Time-Varying Risk Premium and Contagion in Foreign Exchange Markets: Evidence from the 1997 Asian Crisis

Transcription

1 Time-Varying Risk Premium and Conagion in Foreign Exchange Markes: Evidence from he 1997 Asian Crisis Chu-Sheng Tai * Deparmen of Economics and Finance, College of Business Adminisraion, Texas A&M Universiy, MSC 186, 1115 Universiy Blvd., Kingsville, TX , USA Absrac In his paper, I examine simulaneously wheher ime-varying risk premium can explain he predicable excess reurn puzzle (Lewis (1994)), and wheher here are conagion effecs among foreign exchange markes during he 1997 Asian crisis. I use a condiional version of inernaional CAPM (ICAPM) in he absence of purchasing power pariy (PPP) o derive a measure of he risk premium. To incorporae ime-varying feaure of he risk premium ino he model, I allow no only he second momens of asse reurns o change over ime by uilizing mulivariae GARCH-in-mean (MGARCH-M) modeling sraegy, bu also he prices of risks o evolve hrough ime based on some predeermined informaion variables. Esimaion resuls show significan ime-varying risk premia in deviaions from uncovered ineres pariy (UIP), and hese risk premia mainly compensae currency speculaors for bearing no jus marke risk bu currency risk. Overall, he condiional ICAPM wih MGARCH-M srucure is able o explain/predic on average more han 26% (26.138%) of he reurn variaions in foreign exchange markes, a very high reurn predicabiliy compared o previous sudies. Therefore, I can conclude ha he ime-varying risk premium is a very srong candidae in explaining he predicable excess reurn puzzle since he risk premia deeced in his paper are no only saisically significan bu also economically significan. As for he ess of conagion, I find srong pure conagion effecs in boh condiional means and volailiies of foreign exchange markes afer sysemaic risks have been accouned for. Specifically, he conagion-inmean effecs are mainly driven by he pas innovaions in Japan, Hong Kong, and Singapore. As for conagion in volailiy, he lead/lag relaionships appear o be mulidirecional wih Hong Kong playing he dominan role in generaing conagion effecs a volailiy level since all he oher hree markes are significanly influenced by he pas innovaions in Hong Kong. JEL Classificaions: C32; F31; G12 Key Words: Predicable excess reurn puzzle; Conagion; Asse pricing; Time-varying risk premium; Mulivariae GARCH-M * Corresponding auhor. Tel: ; fax: ; cai@amuk.edu

2 Time-Varying Risk Premium and Conagion in Foreign Exchange Markes: Evidence from he 1997 Asian Crisis Absrac In his paper, I examine simulaneously wheher ime-varying risk premium can explain he predicable excess reurn puzzle (Lewis (1994)), and wheher here are conagion effecs among foreign exchange markes during he 1997 Asian crisis. I use a condiional version of inernaional CAPM (ICAPM) in he absence of purchasing power pariy (PPP) o derive a measure of he risk premium. To incorporae ime-varying feaure of he risk premium ino he model, I allow no only he second momens of asse reurns o change over ime by uilizing mulivariae GARCH-in-mean (MGARCH-M) modeling sraegy, bu also he prices of risks o evolve hrough ime based on some predeermined informaion variables. Esimaion resuls show significan ime-varying risk premia in deviaions from uncovered ineres pariy (UIP), and hese risk premia mainly compensae currency speculaors for bearing no jus marke risk bu currency risk. Overall, he condiional ICAPM wih MGARCH-M srucure is able o explain/predic on average more han 26% (26.138%) of he reurn variaions in foreign exchange markes, a very high reurn predicabiliy compared o previous sudies. Therefore, I can conclude ha he ime-varying risk premium is a very srong candidae in explaining he predicable excess reurn puzzle since he risk premia deeced in his paper are no only saisically significan bu also economically significan. As for he ess of conagion, I find srong pure conagion effecs in boh condiional means and volailiies of foreign exchange markes afer sysemaic risks have been accouned for. Specifically, he conagion-inmean effecs are mainly driven by he pas innovaions in Japan, Hong Kong, and Singapore. As for conagion in volailiy, he lead/lag relaionships appear o be mulidirecional wih Hong Kong playing he dominan role in generaing conagion effecs a volailiy level since all he oher hree markes are significanly influenced by he pas innovaions in Hong Kong. JEL Classificaions: C32; F31; G12 Key Words: Predicable excess reurn puzzle; Conagion; Asse pricing; Time-varying risk premium; Mulivariae GARCH-M 1

3 I. Inroducion The uncovered ineres pariy (UIP) hypohesis saes ha he domesic nominal ineres rae equals he foreign nominal rae on a comparable asse plus he expeced change in he exchange rae over he period o mauriy of he asse. Under he sandard assumpion of raional expecaions, and risk neural agens, he ex pos excess reurns of holding foreign currency deposis jus equal he marke rue expeced excess reurns plus a forecas error ha is unpredicable ex ane. Given his join assumpion, ess of UIP are essenially ess of he efficiency of he forward marke for exchange raes if covered ineres pariy (CIP) holds. 1 One imporan conclusion from his marke efficiency sudy is ha here exis predicable componens in excess reurns from holding foreign currency deposis. 2 lieraure. 3 This predicable excess reurn is one of he puzzles in inernaional finance Alhough he hypohesis ha forward exchange raes are unbiased predicor of fuure spo raes has usually been rejeced, mos researchers are sill inconclusive as o wheher he forward bias is due o marke inefficiency (irraionaliy) or o he presence of a ime varying risk premium. 4 1 If CIP holds, he deviaions from UIP can be expressed as he difference beween expeced fuure spo raes and curren forward raes (i.e., forward bias or forward forecas error). 2 Hodrick (1987) provides a deailed survey on he empirical sudies of marke efficiency of forward and fuures markes. 3 See Hodrick (1987), Cumby (1988), Korajczyk and Vialle (1992), Bekaer and Hodrick (1993) and Lewis (1994). 4 See for example, Hansen and Hodrick (1980, 1983), Hodrick and Srivasava (1984), Korajczyk (1985), Mark (1985, 1988), Hodrick (1987), Cumby (1988), and Kaminsjy and Peruga (1990). 2

