Dynamic Parametric and Nonparametric Hedging: Evidence from the Arab Gulf Equity Markets

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1 Inernaional esearc Journal of Finance and Economics ISS Issue 6 May, 207 p:// Dynamic Parameric and onparameric Hedging: Evidence from e Arab Gulf Equiy Markes ami ekili College of Adminisraive Sciences Applied Science Universiy, Kingdom of Barain rami.nekili@asu.edu.b Tel: ; Fax: Hela Miniaoui Gulf Sudies Cener, Qaar Universiy, Qaar miniaoui@qu.edu.qa Tel: ; Fax: Absrac Tis paper examines e opimal edging sraegies in e Arab Gulf equiy markes using a parameric and a nonparameric dynamic approaces in modeling e condiional variances and covariances of equiy reurns. Te parameric approac is based on a mulivariae VA-GACH model of daily reurns, wi BEKK specificaion of Engle and Kroner (995), and e nonparameric approac adops a dynamic sysem based on Filered Hisorical Simulaion (FHS) of Barone-Adesi e al. (999) and nonparameric regression. Tese approaces are en used o calculae opimal porfolio weigs and opimal raios of edging long and sor posiions in e Gulf Cooperaion Council major secors, namely, Service, Financial and Indusrial. Te resuls sow a e nonparameric approac provides iger edging effeciveness and ence superior edging sraegies. Keywords: Mulivariae GACH, Filered Hisorical Simulaion, Opimal Hedging JEL Classificaion: G0, G5. Inroducion Marke risk managemen imposes dealing wi e key issue of conrolling e variances and covariances of individual posiions in an invesmen porfolio. Te risk managemen success of suc aciviy requires aking ino accoun e ime varying feaure of condiional variances and covariances. Hence, invesors' evaluaion of e ineracing dynamics among markes allow for adjusmen and useful implemenaion of edging sraegies. In order o acieve is, edgers are required o gauge eir sraegies wi a meric a allows cecking eir performances. Many approaces ave been developed o esimae an opimal edge raio a is also known as e minimum-variance edge raio. However, ese approaces suffer from e exisence of serial correlaion and eeroscedasiciy in asse price series (Herbs e al., 993). Te collecive evidence sows a GACH-based dynamic edging sraegies are empirically appropriae (see Kroner and Sulan, 993). Ku e al. (2007) applied e dynamic condiional correlaion (DCC) model of Engle (2002) wi error correcion erms o invesigae e opimal edge raios of Briis and Japanese currency fuures markes, and compared e DCC and OLS esimaes. Te empirical resuls sow a e DCC model yields e bes edging performance. Cang e al. (20)

2 Inernaional esearc Journal of Finance and Economics - Issue 6 (207) 8 examined e performance of four models (namely CCC, VAMA-GACH, DCC and BEKK) for e crude oil spo and fuures reurns of wo major inernaional crude oil markes (BET and WTI). Te calculaed opimal edging raios from eac mulivariae condiional volailiy model suggesed imevarying edge raios, wic recommended o sor in crude oil fuures, wi a ig porion of one dollar long in crude oil spo. Te edging effeciveness indicaed a DCC (BEKK) was e bes (wors) model for opimal edge raio calculaion in erms of e variances of porfolio reducion. Furermore, Hakim and McAleer (2009) analyed weer mulivariae GACH models incorporaing volailiy spillovers and asymmeric effecs of negaive and posiive socks on e condiional variance provide differen condiional correlaion forecass. Tey suggesed a incorporaing volailiy spillovers and asymmeric effecs of negaive and posiive socks on e condiional variance does no affec e forecass of condiional correlaions. Te rend sows a mulivariae GACH models ave no ye fully enjoyed e same