World old price and ock reurn in Cina: ini for edin and diverificaion raeie Moamed El Hedi Arouri, Amine Laiani, Duc Kuon Nuyen To cie i verion: Moamed El Hedi Arouri, Amine Laiani, Duc Kuon Nuyen. World old price and ock reurn in Cina: ini for edin and diverificaion raeie. 03. <al-00798038> HAL Id: al-00798038 p://al.arcive-ouvere.fr/al-00798038 Submied on 7 Mar 03 HAL i a muli-diciplinary open acce arcive for e depoi and dieminaion of cienific reearc documen, weer ey are publied or no. Te documen may come from eacin and reearc iniuion in France or abroad, or from public or privae reearc cener. L arcive ouvere pluridiciplinaire HAL, e deinée au dépô e à la diffuion de documen cienifique de niveau recerce, publié ou non, émanan de éabliemen d eneinemen e de recerce françai ou éraner, de laboraoire public ou privé.
World old price and ock reurn in Cina: ini for edin and diverificaion raeie Moamed El Hedi Arouri Univeriy of Auverne, France Moamed.Arouri@u-clermon.fr Amine Laiani LEO, Univeriy of Orlean and ESC Renne Buine Scool amine.laiani@univ-orlean.fr Duc Kuon Nuyen * ISC Pari Scool of Manaemen, France dnuyen@icpari.com * Correpondin auor Abrac In i paper we make ue of everal mulivariae GARCH model (CCC-, DCC-, BEKK-, diaonal BEKK-, and VAR-GARCH) o inveiae bo reurn and volailiy pillover beween world old price and ock marke in Cina over e period from Marc, 004 rou Marc 3, 0. We alo analyze e opimal wei and ede raio for old-ock porfolio oldin and ow ow empirical reul can be ued o build effecive diverificaion and edin raey. Our reul ow evidence of inifican reurn and volailiy cro effec beween old price and ock price in Cina. In paricular, pa old reurn play a crucial role in explainin e dynamic of condiional reurn and volailiy of Cinee ock marke and ould u be accouned for wen forecain fuure ock reurn. Our porfolio analyi ue a addin old o a porfolio of Cinee ock improve i rik-adjued reurn and a old rik expoure can be effecively eded in porfolio of ock over ime. Finally, we ow a e VAR-GARCH model perform beer an e oer mulivariae GARCH model. Keyword: Sock marke, old price, diverificaion and edin effecivene, GARCH model JEL claificaion: G, F3, Q43
. Inroducion Te purpoe of e preen udy i reefold. Our fir objecive i o examine e dynamic reurn and volailiy ranmiion uin a bivariae VAR GARCH model for old and ock marke in Cina. Te empirical model i paricularly advanaeou in a i allow imulaneou ock ranmiion in e condiional reurn and volailiie. We en ue e model reul o compue and analyze e opimal wei and ede raio for old-ock porfolio oldin. We finally ae e diverificaion and edin effecivene of old in Cina baed on differen compein mulivariae GARCH-baed model. Te lieraure on old and oer preciou meal marke a recenly reained paricular aenion from finance reearcer and praciioner. Suc a endency can raiforwardly be explained by e inveor willinne o produce a ede o diverify away e increain rik in e ock marke rou invein in oer ae clae. Indeed, e i volailiy and widepread conaion caued by ucceive financial urbulence and crie over e la decade ave promped inveor o conider alernaive invemen inrumen a a par of diverified porfolio of ock. No only oil ae bu alo major preciou meal includin old emered a naural deirable ae clae eliible for porfolio diverificaion becaue ey offer differen volailiie and reurn of lower correlaion wi ock, a bo ecor and marke level (Arouri and Nuyen, 00; Dakalaki and Skiadopoulo, 0). I i now common a wen rik averion moun due, for example, o increain inabiliy and uncerainy in ock marke or o lon win in e price of oil, mo inveor are direced oward e meal marke and old in paricular, bein viewed a e refuee or afe aven ae in ime of crie. I i u no urpriin a e exiin lieraure on e old ae i par of e one examinin e price dynamic, ocaic properie and role of e commodiie marke in porfolio manaemen. A number of udie ave queioned e repone of preciou meal price o cane in inernaional iniuional and macroeconomic facor (e.., Kaufman and Winer, 989; Criie David e al., 000; Heemkerk, 00; Ciner, 00; Baen e al., 00). Sjaaad and Scacciavillani (996) find, for example, a flucuaion of floain excane rae of major currencie, followin e breakdown of e Breon Wood currency arranemen, ave led o price inabiliy in e world old marke over e period from January 98 o December 990. For eir par, Baen e al. (00) documen e eniiviy of preciou meal volailiy o macroeconomic facor, bu wi differen deree. Te overall reul ue a preciou meal are oo diinc o be conidered a inle ae cla. In