4 Since he zero risk premium is hardly compaible wih he exising applied finance lieraure, his ime-varying risk premium argumen has led o an inensive search for proper specificaion of he risk premium in foreign exchange markes. Theoreical inernaional finance models developed by Solnik (1974), Roll and Solnik (1977), Hodrick (1981), Alder and Dumas (1983), and Sulz (1981, 1984) consider he pricing of foreign currency deposis in much he same way as ha of oher financial asses. In hese models, he excess reurn from holding a foreign currency deposi resuls from a risk premium ha has o be paid o risk averse speculaors for aking he risk of fuure changes in exchange raes. If his foreign exchange risk can no be diversified when forming a well-diversified porfolio, hen sandard porfolio heory ells us ha his risk is sysemaic and should be priced in an asse marke in equilibrium. However, if he foreign exchange risk is compleely diversifiable, i should no command a risk premium. As a resul, if currency speculaion involves sysemaic risk, speculaive reurns should be nonzero and are predicable. In his case, UIP will be violaed even if raional expecaions hold. Anoher line of research in he inernaional financial lieraure which has drawn a lo of aenions in recen years is he sudy of he ransmission of financial shocks/crisis across markes/counries, which has inroduced an imporan disincion beween he wo conceps of inerdependence and conagion. Masson (1998) argues ha here are hree main channels ha financial markes urbulence can spread from one counry o anoher. They are monsoonal effecs, spillovers and pure conagion effecs. Monsoonal effecs, or conagions from common causes end o occur when affeced counries have similar economic fundamenals or face common exernal shocks. For insance, several Asian counries shared common feaures such as a high reliance on foreign denominaed deb and a relaively sable exchange rae agains he U.S. dollar. Thus, he occurrence of a 3

5 crisis across several counries may be due o an iniial disurbance in oher places, and no due o he ransmission of a shock from one counry o anoher. The second ype of financial marke iner-linkages arises from spillover effecs, which may be due o rade linkages or financial inerdependence. For example, Asia counries end o compee in he same expor markes in he Wes as well as in similar producs, so a devaluaion of one currency has a negaive impac on he inernaional compeiiveness of oher counries. In addiional o rade links, spillovers may occur if differen counries are financial inerdependen if hey borrow from he same crediors. For example, a currency crisis in counry A reduces he abiliy of domesic borrowers o replay heir loans o ouside banks, which forces he foreign banks o rebuild heir capial by recalling some of heir loans, including loans made o borrowers in oher counries. Borrowers from counry B hen suffer from credi crunch caused by he impac of he currency crisis in counry A on heir crediors. The firs wo channels of financial crises can be caegorized as fundamenalsdriven crises since he affeced counries share some macroeconomic fundamenals, which implies ha he ransmission of financial crises is due o he inerdependence among hose counries and no necessarily due o conagion. The hird ransmission channel is he pure conagion effec. Conagion here refers o he cases where crisis in one counry riggers a crisis elsewhere for reasons unexplained by macroeconomic fundamenals. For insance, a crisis in one counry may lead crediors and invesors o pull ou from oher counries over which hey have a poor undersanding resuling from informaion asymmeries. The goal of his paper is o es simulaneously boh he exisence of ime-varying risk premium in explaining he predicable excess reurn puzzle and he pure conagion 4

6 effecs among Asian foreign exchange markes during he 1997 Asian crisis 5. Specifically, in his paper I define conagion as significan spillovers of counry-specific idiosyncraic shocks during he crisis afer economic fundamenals or sysemaic risks have been accouned for. In esing for conagion, is exisence depends on he economic fundamenals used. To conrol for he economic fundamenals, mos empirical sudies end o choose hose fundamenals arbirarily, such as by using macroeconomic variables, dummies for imporan evens, and ime rends. The problem wih hese conrol variables is ha conagion is no well defined wihou reference o a heory. To overcome his problem, I rely on an inernaional capial asse pricing model (ICAPM) in he absence of purchasing power pariy (PPP), which provides me a heoreical basis in selecing economic fundamenals. The economic fundamenals under ICAPM are he world marke and foreign exchange risks, so he evidence of conagion is based on esing wheher idiosyncraic risks- he par ha canno be explained by he world marke and foreign exchange risks, are significan in describing he dynamics of condiional mean and volailiy in foreign exchange markes during he crisis. The ICAPM used in his paper also provides anoher avenue o es he exisence of risk premium in foreign exchange markes since previous empirical sudies using consumpion-based asse pricing model o es he exisence of risk premium in explaining he predicable excess reurn puzzle have no been very successful. 6 5 To my knowledge, his is he firs paper o use Asian foreign exchange daa o invesigae he predicable excess reurn puzzle. 6 For example, Mark (1985), Cumby (1988), Kaminsky and Peruga (1990), Backus, Gregory and Telmer (1993) use an ineremporal asse pricing model (IAPM) o es he exisence of a ime-varying risk premium in foreign exchange markes. In his model he risk premium is due o consumpion risk measured by he covariance beween reurns and he marginal uiliy of money. The resuls from hese sudies are disappoining because he observable ingrediens in he risk premium models do no vary 5

7 In addiion o overcoming he drawback of arbirarily choosing economic fundamenals in esing conagion effec in previous sudies, in his paper I employ a differen mehodology o es he exisence of boh ime-varying risk premium and conagion. Specifically, I use a Mulivariae General Auoregressive Condiional Heeroscedasic in Mean (MGARCH-M) model o capure he ime dependencies in he second momen, a sylized propery found in mos financial ime-series, which has been ignored by mos empirical sudies on conagion 7. The MGARCH-M model adoped in his paper also overcomes he drawbacks in previous sudies in esing risk premium hypohesis in explaining he predicable excess reurns puzzle (e.g., Mark (1988), McCurdy and Morgan (1991)). Mark (1988) uses a single-bea CAPM o price he forward foreign exchange conracs from he poin of view of a U.S. invesor. He specifies he beas as ARCH-like process and esimaes he model joinly for four currencies using a generalized mehod of momens (GMM) procedure. His resuls show significan ime variaion for he beas and ess of he overidenifying resricions are no rejeced. However, as poined ou by Mark (1988), he GMM esimaor is robus, bu, in general, is no asympoically efficien. Consequenly, insead of using GMM esimaion, McCurdy and Morgan (1991) also apply he single-bea CAPM wih a bivariae GARCH sufficienly o explain he high degree of variabiliy in asse reurns wihou implausibly large esimaes of he coefficien of relaive risk aversion. (See Engel (1996)) 7 Previous empirical sudies on conagion can be caegorized by mehodology ino four groups: (1) he esing of significan increases in correlaion (Calvo and Reinhar (1996), Baig and Goldfajn (1999), Forbes and Rigobon (1998, 1999) and Park and Song (1999)); (2) he esing of significance in innovaion correlaion (Baig and Goldfajn (1999)); (3) he esing of significan volailiy spillover (Edwards (1998), Edwards and Susmel (1999)); (4) crisis predicion regression (Bae, Karolyi, and Sulz (2000), Eichengreen, Ross, and Wyplosz (1996), Kaminsky and Reinhar (2000), Rijckeghem and Weder (1999), Sachs, Tornell, 6

