Seriesjusewang

1EstimatingtheOptimalHedgeRatiointheIndianEquityFuturesMarketKapilGupta1Dr.
BalwinderSingh2Abstract:ThepresentstudyattemptstosuggestanoptimalhedgeratioforIndiantradersthroughtheexaminationofthreeindices(namely;Nifty,BankNiftyandCNXIT)andeightyfourmostliquidindividualstockfuturestradedonNationalStockExchangeofIndia,overthesampleperiodJan.
2003toDec.
2006.
ThepresentstudycomparestheefficiencyofhedgeratiosestimatedthroughOLS,GARCH(p,q),TARCH(p,q),EGARCH(p,q),VARandVECMintheminimumvariancehedgeratioframeworkassuggestedbyEderington(1979).
Findingsofthepresentstudyconfirmthetheoreticalpropertiesoffuturesmarketsandsuggestthatunconditionalhedgeratioaftercontrollingforbasisrisk,outperformtheconditionalhedgeratio.
ResultsfavourthehedgeratiosestimatedthroughVARorVECMbecausebothmarketsarecointegratedinEngleandGranger(1987)frameworkandthesefindingsareconsistentwithAlexander(1999).
KeyWords:BasisRisk,ConditionalHeteroscedasticity,ErrorCorrection,VolatilityClustering,CointegrationandInformationTransmission.
JELClassification:C13,C22,C32,D81,D82,G12,G14,N25andO16.
1ResearchScholar,DepartmentofCommerceandBusinessManagement,GuruNanakDevUniversity,Amritsar–143005,Punjab,India,Email:Kapilfutures@gmail.
com.
2Reader,DepartmentofCommerceandBusinessManagement,GuruNanakDevUniversity,Amritsar–143005,Punjab,India,Email:bksaini@gmail.
com.
2SectionI:IntroductionExistenceoforganizedfuturesmarketsfurnishlegitimatetraderstohedgenondiversifiableriskelementcontainedintheirportfolioandhelptheinformedmarketparticipantstospeculateonthebasisriskinordertosecureriskfreeprofit,whichisofferedasarewardtorestoremarketequilibrium.
Therewardtorestoremarketequilibriumarisesduetonoisetradingbyuninformedmarketagents,whichinducesinformationasymmetryandtheunderlyingassetstartstradingatdisequilibriumprice,resultingintojumpinthebasisrisk(Cox(1976),Danthine(1978),Carlton(1984),HodgsonandNicholls(1991),Castelino(1992),Mckenzieetal.
,(2001),Chatrathetal.
,(2003)andIlluecaandLafuente(2003)).
Whereas,informedtradingbymarketagentsisexpectedtobringfairnessinpricechangeoftheunderlyingassetandhelpittostabilize,consequentlytherequiredrateofreturnwilldecline(BessembinderandSeguin(1992)andGulenandMayhew(2000)).
Therefore,anorganizedfuturesmarketwouldbeajointproduct,whereportfolioriskinsuranceisfurnishedtohedgers,gamblingtospeculatorsandarbitrageursundertaketheresponsibilitytorestoremarketequilibrium(Telser(1981)).
Academicliteraturehaswidelyappreciatedtheinformationtransmissionroleoffuturesmarkets,whichimpliesthatpricemovementinfuturesmarketcanbeefficientlyusedtopricethecashmarkettransactions(Cox(1976),Peck(1976),Telser(1981),GarbadeandSibler(1983b)andCarlton(1984)).
Sincebothmarketsarelinkedthrougharbitrageprocess(see,GarbadeandSibler(1983b)andMackinlayandRamaswamy(1988)),thereforeconvergenceofbothmarketsonthematuritydateisnatural(seefigure1)howeverintheshort-runbothmaymoveawayfromeachother3.
3Carlton(1984)whileexplainingthecontributionsoforganizedfuturesmarketsmentionedthatfuturesmarketsperformtheroleofpricediscoverer,helpsintransferringriskinvolvedintheportfolio,improvesliquidityintheunderlyingassetmarketandhelpinimprovingthepricediscoveryefficiencyoftheunderlyingassetmarket.
Carlton(1984)furthermentionedthatpredictionofcashmarketthroughfuturesmarketmaysometimeattractuninformedtradersinthemarketwhomakesnoiseanddeterioratesthepricingefficiency.
Whereasatthesametime,jointactionofarbitrageursandspeculatorsinthemarketwillhelpinrestoringtheequilibrium.
3Efficientinformationexchangeroleofthefuturesmarketandstrongandstationerycomovementbetweentwomarkets4providesanimportantinputforhedgerstotransferriskcontainedintheirportfoliotothespeculator'sportfolio5.
Hedgingthroughfuturesmarkethasdifferentconnotationsduetovariedportfolioobjectivesoftraders,thereforedifferenthedgingtheoriespersistviz;conventionalhedgingtheory,Working'shedgingtheory,Portfoliohedgingtheoryetc.
(forexampleseeEderington(1979),HowardandD'Antonio(1984),Castelino(1992),PenningsandLeuthold(2000)andLienandTse(2002)).
Figure1IllustratingCost-of-CarryRelationshipBetweenTwoMarketsOvertheContractCycleTheconventionalhedgingtheory(alsoknownasNavehedging)presumesthatbothfuturesandcashmarketsaresubjecttocommoninformationset,thereforeitsuggeststhathedgershouldtakeinversepositioninthefuturesmarketbutequalinsizetothatinthecashmarket,hencetheportfolioriskwillsignificantlydecline.
Conventionalhedgingtheorypresumesequalpricechangeinbothmarketsduetonewinformationshockbecauseefficiencyofconventionalhedgingtheoryisconditioneduponnomarketpreferencedoctrine.
Thereforetheconventionalhedgingtheorycansuccessfullyprovide4SeeFortenberyandZapata(1997),Alexander(1999),Neuberger(1999),Sahadevan(2002),Linetal.
,(2003),Kumar(2004)andPattarinandFerretti(2004)).
5Forexamplesee,Ederington(1979),Telser(1981),Figlewski(1984),MerrickJr.
(1988),Castelino(1992),KronerandSultan(1993),LienandTse(1998),Neuberger(1999),Jensenetal.
,(2000),PenningsandLeuthold(2000),Frechette(2001),Giaccottoetal.
,(2001),Chenetal.
,(2002),Loetal.
,(2002),Chenetal.
,(2004),LienandWang(2004),Terry(2005)andInandKim(2006)etc.
FuturesPriceEquityPricePriceTimet1t2t34priceriskhedgetotheportfoliomanagerbutfailstotakecareofbasisrisk,becausebothmarketsareinequilibriuminlong-run,howeverinshort-runduetothepresenceofvariousmarketfrictions6bothmarketsobservestatisticallysignificantandstrategicallyexploitablelead-lagrelationship(forexamplesee,Kawalleretal.
,(1987),Ng(1987),StollandWhaley(1990),Chan(1992),WahabandLashgari(1993),ChanandLien(2001),Chenetal.
,(2002),Linetal.
,(2002),Lienetal.
,(2003)andThomas(2006)),whichgeneratesriskfreeprofitmarkingopportunities(forexamplesee,CornellandFrench(1983),MackinlayandRamaswamy(1988),YadavandPope(1990),Chung(1991),Neal(1996),HsuandWang(2004),Lee(2005)andVipul(2005)).
LienandLi(2003)andLien(2003)afterevaluatingdifferenthedgingtheories,suggestedthatwhencapitalallocationintheunderlyingassetislimitedorlow,hedgermayavoidthebasisriskaswellasthemark-to-marketriskandmaychooseforcompletehedgingassuggestedbyconventionalhedgetheorybutwhenthecapitalallocationincreases,hedgerwillprefertounderhedgesothattransactioncostescalationsmaybeavoided(alsoseeLoetal.
,(2002)).
Therefore,inordertohedgebothpriceaswellasbasisrisk,Working(1953)cameoutwithanewhedgingtheory,whichdefineshedgerasriskselectornotasriskavoiderandassumesthatmarketagent'sprimeobjectiveisprofitmaximizationnotriskminimization.
Working'shedgingtheorysuggeststhathedgerpredominantlybehaveslikespeculatorwhostrivestoexploitallprofitmakingopportunitiesavailableinthemarket.
Inotherwords,hedgersspeculateonthechangeinbasisratherthanontheabsolutevalueofbasis.
Therefore,shorthedger7willhedgeportfolioriskifbasisisexpectedtofallotherwisehe/shewillpreferunhedgedportfolio(Castelino(1992)andLiandVukina(1998)).
Working'shedgingtheorythoughimprovesupontheconventionalhedgingtheorybutagainitwasabiasedtheorybecauseitpresumeswasthathedgersalwaysstrivetomaximizetheirwealthatanyrisklevel.
However,Johanson(1960)andStein(1961)observedthathedgerprefersoptimumrisk-returnportfolioinsteadofonlyminimumrisk6Suchas,infrequenttradingofthecomponentstocksofunderlyingindex,differenceintransactioncostintermsofbid/askspreadforthecomponentstocks,differenceintradingcostintermsofbrokerageandotherexpensestoexecuteonetransaction,timedelaysinthecomputationandreportingofthestockindexvaluesandlowinitialinvestmenttotakepositioninfuturesmarketetc.
(fordetail,seeStollandWhaley(1990)).
7Shorthedgemeanswhentraderislonginthecashmarketandhedgesthecashmarketpositionbygoingshortinthefuturesmarket.
5portfoliooraportfolio,whichcanoffermaximumreturn(alsosee,Markowitz(1952)).
Therefore,anewhedgingapproachemergedknownasportfoliohedgingapproach,whichallowsawiderangeofhedgeratiostobeefficientalongwiththeefficientutilitymaximizationfrontierandthehedgermaychoosethebestone,dependinguponhis/herriskpreference(HowardandD'Antonio(1984)andJensenetal.
,(2000)).
Moreover,itiswelladmittedfactthatpresenceofbothinformedaswellasuninformedtradersinbothmarketscausesmeanreversioninthebasis8,consequentlybasisriskvariesoverthecontractcycle.
Therefore,portfoliohedgingapproachbecamemorepopularbecauseitallowsforestimatingtime-varyingoptimalhedgeratios,whichotherwisewasnotpossibleinconventionalandWorking'shedgingtheories(forexamplesee,Myers(1991),AggarwalandDemaskey(1997),TheobaldandYallup(1997),FergusonandLeistikow(1998),KoutmosandPericli(1998),LienandTse(1998),Chenetal.
,(2004),YangandAllen(2004)andBhaduriandDurai(2007)).
Oneofthemostpopularportfolioshedgingtheories(whichalsosuggestsconstanthedgeratio)wasproposedbyEderington(1979),whichpresumesthattraderisriskaverterandfuturesmarketisanunbiasedpredictorofcashmarket.
Therefore,Ederington(1979)(likeconventionalhedgingtheory)prefersahedgeratiowhichreducesthehedgedportfoliovariancetominimumlevelbutunlikethenavehedgeratio,theEderington'shedgeratioisslopecoefficients,whichwillbecomputedastheratioofcovarianceoffuturesandcashmarketreturnsseriestothevarianceoffuturesreturns.
Ederington'shedgingtheoryimpliesthatvarianceofthehedgedportfolioandthecorrelationoffuturesandunderlyingassetarenegativelyassociated,thereforecomovementoftwomarketsandearlyexploitationofarbitrageopportunitiesarepreconditionsforefficienthedging.
Ederington'sefficienthedgeratio9hasbeenempiricallyfoundtobenegativelyassociatedwithhedgehorizonbecausedecreasingtime-to-expirytendstorestricttheflexibilityofhedgedportfolio,whichimpliesthatlongerthehedginghorizon,lowerwill8Meanreversionisapropertyofstochasticprocesswherethevariablevaluetendstorevertbacktosomenormalvalue.
Therefore,stationarybasisispresumedtoobservemeanrevertingbehaviorbecausewhenspreadbetweentwopricesisdifferentfromcost-of-carry,arbitrageur'sactivitywillcorrectthedeviationandbasiswillstartrepresentingitscost-of-carry(Zeng(2001),TheobaldandYallup(2001),MonoyiosandSarno(2002)andPattarinandFerretti(2004)).
9AssumedtocomplywiththepropertiesofOrdinaryLeastSquare(OLS)Model.
Fordetaileddiscussionsee,Ederington(1979).
6bethehedgeratio,howeverassoonasthehedginghorizonnarrows,hedgeratioapproachesunity(Franckle(1980),Figlewski(1984),KamaraandSiegel(1987),Merrick(1988),Castelino(1992),LiandVukina(1998)andChenetal.
,(2002)).
Since,basisriskhasalsobeenfoundtobenegativelyassociatedwithtime-to-expiryoffuturescontract,therefore,onexpirationdate,hedgerwillbeleftwithpriceriskonly,whichimpliesthatduringshort-run(especiallyneartoexpirationdate)conventionalhedgingtheorymayworkefficiently10(LienandTse(1999),Ariasetal.
,(2000),Collins(2000),Lien(2000)andChenetal.
,(2004)).
Ederington'sefficienthedgeratio(whichisnottimevaryinghedgeratio)hasyieldedimmensesupportintheacademicliterature11.
Lien(2005b)suggestedthathedgeratiobaseduponOLS(despiteoftheviolationofstatisticalproperties)willoutperformtimevaryinghedgeratioexceptwhenmajorstructuralchangeshavetakenplaceinthemarket.
FergusonandLeistikow(1998)byapplyingDickey-Fullertest,mentionedthatrejectionofconstanthedgeratiohypothesismaybearesultofinadequatedatapoints,thereforehedgeratiocomputedoverlong-runwillbestationaryandtheirfindingswereconsistentwithGrammatikosandSaunders(1983)andMcNewandFackler(1994)(alsoseeLoetal.
,(2002)).
Penningsetal.
,(1997)alsofoundthatEderington'sefficienthedgeratioisexpectedtoreducetheportfoliovariancetominimumlevelbutPenningsetal.
,(1997)doubteditsefficiencywhenfuturescontractswillobservethintrading.
Moreover,nonsynchronoustradinganomalyincaseofindexfutures(asfoundbyStollandWhaley(1990))maybeanotherprominentfactorresponsibleforspuriouscalculationofminimumvariancehedgeratio(TheobaldandYallup(1997and2001)).
Insuchcase,AndersonandDanthine(1981)suggestedthatcrosshedgingwillefficientlyhelpthehedgerstoachievetheirportfolioobjectiveratherthandirecthedgingasproposedinprevioustheories(alsoseeBrollandWong(1999)).
10Castelino(1992)statedthatbasisriskandfuturespricearenegativelycorrelatedandsincebotharefunctionsoftime-to-expirythereforeminimumvariancehedgeratiomaybelessthanorequaltounitywhenbasisriskiszeroanditdiffersfromunitywhenvarianceofbasisisdifferentfromthevarianceoffuturesprices.
11Forexamplesee,AggarwalandDemaskey(1997),TheobaldandYallup(1997),FergusonandLeistikow(1998),Chenetal.
,(2004),YangandAllen(2004)andBhaduriandDurai(2007).
7ManyempiricalfindingshavefurthersuggestedthatEderington'shedgingtheoryperformsefficientlyintheexpostsettingratherthaninexantesetting,whichimpliesthatEderington'sefficienthedgeratioshouldbecalculatedbyconsideringdataforfuturesaswellascashmarketsofsameperiods.
However,Ederington'shedgeratiocomputedonthebasisofhistoricaldatafailstominimizetheportfoliovariance(Figlewski(1984),KamaraandSiegel(1987),Myers(1991),Holmes(1995),Alexander(1999)Neuberger(1999),Ariasetal.
,(2000),Lien(2000),Giaccottoetal.
,(2001)andLoetal.
,(2002)).
KamaraandSiegel(1987),Myers(1991)andHolmes(1995)suggestedthatsincetraderslackperfectforesightwithrespecttocashandfuturespricerelationshipandthehedgeratiovarieswithtime-to-expiry12thereforehedgeratioestimatedinexantesettingmaybemoreefficientthanthehedgeratioestimatedinexpostsetting.
Furthermore,Franckle(1980)commentedthatsinceanefficientportfolioisexpectedtogenerateriskfreereturnplusriskpremium(asperCapitalAssetPricingModel),hence,Ederington'shedgeratiomustbeinterpretedverycautiouslybecauseariskfreenominalratecanbeobtainedforapredeterminedinvestmenthorizononly.
Therefore,ifatthetimeofopeningpositionsinbothmarkets,hedginghorizonisunknownthenchangeinthehedgeratiomayresultintolargegainsorlosses.
Thisempiricalobservationshouldnotbesurprisingbecausetimevaryingbasisriskwon'tallowhedgeratiotobeconstantoverhedginghorizon(alsoseeFiglewski(1984)andMyers(1991)).
Inaddition,thetraderhasbeenassumedtoberiskaverter,whichseemsunrealbecausehis/herprimeobjectiveistomaximizeportfoliovalue,thereforetraderactsaslossaverterratherthanriskavoider(LienandTse(1998)).
Therefore,iftheportfolioobjectiveoftraderisutilitymaximization,theutilityfunctionwillalwaysbeconcaveiftherearegainsandconvexwhentherearelosses(MyersandHanson(1996)andLien(2001a)).