paricular, old volailiy can be empirically explained by moneary variable. Gold alo eem o be ily eniive o excane rae and inflaion, wic implie a i can offer e be ede durin inflaionary preure and excane rae flucuaion and an opimal porfolio of preciou meal a minimize rik ould be dominaed by old (Hammoude e al., 0). More recen udie ave raer looked a e iue of old price volailiy modelin and informaion ranmiion beween preciou meal and oer commodiie in order o draw e implicaion of e eimaed reul for porfolio diverificaion and edin raeie involvin preciou meal. For example, Hammoude and Yuan (008) make ue of variou GARCH-baed model o examine e properie of condiional volailiy for ree imporan meal (old, ilver, and copper) wile conrollin for ock from world oil price (WTI) and ree-mon US Treaury bill inere rae. Uin daily ree-mon fuure price of e ree meal, ey find a condiional volailiy of old and ilver i more perien, bu le eniive o leverae effec an a of copper. Ti findin lead o ue, on e one and, e imporance of accurae volailiy modelin epecially wen old and ilver are ued a underlyin ae in financial derivaive conrac, and on e oer and e valuable conribuion of ee wo meal in down marke and crii ime. Hammoude e al. (00) documen, from a mulivariae VARMA-GARCH model, weak volailiy pillover acro preciou meal, bu ron eniiviy of meal volailiy o excane rae variabiliy. Tey furer poin ou e role of old a a ede aain excane rae rik wen opimal wei and ede raio are compued. Wile underandin e dynamic ineracion beween old price cane and ock marke i a crucial elemen for porfolio dein, rik manaemen and ae pricin, ee ineracion ave only been examined very recenly by, o e be of our knowlede, wo udie. Baur and Lucey (00) ow a old erve a a afe aven for ock in e US, e UK, and Germany epecially afer exreme neaive ock affecin ock marke. Gold i alo a ede for ock in e US and e UK. Baur and McDermo (00) e weer old repreen a afe aven aain ock of major emerin and developin counrie, and ow a over e period 979 o 009 old i bo a ede and a afe aven for major European ock marke and e US bu no for Auralia, Canada, Japan and lare emerin marke uc a e BRIC counrie. Furermore, old i found a a ron afe aven for mo developed marke durin evere epiode of e recen financial crii. See Arouri e al. (0) for a deailed dicuion of i lieraure. 3
Our udy exend e exiin lieraure ino reurn and volailiy pillover beween old and ock marke, porfolio dein in e preence of bo old and ock, and coice of appropriae model for modelin old-ock ineracion. Specifically, we provide a orou analyi of ow ock and volailiy are ranmied from world old marke o Cinee ock marke and from Cinee ock marke o world old marke. Ti reearc i of paricular inere for everal reaon. Fir, none of e previou udie a conidered e volailiy pillover beween old and ock marke wile a beer underandin of e ranmiion mecanim beween em elp buildin accurae ock valuaion model and accurae foreca of e volailiy of bo marke. Empirical reul from volailiy pillover analyi alo permi o addre everal imporan iue uc a edin raeie, opimal porfolio allocaion, and derivaive manaemen wi repec o e uncerainie aociaed wi old price flucuaion. Noe a e work of Baur and Lucey (00) and Baur and McDermo (00) only provide round for underandin e old-ock reurn relaionip. Second, e linkae beween world old price and Cinee ock marke ave never been examined depie e increain role of Cina in e world economy. Accordin o e IMF aiic, Cina owed, over e la decade, a very i economic row rae ranin from 8.3% (00) and 4.% (007). Ti ron economic performance made Cina e econd lare economy in 00 wi repec o e oal GDP meaured a purcain power pariy. In e meanime, e udy of Lai and Ten (00) ue a e Cinee ock marke i no only a afe aven bu alo a ede for lobal inveor porfolio, in paricular durin ime of financial urbulence. Addiionally, we noe e coninuin ure in Cina old demand in recen year. Te World Gold Council repor on May 7, 0 poined ou a Cina invemen demand for pyical old i more an doubled from 40.7 on a year ao o 90.9 on in e fir quarer of 0. Soarin inernaional marke price, i uncerainie in ock and propery marke, and riin inflaion expecaion are undoubedly candidae facor a ave led o e robu row of e domeic old invemen marke in Cina. Like anywere in e world, old may u be een a a ood alernaive invemen and e be ede o inflaion. Finally, our empirical analyi relie on e mulivariae pecificaion of e vecor auorereive - eneralized auorereive condiional eerokedaiciy model (VAR-GARCH) developed by Lin and McAleer (003). Ti model offer e poibiliy o explore e condiional volailiy dynamic of e reurn erie a well a e condiional cro effec and volailiy pillover beween em. I alo provide meaninful eimae of e model parameer wi fewer compuaional complicaion an oer mulivariae GARCH pecificaion, uc a e full-facor GARCH model. Furermore, e findin can be ued 4
