Evaluating the Hedging Effectiveness in Crude Palm Oil Futures Market during Financial Crises

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1 Evluing e Hedging Effeciveness in Crude Plm Oil Fuures Mrke during Finncil Crises YouHow Go Fculy of Business nd Finnce, Universii Tunku Adul Rmn (UTAR), Perk, Mlysi Emil ddress: goy@ur.edu.my WeeYep Lu (Corresponding uor) Fculy of Economics nd Adminisrion, Universiy of Mly, Kul Lumpur, Mlysi. Emil ddress: wylu@um.edu.my ABSTRACT Tis sudy exmines weer ere is significn cnge in edging effeciveness on Crude Plm Oil (CPO) fuures mrke from Jnury 1986 o Decemer 013. Eig edging models wi differen men nd vrincecovrince specificions ve een evlued. As e voliliy of spo nd fuures mrkes is no similr cross ime, o mrkes exii symmeric informion rnsmission. Our resuls of ouofsmple evluion sow, firsly, e imevrying edge rios wi sis erm produce eer performnce during o finncil crises. Secondly, ig dynmic edge rios during e Asin finncil crisis conriue o e suppor for CCCGARCH model. Tirdly, during glol finncil crisis, BEKKGARCH model ppers o provide more risk reducion s compred o oers. From e perspecive of economic modeling, incorporing e sis erm in modeling e join dynmics of spo nd fuures reurns during e crises provide eer resuls. Tis sudy recommends CPO mrke pricipns o djus eir edging sregies in response o differen movemen in mrke voliliy. Keywords: Generlized uoregressive condiionl eerosedsiciy (GARCH) model, sis erm, minimumvrince edge rios nd edging effeciveness. JEL Clssificion: G1, G13, G14 1

2 1. Inroducion Being one of e world leding producers nd exporers of plm oil, Mlysi lone ccouned for 39 per cen of world producion nd 45 per cen of world expors in 011 sed on e d relesed y e Mlysin Plm Oil Bord (MPOB). Given e prominence of is commodiy o e economy, Mlysin crude plm oil (CPO) fuures mrke s een in exisence in e Kul Lumpur Commodiy Excnge (KLCE) since Ocoer 1980, nd coninued o e one of e cive fuures mrke for CPO reled derivive produc in e world under e plform of Burs Mlysi Derivive (BMD) Berd in 003. Like oer mrke commodiies, e price movemen of CPO is sujeced o flucuion rougou vrious economic climes. As oserved in Figure 1, i sows CPO spo nd fuures reurns ve ig voliliy in ree disinc periods wic correspond o e world economic recession in 1986, Asin finncil crisis in 1997/1998 nd glol finncil crisis in 008/009. Besides e glol economic recession, wic ppened during , Mlysin plm oil ws sujec o series of dverse puliciy lunced y e Americn Soyen Associion. As consequence, Mlysin grow ws led ruply s plm oil price d een lved. In e ferm of Asin finncil crisis, e depreciion of Ringgi cused e resrucuring of e Mlysin derivive mrke o undergo series of regulory reform. In response o is crisis, BMD s CPO fuures conrcs were rded RM,700 per onne e Commodiy nd Monery Excnge (COMMEX) in Novemer 1998 (MPOB, 1998). Susequenly, plm oil s ecome e op foreign excnge erner, exceeding e revenue derived from crude peroleum, peroleum producs y wide mrgin. However, due o e L Nin effec in 008, Mlysin plm oil expor dropped from RM13, 504 million onnes in e ird qurer o RM9, 71 million onnes in e four qurer of 008 due o evy rinfll nd lower fres frui unces (Cenrl Bnk Mlysi, 009). I ws oserved CPO fuures price lso decresed from n verge of RM in e firs qurer of 008 o RM in firs qurer of Since e revivl of Cin nd Indi s gross domesic producion grow in 009, e ol CPO fuures conrc rded s susequenly incresed from 3,003,549 conrcs in 008 o 4,008,88 conrcs in 009 sedily wi e rising of demnd from o counries. Afer recovery in e glol economy in 010, e rising of peroleum crude oil s coninully led o e increse of CPO price nd direcly reduced pricing voliliy fer 011. Te ove ccoun esifies e price movemen of CPO is uncerin nd ofen influenced y economic or environmenl fcors. Hence, o implemen eer edging sregies during economic downurn, ere is need mong mrke pricipns o focus on fuures mrke s mens o minimize e risk of price flucuion. However, ere is 1 Bsed on d re exrced from Tomson DSrem on 1 Jnury 013 See e repor of e Unied Nions Developmen Progrm (009) p. 68.

3 1/6/1986 1/6/1988 1/6/1990 1/6/199 1/6/1994 1/6/1996 1/6/1998 1/6/000 1/6/00 1/6/004 1/6/006 1/6/008 1/6/010 1/6/01 no conclusive evidence o se wic model provides e es edging performnce during exremely volile economic periods. Tis sudy inends o revisi is issue nd exend erlier sudies y using sis erm in modeling e join dynmics of spo nd fuures reurns Condiionl vrince for CPO fuures reurn Condiionl vrince for CPO spo reurn Apr, 1986Jul 6, 1988 Sep 30, 1997Jul 5, 00 Nov 30, 006Dec 19, 011 Figure 1. Univrie condiionl vrince of CPO spo nd fuures reurns, Source: Auor s esimion sed on ExponenilGARCH model of Mlysin CPO spo nd fuures reurns Working (1953) defines edging s e purcse or sle of fuures in conjuncion wi noer commimen, usully in expecion of fvorle cnge in e relion eween spo nd fuures prices. On e oer nd, Ederingon (1979) defines edging effeciveness is vrince reducion in e spo reurn porfolio. In noer sudy, Howrd nd D Anonio (1984) define e edging effeciveness is e rio eween excess reurn per uni of risk in e porfolio of e spo nd fuures posiions o excess reurn per uni of risk in e porfolio of e spo posiion. Tere re wo conriuions of is sudy. Firsly, is sudy invesiges weer e superior edging model cn produce symmeric performnce in reducing e vrince of porfolio cross ree superiods, nmely e world economic recession in 1986, Asin finncil crisis in 1997/1998 nd glol finncil crisis in 008/009 respecively. Tis ssessmen is imporn for e CPO mrke pricipns o know weer ey need o djus or swic eir edging models in miiging price risk cross differen mrke condiions. Secondly, is sudy exends e sudies of Zinudin nd Srudin (011) nd Ong, Tn nd Te (01) on edging effeciveness in e Mlysin CPO fuures mrke y incorporing sis erm (e sor run deviion eween CPO spo nd fuures prices) ino condiionl vrincecovrince srucures of BEngleKrfKroner (BEKK) nd 3

