RETHINKING FORWARD AND SPOT EXCHANGE RATES IN INTERNATIONSAL TRADING

Transcription

1 REHINKING ORWARD AND PO EXCHANGE RAE IN INERNAIONAL RADING Guan Jun Wang, avannah ae Universiy ABRAC his sudy uses alernaive esing mehods o re-examines he relaion beween he forward exchange rae and corresponding fuure spo rae from boh perspecives of he same currency pair raders using boh direc and indirec quoaions in empirical sudy as opposed o he convenional logarihm regression mehod, from one side of raders (ofen dollar sellers) perspecive, using one way currency pair quoaion (ofen direc quoaion). Mos of he empirical esing resuls in his paper indicae ha he forward exchange raes are downward biased from he dollar sellers perspecive, and upward biased from he dollar buyers perspecive. he paper furher conends ha non-risk neuraliy assumpion may poenially explain he exisence of he bias. JEL Classificaions: 3, 37, C2 INRODUCION Any inernaional ransacion involving foreign currency exchange is risky due o economic, echnical and poliical facors which can resul in volaile exchange raes hus hamper inernaional rading. he forward exchange conrac is an effecive hedging ool o lower such risk because i can lock an exchange rae for a specific amoun of currency for a fuure dae ransacion and hus enables raders o calculae he exac quaniy and paymen of he impor and expor prior o he ransacion dae wihou considering he fuure exchange rae flucuaion. However hedging in he forward exchange marke is no wihou cos, and he real coss are he differenial beween he forward rae and he fuure spo rae if he fuure spo rae urns ou o be favorable o one pary, and oherwise, gain will resul. Because of he disinguishing feaure of he symmericiy in foreign exchange marke, forward raes are expeced o neuralize fuure exchange rae risk for boh paries (sellers and buyers of he same currency), and o be fair unbiased esimaors of corresponding fuure spo raes. If he forward rae was an unbiased predicor of he fuure spo rae, he real coss of hedging would be near zero in he long run. Ye, he cos of hedging were ofen found o differ significanly from zero by he inernaional raders, and hese resuls carry imporan implicaions for firms engaged in inernaional rade 09

2 concerning wheher forward conrac should be used. And he relaion beween he forward exchange rae and he corresponding fuure spo rae is also of equally grea concern for academic scholars, porfolio managers, and policy makers. ama (984) indicaes he forward exchange rae is he marke deermined cerainy equivalen of he fuure spo exchange rae, and Chiang (988) indicaes ha he forward rae is an unbiased predicor of he fuure spo rae since i fully reflecs available informaion abou exchange rae expecaions. However, numerous empirical esing resuls fail o suppor he unbiasedness forward exchange rae Hypohesis. hough i is well known ha exchange rae beween wo currencies can be quoed in wo ways: direc quoaion which measures he value of per uni of U dollar in foreign currency and indirec quoaion which measures he value of per uni of foreign currency in U dollar, and he exchange rae expressed in direc quoaion is he reciprocal of he exchange rae expressed in indirec quoaion, prior empirical research examines he relaion beween he forward and corresponding fuure spo exchange rae solely from dollar sellers perspecive from which direc quoaions are used, or dollar buyers perspecive from which indirec quoaions are used, bu no he boh, and risk neuraliy assumpion is imposed on eiher dollar sellers or dollar buyers. his paper uses alernaive esing mehod o re-examines he relaion beween he forward exchange rae and corresponding fuure spo rae from boh perspecives of he same currency pair raders using boh direc and indirec quoaions in empirical esing as opposed o he convenional one side of raders (ofen dollar sellers) perspecive using one way currency quoaion. he reminder of his paper is organized as follows: he nex wo secions discuss forward rae deerminaion, spo rae and uncovered ineres pariy. he fourh ecion provides a brief review of he lieraure on he esing mehods for forward exchange rae unbiasedness hypohesis. ecion 5 suggess alernaive esing mehods. ecion 6 presens esing resuls from boh convenional esing mehods and alernaive esing mehod suggesed by his paper. ecion 7 discusses forward rae unbiasedness hypohesis from boh perspecives of same currency pair raders. ecion 8 concludes. ORWARD EXCHANGE RAE DEERMINAION he deerminaion of forward rae should depend upon he ineres raes beween he money markes of he wo counries, base counry where he base currency is used, and foreign counry where he foreign currency is used. ince invesors have he choice of earning an annual (coninuous) domesic ineres rae, r D, on domesic deposis, or convering heir domesic currency a he spo exchange rae, 0, earning an annual (coninuous) foreign ineres rae, r, on foreign deposis, and hen exchanging he foreign currency for domesic currency a he negoiaed forward, exchange rae, 0, he reurns on he wo alernaives should be he same o eliminae he arbirage opporuniies. herefore, an invesor saring wih one uni of domesic currency can eiher accumulae r D e unis domesic currency a ime, or he or she can exchange one uni of domesic currency now a he spo exchange rae for 0 0