o analyze e diverificaion and edin effecivene acro old ae and ock marke. Some paper ave aken e VAR-GARCH approac o inveiae e volailiy pillover and edin raeie beween Gulf Arab equiy ecor (Hammoude e al., 009), beween previou meal and excane rae (Hammoude e al., 00), beween crude oil po and fuure reurn of e Bren and WTI oil price bencmark (Can e al., 0), and beween oil and ock marke (Arouri e al., 0). Tee udie commonly ue e uiabiliy of e VAR-GARCH model for capurin e dynamic linkae beween differen ae marke a well a buildin opimal porfolio. Overall, we find evidence of inifican volailiy cro effec beween world old price and ock marke in Cina over e period 004-0. In paricular, pa old ock are found o play a crucial role in explainin e ime-varyin paern of condiional volailiy of Cinee ock reurn and ould u be accouned for wen makin volailiy foreca of fuure ock reurn. On e oer and, our porfolio analyi ue a addin e old ae o a well-diverified porfolio of Cinee ock improve i rik-adjued performance and a ock rik expoure can be effecively eded uin old. Moreover, we ow a e VAR-GARCH model perform beer an four alernaive mulivariae volailiy model (CCC-, DCC-, calar and diaonal BEKK-GARCH) ince i provide ier rik-adjued reurn performance and edin effecivene. Te remainder of i aricle i rucured a follow. Secion inroduce our empirical meodoloy. Secion 3 preen e ample daa and eir ocaic properie. Secion 4 dicue e empirical findin and ow eir implicaion on opimal porfolio dein and rik manaemen. Secion 5 provide ome concludin remark.. Empirical meod Since eir appariion, e ARCH/GARCH-family model ave received a paricular aenion from reearcer and praciioner a far a e iue of volailiy modelin and forecain of macroeconomic and financial variable i addreed. Wen e objecive i o inveiae volailiy inerdependence and pillover beween differen ime-erie, mulivariae GARCH pecificaion uc a e CCC-GARCH model of Bollerlev (990), e BEKK-GARCH model of Enle and Kroner (995) or e DCC-GARCH model of Enle (00) ould be more relevan an univariae model. Empirical reul repored in Haan and Malik (007), Anolucci (009), and Kan e al. (009), amon oer, confirm effecively e uperioriy 5
of ee model and ow a ey aifacorily capure e ylized fac of commodiie condiional volailiy a well a e dynamic of volailiy ineracion. Given a we aemp o examine e ock and volailiy pillover beween old price and ock marke in Cina a well a o derive e implicaion of e reul on opimal wei and ede raio for old-ock porfolio oldin, e abovemenioned mulivariae GARCH model are naurally uiable for our reearc queion. However, ee model are involved wi an exceive number of parameer wen e number of variable in e yem i imporan. Tey can alo encouner converence problem durin e eimaion proce, epecially wen addiional exoenou variable are inroduced ino e condiional mean and variance equaion. Tee reaon lead u o employ e VAR-GARCH model developed by Lin and McAleer (003). Ti model ypically combine a mulivariae GARCH proce and a VAR model. I main advanae re on i flexibiliy o model e condiional mean croeffec and condiional volailiy ranmiion beween e erie under conideraion wi fewer compuaional complexiie an oer mulivariae volailiy model. Te abiliy of e VAR-GARCH model o capure cro-marke volailiy ineracion a been confirmed by recen reearc (Can e al., 0; Arouri e al., 0). In i udy, we ue e bivariae VAR-GARCH a baeline model o ed li on e diverificaion and edin effecivene of a porfolio involvin e old ae and ock in Cina. We alo conider four compein bivariae volailiy model (CCC-GARCH, DCC- GARCH, diaonal BEKK-GARCH and calar BEKK-GARCH) for comparion purpoe.. Bivariae VAR()-GARCH(,) We ue e VAR()-GARCH(,) model o accommodae e reurn and volailiy inerdependencie beween old and ock marke. Te condiional mean of our empirical model i pecified a follow R µ ΦR / ε H η ε () were µ i e vecor of conan erm in e VAR. R ( r, r ) i e vecor of reurn on e ock marke index and e old price index, repecively. Φ refer o a ( ) marix of Uin e univariae and bivariae AIC and BIC informaion crieria o cooe e opimal la len of e univariae GARCH(p,q) proce and en a of e bivariae VAR-GARCH model for e pair of old and ock marke, our reul elec one la for bo condiional mean and variance equaion. Tey u lead u o cooe e bivariae VAR()-GARCH(,) pecificaion. 6