8 parameerizaion o price deviaions from UIP for five European currencies. They esimae heir model currency by currency, while Mark (1988) esimaes his model joinly across currencies, so he efficiency migh be sacrificed in McCurdy and Morgan s (1991) sudy. Moreover, heses wo sudies all assume ha PPP hold. Therefore, under he fully parameerized mulivariae model adoped in his paper, no only is he maximum efficiency gain reained in esing he risk premium hypohesis in explaining he predicable excess reurn puzzle, bu also some ineresing saisics are recovered, which are mosly ignored in previous sudies. 8 II. The Theoreical Moivaion We know ha he firs-order condiion of any consumer-invesor s porfolio opimizaion problem can be wrien as: E [ M R i, Ω 1] = 1, i = 1 N (1) where M is known as a sochasic discoun facor (SDF) or an ineremporal marginal rae of subsiuion (IMRS); R, is he gross reurn of asse i a ime and Ω 1 is marke i and Velasco (1996)). None of he conagion sudies menioned above explicily akes he ime dependencies in he second momen ino accoun. 8 Previous papers ha do no have much success in deecing ime-varying risk premia in foreign exchange markes using mulivariae GARCH approach include Giovannini and Jorion (1989) and Baillie and Bollerslev (1990). 7

9 informaion known a ime 1. Wihou specifying he form of M, equaion (1) has lile empirical conen since i is easy o find some random variable M for which he equaion holds. Thus, i is he specific form of M implied by an asse pricing model ha gives equaion (1) furher empirical conen (e.g., Ferson (1995)). Suppose M and have he following facor represenaions: R i, K M = a + β k Fk, + u (2) k=1 K r i, = α i + β ik Fk, + ε i, k= 1 i = 1 N (3) where r i, Ri, R0, = is he raw reurns of asse i in excess of he risk-free rae, R 0,, a ime, and E u F Ω ] = E[ u Ω ] = E[ ε F Ω ] = E[ ε Ω ] 0 [ k, 1 1 i, k, 1 i, 1 = i, k ; F k, are common risk facors which capure sysemaic risk affecing all asses r, including i M ; β ik are he associaed ime-invarian facor loadings which measure he sensiiviies of he asse o he common risk facors, while u is an innovaion and ε i, are idiosyncraic erms which reflec unsysemaic risk. The risk-free rae, R 0, 1, mus also saisfy equaion (1). E M R ] 1 (4) [ 0, 1 Ω 1 = Subrac Eq.(4) from Eq.(1), we obain 8

10 E [ M r i, Ω 1] = 0 i = 1 N (5) Apply he definiion of covariance o equaion (5), obaining: Cov( ri, ; M Ω 1) E [ ri, Ω 1 ] = i = 1 N (6) E[ M Ω ] 1 Subsiue equaion (2) ino equaion (6): β k E[ ri, Ω 1 ] = Cov( ri,, Fk, Ω 1 ) = λk, 1Cov( ri, ; Fk, Ω 1 ) E[ M Ω ] k 1 k (7) where λ k, 1 is he ime-varying price of facor risk. Equaion (7) is a general condiional muli-facor asse pricing model derived from he ineremporal consumpion-invesmen opimizaion problem. In empirical ess, he SDF is projeced ono five facors: he world marke porfolio and four currency reurns. 9 The selecion of hose five facors is heoreically jusified based on eiher he ineremporal CAPM of Meron (1973) or an inernaional version of CAPM in he absence of PPP developed by Adler and Dumas (1983). To exend domesic CAPM ino an inernaional seing, previous researchers assume ha eiher invesors have logarihmic uiliy or PPP holds. However, many empirical sudies have documened ha he violaion of PPP is a norm alhough PPP a bes ends o hold in 9 In his paper, I consider four Asian foreign exchange raes: Japanese yen, Hong Kong dollar, Singapore dollar, and New Taiwan dollar, so here are four currency risks plus one world marke risk. 9

11 he long run. In he absence of PPP resuling from eiher differen consumpion ases or violaion of he law of one price (LOP), invesors from differen counries face differen prices when holding he same asse. In his siuaion, inernaional asse pricing model will conain risk premia which are relaed o he covariances of asse reurns wih exchange raes, besides he radiional marke risk premium. 10 Therefore, a condiional muli-facor asse pricing model conaining world marke and foreign exchange risks (equaion (7)) seems o be reasonable and will be used o es risk premium hypohesis in foreign exchange markes. (e.g., Ferson and Harvey (1994), Dumas and Solnik (1995), and De Sanis and Gerard (1998), among ohers.) I can now rewrie he condiional mulifacor asse pricing model in equaion (7) as r j, = λ m. 1Cov( rj,, rm, Ω 1) + λc, 1Cov( rj, ; rc, Ω 1) + ε j, j = N c 1 (8) where m denoes world marke risk and c is he currency risk. 11 III. Economeric Mehodology The condiional ICAPM in equaion (7) has o hold for every asse. However, he model does no impose any resricions on he dynamics of he condiional second momens. Several mulivariae GARCH (MGARCH) models have been proposed o model he condiional second momens, such as he diagonal VECH model of Bollerslev, 10 See Solnik (1974), Sulz (1981, 1984) and Adler and Dumas (1983). 11 In his paper, he facors are marke porfolio and shor-erm currency deposis, which are raded asses, so we can replace F k, wih r k,. 10

