A Multivariate GARCH Model to Testing Currency Risk Premium. During Crises Periods

Transcription

1 A Mulivariae GACH Model o Tesing Currency isk Premium During Crises Periods Dandan Li Bruce Morley and Aanu Ghoshray Universiy of Bah UK Absrac: This paper examines wheher he currency excess reurn and world sock marke excess reurn move ogeher and wheher he ime varying risk premium could explained he UIP puzzle. The VA-GACH model including Asian financial crisis and recen credi crisis dummies in he mean and variance equaions has been employed o esimae he comovemen beween currency reurns and sock reurns. The exisence of a ime varying risk premium has been esed using a dynamic condiional correlaion DCC model based on he CAPM. We found he lagged marke excess reurn has a significan effec on currency excess reurns excep for he UK and Malaysia and he lagged Thai bah excess reurn has a highly significan effec on he oher Asian currencies excep Japan. This resul is consisen wih he conagion effec from he Thai bah o he regional counries during he Asian financial crisis and also from world sock markes o foreign exchange markes. The significan ime varying risk premium has also been found in mos currencies excep he UK Japan and Canada which suppors he idea ha he UIP puzzle is due o a ime varying risk premium raher han irraionaliy. Furhermore he posiive ime varying bea was found in mos counries and is less han one which indicaes ha expeced currency excess reurns are less volaile han expeced sock marke excess reurn. The condiional beas in Japan and Swizerland are negaive during crisis periods which is consisen wih he unwinding carry rade. Keywords: UIP deviaion; CAPM; MV-GACH; DCC; ime-varying risk premium JL Classificaions: F3 G0 G G5

2 . Inroducion The relaionship beween he ineres rae and he exchange rae has been exensively examined as i is considerable imporan o policymakers. The uncovered ineres rae pariy UIP condiion saes ha domesic currency would be expeced o depreciae by he amoun equal o he ineres rae differenial when domesic ineres raes are higher han foreign ineres raes. However a number of empirical sudies find ha high ineres rae currencies end o appreciae raher han depreciae. This violaion creaes a double profi for he carry rade boh benefiing from he ineres rae differenial and he exchange rae change. However he carry rade is profiable if currencies are sable oherwise speculaors could lose despie he ineres rae difference. Therefore i is necessary o consider foreign exchange risk which will benefi invesmen sraegies risk managemen and asse pricing. According o he sandard porfolio heory if he foreign exchange risk canno diversified in a well-diversified porfolio he sysemaic proporion of expeced excess reurn is regarded as a risk premium. Therefore wheher he ime varying risk premium exiss in financial markes is an imporan issue in boh he heoreical and empirical lieraure. Mos sudies consider ha he failure of UIP is due o he presence of a ime varying risk premium. The aemp o accoun for he ime varying risk premium is based on he capial asse pricing model CAPM. For insance Hansen and Hodrick 983 develop a laen facor asse pricing model o examine he risk premium from invesing in foreign currency deposis. Domowiz and Hakkio 985 relae he risk premium o he condiional variance of exchange raes and ineres raes. Mark 988 applies he CAPM o currency prices. More recenly various versions of he consumpion asse pricing model CCAPM of Lucas 98 have been employed by Backus Gregory and Telmer 993 Bekaer 996 Bekaer Hodrick and Marshall 997 and Mark Wu and Hai 997. The analysis of financial linkages beween markes has become an imporan opic in financial economerics recenly. Previous empirical ess for he foreign exchange risk

3 premium have mainly focused on he foreign exchange marke and ignored he ineracion beween differen financial markes such as sock markes and bond markes. Increasing globalizaion has encouraged invesors o allocae a significan proporion of heir porfolio o foreign asses in order o diversify he unsysemaic risk and earn significan benefis. Porfolio managers may wan o know wheher foreign exchange risk is a priced facor which has direc implicaions for heir hedging sraegies. If i canno be well diversified his risk should be included in he pricing model and he risk premium has o be paid o risk averse speculaors in order o compensae he risk of fuure currency movemens. In his case UIP migh be sill violaed even under raional expecaions. Invesors could diversify he unsysemaic risk and reward higher profi if including differen financial marke asses in heir porfolios. Nowadays currency is ofen being included as an asse in hedge fund porfolios. The covariance beween currency and oher asses in he porfolio is imporan o he performance of he fund. Giovannini and Joeion Bekaer and Hodrick 99 Korajczyk and Vialle 99 Dumas and Solnik 995 and de Sanis and Gerard 998 combine boh foreign exchange markes and sock markes ogeher. The aim of his paper is o examine wo problems wheher he ime varying risk premium in foreign exchange markes could explain he UIP deviaion and wheher he currency excess reurn and he world sock marke excess reurn move ogeher. ngle s 00 dynamic condiional correlaion DCC model has used o analyze hese wo problems including he Asian financial crisis and he credi crisis dummies in boh mean and variance equaions. The differences o previous sudies are in he following aspecs. Firs of all he parameers and condiional covariance are esimaed by he DCC model raher han oher mulivariae GACH models which is he firs ime i has been employed in UIP deviaion analysis. The DCC has grea advanages han he mos used BKK model by reducing he number of parameer o esimae. Secondly he bivariae GACH model does no provide evidence of ime varying currency risk premium in mos sudies herefore we use he mulivariae GACH model followed by Tai 00 o consider differen financial markes ogeher. However if he asse numbers in he porfolio are more han five he mulivariae GACH model become problemaic as ime consuming 3