coefficien. ε ( ε, ε ) i e vecor of e error erm of e condiional mean equaion for ock and old reurn repecively. η ( η, η ) refer o a equence of independenly and idenically diribued (i.i.d) random error; and H i e condiional variance- covariance marix of ock and old reurn. S, and are pecified a follow: C ε α ( ε ) α ( ) () C ε α ( ε ) α ( ) (3) I i obviou from Eq. () and Eq. (3) a e volailiy ranmiion acro e old and ock marke over ime come from wo ource: (i) e cro value of error erm, ( ε ) and ( ε ), wic capure e impac of direc effec of ock ranmiion, and (ii) e cro value of laed condiional volailiie, and, wic direcly accoun for e rik ranfer beween marke. Te aionary condiion require a e roo of e equaion I ALBL 0 mu be ouide e uni circle, were L i a la polynomial, I i a ( ) ideniy marix, and A α α α α and B Le ρ be e conan condiional correlaion, e condiional covariance beween ock and old reurn i modelled a: ρ (4) Accordin o e above pecificaion, our empirical model imulaneouly allow lonrun volailiy perience a well a ock and volailiy ranmiion beween old and ock marke under conideraion. Even ou e aumpion of conan condiional correlaion may be viewed a rericive iven canin economic condiion, e exenion o dynamic condiional correlaion i no poible for inance becaue e aiical properie of uc a model ave no been analyzed a e eoreical level ye. We eimae e parameer of e above bivariae model by quai-maximum likeliood eimaion (QMLE), wic i robu o any deparure from normaliy condiion. See Lin and McAleer (003) for furer deail on neceary and ufficien condiion reardin e coniency of QMLE for e model ued. 7
. Compein bivariae GARCH(,) model We define aain R ( r, r ) a e vecor of e reurn on ock marke index and old price index, and H a e condiional variance-covariance marix of ock and old reurn. We pecify e condiional mean of e bivariae AR()-GARCH(,) a follow R µ ΦR / ε H η ε (5) were / H i a ( ) ymmeric poiive definie marix and, ) η ( η η i e vecor of i.i.d. random error wi E( η ) 0 and Var( η ) I. We furer aume a H follow a bivariae GARCH(,) proce. Differen pecificaion for H u lead o differen mulivariae GARCH-ype model. A we aed earlier, e mo popular mulivariae parameerizaion include e full BEKK-GARCH model of Enle and Kroner (995), e CCC-GARCH of Bollerlev (990) and e DCC- GARCH of Enle (00). iven by Te full BEKK-GARCH wic impoe poiive definiene rericion for H i H C' C A' ε ε ' A B H B (6) ' were C i a (n n) upper rianular marix, A and B are (n n) coefficien marice. decompoiion of e inercep marix. Eac elemen C ' C i e ( i, j) in H depend on e correpondin ' ( i, j) elemen in ( ε ε ) and H. Accordinly, pa ock and volailiy are al- lowed o direcly pill over from a marke o anoer, and ey are capured by coefficien of A and B marice. Since e BEKK-GARCH model uffer from e curve of dimenionaliy and may encouner converence problem, reearcer ofen ue i wo rericed verion: e diaonal BEKK-GARCH and e calar BEKK-GARCH. Te diaonal parameerizaion of e BEKK-GARCH(,) i obained by impoin e diaonaliy of e parameer marice A and B. Te advanae of i diaonalizaion i a e model i uaraneed o be poiive definie and require e eimaion of fewer parameer an e full-rank parameerizaion. Conequenly, e condiional variance and covariance procee ake e followin form: 8
9 C C C ) ( ) ( ε ε α α ε α ε α (7) were and are e condiional variance of r and r repecively. Eq. (7) indicae a direc volailiy ranmiion beween old and ock reurn i no poible becaue e condiional volailiy of eac marke depend only on i own pa ock and pa volailiy. Te diaonal BEKK-GARCH model i covariance aionary under e followin condiion: < S S α, < α, and < α α. Te calar BEKK-GARCH i more rericed an e diaonal BEKK-GARCH. I i derived from e full-rank BEKK-GARCH by impoin a e parameer marice A and B are bo equal o e produc beween a calar and an ideniy marix. I formal repreenaion i iven by ' H b a C C H ε ε (8) Te CCC-MGARCH model of Bollerlev (990) and e DCC-GARCH model of Enle (00) belon o anoer cla of mulivariae GARCH procee were e ime-varyin condiional covariance are parameerized o be proporional o e produc of e correpondin condiional andard deviaion. Here, e objecive i o obain an inuiive and meaninful economic inerpreaion of e condiional correlaion coefficien. Applyin o our reearc queion, e variance-covariance marix of e bivariae CCC- GARCH(,) model i defined a follow: PD D H (9) were ), ( dia D, and ) ( ij P ρ refer o a ( ) marix a conain e conan condiional correlaion ij ρ wi i ii,, ρ. Te condiional variance and covariance are iven by C C ρ ε α ε α ) ( ) ( (0)