populariy in pracice as eir univariae counerpars. Tere are cerain impedimens a inibi praciioners o use ese models. Te lack of eoreical foundaion and e compuaional burden a goes along e increasing number of parameers esimaes in funcion of e number of asses and markes employed consiue a major inibiing facor. Te mulivariae GACH models proposed in e lieraure assume consan condiional correlaions over ime. Models suc as e BEKK model of Engle and Kroner (995), e Dynamic Condiional Correlaion (DCC) model of Engle (2002) and Varying Condiional Correlaion (VCC) model of Tse and Tsui (2002), accommodae for ime varying condiional correlaions. However, suc models do no aac a vecor auoregressive moving average componen a enables examining e cross effecs of bo e condiional volailiy and condiional correlaion. Tis paper builds on e early work of Can, Lim, & McAleer (2005) and Hammoude e al. (2009) in using VA-GACH models in a mulivariae conex. egardless of e populariy of e financial ime series modeling, e main callenge remains in e a priori assumpion of imposing a realisic disribuional srucure in e condiionally eeroskedasic error erms (see Hafner and Herwar, 2006). In addiion, e absence of i.i.d. caracerisics renders e isorical financial ime series inappropriae as a oll of esimaing e condiional variance-covariance marix. Furermore, ere is evidence of ime-varying skewness in equiy reurns, wic if explored could beer enable us o find alernaive sraegies for edging uncovered posiions in e equiy markes. Suc callenges could be me by using a dynamic model based on Filered Hisorical Simulaion (FHS) of Barone-Adesi e al. (999) combined wi nonparameric regression. Suc ecnique as been used by Giannopoulos, ekil and Koumos (200) o examine dependencies in covariance canges and o carry an impulse response analysis o invesigae e dynamic responses o volailiy socks among major equiy markes, namely, US, UK, Germany, and Japan. Based on e alernaive models discussed earlier, is paper examines e sock and volailiy ransmission among ree secors, namely Financial, Service and Indusrial, for e Gulf Cooperaion Council (GCC) counries a include Saudi Arabia, UAE, Qaar, Barain, Kuwai and Oman. I follows using e esimaed resuls o compue e weigs of e secors in an opimal porfolio of eac GCC counry, and e opimal edge raios a minimie overall risk for olding e secors in porfolios. 2. Meodology 2.. onparameric Approac During e las wo decades, e main approac used o model volailiy of financial asses is based on e empirical fac a e firs differences of many asse prices are uncorrelaed and eir squares display serial correlaion. Tis approac models e ime-varying variances of e reurns in Engle's (982) class of auoregressive condiional eeroscedasic (ACH) and Bollerslev's (986) generalied ACH (GACH) models. One of e simples models of is class, and as wi mos of daily ime series, e A-GACH or asymmeric A-GACH. A ypical A-GACH(,) sysem is represened by

3 9 Inernaional esearc Journal of Finance and Economics - Issue 6 (207) = ϕ + µ ε = H / 2 + ε and were is a xvecor of reurn beween ime and, H is e condiional variance of reurns a ime, and are i.i.d innovaions, wi being e number of variables. ( ) / 2 / 2 ε = = D D wi D diag (,, ). Corr = H,, Te model ensures a any isorical paerns are removed and pus in evidence e volailiy persisence and ransmission among differen markes. In e above sysem, e condiional disribuion of e random erms is assumed o be normal. However, is normaliy assumpion is rejeced by many scolars like Fama and Frenc (993) or Longin and Solnik (200), o lis a few. Moreover, e funcional forms of condiional covariance marix and condiional