3 r unis of foreign currency, hen deposiing in a foreign bank o accumulae 0 e unis of foreign currency a ime, and hen reconvering ino domesic currency a he negoiaed forward exchange rae e 0,, and he following condiion mus be me: r D = () r 0 e / If he above condiion did no hold, profiable marke arbirage opporuniies could be exploied wihou incurring any risks. hus forward rae should be deermined as 0, 0, ( r rd ) = 0e (2) PO EXCHANGE RAE AND UNCOVERED INERE PARIY By an agreemen made in 944 a he Breon Woods conference, exchange raes beween he major currencies were fixed. ince 970, he cenral banks have allowed marke forces o deermine exchange raes. An invesor wih one uni of domesic currency have he opporuniy o leave his/her foreign currency posiions uncovered by convering one uni of domesic currency now a he spo rae ino 0 invesing in foreign asses o accumulae r 0 e unis of foreign currency a ime, and hen reconvering ino domesic currency a spo exchange rae value of. ince he is unknown a presen and so he araciveness of holding an uncovered posiion mus be assessed in erms of he probabiliies of differen oucomes for. he assumpion of uncovered ineres pariy posulaes ha markes will equilibrae he reurn on he domesic currency asse wih he expeced value of spo rae a ime, E, of he yield on an uncovered posiion in foreign currency, ha is, r D r e = 0 e / E (3) his is equivalen o Combing (2) and (4) resuls in E = e ( r rd ) 0 (4) 0, = E (5) One should noe ha he expeced value of domesic currency of uncovered posiion, E 0 e r, is greaer han r D e, ha is,

4 0, E > (6) because risk incurred in uncovered posiion. (6) can be generalized o, E > (7) for any and. he Uncovered Ineres Pariy suggess ha forward exchange rae should be an unbiased esimaor of corresponding spo exchange rae. Why do numerous empirical resuls fail o suppor unbiased forward exchange rae hypohesis? o answer his quesion, he firs approach of his manuscrip is o examine boh he convenional esing mehods and he assumpions from which he forward unbiasedness hypohesis is derived. CONVENIONAL EING MEHOD here exiss a large body of lieraure on wheher he forward exchange rae is an unbiased predicor of corresponding fuure spo exchange rae from foreign currency invesors (sellers of dollar) poin of view under risk neuraliy assumpion. he earlies sudies (Bradford 977, renkel, 980, Levich, 979) ofen esed he forward unbiasedness hypohesis of (5) by regressing he log of he spo rae a ime period n on he one-period lagged log of he forward rae. ha is s = α + β + ε (8) n f n where s n = log n, f n- = log (n-),n, and is ime inerval. his is equivalen o s n+ = + βf n + ε n+ n α (9) he join hypohesis ha he consan erm does no differ from zero, he coefficien on he one-period lagged forward rae does no significanly differ from one, and ha he error erm is free of serial correlaion, ha is, α=0, β=, and n whie noises, is formulaed. Regression equaion (9) has been referred o as he level specificaion. he resuls of hese sudies generally suppor he forward rae unbiasedness hypohesis in he sense ha he regression ypically yields a coefficien close o uniy. Due o he non-saionary properies of he log spo and he log forward raes, ess based on a level regression of he log fuure spo rae on he log forward rae resuled in spurious regression problems. his led laer researchers (John 98, ama 984, renkel and roo 989, arno e al 202) o adop a difference version of he log level regression in which he log curren spo rae is subraced from he one period fuure log spo and he log forward rae. hus he regression of he change in he log of he spo exchange rae on he forward discoun (expressed in log form) is considered: 2

