Risk Averse Speculation and Exchange Rate Determination: An Econometric Analysis of the U.S. Dollar versus Euro, Pound, and Yen

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1 Risk Avese Speculaion and Echange Rae Deeminaion: An Economeic Analysis of he U.S. Dolla vesus Euo, Pound, and Yen by D. Ioannis N. Kallianiois and D. Riaz Hussain Economics/Finance Depamen The Ahu J. Kania School of Managemen Univesiy of Scanon Scanon, PA U.S.A. Tel. (570) Fa (570) << JUpavcousi evssea qanavsima meionekhvmaa eij~ ovn a[nqwpon: a v JUgeiva a[neu ejgasiva~, b v Movfwsi~ a[neu apeinofosuvnh~, g v jepavggelma a[neu hjqikh`~ kai; d v Gnw`si~ a[neu caakh`o~.>> janwvnumo~ JEL (Classificaion): C13, C, C53, F31 Key Wods: Esimaion Time-Seies Models Foecasing and Ohe Model Applicaions Foeign Echange Ocobe 005 Pesened a he 3 nd Annual Confeence of he Noheas Business & Economics Associaion a Hya Regency Newpo on Goa Island, Newpo, R.I., U.S.A., Ocobe 8-9, 005 1

2 Risk Avese Speculaion and Echange Rae Deeminaion: An Economeic Analysis of he U.S. Dolla vesus Euo, Pound, and Yen Absac *1 The objecive of his analysis is o deemine he echange ae beween he U.S. dolla and hee ohe majo cuencies, he euo, he, and he by looking a he eal ae of eun and isk ha financial asses have in hese fou economies. Risk avese speculaos will y o maimize hei eun and minimize hei isk by invesing in diffeen counies, bu hese capial flows will affec he value of hese fou cuencies (hei echange aes). The empiical esuls show ha befoe 001 he eal eun in he U.S. was high and he dolla was appeciaed; afe 001, he same eal eun became negaive and he dolla was depeciaed, bu afe 004 he eal euns have gowing posiively, so he dolla is epeced o appeciae. Then, by foecasing isk and eun in counies asses, we can deemine he value of hese cuencies (echange aes) in he fuue. 1. Inoducion I is well esablished ha he volailiy of echange aes displays consideable pesisence. Tha is, lage movemens in spo aes end o be followed by moe lage movemens lae, which inceasing isk and poducing seial coelaion in eal euns. Thus, pas volailiy and cuen one can be used o pedic fuue volailiy and he fowad discoun o pemium of he diffeen cuencies. Invesos in foeign asses mus pay aenion no only o he epeced eun fom hei invesmen aciviy, bu also o he isk ha hey incu. Risk avese invesos y o educe hei eposue duing peiods of high volailiy by pedicing he eal eun of hei invesmen and he volailiy (vaiance) of his eun. This volailiy can be foecased wih a GARCH (p, q) model 3 o a geneic pogam, 4 which give boadly simila esuls. Invesos will inves in asses denominaed in a cuency ha is eal eun will be highe han he ohes and is isk o be he smalles one. Deemining hese asses wih he highes eal eun and lowes isk, we can deemine he echange ae of his specific couny. An ecess demand fo he couny s asses will appeciae is cuency. Some ecen facs ( news ) eveal he effec of speculaion on he diffeen echange aes. On Tuesday Febuay, 005, Souh Koea s Cenal Bank announced ha plans o divesify is foeign echange eseves, which ades ook o mean a slowdown in puchases of dolla-denominaed secuiies. The U.S. dolla fell o pe euo and los value wih espec he ohe majo cuencies. The DJIA slid poins (1.6%) as concens abou he weak dolla spaked a sell-off of he U.S. cuency. Also, Gold suged 7.40 o and oil * We would like o acknowledge he help povided by ou eseach assisans, Mahew Hoejs and Robe Kalaf. Financial suppo fom Heny Geoge Reseach Funds is gaefully acknowledged. The usual disclaime applies. Thei sandad deviaions ae: = , = , and = See, Kallianiois (004a and b). 4 See, Neely and Welle (00). euo UK J