correlaion marix are linear, and ence excluding any possible nonlineariy. Tese wo resricions may lead o inconsisency and inefficiency of esimaions. evereless, e exisence of nonparameric ecniques as elped in amending ese resricions. In is paper, e Filered Hisorical Simulaion (FHS) is adoped and i is combined wi one of e nonparameric regression. Te specificaion of i (),, i =,,, follows a univariae GACH(,) processes. ω + α ε β (2) = + i i i Te Filered Hisorical Simulaion (FHS) follows e following seps: firs e sandardied / 2 residuals are obained for eac index, namely = ˆ ε / ˆ, en condiional variance is generaed by 2 = ω i + β i i, + j + αi µ + j + γ, j=,2,.., (3) + j i o form e innovaions innovaions u i + j + j = + j + j µ ; second e condiional mean is obained by using e, in e following model: + = i + j j ϕ + µ + j + u, j =, 2,.., (4) For eac index e above seps are repeaed recursively o obain differen simulaed paways, wi S is e number of imes e draw from e sandardied residuals is made and is e sample sie, as follows:,,+, +,+,+, + 2, 2,+ 2, + 2,+ 2,+ 2, + / 2, S, S,+ S, + S,+ S,+ S, + Te FHS ecnique imposes e condiional covariances of e sandardied residuals o be consan. Terefore, and o ake ino accoun e dynamic canges in e condiional covariances of e underlying variables, a nonparameric ecnique is used as in Long and Ulla (2005). Te nonparameric esimaion of e condiional covariance marix H is performed by using e adaraya-wason (W) esimaor as follows: H = ' τ= τ= K K λ λ ( s s ) ( s s ) τ τ (5)

4 Inernaional esearc Journal of Finance and Economics - Issue 6 (207) 0 were s is a condiioning variable, K λ (.) = K(./ λ )/ λ, K(.) is a kernel funcion, and λ is e bandwid parameer. Te Gaussian kernel is used wi a bandwid λ = b x.06 S s -/(k+4) and b is based on minimiing e MSE( H ), k is e number of parameers, and S represens e sandard deviaion of s e condiioning variable. Te esimaion of e nonparameric correlaions is performed by decomposing e condiional covariance marix H ino condiional sandard deviaions and correlaions as follows: H = D D (6) were D = diag( /2,,., /2, ), wi is e number of indices, and = [ ρ ij ] is posiive definie wi ρ ii =, i =,,. For j, e off-diagonal elemens of e condiional covariance marix are defined as: /2 /2 H ρ, i j, (7) [ ] = ij i j ij 2.2 Parameric Approac By and large, mulivariae models allow for e possibiliy a some equiy volailiies may sare common persisen componens. Hence, adoping suc models will allow e condiional variances and covariances of equiy markes o influence eac oer. In is paper, we use a vecor auoregressive mulivariae GACH BEKK (named afer Bollerslev, Engle, Kraf and Kroner) model presened by Engle and Kroner (995). Te model is represened as follows: = α + µ + ε, (8) ε = H / 2, were is a x vecor of reurn beween ime - and, H is e condiional variance of reurns a ime, and are i.i.d innovaions, wi being e number of variables. Corr ε ( ) / 2 2 = = D H D /, wi D diag(,, ). = Engle and Kroner (995) propose a parameriaion a imposes posiive definieness resricions. ' ' ' ' H CC+ B H B+ Aε ε A (9) = - and were C is a lower riangular marix of consans, B is a square marix wi parameers b ij a indicae e persisence in condiional volailiy beween asse i and asse j, A is a square marix wi parameers a ij a measure e degree of innovaion from asse i o asse j.,, 3. Opimal Porfolio Weigs and Hedge aios In is secion, we calculae e opimal porfolio weigs and opimal edge raios o idenify e appropriae edging sraegies a accoun for variance-covariance marix dynamics using e models discussed earlier. Le's consider a one dollar porfolio consising of wo asses a ime and were represens e condiional covariance beween asses and 2, and, 2, are respecively e condiional variance of e firs and e second asse. In order o consruc an opimal porfolio design a minimies risk wiou lowering expeced reurns, we apply e meods Kroner and g (998): 22, 2, ω ij, = (0) 2 +, 2, 22, ω 2, = 0 if ω 2, < 0 and ω 2, = if ω 2, >. I is obvious a e weig of e second asse in e one dollar porfolio is ω. Moreover, we consruc a risk minimiing edge raio as Kroner and Sulan 2, 2,