5 s n+ sn = + β ( f n sn ) + ε n+ α (0) he es given by eiher (9) or (0) is equivalen o assuming Es n+ = f n, ha is E log (n+) = log n,(n+) () Regression based ess of forward unbiasedness hypohesis using equaion (0) have performed very poorly he regressions have almos universally shown a negaive coefficien which is usually saisically significan, raher han a value of uniy. he empirical failure of he forward unbiasedness hypohesis has been a puzzle o economiss working in inernaional finance ever since he work of ama (984). As discussed in ecion 2, under uncovered ineres pariy assumpion, equaion (5) can be derived and generalized o E (n+) = n,(n+) (2) However, convenional ess are based on equaion () which differs from equaion (2). ALERNAIVE EING MEHOD As menioned earlier, forward exchange rae unbiasedness hypohesis should be saed ha E =, (3) where + is he spo rae a ime and, + is he lagged forward rae a ime. he simples approach o evaluae he validaion of E =, is o regress he spo rae a ime on he ime lagged forward rae a ime. ha is = α + β, + ε n (4) he join hypohesis can be formulaed as follows: he consan erm does no differ from zero, he coefficien on he lgged forward rae does no significanly differ from one, and ha he error erm is free of serial correlaion, ha is, α=0, β=, and n whie noises. However, he variables in he level form (he fuure spo and curren forward exchange raes) are non-saionary I(), as can be seen in able which provides descripive saisics for he spo exchange rae for wo currencies, Canadian Dollar and New Zealand Dollar. Obviously he normaliy assumpion for he spo rae is violaed, hus, ess based on a regression of he fuure spo rae on he forward rae can resul in spurious regression problems or so-called uni roo problem. o overcome he spurious regression problems, his paper also adops a difference version in which he curren spo rae is subraced from he one period fuure spo and he forward rae. n+ n = + β ( n n ) + ε n+ α (5) 3

6 he es given by (5) is equivalen o assuming E =,. Anoher 0alernaive is o es, = α + ε for he null hypohesis H 0 : α = 0. able 2 provides descripive saisics for he difference of spo exchange rae for wo currencies, Canadian Dollar and New Zealand Dollar. he resuls shown in able and able 2 indicae ha he difference of spo exchange rae is beer conformable wih normaliy assumpion, which also conformed in igure showing he hisogram of he level spo rae and he difference of he spo rae. (6) EMPIRICAL EING REUL he four exchange markes, Canadian dollar, New Zealand dollar, Ausria dollar and Euro dollar, are examined in his paper. he daa employed is daily daa of one monh, hree monhs, six monhs and welve monhs forward and spo exchange raes quoed in foreign currency unis per U.. dollar (direc quoaion) which spanned from ebruary 995 o Augus 200 wih nearly 4000 observaions. All daa were obained from Bloomberg. he regression resuls of equaion (5) were repored in able 3. As can be seen in able 3, null hypohesis H 0 : α = 0 and β = of regression (5) is rejeced in all cases. o reinforce hese resuls, he esimaion resuls of he alernaive regression equaion:, = α + ε, for he null hypohesis H : α 0, is also 0 = repored in able 6 or comparison purposes, ables 4 and 5 repor regressions of equaion (9) and (0). As can be seen in ables 4 and 5, he ess of he convenional regression equaions are consisen wih hose of previous sudies, such as Boohe and Longworh (986), Cumby and Obsfeld (984), ama (984) Maynard and Phillips (200), roo and haler (990) in showing ha relaion (8) is decisively rejeced for all cases. RIK NEURALIY AUMPION Many financial models, such as opion pricing models, are derived under he risk neuraliy assumpion which is quie reasonable. Does he same assumpion hold in foreign exchange markes? Differen from oher markes, in foreign exchange markes, boh sellers of dollar (foreign currency invesors) and buyers of dollar (dollar invesors) are equally involved and he symmeries of he foreign exchange marke are he key feaure ha disinguishes his marke from all ohers. he analysis conduced in ecion 2 is purely from he perspecive of sellers of dollar (foreign currency invesors). Wha would be he resuls if he poin of view of he dollar buyers had been aken? o answer his quesion, he same analysis needs o be conduced from he perspecive of dollar buyers. 4

7 Assume one uni of counry A (domesic counry from counry A invesors perspecive) currency can be exchanged for unis of counry B (foreign counry from counry A invesors perspecive) currency a ime, hen one uni counry B (domesic counry from counry B invesors perspecive) currency can be exchanged for Counry A (foreign counry from counry A invesors perspecive) currency. Assume ime forward rae a ime from counry A invesors perspecive is, + which means forward conrac insures one uni counry A currency o be exchanged o +, unis of counry B currency, or one uni of counry B currency o be exchanged o, + unis of counry A currency. As argued earlier, o eliminae arbirage opporuniy from boh invesors perspecives, equaion e, + mus saisfy he following ( r rd ), = (7) where r D is counry A s annualized ineres rae, and counry B s annualized ineres rae. Denoe = which is he exchange spo rae expressed as per uni of foreign currency. hus under Uncovered Ineres Pariy assumpion, = E 0, (8) Can be obained, where 0, = which is he forward rae expressed as per uni 0, of foreign currency. herefore = E (9) 0, can be obained. I hus has been shown, under risk neuraliy assumpion for boh sellers of dollar (foreign currency invesors) and buyers of dollar (dollar invesors), ha 0, = E and = E hold simulaneously, which violae Jensen s Inequaliy 0, 5