4 and hardly o converge. Thirdly he UIP deviaions in Asian counries have received much less aenion han in developed counries. However wih he increasing imporance of Asian counries in world capial markes i seems ineresing o invesigae he UIP deviaion in Asian counries ogeher wih he Asian financial crisis and he credi crisis. There is no sudy looking a he effec on he currency excess reurn wih boh crises and conagion effecs. The empirical resuls find ha he lagged world marke excess reurn has a significan effec on he currency excess reurns excep in he UK and Malaysia. The lagged Thai bah excess reurn has a highly significan effec on he oher Asian currencies excep Japan. This resul is consisen wih he conagion effec from he Asian financial crisis beginning wih he Thai bah suddenly depreciaing. I found a significan ime varying risk premium in mos currencies excep he UK Japan and Canada. The significan coefficien of covariance risk implies ha he foreign exchange marke in Asian counries is fully inegraed wih he world sock marke. However we don find his resul in he developed counries. Therefore he evidence suppors he idea ha he UIP puzzle is due o he ime varying risk premium raher han irraionaliy. Furhermore nearly all currencies condiional beas are posiive and less han one. This resul indicaes ha expeced currency excess reurns are less volaile han expeced sock marke excess reurn. The condiional beas in Japan and Swizerland are negaive during crisis periods which is consisen wih he unwinding carry rade. The resul of he es for he origin of he ime varying risk premium variaion find ha he marke expeced reurn has relaively large coefficiens which demonsrae ha he ime varying risk premium is mosly dependen on he expeced marke reurn. The remainder of his paper is organized as follows. Secion presens he previous lieraure. In secion 3 he heoreical mehod based on he CAPM is described. Secion 4 discusses he empirical economeric MV-GACH models. Secion 5 presens he daa and main empirical analysis. The las secion concludes and suggess furher areas of sudy and gives some policy implicaions. 4

5 . Lieraure eview There exis a large number of sudies o es he ime varying risk premium in foreign exchange markes based on he CAPM see Hansen and Hodrick 983 Domowiz and Hakkio 985 Mark 988 Baillie and Bollerslev 990 Kaminsky and Periga 990 McCurdy and Morgan 99 ngle 996 Bansal and Dahlquis 000 Francis e al. 00 Chiang and Yang 003 Tai Hansen and Hodrick 983 and Domowiz and Hakkio 985 firs aemp o es he deviaions of he forward rae based on he CAPM. Their resuls provide lile suppor for he exisence of a ime-varying risk premium. Mark 988 esimaes currency risk premium based on a condiional CAPM. He chooses ACH models o capure he ime varying risk premium. The esimaed condiional bea coefficiens are exremely low ranging from 0.00 o 0. which can only explain a small par of he deviaion. Baillie and Bollerslev 990 followed by Domowiz and Hakkio 985 exend he model o he mulivariae GACH model. They sill find lile evidence o suppor he heory. However a variey of following sudies succeed in explaining he ime varying risk premium as a funcion of he condiional covariance using MV-GACH models. Kaminsky and Peruga 990 esimae foreign exchange ime varying risk premium for German mark Japanese yen and Briish pound using a BKK model based on he ineremporal asse pricing model IAPM. The risk premium is due o consumpion risk which is measured by he covariance beween reurns and he marginal uiliy of money. They find ha alhough he ime varying risk premium is an imporan deerminan of he expeced excess reurns a more flexible model is needed raher han he resriced IAPM. McCurdy and Morgan 99 follow he work of Mark 988 using he single bea CAPM o price deviaions from UIP for five currencies. They are also choosing an inernaionally diversified equiy porfolio MSCI as a benchmark. This mehod is differen from Campbell 987 Giovannini and Jorion 987 Korajczyk and Vialle 99 and ngle Ng and ohschild 990. They assume he reurn of he benchmark is unobservable and use a laen variable approach or facor represening porfolios. McCurdy and Morgan 99 use differen insrumens han Mark 988 o predic he 5

6 benchmark porfolio reurn using he bivariae GACH BKK model which esimae he model currency by currency raher han model currencies joinly. The esimaion resuls indicae ha a diagonal MV-GACH specificaion should be sufficien in explaining ime varying condiional second momens. The average risk on UIP deviaion seems exremely large which migh indicae a poenial misspecificaion of he condiional covariance model. Malliaropulos 997 invesigaes he exisence of ime varying risk premium in he UIP deviaion based on he CAPM from seven major currencies and a world equiy index as a benchmark porfolio. Compared o he sudy of McCurdy and Morgan 99 he used a diagonal GACH model wih he consan condiional correlaion CCC insead of a BKK model. The resuls indicae significan condiional sysemaic risk and he ime varying risk premium can be explained by boh expeced excess reurns in he sock marke and ime-varying condiional beas. The explanaory power of he condiional bea model is higher han he consan bea CAPM. The expeced excess reurns are less volaile in foreign exchange markes compared o sock markes. He also finds condiional beas are posiive which means when he excess reurn in sock markes are expeced o increase he dollar is expeced o depreciae. Tai 00 also invesigaes he exisence of ime varying risk premium in UIP deviaions based on he CAPM for Asia-Pacific counries. He finds ha here is no evidence of ime varying risk premium when examining he bivariae GACH-M model for each currency bu here exiss ime varying risk premium in all currencies ogeher when using a MV- GACH model. McCurdy and Morgan 99 also menioned he poenial disadvanage of his bivariae sysem which maybe is inefficien by reaing he se of five currencies and he benchmark porfolio separaely. However his model may have a problem ha large numbers of parameers need o be esimaed which could be difficul. Tai 004 employs an inernaional CAPM for as Asian counries during January 986 o July 998. I repored ha currency excess reurns are driven by sysemaic risk facors. He argues ha deviaions from he UIP condiion are aribuable o he exisence of ime varying risk premium especially in he form of currency risks. 6

