International Research Journal of Applied Finance ISSN Vol. VIII Issue 4 April, 2017

Transcription

1 Exchang Ra Movmn: Efficincy in h Forign Exchang Mark Dr. Ioannis N. Kallianiois Absrac Th objciv of his papr is o s h fficincy in h forign xchang mark by using hr xchang ras ($/, $/, and /$). Diffrn horical modls ar applid, lik h random walk hypohsis, h unbiasd forward ra hypohsis, h composi fficincy hypohsis, and h xchang ra xpcaions basd on anicipad and unanicipad vns ( Nws ). Th mpirical rsuls for hs hr major xchang ras (four currncis) show ha rlaiv fficincy xiss. Th mos fficin mark is h dollar/uro on; h ohr wo marks (dollar/pound and yn/dollar) ar no fficin. Also, saisical ss of conomic fundamnals and xpcd chang in h xchang ra ar usd o capur h fuur spo ra s volailiy and prdicabiliy by using h currn spo (random walk) for h variabls of h four conomis. Th adquacy of h spcificaion of h diffrn modls is prformd o drmin h xchang ra movmn. Kywords: Dmand for Mony and Exchang Ra, Forign Exchang, Forcasing and Simulaion, Informaion and Mark Efficincy, Inrnaional Financial Marks JEL: E4, F3, F47, G4, G5 I. Inroducion Th inrnaional monary sysm had o accommoda xraordinary larg oil-rlad shocks, rad dficis, privaizaions (sll-offs of SOEs), FDI, capial conrols, cnral banks inrvnions, and public and priva dbs ha affcd capial flows among naions, and a variy of risks. Surpluss had o b rcycld (invsd) by buying financial asss from h dfici counris. Th las global financial crisis has incrasd uncrainy and h drgulaion of our financial insiuions has incrasd h gap ( brain sprad ) bwn h mark and poliicians and driorad h agncy problm bwn popl (h principals) and govrnmn-mark (h agns). Labor has los complly is righs and i is xploid undfndd by h inhuman capial and globalizaion ha rquirs wags qualizaion bwn dvloping and dvlopd naions. Th global rrorism, which has is roo from 7 h cnury (Briish, Frnch, Amrican, and Russian Rvoluions), is complly ou of conrol. Th incrasd inrdpndnc among naions and h ralizaion ha conomic policis by srong naions xr prssur on ohr wakr conomis hav o induc lgal rsponss and coopraion among all naions. Bu, wha inrnaional organizaion can forc objcivly inrnaional jusic? Non! An undrsanding of fficincy, xpcaions, and risk in h forign xchang mark is imporan o govrnmn 3 and cnral bank policymakrs, inrnaional financial managrs, From prmann full-im jobs wih halhcar covrag, hy bcam half-im ons wihou halhcar bnfis and now, pr-im wih minimum wags wihou any bnfis. And hy hav h impudnc o call his mploymn and giv an official unmploymn ra of 4.8% (wih January 7). S, hp://daa.bls.gov/imsris/lns4. Bu, h unofficial unmploymn ra is 3.% (Augus 6). S, hp:// S also, Noam Chomsky, Th Dah of h Amrican Univrsiy, Vox Populi, Fbruary 4, pp. -4. hps://voxpopulisphr.com/4/8//noam-chomsky-h-dah-of-h-amrican-univrsiy/ S, Kallianiois (7). 3 W ar alking abou dmocraic govrnmns, hr. Bu, To suppos ha any form of govrnmn will scur libry or happinss wihou any viru in h popl, is a chimrical ida. [Jams Madison (788)]. Today s complxiy, corrupion, libralism, and forign conrols hav dsroyd dmocracis. 95

2 and of cours, o invsors and sudns of inrnaional financ. Th govrnmn policymakrs nd o dsign macro-policis for achiving h goal of maximizaion of hir social wlfar hrough fficin rsourc allocaion. Cnral banks hav o b public and rsponsibl for h wllbing of h ciizns of hir own counry. Inrnaional invsors and financial managrs nd o assss forign ass rurns and risks in ordr o mak opimal porfolio dcisions. Th forign xchang mark fficincy hypohsis is h proposiion ha prics (xchang ra movmns) fully rflc informaion availabl o mark paricipans. Thr ar no opporuniis for h hdgrs or h spculaors o mak supr-normal profis; hus, boh spculaiv fficincy and arbiraging fficincy xis. Numrous sudis hav bn sd for spculaiv