8 which saes ha he expeced value of a sricly concave funcion ( f(x) = x ) of a random variable is sricly less han same convave funcion of expeced value of he random variable. hus one can conclude in foreign exchange markes, he riskneural probabiliy measure for boh sellers of dollar (foreign currency invesors) and buyers of dollar (dollar invesors) is no (necessarily) an accurae model for he price processes of raded asses like currencies, raher, i is imposed by he marke. If risk aversion assumpion is imposed on boh invesors, because of risk premium, and 0, < E (20) < E (2) 0, should hold. (20) and (2) can be generaed o (22), < E and which resul in < E, (23) E >, > (24) E or any and. hus wih he absence of risk neuraliy assumpion for some paricipans in foreign exchange marke, forward exchange rae should no be expeced o be an unbiased esimaor of corresponding spo rae. Because of risk premium, he expeced fuure corresponding spo rae should be higher han he forward rae as shown in (20) and (2). esing (22) and (23) is equivalen o esing and µ = E > (25), 6

9 µ = E, = E > (26), he same four exchange markes which are Canadian Dollar, New Zealand Dollar, Ausria Dollar and Euro Dollar are again used for he empirical esing. he daase consiss of spo exchange rae daa and one monh, hree monhs, six monhs and welve monhs forward exchange rae daa covering he period January 995 o 200. he following regression es is performed for (25) H 0 : <= vs. H : α and >, = α + ε (27) =, = β + ξ (28) or (26) under H 0 : >= vs. H : β < he regression resuls are repored in ables 6 & 7. As can be seen in ables 6 & 7, he empirical ess produce mixed resuls: able 6 shows he resuls from sellers of dollar s perspecive, in which case he exchange raes are expressed as per uni of U dollar, excep for Canadian dollar for U dollar (Canadian dollar/u dollar) forward raes and 6-monh and 2-monh Euro dollar for U dollar (Euro dollar/u dollar) forward raes, forward exchange raes (expressed as per uni of U dollar ) are downward biased esimaors of corresponding fuure spo raes; Canadian dollar/u dollar forward exchange raes are upward biased esimaors of corresponding spo raes, and he hypohesis ha -monh and 3-monh Euro dollar/u dollar forward raes are unbiased esimaors of corresponding fuure spo raes canno be rejeced. able 7 shows he resuls from he buyers of U dollar s perspecive, in which case he exchange raes are expressed as per uni of foreign currency. Excep for U dollar for Canadian dollar (U dollar/canadian dollar) forward raes and U Dollar for Euro dollar (U dollar/euro dollar) forward raes, forward exchange raes (expressed as per uni of foreign currency ) are upward biased esimaors of corresponding + fuure spo raes; U dollar/canadian dollar forward exchange raes are downward + 7

10 biased esimaors of corresponding spo raes; 3-monh U dollar/euro dollar forward raes are downward biased esimaors of corresponding fuure spo raes and 2-monh U dollar/euro dollar forward raes are upward biased esimaors of corresponding fuure spo raes and we canno rejec ha -monh and 6-monh dollar/euro dollar forward raes are unbiased esimaors of corresponding fuure spo raes hypohesis. CONCLUION his sudy re-examines he relaion beween forward and spo exchange raes in inernaional rading. I firs shows analyically he forward rae deerminaion and he raionale of he forward exchange rae unbiasedness hypohesis under risk neural assumpion solely from Dollar sellers (foreign currency invesors) perspecive. his sudy uncovers he flaws in convenional formulaion of he forward rae unbiasedness hypohesis and is esing mehods and proposes wo alernaive esing mehods accouning for non-saionariy, non-normaliy, and heeroscedasiciy for forward exchange rae unbiasedness hypohesis. By using Jensen s inequaliy, he paper demonsraes ha forward exchange rae unbiasedness hypohesis canno hold simulaneously for boh dollar sellers and buyers, and poins ou he risk-neural probabiliy measure is no (necessarily) an accurae model for he price processes of raded asses like currencies and forward exchange rae should no be expeced o be an unbiased predicor of corresponding fuure spo rae. his sudy uses a long sample period ha covers a wide range of major currencies wih forward raes over various forecas horizons (one, hree, six and welve monhs) for he empirical esing o avoid sample specific problems. he esing resuls show ha he forward exchange rae is biased from boh dollar sellers and buyers perspecives which suppor he heoreical argumen ha forward exchange rae should no be expeced o be an unbiased predicor of corresponding fuure spo rae because of he unique feaure in foreign exchange marke: boh dollar sellers and buyers are equally involved and risk neuraliy assumpion does no hold. Mos of he esing resuls indicae he forward exchange rae is downward biased from he foreign currency invesors (sellers of dollar) s perspecive, and i is upwards biased from he dollar invesors (buyers of dollar) s perspecive. he paper furher conends ha non-risk neuraliy assumpion may poenially explain he exisence of he bias. 8