7 3. Theoreical Models The capial asse pricing model is a popular model for explaining reurns of individual asses or he porfolio regarding he reurn of he marke porfolio. The equaion for he CAPM can be wrien as: i f i m f where i denoe he expeced asses reurn f is he risk-free rae and m is he expeced marke porfolio reurn β i is he uncondiional coefficien of he asse o measures he sysemaic risk. The empirical CAPM equaion is as follows: i f i m f i The above equaions for he CAPM assume ha he sysemaic risk is consan over ime. However Bollerslev e al. 988 and Jagannahan and Wang 996 propose he ime varying CAPM which allow he condiional variance of he errors o follow a GACH process and he sysemaic risk o vary over ime. Cov i m i 3 Var This condiional β coefficien is equal o he covariance beween reurns on he individual asse i and reurns on he fully diversified marke porfolio divided by he variance of he marke porfolio. The asse exhibiing a large and posiive covariance wih he marke porfolio is seen as risky because hey are exposed o large flucuaions. isk averse invesors demand a risk premium o compensae hem when hey are buying posiively correlaed asses whereas hey are willing o buy asses which have a low even a negaive correlaion wih he marke. m In he CAPM he invesor s objecive funcion is assumed o be fully deermined by he risky asse s expeced reurn and sandard deviaion. All invesors choose risky asse shares o maximize he Sharp raio. In his case he expeced asse excess reurn is deermined by hree componens he condiional covariance beween marke excess reurn and individual asse excess reurn he condiional variance of marke excess reurn and he expeced marke excess reurn. quilibrium reurns hen arise as a consequence of all agens having he same expecaions and all asses mus be willingly held. An 7

8 8 alernaive view of he deerminaion of equilibrium reurns is provided by he CCAPM. Here he invesor maximizes expeced uiliy ha depends on curren and fuure consumpion subjec o an ineremporal budge consrain Lucas 98. The sysemaic risk of he asse is deermined by he covariance of he asse s reurn wih respec o consumpion raher han is covariance wih respec o he reurn on he marke porfolio as in he sandard CAPM. Lucas 98 developed ineremporal asse pricing models o discuss he risk premium and analyze facors ha affec ime varying risk premium. When esing he CAPM an uler equaion is used o measure he speculaive reurn. ] [ ' ' r C U C U 4 where θ is he discoun facor U C is he marginal uiliy of consumpion C r + is he one-period real reurn on risky asses in erms of he consumpion good. In equilibrium he marginal uiliy of curren consumpion is equal o he expeced discoun uiliy of he real reurn from invesing ha consumpion good in a risky asse. Because he curren consumpion is known equaion 4 can be rearranged as: ] [ ' ' C U r C U 5 If r + is he reurn invesed in a foreign currency equaion 5 becomes: ] [ ' * ' S P C U PS i C U 6 If r + is he reurn invesed in he domesic counry equaion 5 becomes: ] [ ' ' P C U P i C U 7 where P is he domesic currency price of he consumpion good i is he domesic ineres rae i * is he foreign ineres rae S + is he domesic currency price of one uni of foreign currency. Taking he difference beween equaion 6 and 7 we can ge he following model: 0 ] [ ] [ * ' ' d S S i i P P C U C U 8

9 where + is he marginal rae of subsiuion MS defined as U C P ' and ' U C P d + is he deviaion from he UIP or currency risk premium. This equaion saes ha he condiional expecaion beween he MS imes he UIP deviaion should be zero. The equaion can be rewrien as: d ] Cov[ d ] [ ] [ d ] 0 9 [ Cov[ d ] [ d ] 0 [ ] The lef hand side of he equaion is he ime varying risk premium. This equaion demonsraes ha here is a relaionship beween he ime varying risk premium and he ineremporal marginal rae of subsiuion. According o his model domesic invesors who hold open posiions in foreign currencies may face ime varying risk ha is proporional o he condiional covariance of he value of he posiion wih he ineremporal marginal rae of subsiuion of he domesic currency. Because he expeced MS is always posiive he expeced ime varying risk premium is negaively correlaed wih he covariance beween he MS and his risk premium. When invesors are risk averse hey do no like uncerainy he risk premium will be posiive if he condiional covariance is negaive see McCurdy and Morgan 99; Tai 00. This negaive condiional covariance is caused by low marginal uiliy high consumpion wih a high payoff from uncovered long posiions. The risk premium will be negaive when he condiional covariance is posiive. Therefore he foreign invesmen expeced reurn is lower in equilibrium han ha on he domesic invesmen. This is because he flucuaions in he exchange rae are such ha he foreign invesmen provides a hedge agains adverse consumpion oucomes. If he invesor is risk neural + is a consan herefore he risk premium is zero which is he condiion ha no ime varying risk premium in he UIP. Given ha + is no observable addiional assumpions are necessary in order o derive a esable form of he CAPM. This is he problem ha all CCAPM have faced in he empirical lieraure. I is no easy o analyse he ime varying risk premium based on he CCAPM as he empirical model. This is because he macroeconomic daa used in uiliy 9

10 funcions are normally long-run daa. However shor-run daa migh affec invesors decisions on risk and become he reason for he ime varying risk premium. As a resul in order o solve his problem we need o re-express he asse pricing model using a benchmark porfolio on he condiional mean-variance fronier Hansen and ichard 987. We define a benchmark marke porfolio in he condiional mean-variance fronier as follows according o Hansen and ichard 987. Assuming ha a minimum variance porfolio exiss which is perfecly correlaed wih +. A benchmark porfolio is a linear combinaion of he minimum variance porfolio and he risk free rae. One group of he lieraure consruced he benchmark porfolio which is maximally correlaed wih he growh rae of consumpion see Breeden Gibbons and Lizenberger 989; McCurdy and Morgan 990. The ohers use a laen variable approach or facor represening porfolio o esimae he benchmark see Campbell 987; Giovannini and Jorion 987; Korajczyk and Vialle 990; ngle Ng and ohschild 990. We will follow he work by Mark 988 and McCurdy and Morgan 99 using he MSCI world equiy index as he benchmark porfolio. More deails abou he ransformaion of equaions are provided in he appendix. The equilibrium expeced reurn can be expressed as a funcion of is condiional bea imes he excess reurn on he benchmark porfolio which is expressed as follows: Cov[ m d ] [ m ] [ d ] [ m ] Cov[ m d ] Var[ ] Var[ ] m m Cov d ] [ m According o he above equaions he expeced excess reurn on he foreign currency is proporional o he excess reurn on he benchmark porfolio marke porfolio. The risk premium of he foreign exchange is ime varying because i depended on hree ime varying componens: he condiional variance of he marke excess reurn he condiional covariance beween he currency excess reurn and he marke excess reurn and he expeced marke excess reurn. In his paper we do no impose he resricion ha he price of he covariance risk is consan. This was checked by Tai 00 who found ha he consan price of he covariance risk model could no explain he currency ime varying risk premium worse han he ime varying price of covariance risk model. The 0