5 Inernaional esearc Journal of Finance and Economics - Issue 6 (207) (993). In order o minimie risk, a long posiion of one dollar aken in one asse in a given marke sould be edged by a sor posiion of Hedge aio in anoer asse in e same marke a ime : 2, Hedge aio = () 22, According o Jonson (960), e variance of e reurns of e edged porfolio, condiional on e informaion se available a ime - is given by: 2 var =, + Hedgeaio - 2Hedgeaio Hedged 22, 2, (2) and e edging effeciveness could be measured by e variance reducion for any edged porfolio compared wi e unedged porfolio. ( var Unedged - var Hedged )/ var Unedged. Te iger edging effeciveness e larger risk reducion, and a edging meod wi a iger effeciveness is regarded as a superior edging sraegy. 4. Daa and esuls To evaluae e models, we use ree secor indices, namely, Financial, Service and Indus-rial, of six GCC markes UAE, Barain, Kuwa Qaar, Saudi Arabia, and Oman. Te daily closing prices for ese indices for e period April 2, 202 unil Marc 2, 207 were obained from Zawya daabase and respeced sock markes. Due o differences in weekly olidays beween e counries for some ime period and due o counry specific olidays some observaions were deleed. Descripive saisics of daily reurns are presened in Table. Te daily log reurns are defined as: ( p / p ) 00 were p i, is e daily closing value of e secor index i on day. = log, Table : Descripive Saisics for GCC eurns by Secor Secor Financial Service Indusrial Saudi Arabia Mean S.D Skewness Kurosis UAE Mean S.D Skewness Kurosis Qaar Mean S.D Skewness Kurosis Barain Mean S.D Skewness Kurosis Kuwai Mean S.D Skewness Kurosis Oman Mean S.D Skewness Kurosis

6 Inernaional esearc Journal of Finance and Economics - Issue 6 (207) 2 Te iges averages of e daily reurns during e sample period are in Saudi Arabia for e Service secor (0.035%) and Qaar for e Financial secor (0.026%). Te iges sandard deviaion is seen in e Financial secor of e Saudi marke. According o e sample kurosis esimaes, e daily rae of reurns are far from being normally disribued. Te lowes kurosis esimae is 3.95 (Indusrial secor of UAE) wile e iges is 9.44 (Service secor in Qaar). Based on e sample kurosis esimaes, i may be argued a e reurn disribuions in all secors are fa ailed. Te sample skewness sows a e daily reurns ave an asymmeric disribuion in all e markes. Te sample skewnesses are negaive for Oman and Kuwai and posiive for all oer secors indicaing a e asymmeric ail exends more owards negaive values an posiive ones. Tables 2, 3, and 4 presen e esimaion resuls of e VA-MGACH-BEKK model for e variance covariance. Tere is a relaively large and significan ACH effec indicaing e presence of own-volailiy spillovers in all secors across all GCC markes. Wi respec o e Financial secor and is sensiiviy o pas socks (news), e iges is seen in Saudi Arabia and e lowes in Barain and Qaar. Tis is eviden from eir inerconnecedness wi global financial secor as e Saudi marke is more open o foreign invesors an is counerpars in Barain and Qaar. Wi respec o e Service secor, e iges effecs of pas socks or news is in UAE, Barain and Qaar, and lowes in Oman. Tis no surprising as e Service secor in