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1、Analysis of Oil Seeds & Grain Price Volatility in India: A VEC-MVGARCH ApproachAResearchProposalbyDrAlokPandey,Ph.D.AssociateProfessor(Finance)IMTGhaziabadBackgroundOilseedsandwheatgrainshavewitnessedunprecedentedvolatilitiesandpricefluctuationsintherecentpast.Extremevolatilityincommodityprices,part
2、icularlyoffoodcommodities,affectsproducers,consumers,traders,exporters&foodprocurementagenciesofthecentralandstateGovernment.CommoditiesUnderStudyWheatSelectedEdibleOilseedsandOilWheat&EdibleOilPriceForecastWorldWheatPriceVolatilityWhoplaysthebiggestroleinpushingtheglobalwheatpricesnow?ItisIndia.Fol
3、lowingIndiasplantobuymorewheatforbufferstock,thecommodityspricessoaredacrosstheworldwiththeWorldFoodProgramme(WFP)expressingconcernovertheimpactofdwindlingstocksofthecereal.WheatPriceVolatilityAfterIndiainvitedtendersforanunspecifiedquantityofwheatfromtheinternationalmarket,thepriceofwheatcrossedrec
4、ordlevelsoncommodityexchangesonThursday.Asgraintradersreactedtourgenttendersfromgrainimportersandthelowestglobalstocklevelsfor25years,thepricesshotupacrosstheglobe.Indiaistheworldssecond-largestwheatproducerafterChina,butordersfromDelhitobuildupbufferstockspushedpriceofabushelclimbing30centsto$7.88a
5、bushelontheChicagoBoardofTrade.WheatPriceVolatilityInFrance,thepriceofNovembermillingwheatalsosoared.Naturalcalamitieslikedroughtsandfloodsandproductionshortfalls,burgeoningdemandanddwindlingstocksalsocreatedaharvestseasonpanicthatagainpushedthepricesofwheatfurther.SinceApril,ithasrisen75percentonbo
6、thsidesoftheAtlanticafterrecenttendersfromEgyptandIndia.WheatPriceVolatilityIndialastyearsufferedaweakharvestandenteredtheworldmarketaggressivelytoimportwheat.TheInternationalGrainsCouncilexpectsIndiatoimportmorethanthreemilliontonnesthisyear,despiteanimprovedharvest.Analystsbelievethatthereisgrowin
7、ganxietythatthecountryhadbenefitedfromasuccessionofgoodmonsoons.WheatPriceVolatilityTheInternationalGrainCouncilcutitsforecastofworldgrainproductionbysevenmilliontonnesthismonthto607milliontonnes,asitassessedtheimpactofawetsummerinNorthernEurope,weakoutputinUkraineanddroughtinArgentinaandAustralia.C
8、hicagoBoardofTradewheatFuturescontractsetanewall-timehighthisweekascropconcernsroilthemarketagain.TheDecembercontracttookoutlastweekspreviousall-timehighof$7.54.WheatPriceVolatilityPariswheatFuturessettledjustshyoftheirall-timehighandLondon-basedwheatFuturessurpassedtheirprevioustop.MoretalkofAustra
9、liandroughtconditionsandwheatcropwoestherewasanotherreasonforbullstobuy.SpotPriceVolatility(Wheat)Oil&OilseedsOil & OilseedsCasterSeed/CasterOilCoconutOil/CopraCottonSeed/CottonseedOilCrudePalmOilGroundNut/GroundnutOilKapasiaKhalliLinseed/LinseedOilOil&OilseedsMustardOil/MustardSeed/MustardSeedOilRB
10、DPalmolein/RefinedSoyOilRefinedSunflowerOilRiceBranRefinedOilSafflower/SafflowerOilSesamOilSoyMeal/Soybean/SoyabeanOil/SunflowerOil/SunflowerSeedOil&OilSeedsIndiaistheworldsfourthlargestedibleoileconomywith15,000oilmills,689solventextractionunits,251Vanaspatiplantsandover1,000refineriesemployingmore
11、thanonemillionpeople.ThetotalmarketsizeisatRs.600,000Mln.andimportexporttradeisworthRs.130,000Mln.Oil&OilSeedsIndiabeingdeficientinoilshastoimport40%ofitsconsumptionrequirements.Withanannualconsumptionofabout11mln.Tonnes,thepercapitaconsumptionisat11.50kgs,whichisverylowcomparedtoworldaverageof20kgs
12、.Chinaiscurrentlyat17kg.OverviewofEdibleOilEconomyIndianvegetableoilisworldsfourthlargestafterUSA,ChinaandBrazil.Oilseedcultivationisundertakenacrossthecountryintwoseasons,inabout26millionhectares;mainlyonmarginallands,dependentonmonsoonrains(un-irrigated)andwithlowlevelsofinputusage.Yieldsarerather