4 Consn Condiionl Correlion (CCC) represenions. Aloug e sis erm s een confirmed o e fcor influencing e level of spo nd fuures price movemens in e model, is sudy emps o verify weer e sis erm cn susin is superioriy during igly volile periods in genering e es edge rios nd performnce for e cse of e Mlysin CPO fuures mrke. Tis pper is orgnized s follows. Tis secion is followed y lierure review. Te susequen secion ouces on d nd meodology, followed y findings nd empiricl resuls. Te ls secion concludes e discussion nd suggess e implicion of is sudy.. Lierure Review.1. Hedging model specificions Te dee on economeric models for esiming e minimumvrince fuures edge rio s een discussed for mny yers. In erly sudies, Jonson (1960) ws e firs o inroduce opiml edge rio (OHR) in minimizing porfolio vrince in edging sregies. He defined OHR ws e rio eween covrince eween spo nd fuures reurns o e vrince of fuures reurn. Sein (1961) ws e firs o use n ordinry les squres (OLS) meod o regress e spo reurns gins fuures reurns y ssuming covrince exiied imeinvrin crcerisics. Te esimed slope of model could e inerpreed s OHR. Te ig R squred from e esimed liner regression model indiced e OLS edging sregy ws effecive. Tis ssumpion ws furer used y Ederingon (1979), Anderson nd Dnine (1981) nd Hill nd Scneeweis (1981). Nevereless, Ederingon (1979) found e edging effeciveness sed on e R squred from simple regression ws inpproprie o esime OHR ecuse e movemen of e OHR exiied imevrin crcerisics nd correlion eween wo res of reurn lso vrying cross ime. Tis effec leds o riskminimizing edge rios o e imevrying s well. To ccoun for is effec, Generlized Auoregressive Condiionl Heeroscedsiciy (GARCH) frmework is consruced o disply imevrying voliliy of o reurns. As resul, ere ve een numer of proponens for e GARCH frmework wi ec of em demonsred e effeciveness of dynmic edge rios wi respec o e iges vrince reducion (Billie & Myers, 1991; Prk & Swizer, 1995; Tong, 1996; Moscini & Myers, 00; Lien, Tse & Tsui, 00; Floros & Vougs, 004; Amed, 007; nd Zinudin & Srudin, 011). To explin e condiionl covrince eween e spo nd fuures reurns nd esime OHR under e imevrying frmework, Bollerslev, Engle nd Wooldridge (1988) ve exended GARCH model o ecome Bivrie GARCH (BGARCH) model. Wi e respec o is model, Billie nd Myers (1991) found OHR exiied nonsionry movemen cross ime in e Unied Ses six commodiies. Tis nonsionry movemen implied e ssumpion of imeinvrin OHR ws no longer 4

5 inpproprie o e used. Tis demonsred e BGARCH model ppered o fi e d well ecuse e considerle ime vriion in e condiionl covrince mrix. Prk nd Swizer (1995) furer demonsred is superioriy in e corn nd soyen mrkes. In conrs o e evidence s demonsred ove, ey found is model could no gurnee o provide e superior edging sregy o OLS edging sregy wen voliliy movemen ws no sle nd ig, nd s well s e considerion of rnscion cos. As resul, is model conined oo mny prmeers nd did no resric condiionl vrincecovrince mrix o e posiive semidefinie. To ensure e posiive semidefinie in vrincecovrince mrix, Engle nd Kroner (1995) ve developed e vrincecovrince wi BEKK (nme fer B, Engle, Krf nd Kroner) specificion. Susequenly, e GARCH model wi is specificion ws urned o e more flexile for e resercers o sudy edging performnce in vriey commodiy mrkes. For insnce, Moscini nd Myers (00) used BEKK GARCH model for edging of weekly corn prices in Midwes during Tey found is model ws e es, u i could no e used o explin deerminisic sesonliy nd imeomuriy effecs. Floros nd Vougs (004) found e superioriy of is model in cpuring new informion rrivl in e Greek mrke for e period Alizde, Kvussnos nd Mencof (004) compred edging effeciveness cross Roerdm, Singpore nd Houson during using e BEKKGARCH model. Tey poined ou low edging performnce ws due o differen regionl supply nd demnd of crude oil nd peroleum. As discussed y Brooks, Henry nd Persnd (00), symmeric effecs of posiive nd negive reurns cnno e negleced from BEKK prmeerizion in esiming edge rios. Tis could e demonsred roug e GARCH model wi e symmeric effecs provided e superior edging performnce for insmple, u is effeciveness ws low for e ouofsmple. By using Fm s regression pproc (1984) nd simple rndom wlk model, Swizer nd ElKoury (007) ve presened e evidence of e symmeric effecs of d nd good news in improving edging performnce in e New York Mercnile Excnge Division lig swee crude oil fuures conrc mrke from 1986 o 005. During e period , Wu, Gun nd Myers (011) used e symmeric version of e BEKK model o ccoun for possily symmeric effec of voliliy. Tey found evidence of edging sregy cross corn nd crude oil mrkes o e sligly efficien n rdiionl edging sregy in e corn fuures mrke lone. As suggesed y e efficien mrkes ypoesis, e coinegrion relionsip eween spo nd fuures prices sould e exmined ecuse o prices conin socsic rend. Kroner nd Suln (1993) were e firs o dop e GARCH frmework wi n error correcion erm in esiming dynmic edge rios. Tey found is frmework provided e superior edging performnce over more convenionl edging mesures. 5