UAE as been in developmen muc earlier an in e oer markes. Table 2: VA MGACH BEKK Esimaion esuls (Saudi Arabia and UAE) Panel A: Saudi Arabia ormal Error Disribuion Suden- Error Disribuion Coefficien Financial Service Indusrial Financial Service Indusrial α VA() a a 0.22 a a a a C Financial a a C Service a a a a C Indusrial 0.05 a a a a ACH Financial a b a c ACH Service c a c a c ACH Indusrial b a c a GACH Financial a a GACH Service a a GACH Indusrial a a AIC Panel B: UAE ormal Error Disribuion Suden- Error Disribuion Coefficien Financial Service Indusrial Financial Service Indusrial α c c VA() c c c c C Financial 0.09 b C Service b C Indusrial a ACH Financial a a c ACH Service c a c 0.57 c c ACH Indusrial c a a c a GACH Financial a a GACH Service a a GACH Indusrial a b AIC a = % significance level, b = 5% significance level, c = 0% significance level. Wi respec o e Indusrial secor, i is considered e leas sensiive in all secors of all GCC counries. In fac, is secor is more dependen on volailiies relaed o canges in e fundamenals

7 3 Inernaional esearc Journal of Finance and Economics - Issue 6 (207) suc as e supply and demand for oil and naural gas or perocemical producs. We finally noice a similar sensiiviy for all e secors in Kuwai. Table 3: VA MGACH BEKK Esimaion esuls (Qaar and Barain) Panel A: Qaar ormal Error Disribuion Suden- Error Disribuion Coefficien Financial Service Indusrial Financial Service Indusrial α VA() c c C Financial C Service : C Indusrial ACH Financial c b c 0: c ACH Service c a c c c ACH Indusrial b c a GACH Financial 0.92 a a GACH Service a a GACH Indusrial a a AIC Panel B: Barain ormal Error Disribuion Suden- Error Disribuion Coefficien Financial Service Indusrial Financial Service Indusrial α VA() c b C Financial b C Service : c C Indusrial : ACH Financial c c a b ACH Service :225 a a ACH Indusrial :30 c a GACH Financial a a GACH Service c a c a GACH Indusrial a a AIC a = % significance level, b = 5% significance level, c = 0% significance level Looking a e own volailiy spillovers, e Financial secor displays a ig spillover in Qaar and Barain and low in Saudi Arabia. Tis could be inerpreed as ere is more regulaions and bank supervision implemened in Saudi Arabia an is counerpars. On e oer and, e Service secor displays a ig spillover in UAE, Kuwai and Oman, and a low spillover in Qaar. Wereas for e Indusrial secor, e iges spillover is in Qaar, and e lowes is in Kuwai and Oman. Finally, and looking a e iner-secor volailiy spillover, we observe a moderae spillover beween secors in Barain and Oman, and no spillover beween secors in e oer markes. Table 4: VA MGACH BEKK Esimaion esuls (Kuwai and Oman) Panel A: Kuwai ormal Error Disribuion Suden- Error Disribuion Coefficien Financial Service Indusrial Financial Service Indusrial α c VA() b C Financial b 0.00 b C Service C Indusrial b b ACH Financial a b ACH Service a ACH Indusrial c b c 0.73 a

8 Inernaional esearc Journal of Finance and Economics - Issue 6 (207) 4 Panel A: Kuwai ormal Error Disribuion Suden- Error Disribuion Coefficien Financial Service Indusrial Financial Service Indusrial GACH Financial a a c GACH Service a a GACH Indusrial : a a AIC Panel B: Oman ormal Error Disribuion Suden- Error Disribuion Coefficien Financial Service Indusrial Financial Service Indusrial α c VA() a a a 0.93 b a a C Financial 0.39 a a C Service a b a C Indusrial : a c a ACH Financial a b a c c ACH Service a 0:0878 a a c ACH Indusrial b a a b a GACH Financial a c a GACH Service a 0.86 c c a GACH Indusrial a c a AIC a = % significance level, b = 5% significance level, c = 0% significance level Te A-GACH-FHS model resuls