HowardandD'Antonio(1984)developedamodel,whichemphasizeupontheportfolioutilitymaximizationobjectiveandsuggestedthatholdingpositioninfuturesmarketdoesnotdependonlyuponthecorrelationbetweenfuturesandcashmarketbut12SeeKronerandSultan(1993),ParkandSwitzer(1995),LienandTse(1998),HarrisandShen(2003),Poomimarsetal.
,(2003),FlorosandVougas(2004),PattarinandFerretti(2004),YangandAllen(2004),KofmanandMcGlenchy(2005),FlorosandVougas(2006),Hatemi-JandRoca(2006),BhaduriandDurai(2007)andLeeandYoder(2007).
8risk-returnrelativealsoaffectstheportfolioutilitybecausetraderismoreinterestedinthechangeofwealthlockedinportfolioratherthantheabsolutevalueofwealth(Myers(1991),Lien(2001a)andTheobaldandYallup(2001)).
Furthermore,besidesthetheoreticalprogressonaccountofsuggestingoptimumhedgingstrategythroughfuturescontracts(asdiscussedabove),theempiricalliteratureoffutureshedginghasbeenprogressivelybenefitedfromrecentdevelopmentsintheliteratureoffinancialeconometrics(LienandTse(2002)).
Varioushedgingtheoriesincludingconventional,Working'sandEderington'shedgingtheoryassumesconstanthedgingratio,however,largebodyofliterature(seetableI)hasfoundthattimevaryinghedgeratioismoreefficientthanconstanthedgeratio(forexamplesee,Myers(1991),AggarwalandDemaskey(1997),TheobaldandYallup(1997),FergusonandLeistikow(1998),KoutmosandPericli(1998),LienandTse(1998),Chenetal.
,(2004),YangandAllen(2004)andBhaduriandDurai(2007)).
Inaddition,voluminousempiricalliteratureisavailable,whichsuggeststhatsincebothmarketsobservelong-runrelationshipandareintegratedofsameorder,therefore,hedgeratiocomputedthrougherrorcorrectionmethodologydevelopedbyEngleandGranger(1987)maybemoreefficientthanothers(ParkandSwitzer(1995),Castelino(1992),KoutmosandPericli(1998),Alexander(1999),Poomimarsetal.
,(2003),AlizadehandNomikos(2004),FlorosandVougas(2004),PattarinandFerretti(2004),YangandAllen(2004),LienandShrestha(2005),FlorosandVougas(2006),BhaduriandDurai(2007)andBhargavaandMalhotra(2007)).
ThestatisticalcriticismofConventional,Working'sandEderington'shedgingstrategiescanbedrawnfromthefactthathedgeratiosinthesehedgingmodelsareslopecoefficients,whichreflectstheratioofunconditionalcovarianceoffuturesandcashpriceseriestotheunconditionalvarianceoffuturesprices,howevertheoptimalhedgingrulerequiresconditionalmomentsthatdependupontheinformationavailableatthetimewhenhedgingdecisionismade(Myers(1991),LienandLuo(1994)andMyersandHanson(1996)).
Moreover,itisanestablishedfactthatfinancialtimeseriesobservestimevaryingpatternsandvolatilityclusteringistheirinnatefeature13,thereforetime13SeeEngle(1982),Bollerslev(1986),LoandMackinlay(1988)andBollerslevetal.
,(1992).
9varyinghedgeratiomaybestatisticallyaswellaseconomicallymoreappropriateandreliablethanothers(Myers(1991),KronerandSultan(1993),ParkandSwitzer(1995),KoutmosandPericli(1998),HarrisandShen(2003),FlorosandVougas(2004),PattarinandFerretti(2004),KofmanandMcGlenchy(2005),Hatemi-JandRoca(2006),BhaduriandDurai(2007)andLeeandYoder(2007)).
Furthermore,Alexander(1999)establishedthatinexantesetting(wherehistoricalpricescontainsignificantinformationfortheprospectivepricemovementsintwomarkets(Holmes(1995)),andbidirectionalcausalrelationshipbetweentheseisanestablishedfact14),errorcorrectionmethodologyproposedbyEngleandGranger(1987)mayprovidebetterestimateofefficienthedgeratiothanothermethodologies.
ThesefindingswerefurthertestedbyKronerandSultan(1993),LienandLuo(1994),ParkandSwitzer(1995),KoutmosandPericli(1998),LienandTse(1999),Poomimarsetal.
,(2003),AlizadehandNomikos(2004),FlorosandVougas(2004),PattarinandFerretti(2004),YangandAllen(2004),LienandShrestha(2005),FlorosandVougas(2006),Hatemi-JandRoca(2006)andBhaduriandDurai(2007)andtheyallfoundthathedgeratiocomputedthrougherrorcorrectionmethodologyprovidesbetterresultsthanconstanthedgeratio,butitcouldnotoutperformthehedgeratioestimatedthroughdifferentmodelsofGARCHMethodology(exceptLienandTse(1999)andLienandShrestha(2005)).
Moreover,Telser(1981),Neuberger(1999),Giaccottoetal.
,(2001)andLoetal.
,(2002)appreciatedthecoexistenceofmultiplefuturescontractswithvariedexpirydateshavingsameordifferentunderlyingassetbecauseitwillhelptraderstohedgethroughliquidfuturescontracts15and16.
Inordertomitigatetheimpactofilliquidityonhedging14Forexamplesee,Kawalleretal.
,(1987),StollandWhaley(1990),Chan(1992)andWahabandLashgari(1993).
15Inacademicliterature,ithasbeenwidelydocumentedthatfuturescontractsneartheexpirydatearemoreliquidascomparedtothefuturescontractswithfarmaturitydate(SeeMoschiniandMyers(2002)andThomas(2006)).
16Lien(2003)mentionedthatliquidityconstraintineitherorbothmarketsisacriticalfactor,whichforcesthehedgertopartiallyhedgetheundiversifiableriskcomponentssothathedgercanavoidadditionaltransactioncostduetomark-to-marketlosses.
Therefore,optimalfuturespositionincreaseswiththesizeofcapitalallocationinunderlyingasset,whichimpliesthatifthecapitalallocationissmall,thehedgertendstocompletelyhedgeasperconventionalhedgingtheory.
However,theoptimalfuturespositiondecreaseswiththeincreaseincapitalallocation(alsoseeAriasetal.
,(2000),Frechette(2001)andHaighandHolt(2002)).
10activity,tradersprefertohedgethroughneartoexpiryfuturescontractsandachievethelong-termhedgingobjectivebyrollingpositionstothenextcontract.
HarrisandShen(2003)andKofmanandMcGlenchy(2005)examinedsamehypothesisandfoundthatrollingwindowmethodologyoutperformstheconstanthedgeratiobutstillfailedtoprovidebetterforecastthanhedgeratioestimatedthroughdifferentmodelsofGARCHMethodology.
Therefore,timevaryinghedgeratioestimatedthroughappropriateversionofGARCHfamily(suchas,BGARCH,EGARCH,MGARCHetc.
)hasbeenfoundbothstatisticallyaswellaseconomicallyarobusthedgeratio,whichoutperformsotherhedgeratios.
Onthebasisofabovediscussion,twoempiricalissuescanbeextracted,whichareequallyimportantforpolicymarkers,marketmarkers,traders,practitionersandacademicians.
Firstly,iftwomarketsobservestablelong-runrelationship,canitbeeconomicallytranslatedtohelptradersinoptimizingtheirportfoliovalueSecondly,tilldateitisadebatableissuethatwhichhedgeratiocanhelptraderstoachievetheirportfolioobjectivesBothissueshavebeenwidelyexaminedindevelopedmarketslikeU.
S.
A.
andU.
K.
etc.
,whereasinemergingmarkets(whichholdprominentpositionamongdifferentderivativemarketsoftheworld)theseissuesarestillunexplored(seetableI).
InIndia,tothebestofourknowledgeBhaduriandDurai(2007)hasbeentheonlyattempttoaddressthesecondissuebutthatstudysufferswithtwolimitations.
Firstly,thescopeofBhaduriandDurai(2007)islimitedtohedgingthroughNiftyfuturesonly.
AlthoughNiftyfuturesholdsgoodreputationinthemarket(intermsoftradingvolume)butBhaduriandDurai(2007)didnotaddresstheissuewhetheranindexwhoseallconstituentstocksarenotallowedtotradeinthefuturesandoptionssegmentcanprovidesamehedgingefficiency.
Secondly,BhaduriandDurai(2007)restrictedthescopeofstudytohedgingefficiencyofindexportfoliowhereasithasbeenwidelydocumentedthatindexportfoliosufferfromtheproblemofnonsynchronoustradingofconstituentstocks(seeStollandWhaley(1990)).
Therefore,itwouldberathermoreusefulifhedgingefficiencyofindividualstockfuturesisexamined.
ThepresentstudyisanattempttoplugbothlimitationsofBhaduriandDurai(2007).
11Furtherdiscussioninthestudyhasbeenorganizedintothreesections,wheresectionIIdiscussestheresearchdesignincludingdatabaseandresearchmethodologyemployedforestimatingoptimumhedgeratio,sectionIIIdiscussesthehedgedportfoliovarianceresultsfordifferenthedgeratiosestimatedfromvariousmethodologiesemployedandsectionIVwillconcludethestudy.
SectionII:DataBaseandResearchMethodologySincethepresentstudyaimstoexaminethehedgingefficiencyoftheIndianequityfuturesbothintermsofindexaswellasindividualstockportfolios,therefore,(inordertosecuresufficientdatapoints17)thehedgingefficiencyofallthoseindicesandindividualstockfutures,whichhaveobservedatleastonecontinuedtradingyearhistoryintheFuturesandOptions(F&O)segmentofNationalStockExchangeofIndiaason31stDec.
2006.
Thesampleperiodstartson1stJan.
2003i.
e.
theperiodwhenF&OsegmentinIndiabeganobservingimmensesuccessshowninthephenomenalgrowthoftheirtradingvolume.
Therefore,becauseofinsufficientliquidity,initialtrading/inceptionperiodforbothindexaswellasindividualstockfuturescontractshavebeenexcludedfromthesampleperiod.
Moreover,asthescopeofthestudyhasbeenrestrictedtoexaminewhetherequityfuturescontractstradedinIndiaprovidesoptimumhedgingbenefitIfyes,thenwhichstatisticalmethodologywillhelphedgerstocomputeoptimalhedgeratiosothattheycanminimizeportfoliovariancetotheminimumlevelatminimumtradingaswellastransactioncosttoexecutesuchstrategy,resultingintoincreasedportfoliovalue.
Therefore,thestudyincludesonlythosestockswhosepriceshavenotbeenadjustedduetoanycorporateaction(suchasstocksplitsorissueofbonusshares)inordertoavoidthepotentialbiasoftheseoninformationdisseminationefficiencyofstockaswellasstockfuturescontracts,becauseintheliteratureofEfficientMarketHypothesis18,itisanestablishedfactthatinadditiontothepriceadjustmentonrecorddate,thesecorporateactionsaffecttheportfoliovalueduetoinformationleakageandotherpricinganomaliespriortotherecorddateaswell.
Asaresultoftheabovementionedsampleselection17Forreference,seeNath(2003).
18SeeFama(1970and1991)andDimsonandMussavian(1998).
12criterion,thesamplesizeofthestudyrestrictstothreeindices(i.
e.
Nifty,BankNiftyandCNXIT)andeightyfourindividualstocks.
Hedgingtheoryrequiresthattraderhastotakesimultaneoustradingpositionsintwomarketsbutoppositeinsign(refertodetaileddiscussioninsectionI)withthemagnitudeofpredictionofonemarket(cashmarket)throughother(futuresmarket),whichisknownashedgeratio.
Since,estimationofhedgeratioisastatisticalprocess,whichinvolvesregressingcashmarketreturnsonfuturesreturns,therefore,priortoundertakeanystatisticalprocedures,itwillbemoreimportanttoexaminethetimeseriespropertiesofdataunderinvestigation.
Veryfirststepinanyeconometricinvestigationofatimeseriesistoexaminewhetherthetimeseriesunderexaminationcontainsunitroots,ifyes,thenseriesneedstobetransformedforfurtherexamination,otherwisethestatisticalresultswillbespurious.
Thereforetwoeconometrictestprocedures(i.
e.
AugmentedDickeyFuller(ADF)andPhilipsPeron(PP)Tests)havebeenundertakentoinvestigatewhetherthepricesofthreeindicesandeightyfourindividualstocksincashandfuturesmarketsarestationary.
TheresultsintableIIareconsistentwithfindingsintheliteratureoffinancialeconometricsthatfinancialtimeseriescontainsunitroots,therefore,bothseriesaretransformedbytakingfirstlogdifference,whichhaslaterbeenfoundstationery.
Therationaleoftakingfirstlogdifferenceinsteadoffirstdifferencedrawsfromthefactthatstockpricesarealwayssignificantlyskewedbecauseofthedivergenttradinginterestsofdifferenttradersanddifferentperception(s)tosameinformation.
Forinstance,everydipinarisingmarketisconsideredasbuyingopportunity,whichcausesjumpsinthetradingvolumeofsuchstocksandstockpricesstartwanderingawayfromtheirintrinsicvalue.
Takinglogoftheserieshelpresearcherstoavoidskewnesstoanextent,therefore,forfurtherexamination,firstlogdifferenceofbothserieswillbeused(Karpoff(1987)andMoolman(2004))Asalreadymentionedthatbothcashandfuturesmarketsarelinkedthrougharbitrageprocessandthepriceoffuturescontractdeterminedthroughcost-of-carrymodelinlong-runisnotexpectedtobedifferentfromspotpriceplusriskpremiumtoholdpositionsinthecashmarket.
Therefore,appreciatingthestationaryandstablelong-13runrelationshipbetweentwomarkets,differentmodelshavebeenconstructedtohedgetheportfoliorisk.
Sixeconometricalprocedureshavebeenundertaken,whichaddressesvariouseconomicaswellasstatisticalissuesinvolvedinestimatingthehedgeratioandtheefficienthedgeratiowillbeonewhichwillhelphedgerstominimizeportfoliovariancetominimumlevel.
Ederington(1979)suggestedanoptimumhedgeratio,whichpresumesstableandstronglongrunrelationshipbetweentwomarketsandhedgingeffectivenesswilldependuponthecoefficientofR2,thus,highertheR2,moreefficientwillbethehedgeratioandviceversa.
Equation(1)explainstheproceduresuggestedbyEderington(1979),whichwillworkefficientlywhenfuturesreturnsareunbiasedpredictorofprospectivecashmarketreturns.
Inequation(1),Rs,tiscashmarketreturns,Rf,tisfuturesmarketreturns,αoisintercepttermandεtiserrorterm.
Asalreadymentionedthatfuturescontractpriceasperthecost-of-carrymodelisassumedtobeunbiasedpredictorofprospectivecashmarketprice,thereforeinterceptanderrortermshouldnotbesignificantlydifferentfrom0,consequentlyR2willimprove,hencethehedgingeffectiveness.
Rs,t=α0+β1Rf,t+εt1)Equation(1)thoughmaybeeconomicallyjustifiablebutuntilthestatisticalpropertiesoftheestimationprocedurearesatisfied,theestimatedvalueofβ1won'tbereliable.
Inadditiontocontainingunitroots,anotherfeatureoffinancialtimeseriesisthattheseareautocorrelated,whichimpliesthatsuccessivereturnsofonespeculativeassetaresignificantlypredictableandithasbeenevidencedinthehugeliteratureonEfficientMarketHypothesis,whichsuggeststhatsuccessivestockand/orfuturesreturnsarenotrandomratherarefunctionofpreviousinformationset(s)duetomeanreversion,volatilityclustering,informationasymmetryorinefficientmicrostructuresystem19.
Therefore,ifstockreturnsareautocorrelatedthenavoidanceofitmaybiastheestimatedhedgeratio.
Hence,equation(1)repealedtoequation(2)(toincludeautoregressiveterms20ofcashmarketreturns),mayprovidebetterresults,henceimprovedR2,which19Fordetaileddiscussion,seeFama(1970and1991)andDimsonandMussavian(1998).
20OrderofautoregressionhasbeendeterminedonthebasisofSchwartzcriteria.
TheSchwartzcriterionusesafunctionoftheresidualsumofsquarestogetherwithapenaltyforlargenumberofparameters.
14otherwisecouldhavebeenbiasedonaccountofsignificantserialcorrelation.
Inequation(2),Rs,tiscashmarketreturns,Rf,tisfuturesmarketreturns,Rs,t-iisautoregressiveterm(s)whoseordervariesbetweenitopdeterminedasperSchwartzcriteria,αoisintercepttermandεtiserrorterm.
pRs,t=α0+ΣαiRs,t-i+β1Rf,t+εt2)i=1Althoughinclusionofautoregressivetermsofcashmarketreturnsasshowninequation(2)mayimprovestatisticaloutput,butstillontheoreticalgrounds,equation(2)requirestwomorevariables,whicharelaggedfuturesreturnsandjointdynamicsofbothmarketsi.
e.
laggedbasis.
Unbiasedpredictionofprospectivecashmarketpriceisastrongtheoreticalpropertyoffuturescontract;therefore,untilthelaggedfuturespricesareincludedinthemodel,anefficienthedgeratiocan'tbeestimated.