6 Susequenly, numer of resercers ve doped e GARCH wi e error correcion erm in eir sudies. For insnce, Tong (1996) suppored e incorporing e error correcion erm ino men equion of BEKKGARCH model could improve edging performnce in e Tokyo sock index during Coudry (00, 004) found similr resuls wi Tong (1996), were GARCH edging sregy wi e error correcion erm ws ouperformed in e Ausrli, Germny, Hong Kong, Jpn, Sou Africn nd Unied Kingdom fuures mrkes during He furer mde invesigion in e Ausrli, Hong Kong nd Jpn sock mrke during nd confirmed is error erm is crucil in e mos of e cses. Te GARCH model s 11 prmeers in e condiionl vrincecovrince srucure wi BEKK formulion. To oin prsimonious model, Bollerslev (1990) s developed e Consn Condiionl Correlion (CCC)GARCH model consiss of 7 prmeers in order o provide simple compuion nd ensure e posiive semidefinie in e condiionl vrincecovrince mrix (Kroner & Suln, 1993; Ng & Pirrong, 1994; nd Lien e l 00). Alernive esimion of OHR suppored consn correlion eween sndrdized residuls of spo nd fuures reurns (residuls divided y e GARCH condiionl sndrd deviion) provided ig explnory power o e condiionl vrincecovrince of o series, nd ence CCCGARCH model ws preferred in view of is. Empiricl reserc used is model includes: Lien e l (00) nd Amed (007). On e conrry, Lien e l (00) found OLS esimion model ws eer n CCC vecor GARCH model in e currency fuures, commodiy fuures nd sock index fuures during Teir resuls indiced e underperformnce of CCC GARCH model ofen genered oo vrile forecsed vrince. According o e uors, imevrying regimeswicing model s ppered o e eer model o improve e ccurcy of e model in vrince forecsing. Amed (007) compred e effeciveness of imevrying nd rdiionl durionsed consn edge rios in e Unied Ses Tresury mrke. His finding indiced e esimed imevrying edge rio from e CCCGARCH le o cpure e condiionl eeroskedsiciy in e spo mrke. As resul, is model s provided n dvnge in minimizing e vrince for ond invesors o cnge eir posiions in fuures mrke sed on e cnges in cul yields of spo mrke during en yers of rding... Hedging effeciveness in Mlysin CPO fuures mrke Tere re empiricl works reled o edge rio nlysis for e cse of Mlysin plm oil. For insnce, Zinudin nd Srudin (011) climed e differen resricion imposed in e condiionl men equion could ffec e edging effeciveness in e Mlysin CPO fuures mrke. Tey used e BEKKGARCH model wi ree differen men specificions comprising e inercep, Vecor Auoregressive (VAR) nd Vecor Error Correcion model (VECM) o exmine edging effeciveness sed on risk minimizion nd uiliy mximizion. Bsed on risk minimizion wiin e in nd ouofsmple, ey found prsimonious model suc s e BEKKGARCH models wi men inercep nd VAR provided eer edging performnce s compred o 6

7 compliced model suc s e BEKKVECM model. Te difference eween esed models ws smll in erms of uiliy mximizion. In noer sudy y Ong e l (01), wi n OLS meod in esiming e edge rio for ec mon during , ey repored e incresing edge rio during Jnury, 009June, 011 s conriued o 1953 per cen of e edging effeciveness. Tey climed is low level of edging performnce ws due o four evens, (1) e rising of peroleum crude oil, () recovery of world economy in 010, (3) wek impc of e sunmi nd erquke in Jpn, nd (4) de crisis in Europe s cused sle nd consisen movemen of voliliy in e CPO spo mrke. 3. D nd Meodology Tis sudy uses dily closing CPO spo nd fuures prices from Jnury 6, 1986 o Decemer 31, 013 wic consis of 6,78 oservions. Te d re colleced from Tomson Reuers DSrem. In order o reduce e vriiliy of o series nd cieve sionriy, o prices re rnsformed o reurns in e nurl logrimic form. Susequenly, e wole smple period is divided ino ree superiods, e firs su period from April, 1986 o July 6, 1988, e second su period from Sep 30, 1997 o July 5, 00 nd lsly e ird superiod from Novemer 30, 006Decemer 19, 011. As oserved in Tle 1, e lowes mens of o dily reurns wi negive vlues re recorded during e Asin finncil crisis. In e sme period, e lowes sndrd deviion of indices spo mrke s less voliliy. Across e ree periods, i is oserved e sndrd deviion of spo nd fuure reurns sligly incresed o 0.07 nd during e glol finncil crisis.. Tle 1. Descripive sisics of CPO reurns Pnel A: Apr, 1986 Jul 6, 1988 Pnel B: Sep 30, 1997 Jul 5, 00 Pnel C: Nov 30, 006 Dec 19, 011 Spo Fuures Spo Fuures Spo Fuures Oservions Men E E Sd deviion Mximum Minimum Skewness Kurosis JrqueBer * 37.33* 1.91* * * * Noe: * indices null ypoesis is rejeced e 1% level. Bsed on Tle, ugmened DickeyFuller (ADF) nd PillipsPerron (PP) es sisics suppor e rejecion of null ypoeses of uni roo, implying e uni roo is sence for dily CPO spo nd fuures reurns series. Terefore, o reurns re sionry in 7

8 level form. Furermore, vrious models wi differen men nd vrince specificions re esimed in ec superiod. Susequenly, e in nd ouofsmple performnce for ec model is compred o exmine symmeric performnce of edging cross e ree evens. Tle : Uni roo es resuls Augmened DickeyFuller (ADF) PillipsPerron (PP) CPO Spo CPO Fuures Drif * 87.83* Drif nd Trend * * Drif * * Drif nd Trend * * Noes: Null ypoesis ses e exisences of uni roo in reurns. * indices null ypoesis is rejeced e 1% level. 3.1 Model specificions Tis sudy involves reesep pproc. Te firs sep o esime MinimumVrince Opiml Hedge Rio (MVOHR) y using imevrying nd imeinvrin edging models. Second sep is o compue vrince of e porfolio, nd finlly, we proceed o evlue e edging effeciveness using e minimum vrince frmework in ec superiod. Two ypes of imeinvrin edging models re used in is sudy, nmely nïve nd Ordinry Les Squres (OLS). However, if condiionl vrincecovrince mrix is imevrin, Generlized Auoregressive Condiionl Heeroscedsiciy (GARCH) model will e used o esime OHR. Two versions of GARCH models i.e BEngle KrfKroner (BEKK) nd Consn Condiionl Correlion (CCC) represenion re used in is sudy Men specificions In e imevrying frmework, we esime ree ypes of condiionl men specificions. Firs, is sudy considers simple men model s follows: r S, cs S, ; ~ N(0, H ) (1) r F, cf F, S, 1 ; ~ N(0, H ) () F, 1 were r, = dily CPO spo reurn ime S r, = dily CPO fuures reurn ime F S, = unexpeced dily CPO spo reurn cnno e prediced sed on ll informion ou dily CPO spo reurn ville up o e preceding period 8

