenspotandfuturesprices.Empiricalevidencesuggeststhatifspotandfuturespricesarecointegrated,omittingtheequilibriumrelationshipwillleadtomisspecificationproblemsbyunderestimatingthetrueoptimalhedgeratio(seeforinstance[KronerandSultan,1993],[Ghosh,1993] and [Lien,1996]).
Theinclusionoftheerrorcorrectionmechanismintheregimeswitchingframeworkwillthusenableustoexaminewhetherthespeedofadjustmentofspotandfuturespricestothelong-runrelationshipchangesacrossdifferentregimes.Themotivationforthisstemsfromthefactthatsincetherelationshipbetweenspotandfuturespriceschangesovertime,theadjustmenttotheequilibriumprocessshouldalsobetime-dependent.Thisinturnintroducesaninformativelinkbetweenvolatilityandcointegrationallowingforbothtimedependencyandasymmetricbehaviouracrossdifferentstatesinthemarket.OurpaperthereforeisdifferentfromtheLeeandYoder(2007a)SwitchingBEKKstudyinthesensethatourmodelalsoallowsforswitchingintheerrorcorrectioncoefficients.
Inaddition,weevaluatethehedgingeffectivenessoftheproposedmodelusingbothin-andout-of-sampletests.TheperformanceoftheMRShedgeratiosiscomparedtothatofalternativehedgeratiosgeneratedfromavarietyofmodelsthathavebeenproposedintheliteratureandisassessedintermsofvariancereduction,increaseinutilityandreductioninthevalue-at-riskforagivenposition.Thiswayweproviderobustevidenceontheperformanceoftheproposedhedgingstrategy.Finally,inadditiontoprovidingevidenceonthestatisticalsignificanceofthehedgingperformancefromthecompetingmodelsusingWhite’s(2000)RealityCheck,wealsoaddresstheissueofdownsideriskbyexaminingwhethertheeffectsofmean-variancehedgeratiosdifferbetweenlongandshorthedges.
Thestructureofthispaperisasfollows.Section2presentstheminimum-variancehedgeratiomethodologyanddemonstratestheMRS-BEKKmodelestimationprocedure.InSection3,thedataandtheirpropertiesaredescribed.Section4discussestheempiricalresults.ThisisfollowedbyanevaluationofthehedgingeffectivenessoftheproposedstrategiesinSection5;Section6describestherealitycheckfordatasnoopingbias.Section7providesanoteondownsideriskandfinally,conclusionsaregiveninthelastsection.
2.Markovregimeswitchinggarchmodelsandhedging
Marketparticipantsinfuturesmarketschooseahedgingstrategythatreflectstheirindividualgoalsandattitudestowardsrisk.Thedegreeofhedgingeffectivenessinfuturesmarketsdependsontherelativevariationofspotandfuturespricechangesaswellasthehedgeratio.Thehedgeratiothatminimisesthevarianceofthehedgeportfolioisderivedastheslopecoefficientofspotpricechangesonfuturespricechanges,asinEq.
(1).Thiscanalsobeexpressedas
(2)
Therefore,theminimum-variancehedgeratioofEq.
(2)istheratiooftheunconditionalcovariancebetweencashandfuturespricechangesoverthevarianceofthefuturespricechanges.1Eq.
(2)canalsobeextendedtoaccommodatetheconditionalminimum-variancehedgeratio,γ1,t,whichisthetime-varyingequivalentoftheconventionalhedgeratioγ1,inEq.
(1).Thisisbelievedtobemoreefficientinreducingtheriskofahedgedposition,becauseitisupdatedasitrespondstothearrivalofnewinformationinthemarket.Toestimatethisdynamichedgeratio,weemployanMRSVECMfortheconditionalmeansofspotandfuturesreturnswithamultivariateGARCHerrorstructure.Theconditionalmeansofspotandfuturesreturnsarespecifiedas
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