fficincy and arbiraging fficincy by sing h following wo hypohss rspcivly: () h forward discoun is a good prdicor of h chang in h fuur spo ra, implying covrd inrs pariy (CIP), uncovrd inrs pariy (UIP), and raional xpcaions o hold and () h forward discoun nds o b qual o h inrs diffrnial, implying ha CIP holds. Exchang ras ar viwd as rlaiv prics of wo asss (acually, wo cnral banks liabiliis, 4 hir currncis) ha ar radd in organizd marks (h forign xchang mark) and ar influncd by many diffrn domsic facors (fundamnals; producion is h mos imporan on) and of cours, by xpcaions abou h fuur inrnaional vns ( nws ). Thrfor, unanicipad vns will influnc h xchang ras, oo, as i happns wih ohr asss. So far, h flxibl xchang ra sysm has bn succssful in providing naional conomis wih an addd dgr of insulaion from forign shocks and i provids policymakrs wih an addd insrumn for h conduc of rad policy. 5 Unforunaly, h Euro-zon mmbr-naions (du o hir accpanc and impraiv vr sinc uro) hav los his valuabl macroconomic policy ool. 6 This is a criminal ac of h conrolld Europan poliicians agains hir own ciizns. II. Th Forign Exchang Mark Efficincy Th fficin mark hypohsis (EMH) has bn dvlopd in h domsic financ by Eugn Fama sinc arly In financ, h EMH assrs ha financial marks ar informaionally fficin. In consqunc of his, on canno consisnly achiv rurns in xcss of avrag mark rurns on a risk-adjusd basis, givn h informaion availabl a h im h invsmn is mad. In his fficin mark, all nw informaion is quickly undrsood by mark paricipans and ar immdialy discound ino mark prics. Thus, prics of financial asss and hir corrlaion provid signals for opimal porfolio allocaion. Mark fficincy is associad wih h raionaliy of mark xpcaions. Samulson and Nordhaus (985) dfind an fficin mark as on, whr all nw informaion is quickly undrsood by mark paricipans and bcoms immdialy incorporad ino mark prics. This fficin marks hypohsis has bn xnsivly dvlopd and applid in h domsic and inrnaional financ liraur. Is imporanc is du o h fac ha, if h mark is fficin, h currn pric of an ass will fully rflc availabl informaion wih rgard o is valuaion. Th prics of financial asss hus, provid signals for porfolio allocaion. Bu, is his availabl informaion, from our conrolld 4 Which ar backd by hir govrnmns db; hn: liabiliyg x liabiliycb = liabiliy fia mony ( currncy). 5 S, Kallianiois (3a). 6 S, Kallianiois (). 7 S, Fama (97). 96

3 mdia and corrupd marks, h full informaion ha human bings mus hav? Ar h conomic daa corrc or adjusd o saisfy poliical xpdincy? In pracic, w ar sing a lo of manipulaion in ass prics and macro daa saisics. To xamin mark fficincy, w mus drmin whhr mark paricipans could sysmaically arn an xcss profi. If w dsigna R + as sris of ass rurns nx priod and R + as mark xpcaions of hs rurns and ha hr ar no sysmaic unxploid profis ovr im, w can wri, E [ R + R + Π ] = () whr, R + = h acual rurn nx priod, R + = h xpcd rurn drivd from forcasing i on priod ahad, E = is h xpcaions opraor condiiond on h informaion s Π ( Π = πληροφορίι, vry broad and complly full informaion) 8 availabl a h nd of priod. In cas, ha hr ar sysmaic forcas rrors in R +, h informaion would b incorporad ino h forcas procss. Invsors inspc h forcas rrors ( R+ R + = ε + ) o s whhr hr ar unxploid pars ha may b usd o improv hir invsmn sragy. Thus, h sysmaic informaion will b xploid and h rsuling rror bcoms 8 Unforunaly, his is almos impossibl bcaus h public is dlibraly misinformd. Of cours, hr ar vry fw popl ha hy hav full informaion, hy know h TRUTH. W liv in h Ag of Dcpion [Davidson (5)] and our informaion is from h conrolld mdia. Th conrolld and subjciv mass mdia hav conribud o hs problms, h big lis. John Swinon, h formr Chif of Saff a h Nw York Tims was askd o giv a oas bfor h prsigious Nw York Prss Club in 953. H mad his candid confssion ha