12 Engle, and Wooldridge (1988), he consan correlaion (CCORR) model of Bollerslev (1990), he facor ARCH (FARCH) model of Engle, Ng, and Rohschild (1990), and he BEKK model of Engle and Kroner (1995). Among hese four popular MGARCH models, he BEKK model is beer suied for he purpose of his paper because i no only guaranees ha he covariance marices in he sysem are posiive definie, bu also allows he condiional variances and covariances of differen markes o influence each oher, which is very imporan for esing conagion in his paper. Alhough i is ease o undersand, he VECH model migh no yield a posiive definie covariance marix. FARCH assumes ha he covariance marix is driven by he condiional variance process of one porfolio (he marke porfolio), and his assumpion does no hold in his paper since he condiional covariance marix is assumed o be driven no only by marke porfolio bu also by foreign exchange reurns. As for he CCORR model, i resrics he correlaion beween wo asses reurns o be consan over ime, which is unlikely o hold as suggesed by Longin and Solnik (1995) and Karolyi and Sulz (1996). 12 As a resul, a BEKK srucure wih asymmeric volailiy effecs is seleced over he oher MGARCH specificaions o model he condiional second momens of asse reurns and o es conagion effecs among Asian foreign exchange markes. 13 Specifically, he dynamic process for he condiional variance-covariance marix of asse reurns is specified as: H ' ' ' ' ' ' = C C + A H 1 A + B ε 1ε 1 B + G η 1η 1 G (9) 12 Anoher mulivariae GARCH model proposed recenly by Kroner and Ng (1998) is General Dynamic Covariance (GDC) model. The GDC model is a hybrid of he CCOOR model srucure and he BEKK model srucure, so i also resrics he condiional correlaion beween asse reurns o be a consan alhough i is flexible enough o encompass he four mulivariae GARCH models discussed above. 13 The asymmeric volailiy effecs in variances and covariances have been documened in recen papers by, among ohers, Kroner and Ng (1998) and Bekaer and Wu (2000). 11

13 where H is N N ime-varying variance-covariance marix of asse reurns; C is resriced o be a N N upper riangular marix, and A, B, and G are N N free marices of unknown parameers, wih elemens c ij, a ij, b ij, and g ij. The N 1 vecor, η 1, capures he asymmeric impac ha he vecor of pas innovaions has on he condiional covariance marix in a manner similar o ha of Glosen e al. (1993), and is defined as: η = i, 1 ε if i, 1 ε i, 1 < 0, 0 oherwise. In his model he condiional variance and covariance of each asse reurn are relaed o pas condiional variances and covariances, pas squared residuals and cross residuals, and pas squared asymmeric shocks and cross-asymmeric shocks. One drawback of he asymmeric BEKK model is he larger number of parameers ha mus be esimaed. For a sysem of N equaions, ( 2 7 N + N ) here are 2 parameers. For example, a sysem of 5 equaions has 90 parameers. To keep he size of he parameer space manageable, I impose hree consrains. Firs, I assume ha A is a diagonal marix since previous sudies have shown ha he offdiagonal elemens in A end o be insignifican. Second, since he purpose of his paper is o es conagion effecs among foreign exchange markes, I assume ha he conagion-involailiy effecs only occur among foreign exchange markes hemselves, and no wih he world marke porfolio. Tha is, he off-diagonal elemens in B will be zero only for he las row and he las column if he world marke porfolio is he las asse. 14 Finally, I assume ha only he marke asymmeric shocks affec he variance and covariance of asse reurns. Kroner and Ng (1998) show ha he volailiy asymmery of boh small and large sock porfolios in he U.S. sems mosly from shocks in he large sock porfolio. 14 In esimaion, I resric B o be a diagonal marix during non-crisis period, so I can es wheher here is a significan conagion in volailiy during he crisis period. 12

14 Consequenly, i will be ineresing o see if he volailiy asymmery of marke porfolio, a large porfolio, has any effec on shor-erm currency deposi, a small porfolio. The parameer marices A, B, and G now have he following forms: a b11 b12 b13 b a b21 b22 b23 b24 0 A = 0 0 a ; B = b31 b32 b33 b34 0 ; a44 0 b41 b42 b43 b a b G = 0 0 g g g g g 55 This reduces he parameer space considerably while mainaining flexibiliy in modeling he dynamics of condiional second momens. For a sysem of 5 asses, here are 42 parameers including he parameers in marix C insead of 90. Under he assumpion of condiional normaliy, he log-likelihood o be maximized can be wrien as: T T TN 1 1 ' 1 ln L( θ ) = ln 2π ln H ( θ ) ε ( θ ) H ( θ ) ε ( θ ) (10) = 1 = 1 where θ is he vecor of unknown parameers in he model. Since he normaliy assumpion is ofen violaed in financial ime series, I use quasi-maximum likelihood esimaion (QML) proposed by Bollerslev and Wooldridge (1992) which allows inference in he presence of deparures from condiional normaliy. Under sandard regulariy condiions, he QML esimaor is consisen and asympoically normal and saisical inferences can be carried ou by compuing robus Wald saisics. The QML esimaes can be obained by maximizing equaion (10), and calculaing a robus esimae of he covariance of he parameer esimaes using he marix of second derivaives and he 13

15 average of he period-by-period ouer producs of he gradien. Opimizaion is performed using he Broyden, Flecher, Goldfarb, and Shanno (BFGS) algorihm. IV. Hypohesis Tesing Tesing Time-varying Risk Premium Many empirical sudies have shown ha he prices of risks are ime-varying. (e.g., Harvey (1991), Dumas and Solnik (1995), and De Sanis and Gerard (1997, 1998), among ohers.) This ime-varying price of risk is economically appealing in he sense ha invesors use all available informaion o form heir expecaions abou fuure economic performance, and when he informaion changes over ime, hey will adjus heir expecaions and hus heir expeced risk premia when holding differen risky asses. Therefore, o es ime-varying risk premium hypohesis, I allow no only he condiional second momens (covariance risks) o change over ime, bu also he prices of covariance risks o be ime-varying (equaion (8)). The dynamics of prices of risks are chosen according o he heoreical inernaional asse pricing model developed by Adler and Dumas (1983). In heir model, he price of world marke risk is a weighed average of he coefficiens of risk aversion of all naional invesors. Since he weighs measure he relaive wealh of each counry and if all invesors are risk averse, he world price of marke risk should be posiive. Thus, similar o Bekaer and Harvey (1995) and De Sanis and Gerard (1997, 1998) an exponenial funcion is used o model he dynamic of λ m, 1 and for he dynamics of λ c, 1, 14