Inaddition,FamaandFrench(1986)21appreciatedthefunctionofbasisaserrorcorrectionterm,whichcorrectsthedeviationbetweencurrentcashmarketpricefromitsequilibriumprice(i.
e.
forwardpriceassumingfuturesmarketsareefficientpricediscoveryvehicles).
Therefore,equation(4)improvesuponequation(2)byincludinglaggedfuturesreturnsandlaggedbasis.
Firstlagofbothfuturesreturnsandlaggedbasishasbeenincludedinequation(4)because,thecurrentstudyemploysdailydata,whereasarbitrageopportunitiesinahighlyliquidmarketlikeIndia22arenotexpectedtopersistforlongerduration.
Therefore,firstlagofbothvariableswillbesufficienttocapturearbitrageopportunitiesbetweentwoSpecifically,theSchwartzinformationcriterionminimizestheexpression:T*log(RSS)+K*(logT),whereTisthenumberofobservations,RSSisthesumofthesquaredresidualsandKisthenumberofregressors.
Laggedtermsprovideanexplanationoftheshort-rundeviationsfromthelong-runequilibriumforthetwotestequations.
21FamaandFrench(1986)statedthatifmispricingisgovernedbymarketfactorsonlythenactualbasis(i.
e.
Ft-St)shouldpredictthetheoreticalbasis(i.
e.
St,T-St)andifβispositiveandsignificantinequation(3),itimpliesthatvarianceofactualbasisresultsincorrectingthespotpricedeviationfromitsequilibrium.
St,T-St=α+β(Ft-St)+t,T3)Where,St,T=TheoreticalfuturespriceoftheunderlyingassetattimetwithmaturitydateT.
St=Currentmarketpriceoftheunderlyingasset.
α=Constantterm.
Ft=Currentfuturesprice.
t,T=Randomerrorterm.
22SeeMonthlyDerivativesMarketUpdatesPublishedbyNationalStockExchangeofIndia(www.
nseindia.
com).
15markets.
Inequation(4)inadditiontovariablesasdefinedinequation(2),Rf,t-1representslaggedfuturesreturnsand(Rf,t-1-Rs,t-1)symbolizeslaggedbasis.
pRs,t=α0+ΣαiRs,t-i+β1Rf,t+β2Rf,t-1+β3(Rf,t-1-Rs,t-1)+εt…………….
(4)i=1Estimatedvalueofβ1willbethehedgeratio,whichwillguidehedgerstodecideupontheoptimumamountofpositioninfuturesmarketinordertohedgecurrentcashmarketholdings.
Inthepresenceofefficienttradingsystem,thestrongandstablelong-runrelationshipbetweentwomarketswillhelpthehedgeratiotobeequaltoorlessthanone(providingpartialhedging)assumingthathedgerislossaverternotriskaverter.
Theestimationprocedureaslaiddowninequation(4)maybeeconomicallyjustifiablebecauseKamaraandSiegel(1987),Myers(1991)andHolmes(1995)suggestedthatastraderslackperfectforesightwithrespecttocashandfuturespricerelationshipandthehedgeratiovarieswithtime-to-expiry23,thereforethehedgeratioestimatedinexantesetting24maybemoreefficientthanthehedgeratioestimatedinexpostsetting.
However,theliteratureonfinancialeconometricshasobservedthatstockreturnssufferwiththeproblemofvolatilityclustering,whichimpliesthataninformationsetcontinuestoaffectstockreturnvolatilityoffewperiodsahead.
Inotherwords,volatilityclusteringimpliesthatlargepricechangeswillbefollowedbylargepricechangesandsmallpricechangeswillbefollowedbysmallpricechanges.
Inequation(4)ifthevarianceoferrortermisconstant25,thehedgeratioestimationthroughOrdinaryLeastSquare(OLS)methodwillbevalid,however,largebodyofliteraturehasevidencedthatstockreturnsareheteroscedasticinnature.
Therefore,AutoregressiveConditionalHeteroscedasticitymodel(ARCH)maybeabetterproceduretomakerobuststatisticalestimations.
InARCHmodel(firstintroducedbyEngle(1982)),themeanequationisspecifiedinthebaselinescenariobyanAR(p)23SeeKronerandSultan(1993),ParkandSwitzer(1995),LienandTse(1998),HarrisandShen(2003),Poomimarsetal.
,(2003),FlorosandVougas(2004),PattarinandFerretti(2004),YangandAllen(2004),KofmanandMcGlenchy(2005),FlorosandVougas(2006),Hatemi-JandRoca(2006),BhaduriandDurai(2007)andLeeandYoder(2007).
24Inexantesetting,historicalreturnscontainsignificantinformationfortheprospectivepricemovementsinthemarket.
(see,Holmes(1995)).
25LangrageMultiplierTestwhosenullhypothesisstatesthatvarianceoferrortermishomoscedastic.
ThereforerejectionofnullhypothesiswillaskresearchertoapplyappropriatemodeloutofGARCHfamily.
16processandotherendogenousvariablessuchasinequation(4)andtheconditionalvarianceisregressedonconstantandlaggedvaluesofsquarederrortermsasshowninequation(5)ht=ω+α1ε2t-1+α2ε2t-2αpε2t-p5)ThisARCHmodelwasgeneralizedbyBollerslev(1986)leadingtogeneralizedARCHclassofmodelscalledGARCHinwhichtheconditionalvariancedependsnotonlyonthesquaredresidualsofthemeanequationbutalsoonitsownpastvalues.
TheGARCH(p,q)modelisgivenbyequation(6)pqht=ω+Σαiε2t-i+Σβjht-j+υt6)i=1j=1Where,htistheconditionalvolatility,αiisthecoefficientofARCHtermwithorderitopandβjisthecoefficientofGARCHtermwithorderjtoq.
Theconditionalvolatilityasdefinedinequation(6)isdeterminedbythreeeffectsnamelytheintercepttermgivenbyω,theARCHtermexpressedbyαiε2t-iandtheforecastedvolatilityfromthepreviousperiodcalledGARCHcomponentexpressedbyβjht-j.
Parametersωandαshouldbehigherthan0andβshouldbepositiveinordertoensureconditionalvariancehttobenonnegative.
Besidesthis,itisnecessarythatαi+βj018Theequation(4)estimatedthroughOLS,GARCHorEGARCHprocessmayprovidebetterestimateofthehedgeratiobutoptimalityofhedgeratiowillstillbedoubtfulbecausebothmarketsobservessignificantlead-lagrelationshipintermsofvolatilityspilloverandinformationdissemination.
Therefore,estimatinganoptimalhedgeratiobyregressingonlythecashmarketreturnsonlaggedreturnsofbothfuturesandcashmarketmaybebiasedbecauseotherwayroundisalsotrueasvolatilityspilloverisbidirectionalandcontinuous.
Therefore,inthepresentcase,eitherVectorAutoregressionModel(VAR)(whenthereturnsofbothmarketsunderconsiderationaresignificantlyautocorrelated)orVectorErrorCorrectionMethodology(VECM)(whenbothmarketsarecointegrated)mayprovideefficientspeculativeforecastshencerobusthedgeratiomaybeestimated.
VARmodelsimultaneouslyregressthelaggedreturnsofbothvariables,whereas,VECMinadditiontolaggedreturnsalsoconsiderstheerrorcorrectionterm(ifbothseriesarecointegrated).
Hencebothmethodologiesestimatetheoptimalhedgeratiobyconsideringtheoreticalrelationshipbetweentwomarkets(i.
e.
lead-laginshort-runandcointegrationinlong-run),whichconfirmsthevolatilityspilloverbetweentwomarketsthrougharbitrageprocess.
Equations(9)and(10)specifytheestimationprocessofVARmethodologyandequations(11)and(12)stimulatetheestimationprocedureofVECM.
ThehedgeratioonthebasisofVARandVECMwillbecomputedasσs,f/σ2fwhereσs,f=cov(εft,εst)andσ2f=var(εft).
MNRs,t=∑αiRs,t-i+∑βjRf,t-j+εst9)i=1j=1OPRf,t=∑αkRs,t-k+∑βlRf,t-l+εft10)k=1l=1pqmRf,t=α0f+Σαif(Ft-i–St-i)+ΣβfRf,t-j+ΣβfRs,t-k+εft11)i=1j=1k=1pnoRs,t=α0s+Σαis(Ft-i–St-i)+ΣβsRs,t-l+ΣβsRf,t-h+εst12)i=1l=1h=1Innutshell,thepresentstudyestimatesoptimalhedgeratioindifferentstatisticalandeconomictheoryframework,henceaimstoproposeefficienthedgeratioestimationmethodology,whichisbothstatisticallyaswellastheoreticallyrobust.
Afterestimating19theoptimalhedgeratiothroughabovementionedsixstatisticalprocedures(i.
e.
OLS,GARCH,EGARCH,TARCH,VARandVECM),thehedgingeffectivenessofallhedgeratioswillbecomparedandtheoptimalhedgeratio,whichreducestheportfoliovariancetominimumlevelwillbeproposedasefficienthedgeratio.
Theefficiencyofoptimalhedgeratiowillbemeasuredthroughequation(13).
WhereVar(U)andVar(H)representsvarianceofun-hedgedandhedgedportfoliosrespectively.
σsandσfarestandarddeviationofthecashandfuturesreturnsrespectively,σs,frepresentsthecovariabilityofthecashandfuturesreturnsandh*istheoptimalhedgeratio.
Var(U)–Var(H)13)Var(U)Var(U)=σs214)Var(H)=σs2+h*2σf2–2h*σs,f15)SectionIII:AnalysisandDiscussionPriortodiscussingtheoptimalhedgeratioestimationresultsthroughvariouseconometricproceduresproposedinsectionIIandcomparingtheirefficiencyinreducingtheportfoliorisk,itismoreimportantfirsttodiscussthetimeseriespropertiesofseriesunderexamination.
TableIIIprovidesimportantinformationrelatingtothesummarystatisticsoffuturesandcashmarketsandforjointmovementintwomarkets(i.
e.
Basis).
TableIIIprovidesthatreturnsofbothfuturesandcashmarketsaresignificantlyskewed(negativelyskewedinmostofcases)andtheircoefficientofkurtosisissignificantlydifferentfromthree,whichimpliesthatfuturesandcashmarketreturnsdoesnotconformtonormaldistribution.
ThenullhypothesisthatfuturesandcashmarketreturnsfollownormaldistributionisfurthertestedthroughJarque-Beratest,butJarque-Beracoefficientsignificantlyrejectsthenullhypothesisforallindicesaswellasindividualstockfuturesandcashmarketreturns.
FindingasymmetricreturnsinfuturesandcashmarketisnotanewobservationandsummarystatisticsinthecurrentstudyareconsistentwiththefindingsofKendall(1953),Fama(1965),StevensonandBear(1970),Chen(1996),Reddy(1997)andKamath(1998).
Rejectingthenullhypothesisthatreturnsofspeculativeassetsdoesnotfollownormaldistribution,suggeststhatinformationdisseminationprocessmaynotbeefficient20andthereturnarenotsymmetricallydistributedamongbuyersandsellers.
Significantlyskewedreturnsimpliesthatextremelydivergentriskperceptionsforsameinformationsetpersistsinthemarket,whichmaynotallowfuturesandcashmarketreturnstorepresenttheirintrinsicvalueandindicatesthatmarketsdonotadequatelydiscounttheriskpremiumincludedinthenewinformationsettraveledtothemarket.
Asymmetryinthecashandfuturesmarketreturnsisnotanunexpectedphenomenonbecausetraderswithvariedtradinginterests,interactinthemarketandreactheterogeneouslytodifferentnews.
Forinstance,theriskaversenatureoftradersinthemarketmaybeaprominentcausefortheasymmetricreturns(Moolman(2004))becauseduetohighdegreeofvolatilityinspeculativemarkets,bothoptimisticandpessimisticviewsoftraderstonewinformationcausesunexpectedvariationsinprices(DiaglerandWiley(1999)).
Furthermore,inspeculativemarketslikestock,derivativesandcommoditymarkets,ithasbeenobservedthatvolumeonuptick(positivenews)isalwayshigherthanthevolumeondowntick(pessimisticnews),becauseinbullmarkettradersconsidereverydipinthestock/indexasanopportunitytobuy,whichinturncausesspeculativeasset'sreturnstobehaveasymmetrically(fordetailsee,Karpoff(1987)).
Inaddition,basis(whichisaproxyforjointdynamicsbetweenfuturesandcashmarkets)alsoobservesasymmetricbehavior,wherebasisissignificantlyskewedandcoefficientofkurtosissignificantlydiffersfromthree.
Animportantobservationinthesummarystatisticsofbasisisthatitisnegativelyskewedforallindicesandindividualstocks(exceptforDIVISLAB,JINDALSTELandNDTV),whichimpliesthatmoreorlessfuturesareinbackwardationstate,whichmayoffersignificantarbitrageopportunitiestotradersasfoundbyVipul(2005)butasthemeanvalueofbasisismeager(approximatelyclosetozero),thereforeavailablearbitrageopportunitiesseemsnottopersistforlongertimeduration.
ThisobservationsupportsthesampleselectioncriterionbecausesampleunderstudycoverstheperiodwhenIndianequityfuturesmarketbeganobservingphenomenalgrowthintradingvolumethussampleselectioncriterionconformstomarketcompletionhypothesis,whichsuggeststhatinaliquidmarketarbitrageopportunitiesdoesnotlastlong.
Inaddition,thenegativelyskewedbasisprovidesimportantinformationrelatingtotheexploitationofarbitrageopportunitiesandreestablishmentofequilibriumbetween21twomarkets.
Kawalleretal.
,(1987),Ng(1987),StollandWhaley(1990),Chan(1992),WahabandLashgari(1993),Martikainenetal.
,(1995),ArshanapalliandDoukas(1997),JongandDonders(1998),Pizzietal.
,(1998),Boothetal.
,(1999),MinandNajand(1999),Tse(1999),Frinoetal.
,(2000),Chanandlien(2001),Chenetal.
,(2002),Linetal.
,(2002),Thenmozhi(2002),Linetal.
,(2003),Lienetal.
,(2003),Covrigetal.
,(2004),Kenourgios(2004),PattarinandFerretti(2004),SoandTse(2004),Zongetal.
,(2004),MukherjeeandMishra(2006)andThomas(2006)werefewprominentworks,whichhavefoundthatduringlong-runbothmarketsareinequilibriumhoweverexploitablearbitrageopportunitieswereavailableduringshort-run,reflectedintheformoflead-lagrelationshipbetweentwomarketsasaresultofthepresencevariousmarketfrictionsasobservedbyStollandWhaley(1990).
Typesoftradersinthemarketmaybeapotentialfactoraffectingthetheoreticaldistributionofspeculativeasset'sreturns.
ItisanadmittedfactthatIndiancashmarketispredominantlyrunbyforeignaswellasdomesticinstitutionalinvestorsandretailinvestorsplayslittleroleinthemarketmovements.
Ontheotherhand,infuturesmarketretailinvestorsparticipationisverysignificantandinstitutionalinvestorshavelittleroletoplay26.
Thereforeasymmetricprofileofinvestorsinbothmarketsmaybeastrongdeterminantforsignificantasymmetryinbasisbecauseinstitutionalinvestorsbasetheirtradingdecisiononsophisticatedanalysisundertakenbyateamofprofessionalwhereasretailtradersbasetheirdecisiononfirm-specificorinsiderinformation(Thomas(2006)),whichwillbelittlestaleorlateresultantlytimingoftradingbytwogroupofinvestorswillbedifferent,hencenewinformationwilltaketimetodieoutandwillcauseasymmetricjumpsintheconditionalvolatilityofbothmarkets.
Moreover,exploitationofavailablearbitrageopportunitiestosecurerewardoutofmarketdisequilibriumcausesmeanreversioninbasis,whichimpliesthatincreaseinspreadonaccountofreactionbydifferentmarketagentsrevertsbacktoitsintrinsicvaluebecausebasislikeanyfinancialtimeseriespossessesasymptoticproperty.
Therefore,stationarybasisispresumedtoobservemeanrevertingbehaviorbecausewhenspreadbetweentwopricesisdifferentfromcost-of-carry,arbitrageur'sactivitywillcorrectthe26Forreference,seeMonthlyDerivativesMarketUpdatepublishedbyNationalStockExchangeofIndia(www.
nseindia.
com).
22deviationandbasiswillstartrepresentingcost-of-carryoftheunderlyingasset(Zeng(2001),TheobaldandYallup(2001),MonoyiosandSarno(2002)andPattarinandFerretti(2004)).
Thus,meanrevertingbehaviorandnegativecorrelationbetweenbasisandtime-to-expiryofacontractmaybeanotherpotentialreasonforbasistobenegativelyskewed.
Inaddition,positivemeanvalueofreturnsforallindicesandindividualstocksinbothmarketsmaybeduetothesampleselectionbiasbecausethesampleperiodunderstudyobservedsteadybull-runintheIndianequitymarketandthiswastheperiodwhenmajorsourcesofFDIandFII(viz,USA,UKandJapan)wereaggressivelyattractedtowardsthemushroomgrowthintheIndianeconomy,consequentlytherewashugebuyingpressureinthemarket,whichreflectedintothephenomenalgrowthofIndianstockmarketindiceslikeSENSEXandNIFTY,whichgrewfrom3400to13800and1100to4000respectivelyduringthesampleperiod27.