hr is no indpndn prss. [I s worh noing ha Swinon was calld Th Dan of His Profssion by ohr nwsmn, who admird him graly]. H said, Thr is no such hing, a his da of h world s hisory, in Amrica, as an indpndn prss. You know i and I know i. Thr is no on of you who dars o wri your hons opinions, and if you did, you know bforhand ha i would nvr appar in prin. I am paid wkly for kping my hons opinion ou of h papr I am conncd wih. Ohrs of you ar paid similar salaris for similar hings, and any of you who would b so foolish as o wri hons opinions would b ou on h srs looking for anohr job. If I allowd my hons opinions o appar in on issu of my papr, bfor wny-four hours my occupaion would b gon. Th businss of h journaliss is o dsroy h ruh, o li ourigh, o prvr, o vilify, o fawn a h f of mammon, and o sll his counry and his rac for his daily brad. You know i and I know i, and wha folly is his oasing an indpndn prss? W ar h ools and vassals of rich mn [dark powrs] bhind h scns. W ar h jumping jacks, hy pull h srings and w danc. Our alns, our possibiliis and our livs ar all h propry of ohr mn. W ar inllcual prosius. (John Swinon, as h formr Chif of Saff a h Nw York Tims, bfor h Nw York Prss Club in 953). Also, a poliician said, Onc a naion pars wih h conrol of is currncy and crdi, i mars no who maks h naions laws. Usury, onc in conrol, will wrck any naion. Unil h conrol of h issu of currncy and crdi is rsord o govrnmn and rcognizd as is mos sacrd rsponsibiliy, all alk of h sovrigny of parliamn and of dmocracy is idl and fuil. [William Lyon Macknzi King, Canadian Prim Minisr (874-95)]. S, hp://quos.libry-r.ca/quo_blog/william.lyon.macknzi.king.quo.f67. Furhrmor, h ohr sid ( h rulrs ) said, W ar graful o h Washingon Pos, h Nw York Tims, Tim Magazin and ohr gra publicaions whos dircors hav andd our mings and rspcd hir promiss of discrion for almos 4 yars...i would hav bn impossibl for us o dvlop our plan for h world if w had bn subjcd o h lighs of publiciy during hos yars. Bu, h world is mor sophisicad and prpard o march owards a world govrnmn. Th supr-naional sovrigny of an inllcual li and world bankrs is surly prfrabl o h naional auo-drminaion pracicd in pas cnuris. (This frighful quo is from David Rockfllr). S, hp:// Ὁ Θεός νά µᾶς λυπηθῇ κί νά µᾶς ἐλεήσῃ. 97

4 whi nois. 9 To saisfy h fficincy condiion [q. ()], an opimal forcas of ass prics is consisn wih raional xpcaions bhavior. In h forign xchang marks, h fficin marks hypohsis has bn applid o h spo mark and o h forward mark. Equaion () can b usd o xprss h spo xchang ra as follows, E [ s + s + Π ] = () whr, s + = h ln (naural logarihm) of h spo xchang ra and s + = h ln of h xpcd spo ra basd on informaion availabl a im. Th abov quaion [q. ()] sas ha h xpcaions rrors will b zro on avrag so ha, no xcss profis can b xploid in h forign xchang marks. Th difficuly is how o form h opimal forcas valu ha rsuls in rsiduals displaying no informaional conn. W can us AR( p) or MA(q) procsss or a muli-variabl on basd on conomic hory (fundamnals) or a ransfr funcion (combinaion of fundamnals and im sris). II. Th Random Walk Hypohsis L h currn valu of s b qual o las priod s valu ( s ) plus a whi-nois rm ( ε ), s = s + ε (3) or s = ε (4) s Th random walk modl is clarly a spcial cas of h AR() procss: s = + s + ε, whn = and =. In pracic, h invsor dos no nd all h informaion in Π ha ar basd on xprinc, mpirical knowldg, mark condiions, hisory, poliics, round knowldg, and ru wisdom, bcaus hy hav vry high informaion coss. Thn, a raional invsor may us a smallr s of informaion I o form xchang ra xpcaions. Economiss hav obsrvd ha h xchang ra follows a random walk procss, which mans ha h xpcd xchang ra nx priod s + is qual o h currn spo ra s. Thus, + s (5) s = Now, subsiuing q. (5) ino q. () and using informaion I, w g, E [ s s I ] = (6) + 9 Whi nois procss is a squnc { ε } if ach valu in h squnc has a man valu of zro, a consan varianc, and is srially uncorrlad. If h noaion E (R) dnos h horical man valu of R, h squnc { ε } is a whi-nois procss for ach im priod, E ( ε ) =, E ( ε = σ, and E ( ε, ε ) =. S, Endrs (995, pp ). Th informaion s I is a subs of Π ( I Π ) bcaus our (for h majoriy of h popl) informaion is parial, scoral, local, and scular informaion (incompl knowldg and fak nws) and no broadr, compl, complx, hisorical, and corrc global informaion (ru wisdom). ) 98