Bollerlev (990) ow a e poiivene of e coefficien aociaed wi ARCH and GARCH erm i indeed no required o obain a poiive definie marix P. Te model i covariance aionary wen e roo of de( I A B) 0 complex plan, were I i a ( ) ideniy marix and λ λ are ouide e uni circle of e α A 0 0 α and B 0 0 Enle (00) propoe e DCC-GARCH(,) model a allow e condiional correlaion marix o vary over ime a follow ( ) / / dia( Q ) Q ( dia( Q )) P () were Q ( ij ) i a ( ) ymmeric poiive definie marix iven by q Q ( ) Q αη η Q α () In Eq. (), α and are non-neaive calar uc a α <, and Q i a ( ) marix of uncondiional correlaion of e andardized error η. Te condiional variance are pecified a univariae GARCH(,) procee, imilar o oe of e CCC-GARCH model. Enle (00) indicae a e pecificaion of e dynamic condiional correlaion rucure preen no obacle o model eimaion. Overall, e bivariae GARCH-ype model preened above do no explicily allow for ock and volailiy cro-effec beween old and ock marke reurn, a compared o e VAR-GARCH model. I i u expeced a our bencmark model provide a beer decripion of e dynamic linkae beween marke of inere and allow for more accurae deciion reardin porfolio diverificaion and edin effecivene. 3. Daa and preliminary analyi Our ample daa coni of daily ime erie of e Cinee ock marke and 3-mon old fuure price (GOLD3M) over e period from Marc, 004 o Marc 3, 0. Te MSCI Cina Index wic i a free-floa weied equiy index developed wi a bae value of 00 a of December 3 99 by Moran Sanley Capial Inernaional i ued o repreen e overall performance of e Cinee ock marke. Te old fuure, widely raded a COMEX (Commodiy Excane) in New York, are ued o repreen e world old marke 0
flucuaion. Teir price are meaured in US dollar per roy ounce. 3 Daa were exraced from MSCI and Bloomber daabae. We compue e reurn erie by akin e difference in e loarim of wo conecuive price. Fiure. Sock and old price dynamic 00 Cina MSCI Index 400 Fuure Gold Index 90 80 00 70 000 60 50 800 40 30 600 0 005 006 007 008 009 00 0 400 005 006 007 008 009 00 0 Te ime-pa followed by e MSCI Cina index and old fuure price are depiced in Fiure. We ee a e Cinee ock marke are common pae of marke dynamic wi e world ock marke. I experienced coninuin aracivene ince e end of 004 unil e end of 007, en owed inifican decreae due o e effec of e lobal financial crii beween e beinnin of 008 and e mid-009, and ared o recover aferward. Te evoluion of old fuure price i paricularly marked by an increain rend over e wole udy period and eir arp increae over e recen year. Te common widom of e financial communiy i a e role of old a an alernaive invemen a well a a ede inrumen durin financial marke urbulen ime a conribued o drive up eir price. Table preen eleced decripive aiic for e reurn erie. Te old marke provided ier daily reurn an e Cinee ock marke over our udy period. Te evere impac of e recen lobal financial crii 007-009 eem o be e main reaon a explain e underperformance of e Cinee ock marke a well a e performance of e world old marke. Te uncondiional volailiy, a meaured by andard deviaion, i ubanially ier for e ock marke an for e old marke. A a reul, old wa a beer invemen wi ier rik-adjued reurn. Ti findin u ue a old mi be a ood ede for porfolio of ock, epecially in ime of crie and bear marke period. 3 We alo eimaed our empirical model wi old po, alo raded a COMEX in New York, bu e reul remain inac. Tee reul can be made enirely available under reque addreed o correpondin auor. Noe finally a e correlaion beween old po and old fuure i 0.853 over e udy period.
Table. Decripive aiic and ocaic properie of reurn erie MSCI Cina Gold Mean (%) 0.057 0.067 Maximum (%) 4.044 8.65 Minimum (%) -.836-7.574 Sandard deviaion.00.6 Skewne -0.044-0.3 Kuroi 9.459 7.0 Jarque-Bera 387.0 354.089 Q(5) 37.346 43.78 Q (5) 870.689 378.95 ARCH(5) 38.06 40.76 ADF -4.00-4.760 PP -4.00-4.785 Noe: Te able repor e baic aiic of reurn erie a well a eir ocaic properie. Jarque-Bera i e empirical aiic of e Jarque-Bera e for normaliy baed on kewne and exce kuroi. Q(5) and Q (5) are e empirical aiic of e Ljun-Box e for auocorrelaion applied o reurn and quared reurn erie. ARCH refer o e empirical aiic of e Enle (98) e for condiional eerocedaiciy. ADF and PP are e empirical aiic of e Aumened Dickey-Fuller and Pillip-Perron uni roo e. We preen e model wi a conan and a rend, bu e reul are imilar wen model wiou a conan and/or a rend are ued. and indicae e rejecion of e null ypoee of normaliy, no auocorrelaion, no ARCH effec, and uni roo a e 5% and % level, repecively. Wi