16 a linear specificaion is adoped because he model does no resric he price of currency risk o be posiive. ' λ exp( ϕ z ) 1 (11) = m, 1 m λ ϕ z (12) = ' c, 1 c 1 where Z 1 is a vecor of informaion variables observed a he end of ime 1 and ϕ s are ime-invarian vecors of weighs. Thus, he price of each source of currency risk is assumed o be a linear funcion of he informaion variables in Z 1, and he price of world marke risk is assumed o be an exponenial funcion of informa ion variables in Z 1. Given he dynamics of prices of risks, I can hen es he ime-varying risk premium hypohesis by esing wheher he informaion variables in Z 1 are significan in addiion o significan GARCH parameers. Tesing Conagion in Mean and Volailiy To es wheher a counry s pas idiosyncraic shocks have significan impac on he oher counries condiion reurns (conagion in mean) during he crisis, I incorporae counry-specific pas innovaions ino equaion (8). Specifically, he equaion (8) can be modified as: r = λ ( + ε j, m. 1Cov rj,, rm, Ω 1 ) + λc, 1Cov( r j, ; rc, Ω 1 ) + dummy( d ijε i, 1 ) c i j j, ; i, j (13) 15

17 where "dummy" is a dummy variable, which is equal o one during Asian crisis and zero oherwise. 15 Thus, he conagion in mean hypohesis can be examined by esing wheher he coefficiens, d ij, are individually or joinly significan afer he sysemaic risks have been accouned for. To es conagion in volailiy hypohesis, we can es wheher he off-diagonal elemens in marix B are individually or joinly significan. For example, a es of null hypohesis ha b, is zero ( H 0 ) means ha here is no conagion in volailiy from i j 0 : b i, j = counry i o counry j. Similarly, a es of null hypohesis ha b, is zero for all i i j ( H b = 0; i 0 : i, j ) implies ha he condiional volailiy of counry j is no affeced by he oher counries idiosyncraic shocks. IV. Daa and Summary Saisics I analyze four Asian currency deposi raes: one-week Euroyen deposi rae ( JP ), one-week Hong Kong deposi rae ( HK ), one-week Singapore deposi rae (SG ), and 10- day Taiwan money marke rae (TA ). 16 The value-weighed Morgan Sanley Capial Inernaional (MSCI) world index (MSWRLD ) is proxied for world marke risk. 7-day Eurodollar deposi rae is used as condiionally risk-free rae o compue he excess reurns 15 I assume Asian crisis began in he firs week of July 1997 (July 4, 1997) and ended in he las week of June 1998 (June 26, 1998). 16 Ideally I would like o use ineres rae daa from oher Asia-Pacific counries such as Indonesia, he Philippines, Souh Korea, Thailand, and Malaysia ec., bu he shor-erm ineres rae daa for hose counries are no available from Daasream. 16

18 on he MSCI world index, and he four Asian currency deposi raes (or he deviaions from UIP). In paricular, he excess equiy reurns are compued as: r i, p us$ = ln( ) ln(1 + i 1 ) where p is he MSCI world oal reurn index (dividend p 1 included) a ime, and i is 7-day Eurodollar deposi rae known a ime 1. The US$ 1 excess currency reurns (or he deviaions from UIP) are compued as: r i, * s US$ = ln(1 + i 1) + ln( ) ln(1+ i 1 ) where s is he spo rae a ime expressed as s 1 domesic price (he U.S dollar) of one uni of Asian currency; i * 1 is he shor-erm Asian currency deposi rae known a ime 1. I selec a se of condiioning variables ha have been widely used in he inernaional asse pricing lieraure (e.g., Harvey (1991), Bekaer and Hodrick (1992), Ferson and Harvey (1993), Bekaer and Harvey (1995), and De Sanis and Gerard (1997, 1998), among ohers). They are excess dividend yield measured by he dividend yield on S&P 500 index in excess of he 7-day Eurodollar deposi rae ( DIV ), he change in 7-day Eurodollar deposi rae ( EURO ), he change in he U.S. erm premium, measured by he yield difference beween 10-year Treasury consan mauriy rae and 7-day Eurodollar rae ( USTP ), he U.S. defaul premium, measured by he yield difference beween Moody s Baa-raed and Aaa-raed U.S. corporae bonds ( USDP ), and a consan (CONSTANT ) The excess dividend yield ( DIV ) is highly correlaed wih he U.S. erm premium (USTP ), so similar o De Sanis and Gerard (1997, 1998) I use firs difference of he U.S. erm premium ( USTP ) as one of he insrumens. 17

19 Observaions are sampled a weekly inervals. The weekly daa ranges from January 2, 1987 o March 23, 2001, which is a 743-daa-poin series. However, I work wih raes of reurn and use he firs difference of condiioning variables, and finally all he condiioning variables are used wih a one-week lag, relaive o he excess reurn series; ha leaves 740 observaions expanding from January 23, 1987 o March 23, All he daa are exraced from Daasream. Table 1 presens summary saisics of he coninuously compounded excess world equiy reurns and currency reurns. As can be seen from Panel A, he MSWRLD has he highes mean reurns (0.075%) and highes sandard deviaion (2.112%). Comparing he performance of four currency reurns, he TA is he bes one wih he mean reurn of 0.02%, and he JP is he wors one wih a negaive mean reurn of 0.024%. Table 1 also repors skewness, excess kurosis, Bera-Jarque and Ljung-Box saisics. In mos cases, he index of kurosis and he Bera-Jarque es saisic srongly rejec he hypohesis of normally disribued reurns. The Ljung-Box es saisics for raw reurns ( LB (20) ) are significan a he 1% level in hree currencies, implying srong linear dependencies among hose reurns. For squared reurns, LB 2 (20) is significan a he 1% level for all he series, indicaing srong nonlinear dependencies in boh currency and equiy reurns. This is consisen wih he volailiy clusering observed in mos sock and foreign exchange markes: Large (small) changes in prices end o be followed by large (small) changes of eiher sign. The GARCH models used in his sudy are well known o capure his propery. 18