11 condiional bea is he marginal conribuion of he foreign currency risk premium o he overall marke risk. This condiional bea posiively depends on he condiional covariance beween currency reurns and marke reurns and negaively on he condiional variance of he marke excess reurn. 4. conomeric Models 4. Modelling he Mean quaion: The firs model is based on he idea of a conagion effec during he crises period which suggess ha boh he lagged currency excess reurn in he relaed region and he lagged world sock marke excess reurn have predicable power. This relaionship could inerpre ino he following equaions based on VA-GACH model: r n r r dummy dummy i i i i i m i i i i r r dummy dummy m m m m m m m where r i+ is he individual currency excess reurn a ime +which is defined as he difference beween he ineres rae differenial and exchange rae change r m+ is he sock marke excess reurn. The wo dummy variables represen he Asian financial crisis and credi crisis. The reason for he wo crises dummies in he mulivariae model is ha hese crises have a sysemic effec which is no only relaed o he original counry being quickly ransmied all over he world o several inernaional markes. The negaive currency excess reurn means ha you will ge a higher reurn if borrowing in he domesic marke convering o he foreign currency and invesing in he foreign marke and hen change he reward ino he domesic currency a a fuure exchange rae. This higher reurn will compensae for he higher risk. In his VA-GACH model we are rying o es wheher he lagged variables could predic he curren expeced value. The currency excess reurn is he dependen variable wih one period lagged currency excess reurn and lagged marke excess reurn as is The UIP deviaion is defined as follows: S i i * * i i s s S r

12 independen variables. In he second equaion he expeced marke excess reurn is esimaed by a consan and he lagged marke risk premium. We will discuss anoher mehod o esimae he expeced marke risk premium in he second model. This is he firs ime he VA-GACH model has been used o analyse he currency risk premium ogeher wih equiy marke risk premium. Iglesias and Phillips 00 model he Spanish ineres rae hrough esimaing he ime-varying risk premium for France Germany and Spain using a VA-GACH. They find he exisence of a ime-varying risk premium for Spain depends on German volailiy. Polasek and en 00 esimae a VA-GACH o invesigae wheher he volailiy of he sock reurn from US Germany and Japan will feed back on he reurns hemselves. In he second model we follow he heoreical CAPM model wih ime varying bea o obain esable equaions. I can be wrien as: mi i 0 i 0 m i i idummy idummy i m r r m rm m 0 m m 3 where r i+ is he currency excess reurn r m+ is he marke excess reurn σ m+ σ i+ and σ mi+ are he condiional variance of marke excess reurn condiional variance of each individual currency excess reurn and condiional covariance beween marke reurn and each currency reurn respecively. The expeced marke excess reurn is consruced from a consan and he condiional variance of he marke excess reurn. The reason for including he condiional variance of he marke risk premium is o capure he effec of changes in he level of he marke risk. These risk variables are generaed from he MV- GACH model and add o he mean equaion. We have followed he paper by Tai 00 by including he condiional variance of currency excess reurns. Therefore he ime varying risk premium could compensae currency speculaors for bearing boh marke risk and currency risk. 4. Modeling he Condiional Variances and Covariance There are a grea number of models o esimae he condiional variance-covariance marix. The mos widely used are MV-GACH models which included he VCH and

13 diagonal VCH model Bollerslev ngle and Wooldridge 988 full BKK diagonal BKK scalar BKK ngle and Kroner 995 Condiional Consan Correlaion CCC model Bollerslev 990 and Dynamic Condiional Correlaion DCC model see Tse and Tsui 00 and ngle 00. The mulivariae GACH models are summarized in Silvennoinen and Teräsvira 008 and Shues and Niklewski 00. However here are also wo main difficulies for MV-GACH class models. Firs of all he dimension of variance-covariance marix increases rapidly wih he increase in he number of asses. The number of parameers in an MV-GACH model ofen increases rapidly wih he dimension of he model he specificaion should be parsimonious enough o allow for relaively easy esimaion of he model and also allow for easy inerpreaion of he model s parameers. However parsimony ofen means simplificaion and models wih only a few parameers may no be able o capure he relevan dynamics in he covariance srucure. Second some MV-GACH models fail o saisfy he requiremen of being posiive semi-definie. CCC and DCC models use he condiional variances and correlaions insead of sraighforward modeling of he condiional covariance marix. I benefis from he inuiive inerpreaion of correlaions. Numerical difficulies are common in he esimaion of BKK models. The BKK esimaion only allows he mulivariae GACH model have relaively low dimension. Wih more han five or six asse reurns in he model could be viewed wih some cauion since he likelihood surface becomes exremely fla and i is difficul o maximize. In he case ha m=6 we need o esimae 93 parameers in he variance equaion and i is consequenly hard o ge convergence. Alhough he CCC model could reduce he number of parameers and makes he esimaion simple he assumpion of he condiional correlaion being consan may seems oo resricive and unrealisic. Therefore we will use he DCC model by making condiional correlaions ime dependen. DCC models guaranee he ime dependen condiional correlaion marix o be posiive under simple condiions on he parameers and i is useful when modeling a high dimensional daa se. 3