9 F, = unexpeced dily CPO fuures reurn cnno e prediced sed on ll informion ou dily CPO fuure reurn ville up o e preceding period = informion se ville o ime 1 1 H = condiionl vrince of dily CPO spo nd fuures reurns ime respecively Second, we model e condiionl men equion y considering o CPO reurns lgged erm rs, i, rf, i o cpure e sor run ssociion eween CPO spo nd fuures reurns. Hence, vecor uoregressive (VAR) men modeling is specified s follows: k k r S, cs S, irs, i S, irf, i S, i1 i1 k k r F, cf F, irs, i F, irf, i F, i1 i1 ; ~ N(0, H ) (3) S, 1 ; ~ N(0, H ) (4) F, 1 Tird, we include lgged one of sis ( Z 1 ) o mesure e longrun relionsip eween e CPO spo nd fuures prices. For e condiionl men equion, is sudy follows model specificion y Lien nd Yng (008). 3 Bo condiionl mens of CPO spo nd fuures reurns re wrien s equions (5) nd (6). k k r S, cs S, irs, i S, irf, i S Z 1 S, i1 i1 ; S, 1 ~ N(0, H ) (5) k k r F, cf F, irs, i F, irf, i F Z 1 F, i1 i1 ln ; F, 1 ~ N(0, H ) (6) In equions (5) nd (6), Z 1 is mesured yln P S, 1 ln PF, 1, were ln P S, 1 nd P re denoed s dily CPO spo nd fuures prices in nurl logrimic form F, 1 ime 1 respecively. A negive sis indices fuures price exceeds spo price ime 1. In order o elimine deviion from e long run relionsip eween o prices, e fuures price ends o decese weres e spo price ends o increse ime. Tis leds o S 0 nd F 0, s well s les one of prmeer is nonzero. Oerwise, i is for posiive sis Vrincecovrince specificions If condiionl vrincecovrince s imevrying srucure, GARCH (1,1) model is used. To minin posiive semidefinie of e esimed prmeers in e vrincecovrince srucure, we dop e wo differen specificions of condiionl vrincecovrince. 3 Refer o Lien nd Yng (008) pp.16. 9

10 Firs specificion of imevrin model is generl BEKKGARH (1,1) model (Engle & Kroner, 1995), were H is defined s follows: H ' CC A ' 1 1 ' A GH 1 G ' H SS H SF C SS C SF A SS A SF G SS GSF H ; C ; A ; G ; nd H FS H FF 0 CFF AFS AFF GFS GFF S,. F, C A G SS, SS SS S, 1 SS SS, 1 C A G FF, FF FF F, 1 FF FF, 1 C A SF, SF SF S, 1 F, 1 SF SS, 1 FF, 1 were G (7) H = condiionl covrince mrix ime C = consn coefficien prmeers for dily CPO spo nd fuures reurns respecively A = squred error lgged coefficien prmeers for dily CPO spo nd fuures reurns respecively G = voliliy lgged coefficien prmeers for dily CPO spo nd fuures reurns respecively = error erms for dily CPO spo nd fuures reurns respecively, = condiionl vrince of dily CPO spo reurn ime SS FF, = condiionl vrince of dily CPO fuures reurn ime SF, = condiionl covrince ime Bsed on equion (7), e BEKK prmeerizion requires esimion of 11 prmeers in e condiionl vrincecovrince srucure. Tis specificion ssumes spillover prmeers re consn ASF AFS, GSF GFS rougou e enire smple periods wiou king correlion ino ccoun. 4 Wi less numer of prmeers, is model minins e posiive semidefinie of esimed prmeers for condiionl vrince nd covrince. Tis condiion cn e sisfied y imposing prmeer consrins of 0 A G 1. Te second specificion of e imevrin model is CCCGARCH (1,1) of wic is esimed y king sndrdized residuls of spo nd fuures reurns (residuls divided y e GARCH condiionl sndrd deviion) ino condiionl correlion mrix (Bollerslev,1990). Bsed on is model, e condiionl correlion is ssumed o e imeinvrin. Susequenly, H is defined s follows: H D RD, were dig D i, 4 Refer o ricle of Wu e l (011) from pp.1056 o

11 Vr S,, F, 1 SS, FS, SS, SS SS S, 1 SS SS, 1 FF, FF FF F, 1 FF FF, 1 SF, SS, FF, E 1 ' 1 1 D H D, SF, FF, SS, 0 0 FF, 1 1 SS, 0 0 FF, (8) were H = condiionl covrince mrix ime R = correlion mrix of sndrdized residuls for dily CPO spo nd fuures reurns, = condiionl vrince of dily CPO spo reurn ime SS FF, = condiionl vrince of dily CPO fuures reurn ime SF, = condiionl covrince ime = correlion coefficien eween sndrdized residuls of dily CPO spo nd fuures reurns Ps sudies ve used e CCCGARCH model ecuse i is prsimonious model wi 7 prmeers provides simple compuion (see Kroner & Suln, 1993; Ng & Pirrong, 1994; nd Lien e l 00). Bsed on equion (8), posiive semidefinie of e condiionl vrincecovrince mrix is gurneed y ssuring 0nd 0, SS, were 0, 0, 0, nd 0 1 for individul GARCH (1,1) process. FF, According o Ng nd Pirrong (1994), size of sis ffecs price voliliy in e energy fuures mrke. Tis implies spo nd fuures mrkes re more volile wen e size of sis is lrge, suggesing rirge civiies re ineffecive. Kogn, Livdn nd Yron (003) predic e voliliy of spo or fuures reurns nd e sis ve Vspe effec. To cpure e effec of e sor run deviion eween o prices on e condiionl vrincecovrince H ), e lgged one of sis squred is included ino ( H equion follows BEKK nd CCC seings o ecome equion (9) s follows: Z for k SS, FF, SF (9) k, k k k, 1 k k, 1 k 1 Te esimion of ll GARCH models ove is crried ou y mximizing vlue of loglikeliood using equion (10) s follows: T 1 ' T ln 1/ ln H H L (10) 1 3. Minimumvrince edge rio (MVHR) esimion 11

12 Te MVHR poin in ime 1 is en clculed using equion (11) s rio of e condiionl covrince eween spo nd fuures SF, o e condiionl vrince of fuures FF,. Te oined MVHRs from e BEKK nd CCCGARCH (1,1) models re used o clcule vrince of porfolio nd edging effeciveness. SF, 1 (11) 1 FF, 3.3 Vrince of porfolio In e imevrying nlysis, vrince of porfolio H p, is clculed y susiuing dynmic MVHR (from equion (11)), condiionl vrince in e CPO spo mrke, condiionl vrince in e CPO fuures mrke nd condiionl covrince of o CPO reurns ino equion (1). 1 FF, 1 SF H p, SS,, (1) 3.4 Hedging performnce mesuremen Te ls sep is o evlue e edging effeciveness for imeinvrin nd imevrin models sed on risk minimizion conex, were i is e mos frequenly used s e edging performnce mesure. According o Ederingon (1979), e risk minimizion is mesured using equion (13) o compue e percenge of vrince reducion in djusing edging sregy. Te edging sregy is effecive if e vrince of reurn on edged porfolio (refer o equion (1)) pproximely equl o zero s compred o unedged porfolio. H p, ( Unedged ) H p, ( Hedged ) Percenge of vrince reducion 100 (13) H ( Unedged ) were H p, ( Unedged ) = vrince of porfolio from n unedged sregy or uncondiionl vrince of dily CPO spo reurn H p, ( Hedged ) = vrince of porfolio from edging sregy (refer o equion (1)) 4. Resuls 4.1 BEKK nd CCC esimions wi differen men nd vrincecovrince specificions Firs of ll, e BEKK nd CCCGARCH models wi differen men nd vrince specificions re esimed in ec superiod. Te esimed resuls for ese models re summrized in Tle 3 nd Tle 4 respecively. From Tle 3, i is oserved e vrinces of CPO spo nd fuures reurns wi BEKK frmework re igly influenced y eir own ps squred residuls ( A p, SS 1