5 This quaion (6) suggss ha if h forign xchang mark is fficin, h currn xchang ra will rflc all h availabl informaion and h unxpcd chang in h spo ra ( s+ s ), is ssnially causd by h random shock ε +, which his h mark bwn im and im +. Mark raionaliy suggss ha h invsor finds no paricular parn from h hisory of ε +. This random walk (mark fficincy) can b sd as follows: s = + s + ε (7) If and, h forign xchang mark is fficin. This random walk hypohsis xplains h rraic bhavior of xchang ra movmns. Exchang ras rspond o nws (surpriss), which ar unprdicabl. Thus, xchang ras mov randomly bcaus hy rspond snsiivly o h unxpcd vns ha randomly hi h marks. II. Th Unbiasd Forward Ra Hypohsis Anohr way o masur h xpcd xchang ra is o us h forward xchang ra ( f ). Th forward ra has bn viwd as an unbiasd prdicor of h fuur spo ra ( Th Unbiasd Forward Ra Hypohsis ). Th validiy of his UFRH implis ha h invsor is risk-nural, ransacion coss ar insignifican, and h arrival of imporan informaional vns is random. This hypohsis is drivd from an fficin arbirag aciviy by invsors and i is xprssd as, + f (8) s = Subsiuing s + in q. () wih f and smallr informaion s I (du o lack of compl informaion bcaus of is normous cos), w hav, E [ s f I ] = (9) + Equaion (9) sas ha h forcas rrors rsuling from using forward ras o prdic h fuur spo ras will b zro on avrag. A nonzro valu, E [ s+ f I ], suggss h rjcion of h unbiasd forward ra hypohsis, du o high ransacion coss associad wih arbirag; a risk prmium ( rp ) if invsors ar no risk-nural; and a spcificaion rror if h modl is no wll spcifid. This UFRH (mark fficincy) can b sd as follows: s = + f + ε () If and, h forign xchang mark is fficin; las priod s forward ra prdics h currn spo ra. Prics rflc all rlvan availabl informaion; hus, h rsiduals in q. () should conain no informaion and, hrfor, should b srially uncorrlad [ E ( ε, ε ) = ]. Furhr, undr h assumpion of risk nuraliy, if h forward xchang ra is an unbiasd prdicor of h fuur spo xchang ra [ f = s + ]; hn, h consan rm should b closd o zro [ ] and h slop cofficin (acually, lasiciy) should b closd o uniy [ ]. For xampl, w saw wha happnd wih h Briish pound ( ), whn Briish vod o a rfrndum on Jun 3, 6 o lav h EU. (hp:// ). Th pound dprciad by 9% wih rspc h U.S. dollar. (hp://mony.cnn.com/6/6/4/invsing/pound-crash-u-rfrndum/ ). 99

6 In addiion, if forward xchang ras prvailing a priod summariz all rlvan informaion availabl a ha priod, hs xchang ras should also conain h informaion ha is summarizd in daa corrsponding o priod and so on. I follows ha including addiional laggd valus of h forward ras in q. () should no graly affc h cofficins of drminaion and h sum of hs cofficins mus no diffr significanly from uniy (h inclusion of addiional laggd variabls dos no improv h fi). 