14 Insead of calculaing he condiional variance-covariance marix direcly CCC and DCC calculae i indirecly hrough he condiional correlaions and condiional sandard deviaions. The simples model is he CCC proposed by Bollerslev 990 in which he condiional correlaions are consan. Therefore he condiional covariance is proporional o he produc of he corresponding condiional sandard deviaions. This resricion grealy reduces he number of parameers and makes he esimaion simple. Alhough he CCC model has some advanages in many aspecs he assumpion of he condiional correlaions being consan may seem oo resricive and unrealisic in many empirical pracices. ngle and Sheppard 00 proposed a generalizaion of he DCC model by making he condiional correlaion marix ime dependen. The DCC model guaranees he ime dependen condiional correlaion marix o be posiive definie under simple condiions on he parameers. The DCC model is useful when modeling high dimensional daa ses. There are wo sages for DCC model esimaion: obaining he condiional variance wih a univariae GACH model a firs and hen calculaing he condiional covariance. The DCC model demonsraed by ngle and Sheppard 00 and ngle 00 is as follows: H D D / / diag{ } diag{ } 4 C A B ' 0 where 0 is he uncondiional covariance marix. However isn he sequence of covariance marix. Insead i is used solely o provide he correlaion marix. The acual H marix is generaed using univariae GACH models for he variance combined wih he correlaions produced by he. ngle 00 indicaes ha DCC models are more compeiive han he ohers some of which are difficul for a large mulivariae sysem. However he DCC model has a weakness when n is large because all he correlaion processes are resriced o have he same dynamic srucure. The parameers of BKK CCC and DCC models are esimaed by maximum likelihood funcion. The log likelihood funcion of he join disribuion is compued from he sum of all he log likelihood funcions of he condiional densiies suggesed by ngle and 4

15 Kroner 995. Differen GACH class models have heir own log likelihood funcions according o differen resricions and assumpions. For he CCC and DCC models he log likelihood funcion could be decomposed as follows: T ' log r D D L log log D T ' log log D log 5 The properies of maximum likelihood esimaion in GACH models are sill debaed in he lieraure. One of he problems of maximum likelihood esimaion is ha i is assuming a normal disribuion. As we know volailiy models used in finance are nonlinear in paricular he kurosis of mos financial asses reurns is larger han hree which means ha hey have fa ails lepokuric and no a normal disribuion. Wih an assumpion abou he condiional disribuion of reurns he parameers of he mulivariae GACH model can be esimaed by he quasi-maximum likelihood esimaion ML proposed by Bollerselv and Wooldridge 99 using he nonlinear maximum likelihood. The ML esimaor is consisen and asympoically normal and saisical inferences can be carried ou by compuing robus Wald saisics repored by Tai 00. Opimizaion is performed using he BFGS algorihm. r 5. Daa and mpirical Analysis Monhly observaions on exchange raes and ineres raes were used o consruced UIP deviaions. The sample covers he ime period from March 99 o May 009 for Asian counries and from June 990 o May 009 for developed counries. The world sock marke reurns are calculaed by he Morgan Sanley Capial Inernaional MSCI world index. All he daa is from Daasream. Table presens summary saisics for he currency excess reurns and he world sock marke excess reurn. The mean of he UIP deviaion is no saisically differen from The world sock marke excess reurns= P us ln ln i P P is he MSCI index price 5

16 zero for any counries. Half of he mean excess reurns are negaive. The UIP deviaion is saionary for all counries based on he ADF es and Zivo es wih a srucural break. The excess reurn on he MSCI world index has he highes sandard deviaion compare wih oher currency excess reurns. Mos of he daa series exhibi significan skewness and kurosis indicaing non-normaliy in reurns. This is also confirmed by he Jarque- Bera es for normaliy which is saisically significan. Uncondiional correlaions among currency excess reurns and sock marke excess reurn are also displayed in he able. Mos correlaions are relaively low indicaing ha he co-movemen of currency excess reurn among counries is no srong and even less wih he world sock marke. The co-movemen of currency excess reurn in Asian counries is no as srong as hose found in developed counries. Japan is an excepion in boh cases which has a relaively low correlaion wih oher excess reurns. The plos of currency and marke excess reurns are displayed in Figure. The excess reurns from Asian counries change srongly in he period of he Asian financial crisis beween July 997 and December 998 raher han in he credi crisis period. However i is sill a significan change during he credi crisis which demonsraed how he conagion effec from he world sock marke spreads o he foreign exchange marke. Singapore has been mildly affeced by he Asian financial crisis compared wih oher counries due o he acive governmen s managemen. Japan has huge currency reserves so i was easily defended and quickly bounced back. Therefore he excess reurn from he Japanese yen does no have such a big variaion during he crises periods. Malaysia imposed capial conrols as an emergency mehod in Sepember 998 including boh sric exchange conrols and limis on ouflows from porfolio invesmen as we can noe he excess reurn from 998 o 006 is hardly changed. I also uses anoher policy ool a he disposal of governmens responding o currency crises which is he implemenaion of fixed exchange raes. The ineresing hing is ha he excess reurn of he Thai bah is posiive before he Asian crisis. This is because from 99 capial conrols were canceled and he domesic capial marke was opened o foreign invesors however he exchange rae policy is pegged o he US dollar. In order o sabilize he exchange rae he governmen needs o se high ineres raes and can use macroeconomics policy hrough 6