13 nd A FF ) nd own ps vrinces ( G SS ndg FF ) in e mos of cses. Mos of e coefficiens of A SF nd G SF in covrince equions re found s significn, indicing e voliliy in o mrkes exii inercive effec. Te coefficiens of S nd F in e condiionl men equion re significn in e mos of superiods, weres e coefficiens of SS, FF nd SF re mjoriy insignificn in e vrincecovrince equions, especilly during e Asin finncil crisis (Pnel B). Tis implies incorporing lgged one of sis is crucil in modelling e condiionl men insed of e vrincecovrince. As oserved in Tle 4, e consn condiionl correlion ssumpion provides e significn coefficiens of SS nd FF in e mos of superiods. Tis revels e ps squred residuls ve n effec on e condiionl vrince of spo nd fuures. Similr finding s een found for e coefficien of SS. For e coefficien of FF, i indices e ps vrince of fuures mrke insignificnly ffecs is own curren vrince in e mos of cses during e Asin finncil crisis (Pnel B). Te coefficien ofs is found o e igly significn s compred o F, indicing e lgged one of sis s n explnory power in descriing e condiionl men of spo mrke insed of fuures mrke. Bo coefficiens of FF nd SF indice e sis erm conriues significn effec on eier e condiionl vrince of spo or fuures mrkes in Pnel A nd Pnel B, u is erm is found o ve significn effec on o mrkes in Pnel C. Furermore, e consn condiionl correlions eween sndrdized residul of spo nd fuures reurns re found o e e sronges during e Asin finncil crisis (Pnel B). Tese correlions re found o e wek in e susequen crisis (Pnel C). For dignosic esing, Ljung Box sisics of e 15 order re presened in Tle 3 nd Tle 4. Tese sisics re sed on sndrdized residuls nd eir squres, implying ere is no need o encompss iger order ARCH process (Ginnopoulos, 1995). In Pnel A, i indices VARBEKKGARCH model free from seril correlion nd ARCH prolems in o residul series. Susequenly, in Pnel B nd Pnel C, e GARCH models wi e sor run nd long run relionsips of o series ve no seril correlion in e sndrdized residuls nd e sndrdized squred residuls s compred o e inercepgarch model. Bsed on ese esimed models, e minimumvrince edge rios re consruced nd is descripive sisics for e innd ouof smple nlysis re repored in Tle 5. 13

14 Tle 3: Te esimion resuls of BEKKGARCH (1,1) model y using mximum likeliood during e wole period Pnel A: Apr, 1986 Jul 6, 1988 Pnel B: Sep 30, 1997 Jul 5, 00 Pnel C: Nov 30, 006 Dec 19, 011 Inercep VAR Bsis Inercep VAR Bsis Inercep VAR Bsis Condiionl men equion: c S (0.001) (0.0011) S, (0.095) S, (0.04) S, (0.0481) S, (0.0494) S, ** (0.0549) S, * (0.0393) S, *** (0.0443) S, *** (0.0474) S c F (0.0008) (0.0007) F, *** (0.0318) F, (0.031) F, *** (0.0345) F, (0.0391) F, ** (0.048) F, (0.0447) F, (0.0476) F, * (0.0441) F *** (0.0011) (0.0971) (0.0505) 0.0 (0.0517) *** (0.033) (0.039) *** (0.0316) *** (0.0371) *** (0.036) *** (0.019) ** (0.0016) 0.176*** (0.063) (0.070) *** (0.0337) ** (0.0344) ** (0.0487) (0.0443) (0.0473) (0.0456) 0.097* (0.0156) (0.0005) (0.0005) 0.08 (0.0311) (0.0006) (0.0313) (0.0008) (0.0008) 0.10*** (0.0335) *** (0.001) ** (0.0309) (0.016) 0.06 (0.0168) *** (0.0160) (0.048) (0.0008) (0.0007) 0.358*** (0.0361) ** (0.0038) 0.005** (0.0011) *** (0.0391) 0.00*** (0.0005) 0.003*** (0.0004) (0.0166) ** (0.014) 0.003*** (0.0007) (0.0167) *** (0.04) *** (0.0407) (0.049) * (0.0449) 0.059** (0.011) (0.0078) 14