3 climbed o 51.4 pe bael. 5 In addiion, eois aacks globally ose las yea (004) o abou 650 fom 175 in 003, said congessional aides biefed by Sae Depamen and inelligence officials. 6 A eois aack in London on July 7, 005 caused socks woldwide o fall; he London socks (FTSE 100 inde) fell by 00 poins, he DJIA fell by 50 poins, U.K. slumped o fom , bonds gained (10-yea AAA=4.80%), oil in N.Y. fell by 5 o 57, and gold pice inceased by 4 o 430 pe oy ounce; bu afe his shudde in he makes, hey ebounded quickly. 7 On Monday, Ocobe 3, 005, Tukey invaded EU and we wee epeced o see some effecs on euo, bu nohing happened; i did no change a all. 8 Then, invasions have no effecs on echange aes, only speculaions do. Sange wold and i is becoming wose evey day! Economiss and all social scieniss will have a vey had ime o analyze his fabicaed ani-socieal wold. Alhough a numbe of economic models have been used o inepe echange ae movemens, viually none of he eising models can eplain echange ae behavio well because i is so much speculaion in his make and i makes economic heoies useless. Some economiss aemp o inepe he phenomenon of deviaion of he acual cuency values fom hei fundamenal values as speculaive bubbles. Paiculaly, economic agens fom hei echange ae epecaions based on a ceain kind of eapolaive behavio. 9 Thus, favoable changes in financial vaiables o in he invesmen envionmen may end o geneae an echange ae appeciaion ha, in un, may lead o epecaions of a fuhe appeciaion. Bu, hee, especially wih he euo, we did no have any changes in fundamenals. The above pocess coninues as long as he make believes he cuency pice will pesis moving in he same diecion. Since he acual pice moves fahe away fom he fundamenals as ime passes, capial gains would have o be sufficienly lage o compensae he isk of a busing bubble, which i is no obvious fo he euo a his momen. Speculaions and speculaive bubbles have gained some empiical suppo in echange ae deeminaion lieaue. Thee wee found in he DM/ and FF/ aes fo he peiod June o Ocobe Evidence indicaes ha he Geman mak was ovevalued wih espec o is fundamenal value by 1% and Fench fanc by 11%. 10 A speculaive bubble was also found in he Unied Saes, whee he dolla appeciaed subsanially fo he peiod 1980 hough The same seems o be he case wih he Euo-zone; euo has been appeciaed wihou any changes in he fundamenals (ecep he Iaqi wa and he fea of anohe wa) since he begging of 003 eached /euo on Decembe 30, 004 and coninues o be ovevalued. 11 On Ocobe 6, 005 i was 1.19 /euo. 1 5 See, The Wall See Jounal, Febuay 3, 005, pp. A1, C1, C, and C3; and Dolla Declines as Bank of Koea Plans o Divesify Cuency Reseves, Bloombeg.com, // See, The Wall See Jounal, Apil 7, 005, p. A1. 7 A goup pupoing o be he eois oganizaion al-qaeda claimed esponsibiliy fo eplosions duing moning ush hou acoss London. The public anspoaion sysem was shuing down. Bloombeg.com, July 7, 005 and The Wall See Jounal, July 8, 005, p. C1. 8 See, The Wall See Jounal, Ocobe 4, 005, pp. A1, A15, and A16. 9 See, Tucke, Madua, and Chiang (1991, p. 5). 10 See, Woo (1987). 11 Euo was /euo on Decembe 31, 001 and has been appeciaed by 54.84% in hee yeas. See, Kallianiois (005a). 1 Bloombeg.com (10/6/005). 3

4 . Pofolio Divesificaion and he Euo Shoage This analysis is including pofolio balance and is implicaions fo echange aes. A saing poin is he hypohesis ha eal money demand depends no only on income, he convenional ansacions vaiable, bu also on inees ae and on wealh, he speculaive demand. The inenaionalizaion of business and invesmen oppouniies induce speculaos o divesify hei pofolios of asses denominaed in a vaiey of cuencies so ha hey can maimize hei wealh and many imes, we have epeienced dasic effecs on he value of cuencies because hese speculaos decided o change ovenigh he conen of hei pofolia. 13 These shifs in wealh induced by cuen accoun imbalances o pofolio divesificaion ceae moneay imbalances leading o adjusmens in long-un pice level epecaions and hus o echange ae movemens. Wih pefec mobiliy of capial, hese specificaions of money demand imply ha he eal money demand of a couny wih a suplus o acquiing is asses ises while i falls aboad. The elaive pice level of he couny wih a suplus o wih a high demand of is asses declines and, heefoe, echange aes fo given ems of ade end o appeciae. The demand fo monies is affeced by an inenaional edisibuion of wealh. Pofolio effecs can aise in he cone of impefec asse subsiuabiliy. Wih unceain eal euns, pofolio divesificaion makes asses impefec subsiues and gives ise o deeminae demands fo he especive secuiies and o eal yield diffeenials o a highe isk pemium ha one cuency offes elaive o he ohes. A pofolio model could povide an eplanaion of he unanicipaed euo appeciaion ha is only pooly accouned fo by speculaion, high isk of holding U.S. dolla asses, 14 and fuue unceainy. The sysem of fleible echange, he macoeconomic policies, and he laely disubances 15 have ceaed an incenive fo pofolio divesificaion, ha he euo will occupy a lage shae in an efficienly divesified pofolio, and ha he esuling pofolio shifs o capial flows accoun fo some of he unanicipaed appeciaion of his new cuency and no he EMU fundamenals. We would like o measue he eal euns on asses denominaed in fou diffeen cuencies, hee. The nominal sho-em inees ae mus be as follows (wih e ane and e pos calculaion), depending whehe he cuency is a a fowad discoun o a a fowad pemium: 13 In June 1997, he Asian cuency cises saed. The Thai bah devaluaed in July, followed soon afe by he Indonesian upiah, Koean won, Malaysian inggi, and Philippine peso. Following hese iniial echange ae devaluaions, Asian economies plummeed ino ecessions. The Indonesian pesiden wen public and blamed speculaos (he named even one, Geoge Soos) who shifed hei sho-em invesmens ou of he couny. Ne day his poo pesiden was foced o eign. See, Eieman, Sonehill, and Moffe (004, p. 30), Rajan and Zingales (1998), and Singal (1999). 14 Some news wee: Syians funds will feeze in he U.S. banks. (TV News, Mach 6, 005). Dolla declined as Bank of Koea plans o divesify cuency eseves. (Bloombeg.com, Febuay, 005). 15 The U.S. Teasuy epoed he fedeal defici hi a monhly ecod of billion in Febuay of 005. Geenspan old he Council on Foeign Relaions deficis pose a bigge isk o he U.S. han ade imbalances o low savings. (The Wall See Jounal, Mach 11, 005, p. A1). 4