neaive kewne coefficien and kuroi coefficien above ree, e diribuion of Cinee ock marke and old reurn are ypically aymmeric, and e probabiliy of obervin lare neaive reurn i ier an a of a normal diribuion. Te Jarque- Bera e aiic clearly confirm e rejecion of e null ypoei of normaliy for bo reurn erie. Te reul from e Ljun-Box e indicae evidence of auocorrelaion in reurn and quared reurn erie for bo old and ock marke. Te ARCH e for condiional eerocedaiciy provide ron evidence of ARCH effec in bo reurn erie, wic conequenly ue e uefulne and uiabiliy of GARCH-ype model for examinin volailiy dynamic and ranmiion of old and ock marke in Cina. Finally, wo commonlyued uni roo e, Aumened Dickey-Fuller (ADF) e and Pillip-Perron (PP) e, are performed in order o examine e aionariy propery of e erie conidered. Te reul indicae a reurn erie are aionary, and u ey can be raiforwardly ued for furer analyi. 4. Reul and porfolio implicaion Ti ecion dicue e eimaion reul of our bivariae VAR()-GARCH(,) model for old reurn and ock marke reurn in Cina. We paricularly focu on e exen of volailiy ranmiion beween e marke conidered. Te compein model (CCC- GARCH, DCC-GARCH, diaonal BEKK-GARCH, and calar BEKK-GARCH) are alo
eimaed, bu e reul are no own ere in order o conerve pace. Finally, we compare e diverificaion and edin effecivene acro model. 4. Volailiy cro-effec in old and ock marke in Cina Table preen e eimaion reul of our bivariae VAR()-GARCH(,) model, oeer wi aiical e applied o andardized reidual. Takin a cloe look a e eimae of e mean equaion, we find a own auorereive parameer are no inifican for bo marke under conideraion. Te one-period laed old reurn are found o inificanly affec e curren reurn of Cinee ock marke a e % level. Ti implie a one can predic Cinee ock reurn by uin pa old reurn over ime. Some recen paper alo documen a Cinee ock marke i no weak-form efficien almo all e ime (ee, e.., Groenwold e al., 004; Gao and Klin, 005). Inverely, pa ock marke reurn in Cina a no impac on old reurn. Table. Eimae of VAR()-GARCH(,) model for old reurn and ock marke reurn in Cina MSCI Cina Gold Con(µ) 0.084 *** (0.03) 0.067 *** (0.04) Sock(-) 0.03 (0.05) 0.009 (0.05) Gold(-) 0.40 *** (0.08) 0.00 (0.06) Con(v) 0.38 *** (0.040) 0.09 *** (0.06) ( ε ) 0.95 *** 0.050 ** (0.08) (0.03) ( ε ) 0.05 * 0.84 *** (0.055) (0.05) 0.947 *** -0.000 (0.006) (7.38) 0.07 0.977 *** (0.088) (0.004) ρ 0.37 *** (0.0) LoL -657.688 AIC 6.87 SIC 6.93 JB 59.333 668.78 Q(5) 30.57.733 Q²(5) 9.937 4.675 ARCH(5) 4.665 3.68 Noe: Sock(-), Gold(-), and ρ are e one-period laed reurn of Cinee ock marke and old marke, and condiional conan correlaion, repecively. Con(µ) and Con(v) are e conan erm in e condiional mean and variance equaion. *, **, and *** indicae inificance a e 0%, 5%, and % level, repecively. Te AIC and BIC crieria meaure e relaive oodne of fi of e eimaed model. JB, Q(5), Q²(5), and ARCH(5) refer o e empirical aiic of e Jarque-Bera e for normaliy, e Ljun-Box e for auocorrelaion of order 5 applied o andardized reidual and quared andardized reidual, and e Enle (98) e for condiional eerocedaiciy of order 5, repecively.,, and indicae e rejecion of e null ypoei of aociaed aiical e a e 0%, 5%, and % level, repecively. 3
A o e coefficien aociaed wi of ARCH and GARCH erm, wic capure ock and volailiy independence in e condiional variance equaion, we find common paern for bo old reurn and ock reurn in Cina. Fir, ee coefficien appear o be ily inifican. Second, e eimaed condiional volailiy erie do no cane very rapidly under e effec of reurn innovaion iven e mall ize of ARCH coefficien. Tey end inead o develop radually over ime wi repec o ubanial effec of pa volailiy, advocaed by e lare value of GARCH coefficien. Accordinly, inveor and fund manaer eekin profi from radin old and Cinee ock may conider acive invemen raeie baed on volailiy perience and curren marke rend. I would be adviable, for example, o increae e amoun of porfolio invemen if marke are acually riin and o decreae i if ey are fallin, all wile keepin in mind a e viabiliy of uc raeie depend on e abiliy and e ren of performance beween ucceive period. Te exen of volailiy ranmiion beween old marke and Cinee ock marke i paricularly inerein. Our findin ow a pa old ock play a crucial role in explainin e ime-dynamic of condiional volailiy of ock reurn in Cina and ould u be accouned for wen makin volailiy foreca of fuure ock reurn. Moreover, e condiional volailiy of old reurn i inificanly affeced by unprediced cane in e reurn on e MSCI Cina index, ( ) ε. A ock o Cinee