20 The uncondiional correlaion coefficiens for he condiioning variables are repored in Panel B of Table 1. All he correlaion coefficiens are below 0.5, indicaing ha he seleced variables conain sufficienly orhogonal informaion. VI. Empirical Evidence The quasi-maximum likelihood esimaion of he condiional ICAPM (equaion (13)) is repored in Table 2. The hypohesis ess regarding he prices of risks and he predicabiliy of condiioning variables are presened in Table 3. The hypohesis ess concerning he conagion in mean and volailiy are shown in Table 4. Finally, summary saisics concerning he sources of risk premia and diagnosic es saisics for he sandardized residuals are repored in Table 5. Evidence of Time-varying Risk Premium Firs, considering he es resuls for he exisence of ime-varying risk premium. The resuls are very encouraging. For example, he join null hypohesis of zero prices of marke and currency risks is srong rejeced by Wald saisic (Wald = ) wih a p- value of zero. The join null hypohesis of consan prices of marke and currency risks is also significanly rejeced (Wald = ). Nex, he join null hypohesis of consan prices of currency risks is srongly rejeced by Wald es (Wald = ), and he join null hypohesis of consan price of marke risk is also rejeced (Wald = ). These es resuls imply ha boh marke and currency risks are no only priced bu also ime 19

21 varying. Finally, he null hypohesis of consan price of currency risk for each currency is esed individually, and Wald es saisic rejecs he null a he 1% level in every case, implying ha all four exchange raes are sources of he ime-varying currency risk premium. These resuls are consisen wih he findings of Dumas and Solnik (1995) and De Sanis and Gerard (1998). 18 The condiioning variables seleced in his paper are all very useful in predicing he dynamics of he risk prices as can be seen from he hypohesis ess (#10 - #13) repored in Table 3. Tha is, he null hypohesis of zero predicabiliy of condiioning variable is srongly rejeced by Wald saisic a he 1% level in all cases. Alhough saisically significan ime-varying risk premia are found, an ineresing quesion o ask is o wha exen hese predicable risk premia are economically significan. In answering his quesion, I compued pseudo 2 R saisic calculaed as he raio beween he sum of squared fied value of he risk premium and he sum of squared acual risk premium (deviaions from UIP). As can be seen from Table 5, he repored pseudo 2 R s range from 4.54% for JP o % for HK, wih an average of %, which is significan higher han hose repored in similar sudies. 19 These relaively high pseudo- R 2 s indicae ha he model perform very well in explaining he deviaions from UIP. Based on hese empirical resuls, we can safely conclude ha he predicable excess reurn puzzle is due o he exisence of ime-varying risk premia, and he sources of he risk premia come no only from marke risk, bu also from currency risk. 18 Boh Dumas and Solnik (1995) and De Sanis and Gerard (1998) use excess reurns on one-monh European currency deposi raes o proxy for currency risks; however, in his paper one-week Asian currency deposi raes are employed o es he exisence of ime-varying currency risk premia. 19 The average pseudo- R 2 s in similar sudies are only abou 2.22% in McCurdy and Morgan (1991), and 4.06% in De Sanis and Gerard (1998). 20

22 Evidence of Conagion in Mean and Volailiy Nex, considering he es resuls of conagion effecs on he firs momen of foreign exchange reurns, i can be seen from Table 4 ha hese effecs are saisically significan for all four markes. For example, he join null hypohesis of no conagion in reurn shocks for JP ( H0 : d, = 0; i = HK, SG TA ) during he crisis is srongly rejeced i JP, by Wald saisic (Wald = ) a he 1% level. The same rejecion also applies o he oher hree markes. To find ou he sources of conagion in reurn shocks for JP, we can examine he individual significance of conagion-in-mean parameer, d i, JP, repored in Table 2 based on robus sandard errors. Basically, he curren reurns in JP are negaively affeced by pas reurn shocks in he HK ( d, = ). Similarly, he HK JP curren reurn shocks in HK are due o he pas reurn shocks in JP ( d JP, HK = 0.012) and SG ( d, = ). For he case of SG, is curren reurn shocks basically come from SG HK he pas reurn shocks in JP ( d JP, SG = ). Finally, he curren reurns in TA are influenced by HK ( d HK, TA = ) and SG ( SG TA d, = 0.234). By examining he significance of hose individual conagion-in-mean coefficiens, we can see ha basically all he conagion-in-mean effecs originae from hree markes: JP, HK, and SG, and none from TA. Alhough conagion-in-mean effecs are saisically significan, a more ineresing quesion o ask is o wha exen hese effecs are economically significan in erms of generaing abnormal profis afer ime-varying risk premia have been accouned for. To answer his quesion, I compue percenage of variaion in each one of he four foreign exchange reurns ha can be explained on he basis of pas informaion generaed by JP, HK, and SG. The percenages no repored here range from 1.115% for JP o 5.592% for TA, wih an average of 3.059%. These percenages are very small, and if 21

23 ransacion coss are aken ino accoun, hen we can safely conclude ha he four markes are weak-form efficien. Turning o conagion effecs on he condiional volailiy of foreign exchange reurns, i can be seen from Table 4 ha he join null hypohesis of no conagion in volailiy shocks during he crisis is srongly rejeced by Wald saisic in all cases. To examine he possible sources of volailiy shocks, we can examine he individual significance of conagion-in-volailiy parameer, b i, j, repored in Table 2 based on robus sandard errors. Basically, he condiional variance of each marke is affeced posiively by is pas innovaions in all cases. Tha is, he diagonal elemens in marix B are all significan a he 1% level. As for he off-diagonal elemens, JP is affeced by he pas innovaions in HK ( b HK, JP = 0.010); HK is affeced by pas innovaions in JP ( b JP, HK = 1.638) and TA ( b TA, HK = 8.593); SG is affeced by he pas innovaions in JP ( b JP, SG = 0.170), HK ( b HK, SG = ), and TA ( b TA, SG = ), and finally TA is influenced by HK ( b HK, TA = 0.068), and SG ( b SG, TA = 0.573). Overall, he conagion effecs in condiional second momens are very significan in Asian foreign exchange markes, and hey occur in a mulidirecional way, wih HK being he dominan one since i affecs all he oher hree markes. Table 2 also presens he parameer esimaes ( g m, j ) of asymmeric volailiy shocks from he world equiy marke ( MSWRLD ). 20 The parameers are all significan a he 1% level excep TA, implying ha marke asymmeric shocks have significan impac on he condiional volailiy of Asian foreign exchange 20 To save space, Table 2 does no repor he parameer esimaes in marices C and A of condiional variance process since hose esimaes are no paricularly ineresing in his paper, bu heir resuls are available upon reques. 22