5 e e S T = + π + fd (1) i e e o i = + π fp () S T These equaions can be epanded as, i S T = + + ( p 1 p ) + ( f s ) (3) o i + p p ) ( f s ) (4) S T = ( + 1 and by lagging pices and echange aes one peiod (avoiding hei foecasing), we have an e pos measue of he nominal ae of eun of an asse, i S T = + ( p p 1 ) + ( s s 1 ) (5) o i + p p ) ( s s ) (6) S T = ( 1 1 Then, he e ane and he e pos eal euns will be: S T e e = i π fd (7) and e e o = i π + fp (8) S T = is T ( p p 1 ) ( s s 1 ) (9) = is T ( p p 1 ) + ( s s 1 ) (10) whee, i S-T =he nominal sho-em inees ae (eun), = he eal ae of inees, p=he inflaion ae, fd=he fowad discoun of he cuency, fp=he fowad pemium, p=he ln of pice inde, s=he ln of spo echange ae, f=he ln of fowad echange ae, and e he epeced value of he vaiable. Now, we ake he uiliy funcion of an inveso who wans o maimize his end-of-peiod eal wealh (w) by invesing on home () and foeign ( * ) secuiies and o deemine he opimal pofolio shae of foeign secuiies (). Ma U = u( w, ) (11) w whee, U=he uiliy funcion, w =he mean of he end-of-peiod andom wealh, and vaiance of wealh, =he eal eun on home secuiies, w =he * S =he eal eun of diffeen foeign 5

6 secuiies, and =he opimal pofolio shae (weighs) on diffeen cuencies denominaed secuiies. The soluion of eq. (11) will be o consuc a pofolio of fou diffeen asses, which will maimize is eun, E(R P ), and minimize is isk,. RP E ( R ) (1) P = euo euo The Vaiance Covaiance Mai euo euo Cov(, euo ) Cov(, ) Cov(, ) euo euo Cov(, euo ) euo Cov( euo, ) Cov( euo, ) Cov(, ) Cov( euo, ) Cov(, ) Cov(, ) Cov( euo, ) Cov(, ) Then, R P euo euo Cov( Cov( euo,, Cov( euo euo ) +, ) + euo ) + Cov( Cov( = euo, euo, Cov( ) ), ) (13) euo euo,euo,, Sandad Deviaions and Coelaion Coefficiens euo euo ρ, ρ euo, ρ, ρ ρ euo euo, ρ euo, ρ ρ euo, ρ, ρ ρ euo, ρ, o 6

7 R P = euo euo ρ ρ,, ρ + euo euo euo, euo euo euo euo + ρ +, ρ euo, ρ, euo (14). The ne sep is o deemine he opimal pofolio shae (weighs),, euo,, and 3. The Basic Model of Opimal Pofolio Selecion The basic model of pofolio selecion fo a isk-avese peson is as follows: Suppose he uiliy funcion fo a isk-avese peson is U = E(R) ½A (15) whee, E(R) is he epeced eun of he asse o a pofolio of asses, A is he coefficien of isk avesion of an individual (fo isk-avese pesons, A is posiive; ypically, i is 1, o ), and is he vaiance of he asse. Fo a fou-secuiy pofolio, he uiliy funcion becomes The consains ae 4 U = i=1 4 4 w i E(R i ) ½A w i w j cov(i,j) (16) i=1 j=1 4 w i = 1 (17) i=1 w i 0, fo i = (18) Fo he ime being, we will ela he second consain (18) and allow negaive weighs of asses. Incopoaing he consain ha he sum of he weighs is one, he epeced eun of a fou-secuiy pofolio is E(R p ) = w 1 R 1 + w R + w 3 R 3 + (1 w 1 w w 3 )R 4 (19) Similaly, he vaiance of a fou-secuiy pofolio is va(r p ) = w 1 va 1 + w va + w 3 va 3 + (1 w 1 w w 3 ) va 4 + w 1 w cov 1 + w 1 w 3 cov 13 + w 1 (1 w 1 w w 3 )cov 14 + w w 3 cov 3 + w (1 w 1 w w 3 )cov 4 7