Inadditiontothetheoreticaldistributionalpropertiesoffuturesandcashmarkets,anotherimportantobservationcanbedrawnfromunitroottestresults,whichsuggeststhatreturnsinbothfuturesandcashmarketsaresignificantlypredictable,thusrefutingthenullhypothesisofEfficientMarketTheorythatreturnsinspeculativemarketsfollowrandomwalkmodel28.
Randomwalkmodelrequiresthatpricechangesinspeculativemarketsshouldbeafunctionofnewinformationsetandassetpricesimmediatelydiscountsallrelevantinformationasitbecomesavailable,whichimpliesweakformefficiencyofthespeculativeasset(fordetail,seeFama(1970)).
However,stationeryfuturesandcashmarketreturnssuggeststhatinformationdisseminationefficiencyinIndianequityfuturesandcashmarketsisweakandinformedtraderscanframemarketstrategiestoexploitarbitrageand/orspeculativeopportunitiesasthesebecomeavailable.
ThesefindingsareconsistentwithearlyworksonsimilarhypothesisinIndiancapitalmarketbyBarua(1981),Sharma(1983),Gupta(1985),Rao(1988),Chaudhuri(1991),Reddy(1997),Mishra(1999),AnshumanandGoswami(2000),RanjanandPadhye27Source,www.
bseindia.
comforSENSEXandwww.
nseindia.
comforNIFTY.
28ForreferenceontestingtheRandomWalkHypothesisbyapplyingStationarityTests,seeCrowderandPhengpis(2005)andEvans(2006).
23(2000),PantandBishnoi(2001),Nath(2002),Marisetty(2003),MangalaandMittal(2005)andGuptaandSingh(2006b).
Furthermore,stationarybehaviorofoneadditionalvariablethatis"Basis"providesimportantinformationrelatingtothejointdynamicsofIndianfuturesandcashmarkets.
Asthecost-of-carrymodel(whichisfollowedtodeterminethepriceoffuturescontracts)suggeststhatpriceofafuturescontractatanytimeshouldbesumofthespotpriceofunderlyingassettradedincashmarketandriskpremiumtoholdsuchasset.
Thereforeonmaturitydatewhenriskpremiumceases,bothmarketswillconverge.
StationerybehaviorandlowmeanofbasisintableIIandIIIrespectivelyconfirmsthatbothmarketsobservestableandstrongcomovementoverthecontractcycle,whichimpliesthatbothmarketsareinlong-runequilibriumhoweverexploitablearbitrageopportunitiesmaybeavailableduringveryshort-run.
ThesefindingsareconsistentwithFortenberyandZapata(1997),Alexander(1999),Neuberger(1999),Sahadevan(2002),Linetal.
,(2003),PattarinandFerretti(2004)andKumar(2004).
FortenberyandZapata(1997)andKumar(2004)furthermentionedthatabsenceofstationaryandpredictablebasismaybearesultofeitherimmaturityofthemarket(s)and/orinappropriateregulatoryframework.
Stationerybasisandstrongcomovementbetweenfuturesandcashmarketsduringlong-run29motivatestheauthorstomodifytheminimumvariancehedgeratioestimationmodel,whichwasproposedbyEderington(1979)(asgiveninequation(1))toincludefirstlagoffuturesreturnsandbasis,thustheoriginalmodelwasrepealedtoequation(4),whichwillhelptraderstopredictfuturespotpricemovementsonthebasisofcurrentfuturespriceandlagsofspotpriceitself.
Hedgeratioestimationthroughequation(4)(withappropriateestimationprocedurelikeOLS,GARCH,EGARCHandTARCH)thoughtheoreticallyseemsbetterthanthatproposedinEderington(1979)buttheresultsofvariancereductionthroughdifferentoptimalhedgeratiosestimatedbyapplyingsixeconometricmethodologiesinthepresentstudyfavorstheestimationofoptimalhedgeratiothrougheitherVARorVECM.
29Inordertodeterminethelong-runrelationshipbetweenfuturesandcashmarkets,thecointegrationprocedureproposedbyJohansenandJuselius(1990)hasbeenundertakenandtheresultsofλMaxandλTracetestssuggeststhatbothmarketsareinequilibriumduringlong-run.
Inordertosavethespace,resultsofcointegrationtestsarenotattachedwiththispaperbutareavailableondemand.
24HedgeratiosestimatedthroughVARmethodologywaslowestforthreeindices(namelyBankNifty,CNXITandNifty)ascomparedtothatestimatedthroughothermethodologiesandthetimevaryinghedgeratiosestimatedthroughGARCH,EGARCHorTARCHmethodologieswashighest,whichimpliesthatignoringthetheoreticalrelationshipbetweenseriesunderexaminationescalatesthehedgingcost,whichislaterreflectedinthelowerportfoliovalue.
Thesefindingssupportthetheoreticalrelationshipbetweentwomarkets,becauseCNXITandNiftyobservessignificantbidirectionalcausalitywhereas,cashmarketreturnssignificantlycausedfuturesreturnsforBankNifty.
Moreover,thecausalrelationshipbetweentwomarketswiththeaidofImpulseResponseAnalysiscouldbefurtherinterpretedintermsoflead-lagrelationshipbetweentwomarkets.
ItwasobservedthatincaseofBankNiftyandNifty,cashmarketleadsfuturesmarketandincaseofCNXITfuturesmarketleadscashmarket.
Furthermore,incaseofBankNifty,itdependsuponfuturesmarkettocorrectthedisequilibriumwhereasincaseofNifty,theerrorcorrectiontermissignificantforbothmarketsbutthemagnitudeofthecoefficientoferrorcorrectiontermsuggeststhatinordertoreestablishmarketequilibrium,futuresmarkethastomakedoubleadjustmentascomparedtothatbycashmarket.
ThefindingsthatcashmarketleadsfuturesmarketinIndiaarenotnewobservationsandareconsistentwiththeearlyfindingsofGuptaandSingh(2006c),MukherjeeandMishra(2006)andThomas(2006).
Thetheoreticalrelationshipbetweentwomarketsseemstobeasignificantfactorcontributingtotheefficiencyoftheoptimalhedgeratio.
ThusfindingVARorVECMhedgeratiosbetterthantimevaryinghedgeratiosestimatedthroughGARCH,TARCHandEGARCHisjustifiableandtheseresultsareconsistentwiththefindingsofCastelino(1992),ParkandSwitzer(1995),KoutmosandPericli(1998),Alexander(1999),Poomimarsetal.
,(2003),AlizadehandNomikos(2004),FlorosandVougas(2004),PattarinandFerretti(2004),YangandAllen(2004),LienandShrestha(2005),FlorosandVougas(2006),BhaduriandDurai(2007)andBhargavaandMalhotra(2007).
Furthermore,outofeightyfourindividualstocksunderexamination,fiftyfour(64.
28%)andnine(10.
71%)stocksfavourtheoptimalhedgeratioestimatedthrough25VARandVECMrespectively,fifteen(17.
86%)andfour(4.
76%)stockssupportsOLSandGARCHhedgeratiorespectively,whereasfive(5.
95%)stockseachfavoursthehedgeratioestimatedthroughEGARCHandTARCHmethodologyrespectively30.
Outoftotalnumberofstocksunderexamination,approximately93%stocksfavorsconstanthedgeratioandoutoftotalstocksfavoringconstanthedgeratio,81%stocksfavortheoptimalhedgeratioestimatedthroughVARorVECM,whichisconsistentwiththeresultsofoptimalhedgeratioforindicesasdiscussedabove.
Therefore,overallresultsinthecurrentstudyfavorsconstanthedgeratio,whichareconsistentwithLien(2005b)whosuggestedthathedgeratiobaseduponOLS(despiteofviolationofstatisticalproperties)willoutperformtimevaryinghedgeratioexceptwhenmajorstructuralchangeshavetakenplaceinthemarket.
Moreover,FergusonandLeistikow(1998)byapplyingDickey-Fullertest,mentionedthatrejectionofconstanthedgeratiohypothesismayberesultofinadequatedatapoints,thereforehedgeratiocomputedoverlong-runwillbestationary.
SincethesampleperioddidnotobserveanystructuralchangeintheIndiancashorfuturesmarketandthesampleperiodcontainssufficientdatapoints(seeNath(2003))drawnoutofliquidmarket,thusourresults(asdiscussedabove)areconsistentwiththefindingsofGrammatikosandSaunders(1983),McNewandFackler(1994),FergusonandLeistikow(1998),Loetal.
,(2002)andLien(2005b).
Furthermore,manyempiricalfindingshavesuggestedthatEderington'soptimalhedgeratioperformsbetterintheexpostsettingratherthaninexantesetting,whichimpliesthatEderington'sefficienthedgeratioshouldbecalculatedbyconsideringdataforfuturesaswellascashmarketsofsameperiods.
However,asalreadymentionedthatinequation(4),optimalnumberoflagsofcashmarketreturns(onthebasisofSchwarzInformationCriteria),onelagofbothfuturesreturnsandbasiswasincludedtoefficientlyforecastthecashmarketchanges.
Therefore,theoptimalOLShedgeratio(intableIV)doesnotsufferfromthecriticismofEderington'shedgeratiobyFiglewski(1984),30Thetotalnumberofoptimalhedgeratios(92)exceedsthetotalnumberofstocks(84)becausesevenstocks(namely,HEROHONDA,IDBI,IPCL,KTKBANK,ORIENTBANK,RELCAPITALandSCI)haveoptimalhedgeratioformorethanonemethodology.
26KamaraandSiegel(1987),Myers(1991),Holmes(1995),Alexander(1999)Neuberger(1999),Ariasetal.
,(2000),Lien(2000),Giaccottoetal.
,(2001)andLoetal.
,(2002).
Findingsinthestudyareequallyimportantfortraders,regulatorybodies,practitionersandacademiciansbecauseitcommentsuponthetheoreticalrelationshipbetweentwomarketsandinterpretsuchrelationshipineconomictermstoreducetheportfoliorisk.
Theauthorshavefoundthathedgingthroughindexfuturesreducesportfoliovariancebyapproximately96%whereasincaseofindividualstocks,thereductioninportfoliovariancerangesbetween79%forSUNPHARMAand98.
50%incaseofTITAN.
Therefore,itisevidentfromabovediscussionthatstrongandstablecomovementbetweenIndianequityfuturesandcashmarketswillbehelpfulfortraderstosignificantlyreduceportfoliovariancesubjecttothecoefficientofdeterminantbetweentwomarketsassuggestedbyEderington(1979).
Sincetheefficiencyofoptimalhedgeratioissubjecttostrongandstablecomovementbetweenfuturesandcashmarkets,therefore,theseresultscanhelpTheSecuritiesandExchangeBoardofIndia(SEBI)inpolicyframing31.
Therefore,priortoannounceanypolicychanges,SEBIshouldgivedueconsiderationtotheirpotentialimpactuponthecost-of-carryrelationshipbetweentwomarketsbecauseanyreformintheIndiancapitalmarketwillaffectthehedgingefficiencyofderivativesmarket.
ThusSEBIshouldmakeeffortstostrengthentherelationshipbetweentwomarketsbyremovingvariousimperfectionsintheIndianderivativesmarketslikerestrictiononinstitutionaltraderstoparticipateinfuturesmarket,largelotsizesincaseofindividualstockfutures,underdevelopmentofequityoptionsmarketetc.
SectionIV:ConclusionLastoneandhalfdecadehasbroughtseachangeintheIndiancapitalmarketsuchas,screenbasedtradingreplacedopenoutcrytradingsystem,demataccountsreplaced31ReductioninticksizeofTSE35IndexParticipationUnitsfrom0.
60%to0.
25%oftheprevailingpriceimproveditspricediscoveryefficiencyinCanada,whichimpliesthatimprovementsincontractspecificationsimprovepricediscoveryefficiencyoftheasset.
Furthermore,Jiangetal.
,(2001)foundthatcontemporaneousrelationshipbetweenfuturesandcashmarketstrengthenedwithremovalofshortsellingrestrictionsintheHongKongcashmarketparticularlywhenthemarketwasundergoingbearphaseandtheunderlyingassetwasrelativelyoverpriced.
Therefore,irrationaltradingspecificationsofthefuturescontractswillberesponsibleforviolationofthecommonnotionthatanassetwhichinvolveszeroinvestmentwillalwaysbebetterpricediscoveryvehicle(Beaulieuetal.
,(2003)).
27sharecertificates,floortradingreplacedbyinternettrading,badlatradinghasbeenbanned,compulsoryrollingsettlementwasintroduced,fixedpriceissueswerereplacedbypartialorcompletebookbuildingissuesinprimaryissuemarket,establishmentofinterconnectedstockexchangeetc.
OneofthemostimportantreformsintheIndiancapitalmarkethadbeentointroduceequityderivatives(futuresandoptions)asefficientpricediscoveryandhedginginstrument.
ThesuccessofderivativestradinginIndiancapitalmarketcanbeadjudgedfromthefactthatindexandindividualstockfuturescontractshavebeencontinuouslyratedamongsttopfiveexchanges(intermsoftradingvolume)intheworld32.
Volumeexplosioninthefuturesmarkethasbeenasubjectofinterestforpractitioners,traders,regulatorybodiesandacademiciansbecausehugevolumeinthemarketespeciallythroughretailtraders(becauseretailtraderscontributestoapproximately60%oftotaltradingvolumeinIndianderivativesmarket)raisesmanyquestionsrelatingtotheinformationdisseminationefficiencyoffuturesmarketsaswellasthechangeinpricediscoveryefficiencyofcashmarketaftertheintroductionoffuturestrading,hedging,arbitrageefficiencyoffuturesmarketandanotherimportantquestionwhetherfuturestradinghasstabilizedordestabilizedthecashmarket.
AlltheseissueshavebeenadequatelyansweredinthedevelopedmarketsaswellasemergingmarketsbuthedgingefficiencyoftheIndianequityfuturesmarkethasnotyetbeengivendueattention.
Tothebestofresearcher'sknowledge,BhaduriandDurai(2007)hasbeentheonlywork(seesectionI),whichexaminedthehedgingefficiencyofIndianequityfuturesmarketbutthescopeofthatstudyaswell(likestudiesconductedindevelopedmarkets)isrestrictedtotheinvestigationofhedgingefficiencyofIndex(i.
e.
Nifty)futuresonly.
Therefore,presentstudyhasbeenanattempttofilltheliteraturegapbyexaminationofthehedgingefficiencyofbothindexaswellasindividualstockfuturescontractstradedonNationalStockExchangeofIndiaoverthesampleperiodJan.
2003toDec.
2006.
32ForreferenceseeMonthlyDerivativesMarketUpdatesPublishedbyNationalStockExchangeofIndia(www.
nseindia.
com).
28Thestudyfindsasymmetricandsignificantlykurticfuturesandcashmarketreturns,whichrefutesthenullhypothesisthatinanefficientspeculativemarketreturnsaresymmetricallydistributedamongbuyersandsellers.
Furthermore,bothfuturesandcashmarketreturnshavebeenfoundstationery,whichrejectsthehypothesisthatinaliquidstockmarketsuccessivepricemovementsfollowsrandomwalkmodel,whichimpliesthatinformationdisseminationprocessinbothfuturesandcashmarketsisnotefficient.
Inaddition,jointdynamicsofbothmarkets(i.
e.
Basis)hasbeenfoundstationery,whichimpliesthatstablelong-runrelationshipbetweentwomarketspersist,whichwaslaterconfirmedthroughJohansenandJuselius(1990)cointegrationtestresults(Cointegrationresultsarenotreportedbutareavailableondemand).
Afterexaminingthenatureofseriesunderconsiderationandtherelationshipbetweentwomarkets,thehedgingefficiencyofbothindexaswellasindividualstockfuturescontractshasbeeninvestigatedintheminimumvariancehedgeratioframeworkassuggestedbyEderington(1979).
Theoriginalmodelwasrepealedtoaccommodatethetheoreticalrelationshipbetweentwomarkets(fordetailseesectionII)andthefinalmodelwasestimatedthroughsixeconometricprocedures(subjecttothefitnessofmodel)namely,OLS,GARCH,TARCH,EGARCH,VARandVECM.
ThestudyfindsthathedgeratioestimatedthroughVARorVECMreducedtheportfoliovariancebymaximumextent,whereasothermethodologiesbyconsideringthestylizedfeaturesoffuturesandcashmarkets,estimatedhigherhedgeratios,requiringhigherinitialinvestment,whichwaslatershowninthereducedportfoliovalue.
ResultsinthepresentstudyareconsistentwiththefindingsofCastelino(1992),ParkandSwitzer(1995),KoutmosandPericli(1998),Alexander(1999),Poomimarsetal.
,(2003),AlizadehandNomikos(2004),FlorosandVougas(2004),PattarinandFerretti(2004),YangandAllen(2004),LienandShrestha(2005),FlorosandVougas(2006),BhaduriandDurai(2007)andBhargavaandMalhotra(2007),whofoundthatignoringthetheoreticalrelationshipbetweenfuturesandcashmarketswillescalatethehedgeratio.