3 s = + f + f + ε () Hnc, if and + h forign xchang mark is fficin; las priods forward ras prdic h currn spo ra. II.3 Th Composi Efficincy Hypohsis Th composi fficincy hypohsis combins h prvious wo hypohss (h random walk and h unbiasd forward ra hypohss). I suggss ha h xpcd fuur spo xchang ra is a wighd avrag of h currn spo ra and h forward ra, as follows, + = w s + ( w f () s ) whr, w = h wigh of h spo ra Equaion () is basd on h informaion conaind in h spo and forward ras. W assum raional xpcaions, hr, oo. Th informaion conaind in h spo ra ( s ) rflcs currn mark condiions and summarizs all hisorical informaion ha affcs xchang ras. Th forward ra ( f ) rflcs all h informaion concrning facors ha ar xpcd o drmin fuur xchang ras. Thrfor, h Composi Efficincy Hypohsis conains wo ss of informaion affcing h fuur spo xchang ra; firs, pas hisorical informaion and scond, raional xpcaions of h mark paricipans. On problm migh sill xis: wha will b h valu of ach on of h wighs on h spo and forward ras? Th composi fficincy can b sd as follows: s = β + βs + β f + ε (3) Thn, if β, β = w, β = ( w), and β + β = w + ( w), which mans ha h forign xchang mark is fficin. III. Exchang Ras Volailiy and Prdicabiliy Th xchang ras hav bn vry volail sinc h 97s, whn h xchang ras bcam flxibl. 4 As an xampl, h sandard dviaion of h spo xchang ra bwn h U.S. dollar and h uro has bn, σ s = ±.8% pr monh, as Graph shows; bwn U.S. dollar and Briish pound, σ s = ±.7% (Graph ); and bwn Japans yn and U.S. dollar, σ s = ±4.6% (Graph 3). Thus, h prdicabiliy of h xchang ra has bcom vry difficul. Ths wo characrisics of xchang ras (volailiy and unprdicabiliy) ar 3 W can s his q. () by using mor laggd valus han wo and o s is fficincy, if S, Kallianiois (6b).

7 ypical of aucion ass marks and hav worsnd afr 8 wih h global financial crisis and h nw sysmic risk ha h world conomis ar facing. In our forign currncy marks, currn spo xchang ras rflc xpcaions concrning h fuur cours of vns (mark, poliical, conomic, inrnaional) and nw informaion (global nws ar insananously known o vryon), which inducs changs in xpcaions and ar immdialy rflcd in corrsponding changs in xchang ras (and all ass prics); hus, rducing unxploid profi opporuniis from arbirag. Howvr, spculaors, insidrs, and mark-makrs ar hriving and proving a h sam im ha infficincy xiss in all h asss and xchang ras marks.. Graph : Volailiy of h spo xchang ra ($/ ) DEUS No: DEUS s = s s, daa from 999: o 6:6. Sourc: Economagic.com. = Graph : Volailiy of h spo xchang ra ($/ ) DUKS No: DUKS s = s s, daa from 97: o 6:6. Sourc: Economagic.com =

8 . Graph 3: Volailiy of h spo xchang ra ( /$) DJS No: DJS = s = s s, daa from 97: o 6:6. Sourc: Economagic.com Th srong dpndnc of currn prics (spo xchang ras) on xpcaions abou h fuur is uniqu o h drminaion of ass prics. This srong dpndnc causs many problms in our conomy and our social wlfar; spcially in priods ha ar dominad by uncrainis, nw informaion, rumors (propagandas), announcmns and nws (h conrolld mdia play a major rol in oday s social wlfar). 5 All hs, mosly ngaiv nws chang our xpcaions (mak us, mosly, pssimisic) and ar h prim caus of flucuaions in ass prics. Consqunly, sinc h informaion, which alrs xpcaions ar nw ( nws ), h rsuling flucuaions in pric (xchang ra) canno b prdicd by laggd forward xchang ras, which ar basd on pas informaion. During hs uncrain priods, w should xpc xchang ras (and all ohr ass prics) o xhibi larg flucuaions. Thus, pas prics, which ar basd on pas informaion, migh b imprcis o forcas fuur prics. Th nw informaion canno b anicipad and hs surpriss ar affcing h spo xchang ras. This viw on xchang ra movmns can b xploid wih h following modl: s = E Φ + + δ E ( s+ s ) (4) whr, Φ rprsns only h conomic fundamnals, which affc h xchang ra in priod [i.., q. (5)] and E ( s+ s ) capurs h xpcd prcnag chang in h xchang ra bwn h currn priod ( ) and h nx priod ( + ), basd on h informaion availabl oday ( ). Th conomic fundamnals ar h wll-known facors prsning blow by q. (5): Φ s = ( m m ) β ( y y ) + γ ( i i ) + ε (5) 5 All h mdia ar complly conrolld and hy provid o h public wha h dark powrs insruc hm o rpor. W nd o do som divrsificaion of h diffrn sourcs of nws (domsic and forign) and o driv our own conclusion and infrncs. W liv in h cnury of misinformaion and of poliical corrcnss ( h big li ).