24 markes. 21 However, his marke asymmeric volailiy shocks affec each marke differenly. For insance, hey affec HK in a posiive way ( g, = 0.049), bu in a negaive way for JP ( g m, JP = ) and SG ( g m, SG = ), implying ha negaive world equiy reurn shocks induce higher condiional volailiy in HK han posiive reurn shocks, bu hey reduce he condiional volailiy in JP and SG. mhk Economic Explanaions As discussed in inroducion, he pure conagion effec may arise from informaion asymmeries in financial markes. As poined ou by Calvo and Mendoza (2000), invesor may downplay naional specificiies and asymmeries, and consider several counries in a region as subsanially homogenous. A new piece of informaion concerning one counry can hen be exrapolaed and applied o he enire region. Calvo and Mendoza (2000) also argue ha as he number of counries in a porfolio increases, i is increasingly cosly o acquire counry-specific informaion which forces he porfolio manager o follow he lead of he invesor mos likely o be informed of he prospecs of one paricular counry a phenomenon called herding behavior. For example, considering wo porfolio managers invesing in asses issued by counry A and B. Because of informaion processing coss, he wo managers choose o focus heir analyical effors on, respecively, counry A and counry B. Due o her limied knowledge of counry B, counry A s specialis deermines he shares of counry B s asses in her porfolio by replicaing he behavior of counry B s 21 De Sanis, Gerard, and Hillion (2000) finds ha marke asymmeric shocks are no very srong in inernaional equiy markes, bu hey do no es wheher hey are significan for foreign exchange markes. 23

25 specialis. The key aspec of such as sraegy is ha counry A s specialis observes he acion bu no he ulimae moivaion of counry B s specialis. For insance, a sale of counry B s asses by counry B s specialis may be he resul of bad news abou counry B, or he liquidiy demand from invesors. If he sale is due o liquidiy demand, hen he mimicking behavior of counry A s specialis will cause a generalized capial ouflow from counry B, even hough here is no deerioraion in counry B s fundamenals. To relae he herding behavior argumen o he significan conagion found in his paper, we can hink of he porfolio manager as a money marke muual fund manager. When a shock his one counry in Asia, fund manager would wan o pull ou of heir posiions because he cos of underperforming he group average is much higher han he benefi of ouperforming he group, which leads o large excess co-movemens wihin Asia. Residual Diagnosics To access he fi of he condiional ICAPM wih MGARCH specificaion, Ljung- Box ess are performed on sandardized residuals (LB ) and squared sandardized 2 residuals ( LB ). Under he mulivariae framework, he sandardized residuals a ime is compued as Z = ε, where H 1/ 2 1/ 2 H is he inverse of he Cholesky facor of he esimaed variance-covariance marix. The resuls of ess for serial correlaion up o 20 lags are repored in Table 5 along wih Bera-Jarque ( B J ) es saisics. LB and 2 LB saisics of order 20 show no serious linear and nonlinear dependencies for he sandardized residuals of foreign exchange reurns, wih one excepion in which LB 2 (20) is significan a he 1% level for HK. As for B J es saisics, hey are all significan, indicaing deparures from normaliy, which jusifies he use of robus sandard errors 24

26 compued from using he quasi-maximum likelihood mehod of Bollerslev and Wooldridge (1992). Overall he MGARCH(1,1)-M specificaion fis he daa very well. The Size of Risk Premia One advanage of modeling he condiional second momens via mulivariae GARCH approach is ha i enables one o recover some ineresing saisics such as condiional volailiy, and, more imporanly, he size of differen risk premia. These ineresing saisics will no be available if one leaves he condiion second momens unspecified such as he pricing kernel approach employed by Dumas (1993) and Dumas and Solnik (1995). 22 Table 5 repors hose saisics. For example, he prediced oal risk premium is measured by TRP λ h jc, ; j = JP, HK, SG, TA (14) j, = m, 1h jm, + λc, 1 c and ranges from % for JP, % for SG, % for HK, and % for TA, o 0.033% for MSWRLD. The TRP j, can be decomposed ino wo componens: currency risk premium ( CRP, ) and marke risk premium ( MRP, ). The currency risk premium is measured by j j CRP = λ h jc, ; j = JP, HK, SG, TA (15) j, c, 1 c 22 See he commens provided by Campbell Harvey in Dumas (1993). 25

27 and he marke risk premium is measured by = λ ; j = JP, HK, SG, TA (16) MRP j, m, 1h jm, The prediced oal risk premia are basically dominaed by he currency risk premia excep MSWRLD, which is dominaed equally by boh world marke risk and currency risk. For insance, he currency risk premium is % for JP, % for HK, % for SG, and % for TA. Furhermore, he dynamics of prediced imevarying risk premium in foreign exchange markes are mainly driven by he ime variaion of currency risk prices because boh he sample means and sandard deviaions of imevarying risk prices are greaer han hose of condiional volailiies. These saisics poin ou he imporan role of ime-varying price of risk relaive o he condiional volailiy in describing he dynamics of asse reurns. A useful complemen o Table 5 is o display he ime-series plos of hose ineresing saisics. Figure I conain plos of acual risk premia (deviaions from UIP) and prediced risk premia. I can be seen ha he dynamics of he prediced risk premia follow very closely o hose of acual risk premia, especially during he period of Asian crisis. These close resemblances have been confirmed by he relaively high pseudo- saisics repored in he las row of Table 5. Figure II presen he plos of ime-varying prices of currency risks and condiional volailiies. As can be seen from he plos, he prices of four currency risks flucuae significanly beween posiive and negaive values and range from o for JP, o for HK, o for SG, and o for TA. However, he variaion of condiional 2 R 26