8 + w 3 (1 w 1 w w 3 )cov 34 (0) The uiliy funcion becomes U = w 1 R 1 + w R + w 3 R 3 + (1 w 1 w w 3 )R 4 ½A[w 1 va 1 + w va + w 3 va 3 + (1 w 1 w w 3 ) va 4 + w 1 w cov 1 + w 1 w 3 cov 13 + w 1 (1 w 1 w w 3 )cov 14 + w w 3 cov 3 + w (1 w 1 w w 3 )cov 4 + w 3 (1 w 1 w w 3 )cov 34 ] (1) We se he deivaives of he uiliy funcion wih espec o he hee weighs, w 1, w, and w 3, o be zeo. This gives us U = R 1 R 4 + [va 4 cov 14 + ( cov 14 va 1 va 4 )w 1 w 1 + (cov 14 + cov 4 cov 1 va 4 )w + (cov 34 + cov 14 va 4 cov 13 )w 3 ] A = 0 () U = R R 4 + [va 4 cov 4 + (cov 14 + cov 4 va 4 cov 1 )w 1 w + ( cov 4 va 4 va )w + (cov 4 + cov 34 cov 3 va 4 )w 3 ] A = 0 (3) U = R 3 R 4 + [va 4 cov 34 + (cov 14 + cov 34 va 4 cov 13 ) w 1 w 3 + (cov 4 + cov 34 va 4 cov 3 ) w + ( cov 34 va 3 va 4 ) w 3 ] A = 0 (4) Solving equaions (-4) fo w 1, w, w 3, we ge whee w 1 = α/δ, w = β/δ, w 3 = γ/δ (5) α = [{R 4 R R 3 + A(cov 3 cov 4 cov 34 )}cov 3 + (R R 3 )cov 4 + (R 3 R )cov 34 ]cov 14 + [(R 4 R )cov 34 + (R R 4 A cov 4 )cov 3 + (A cov 4 + R 3 A cov 34 R 4 R )cov 4 ] cov 13 + [(R 3 R 4 A cov 34 ) cov 3 + ( R 4 + A cov 34 + R R 3 ) cov 34 + ( A cov 34 + R 4 R 3 ) cov 4 ] cov 1 + ( R 1 + R ) cov 34 + [(R 1 R 4 R ) cov 34 + (A cov 34 R 3 R 4 + R 1 ) cov 4 + (R 4 R 1 ) cov 3 ] cov 3 8

9 + [(R + R 3 R 1 A cov 3 ) cov 3 + (R + A cov 3 R 3 ) cov 13 + (R 3 R + A cov 3 ) cov 1 ] va 4 + [(R 1 R R 3 ) cov 34 + (R 3 R 1 ) cov 4 ] cov 4 + [(R + A cov 4 R 4 ) cov 14 + ( R + A cov 4 + R 4 ) cov 1 + (R R 1 + R 4 A cov 4 ) cov 4 + ( R + R 1 A cov 1 ) va 4 ] va 3 + [(R 4 R 3 + A cov 34 )cov 13 + (R 4 + R 3 R 1 A cov 34 )cov 34 + (R 3 R 4 + A cov 34 ) cov 14 + (R 1 A cov 13 R 3 ) va 4 + (R 1 R 4 + A va 4 A cov 14 ) va 3 ] va (6) β = [(R 1 R ) cov 34 + (R 4 R 1 ) cov 3 + (R 3 R 1 ) cov 4 ] cov 34 + [(R 1 R 3 )cov 3 + (R 3 + Acov 3 + R 1 Acov 13 R )cov 13 + (R 3 R 1 + Acov 13 )cov 1 ]va 4 + [(R 1 R 3 )cov 4 + (R R 3 R 1 )cov 34 + (R 3 R 1 R 4 Acov 34 )cov 3 + (Acov 3 + R 3 R )cov 14 ]cov 14 + [(R 1 R 4 R 3 + Acov 34 )cov 34 + (R 3 R 4 Acov 34 )cov 13 + (R 4 R 3 Acov 34 )cov 14 ]cov 1 + [(R 1 R 4 )cov 3 + (R R 3 R 4 Acov 3 Acov 4 + Acov 34 )cov 14 + (R R 4 R 1 )cov 34 + ( R 3 R 1 + R 4 A cov 34 )cov 4 + (R 4 + A cov 4 R )cov 13 ]cov 13 + [(R 1 R + R 4 + A cov 4 A cov 14 ) cov 14 + (A cov 14 + R 4 R 1 ) cov 1 + (R R 1 A cov 1 ) va 4 + (R 1 R 4 ) cov 4 ] va 3 + [(R 3 + R 4 R A cov 34 ) cov 34 + (R 3 R 4 + A cov 34 ) cov 4 + (R 4 R 3 + A cov 34 ) cov 3 + (R R 3 A cov 3 ) va 4 + (R R 4 A cov 4 + A va 4 ) va 3 ] va 1 (7) γ = [(R R 3 + Acov 3 )cov 14 + (R 3 R R 1 )cov 4 + (R 1 R )cov 34 + (R R 1 R 4 Acov 4 )cov 3 ]cov 14 + [(R R 1 ) cov 34 + (R 1 R 3 ) cov 4 ] cov 4 + [(R 1 R 4 ) cov 34 + (A cov 14 + R 4 R 1 ) cov 13 + (R 1 + R 4 R 3 + A cov 34 A cov 14 ) cov 14 + (R 3 R 1 A cov 13 ) va 4 ] va + [(R 1 R 4 ) cov 3 + (R 3 R 1 R 4 A cov 34 ) cov 4 + ( R 4 R + A cov 4 + R 3 A cov 34 A cov 3 ) cov 14 9