13、lowatlessthanonetonperhectare.Threeoilseeds-Groundnut,SoybeanandRapeseed/Mustard-togetheraccountforover80percentofaggregatecultivatedoilseedsoutput.MustardseedalonecontributesRs.120,000Mln.turnoveroutofRs.600,000Mln.oilseedbasedSectordomesticturnover.Cottonseed,Copraandotheroil-bearingmaterialtoocon
14、tributetodomesticvegetableoilpoolOverviewofEdibleOilEconomyCurrently,Indiaaccountsfor7.0%ofworldoilseedsoutput;7.0%ofworldoilmealproduction;6.0%ofworldoilmealexport;6.0%ofworldveg.oilproduction;14%ofworldveg.oilimport;and10%oftheworldedibleoilconsumptionWithsteadygrowthinpopulationandpersonalincome,
15、Indianpercapitaconsumptionofedibleoilhasbeengrowingsteadily.However,oilseedsoutputandinturn,vegetableoilproductionhavebeentrailingconsumptiongrowth,necessitatingimportstomeetsupplyshortfall.OverviewofEdibleOilEconomyOverviewofEdibleOilEconomy(QuantityinMillionTonnes)Crop2-Jan3-Feb4-Mar5-Apr05-06(F)M
16、ajorOilseedsGroundnut74.48.266.4Rape/Mustard5.13.96.26.67Soybean5.64.67.95.86.5OtherSix32.233.73.6Sub-Total20.715.1*25.322.123.5OthersCottonseed5.14.55.56.68.5Copra0.90.70.70.70.6GrandTotal26.720.331.529.432.6*ReducedduetoDrought.80percentofIndiasdomesticoiloutputcomesfromtheprimarysourcethatisninec
17、ultivatedoilseedsandtwomajoroil-bearingmaterials(CottonseedandCopra).Thesecondarysourcecomprisesofsolventextractedoils,Ricebranoil,oilsfromminorandtree-borneoilseedsetc.OverviewofEdibleOilEconomyMarketPotentialThepercapitaconsumptionofoilinIndiais11.5kg/yeariswaybelowtheworldaverageof18kg.Evenchinai
18、sat17kg.By2021thepercapitaconsumptionofoilinIndiaislikelytobe15.6kg.Thereishugepotentialofgrowth.ThedemandforedibleoilsisexpectedtoincreasefromOilYear2004-05levelsof10.9Mln.tonnesto12.3Mln.tonnesby2006-07(twoyears).Thisassumesapercapitaconsumptionincreaseof4%andapopulationgrowthof1.9%whichtranslates
19、toanoverallgrowthindemand6%p.a.Basedontheaboveassumptions,edibleoildemandintheyear2021isexpectedtobe21.3milliontonnes.DemandProjectionEdibleOil200420102015TotalDemand(Mln.Tonnes)10.915.621.3TotalAreaunderOilseeds(Mln.Hectares)23.42832Yield(Tonnes/hectare)1.071.21.4ProductionofOilseeds(Mln.tonnes)25.
20、133.644.8Domesticsupplyofedibleoils(Mln.tonnes)710.113.4Totaledibleoilimports-(Mln.tonnes)4.35.98.3Importsasshareofdemand39.40%38.10%39.50%DemandProjection(Contd.)Indiawillcontinuedependenceonimportstotheextentof40%ofitsconsumptionrequirements.Theimprovementinyieldsandtheincreaseinareaundercultivati
21、onwillensurethatthedomesticoilseedproductionissufficienttomeet60%ofconsumptionrequirements.IncreasedsupportfromtheGovernmentYearMinimumsupportPriceRs.perMTFY200111,000FY200212,000FY200313,000FY200416,000FY200517,000FY200617,250IncreasedsupportfromtheGovernmentThegovernmentisincreasingitsfocusontheed
22、ibleoilindustry,giventhatithasthesecondlargestimportbillaftercrudepetroleum.Thesupportedpriceofmustardseed,whichwasRs11,000perMTin2001,wasincreasedtoRs17,250perMTby2006.Consequently,mustardseedcultivationalsoincreasedfrom5MMTto7.0MMTin2006.Themainemphasisofthegovernmentisonreducingtheimportbill,andt
23、hisstephashelpedtoacertainextent.SpotPriceVolatility(Wheat)SpotPriceVolatility(RMSeedOil)SpotPriceVolatility(RefinedSoyOil)ObjectivesThispaperproposesamultivariate vector error-correction generalized autoregressive conditional heteroscedasticitymodeltoinvestigatetheeffectofoilseedsandwheatgrainprice
24、sinneighbouringcountriesofAsiaonitsIndianequivalents.WeproposetotestwhetherinthelongrunthelawofonepriceholdsandwhetherintheshortrunthemodelcapturesthesalientfeaturesofIndiancommodityprices(oilseedsandwheatgrain).Objectives(Contd.)Thismodelwillbeusedtocomputerollingforecastsoftheconditionalmeans,vari