Inaddition,thehedgeratioestimatedthroughOLS(despiteoftheviolationofstatisticalproperties)providesbetterhedgingthanthehedgeratiosestimatedthrougheitherofconditionalheteroscedasticitymodelappliedinthestudy.
29ThestudyalsofindsthathedgingthroughindexfuturesinIndiareducesportfoliovarianceby96%howeverhedgingthroughindividualstockfuturesreducesportfoliovarianceintherangeof79%forSUNPHARMAand98.
50%incaseofTITANsubjecttothestrengthofliaisonandstablecomovementbetweentwomarkets,whichisconsistentwiththefindingsofEderington(1979).
Findingsofthestudyareimportantfortradersbecauseitsuggeststhathedgersshouldhedge(eitherstraightorcrosshedge)throughliquidfuturescontractssothattheycanavoidhedgingcostescalationsandtheyshouldestimatethelong-runhedgeratioonthebasisofcost-of-carryrelationshipbetweentwomarkets.
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40TableIEmpiricalEvidenceonHedgingEfficiencyofFuturesMarketsAuthor(YearofStudy)MarketUnderstudySymbolsSamplePeriodMethodologyAppliedHedgingEffectivenessEderington(1979)U.
S.
A.
GNMAandT-BillFuturesMarketsJan.
1976toDec.
1977andMar.
1976toDec.
1977OLSFutureshedgingisbetterforlongerperiodthanshortperiodFiglewski(1984)U.
S.
A.
S&P500,NYSE,AMEX,NASDAQ,DOWJune1982toSept1983OLSBasisriskdisturbsthehedgingeffectivenessthereforeoneweekhedgingisbetterthanovernighthedging.
KamaraandSiegel(1987)U.
S.
A.
SoftWheatandHardWheatJan.
1970toMarch1981OLSFarperiodhedgingisbetterthanneartoexpirationperiodMyers(1991)U.
S.
A.
WheatFuturesJune1977toMay1983OLSandBGARCHTimevaryinghedgeratioisbetterthatconstanthedgeratioKronerandSultan(1993)U.
S.
A.
BP,CD,GM,JYandSFFeb.
1985toFeb.
1990Nave,OLS,ECMandECM-GARCHTimevaryingerrorcorrectionmethodologytakescareoftransactioncostthusoutperformsothermethodologies.
LienandLuo(1994)U.
S.
A.
BP,CD,GM,JYandSFMarch1980toDec.
1988OLS,BGARCH,ECMIftraderisextremelyriskaverter,bothconstantandtimevaryinghedgeratiosareequallyefficientwhereastoachieveutilitymaximizationobjectiveGARCHhedgeratioismostefficientHolmes(1995)U.
K.
FTSE100FuturesandFTSE100IndexJuly1984toJune1992ExPostMVHR,ExAnteMVHRandBetaMVHRbaseduponhistoricaldataisbetterParkandSwitzer(1995)U.
S.
A.
andCanadaS&P500,MMIandTSE35June1988toDec.
1991Nave,OLS,OLSwithCointegrationandBGARCHTimevaryinghedgeratioissuperiortoconstanthedgeratiosContd……….
41AggarwalandDemaskey(1997)HongKong,SouthKorea,Singapore,Taiwan,Indonesia,PhilippinesandThailandBP,CD,GM,JYandSFJan.
1983toDec.
1992NaveandOLSCrosshedgingisbeneficialTheobaldandYallup(1997)U.
K.
FTSE100FuturesandFTSE100IndexJan.
1985toDec.
1995OLSFuturescontractscanprovidehedgingbenefitonlywhenbothmarketsdonotsufferwiththeproblemofnonsynchronoustrading.
LiandVukina(1998)U.
S.
A.
CornYieldFuturesJan.
1951toDec.
1994OLSDualhedgingthroughpriceaswellasyieldfuturescontractscanbemoreeffectivethanthroughpricefuturesonlyLienandShaffer(1999)Japan,U.
S.
A.
,SouthKorea,HongKongandSpainNikkei,S&P500,TOPIX,KOSPI,HangSengandIBEXFuturesSept.
1986toSept.
1989,April1982toApril1985,April1990toDec.
1993,May1996toDec.
1996,Jan.
1987toDec.
1989andApril1993toMarch1995Minimum-ExtendedGiniHedgeRatioTheextendedGinicoefficientasanalternativemeasureofdispersionhasstrongtheoreticalpromiseforuseinfutureshedgingbecauseitdoesnotrequiretherestrictiverequirementofquadraticutilityfunctionsLienandTse(1999)SingaporeNikkeiFuturesJan.
1989toAug.
1997ARFIMA-GARCH,OLS,VAR,EC,FIECConsiderationofcointegrationframeworkimprovesthehedgingperformanceNeuberger(1999)U.
S.
A.
CrudeoilfuturesJuly1986toDec.
1994ExanteOLSRolloveroffuturescontractsaddstohedgingeffectiveness.
KavussanosandNomikos(2000)U.
K.
BIFFEXAug.
1988toOct.
1997OLS,VECM-GARCHStructuralchangeshelpsinimprovinghedgingefficiencyoffuturesmarketContd……….
42Chenetal.
,(2001)U.
S.
A.
S&P500FuturesApril1982toDec.
1991M-GSV,MEG,Sharpe,OLSandStandardMeanVarianceM-GSVminimizestheportfoliovariancebymaximum.
HaighandHolt(2002)U.
K.
Corn,Soybean,WheatandBIFFEXMay1985toJan.
1998OLS,SURandBEKKThoughtimevaryinghedgeratioismoreexpensivebutrewardintermsofreducedvolatilityconsiderableoutweightheextratransactioncosts.
MoschiniandMyers(2002)U.
S.
A.
CornFuturesJan.
1976toJune1997BEKK,GARCHandOLSSupportstimevaryinghedgeratioChenetal.
,(2002)TaiwanTAIFEXTAIEX-TAIEXandSGXMSCIb-MSCIbJuly1998toJuly2000OLS,BayesianApproachHedgingeffectivenessobservespositiverelationshipwithhedginghorizonHarrisandShen(2003)U.
K.
FTSE100FuturesandFTSE100IndexMay1984toMay2002EWMA,RollingWindowROHRTimevaryinghedgeratioisbetterbutROHRwhichaccountsfornonnormalityofdataprovesbetterhedgeratio.
Veld-MerkoulovaandRoon(2003)U.
S.
A.
Crudeoil,orangejuiceandlumberFeb.
1984toJune1998Jan.
1973toMay1998Jan.
1974toMarch1998NaveandOneFactorModelPresenceofmultiplematuritycontractshelpstoefficientlyachievetheobjectiveofmean-varianceportfolioAlizadehandNomikos(2004)U.
S.
A.
,U.
K.
S&P500FuturesandS&P500IndexandFTSE100FuturesandFTSE100IndexMay1984toMarch2001OLS,ECM,GARCHandMarkovRegimeSwitchingModelsByallowingthehedgeratiotobedependentuponthestateofmarket,onemayobtainmoreefficienthedgeratio.
Chenetal.
,(2004)U.
S.
A.
,U.
K.
Canada,Japan,Australia7StockMarketIndexfutures,11Commodityfutures,2metalsand5currenciesJune1982toDec.
1997OLSShort-runhedgeratioissignificantly<1butasthehedgehorizonincreasesitapproachesto1andthehedgingeffectivenessalsoimproves.
Contd……….
43PattarinandFerretti,(2004)ItalyFib30andMib30IndexNov.
1994toSept.
2002NAVE,OLS,ECM,GARCH,EWMATimevaryinghedgeratiobaseduponEWMAisbetterYangandAllen(2004)AustraliaAOIandSPIJune1992toDec.
2000OLS,VAR,VECMandMGARCHRiskminimizationtheorypreferstimevaryinghedgeratiohoweverwhenreturneffectsarealsoconsidered,theutilitybasedmeasureprefersOLS.
Duringout-of-samplehedgingdynamichedgeratioprovesbetterthanOLS.
KofmanandMcGlenchy(2005)HongKongHSIFandHISJan.
1994toJuly2003Nave,Expandingwindow,RollingWindow,EWLSandROCDynamichedgingisbetterthanconstanthedgingLienandShrestha(2005)U.
S.
A.
,U.
K.
Canada,Japan,AustraliaSevenStockIndexFutures,Twopreciousmetals,fivecurrenciesandTencommodities1982to1997ECM(AIC)andECM(FIC)BothareequallyfruitfulbutECM(AIC)islittlebitbetterthanother.
FlorosandVougas(2006)GreeceFTSE/ASE20IndexFuturesandFTSE/ASEMid40IndexFuturesAug.
1999toAug.
2001andJan.
200toAug.
2001OLS,ECM,VECMandBGARCHTimevaryinghedgeratioissuperiortoconstanthedgeratiosInandKim(2006)U.
S.
A.
S&P500FuturesandS&P500IndexApril1982toDec.
2001WaveletAnalysisHedgingeffectivenessdoesnotonlydependsuponhedginghorizonbutriskaversionofhedgeralsoaffectsthehedgingeffectiveness.
InvestorwithlowriskaversionhaveshortrunHEandviceversa.
BhaduriandDurai(2007)IndiaNiftyFuturesandNiftySept.
2000toAug.
2005OLS,ECM,BVARandMGARCHGARCHmodelperformsbetterinthelongrunwhereasOLSisabettermeasureduringshort-run.
Contd……….
44BhargavaandMalhotra(2007)U.
S.
A.
CottonandSoybeansFuturesJan.
1994toDec.
1999andJan.
1995toDec.
2000Traditionalregressionmethod,ModifiedregressionmethodandECMTraditionalregressionmethodperformsbetterthanothersLeeandYoder(2007)U.
K.
CornandNickelFuturesandSpotMarketsJan.
1991toDec.
2004RS-BEKK,BEKKandOLSTimevaryinghedgeratioperformsbetter.
Source:Compiledfromvariousempiricalstudies.
Where,AIC=AkaikeInformationCriteria,AOI=AllOrdinarySharePriceIndex,BP=BritishPound,CD=CanadianDollar,ECM=ErrorCorrectionMethodology,EWMA=ExponentialWeightedMovingAverage,GARCH=GeneralizedAutoregressiveConditionalHeteroscedasticity,GM=GermanMark,,HIS=HangSengIndex,HSIF=HangSengIndexFutures,MVHR=MinimumVarianceHedgeRatio,SF=SwissFranc,SPI=SharePriceIndexFutures,OLS=OrdinaryLeastSquare,U.
S.
A.
=UnitedStatesofAmerica,U.
K.
=UnitedKingdom,VAR=VectorAutoregression.
45TableIIUnitRootTestResultsAugmentedDickeyFullerTestPhilipsPerronTestSymbolsVariablesWithoutDriftWithDriftandTrendWithoutDriftWithDriftandTrendFUTURES-16.
73*-16.
76*-16.
74*-16.
65*CASH-14.
19*-14.
26*-16.
24*-16.
20*BANKNIFTYBASIS-6.
32*-6.
34*-10.
21*-10.
22*FUTURES-30.
17*-30.
34*-30.
48*-31.
03*CASH-29.
04*-29.
21*-29.
30*-29.
75*CNXITBASIS-6.
49*-6.
58*-16.
15*-16.
36*FUTURES-31.
16*-24.
31*-31.
16*-31.
33*CASH-23.
77*-24.
01*-28.
52*-28.
72*NIFTYBASIS-7.
76*-8.
61*-12.
25*-13.
80*FUTURES-18.
74*-18.
94*-18.
97*-19.
05*CASH-17.
77*-17.
97*-17.
93*-18.
06*ABBBASIS-8.
24*-8.
35*-8.
09*-8.
19*FUTURES-31.
38*-31.
61*-31.
39*-31.
62*CASH-30.
82*-31.
06*-30.
82*-31.
07*ACCBASIS-10.
24*-10.
78*-10.
29*-10.
82*FUTURES-18.
95*-18.
92*-18.
95*-18.
92*CASH-18.
53*-18.
49*-18.
54*-18.
50*ALBKBASIS-3.
34*-3.
38**-4.
02*-4.
10*FUTURES-15.
98*-15.
94*-18.
98*-18.
93*CASH-16.
16*-16.
12*-18.
30*-18.
25*ALOKTEXTBASIS-5.
70*-5.
80*-7.
55*-7.
72*FUTURES-21.
84*-21.
84*-25.
35*-25.
34*CASH-21.
53*-21.
53*-24.
86*-24.
85*ANDHRABANKBASIS-7.
31*-9.
09*-12.
46*-13.
35*FUTURES-20.
34*-20.
45*-24.
89*-24.
94*CASH-20.
27*-20.
40*-24.
65*-24.
71*ARVINDMILLSBASIS-31.
06*-31.
02*-77.
93*-77.
95*FUTURES-15.
58*-15.
66*-18.
57*-18.
62*CASH-18.
24*-18.
29*-18.
15*-18.
19*ASHOKLEYBASIS-6.
37*-7.
03*-7.
59*-8.
23*FUTURES-19.
65*-19.
73*-19.
66*-19.
73*CASH-19.
70*-19.
79*-19.
70*-19.
79*AUROPHARMABASIS-5.
07*-6.
87*-12.
73*-15.
13*FUTURES-31.
07*-31.
26*-31.
07*-31.
26*CASH-31.
29*-31.
48*-31.
29*-31.
48*BAJAJAUTOBASIS-6.
84*-6.
92*-13.
16*-13.
26*FUTURES-22.
19*-22.
18*-26.
05*-26.
06*CASH-21.
67*-21.
66*-24.
90*-24.
91*BANKBARODABASIS-7.
33*-7.
60*-12.
83*-13.
29*FUTURES-25.
86*-25.
89*-25.
72*-25.
74*CASH-25.
83*-25.
86*-25.
69*-25.
71*BANKINDIABASIS-7.
82*-9.
71*-13.
78*-14.
77*FUTURES-28.
87*-29.
01*-28.
78*-28.
93*CASH-28.
54*-28.
69*-28.
44*-28.
59*BELBASIS-6.
96*-8.
62*-14.
67*-17.
68*FUTURES-24.
97*-25.
41*-29.
68*-30.
03*CASH-24.
72*-25.
16*-29.
28*-29.
65*BHELBASIS-8.
31*-8.
42*-20.
03*-20.
03*FUTURES-20.
82*-20.
78*-20.
82*-20.
78*CASH-16.
37*-16.
35*-20.
66*-20.
63*BILTBASIS-6.
47*-7.
85*-9.
78*-11.
40*46FUTURES-18.
26*-18.
29*-18.
26*-18.
28*CASH-17.
71*-17.
74*-17.
71*-17.
75*BONGAIREFNBASIS-5.
05*-5.
08*-5.
27*-5.
31*FUTURES-29.
69*-29.
70*-29.
74*-29.
75*CASH-30.
61*-30.
63*-30.
62*-30.
66*BPCLBASIS-7.
12*-7.
37*-16.
25*-16.
45*FUTURES-22.
24*-22.
24*-26.
75*-26.
80*CASH-22.
15*-22.
15*-27.
34*-27.
40*CANBANKBASIS-7.
11*-7.
21*-13.
32*-13.
55*FUTURES-21.
73*-21.
82*-21.
69*-21.
79*CASH-21.
47*-21.
57*-21.
44*-21.
54*CENTURYTEXTBASIS-3.
06*-6.
08*-6.
84*-12.
04*FUTURES-19.
21*-19.
21*-19.
21*-19.
20*CASH-19.
34*-19.
35*-19.
34*-19.
35*CESCBASIS-4.
74*-5.
96*-10.
32*-12.
62*FUTURES-19.
59*-19.
56*-19.
59*-19.
56*CASH-18.
96*-18.
94*-18.
97*-18.
94*CHAMBLFERTBASIS-4.
13*-4.
13*-4.
98*-4.
99*FUTURES-20.
46*-20.
52*-20.
46*-20.
53*CASH-20.
59*-20.
67*-20.
59*-20.
68*COLGATEBASIS-6.
59*-11.
23*-11.
20*-11.
78*FUTURES-17.
64*-17.
59*-17.
61*-17.
56*CASH-17.
14*-17.
10*-17.
08*-17.
04*CORPBANKBASIS-6.
27*-6.
85*-8.
98*-9.
80*FUTURES-19.
76*-19.
80*-19.
76*-19.
81*CASH-19.
58*-19.
62*-19.
58*-19.
62*CUMMINSINDBASIS-5.
45*-7.
05*-8.
96*-11.
50*FUTURES-18.
68*-18.
83*-18.
71*-18.
83*CASH-18.
21*-18.
36*-18.
25*-18.
37*DIVISLABBASIS-5.
56*-8.
29*-11.
27*-15.
07*FUTURES-19.
70*-19.
66*-19.
71*-19.
67*CASH-19.
36*-19.
32*-19.
35*-19.
31*ESCORTSBASIS-18.
69*-19.
10*-18.
69*-19.
09*FUTURES-20.
53*-20.
49*-20.
62*-20.
59*CASH-20.
36*-20.
32*-20.
48*-20.
44*ESSAROILBASIS-2.
82*-9.
00*-7.
63*-13.
69*FUTURES-16.
78*-16.
76*-20.
21*-20.
18*CASH-17.
37*-17.
35*-20.
51*-20.