17 reducing he ineres rae o simulae he economy. This high ineres rae could induce speculaion and he pegged exchange rae policy reduces he exchange rae risk. Speculaors could reward a higher pay off wihou higher risk. The world sock marke excess reurn and currency excess reurns from UK Ausralia and Canada dramaically declined in 008 even becoming negaive which are affeced by he credi crisis. The excess reurn from he Briish pound had a sharp decrease in Sepember 99 and experienced exreme volailiy following he pressure on he Ialian lira. Serling fell hrough is floor and consequenly lef he uropean Moneary Sysem MS and hen floaed freely on he marke. The excess reurns of he Ausralian dollar and he Canadian dollar have similar paerns wih relaively less volailiy before he credi crisis. The condiional variance from he VA-GACH model in Figure appears o increase dramaically around 997 in he Asian counries corresponding o he Asian financial crises. Malaysia Thailand and Souh Korea have a relaively high increase in he condiional variance. I is ineresing o noe ha he condiional variance increases much more for Souh Korea and Malaysia during he credi crisis period and even higher in Souh Korea during credi crisis. Our resuls show ha he financial sysems of mos Asian economies are currenly robus when compared o heir siuaion during he Asian financial crisis. This is because in he decade beween 997 and 008 mos Asian economies srenghened heir moneary sysems and adoped a sronger se of banking regulaions. The condiional variances in all he developed counries are similar which have a spike in Sepember 008. However he UK had experienced he M crisis in Sepember 99 which is consisen wih previous explanaions. Figure 3 illusraes he condiional correlaion beween he currency excess reurn and marke excess reurn. Nearly all he dynamic correlaion srucures are posiive excep Souh Korea implying ha he currency excess reurn and sock marke excess reurn are posiively correlaed. The sharp declines in he inernaional sock marke excess reurn and depreciaion in he currency have resuled in a significan change in he condiional correlaion. Souh Korea has a relaively serious impac in boh crisis periods. A sudden swich in exchange rae regime in lae 997 led o a rise in uncerainy and increased he 7

18 negaive condiional correlaion o he opposie of oher currencies. The condiional correlaion in Japan does no change compared wih ohers. This migh be because Japan is a major world economy which gives more srengh o he Japanese yen in imes of financial crisis. And also he Japanese yen is one of he mos popular carry rade currencies which is generally agains cycle appreciaion during he crisis period. I is ineresing o noe ha he condiional correlaion beween currency excess reurn and sock marke excess reurn increased significanly and posiively afer he credi crisis excep in Japan and Thailand which indicaes high co-movemen beween differen financial markes during he crisis period afer he sock marke clash. Figure 3 also includes he condiional correlaion coeffciens beween he Thailand excess reurn and ohers. These ime varying paens show ha he condiional correlaions incresed afer he Asian financial crisis and reached he highes level a his ime. A he beginning of he crisis he condiional correlaions decreased in Souh Korea and Singapore because Thailand depreciaed is currency hen invesors wihdraw heir fund from Thailand and invesed hem in oher counries in he same region. However wih he crisis expand he asse price in oher neighboring counries declined due o he conagion effec spreading hrough various channels. In his pocess he currency excess reurns shown increased heir correlaions. During he period from July 997 o 998 he Asian financial crisis spread rapidly and sequenially from one counry o anoher in a shor inerval of inense crises. Table presens he VA-MV-GACH model considering he co-movemen of currency excess reurn in Asian counries where he lagged currency excess reurn and he lagged marke excess reurn are used o esimae he expeced value. The main finding is ha he one period lagged Thailand currency excess reurn has a highly significan effec on he oher currency excess reurns everywhere excep Japan. This is no surprising as Singapore Malaysia and Souh Korea were facing a recession and depreciaion when i suffered he conagion effecs from he Asian financial crisis which began wih he floaing of he Thai bah in July 997. As an open economy hey are exremely vulnerable o exernal developmens especially in he surrounding region in which hey have common feaures such as a high reliance on foreign denominaed deb and a 8

19 relaively sable exchange rae agains he US dollar. The lagged marke excess reurn is significanly posiively relaed o he currency excess reurn excep in Malaysia which demonsraes ha he world sock marke excess reurn should be considered in he currency risk premium pricing model which is based on he CAPM. The lag of each currency risk premium has significan explanaory power o esimae is own curren risk premium wih he excepion of Souh Korea. We include wo crises dummies in he mean and variance equaions which are esing he financial crisis effec. The sock marke has a significan effec based on he 008 credi crisis bu is insignifican in he Asian financial crisis. Is own lagged value does no seem o help forecasing marke excess reurn as expeced by he financial price daa. The resuls for he developed counries in Table 3 repors a similar conclusion he lagged currency excess reurn has he mos explanaory power. Compared wih Asian counries he lagged Japanese yen is highly significan which demonsraes he excess reurn of he Japanese yen have more effec on he developed counries currency excess reurn based on is advanced economy. Wih regard o he GACH process he esimaed parameers are highly significan a he 5% level. The esimaion saisfies he saionary condiions for he variance and covariance process. Table 4 repors he resuls from MV-GACH-M based on he CAPM. In his model we es he price of covariance risk and is own variance risk. The inercep in he marke excess reurn equaion is significanly posiive excep for Japan indicaing ha holding an inernaional diversified equiy porfolio rewarded invesors wih excess reurn. All he counries have a significan coefficien on he covariance beween marke excess reurn and currency excess reurn which means ha par of he ime varying risk premium comes from he covariance risk. The coefficien of he price of covariance risk is posiive for Japan and Souh Korea where domesic invesors would like o inves in he domesic markes when he covariance risk is high. The coefficien on he condiional variance of is own counry specific risk is posiively significan excep for Japan which indicaes he oher source of ime varying risk premium. Hypohesis ess regarding he ime varying risk premium is also included in he able and confirms he conclusion ha he ime 9