9 Equaion (4) rprsns a mor gnral xchang ra drminaion formula, which may b viwd as a rducd form ha can b drivd no only from q. (5), bu from a variy of ohr modls of xchang ra drminaion (lik, h ransfr funcion). 6 Assuming ha xpcaions ar raional in q. (4), h currn xchang ra and currn xpcaions of fuur xchang ras ar linkd and boh dpnd on xpcaions concrning h fuur fundamnals ( E Φ + ). Thus, h spo xchang ra dpnds on h currn xchang ra and on h xpcd prcnag chang in h fuur. Du o profi opporuniis from arbirag his link [q. (4)] mus b srong, a las, for h xchang ras xpcd in h nar fuur. Basd on h abov argumn, w xpc a high corrlaion bwn movmns of spo and forward ras. Th corrlaion cofficin bwn h spo and forward ra ($/ ) is so far: ( ρ s, f = +. 98), for ($/ ) is ρ s, f = +. 99, and for ( /$) is ρ s, f = +. 99, bcaus boh ras rspond a h sam im o h sam flow of nw informaion (prmann or ransiory). Also, h conmporanous spo and forward xchang ras ar approximaly qual, showing ha h mark s bs forcas of h fuur spo ra is h currn spo ra. This phnomnon rvals ha xchang ras follow a random walk procss. IV. Exchang Ra Expcaions and Unanicipad Evns ( Nws ) An imporan characrisic of h raional xpcaions hypohsis is ha unanicipad vns, surpriss, and nws ar affcing asss rurns, prics, and ral variabls in our conomis, which ar snsiiv o informaion. 7 Th rcogniion, h las half of h cnury, ha xpcaions ar xrmly imporan o h conomic dcision-making procss has ld o a major rvoluion in macroconomic and financial analysis, bu a h sam im has incrasd insabiliy and uncrainy. Th raional xpcaions hypohsis dvlopd iniially by Muh (96) has playd a criical rol in our mark-orind sysm and i sas ha xpcaions rflcd in mark bhavior will b opimal forcass using all availabl informaion. In h conx of xchang ra drminaion, i is mphasizd ha h prdominan caus of xchang ra movmns ar h unanicipad nws (surpriss). 8 Thus, or s = s + s (6) u u whr, s = h xpcd xchang ra and s = h unxpcd par of h xchang ra. As i was mniond abov, h forward xchang ra summarizs h informaion ha is availabl o h mark whn his forward ra is bing s [ f = E ( s+ I ) ]. Thrfor, h spo ra can b xprssd as a funcion of facors, which hav bn known in advanc and ar summarizd by h laggd forward ra plus a funcion of h nws and a srially uncorrlad rror rm, as follows: s = " + + f + " Nws ε (7) whr, " Nws" = macro-variabls usd in masuring h nws. 6 For ohr modls, s Kallianiois (3a, p. 88). 7 S, Mishkin (983). 8 S, Dornbusch (978), Bilson (978), Frnkl and Mussa (98), Isard (98), and Frnkl (984). 3

10 Equaion (7) can b applid o an mpirical analysis of h rol of unanicipad vns nws as a drminan of h spo xchang ra. Th difficuly is in idnifying h macrovariabls, which can b usd in masuring h nws. Imporan variabls ha ar affcing h xchang ra can b h inrs ras (h rlaionship of h IRP or IRA) in h wo counris bcaus hy ar mark drmind and nws ar affcing hm promply. Thn, by making h assumpion ha h (financial) ass mark clars fas and ha h nws ar immdialy rflcd in unxpcd changs in h inrs ras, q. (7) can b rwrin wih an xra rm, which rprsns h surpris bwn h inrs diffrnial and h xpcd inrs diffrnial bwn h wo counris. s = + f + [( i i ) E ( i i )] + ε (8) whr, + f = h xpcd xchang ra, [( i i ) E ( i i )] = h unxpcd (h innovaion) par of h xchang ra ( nws ), ( i i ) = h acual inrs diffrnial in h wo counris, and E ( i i ) = h xpcd inrs diffrnial basd on