54*FEDERALBANKBASIS-6.
17*-6.
94*-9.
13*-10.
26*FUTURES-22.
78*-22.
79*-28.
56*-28.
57*CASH-22.
62*-22.
63*-27.
92*-27.
93*GAILBASIS-6.
74*-7.
51*-9.
21*-10.
33*FUTURES-20.
47*-20.
54*-20.
48*-20.
57*CASH-16.
45*-16.
56*-20.
06*-20.
16*GLAXOBASIS-5.
98*-5.
99*-9.
80*-9.
83*FUTURES-19.
62*-19.
61*-19.
67*-19.
66*CASH-19.
63*-19.
62*-19.
67*-19.
70*GNFCBASIS-4.
39*-4.
97*-5.
47*-6.
43*FUTURES-30.
81*-31.
09*-30.
85*-31.
09*CASH-30.
67*-30.
96*-30.
73*-30.
96*GRASIMBASIS-9.
36*-9.
74*-13.
78*-14.
39*FUTURES-32.
26*-32.
31*-32.
66*-32.
99*CASH-31.
61*-31.
66*-32.
02*-32.
28*HCLTCHBASIS-5.
45*-6.
10*-23.
73*-23.
89*FUTURES-24.
58*-24.
75*-31.
90*-32.
26*CASH-24.
69*-24.
86*-32.
06*-32.
43*HDFCBASIS-9.
23*-9.
38*-17.
95*-18.
14*47FUTURES-30.
64*-22.
96*-30.
71*-31.
00*CASH-23.
07*-23.
26*-31.
06*-31.
44*HDFCBANKBASIS-7.
88*-8.
19*-18.
06*-18.
51*FUTURES-30.
33*-30.
39*-30.
40*-30.
55*CASH-30.
63*-30.
69*-30.
81*-31.
00*HEROHONDABASIS-7.
86*-8.
08*-9.
55*-9.
85*FUTURES-30.
68*-30.
67*-30.
68*-30.
67*CASH-29.
54*-29.
53*-29.
52*-29.
50*HINDLEVERBASIS-7.
85*-7.
88*-10.
08*-10.
11*FUTURES-29.
48*-29.
46*-29.
46*-29.
44*CASH-28.
60*-28.
58*-28.
57*-28.
54*HINDPETROBASIS-9.
32*-9.
42*-12.
42*-12.
58*FUTURES-22.
92*-23.
11*-28.
09*-28.
40*CASH-22.
72*-22.
90*-27.
75*-28.
06*ICICIBANKBASIS-5.
65*-7.
05*-14.
67*-15.
69*FUTURES-18.
90*-18.
86*-18.
88*-18.
84*CASH-18.
70*-18.
66*-18.
68*-18.
64*IDBIBASIS-3.
75*-6.
32*-7.
41*-9.
55*FUTURES-14.
65*-14.
64*-18.
48*-18.
45*CASH-14.
61*-14.
60*-18.
75*-18.
71*IDFCBASIS-4.
85*-4.
98*-6.
10*-6.
30*FUTURES-18.
27*-18.
23*-18.
24*-18.
19*CASH-17.
93*-17.
89*-17.
85*-17.
80*IFCIBASIS-2.
57*-9.
34*-6.
45*-13.
97*FUTURES-18.
90*-18.
86*-18.
91*-18.
86*CASH-18.
92*-18.
88*-18.
93*-18.
88*INDUSINDBANKBASIS-4.
58*-7.
05*-8.
16*-10.
85*FUTURES-17.
73*-17.
71*-17.
78*-17.
78*CASH-15.
53*-15.
52*-17.
93*-17.
93*IOBBASIS-6.
29*-6.
65*-7.
74*-7.
83*FUTURES-24.
42*-20.
07*-24.
38*-24.
35*CASH-23.
53*-23.
50*-23.
52*-23.
49*IOCBASIS-7.
13*-7.
16*-15.
13*-15.
18*FUTURES-25.
19*-25.
25*-33.
22*-33.
32*CASH-25.
29*-25.
35*-32.
82*-32.
93*IPCLBASIS-7.
10*-8.
62*-8.
08*-8.
80*FUTURES-20.
06*-20.
10*-20.
05*-20.
10*CASH-19.
19*-19.
23*-19.
13*-19.
21*JETAIRWAYSBASIS-5.
87*-6.
16*-13.
36*-13.
69*FUTURES-9.
09*-9.
21*-18.
32*-18.
35*CASH-9.
03*-9.
16*-18.
12*-18.
16*JINDALSTELBASIS-4.
59*-7.
51*-10.
25*-13.
50*FUTURES-19.
25*-19.
20*-19.
22*-19.
17*CASH-18.
78*-18.
74*-18.
74*-18.
69*JPHYDROBASIS-4.
60*-8.
05*-7.
11*-12.
28*FUTURES-21.
01*-20.
97*-21.
01*-20.
97*CASH-21.
54*-21.
49*-21.
55*-21.
50*JSTAINLESSBASIS-6.
01*-8.
68*-8.
38*-11.
82*FUTURES-20.
04*-20.
04*-20.
04*-20.
04*CASH-19.
74*-19.
74*-19.
74*-19.
74*KTKBANKBASIS-3.
94*-4.
09*-4.
87*-5.
15*FUTURES-18.
65*-18.
65*-18.
61*-18.
61*CASH-18.
46*-18.
46*-18.
46*-18.
46*LICHSGFINBASIS-4.
68*-4.
93*-5.
89*-6.
41*FUTURES-29.
41*-29.
59*-29.
41*-29.
60*CASH-29.
31*-29.
49*-29.
31*-29.
51*MARUTIBASIS-8.
11*-8.
58*-16.
10*-17.
05*48FUTURES-16.
79*-16.
83*-21.
10*-21.
10*CASH-16.
88*-16.
94*-21.
10*-21.
15*MATRIXLABSBASIS-6.
12*-6.
56*-4.
77*-5.
04*FUTURES-19.
82*-19.
78*-19.
81*-19.
76*CASH-19.
74*-19.
69*-19.
74*-19.
69*MRPLBASIS-3.
95*-6.
22*-5.
98*-8.
63*FUTURES-23.
84*-23.
84*-29.
73*-29.
72*CASH-23.
81*-23.
80*-30.
09*-30.
08*MTNLBASIS-8.
84*-9.
57*-11.
33*-12.
33*FUTURES-17.
96*-17.
92*-17.
87*-17.
82*CASH-17.
73*-17.
69*-17.
62*-17.
57*NAGARFERTBASIS-3.
57*-7.
23*-7.
09*-14.
01*FUTURES-29.
07*-29.
07*-29.
02*-29.
02*CASH-28.
17*-28.
18*-28.
09*-28.
09*NATIONALUMBASIS-5.
73*-6.
77*-11.
98*-13.
95*FUTURES-18.
38*-18.
34*-18.
39*-18.
35*CASH-18.
28*-18.
24*-18.
25*-18.
21*NDTVBASIS-2.
88*-9.
66*-9.
54*-15.
24*FUTURES-18.
68*-18.
66*-18.
64*-18.
62*CASH-17.
80*-17.
78*-17.
71*-17.
69*NEYVELILIGBASIS-5.
58*-7.
44*-10.
43*-13.
43*FUTURES-19.
58*-19.
53*-19.
56*-19.
52*CASH-19.
01*-18.
97*-18.
98*-18.
93*NICOLAPIRBASIS-5.
21*-5.
57*-11.
29*-11.
93*FUTURES-22.
51*-22.
55*-22.
53*-22.
60*CASH-18.
19*-18.
27*-22.
25*-22.
31*NTPCBASIS-4.
99*-5.
90*-9.
62*-11.
05*FUTURES-21.
91*-21.
91*-24.
89*-24.
88*CASH-22.
46*-22.
46*-24.
61*-24.
60*ORIENTBANKBASIS-8.
81*-9.
06*-10.
77*-11.
12*FUTURES-15.
70*-15.
69*-18.
89*-18.
86*CASH-19.
63*-19.
60*-19.
60*-19.
58*PATNIBASIS-8.
37*-9.
84*-13.
86*-14.
48*FUTURES-26.
68*-26.
71*-26.
61*-26.
64*CASH-25.
98*-26.
01*-25.
91*-25.
92*PNBBASIS-4.
83*-4.
98*-9.
02*-9.
19*FUTURES-29.
54*-29.
52*-29.
50*-29.
49*CASH-29.
04*-29.
03*-28.
99*-28.
97*POLARISBASIS-5.
21*-7.
92*-8.
95*-14.
77*FUTURES-22.
08*-22.
07*-28.
34*-28.
33*CASH-21.
52*-21.
51*-27.
60*-27.
57*RELBASIS-4.
45*-4.
48*-10.
55*-10.
60*FUTURES-19.
62*-19.
74*-19.
70*-19.
77*CASH-19.
29*-19.
41*-19.
37*-19.
43*RELCAPITALBASIS-3.
18*-7.
54*-6.
62*-11.
88*FUTURES-31.
77*-31.
90*-31.
78*-31.
90*CASH-32.
65*-32.
78*-32.
64*-32.
80*RELIANCEBASIS-6.
55*-8.
79*-14.
54*-17.
05*FUTURES-30.
31*-30.
40*-30.
28*-30.
39*CASH-23.
64*-23.
78*-29.
70*-29.
81*SBINBASIS-6.
58*-7.
88*-9.
22*-11.
73*FUTURES-28.
86*-28.
87*-28.
79*-28.
80*CASH-29.
40*-29.
41*-29.
36*-29.
37*SCIBASIS-8.
63*-9.
20*-12.
44*-13.
13*FUTURES-18.
56*-18.
67*-18.
64*-18.
71*CASH-18.
37*-18.
49*-18.
45*-18.
52*SRFBASIS-4.
81*-6.
51*-6.
58*-9.
41*49FUTURES-20.
08*-20.
04*-20.
10*-20.
07*CASH-18.
68*-18.
65*-18.
63*-18.
60*STARBASIS-4.
57*-5.
10*-12.
44*-13.
06*FUTURES-20.
97*-21.
11*-20.
97*-21.
16*CASH-20.
57*-20.
70*-20.
58*-20.
78*SUNPHARMABASIS-3.
11*-10.
56*-7.
54*-10.
57*FUTURES-20.
70*-20.
72*-24.
29*-24.
29*CASH-20.
71*-20.
73*-24.
55*-24.
56*SYNDIBANKBASIS-6.
07*-6.
20*-9.
50*-9.
77*FUTURES-21.
80*-21.
85*-21.
80*-21.
88*CASH-21.
16*-21.
24*-21.
15*-21.
24*TATACHEMBASIS-2.
58*-2.
58-5.
45*-5.
49*FUTURES-31.
41*-31.
55*-31.
44*-31.
65*CASH-24.
07*-24.
27*-30.
73*-30.
90*TATAMOTORSBASIS-6.
18*-6.
33*-14.
80*-15.
44*FUTURES-24.
69*-24.
87*-30.
26*-30.
39*CASH-24.
57*-24.
76*-29.
52*-29.
65*TATAPOWERBASIS-7.
25*-7.
75*-11.
54*-12.
38*FUTURES-28.
31*-28.
43*-28.
19*-28.
27*CASH-28.
08*-28.
22*-27.
96*-28.
04*TATATEABASIS-7.
01*-7.
58*-10.
77*-11.
95*FUTURES-18.
14*-18.
27*-18.
15*-18.
24*CASH-18.
00*-18.
13*-18.
01*-18.
09*TITANBASIS-4.
24*-7.
62*-6.
50*-10.
19*FUTURES-18.
92*-18.
96*-18.
90*-18.
92*CASH-18.
44*-18.
48*-18.
39*-18.
42*TVSMOTORSBASIS-4.
99*-5.
67*-9.
06*-10.
49*FUTURES-25.
56*-20.
94*-25.
38*-25.
39*CASH-21.
29*-21.
32*-25.
69*-25.
71*UNIONBANKBASIS-7.
87*-8.
22*-12.
00*-12.
50*FUTURES-19.
68*-19.
74*-19.
69*-19.
72*CASH-20.
04*-20.
08*-20.
04*-20.
11*UTIBANKBASIS-8.
45*-8.
79*-13.
21*-13.
68*FUTURES-19.
21*-19.
17*-19.
21*-19.
17*CASH-19.
35*-19.
31*-19.
38*-19.
34*VIJAYABANKBASIS-5.
13*-8.
30*-9.
62*-12.
64*FUTURES-18.
52*-18.
56*-18.
48*-18.
50*CASH-17.
76*-17.
80*-17.
66*-17.
68*WOCKPHARMABASIS-4.
81*-6.
06*-9.
30*-12.
21**and**Significantat1%and5%significancelevelrespectively.
50TableIIIDescriptiveStatisticsSymbolsVariablesCountMeanStd.
Dev.
SkewnessKurtosisJarque-BeraFUTURES3850.
0013350.
018441-0.
4023224.
92633069.
73120*CASH3850.
0013030.
017815-0.
3429604.
80610459.
71997*BANKNIFTYBASIS3850.
0001450.
004792-1.
3313757.
626209455.
8728*FUTURES8330.
0015430.
018978-0.
45309816.
481916337.
159*CASH8330.
0015400.
018263-0.
15068510.
599002007.
378*CNXITBASIS8339.
52E-050.
004863-0.
97118610.
698062187.
767*FUTURES9980.
0012830.
016032-1.
33524916.
589767976.
229*CASH9980.
0012850.
014715-1.
11883012.
022163593.
070*NIFTYBASIS998-0.
0018520.
004742-1.
3368377.
7764681245.
969*FUTURES4170.
0027720.
022791-0.
3399257.
085139297.
9909*CASH4170.
0027680.
021458-0.
2800585.
979046159.
6492*ABBBASIS4170.
0039750.
038626-0.
99507610.
685341095.
062*FUTURES9980.
0020740.
022250-0.
2509756.
084294397.
9166*CASH9980.
0018580.
021621-0.
1835685.
662628294.
3933*ACCBASIS9980.
0122910.
046800-0.
7934999.
8953912040.
148*FUTURES4230.
0002940.
021564-0.
2232524.
70078654.
36834*CASH4230.
0002320.
021425-0.
4058195.
16943094.
33782*ALBKBASIS4230.
0012320.
014579-3.
24739713.
339292621.
382*FUTURES3950.
0001340.
0263110.
0658735.
19053079.
25971*CASH3950.
0001370.
0262820.
0177935.
27995585.
57444*ALOKTEXTBASIS3950.
0017710.
010369-2.
75438915.
911633243.
228*FUTURES8330.
0008100.
029950-0.
3383938.
4119931032.
493*CASH8330.
0008270.
029366-0.
2835428.
193922947.
4825*ANDHRABANKBASIS8330.
0026790.
007080-1.
7672118.
2700471397.
549*FUTURES8130.
0001460.
030516-0.
2795575.
144003166.
3044*CASH8130.
0001540.
029736-0.
2989705.
452913215.
9300*ARVINDMILLSBASIS8130.
0043820.
004635-0.
2945555.
244214182.
3676*FUTURES4220.
0018170.
025420-0.
1810665.
608429121.
9411*CASH4220.
0018240.
025064-0.
1276055.
27048791.
78925*ASHOKLEYBASIS4220.
0031940.
008299-3.
21724215.
924403665.
116*FUTURES4060.
0020810.
0250010.
4797214.
71590165.
38025*CASH4060.
0020890.
0247490.
6783566.
310551216.
5403*AUROPHARMABASIS4060.
0042880.
006542-2.
80909627.
3411510556.
94*FUTURES9980.
0016390.
019676-0.
1049256.
148982414.
1751*CASH9980.
0016420.
019678-0.
0409345.
004078167.
2910*BAJAJAUTOBASIS998-0.
0010490.
008782-1.
9113278.
6522671936.
154*FUTURES8330.
0005970.
033301-0.
82389517.
862077760.
657*CASH8330.
0006120.
031868-0.
49066811.
580422588.
779*BANKBARODABASIS8330.
0019310.
008273-2.
81513318.
320029246.
403*FUTURES8330.
0015960.
034389-0.
1666606.
004010317.
0668*CASH8330.
0016210.
034037-0.
0740835.
676542249.
4081*BANKINDIABASIS8330.
0024040.
006736-1.
5858898.
5244131408.
440*FUTURES9760.
0019470.
0250390.
0608807.
305953754.
6129*CASH9760.
0019500.
0241190.
1388797.
309824758.
5037*BELBASIS9760.
0035050.
005707-0.
7556535.
499208346.
8902*FUTURES9980.
0025890.
024581-1.
18668223.
8518218314.
60*CASH9980.
0025910.
024130-0.
62013714.
831315884.
793*BHELBASIS998-0.
0002480.
006504-1.
56246411.
291073264.
584*FUTURES406-2.
81E-050.
025048-0.
5797968.
185470477.
6210*CASH406-3.
29E-500.
024139-0.
6788918.
284907503.
6737*BILTBASIS4060.
0031830.
005823-1.
1541016.
462803292.
9764*FUTURES406-0.
0017090.
025518-0.
4428678.
706698564.
1865*CASH406-0.
0017160.
024594-0.
5644799.
040376638.
7851*BONGAIREFNBASIS4060.
0018340.
014850-3.
31970713.
764682705.