15 Tle 3: (Coninued) Pnel A: Apr, 1986 Jul 6, 1988 Pnel B: Sep 30, 1997 Jul 5, 00 Pnel C: Nov 30, 006 Dec 19, 011 Inercep VAR Bsis Inercep VAR Bsis Inercep VAR Bsis Condiionl vrincecovrince equion: *** 1.8E05**.53E05* 7.50E06*** 1.E05*** 1.30E05*** 0.000*** 0.000*** *** C SS (1.41E05) (5.03E06) (1.38E05) (1.77E06) (.7E06) (.87E06) (.5E05) (.94E05) (1.60E05) 1.57E05*** 1.7E05** 1.50E05* 7.E06** *** ** 8.8E05*** 8.60E05*** 5.05E05*** C FF (5.64E06) (8.00E06) (7.87E06) (.94E06) (5.03E05) (4.9E05) (1.E05) (1.1E05) (1.1E05) 1.80E05** 6.84E06** 9.97E E06*** 1.93E05*** 1.80E05***.9E05***.9E05*** *** C SF (7.44E06) (.80E06) (8.0E06) (1.11E06) (5.89E06) (5.54E06) (7.67E06) (7.71E06) (1.59E05) *** *** 0.806*** 0.331*** 0.337*** 0.71*** 0.17*** 0.754*** A SS (0.073) (0.016) (0.0665) (0.0175) (0.03) (0.031) (0.006) (0.031) (0.087) *** *** *** *** *** 0.149*** *** 0.818*** *** A FF (0.047) (0.0497) (0.041) (0.0116) (0.07) (0.06) (0.0179) (0.0) (0.013) *** 0.581*** *** *** *** 0.184*** *** 0.3*** A SF (0.0034) (0.0008) (0.007) (0.000) (0.0005) (0.0006) (0.0004) (0.0005) (0.0006) *** 0.987*** *** *** 0.944*** 0.93*** *** 0.813*** G SS (0.0159) (0.0067) (0.0318) (0.0065) (0.01) (0.0103) (0.05) (0.091) (0.147) 0.900*** *** 0.958*** *** *** 0.883*** 0.64*** 0.641*** *** G FF (0.031) (0.065) (0.0189) (0.006) (0.0506) (0.0467) (0.04) (0.03) (0.039) *** *** *** *** *** *** *** 0.515*** *** G SF (0.0004) (0.000) (0.0006) (1.73E05) (0.0005) (0.0005) (0.0006) (0.0006) (0.0057) 0.005*** 1.30E *** SS (0.0009) (.80E05) (0.0011) 1.46E *** FF (0.000) (0.004) (0.001) E SF (0.0006) (4.38E05) (0.001) L Tes for iger order ARCH effec Spo equions: Fuures equions: Q.983* *** 8.979** * Q 7.300** *** 8.875** Q *** *** * 0.03 Q Noes: 1. () InercepBEKKGARCH models re esimed y equions (1), (), nd (7). () Vecor uoregressive (VAR)BEKKGARCH models re esimed y equions (3), (4) nd (7). (c) BsisBEKKGARCH models re esimed y equions (5), (6) nd (9).. *, ** nd *** indice e sisicl significnce e 10%, 5% nd 1% levels respecively. 3. Numers in preneses re e sndrd errors. 4. L is e vlue of e loglikeliood funcion clculed y equion (10). 5. Q nd Q re e Ljung Box sisics of sndrdized residuls nd sndrdized squred residuls. 15

16 Tle 4: Te esimion resuls of CCCGARCH (1,1) model y using mximum likeliood during wole period Pnel A: Apr, 1986 Jul 6, 1988 Pnel B: Sep 30, 1997 Jul 5, 00 Pnel C: Nov 30, 006 Dec 19, 011 Inercep VAR Bsis Inercep VAR Bsis Inercep VAR Bsis Condiionl men equion: c S (0.0013) (0.0011) S, (0.0348) S, (0.0441) S, (0.0570) S, (0.059) S, * (0.059) S, ** (0.0360) S, *** (0.0408) S,4 0.45*** (0.0455) S c F (0.0008) (0.0007) F, *** (0.0407) F, (0.0309) F, ** (0.0371) F, (0.0399) F, ** (0.0487) F, (0.0456) F, (0.047) F, (0.0439) F *** (0.0008) *** (0.0036) 0.053*** (0.007) (0.04) *** (0.0101) 0.04 (0.000) *** (0.0184) *** (0.011) *** (0.009) 0.131*** (0.0077) 0.00 (0.0018) *** (0.096) (0.0358) *** (0.034) (0.0403) * (0.054) (0.047) (0.0504) (0.0453) (0.017) (0.0004) (0.0005) (0.0314) (0.0006) (0.03) (0.0008) (0.0008) 0.140*** (0.046) *** (0.0009) ** (0.0396) (0.0168) (0.019) 0.168*** (0.0187) (0.078) 5.16E05 (0.001) (0.0008) 0.358*** (0.0355) ** (0.0035) 0.00* (0.0011) *** (0.0365) 0.004*** (0.0005) (0.0005) 0.03 (0.0183) *** (0.011) *** (0.0007) (0.0175) 0.19*** (0.041) ** (0.018) 0.04 (0.0431) (0.0453) 0.016* (0.009) * (0.0077) 16

17 Tle 4: (Coninued) Pnel A: Apr, 1986 Jul 6, 1988 Pnel B: Sep 30, 1997 Jul 5, 00 Pnel C: Nov 30, 006 Dec 19, 011 Inercep VAR Bsis Inercep VAR Bsis Inercep VAR Bsis Condiionl vrincecovrince equion: *** * SS (1.10E05) (0.0001) 1.65E05** 1.7E05** FF (.389) (8.3E06) 0.0*** SS (0.0005) (0.0157) 0.15*** 0.161*** FF (0.0369) (0.041) 0.58*** * SS (0.0131) (0.767) 0.801*** (0.0505) 0.81*** FF (0.0411) SS FF 7.47E05*** (1.14E05) 1.89E05** (9.63E06) *** (0.0304) *** (0.0437) 0.004*** (0.001) *** (0.054) 0.006*** (0.0008).40E05 (0.0004) 9.E06*** (.36E06) (0.0003) *** (0.0163) 0.007*** (0.0001) *** (0.0178) (0.44) 9.11E10*** (.33E06) * (0.000) *** (0.0154) (0.0116) 0.864*** (0.0170) (0.3306) 9.91E06*** (.53E06) 1.5E05 (3.58E06) *** (0.0158) *** (0.0003) *** (0.0176) *** (0.0063) 1.34E05 (1.97E05).51E05*** (6.49E06) 0.000*** (.46E05) 8.E05*** (1.1E05) *** (0.0104) *** (0.033) 0.63*** (0.04) 0.408*** (0.094) 0.000*** (.8E05) 8.E05*** (1.19E05) *** (0.0136) 0.637*** (0.0466) *** (0.0366) 0.413*** (0.096) *** (1.8E05) *** (1.63E05) 0.101*** (0.016) *** (0.0395) (0.0373) 0.617*** (0.0403) *** (0.0011) 0.009*** (0.001) Condiionl correlion equion: 0.103** *** 0.160** 0.98*** *** *** * 0.061** ** (0.0439) (0.0441) (0.049) (0.099) (0.06) (0.067) (0.0301) (0.0316) (0.0315) L Tes for iger order ARCH effec Spo equions Fuures equions Q 4.064* *** 7.95** Q 6.183***.914* *** Q *** Q Noes: 1. () InercepCCCGARCH models re esimed y equions (1), () nd (8). () Vecor uoregressive (VAR)CCCGARCH models re esimed y equions (3), (4) nd (8). (c) BsisCCCGARCH models re esimed y equions (5), (6) nd (9).. *, ** nd *** indice e sisicl significnce e 10%, 5% nd 1% levels respecively. 3. Numers in preneses re e sndrd errors. 4. L is e vlue of e loglikeliood funcion clculed y equion (10). 5. Q nd Q re e Ljung Box sisics of sndrdized residuls nd sndrdized squred residuls. 17