informaion availabl in priod. By aking ino considraion h mos imporan rlaionship in inrnaional financ, h inrs ra pariy (IRP), h xpcd inrs diffrnial can b compud from a rgrssion by using laggd valus of h spo and forward ras and laggd valus of h inrs diffrnial, as follows, E ( i i ) ( i i ) = β + β s + β s + β 3 f + β 4 f + β 5 ( i i ) + β 6 ( i i ) + ε (9) Now, w ak h diffrnc bwn h acual inrs diffrnial [( i i ) ID ] minus h compud xpcd inrs diffrnial [ E ( i i ) IDF ], which rprsns h nws. Ths wo valus ar usd in q. (8); and by running his rgrssion, h compur will giv is cofficins. If and, h forign xchang mark is fficin. In h cas ha, his mans ha h currn xchang ra is affcd by xpcaions concrning h fuur cours of vns and ha h unanicipad changs in h xchang ra ar primarily du o innovaions. Mos of h acual changs in xchang ras ar unanicipad, which mans ha mos of h acual changs in xchang ras ar du o nws. V. Empirical Rsuls An mpirical s of fficincy is a join s of fficincy (full informaion) and h quilibrium (harmony) modl. By quilibrium, w man an inrnal, xrnal, rnal, and global balanc ha mus xis in marks and sociis bcaus w (vry individual) mus b in balanc and liv in harmony wih ourslvs, h ohrs, and h nir socio-conomic nvironmn; 9 ohrwis, how can hr b an quilibrium? Rcn ss conducd by Kallianiois (6b) show ha h vidnc supporing h unbiasd forward ra hypohsis is qui wak. H found ha a non-consisn risk prmium is prsn in svral major forign xchang marks ($/, $/, and /$). Th implicaion of hs mpirical findings is ha on canno us h forward ra dircly as a masur for h fuur spo ra bcaus hr ar many inrvnions in h forign xchang mark. 3 9 S, Kallianiois (7 and 6a). 4

11 Th objciv, hr, is o provid som vidnc concrning h horis of xchang ra movmn and mark fficincy. Las squars rgrssion analyss ar usd, which provids a mhod for fiing h mahmaical funcions discussd in hory abov o obsrvd daa. Th daa ar coming from Economagic, Eurosa, and Bloombrg and hy ar monhly. Also, sing of h abov hypohss, and prsning hr can hlp h radrs undrsand h horis and b abl o do mpirical rsarch by using h xising daa in diffrn conomis and currncis. W sar wih h random walk (mark fficincy), which is prsnd in Tabl. Bwn h U.S. dollar and uro ($/ ), h rsuls show, (saisically insignifican) and =.986 (saisically significan a h % lvl); hn, h mark for his s is fficin. Tabl : Tsing for Random Walk, Eq. (7) s = + s + ε if and R SSR F D W N $/ , (.3) (.) $/ , (.3) (.6) /$ , (.4) (.3) No: R = R-squard, SSR = sum of squard rsiduals, F = F-Saisic, D W = Durbin-Wason Saisic, N = numbr of obsrvaions, = significan a h % lvl, = significan a h 5% lvl, and = significan a h % lvl. Sourc: Economagic.com, Bloombrg, and Eurosa. Thn, bwn h U.S. dollar and Briish pound ($/ ) h rsuls ar, (saisically significan a h % lvl) and =.987 (saisically significan a h % lvl); hus, h mark for his s is no vry fficin for his long priod (from 97: o 6:6). Bu, i is fficin if w us daa from 999: o 6:6. Lasly, h mark fficincy bwn h Japans yn and h U.S. dollar ( /$) is sd and givs, (saisically significan a h % lvl) and =.995 (saisically significan a h % lvl); consqunly, h mark for his s is no vry fficin. I is also fficin, if h daa ar from 999: o 6:6. Thn, h UFRH is sd wih q. () and is prsnd in Tabl a. For h U.S. dollar and uro, h rsuls ar as follows, (saisically insignifican) and.965 = (saisically significan a h % lvl); hn, h forign xchang mark for ($/ ) xchang ra is fficin and h forward ra is an unbiasd prdicor of h fuur spo ra. Also, h UFRH for h U.S. dollar and Briish pound, givs. (saisically significan a h 5% lvl) and =.97 (saisically significan a h % lvl), which shows ha h forign xchang mark for ($/ ) xchang ra is rlaivly fficin. 5