28 volailiy for each marke is relaively small compared o hose of currency risk prices, bu i increases significan during he 1997 Asian crisis for all four markes. VI. Summary and Concluding Remarks In his paper, I sudy he ime-varying prices of risks and condiional volailiies in four Asian foreign exchange markes in an aemp o provide a new evidence of imevarying risk premium in explaining he predicable excess reurn puzzle. I also aemp o es wheher here are conagion effecs in boh condiional means and volailiies of hose markes during he 1997 Asian crisis. To derive a measure of he risk premium, I apply a condiional version of inernaional CAPM (ICAPM) in he absence of PPP, and he model is esimaed and he parameer resricions are esed based on he asse pricing heories. To incorporae ime-varying feaure of he risk premium ino he model, I allow no only he second momens of asse reurns o change over ime by uilizing MGARCH-M modeling sraegy, bu also he prices of risks o evolve hrough ime based on some prespecified condiioning variables. Esimaion resuls show significan ime-varying risk premia in he deviaions from UIP, and hese risk premia mainly compensae currency speculaors for bearing no jus marke risk bu currency risk. This empirical evidence implies ha an inernaional asse pricing model under PPP would no deliver economically significan risk premia in foreign exchange markes. The resuls also indicae ha he dynamics of foreign exchange reurns are mainly due o he ime-variaions of currency risk prices, implying ha incorporaing ime-varying prices of risks ino he asse pricing model is more imporan 27

29 han jus modeling he condiional volailiies of asse reurns. Overall, he condiional ICAPM wih MGARCH-M srucure is able o explain/predic on average more han 26% (26.138%) of he reurn variaions in foreign exchange markes, a very high reurn predicabiliy compared o previous sudies. Therefore, we can safely conclude ha he ime-varying risk premium is a very srong candidae in explaining he predicable excess reurn puzzle since he risk premia deeced in his paper are no only saisically significan bu also economically significan. As for he ess of conagion, I find srong pure conagion effecs in boh he condiional means and volailiies of foreign exchange markes afer sysemaic risks have been accouned for. Specifically, he conagion-in-mean effecs are mainly driven by he pas innovaions in Japan, Hong Kong, and Singapore. As for conagion in volailiy, he lead/lag relaionships appear o be mulidirecional wih Hong Kong playing he dominan role in generaing conagion effecs a volailiy level since all he oher hree markes are significanly influenced by he pas innovaions in Hong Kong. Finally, marke asymmeric volailiy shocks are also found o be significan for Japan, Hong Kong, and Singapore. 28

30 References Adler, M. and B. Dumas, 1983, Inernaional porfolio choice and corporae finance: A synhesis, Journal of Finance 38, Bae, K.-H., G. A. Karolyi, and R. Sulz, 2000, A New approach o measuring financial conagion, NBER Working Paper, No Backus, D.K., A.W. Gregory and C.I. Telmer, 1993, Accouning for forward raes in markes for foreign currency, Journal of Finance 48, Baig, T. and I. Goldfajn, 1999, Financial marke conagion in he Asian Crisis, IMF Saff Papers, 46, Baillie, R.T. and T. Bollerslev, 1990, A mulivariae generalized ARCH approach o modeling risk premia in forward foreign exchange rae markes, Journal of Inernaional Money and Finance 9, Bekaer, G. and C.R. Harvey, 1995, Time-varying world marke inegraion, Journal of Finance 50, Bekaer, G. and R.J. Hodrick, 1992, Characerizing predicable componens in excess reurns on equiy and foreign exchange markes, Journal of Finance 47,

31 Bekaer, G. and R.J. Hodrick, 1993, On biases in he measuremen of foreign exchange risk premiums, Journal of Inernaional Money and Finance 12, Bekaer, G. and G. Wu, 2000, Asymmeric volailiy and risk in equiy markes, Review of Financial Sudies 13, Bollerslev, T., R. F. Engle and J. M. Wooldridge, 1988, A capial asse pricing model wih ime-varying covariance, Journal of Poliical Economy 96, Bollerslev, T. and J. Wooldridge, 1992, Quasi-maximum likelihood esimaion and inference in dynamic models wih ime varying covariances, Economeric Review 11, Calvo, G. A. and E. G. Mendoza, 2000, Raional herd behavior and he globalizaion of securiies marke, Journal of Inernaional Economics 51, Calvo, S. and C. R. Reinhar, 1996, Capial flows o Lain America: Is here evidence of conagion Effecs?, in Privae Capial Flows o Emerging Markes, ed. by G. A. Calvo, M. Goldsein, and E. Hochreier. Insiuion for Inernaional Economics: Washingon D.C. Cumby, R.E., 1988, Is i risk? Explaining deviaions from uncovered ineres rae pariy, Journal of Moneary Economics 22,

32 De Sanis, G. and B. Gerard, 1997, Inernaional asse pricing and porfolio diversificaion wih ime-varying risk, Journal of Finance 52, De Sanis, G. and B. Gerard, 1998, How big is he premium for currency risk?, Journal of Financial Economics 49, De Sanis, G., B. Gerard and P. Hillion, 2000, The relevance of currency risk in he EMU, mimeo, UCLA. Dumas, B., 1993, A es of he inernaional CAPM using business cycles indicaors as insrumenal variables, in J. Frankel, Eds.: The inernaionalizaion of equiy markes (universiy of Chicago Press, Chicago, IL). Dumas, B. and B. Solnik, 1995, The world price of exchange rae risk, Journal of Finance 50, Edwards, S., 1998, Ineres Rae Volailiy, Capial Conrols and Conagion, NBER Working Paper, No Edwards, S., and R. Susmel, 1999, Ineres rae volailiy in emerging markes: Evidence from he 1990s, mimeo, UCLA and Universiy of Houson. Eichengreen, B., A. K. Rose, and C. Wyplosz, 1996, Conagious currency crises, NBER Working Paper, No