10 + ( R 1 R + R 4 ) cov 34 + ( A cov 4 R 4 + R ) cov 13 + ( R 3 + R 4 + A cov 34 ) cov 1 ] cov 1 + [( R 4 + R 1 R + A cov 4 ) cov 4 + ( A cov 4 R + R 4 ) cov 14 ] cov 13 + (R 4 R 1 ) cov 4 cov 3 + [(A cov 3 + R + R 1 + A cov 13 R 3 A cov 1 ) cov 1 + ( R + R 1 ) cov 3 + ( R 1 + R ) cov 13 ] va 4 + [( A cov 4 + R 4 + R + A cov 34 R 3 ) cov 4 + ( R 4 + R ) cov 34 + ( R + R 3 A cov 3 ) va 4 + (R 4 + A cov 4 R ) cov 3 + (R 3 + A va 4 R 4 A cov 34 ) va ] va 1 (8) δ = A{[va 1 va + (va + va 1 )va 3 ]va 4 + va 1 va va 3 + [cov 1 va 4 va 1 va 4 + (va 4 + cov 1 )cov 13 + (cov 14 va 4 va 1 )cov 3 + (cov 14 cov 13 cov 1 )cov 14 ]cov 3 + [cov 1 va 3 va va 3 + va cov 13 (va + va 3 )cov 14 ]cov 14 + [cov 1 va 4 (va 4 + va )cov 13 va va 4 ]cov 13 [va 4 va 3 + (va 3 + va 4 )cov 1 ]cov 1 + [(cov 1 va 1 )va 3 + (cov 13 cov 1 )cov 13 + (va 3 cov 13 + cov 1 )cov 14 + (cov 13 va 3 va 1 )cov 4 + (va 1 cov 13 cov 14 )cov 3 ]cov 4 + [(va cov 1 )cov 13 va 1 va + cov 1 + (cov 3 + va 1 cov 1 cov 13 )cov 4 + (va 1 cov 14 cov 1 )cov 3 + (cov 13 cov 1 + va )cov 14 + (cov 1 va va 1 )cov 34 ]cov 34 } (9) Suppose he vaiance-covaiance mai fo fou asses is Then va 1 =.04, va =.08, va 3 =.1, va 4 =.16, cov 1 =.03, cov 13 =.04, cov 14 =.05, cov 3 =.05, cov 4 =.06, cov 34 =

11 (1) Assume ha he coefficien of isk avesion, A = 1. Fuhe, assume ha he epeced euns fom he fou asses ae: R 1 =.10, R =.1, R 3 =.14, R 4 =.16 Subsiuing hese numbes, we find, he opimal weighs o be: The epeced eun of he pofolio is w 1 =.0, w =.6, w 3 =.34, w 4 =.38. E(R p ) =.0*.1 +.6* * *.16 =.1384 The vaiance of euns of he pofolio is va(r p ) = 0.088, o ( R p ) =.877. The maimum value of he uiliy funcion is Ma U =.100 If we selec only he fis asse, he uiliy is.1.5*.04 =.08. Similaly, if we choose only he second, o hid, o fouh asse, he uiliy in each case is.08. If we disibue he money evenly in he fou asses, ha is w 1 = w = w 3 = w 4 =.5, hen he uiliy is U = () Assume ha he coefficien of isk avesion, A = 0.5. If a peson is willing o ake moe isk, his A is possibly.5. The weighs of he pofolio in his case ae w 1 =.9000, w =.3000, w 3 =.7, and w 4 =.9. (3) Assume ha he coefficien of isk avesion, A=1.5. Fo a peson, who is moe iskavese, he coefficien A = 1.5. Fo him he opimal weighs ae w 1 =.367, w =.467, w 3 =.00, w 4 =.067. Fo less isk-avese individuals, he fouh weigh will ge highe a he epense of he fis weigh. The ciical A, whee he fis weigh becomes zeo is Wih he consain of all posiive weighs, we can solve he poblem fo pesons wih A > Asses Risk and Reun Revisied We assume ha a spo echange ae S follows a andom walk, S ε (9) + 1 = S + +1 whee, ε + 1 ~ N(0, ). The vaiance of he eo em depends on, and he objecive of he model is o chaaceize he way, in which his vaiance changes ove ime. This volailiy of he echange ae measues he fd o fp of a cuency and affecs he eal eun of he asses 11