992*FUTURES9980.
0003830.
024143-0.
1850786.
791118603.
3571*CASH9980.
0004100.
0239290.
0849305.
798982326.
9726*BPCLBASIS998-0.
0019180.
010126-3.
20983326.
2641824219.
55*51FUTURES8330.
0009360.
030764-0.
2506106.
433211417.
8244*CASH8330.
0009570.
030920-0.
0654596.
402834402.
4923*CANBANKBASIS8330.
0010750.
008502-2.
69208515.
376316322.
552*FUTURES4220.
0026840.
035582-0.
3694696.
724674253.
5381*CASH4220.
0026770.
034392-0.
3960106.
884538276.
3560*CENTURYTEXTBASIS4220.
0043850.
004284-0.
6413265.
113970107.
5056*FUTURES4060.
0013300.
027587-0.
8698239.
273369716.
9542*CASH4060.
0013260.
027025-1.
00683810.
940871135.
317*CESCBASIS4060.
0036120.
005945-1.
2896946.
360096303.
5440*FUTURES4060.
0005210.
024639-0.
3901656.
468803213.
8522*CASH4060.
0005250.
023743-0.
5864536.
953154287.
6363*CHAMBLFERTBASIS4060.
0009510.
014609-2.
4788828.
652594956.
3200*FUTURES4220.
0015560.
0247360.
87306811.
777481408.
303*CASH4220.
0015280.
0233661.
12407512.
497081674.
791*COLGATEBASIS4220.
0024420.
006500-2.
45824414.
084892585.
568*FUTURES385-9.
56E-050.
029089-0.
3106878.
409757475.
6606*CASH385-9.
44E-050.
028359-0.
2313587.
591893341.
6809*CORPBANKBASIS3850.
0022240.
007254-0.
8992964.
41688885.
01406*FUTURES3800.
0018880.
0291010.
3407405.
30117091.
19684*CASH3800.
0018880.
0276540.
3491895.
17746782.
79397*CUMMINSINDBASIS3800.
0037750.
005524-0.
8913106.
370101230.
1425*FUTURES4060.
0028550.
027671-0.
1564066.
595236220.
3154*CASH4060.
0028490.
026382-0.
2434157.
151616295.
5836*DIVISLABBASIS4060.
0050370.
0062161.
42937626.
811899730.
106*FUTURES3950.
0007630.
038772-0.
0394554.
86309757.
23151*CASH3950.
0007730.
0378680.
0514795.
05886869.
94029*ESCORTSBASIS3950.
0061510.
038586-0.
1349325.
23408383.
34425*FUTURES4060.
0010440.
0411880.
1384417.
144109291.
8176*CASH4060.
0010340.
0404390.
1672227.
628565364.
3084*ESSAROILBASIS4060.
0052280.
004320-0.
1350103.
92156315.
60036*FUTURES4060.
0008140.
027951-0.
3434007.
535135355.
9122*CASH4060.
0007900.
027611-0.
2719828.
000690428.
0390*FEDERALBANKBASIS4060.
0029990.
007755-2.
18278311.
188241456.
617*FUTURES8130.
0007300.
029285-0.
07606929.
4021223614.
10*CASH8130.
0007870.
028511-0.
09607924.
9759816360.
97*GAILBASIS813-0.
0019800.
010168-1.
7244537.
2454081013.
487*FUTURES4220.
0012180.
023397-0.
0682186.
968143277.
1973*CASH4220.
0011690.
021536-0.
1443715.
917356151.
1171*GLAXOBASIS4220.
0003090.
008384-1.
3740975.
874785278.
1149*FUTURES4060.
0006420.
029120-0.
0210577.
329326317.
1002*CASH4060.
0006380.
0285220.
0158367.
404770328.
2341*GNFCBASIS4060.
0037140.
008721-3.
57208318.
469844911.
842*FUTURES9980.
0021800.
0220670.
2793247.
077563704.
3638*CASH9980.
0021980.
0218030.
3593037.
023161694.
5339*GRASIMBASIS9980.
0013510.
005973-0.
7361944.
074133138.
1268*FUTURES9760.
0013870.
027283-0.
3965419.
9313231979.
337*CASH9760.
0014090.
026749-0.
5164778.
8571871438.
528*HCLTCHBASIS976-0.
0004050.
007440-4.
65956762.
55508147768.
57*FUTURES9980.
0015240.
0215350.
45797210.
871272611.
263*CASH9980.
0015220.
0219930.
3258516.
623006563.
4911*HDFCBASIS998-0.
0010910.
006983-1.
9321819.
8502962572.
338*FUTURES8330.
0016270.
021293-0.
90058433.
2299031830.
71*CASH8330.
0016260.
0218720.
16314331.
9549129102.
70*HDFCBANKBASIS833-0.
0013940.
007019-1.
92646716.
239576599.
142*FUTURES9760.
0011200.
021874-0.
0372834.
855592140.
2505*CASH9760.
0011240.
022953-0.
0599754.
40121780.
43041*HEROHONDABASIS976-0.
0026070.
011626-2.
88021514.
441406672.
918*52FUTURES9980.
0001740.
020556-0.
4117788.
2050801154.
815*CASH9980.
0001750.
020382-0.
3005277.
9197601021.
507*HINDLEVERBASIS998-0.
0003500.
009383-3.
79775722.
5232318248.
77*FUTURES998-9.
67E-050.
024773-0.
2471587.
106269711.
3159*CASH998-9.
14E-050.
023750-0.
2910956.
565608542.
7666*HINDPETROBASIS9980.
0010620.
009080-3.
42446419.
6462413473.
21*FUTURES9760.
0018250.
022797-0.
0035876.
651226542.
1477*CASH9760.
0018270.
0229090.
1256775.
805752322.
7072*ICICIBANKBASIS976-0.
0022420.
010131-1.
5087055.
872128705.
7246*FUTURES422-0.
0002510.
030504-0.
0007066.
125992171.
8213*CASH422-0.
0002420.
0297660.
0182296.
363526198.
9491*IDBIBASIS4220.
0037650.
005785-2.
06135411.
109351455.
165*FUTURES3410.
0003370.
0255040.
5192856.
892131230.
5630*CASH3410.
0003350.
0252230.
5788606.
718258215.
4802*IDFCBASIS3410.
0017890.
008195-2.
31744110.
577661121.
082*FUTURES395-0.
0001700.
0402090.
2065556.
082381159.
1806*CASH395-0.
0001820.
0386980.
1393276.
106062160.
0617*IFCIBASIS3950.
0081170.
005607-0.
3119993.
92042620.
35169*FUTURES406-0.
0004370.
037144-0.
3016247.
088246288.
8971*CASH406-0.
0004530.
036060-0.
2376057.
189613300.
7560*INDUSINDBANKBASIS4060.
0043200.
005991-1.
4319886.
732466374.
4277*FUTURES4220.
0010460.
029337-0.
2067585.
34814699.
95746*CASH4220.
0010590.
0286890.
0399685.
31288294.
17304*IOBBASIS4220.
0025060.
009047-2.
32994111.
059531523.
955*FUTURES8130.
0002570.
026377-0.
74185714.
018384187.
158*CASH8130.
0002670.
025008-0.
3005579.
5654491472.
426*IOCBASIS8130.
0008060.
008691-3.
78353430.
4055727382.
03*FUTURES9760.
0011880.
028615-0.
34866621.
7401314301.
60*CASH9760.
0011960.
027993-0.
26402520.
8999913041.
33*IPCLBASIS9760.
0031180.
008364-4.
06538429.
1402430476.
48*FUTURES447-0.
0016710.
024585-0.
96619711.
332461362.
680*CASH447-0.
0016730.
023963-0.
2922088.
809893635.
0454*JETAIRWAYSBASIS447-0.
0007060.
007656-1.
4200266.
720142407.
9871*FUTURES4220.
0018860.
027820-1.
29097313.
932832218.
899*CASH4220.
0019110.
027083-1.
22684312.
896871828.
113*JINDALSTELBASIS4220.
0042150.
0058850.
2939486.
778386257.
1004*FUTURES424-0.
0001080.
025078-0.
2222767.
423126349.
1229*CASH424-0.
0001160.
024048-0.
4142477.
518913372.
8900*JPHYDROBASIS4240.
0057210.
005045-0.
2676515.
494220114.
9690*FUTURES4060.
0003870.
0359120.
3086388.
646619545.
8220*CASH4060.
0004100.
0350340.
3733289.
414194705.
4145*JSTAINLESSBASIS4060.
0046300.
005711-1.
2902957.
801603502.
6760*FUTURES3950.
0015340.
0323990.
7428048.
116029467.
1004*CASH3950.
0015390.
0311470.
7602137.
596209385.
7311*KTKBANKBASIS3950.
0026090.
010235-2.
66257610.
474271386.
153*FUTURES422-0.
0009590.
022164-0.
3530686.
924634279.
5993*CASH422-0.
0010050.
021463-0.
3664556.
390991211.
6326*LICHSGFINBASIS4220.
0029560.
009162-2.
58193311.
744531813.
410*FUTURES8690.
0019920.
0255300.
1437405.
475066224.
8030*CASH8690.
0019940.
0256180.
2196045.
094221165.
7859*MARUTIBASIS8690.
0009900.
005719-0.
7667885.
023050233.
3479*FUTURES4220.
0004930.
0285620.
5167139.
585583781.
3660*CASH4220.
0004860.
0272170.
95475310.
804311135.
065*MATRIXLABSBASIS4220.
0005210.
020014-5.
56208536.
5770521999.
66*FUTURES422-0.
0002980.
028653-0.
1243717.
606824374.
2559*CASH422-0.
0002710.
027545-0.
0479587.
832747410.
8282*MRPLBASIS4220.
0045050.
005729-1.
2284385.
230728193.
6344*53FUTURES9980.
0003950.
026942-0.
0043906.
994797663.
6067*CASH9980.
0003950.
0269110.
1030276.
617215545.
8520*MTNLBASIS9980.
0024870.
006506-2.
13017411.
437593715.
198*FUTURES395-0.
0003240.
032234-0.
4666618.
717735552.
4005*CASH395-0.
0003280.
030799-0.
3805868.
194810453.
6811*NAGARFERTBASIS3950.
0071190.
005592-1.
2555579.
429140784.
0674*FUTURES9760.
0008820.
028790-0.
6377959.
1885471623.
626*CASH9760.
0009150.
027043-0.
6142647.
778732990.
0529*NATIONALUMBASIS976-0.
0009190.
011090-1.
9969109.
6432972443.
416*FUTURES4060.
0004230.
035213-0.
6989905.
914259176.
7327*CASH4060.
0004260.
034415-0.
7020155.
918178177.
4061*NDTVBASIS4060.
0053040.
0047340.
3870268.
847174588.
5072*FUTURES422-0.
0004770.
029089-0.
37230211.
015271139.
382*CASH422-0.
0004730.
027605-0.
25549711.
875591389.
737*NEYVELILIGBASIS4220.
0040360.
005690-1.
3372188.
289599617.
7460*FUTURES4220.
0005050.
0266060.
3585078.
103587467.
0259*CASH4220.
0004900.
0249570.
2591007.
086441298.
3457*NICOLASPIRBASIS4220.
0022540.
007874-1.
5701457.
258059492.
2012*FUTURES5340.
0011080.
0183650.
0604404.
90966181.
46655*CASH5340.
0011080.
0182420.
1003414.
68106463.
77407*NTPCBASIS5340.
0025810.
004999-0.
7703154.
737951120.
0169*FUTURES8330.
0002960.
030977-0.
99553318.
057818007.
277*CASH8330.
0003260.
030432-0.
80897516.
587966499.
153*ORIENTBANKBASIS8330.
0018290.
007996-3.
58584424.
4653317777.
38*FUTURES4220.
0005570.
0244560.
77459410.
17715947.
9438*CASH4220.
0005570.
0238961.
17023211.
780441451.
923*PATNIBASIS4220.
0032180.
007121-5.
89757978.
73916103311.
70*FUTURES8330.
0012680.
029463-0.
3891008.
3491881014.
157*CASH8330.
0012890.
028943-0.
2949567.
392712681.
8077*PNBBASIS833-0.
0006380.
011536-3.
22609916.
898088149.
084*FUTURES9760.
0001400.
034277-0.
5196527.
174737752.
6825*CASH9760.
0001340.
033443-0.
4722967.
494669857.
8348*POLARISBASIS9760.
0046700.
004816-0.
5051434.
977865200.
5936*FUTURES699-0.
0004990.
027611-2.
49587148.
0815659917.
84*CASH699-0.
0005050.
025437-1.
84865037.
6928835452.
87*RELBASIS6990.
0006860.
009461-3.
82079523.
2517613645.
87*FUTURES4220.
0027940.
0349570.
1482799.
839599824.
0967*CASH4220.
0027880.
0345790.
26631010.
28676938.
6079*RELCAPITALBASIS4220.
0043770.
004117-1.
3000508.
519489654.
5444*FUTURES9980.
0014500.
021022-1.
94130123.
3211017798.
58*CASH9980.
0014530.
021628-2.
89147940.
2122158973.
11*RELIANCEBASIS9980.
0029350.
005287-2.
57332025.
2164121625.
69*FUTURES9980.
0014740.
022421-0.
8450299.
8281682057.
551*CASH9980.
0014790.
021559-0.
7607328.
3681031294.
547*SBINBASIS9980.
0032860.
005472-1.
6910519.
3586852156.
990*FUTURES9760.
0009790.
029597-0.
68170912.
878964044.
408*CASH9760.
0009840.
029558-0.
27728514.
136595056.
132*SCIBASIS9760.
0028170.
008808-3.
57078023.
6897519482.
08*FUTURES3950.
0007990.
0410220.
1359587.
368090315.
2454*CASH3950.
0007910.
0400560.
2749107.
632840358.
2240*SRFBASIS3950.
0042050.
005249-1.
5095337.
621817501.
5835*FUTURES3950.
0010830.
0323320.
7297239.
359736700.
7337*CASH3950.
0010980.
0302010.
7936527.
658975398.
7127*STARBASIS3950.
0030250.
011056-3.
62356524.
971278809.
446*FUTURES4220.
0017830.
018775-0.
1676204.
55841944.
68023*CASH4220.
0017440.
018986-0.
1466695.
08442877.
90977*SUNPHARMABASIS422-0.
0068600.
009731-1.
7736728.
085354675.
9819*54FUTURES8130.
0012400.
032792-0.
21432112.
098462810.
463*CASH8130.
0012480.
032233-0.
16256110.
616961968.
946*SYNDIBANKBASIS8130.
0019160.
009703-2.
61363913.
821784892.
747*FUTURES4220.
0009090.
0226660.
1144378.
905212614.
0788*CASH4220.
0008910.
0201210.
0511866.
830779258.
2174*TATACHEMBASIS422-0.
0020170.
016568-2.
69851810.
487171497.
848*FUTURES9980.
0017050.
024067-0.
3914775.
661021319.
9444*CASH9980.
0017160.
023699-0.
2194464.
41691691.
49484*TATAMOTORSBASIS9980.
0008070.
007141-2.
1136379.
4525822474.
443*FUTURES9980.
0016110.
025291-0.
94081013.
842045035.
337*CASH9980.
0016180.
024284-0.
97566412.
143873635.
132*TATAPOWERBASIS9980.
0002360.
009586-3.
06483617.
8918810784.
26*FUTURES9980.
0014220.
021926-0.
2938217.
626037904.
2521*CASH9980.
0014230.
021389-0.
2459597.
387312810.
4795*TATATEABASIS9980.
0024750.
006628-1.
3220606.
407631773.
5881*FUTURES4060.
0028180.
0341110.
6115608.
413550521.
0765*CASH4060.
0028100.
0336190.
7662759.
415784736.
0610*TITANBASIS4060.
0042380.
004833-1.
3344177.
068273400.
4771*FUTURES4060.
0005050.
0308240.
0326985.
19833581.
82514*CASH4060.
0004990.
0296220.
0333435.
34406593.
02620*TVSMOTORSBASIS4060.
0032390.
007113-2.
23900211.
241381488.
208*FUTURES8330.
0011260.
030345-0.
2938906.
256172379.
9918*CASH8330.
0011570.
030585-0.
2094846.
577444450.
2933*UNIONBANKBASIS8330.
0020510.
007399-1.
9484799.
8485632155.
009*FUTURES4220.
0017480.
024848-0.
1346324.
77017456.
37252*CASH4220.
0017020.
025921-0.
1630134.
99093571.
56621*UTIBANKBASIS422-0.
0006490.
008231-2.
20759914.
171952537.
387*FUTURES422-0.
0005250.
0256940.
4874747.
548503380.
4929*CASH422-0.
0005410.
0256970.
8220269.
802587861.
1981*VIJAYABANKBASIS4220.
0043780.
005747-0.
7018114.
74434588.
14346*FUTURES4229.
87E-050.
023289-0.
3539514.
94712475.
47499*CASH4225.
37E-050.
022064-0.
1948784.
51171742.
85407*WOCKPHARMABASIS4220.
0041690.
006388-2.
11917111.
275961520.
168**Significantat1%significancelevel.
55TableIVOptimalHedgeRatiosS.
No.
SYMBOLOLSGARCHTARCHEGARCHVARVECM1BANKNIFTY0.