20 varying risk premium exiss. The ime varying risk premium only comes from he covariance risk for Japan bu conains boh covariance and variance risk in he oher four counries. All he Asian counries have become inegraed wih he world sock marke which is consisen wih Bekaer and Harvey 995 bu differen from Francis e al 00. The reason for his inegraion is because i is relaively liquid and highly capialized. The Asian financial crisis dummy variable is significan excep for Souh Korea and he credi crisis dummy is significan excep for Japan and Thailand. Japan was less affeced by he credi crisis because of he relaively sable banking secor hrough avoiding real esae backed securiies financial srucures and high levels of borrowing and leveraging. The only facor deerioraes Japanese sock markes is exchange raes which appreciae nearly 8% during he credi crisis period. This huge appreciaion increases he excess reurn of he Japanese yen which has an opposie movemen o he world sock marke. In his case invesors implemen unwind carry rade sraegies dramaically reducing he shor yen posiion which had been buil up as a par of carry rade. The resuls for he developed counries are in Table 5. Only Ausralia has a significan covariance risk coefficien and Swizerland has a significan variance risk coefficien a he 5% level. UK Japan and Canada have no significan ime varying risk premium. This could be he covariance risk wih he world sock marke or he variance risk iself could no capure he risk premium. The credi crisis dummy variable in he UK Ausralia and Canada are negaively significan which is he same as in he world sock marke suggesing a reducion in he excess reurn. The plos of he esimaed condiional ime varying beas are displayed in Figure 4. The graphs exhibi significan differences in he dynamic beas which are likely o be refleced in he esimae of he ime varying risk premium. The ime varying beas display dramaic flucuaion during he crises periods. Only Souh Korea has a negaive bea. The negaive bea suggess ha Korean won deposis provide a benefi for inernaional porfolio diversificaion for equiy invesors. As can be seen from graphs hey are more volaile only during he crises periods. The condiional beas in developed counries are smaller han Asian counries during boh crises periods which illusraes ha advanced 0

21 economies are less vulnerable han developing counries due o heir sable policies and improvemens in he regulaion. I is ineresing o noe ha for nearly all currencies considered esimaed condiional beas are posiive and less han one. This resul indicaes ha expeced currency excess reurns are less volaile han expeced sock marke excess reurn. Thus open foreign currency posiions can be considered as a defensive sock. They conain less sysemaic risk han world sock markes and consequenly require a lower rae of reurn. When he sock marke excess reurn is expeced o increase he currency excess reurns increase and domesic currency appreciaed. Anoher ineresing finding is ha boh Japan and Swizerland have a negaive bea during mid-990s 00 and credi crisis period which is consisen wih unwinding of he carry rade. During he period of he marke clash he expeced marke excess reurn would be low or negaive combined wih he negaive bea we would have a relaively higher excess reurn. This higher excess reurn means ha by selling he foreign US asse and invesing in he domesic marke cause he Japanese yen and Swiss franc o appreciae. As we know from he heoreical CAPM model he asses risk premium is deermined by he condiional covariance condiional variance of marke excess reurn and expeced marke reurn. From he previous empirical resuls we prove ha he ime varying risk premium could explain he UIP violaion. Therefore we run a regression o decide he origin of his ime varying risk premium variaion. The condiional bea and marke expeced reurn as he independen variables and expeced currency risk premium as he dependen variable. Table 6 demonsraes he regression resuls. Boh ables have highly significan which could explain mos variaion of he dependen variable excep Japan. The coefficiens of bea and expeced marke reurn are significan a he % level wih some excepion. Comparing he coefficiens of bea and marke expeced reurn we find ha he marke expeced reurn has a relaively large coefficien which demonsraes ha he ime varying risk premium is mosly dependen on he expeced marke reurn.

22 6. Conclusion The aim of his paper is o sudy he co-movemen beween financial markes and he exisence of he ime varying risk premium. The co-movemen beween foreign exchange markes and world sock markes was esimaed by he VA-GACH model and we find ha he lagged Thai bah excess reurn has a highly significan effec on he oher Asian currencies excep Japan. This resul is consisen wih he conagion effec from he Asian financial crisis beginning wih he Thai bah suddenly depreciaing. The lagged world sock excess reurn is significanly relaed o currency excess reurn excep in he UK and Malaysia which indicaes he marke excess reurn should be considered in currency risk premium pricing models. The ime varying risk premium was esed using he DCC model based on he CAPM. We found a significan ime varying risk premium in mos currencies excep he UK Japan and Canada. The ime varying risk premium in his paper can be explained by he condiional covariance risk and he condiional variance risk. The significan coefficien of covariance risk implies ha he foreign exchange marke in Asian counries is fully inegraed wih he world sock marke. However in he developed counries we hardly reach he same conclusion. Therefore he evidence suppors he idea ha he UIP puzzle is due o he ime varying risk premium raher han irraionaliy. Furhermore nearly all currencies condiional beas are posiive and less han one. This resul indicaes ha expeced currency excess reurns are less volaile han expeced sock marke excess reurn. The condiional beas in Japan and Swizerland are negaive during crisis periods which is consisen wih he unwinding carry rade. The resul of he regression o decide he origin of his ime varying risk premium variaion find ha he marke expeced reurn has relaively large coefficiens which demonsrae ha he ime varying risk premium is mosly dependen on he expeced marke reurn.