12 denominaed in his specific cuency. In ode o measue he echange ae isk, we use Bolleslev s (1986) model, which is an eension of Engle s (198) oiginal wok by developing a echnique ha allows he condiional heeoscedasic vaiance o be an ARMA pocess. This pocess is he Genealized ARCH (p, q), called he GARCH (p, q), in which he vaiance is given by q p = + ω α j ε j + j= 1 j= 1 j j β (30) whee, ε = he disubances o esimaed esiduals and = he vaiance of ε }. When α + β < 1, he vaiance pocess displays mean evesion o he uncondiional epecaion of, ω /( 1 α β ). Tha is, foecass of volailiy in he disan fuue will be equal o he uncondiional epecaion of, ω /( 1 α β ). The GARCH model has been used o chaaceize paens of volailiy in U.S. dolla foeign echange makes 16 and in he Euopean Moneay Sysem. 17 Meese and Rogoff (1983) conclude ha echange ae models do a poo job of acking movemens ove sho hoizons. Then, he macoeconomic vaiables (money supply, income, inees ae, pice level, deb, ec.) can eplain changes in echange ae ove medium and long hoizons. Cuency ades, speculaos, and ohe make paicipans who focus on he shoem hoizon look beyond macoeconomic models. They, seach fo signs (like isk and eun) of sho-em changes in he demand fo cuencies (asses denominaed in specific cuency), using any available measues of make ansacions, behavio, and news. I is impoan fo economiss o model sho-em echange ae dynamics and deemine (foecas) he fuue value of he diffeen cuencies. Speculaos in he fuue make ae consanly inepeing public and pivae infomaion abou ongoing shifs in foeign cuency demand as hey develop hei diecional views. 18 The fis sep in evaluaing he sengh of any elaionship beween eal ae of eun and echange aes is o look fo visual evidence. Ploing he levels of he eal ae of eun agains echange ae levels eveals no obvious paens. Howeve, a faily clea elaionship emeges when looking a changes in he wo vaiables. Knowing he change of he eal ae of eun of a couny would have allowed someone o guess coecly he diecion of he, euo,, and. We can un egessions o see he effecs of eal eun and isk on he echange ae, oo. { s = a 0 + a1 + a + ε (31) 16 See, Baillie and Bolleslev (1989 and 1991). 17 See, Neely (1999). 18 See, Kligaad and Wei (004). 1

13 whee, s =he spo echange ae, =he eal ae of eun, and eal ae of inees, calculaing wih he use of eq. (30). =he vaiance (isk) of he A simila equaion can be un by esing he eal ae of inees as a funcion of spo echange ae and isk. 1s s = β 0 + β + β 3 + ε (3) Fuhemoe, ess show ha movemens of ae of eun and is isk in one couny anicipae how speculaos change hei demand and supply of asses denominaed in his specific cuency. The naue of echange ae dynamics could ague abou he conempoaneous elaionship beween eun/isk and echange aes and hei fuue ends. Cuency make paicipans ae heeogeneous and ac on hei own bis of pivae infomaion, as well as on public infomaion. 19 Eamples of pivae infomaion include paicipans epecaions of fuue economic vaiables, pecepions of official and pivae seco demand, and pecepions of developing shifs in global liquidiy and isk aking. Speculaos ac immediaely in advance of echange ae movemens in a way ha anicipaes he diecion of echange aes and he ae of eun. Ou objecive is o seek daa o help us undesand wha is diving he echange ae a any given ime. Vaiables ha ae viewed as fundamenal o dicaing cuency values (elaive money supply, oupu, inflaion aes, inees ae diffeenials, ec.) ae consanly analyzed and foecas. Vaious ansacion daa ae also eamined o deemine demand changes in diffeen cuencies. The esuls sugges ha eal ae of eun and isk in diffeen counies mei inclusion in policy analysis and in ongoing eseach on echange ae dynamics and deeminaion. 5. Some Peliminay Empiical Resuls So fa, we have discussed he heoeical pa of he ae of eun of an asse denominaed in foeign cuency, he ae of eun of a pofolio of cuencies and he measuemen of isk of he individual cuency, due o unanicipaed echange ae movemens, and he calculaion of pofolio isk. The daa, aken fom economagic.com and imfsaisics.og, ae monhly fom 1973:03 o 005:08. They compise spo echange ae, money supply (M), consume pice inde (CPI), fedeal funds ae, 3-monh T-bill ae, pime ae, govenmen bonds ae, eal GDP, cuen accoun, unemploymen ae, budge defici, naional deb, pesonal saving ae, pice of gold, pice of oil, and sock make inde (DJIA). Table 1 pesens he mean values and sandad deviaions of diffeen vaiables (spo echange ae, fowad discoun o fowad pemium, eal ae of eun, sho-em inees aes, inflaion aes, ec.). Also, i gives coelaion coefficien beween hese vaiables. The sample is divided ino hee peiods 1973:03-005:08, 1973:03-001:1, and 00:01-005:08. The U.S. dolla was a a pemium wih espec o euo,, and unil 001:1 and i is a a discoun 19 See, Evans and Lyons (00). 13