in Table 5 confirm e exisence of a igly significan GACH effecs in all secors of all e GCC markes indicaing e presence of own-marke volailiy persisence. Te own-marke volailiy spillover effecs are ig for all e markes ranging from 0.45 for e Service secor in Qaar o for e Service secor in Kuwai. Tis sows a all individual secors in all GCC markes sow posiive sensiiviy o pas own volailiy. Table 5: A-GACH-FHS Esimaion esuls Saudi Arabia Coefficien Financial Service Indusrial Financial Service Indusrial ϕ c A() a b b a b W a b c a c c α b a b a c c β a a a a a a Qaar UAE Barain Coefficien Financial Service Indusrial Financial Service Indusrial ϕ b A() b b c W b a a a c α a a a a b c β a a a a a a Kuwai Oman Coefficien Financial Service Indusrial Financial Service Indusrial ϕ c A() c a a b W c a b a α 0.08 b c c a b a β a a a a a a a = % significance level, b = 5% significance level, c = 0% significance level. Te average values of opimal weigs for e secors in eac GCC counry are repored in Table 6. For insance, e average value of opimal weigs of a porfolio comprising e Financial and

9 5 Inernaional esearc Journal of Finance and Economics - Issue 6 (207) Service secor indices in Saudi Arabia is using BEKK-ormal, using BEKK-Suden-, and using FHS model. Tis suggess a e opimal olding of e Financial index in one dollar of Financial/Service index porfolio for Saudi Arabia is beween $0.46 and $0.48, compared wi $52 o $54 for e Service index. Consequenly, is may recommend invesors in Saudi Arabia o own more Service socks an Financial socks in eir porfolios. Tis finding is opposie o e resul in Hammoude and Al-Gudea (2006). Te case is differen for UAE, Oman and Kuwa were a porfolio of Service/Indusrial dominaes e Financial/Service porfolios, possibly due o e iges own volailiy and sock spillovers in e Service secor in ese markes. Table 6: Opimal Hedging Sraegies ormal Error Disribuion Suden- Error Disribuion Porfolio Weig Hedge aio Weig Hedge aio BEKK FHS BEKK FHS BEKK FHS BEKK FHS Saudi Arabia Financial/Service Financial/Indusrial Service/Indusrial UAE Financial/Service Financial/Indusrial Service/Indusrial Qaar Financial/Service Financial/Indusrial Service/Indusrial Barain Financial/Service Financial/Indusrial Service/Indusrial Kuwai Financial/Service Financial/Indusrial Service/Indusrial Oman Financial/Service Financial/Indusrial Service/Indusrial Table 6 also repors e average values of Hedge aio for e GCC markes. Adoping e same edging sraegy, one dollar long in e Financial index, for example in e Saudi marke, sould be sored by $0.55 o $0.57 in e Service secor. Te mos expensive edge in e oer GCC markes is by edging e Service index wi sor posiions in e Financial or Indusrial secor. As sown in e opimal porfolio weig columns in Tables 6, ere are no big differences among e BEKK models, wic are in reurn sligly differen an e FHS model. Similar conclusions could be drawn wi e resuls of e Hedge aios. However, we sould look closely a ow muc gain in minimiing e variance of e edged porfolio using eac of e models sudied. Table 7 displays one example of e edging effeciveness calculaed for Barain, e iges edging effeciveness o edge long posiions is beween e Service and Indusrial in Barain, and e Financial and Indusrial in Kuwai. However, e FHS model provides e iges edging effeciveness an is counerpar e BEKK model (wi bo ormal and Suden- disribued errors). In fac, e variance reducion of e edged porfolio, Service/Indusrial for Barain and Financial/Indusrial for Kuwa is muc iger an e one provided by e BEKK model. Tis suggess a e nonparameric approac leads o superior edging sraegies an e parameric approac.