18 4. Impc of srucurl cnge on esimed minimumvrince edge rio (MVHR) Te summry of resuls in Tle 5 indices mens of edge rios re cnging significnly over e ree superiods. On verge, e ig opiml edge rios re found during e Asin finncil crisis (Pnel B) for ou 0.5 (insmple) nd 0.3 (ouofsmple). Furermore, e OLS edge rio is found o e similr o GARCH edge rios implying edging effeciveness of CPO fuures conrc sed on OLS nd GARCH sregies could e very comprle during e Asin finncil crisis. As oserved, edge rios esimed y GARCH models for ouofsmple period in Pnel B sow iger sndrd deviions s compred o oer superiods. Tis implies edgers need o mke iger djusmen in e edge rio during e Asin finncil crisis s compred o e glol finncil crisis. In summry, e impc of e Asin finncil crisis on edge rios is e lrges mong e ree crises. Tle 5: Summry sisics of edge rios Insmple Ouofsmple Hedge sregy Men SD Men SD Pnel A: Apr, 1986 Jul 6, 1988 Nïve edge 1 NA 1 NA OLS edge InercepBEKKGARCH edge VAR BEKKGARCH edge BsisBEKKGARCH edge InercepCCCGARCH edge VARCCCGARCH edge BsisCCCGARCH edge Pnel B: Sep 30, 1997 Jul 5, 00 Nïve edge 1 NA 1 NA OLS edge InercepBEKKGARCH edge VAR BEKKGARCH edge Bsis BEKKGARCH edge InercepCCCGARCH edge VARCCCGARCH edge Bsis CCCGARCH edge Pnel C: Nov 30, 006 Dec 19, 011 Nïve edge 1 NA 1 NA OLS edge InercepBEKKGARCH edge VAR BEKKGARCH edge BsisBEKKGARCH edge InercepCCCGARCH edge VARCCCGARCH edge Bsis CCCGARCH edge Noes: Ordinry les squres (OLS) edge rio is slope of regression y regressing spo reurn gins fuures reurn. Te BEKK nd CCCGARCH edge rios re clculed y equion (11). SD is denoed s sndrd deviion. Te SD of e nïve edge is no ville s e rio remins consn over ime. Te SD of OLS edge rio is sndrd error of slope for fuures reurn. 18

19 4.3 Impc of srucurl cnge on edging effeciveness Tle 6 repors e vrince of porfolio nd vrince reducion for unedged nd edged reurns produced y nïve, minimum vrinceols nd vrious GARCH edging models. Tle 6: Hedging effeciveness of Mlysin CPO fuures Hedge sregy Vrince of porfolio Insmple Vrince reducion (%) Vrince of porfolio Ouofsmple Vrince reducion (%) Pnel A: Apr, 1986 Jul 6, 1988 Unedged CPO porfolio Hedged CPO porfolio: Nïve edge OLS edge InercepBEKKGARCH edge VARBEKKGARCH edge Bsis BEKKGARCH edge InercepCCCGARCH edge VARCCCGARCH edge BsisCCCGARCH edge Pnel B: Sep 30, 1997 Jul 5, 00 Unedged CPO porfolio Hedged CPO porfolio: Nïve edge OLS edge InercepBEKKGARCH edge VARBEKKGARCH edge Bsis BEKKGARCH edge InercepCCCGARCH edge VARCCCGARCH edge BsisCCCGARCH edge Pnel C: Nov 30, 006 Dec 19, 011 Unedged CPO porfolio Hedged CPO porfolio: Nïve edge OLS edge InercepBEKKGARCH edge VARBEKKGARCH edge BsisBEKKGARCH edge InercepCCCGARCH edge VARCCCGARCH edge BsisCCCGARCH edge Noes: 1. Te vrince of unedged CPO porfolio is genered from e vrince of CPO spo reurn.. Te vrince of edged CPO porfolio is compued y equion (1). 3. Te risk reducion is clculed y equion (13). As oserved in Tle 6, i sows nïve sregy is e wors sregy s i increses e risk of edged porfolio. Te VARBEKKGARCH model is found s e superior model in Pnel A s i reduces per cen of e risk (insmple) nd per cen of e risk (ouofsmple). In Pnel B, esides ving relively ig dynmic edge rios wiin e rnge of (insmple) nd (ouofsmple) s 19

20 sown in Tle 5, n ssumpion of CCCGARCH model wi e sis erm offers e mos effecive risk reducion of nd per cen for e in nd ouofsmple respecively. In Pnel C, sisbekkgarch model cieves e iges risk reducion of over 117 per cen for o in nd ouofsmple. Overll, i is cler e edging sregies wi e sis erm generlly ouperform in reducing e risk of CPO porfolio in Pnel B nd Pnel C. As compred eween Pnel B nd Pnel C, e mrginl differences mong models sugges e CPO fuures edging sregies underperform cross e Asin nd glol finncil crises for o in nd ouofsmple respecively. As invesors more concern ou fuure performnce, e ouofsmple sows risk reducion of e superior model declines srply from o 1.8 per cen. Te low level of edging effeciveness is oserved wen fuures reurn exiis ig voliliy nd filed disriuion over e period of Overll, e resul indices e linkge eween spo nd fuures prices in e long run (sis) is imporn o fi e exreme voliliy during e glol finncil crisis. In conrs, including sis effec ino e GARCH model cnno susin is ig performnce in reducing e risk during e glol finncil crisis s compred o previous crisis. 5. Conclusions Tis sudy exends Zinudin nd Srudin (011) on Mlysin crude plm oil (CPO) fuures mrke y exmining e edging effeciveness sed on e minimumvrince edge rios from eig model specificions. Tese models were evlued during e ree finncil crises nmely, e world economic recession in 1986, Asin finncil crisis in 1997/1998 nd glol finncil crisis in 008/009 respecively. Susequenly, innd ouof smple of e minimum vrince of edge rio is compred during ec superiod. As e in nd ouofsmple nlysis provides sme finding, is sudy focuses on e ouofsmple forecsing evluion resuls. Nole findings re: Firs, i is evidenly cler GARCH models wi sis erm ouperform oers during e Asin finncil crisis (AFC) nd glol finncil crisis (GFC) respecively. Second, during e Asin finncil crisis, e ig dynmic edge rios conriue o e superioriy of CCCGARCH model wi risk reducion of per cen. Te declining edge rio in GFC leds o e emergence of BEKKGARCH model wic provides e mos risk reducion of 17.6 per cen. Tird, from AFC o GFC, e risk reducion of edging sregy declines srply from o 17.8 per cen. Two possile resons re; Firsly, unlike AFC, e epicener of GFC ws in e Unied Ses nd susequenly exended o Europe. Secondly, episode of d news ws relesed o e mrke one fer noer in prolonged period, wic cused ineffeciveness of edging sregy s socks were lrgely unniciped. Overll, is sudy concludes: Firs, e ig dynmic edge rio during e Asin finncil crisis implies CPO mrke pricipns re sensiive o CPO spo nd fuures movemen. Second, e superior GARCH model wi e sis erm cnno 0