25、ancesandcovarianceofthepricesofoilseedsandwheatgrainoneyearahead.Weexpectthatthismodelwillproducesuperiorforecastscomparedtothosebasedonacommonlyusedmethodologyofanautoregressiveconditionalmeanmodelwherethesecondmomentsareestimatedusingafixedweightmovingaverage.ObjectivesTomeasurethedegreeofpriceins
26、tabilityofimportantagriculturalcommoditiesinthemajorinternationalanddomesticmarkets.Thecommoditiesselectedforthestudyarewheat,palmoil,groundnutoil,soybeanoilandcoconutoil.ToComparethepatternsofvariabilityinAsianmarketsandunderstanditsimplicationsforIndianproducersandconsumers.Objectives(Contd.)Toexa
27、minewhethertheconditionalmeanrelationshipbetweenAsianandIndiangrainandoilseedpricescanbecharacterizedbyavectorerrorcorrection(VEC)model.Toexaminehowwelldotheone-yearaheadforecastsoftheconditionalfirstandsecondmomentsfromtheVEC-MVGARCHmodelcomparewiththosegeneratedusingtheChavasandHolt(1990)methodolo
28、gyandwhetherthereisasignificantdifferenceintheseforecastsusingHansens(2001)recentlydevelopedtestofsuperiorpredictiveability(SPA).MethodologyTheresearchmethodologybroadlyisbasedonfollowingthreesteps:1.ModelingtheMeanandVolatilityofIndianoilseedsandwheatgrainpricesusingARCH,GARCHandARIMAmodels.2.Testi
29、ngthedatatoexaminewhethertheconditionalmeanrelationshipbetweenAsian(fewselectcountriesindependently)andIndianoilseedandwheatgrainpricescanbecharacterizedbyavectorerrorcorrection(VEC)modelbasedonshortandlongruntheoryofLawofOnePrice(LOP).3.ExpandingtheVECmodeltoallowforthemodelingofthetimevaryingsecon
30、dmomentsofdomesticoilseedsandgrainpricesusingaMVGARCHmodel.StandardApproachtoEstimatingVolatilityDefinesnasthevolatilityperdaybetweendayn-1anddayn, asestimatedatendofday n-1DefineSiasthevalueofmarketvariableatendofdayiDefineui= ln(Si/Si-1)SimplificationsUsuallyMadeDefine uias(Si-Si-1)/Si-1Assumethat
31、themeanvalueofuiiszeroReplacem-1bymThisgivesWeightingSchemeInsteadofassigningequalweightstotheobservationswecansetARCH(m)ModelInanARCH(m)modelwealsoassignsomeweighttothelong-runvariancerate,VL:EWMAModelInanexponentiallyweightedmovingaveragemodel,theweightsassignedtotheu2declineexponentiallyaswemoveb
32、ackthroughtimeThisleadstoAttractionsofEWMARelativelylittledataneedstobestoredWeneedonlyrememberthecurrentestimateofthevariancerateandthemostrecentobservationonthemarketvariableTracksvolatilitychangesRiskMetricsusesl=0.94fordailyvolatilityforecastingGARCH(1,1)InGARCH(1,1)weassignsomeweighttothelong-r
33、unaveragevariancerateSinceweightsmustsumto1g + a + b =1GARCH(1,1)continuedSettingw = gVtheGARCH(1,1)modelisandExampleSupposeThelong-runvariancerateis0.0002sothatthelong-runvolatilityperdayis1.4%ExamplecontinuedSupposethatthecurrentestimateofthevolatilityis1.6%perdayandthemostrecentpercentagechangein
34、themarketvariableis1%.ThenewvariancerateisThenewvolatilityis1.53%perdayGARCH(p,q)MaximumLikelihoodMethodsInmaximumlikelihoodmethodswechooseparametersthatmaximizethelikelihoodoftheobservationsoccurringExample1Weobservethatacertaineventhappensonetimeintentrials.Whatisourestimateoftheproportionofthetim
35、e,p,thatithappens?TheprobabilityoftheeventhappeningononeparticulartrialandnotontheothersisWemaximizethistoobtainamaximumlikelihoodestimate.Result:p=Example2EstimatethevarianceofobservationsfromanormaldistributionwithmeanzeroApplicationtoGARCHWechooseparametersthatmaximizeVarianceTargetingOnewayofimp
36、lementingGARCH(1,1)thatincreasesstabilityisbyusingvariancetargetingWesetthelong-runaveragevolatilityequaltothesamplevarianceOnlytwootherparametersthenhavetobeestimatedHowGoodistheModel?TheLjung-BoxstatistictestsforautocorrelationWecomparetheautocorrelationoftheui2withtheautocorrelationoftheui2/si2Co