14 afe 00:01 o pesen. The eal ae of eun fo a Euopean invesing in he U.S. is negaive; he same is ue fo a Biish. Fo a Japanese inveso o inves in he U.S., he eun is posiive. Then, we do no epec an incease in demand fo U.S. financial asses and hee will be no appeciaion of he U.S. dolla, due o hese negaive eal euns. Table shows he mean values and sandad deviaions of he diffeen economic fundamenals. Some vaiables ha have changed dasically in he U.S. ae he sho-em inees aes (vey low) and he negaive eal isk fee ae of inees; also, he high isk (RP=3.43), he cuen accoun defici, he budge defici, naional deb, low savings, high pice of gold and oil. Table 3 gives he coelaion beween he echange aes and he fundamenals. The (/euo) echange ae is highly coelaed wih fedeal funds ae, T-Bill ae, and pime ae; also, wih he isk pemium, he unemploymen ae, and he budge defici. Fom 00:01 o now he coelaions ae small; hen, he (/euo) echange ae does no depend on fundamenals. The same holds fo he ohe wo echange aes (/) and (/). Table 4 povides he causaliy ess beween he economic fundamenals in he U.S.A. and he hee diffeen echange aes. Fom 1973:03 o 001:1, he inflaion ae and he eal isk fee ae of inees caused he (/euo) echange ae; also, he money supply, he eal GDP gowh, he unemploymen ae, and he DJIA caused he (/) ae; and he isk pemium and he budge defici caused he (/) echange ae. Fom 00:01 o pesen, he (/euo) echange ae does no depends on any fundamenals (jus speculaion); he (/) echange ae is caused by he pesonal saving ae; and he (/) ae is caused by he pice of gold. Tables 5a, 5b, and 5c give he vaiance-covaiance and he sandad deviaion and coelaion coefficiens maices fo fou diffeen eal aes of inees. The eal eun ha an Ameican eceives by invesing in U.S. T-Bills ( A ), he eal eun ha a Euopean makes by invesing in he same insumen ( EU ), he eal eun ha a Bion is making fo he same invesmen ( B ), and he eal eun ha a Japanese is eceiving by invesing in U.S. T-Bills ( J ). The eal eun is high fom 1999:01 o 001:1 (fom.177% o %) and he isk vey high, oo (fom 3.107% o 31.39%). This high eal eun on U.S. financial asses has caused he dolla o appeciae (fom 4.076% o 9.011% p.a.). Afe he inoducion of he Euo-noes (00:01), he eal eun on he U.S. financial asses is becoming negaive (-1.00% o %) and he isk sayed a he same level as befoe (fom 3.415% o 30.0%). These negaive euns have caused he dolla o depeciae (fom 3.649% o 8.398% p.a.). Then, speculaos ae seeking highe euns ouside of he U.S. and his capial ouflows have depeciaed he U.S. dolla. The highes appeciaion is in euo, follows by, and lasly, he. Finally, Table 6 shows ha he high euns befoe 00 have been caused by he high eal eun in he U.S., he high inflaion, and he high gowh in he value of he dolla. The low euns afe 00 have been caused, due o a decline in eal euns fo Euopeans and Bions, educions in T-bill ae, and depeciaion of he U.S. dolla wih espec he euo. Of couse, daa fom Euo-zone, U.K., and Japan ae needed o es he effecs of hose counies fundamenals on he hee echange aes, which is an analysis ha will be done in he fuue. 14