ock marke, reardle of i in, u implie an increae in e volailiy of old reurn. On e oer and, pa volailiy of Cinee ock marke, repreened by, a no inifican effec on e old reurn volailiy. A for e oppoie direcion, e impac of pa old volailiy, condiional volailiy of Cinee ock marke i alo aiically ininifican., on e Turnin ou o e eimae of e conan condiional correlaion (CCC), we find a Cinee ock marke reurn are poiively correlaed wi old reurn, bu e cro-marke correlaion i relaively weak (0.37). One may expec, in view of i findin, ubanial ain from avin bo ae in e ame porfolio. Moreover, i i obviou a e inifican volailiy cro-effec we ow previouly require porfolio manaer and inveor o quanify e opimal wei and edin raio o properly deal wi e comovemen beween old and Cinee ock reurn. Laly, e reul of dianoic e baed on andardized reidual ow a e deparure from normaliy and e erial correlaion are realy reduced and a ere are no 4
ARCH effec, a compared o e aiic we repor for e reurn in Table. Tu, e bivariae VAR()-GARCH (,) model offer a flexible way o capure e join dynamic of old reurn and Cinee ock marke reurn. 4. Opimal porfolio dein and edin raio in e preence of old We now ow e implicaion of our previou reul on old-ock opimal porfolio. To i end, we conider a eded porfolio made up of old and Cinee ock marke index in wic an inveor eek o proec imelf from expoure o ock price movemen by invein in e old ae. In pracice, e inveor objecive i o minimize e rik of i old-ock porfolio wile keepin e ame expeced reurn. Followin Kroner and N (998), we deermine e opimal oldin wei of old in a one-dollar porfolio of ock/old a ime, denoed by w, a follow w (3) were, and refer repecively o e condiional volailiy of e old reurn, e condiional volailiy of e Cinee ock marke index reurn and e condiional covariance beween old and ock reurn a ime. Tee erie are eimaed from our bencmark bivariae VAR()-GARCH(,) model and four compein bivariae GARCH-baed model we preened in Secion. Wen or ellin i no allowed, e mean-variance porfolio opimizaion approac impoe e followin conrain on e opimal wei of old: w 0, if w, if, if w < 0 0 w w > From Eq. (3), e proporion of weal a e inveor pu on e Cinee ock mar- ke index i. w Now if e objecive of our inveor i o opimally ede e rik of i invemen in ock marke, e ould ake an appropriae poiion on e old marke o a i minimize e rik of e eded porfolio. Concreely, a lon poiion (buyin) of one dollar on e ock emen mu be eded by a or poiion (ellin) of dollar on e old ae. Followin Kroner and Sulan (993), e opimal ede raio can be expreed a 5
(4) Te averae value of realized opimal wei w and opimal ede raio repored in Table 3. A lance a e coefficien ow a e opimal wei for e old ae in e eded porfolio i 0.330 accordin o our VAR()-GARCH(,) model and varie from 0.3 o 0.333 wi repec o compein bivariae GARCH-baed model. Te ie opimal wei for old of 0.333 i obained for e CCC-GARCH and DCC-GARCH model, wile e calar BEKK-GARCH model provide e lowe one (0.3). Overall, our reul ow a, o minimize e rik wiou lowerin e expeced reurn of e old-ock porfolio, e inveor operain in Cinee ock marke ould old more ock an old. Ti findin can be effecively explained by e low correlaion of old reurn wi ock reurn in Cina, and en imply addin a mall porion of old o a diverified porfolio of Cinee ock will reduce ubanially i overall rik for a iven level of expeced reurn. Table 3. Opimal wei and ede raio for porfolio of old and ock in Cina VAR-GARCH CCC-GARCH DCC-GARCH Scalar BEKK- Diaonal BEKK- GARCH GARCH w 0.330 0.333 0.333 0.3 0.35 0.97 0.9 0.94 0.78 0.88 Noe: Te able repor averae opimal wei of old and ede raio for an old-ock porfolio uin condiional variance and covariance eimaed from our bencmark model and four compeiive volailiy-pillover model: VAR()- GARCH(,), diaonal BEKK-GARCH(,), DCC-GARCH(,), CCC-GARCH(,), and calar BEKK-GARCH(,). For all model conidered, e condiional mean equaion conain a conan erm and an auorereive componen. are Te averae opimal ede raio,, are enerally low and do no exceed 0.. Ti findin a everal imporan implicaion for or eder. Fir, e low ede raio ue a ock invemen rik can imply be eded by akin or poiion in e old fuure marke. Te lare raio i obained from e VAR-GARCH model (0.97), followed cloely by e DCC-GARCH and e CCC-GARCH. Ti implie a one dollar lon (buy) in e Cinee ock marke index ould require e inveor o o or 9.7 cen in e old fuure marke. Te lowe ede raio i obained in e cae of e calar BEEK- GARCH model (0.78), meanin a e inveor mu ell e malle quaniy of old in e old fuure marke. Aloeer, our findin for opimal ede raio uppor wi e view a e old ae ould be an ineral par of a diverified porfolio of ock and elp reduce e rik of e eded porfolio, paricularly in period of crii. 6