23 eference: Backus D.K. A.W. Gregory and C.I. Telmer 993 Accouning for Forward aes in Markes for Foreign Currency Journal of Finance Baillie.T. and T. Bollerslev 990 A Mulivariae Generalized ACH Approach o Modeling isk Premia in Forward Foreign xchange ae Marke Journal of Inernaional Money and Finance Bansal. and M. Dahlquis 000 The Forward Premium Puzzle: Differen Tales from Developed and merging conomies Journal of Inernaional conomics Bekaer G. 996 The Time Variaion of isk and eurn in Foreign xchange Markes: A General quilibrium Perspecive eview of Financial Sudies Bekaer G. and C.. Harvey 995 Time-Varying World Marke Inegraion Journal of Finance Bekaer G. and.j. Hodrick 99 Characerizing Predicable Componens in xcess eurns on quiy and Foreign xchange Markes Journal of Finance Bekaer G..J. Hodrick and D.A. Marshall 00 Peso Problem xplanaions for Term Srucure Anomalies Journal of Moneary conomics Bollerslev T. 990 Modeling he Coherence in Shor-un Nominal xchange ae: A Mulivariae Generalized ACH Model eview of conomics and Saisics Bollerslev T.. ngle and J.M. Wooldridge 988 "A Capial Asse Pricing Model wih Time Varying Covariances" Journal of Poliical conomy Bollerslev T. and J.M. Wooldridge 99 uasi-maximum Likelihood simaion and Inference in Dynamic Models wih Time-Varying Covariance conomerics eviews Breeden D.T. M.. Gibbons and.h. Lizenberger 989 mpirical Tess of he Consumpion Oriened CAPM Journal of Finance

24 Campbell J.Y. 987 Sock eurns and he Term Srucure Journal of Financial conomics Chan K.C. G.A. Karolyi and.m. Sulz 99 Global Financial Markes and he isk Premium on US quiy Journal of Financial conomics Chiang T.C. and S. Yang 003 Foreign xchange isk Premiums and Time-Varying quiy Marke isks Inernaional Journal of isk Assessmen and Managemen de Sanis G. and B. Gerard 998 How Big is he Premium for Currency isk? Journal of Financial conomics Domowiz I. and C.S. Hakkio 985 Condiional Variance and isk Premium in he Foreign xchange Marke Journal of Inernaional conomics Dumas B. and B. Solnik 995 The World Price of xchange ae isk Journal of Finance ngel C. 996 The Forward Discoun Anomaly and he isk Premium: A Survey of ecen vidence Journal of mpirical Finance ngle. 00 Dynamic Condiional Correlaion A Simple Class of Mulivariae GACH Models Journal of Business and conomic Saisics ngle. and Kroner K.F. 995 Mulivariae Simulaneous Generalized ACH conomeric Theory -50. ngle. and V.K. Ng and M. ohschild 990 Asse Pricing wih a Facor ACH Covariance Srucure: mpirical simaes for Treasury Bills Journal of conomerics ngle. and K. Sheppard 00 Theoreical and mpirical Properies of Dynamic Condiional Correlaion Mulivariae GACH Mimeo UCSD. 4

25 Fama. and K. French 993 Common isk Facors in he eurns o Socks and Bonds Journal of Financial conomerics Francis B.B. I. Hasan and D.M. Huner 00 merging Marke Liberalizaion and he Impac on Uncovered Ineres ae Pariy Journal of Inernaional Money and Finance French K.. G.W. Schwer and.f. Sambaugh 987 xpeced Sock eurns and Volailiy Journal of Financial Sudies Giovannini A. and P. Jorion 987 Ineres aes and isk Premia in he Sock Marke and in he Foreign xchange Marke Journal of Inernaional Money and Finance Giovannini A. and P. Jorion 989 The Time Variaion of isk and eurn in he Foreign xchange and Sock Markes Journal of Finance Hansen L.P. and.j. Hodrick 983 isk Averse Speculaion in he Forward Foreign xchange Marke: An conomeric Analysis of Linear Models. In Frenkel J.A. ds. xchange aes and Inernaional Macroeconomics Universiy of Chicago Press for Naional Bureau of conomic esearch 3-5. Hansen L.P. and S.F. ichard 987 The ole of Condiioning Informaion in Deducing Tesable esricions Implied by Dynamic Asse Pricing Models. conomerica Harvey C.. 99 The World Price of Covariance isk Journal of Finance Iglesias.M. and G. D.A. Phillips 00 Anoher Look abou he voluion of he isk Premium: a VA-GACH-M Model conomic Modelling Jagannahan. and Z. Wang 996 The Condiional CAPM and he Cross-Secion of xpeced eurns Journal of Finance Kho B.C. 996 Time-Varying isk Premia Volailiy and Technical Trading ule Profis: vidence from Foreign Currency Fuures Markes Journal of Financial conomics

26 Kaminsky G.L. and. Peruga 990 Can Time-Varying isk Premium xplain xcess eurns in he Forward Marke for Foreign xchange? Journal of Inernaional conomics Korajczyk.A. and C.J. Vialle 99 quiy isk Premia and he Pricing of Foreign xchange isk Journal of Inernaional conomics Liew J. and M. Vassalou 000 Can Book-o-Marke Size and Momenum be isk Facors ha Predic conomic Growh? Journal of Financial conomics Ling S. and M. McAleer 003 Asympoic Theory for a New Vecor AMA-GACH Model conomeric Theory Lucas.. 98 Ineres aes and Currency Prices in a Two-Counry World Journal of Moneary conomics Malliaropulos D. 997 A Mulivariae GACH Model of isk Premia in Foreign xchange Markes conomic Modelling Mark N. 985 On Time Varying isk Premia in he Foreign xchange Marke: An conomeric Analysis Journal of Moneary conomics Mark N. 988 Time-Varying Beas and isk Premia in he Foreign xchange Conracs Journal of Financial conomics Mark N. W. Hai and Y. Wu 997 Undersanding Spo and Forward xchange ae egressions Journal of Applied conomerics McCurdy T.H. and I. Morgan 99 Tess for a Sysemaic Componen in Deviaions from Uncovered Ineres ae Pariy eview of conomics Sudies McCurdy T.H. and I. Morgan 99 vidence of isk Premium in Foreign Currency Fuures Markes eview of Financial Sudies