21 susin is performnce in erms of risk reducion during e crisis period. Tis sows e Mlysin CPO fuures mrke provides low level of edging effeciveness during e glol finncil crisis, wic is minly cused y excess kurosis in e mrkes. Tis finding is found o e inconsisen wi Ong e l (01) wo find sle movemen of CPO spo price in conriues o e low level of edging effeciveness. Te policy implicion is cler. Aloug e effeciveness of Mlysin CPO fuures is low during e recen crisis, e minimumvrince edge rio nlysis s mnged o compre e performnce of vrious edging models. By undersnding e effeciveness of vrious edging models, e CPO mrke pricipns cn swic eween e models in differen voliliy periods o cover eir risk exposure in e spo mrke. References Amed S. (007) Effeciveness of imevrying edge rio wi consn condiionl correlion: n empiricl evidence from e US resury mrke. ICFAI Journl of Derivives Mrkes 4(): 30. Alizde, A.H., Kvussnos, M.G. nd Mencof, D.A. (004) Hedging gins unker price flucuions using peroleum fuures conrcs: consn versus imevrying edge rios. Applied Economics 36 (1): Anderson, R.W. nd Dnine, J.P. (1981) Cross edging. Te Journl of Poliicl Economy 89(6): Billie, R.T. nd Myers, R.J. (1991) Bivrie GARCH esimion of e opiml commodiy fuures edge. Journl of Applied Economerics 6(): Bollerslev, T. (1990) Modelling e coerence in sorrun nominl excnge res: mulivrie generlized ARCH model. Review of Economics nd Sisics 7(3): Bollerslev, T., Engle, R.F. nd Wooldridge, J.M. (1988) A cpil sse pricing model wi imevrying covrinces. Journl of Poliicl Economy 96(1): Brooks, C., Henry, O.T. nd Persnd, G. (00) Te effec of symmeries on opiml edge rio. Te Journl of Business 75(): Cenrl Bnk Mlysi (009) Monly Sisicl Bullein July 009. Kul Lumpur: Cenrl Bnk. Coudry, T. (00) Sorrun deviions nd opiml edge rio: evidence from sock fuures. Journl of Mulinionl Finncil Mngemen 13():

22 Coudry, T. (004) Te edging effeciveness of consn nd imevrying edge rios using ree Pcific Bsin sock fuures. Inernionl Review of Economics nd Finnce 13(4): Ederingon, L.H. (1979) Te edging performnce of e new fuures mrke. Journl of Finnce 34(1): Engle, R.F. nd Kroner, K.F. (1995) Mulivrie simulneous generlized ARCH. Economeric Teory 11(1): Fm, E.F. (1984) Forwrd nd spo excnge res. Journl of Monery Economics 14(3): Floros, C. nd Vougs, D.V. (004) Hedge rios in Greek sock index fuures mrke. Applied Finncil Economics 14(15): Ginnopoulos, K. (1995) Esiming e ime vrying componens of inernionl sock mrkes' risk. Te Europen Journl of Finnce 1(): Howrd, C.T. nd D Anonio, L.J. (1984) A riskreurn mesure of edging effeciveness. Journl of Finncil nd Quniive Anlysis 19(1): Hill, J. nd Scneeweis, T. (1981) A noe on e edging effeciveness of foreign currency fuures. Journl of Fuures Mrkes 1(4): Jonson, L.L. (1960) Te eory of edging nd speculion in commodiy fuures. Te Review of Economic Sudies 7(3): Kroner, K.F. nd Suln, J. (1993) Time vrying disriuion nd dynmic edging wi foreign currency fuures. Journl of Finncil nd Quniive Anlysis 8(4): Kogn, L., Livdn, D. nd Yron, A. (003) Fuures prices in producion economy wi invesmen consrins. Working Pper, MIT. Lien, D., Tse, Y.K. nd Tsui, A.K.C. (00) Evluing e edging performnce of e consncorrelion GARCH model. Applied Finncil Economics 1(11): Lien, D. nd Yng, L. (008) Hedging wi Cinese mel fuures. Glol Finnce Journl 19(): Mlysin Plm Oil Bord. Aville from p:// Accessed 4 Ocoer 01. Moscini, G.C. nd Myers, R.J. (00) Tesing for consn edge rios in commodiy mrkes: mulivrie GARCH pproc. Journl of Empiricl Finnce 9(5):

23 Ng, V.K. nd Pirrong, S.C. (1994) Fundmenls nd voliliy: sorge, spreds, nd e dynmics of mels prices. Journl of Business 67():0330. Ong, T.S., Tn, W.F. nd Te, B.H. (01) Hedging effeciveness of crude plm oil fuures mrke in Mlysi. World Applied Sciences Journl 19(4): Prk, T.H. nd Swizer, L.N. (1995) Timevrying disriuion nd e opiml edge rios for sock index fuures. Applied Finncil Economics 5(3): Sein, J.L. (1961) Te simulneous deerminion of spo nd fuures prices. Te Americn Economic Review 51(5): Swizer, L.N. nd ElKoury, M. (007) Exreme voliliy, speculive efficiency, nd e edging effeciveness of e oil fuures mrkes. Journl of Fuures Mrkes 7(1): Tong, W.H.S. (1996) An exminion of dynmic edging. Journl of Inernionl Money nd Finnce 15(1): Unied Nions Developmen Progrm (UNDP)(009) Te Glol Finncil Crisis nd e Mlysin Economy: Impc nd Response. A Join Repor y e Insiue of Sregic nd Inernionl Sudies (ISIS) nd e Fculy of Economics nd Adminisrion (UNDP Mlysi). Working, H. (1953) Fuures rding nd edging. Te Americn Economic Review 43(3): Wu, F., Gun, Z. nd Myers, R.J. (011) Voliliy spillover effecs nd cross edging in corn nd crude oil fuures. Journl of Fuures Mrkes 31(11): Zinudin, R. nd Srudin, R.S. (011) Muli men GARCH pproc o evluing edging performnce in e crude plm oil fuures mrke. Asin Acdemy of Mngemen Journl of Accouning nd Finnce 7(1):