10 Inernaional esearc Journal of Finance and Economics - Issue 6 (207) 6 Table 7: Opimal Hedging Effeciveness for Barain Porfolio BEKK ormal Suden FHS Unedged Financial/Service Hedging Effeciveness 40.7% 40.7% 4.% Financial/Indusrial Hedging Effeciveness 6.9% 7.3% 9% Service/Indusrial Hedging Effeciveness 49.5% 49.4% 46.2% oes: Hedging Effeciveness is e variance reducion of e edged porfolio compared o e unedged porfolio. (var Unedged var edged )=var Unedged. A iger edging effeciveness indicaes a larger variance reducion and ence a superior edging sraegy 6. Summary and Concluding emarks Tis paper reieraes e imporance of measuring condiional variances and covariances of asse reurns in edging sraegies. In doing so, wo approaces are adoped, one parameric and based on a mulivariae GACH model, and one nonparameric based on Filered Hisorical Simulaion. Te findings sow a e VA-GACH-BEKK wi ormal and Suden- errors provide similar resuls in erms of edging raios, porfolio variance reducion and edging effeciveness, wic suggess a dynamic asymmery may no be crucial empirically. Moreover, e FHS approac performs beer in erms of porfolio variance reducion and edging effeciveness. Tis suggess a e nonparameric approac leads o superior edging sraegies an e parameric approac. Fuure researc will consider piing e nonparameric approac agains e parameric one in an all-secor-porfolio conex and invesigaing e edging sraegies in olding long posiions in differen markes in erms of edging effeciveness. eferences [] Barone-Adesi G., K. Giannopoulos and L. Vosper, 999. Va wiou Correlaions for on- Linear Porfolios. Journal of Fuures Markes 9, pp [2] Bollerslev, T., 986. Generalied Auoregressive Heeroskedasiciy. Journal of Economerics, 3, pp [3] Can, F., Lim, C., and M., McAleer, Modelling mulivariae inernaional ourism demand and volailiy. Tourism Managemen, 26, pp [4] Cang, C.L., M. McAleer, and., Tansuca, 20. Crude oil edging sraegies using dynamic mulivariae GACH. Energy Economics 33(5), pp [5] Engle,.F., and K.F. Kroner, 995. Mulivariae simulaneous generalied ACH. Economeric Teory, pp [6] Engle,.F., Dynamic condiional correlaion: A simple class of mulivariae generalied auoregressive condiional eeroskedasiciy models. Journal of Business and Economic Saisics 20, pp [7] Fama, E. and K., Frenc (993). Common isk Facors in e eurns on Socks and Bonds. Journal of Financial Economics 33, pp [8] Giannopoulos K.,., ekil and G., Koumos, 200. Volailiy Spillovers and Price Inerdependencies; A Dynamic non Parameric Approac. Inernaional esearc Journal of Finance and Economics 45, pp [9] Hakim, A., and M., McAleer, Forecasing condiional correlaions in sock, bond and foreign excange markes. Maemaics and Compuers in Simulaion 79, pp

11 7 Inernaional esearc Journal of Finance and Economics - Issue 6 (207) [0] Hafner, C.M., and H., Herwar, Volailiy Impulse esponse Funcions for Mulivariae GACH Models: An Excange ae Illusraion. Journal of Inernaional Money and Finance 25, pp [] Hammoude, S., and S., Al-Gudea, eurn, risk and global facors in Saudi equiy secors. Journal of Emerging Markes 0, pp [2] Hammoude, S., Y. Yuan, and M., McAleer, Sock and volailiy spillovers among equiy secors of e Gulf Arab sock markes. Te Quarerly eview of Eco-nomics and Finance 49, pp [3] Herbs, A., D., Kare, and J., Marsall, 989. A ime varying, convergence adjused, minimum risk fuures edge raio. Advances in Fuures and Opions esearc 6, pp [4] Kroner, K.F. and J., Sulan, 993. Time-varying disribuions and dynamic edging wi foreign currency fuures. Journal of Financial and Quaniaive Analysis 28, pp [5] Kroner, K.F. and V.K., g, 998. Modeling Asymmeric Comovemens of Asse eurns. eview of Financial Sudies, pp [6] Ku, Y.H., H., Cen, and K., Cen, On e applicaion of e dynamic condiional correlaion model in esimaing opimal ime-varying edge raios. Applied Economics Leers 7, pp [7] Long, X. and A., Ulla, 2005, onparameric and Semiparameric Mulivariae GACH Model, Cambridge Universiy, mimeo. [8] Longin, F., and B. Solnik, 200. Exreme Correlaion of Inernaional Equiy Markes, Journal of Finance 56, pp [9] Tse, Y.K. and A.K.C., Tsu A mulivariae generalied auoregressive condiional eeroscedasiciy model wi ime-varying correlaions. Journal of Business and Economic Saisics 20, pp