4.3 Diverificaion and edin effecivene In ubecion 4. we ow, baed on e eimaion of eleced bivariae GARCH model, a addin e old ae in e diverified porfolio of ock lead o improve i rikadjued performance. One may, owever, wonder ow effecive are e diverificaion and e edin aociaed wi e old ae? For i reaon, we propoe o run porfolio imulaion o empirically examine e diverificaion and edin effecivene of old. Tee porfolio imulaion are baed on our opimal porfolio wei and edin raio. More preciely, we ue e eimae of our VAR-GARCH and four compein bivariae GARCH model o build wo diinc porfolio: a porfolio compoed of Cinee ock only (PF I) and a old-ock porfolio wi e opimal wei calculaed in ubecion 4. (PF II). For eac model, e effecivene of e porfolio diverificaion i evaluaed by comparin e realized rik and reurn caraceriic of e conidered porfolio (PF I v. PF II). In e meanime, e effecivene of edin acro conruced porfolio can be aeed by examinin e realized edin error (HE) wic are deermined a follow (Ku e al., 007) were Varuneed Vareded HE (5) Varuneed Var refer o e variance of e eded porfolio reurn (PF II), and Var e eded uneded variance of e uneded porfolio reurn (PF I). Eq. (5) indicae a e ier e HE raio, e more effecive e edin in erm of porfolio variance reducion. Te model a enerae e ie HE raio i e be one o be ued for buildin old-ock edin raey. Table 4. Porfolio dein and diverificaion in preence of e old ae Mean Sandard Realized rik-adjued deviaion reurn ( 00) PF I 0.056.03.796 PF II VAR-GARCH 0.0596.4358 4.50 PF II Diaonal BEKK-GARCH 0.0595.453 4.0975 PF II Scalar BEKK-GARCH 0.0595.4576 4.0830 PF II DCC-GARCH 0.0596.445 4.364 PF II CCC-GARCH 0.0596.445 4.364 Noe: Ti able compare e realized rik-adjued reurn, meaured by relain eac porfolio mean o i andard deviaion, of differen porfolio. Fiure in boldface indicae e ie mean, andard deviaion, and rik-reurn rade-off. PF I i a porfolio of 00% ock. PF II i a weied old-ock porfolio in wic e wei are iven by e opimal wei repored in Table 4. Te reul from porfolio imulaion in Table 4 ow a addin e old ae o e diverified porfolio of ock improve i rik-adjued reurn raio reardle of e model 7
ued. More inereinly, our bencmark VAR-GARCH model provide e be rik-adjued reurn raio, cloely followed by e DCC and CCC-GARCH model. Table 5. Hedin effecivene Variance (%) Hede effecivene (%) PF I 4.0454 ----- PF II VAR-GARCH.065 49.0409 PF II Diaonal BEKK-GARCH.6 47.808 PF II Scalar BEKK-GARCH.45 47.4843 PF II DCC-GARCH.0778 48.6373 PF II CCC-GARCH.0778 48.6373 Noe: Ti able repor e porfolio variance and ede effecivene raio, compued uin Equaion (4). Number in boldface indicae e eded porfolio wi lowe variance and e ie variance reducion. PF I i a porfolio of 00% ock. PF II i a weied old-ock porfolio in wic e wei are iven by e opimal wei repored in Table 4. Table 5 preen e edin effecivene (HE) raio for e model we conider. Te reul ow a edin raeie involvin ock and old ae lead o reduce coniderably e porfolio rik (variance), a compared o e rik of e porfolio made up of ock only. Te variance reducion rane from 47.48% for e calar BEKK-GARCH model o 49.04% for e VAR-GARCH model. Ti findin, conien wi e analyi of porfolio dein and diverificaion, u conolidae e dominan poiion of e VAR- GARCH model a i elp reducin e lare par of e iniial porfolio variance. Te diaonal and calar BEKK-GARCH model are e wor model in erm of porfolio variance reducion. Can e al. (0) reac imilar concluion wen ey ue e ame model o calculae opimal porfolio wei and opimal ede raio for e crude oil po and fuure reurn of wo major crude oil bencmark, Bren and WTI. 6. Concluion In i paper, we inveiae e exen of volailiy ranmiion, porfolio dein, and edin effecivene in old and ock marke in Cina. We employ e recen VAR- GARCH modelin approac, wic allow for volailiy pillover cro effec, we find inifican volailiy ranmiion beween Cinee ock marke and world old marke. Te examinaion of opimal wei and ede raio ue a opimal porfolio ould ave ock ouwei old ae and a e ock invemen rik can be eded wi relaively low edin co by akin a or poiion in e old fuure marke. In paricular, we ow a opimally eded old-ock porfolio ouperform radiional porfolio of ock reardle of bivariae volailiy model, and a our baeline VAR-GARCH model i e be performin model in erm of bo diverificaion and edin effecivene. On e 8
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