11 REERENCE Aggarwarl, R. Lucey, B. and Mohany. (2009) he orward Exchange Rae Bias Puzzle Is Persisen: Evidence from ochasic and Nonparameric Coinegraion ess. inancial Review, Vol 44, No. 4, pp Boohe, P. and Longworh, D. (986) oreign Exchange Marke Efficiency ess:implicaions of Recen Empirical indings Journal of Inernaional Money and inance,vol 5, pp Chakrabory, A, and Evans, G. W.(2008) Can Perpeual Learning Explain he orward-premium Puzzle? Journal of Moneary Economics, Vol. 55, No.3, pp Chakrabory, A. and ephen, E. H.( 2008) Economerics of he orward Premium Puzzle Economics Bullein, Vol. 6, No. 4, pp. -7. Chiang,.C. (988) he orward Rae as a Predicor of he uure po Rae - a ochasic Coefficien Approach Journal of Money, Credi and Banking, Vol.20, No. 2, pp Cornell, B.(977) po Raes, orward Raes and Exchange Marke Efficiency Journal of inancial Economics, Vol.5, No., pp ama, E.,. (984) orward and po Exchange Raes Journal of Moneary Economics, Vol.4, No. 3, pp renkel, J., A. (980) Exchange Raes, Prices and Money: Lessons from he 920 s American Economic Review, Vol.70, No.2, pp Goodhar, C. A., McMahon, P. C., and Ngama, Y. L. (992) Does he orward Premium/Discoun Help o Predic he uure Change in he Exchange Rae? coish Journal of Poliical Economy, Vol. 39, No. 2, pp Han B. and Wang. Y. (20) Invesor Overconfidence and he orward Premium Puzzle Review of Economic udies, Vol 78, pp Hodrick L.P. (987) he Empirical Evidence on he Efficiency of orward and uures oreign Exchange Markes In undamenals of Pure and Applied Economics,Chur wizerland: Harwood Academic. Longworh D. (98) esing he Efficiency of he Canadian-U Exchange Marke Under he Assumpion of No Risk Premium Journal of inance, Vol 36, pp ama, E.. (984) orward and spo exchange raes Journal of Moneary Economics, Vol.4, roo K.A. and haler R.H.(990) oreign Exchange Journal of Economic Perspecives,vol 4. pp Engel C. (996) he orward Discoun Anomaly and he Risk Premium: A urvey of Recen Evidence Journal of Empirical inance, Vol 3, pp Baillie R.. and Bollerslev,. (2000) he orward Premium Anomaly is no as Bad as You hink Journal of Inernaional Money and inance, Vol 9, pp Maynard, A. and Phillips P.C.B. ( 200) Rehinking an Old Empirical Puzzle: Economeric Evidence on he orward Discoun Anomaly Journal of Applied Economerics, Vol 6, pp arno L. and aylor M.P. (2002) he Economics of Exchange Raes Cambridge 9

12 Universiy Press, Cambridge. arno, L., Valene, G. and Leon, H. (2006) Nonlineariy in Deviaions from Uncovered Ineres Pariy: An Explanaion of he orward Bias Puzzle Review of inance, Vol. 0, No.3, pp arno, L., chneider, P., and Wagner, C. (202) roperies of oreign Exchange Risk Premiums Journal of inancial Economics, forhcoming ercu, P. and Vinaimon,. (2006) he orward Bias in he ECU: Peso Risks vs. ads and ashions Journal of Banking and inance, Vol. 30, No.8, pp

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