37、rrelationsandCovariancesDefinexi=(Xi-Xi-1)/Xi-1andyi=(Yi-Yi-1)/Yi-1Alsosx,n:dailyvolofXcalculatedondayn-1sy,n:dailyvolofYcalculatedondayn-1covn:covariancecalculatedondayn-1Thecorrelationiscovn/(su,n sv,n)UpdatingCorrelationsWecanusesimilarmodelstothoseforvolatilitiesUnderEWMAcovn=l covn-1+(1-l)xn-1y
38、n-1PositiveFiniteDefiniteConditionAvariance-covariancematrix,W W, isinternallyconsistentifthepositivesemi-definiteconditionforallvectorswExampleThevariancecovariancematrixisnotinternallyconsistentModellingVolatilityTakeastructuralmodelwithutN(0,2)typicallyassumeshomoscedasticityifthevarianceoftheerr
39、orsisnotconstantthiswouldimplythatstandarderrorestimatescouldbewrong.Isthevarianceoftheerrorslikelytobeconstantovertime?Notforfinancialdata.ModellingVolatilitySocanwemodeltime-varyingvolatilityoftheerrors?Recallthedefinitionofthevarianceofut:t2=Var(ut ut-1, ut-2,.)=E(ut-E(ut)2 ut-1, ut-2,.=Eut2 ut-1
40、, ut-2,.sinceE(ut)=0Whatmightvarianceofudependon?LaggedsquarederrorsThisisEnglesARCH(1)modelAutoRegressiveConditionalHeteroscedasticity(ARCH)EasilygeneralisabletoanARCH(q)formOftenlargevaluesofqrequiredtocapturevolatilityprocessesComeswithproblemsmanycoefficientstoestimatenon-negativityconstraintsva
41、riancecannotbenegativesoestimatedalphasallneedtobepositivetoensuredefinitelypositivevarianceforallerrorsGeneralisedARCH(GARCH)Allowconditionalvariancetoalsodependonitsownlaggedvalue:ThisisaGARCH(1,1)modelAGARCH(p,q)modelfollows:GARCH(1,1)ModelGARCH(1,1)ModelGARCH(1,1)isarestrictedinfiniteorderARCHmo
42、delyetonlyneedsthreeparameterstobeestimated0istheconstant1istheeffectoflastperiodserror1istheeffectoflastperiodsvariance1+1givesthepersistenceofthevolatility:1+11impliesvolatilityexplodesMoreaboutGARCHConditionalvarianceistime-varyingandcanbemodelledbyGARCHUnconditionalvarianceisconstant,andisgivenb
43、yThisisdefined1+10Non-negativityconstraintis00,10,10and1+0NewsImpactCurvesNICsplotthisimpactofashock(“news)onconditionalvarianceExtensionsGARCH-in-meanFinancesuggeststhatexpectedreturnsdependonexpectedriskTodaysreturnsshoulddependontodays(sometimesyesterdays)conditionalstandarddeviation(orsometimesv
44、ariance)GARCH-in-MeanAnincreaseinrisk,givenbytheconditionalstandarddeviationleadstoariseinthemeanreturnThevalueofgivestheincreaseinreturnsneededtocompensateforagiveincreaseinriskSoisameasureofriskaversionExtensionsMultivariateGARCHUnivariateGARCHmodelscapturetheevolutionofconditionalvariancesMultiva
45、riateGARCHmodelsalsocapturemovementsinconditionalcovariancesTheselookquitecomplicatedandusealotofmatrixalgebraButarereallyquitesimple(honest)MultivariateGARCHVECHmodel,2assetcaseweheremodeltheconditionalvariance-covariancematrix21parameterstoestimateMultivariateGARCHDiagonalVECHmodelRestrictedversio
46、nofVECHmodelonly9parameterstoestimateandworksprettywellApplicationBollerslev,EngleandWooldridge(1988)MultivariatediagonalVECHGARCH-in-meanmodelUST-bills(asset1)UST-bonds(asset2)USequities(asset3)1959Q1-1984Q2ApplicationInterpretationCoefficientofriskaversionwas0.5,inlinewiththeoryPersistenceofshocks
47、toconditionalvariancehighforT-bills(0.445+0.466)butlowforbonds(0.188+0.441)andstocks(0.078+0.469)Butstockvariancesnotwellcaptured(noelementstatisticallysignificant)unconditionalcovariancebetweenbillsandbondspositive(h12). Negativebetweenbillsandstocks(h13)andbondsandstocks(h23)sincelaggedconditionalcovariancesnegativeandlargerthanerrorcross-productsPracticalUsesTime-varyingoptimalhedgeratioHtConditionalCAPMbetasVECModelsTheChavasHoltMethodology(1990)HansensTestofSPA(2001)TheMVGARCHModelSourcesofDataLimitationsoftheStudy