9543250.
9767780.
979427H0.
9768220.
945011L0.
9541102CNXIT0.
9582190.
9823940.
9835210.
991445H0.
956613L0.
9586913NIFTY0.
9072410.
9207500.
921465H0.
9214470.
904111L0.
9137274ABB0.
9127040.
9358550.
9523620.
953889H0.
904726L0.
9101825ACC0.
9546420.
9573480.
9753830.
976054H0.
950969L0.
9538246ALBK0.
946337N.
A.
N.
A.
N.
A.
0.
948235H0.
933401L7ALOKTEXT0.
958443L0.
9731280.
981862H0.
9802720.
9626470.
9723218ANDHRABANK0.
9743910.
9806680.
9824910.
982571H0.
970474L0.
9786169ARVINDMILLS0.
9690020.
9700210.
973318H0.
9722960.
9634780.
963178L10ASHOKLEY0.
9652870.
986265H0.
9823360.
9768270.
960472L0.
96243111AUROPHARMA0.
943356N.
A.
N.
A.
N.
A.
0.
943692H0.
938530L12BAJAJAUTO0.
9605010.
9979231.
001164H0.
9944420.
955667L0.
96297613BANKBARODA0.
9457340.
9629700.
977531H0.
9762930.
945709L0.
95125114BANKINDIA0.
9823850.
9900920.
994005H0.
9936290.
976964L0.
98545115BEL0.
953256HN.
A.
N.
A.
N.
A.
0.
948546L0.
95323616BHEL0.
958345HN.
A.
N.
A.
N.
A.
0.
9578450.
953114L17BILT0.
9412320.
9526420.
962219H0.
9610040.
936157L0.
93773418BONGAIREFN0.
9254230.
9339280.
908194L0.
9346940.
9195040.
943417H19BPCL0.
9454230.
9639600.
9874000.
998869H0.
942187L0.
95859920CANBANK0.
9841800.
9910280.
9938271.
002752H0.
980598L0.
98185021CENTURYTEXT0.
963095HN.
A.
N.
A.
N.
A.
0.
960754L0.
96231722CESC0.
9472050.
9491220.
958047H0.
9548390.
9418820.
938909L23CHAMBLFERT0.
922341N.
A.
N.
A.
N.
A.
0.
916986L0.
933672H24COLGATE0.
9277580.
9566100.
966530H0.
966530H0.
916193L0.
92967925CORPBANK0.
9623030.
9681250.
969059H0.
9668420.
951816L0.
95704626CUMMINSIND0.
938138HN.
A.
N.
A.
N.
A.
0.
932345L0.
93612627DIVISLAB0.
9564110.
9655860.
9738340.
976852H0.
931019L0.
95368228ESCORTS0.
968391HN.
A.
N.
A.
N.
A.
0.
964717L0.
96634029ESSAROIL0.
969641HN.
A.
N.
A.
N.
A.
0.
9685450.
966547L30FEDERALBANK0.
9563360.
959471H0.
9547410.
9582610.
9512190.
938818L31GAIL0.
9575670.
967431H0.
9659530.
9606740.
954746L0.
95808332GLAXO0.
8975840.
9101950.
9391070.
942953H0.
887324L0.
88875833GNFC0.
965649N.
A.
N.
A.
N.
A.
0.
960971L0.
968097H34GRASIM0.
970778N.
A.
N.
A.
N.
A.
0.
968321L0.
973551H35HCLTCH0.
9669560.
9911140.
9920090.
997673H0.
963477L0.
97126536HDFC1.
0012051.
0206661.
0207841.
028577H0.
994144L0.
99563137HDFCBANK1.
0090901.
0155431.
0173521.
019549H1.
004205L1.
00916938HEROHONDA0.
999769N.
A.
N.
A.
N.
A.
0.
999800H0.
978935L39HINDLEVER0.
9655390.
9874120.
992936H0.
9888890.
960892L0.
96804040HINDPETRO0.
9322710.
9396420.
9386351.
000936H0.
926845L0.
93963541ICICIBANK0.
953019L0.
975379H0.
9751630.
9711140.
9547360.
96048942IDBI0.
9648840.
9755070.
977574H0.
9755950.
959912L0.
96481643IDFC0.
9636840.
9757630.
978087H0.
9756520.
9549680.
939510L44IFCI0.
9576990.
9603950.
9607840.
961568H0.
951049L0.
96001245INDUSINDBANK0.
9588580.
9606190.
970285H0.
9702690.
9547560.
953694L46IOB0.
9635010.
982740H0.
9764220.
9696850.
954705L0.
96339247IOC0.
9268730.
9405230.
942203H0.
9285590.
923865L0.
92978448IPCL0.
968143H0.
9639340.
9655910.
9661840.
9657010.
960829L49JETAIRWAYS0.
9496710.
939650L0.
9648250.
975767H0.
9418930.
95478450JINDALSTEL0.
960258HN.
A.
N.
A.
N.
A.
0.
952262L0.
9526575651JPHYDRO0.
948162HN.
A.
N.
A.
N.
A.
0.
9373650.
936154L52JSTAINLESS0.
9609630.
9607040.
967406H0.
9667430.
953477L0.
95582553KTKBANK0.
950089HN.
A.
N.
A.
N.
A.
0.
9479650.
947531L54LICHSGFIN0.
935007HN.
A.
N.
A.
N.
A.
0.
9298000.
920178L55MARUTI0.
9905480.
9922191.
000960H0.
9992700.
989256L0.
99286756MATRIXLABS0.
8998630.
9224760.
940174H0.
9061150.
9033170.
899701L57MRPL0.
9493500.
9533260.
9527270.
962575H0.
943742L0.
95018258MTNL0.
9841750.
992940H0.
9856090.
9877720.
981108L0.
98475459NAGARFERT0.
948359N.
A.
N.
A.
N.
A.
0.
940287L0.
954510H60NATIONALUM0.
920248H0.
9163450.
9165340.
9164140.
912135L0.
91895761NDTV0.
9724840.
9718050.
985647H0.
9812970.
964819L0.
97036162NEYVELILIG0.
940307HN.
A.
N.
A.
N.
A.
0.
932623L0.
93633363NICOLASPIR0.
9113810.
9200170.
9344070.
948092H0.
905843L0.
90891664NTPC0.
968335HN.
A.
N.
A.
N.
A.
0.
963719L0.
96563965ORIENTBANK0.
9692990.
953482L0.
9689980.
9688930.
9610770.
970264H66PATNI0.
935187HN.
A.
N.
A.
N.
A.
0.
920845L0.
92996167PNB0.
9638600.
9613310.
9607650.
9597280.
958686L0.
977065H68POLARIS0.
9721540.
9706920.
9743870.
974904H0.
9698810.
967509L69REL0.
9078020.
9607320.
972070H0.
9709360.
901684L0.
91375070RELCAPITAL0.
9782110.
973013L0.
9764430.
979334H0.
9793000.
97686271RELIANCE0.
9940860.
9809580.
978266L0.
9808390.
995285H0.
98886872SBIN0.
9538160.
9557420.
9554130.
9565280.
950890L0.
958962H73SCI0.
9755160.
967939L0.
9700050.
9706450.
9727810.
978573H74SRF0.
9706480.
9795030.
9782190.
981196H0.
9670640.
963270L75STAR0.
888055N.
A.
N.
A.
N.
A.
0.
893274H0.
881545L76SUNPHARMA0.
9119380.
9326850.
933352H0.
9291060.
907949L0.
92630777SYNDIBANK0.
9693230.
9874560.
990526H0.
9893870.
965842L0.
96921278TATACHEM0.
8378070.
9189460.
9024950.
923732H0.
818968L0.
84954179TATAMOTORS0.
9675580.
9885080.
9818230.
992923H0.
9619090.
955582L80TATAPOWER0.
932961L0.
9554350.
961104H0.
9583510.
9341840.
94162481TATATEA0.
9589700.
9626440.
9641360.
965601H0.
954237L0.
96058782TITAN0.
977876HN.
A.
N.
A.
N.
A.
0.
9759980.
972918L83TVSMOTORS0.
9356100.
9469360.
9511290.
953403H0.
9357410.
934675L84UNIONBANK0.
9939810.
9970090.
998034H0.
9924750.
990109L0.
99537085UTIBANK0.
9996881.
023904H1.
0176791.
0195520.
994333L1.
01313386VIJAYABANK0.
9854740.
974782L0.
9837830.
987734H0.
9751700.
97666187WOCKPHARMA0.
9327710.
9454090.
9487000.
952743H0.
923674L0.
926119N.
A.
=Methodologynotapplicable,H=HighesthedgeratioandL=Lowesthedgeratio.
57TableVVarianceReductionS.
No.
SYMBOLOLSGARCHTARCHEGARCHVARVECM1BANKNIFTY0.
9508050.
9496750.
949471L0.
9496720.
950957H0.
9508112CNXIT0.
9559300.
9544020.
9543000.
953505L0.
955987H0.
9559123NIFTY0.
9612930.
9608420.
960806L0.
9608070.
961336H0.
9611314ABB0.
9007010.
8991060.
8972300.
897026L0.
900970H0.
9008025ACC0.
9609240.
9609040.
9603770.
960344L0.
9609260.
960927H6ALBK0.
914810N.
A.
N.
A.
N.
A.
0.
914822H0.
914537L7ALOKTEXT0.
916689H0.
9164120.
916042L0.
9161210.
9166540.
9164388ANDHRABANK0.
9646820.
9644940.
9644240.
964421L0.
964759H0.
9645659ARVINDMILLS0.
9808520.
9808430.
980797L0.
9808130.
980866H0.
98086510ASHOKLEY0.
9402810.
939434L0.
9396610.
9399270.
940347H0.
94032611AUROPHARMA0.
921277N.
A.
N.
A.
N.
A.
0.
921282H0.
921186L12BAJAJAUTO0.
9064730.
9044540.
904147L0.
9047600.
906530H0.
90642613BANKBARODA0.
9631280.
9625570.
961570L0.
9616720.
963129H0.
96301614BANKINDIA0.
9670790.
9668770.
966728L0.
9667440.
967149H0.
96701315BEL0.
960165LN.
A.
N.
A.
N.
A.
0.
960236H0.
960165L16BHEL0.
945072LN.
A.
N.
A.
N.
A.
0.
9450760.
945088H17BILT0.
953608H0.
9534650.
953128L0.
9531810.
9535820.
95359618BONGAIREFN0.
8928290.
8924840.
893052H0.
8924450.
8929780.
891914L19BPCL0.
8882470.
8874730.
8854930.
884116L0.
888311H0.
88776920CANBANK0.
957005H0.
9569460.
9568950.
956629L0.
9569990.
95700421CENTURYTEXT0.
957477LN.
A.
N.
A.
N.
A.
0.
957557H0.
95750522CESC0.
958038L0.
9580810.
958180H0.
9581640.
9578780.
95776423CHAMBLFERT0.
905836N.
A.
N.
A.
N.
A.
0.
905865H0.
905572L24COLGATE0.
9345940.
9327270.
931654L0.
931654L0.
934818H0.
93452725CORPBANK0.
9475910.
9473940.
947355L0.
9474430.
947767H0.
94770826CUMMINSIND0.
968903N.
A.
N.
A.
N.
A.
0.
968901L0.
968910H27DIVISLAB0.
9417780.
9410670.
9402690.
9399400.
942781H0.
94195428ESCORTS0.
942228LN.
A.
N.
A.
N.
A.
0.
942369H0.
94231029ESSAROIL0.
981288HN.
A.
N.
A.
N.
A.
0.
9812800.
981259L30FEDERALBANK0.
9410670.
9410700.
9410580.
941071H0.
9410200.
940683L31GAIL0.
9504590.
950182L0.
9502360.
9503940.
950500H0.
95044932GLAXO0.
9223770.
9217880.
9190220.
918505L0.
922579H0.
92256633GNFC0.
966496N.
A.
N.
A.
N.
A.
0.
966500H0.
966476L34GRASIM0.
959930N.
A.
N.
A.
N.
A.
0.
959938H0.
959907L35HCLTCH0.
9158110.
9137820.
9136840.
913022L0.
916003H0.
91553836HDFC0.
9255910.
9245380.
9245290.
923902L0.
925793H0.
92575937HDFCBANK0.
9175650.
9172220.
9171120.
916970L0.
917773H0.
91756238HEROHONDA0.
910895HN.
A.
N.
A.
N.
A.
0.
910895H0.
910436L39HINDLEVER0.
9278950.
9269480.
926554L0.
9268490.
927971H0.
92783640HINDPETRO0.
9331860.
9330290.
9330570.
927141L0.
933227H0.
93302941ICICIBANK0.
889314H0.
888583L0.
8885940.
8887990.
8892930.
88918042IDBI0.
978009H0.
9778930.
977843L0.
9778920.
9779820.
978009H43IDFC0.
9165760.
9160140.
915872L0.
9160210.
9167960.
916804H44IFCI0.
9773000.
9772560.
9772480.
977231L0.
977342H0.
97726345INDUSINDBANK0.
9804030.
980408H0.
980322L0.
9803230.
9803640.
98034846IOB0.
9485900.
947760L0.
9481180.
9484080.
948711H0.
94859247IOC0.
9182490.
9174900.
917368L0.
9181780.
918360H0.
91812248IPCL0.
9750160.
9750160.
975021H0.
975021H0.
975021H0.
974993L49JETAIRWAYS0.
9179580.
918183H0.
9172160.
916380L0.
9181510.
91776250JINDALSTEL0.
952676LN.
A.
N.
A.
N.
A.
0.
952778H0.
95277651JPHYDRO0.
947974LN.
A.
N.
A.
N.
A.
0.
9481850.
948193H52JSTAINLESS0.
974178H0.
9741770.
9741610.
9741670.
974089L0.
97413053KTKBANK0.
971422LN.
A.
N.
A.
N.
A.
0.
971429H0.
971429H5854LICHSGFIN0.
928263HN.
A.
N.
A.
N.
A.
0.
9282560.
928092L55MARUTI0.
9673030.
9672880.
967120L0.
9671640.
967311H0.
96728156MATRIXLABS0.
894986H0.
8945040.
893340L0.
8949650.
8949850.
89498557MRPL0.
9776230.
9776160.
9776190.
977467L0.
9775750.
977625H58MTNL0.
969045H0.
9689520.
9690400.
969025L0.
9690410.
96904359NAGARFERT0.
966231N.
A.
N.
A.
N.
A.
0.
966320H0.
966067L60NATIONALUM0.
934873L0.
9349610.
9349580.
9349600.
935018H0.
93490661NDTV0.
9772560.
9772640.
976901L0.
9770580.
977296H0.
97727962NEYVELILIG0.
960659LN.
A.
N.
A.
N.
A.
0.
960766H0.
96073163NICOLASPIR0.
9223890.
9221000.
9212410.
919987L0.
922486H0.
92244164NTPC0.
951203HN.
A.
N.
A.
N.
A.
0.
951177L0.
95119365ORIENTBANK0.
9653510.
9652250.
965354H0.
965354H0.
9653500.
965342L66PATNI0.
895364N.
A.
N.
A.
N.
A.
0.
895466H0.
895451L67PNB0.
9486920.
9487220.
9487270.
9487350.
948740H0.
948319L68POLARIS0.
9859040.
9859120.
9858830.
985876L0.
985915H0.
98591469REL0.
9442280.
9393660.
937466L0.
9376700.
944364H0.
94401170RELCAPITAL0.
9839540.
983895L0.
9839400.
983960H0.
983960H0.
98394471RELIANCE0.
9595590.
9590540.
9589100.
959048L0.
9595890.
95939872SBIN0.
9762940.
9762750.
9762780.
9762640.
9763080.
976224L73SCI0.
9432820.
9433080.
943312H0.
943312H0.
9433040.
943238L74SRF0.
989289H0.
9892170.
9892370.
989184L0.
9892710.
98922375STAR0.
889724N.
A.
N.
A.
N.
A.
0.
889609L0.
889779H76SUNPHARMA0.
7868260.
7858040.
785757L0.
7860400.
786926H0.
78620777SYNDIBANK0.
9620990.
9615650.
961407L0.
9614680.
962124H0.
96210078TATACHEM0.
8410570.
8278930.
8319130.
826595L0.
841723H0.
84018779TATAMOTORS0.
9557790.
955117L0.
9554260.
9548620.
955803H0.
95575180TATAPOWER0.
937454H0.
9367460.
936394L0.
9365740.
9374430.
93731181TATATEA0.
9599630.
9599240.
9599000.
959872L0.
959971H0.
95994982TITAN0.
984268HN.
A.
N.
A.
N.
A.
0.
9842650.
984244L83TVSMOTORS0.
9618400.
961870H0.
9618110.
961763L0.
9618420.
96182584UNIONBANK0.
9663300.
9663020.
966288L0.
9663370.
966339H0.
96631985UTIBANK0.
8927420.
891582L0.
8919830.
8918700.
892852H0.
89223186VIJAYABANK0.
9482450.
948377H0.
9482810.
948188L0.
9483760.
94837187WOCKPHARMA0.
9404800.
9399110.
9397040.
939417L0.
940670H0.
940637N.
A.
=Methodologynotapplicable,H=HighestvariancereductionandL=Lowestvariancereduction.