15 6. Policy Implicaions Even hough ha he U.S. dolla has depeciaed dasically since 001 (i.e., -5.66% wih espec o euo), 0 he cuen accoun deficis have assumed eaodinay popoions. A cuen accoun defici is mached by a capial accoun suplus. In ohe wods, a couny wih a cuen accoun defici suendes claims on fuue income (physical asses, socks, and bonds) o foeignes. The ongoing U.S. cuen accoun defici anslaes ino an aveage of billions dollas in ne capial impos pe business day. Tha is, foeign invesos have been accumulaing U.S. asses a an unusually high ae. Foeign invesos migh become way of holding inceasingly lage poions of hei wealh in U.S. asses. In ode o pomoe coninued invesmen in he Unied Saes, U.S. asses would hen have o become moe aacive. One way of aacing foeign invesmens is o lowe he pice of he asse in foeign cuency ems. A decline in he foeign echange value (depeciaion) of he dolla would do jus ha. Theefoe, a lage cuen accoun defici migh be epeced o depess he value of he dolla ove ime. A easonable quesion aises now; bu, wha abou he pesisen cuen accoun defici? Indispensably, ade policies mus impove i and ciizens mus make hei demands fo impos moe elasic ( ε M > 1) fo hei own good and hei couny s benefis. The following ideniy holds fo an economy, Y E = T G + S I = X M (33) whee, Y=income (GDP), E=ependiues, T=aes, G=govenmen spending, S=saving, I=invesmen, X=epos, and M=impos. If (X-M<0) in he above eq. (33), a devaluaion migh impove his cuen accoun defici. Bu, a necessay and sufficien condiion (Mashall-Lene) mus hold, ε + ε M * > 1 (34) M whee, ε M =he domesic pice elasiciy of he demand fo impos and ε * =he foeign pice elasiciy of demand fo hei impos. Then, he pocess could be as follows (if Mashall-Lene condiion holds): CAD ( KAS) Passes ( S) CAD whee, CAD=cuen accoun defici and KAS=capial accoun suplus. The cuen accoun and capial accoun ae wo sides of he same coin. A couny ha is unning a cuen accoun defici ( M Goods > X Goods) is necessaily also unning a capial accoun suplus X > M ). Foeign-owned asses in he Unied Saes inceased fom ( Financial Asses Financial Asses less han.5 illion in 1990 o ove 10 illion by he end of 003. Ove he same peiod, U.S.- M 0 See, Kallianiois (005b, Table 1). 15

16 owned asses aboad inceased fom.3 illion o nealy 7.9 illion. 1 Even hough ha he eal eun is lowe in he U.S., invesos inves hee, because of he unpaalleled efficiency, sabiliy, anspaency, and liquidiy of he U.S. financial makes. Invesos find ha dolla-denominaed claims ae an aacive elemen of any inenaional pofolio. This pocess of invesos seeking he mos beneficial combinaion of isk and eun, ebalancing pofolio when oppouniies aise, gives ise o a souce of capial accoun dynamics ha is unelaed in any diec way o he paen of ade in goods and sevices. Figue 1 shows a smoohing of he seies (he fou eal euns in U.S. ha foeign invesos face) by using he Hodick-Pesco (1997) file o obain a smooh esimae of he long-em componens of he seies ( s). The gaph eveals ha he L-T eal euns ae inceasing fo foeign invesos invesing in he U.S. financial asses; hen, his demand fo U.S. asses will appeciae he U.S. dolla, oo. 7. Concluding Commens The objecive of his analysis is o deemine he echange aes beween he U.S. dolla and hee ohe cuencies, he euo, he, and he. Laely, he U.S. dolla is loosing value wih espec he ohe hee majo cuencies of he wold and we wan o see if his depeciaion depends on economic fundamenals (lowe eal eun in he U.S. and highe isk) o i is jus speculaion fom individuals o counies, which hold lage amouns of foeign asses denominaed in diffeen cuencies. The peliminay conclusion is, hee, ha, due o high isk (was and poliical conflics) and low euns many speculaos have invesed in euos, s, and s insead in dollas denominaed asses. Hisoically, he U.S. has fozen he foeign asses inside he U.S. when a conflic aises. The L-T smoohing of hese euns shows ha hey ae gowing, so he demand fo U.S. invesmen will incease and he U.S. is epeced o appeciae in he fuue. Invesos know his and speculaos ake advanage of his knowledge. Also, by consucing a pofolio of fou diffeen asses, we can maimize he uiliy funcion of a speculao by maimizing his eun and minimizing his isk. Fom hese eal euns, we can conclude if he cuency will appeciae o no. High epeced eal eun on asses denominaed in euos means ha euo is epeced o appeciae. The peliminay ess show ha economic fundamenals have less effec on echange aes, laely; hen, echange aes depend mosly on speculaion, due o he epeced isk and eun. The pape needs some moe dae fom all he counies involved and moe saisical and pofolio analysis o give bee esuls. 1 See, Pakko (004). 16

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