12 Furhr, h UFRH for h Japans yn and h U.S. dollar, is as follows: Th. 99 (saisically significan a h % lvl) and =.979 (saisically significan a h % lvl); hus, h forign xchang mark for ( /$) xchang ra is infficin. Tabl a: Tsing for h Unbiasd Forward Ra Hypohsis (UFRH), Eq. () s = + f + ε if and R SSR F D W N $/ , (.6) (.) $/ , (.5) (.) /$ , (.33) (.7) No: S, Tabl. Sourc: S, Tabl. Now, h UFRH is sd wih q. () and h rsuls ar givn in Tabl b. For h xchang ra bwn h U.S. dollar and h uro, i is as follows, (saisically insignifican) and + =.4.4 =.96 (wih saisically significan a h % lvl); hn, his forign xchang mark is fficin. For h U.S. dollar and h Briish pound, h rsuls ar. 4 (saisically significan a h % lvl) and + = =.969 (wih saisically significan a h % lvl and a h 5% lvl); hn, his forign xchang mark is rlaivly fficin. Finally, h UFRH is sd for h Japans yn and h U.S. dollar, which givs,. 6 (saisically significan a h % lvl) and + = =.978 (wih saisically significan a h % lvl and a h % lvl); hn, his forign xchang mark is rlaivly fficin. Tabl b: Tsing for h Unbiasd Forward Ra Hypohsis (UFRH), Eq. () s = + f + f + ε if and R SSR F D W N $/ , (.6) (.66) (.66) $/ , (.5) (.34) (.35) /$ , (.33) (.35) (.35) No: S, Tabl. Sourc: S, abl. 6

13 Furhr, h composi fficincy, q. (3), is prsnd in Tabl 3. For h U.S. dollar and uro h rsuls ar, β (saisically insignifican) and β + β = =.97 (wih β saisically significan a h % lvl); hn, h composi fficincy holds, bu only h forward ra conribus o h fuur spo ra. Thn, h composi fficincy for h U.S. dollar and Briish pound givs h rsuls: β.4 (saisically significan a h % lvl) and β + β = =.968 (wih βsaisically significan a h 5% lvl and β saisically significan a h % lvl); consqunly, h composi fficincy rlaivly holds and boh spo and forward ras conribu o h fuur spo ra. Lasly, h composi fficincy for h Japans yn and h U.S. dollar is sd and h rsuls ar: Th β =.5 (saisically significan a h % lvl) and β + β = =.977 (wih βsaisically insignifican and β saisically significan a h % lvl); hus, h composi fficincy rlaivly holds, bu only h forward ra conribus o h fuur spo ra. Tabl 3: Th Composi Efficincy, Eq. (3) s = β + βs + β f + ε if β, β = w, β = ( w), and β + β = w + ( w) β β β R SSR F D W N $/ , (.6) (.4) (.) $/ , (.5) (.65) (.64) /$ , (.33) (.65) (.64) No: S, Tabl. Sourc: S, Tabl. In addiion, sing q. (4), w wan o s if h currn xchang ra and h currn xpcaions of fuur xchang ras ar linkd and if boh dpnd on xpcaions concrning h fuur fundamnals ( E Φ + ). By using ( s s ) for h rm E ( s+ s ), w hav h following rsuls prsnd in Tabl 4, for h $/, $/, and /$ xchang ras. Also, h abl shows and a scond column wih h corrcion of h srial corrlaion of h rror rm. Th rsuls rval ha h xpcd fuur spo ra is significan, as wll as h fuur fundamnals, which mans ha h mark bs forcas of h fuur spo ra is h currn spo ra. Th currn xchang ra and h currn xpcaions of h fuur xchang ra ar linkd on xpcaions rgarding h fuur fundamnals. This indicas ha xchang ras follow a random walk. Lasly, Tabl 5 ss h xchang ra xpcaions and h nws. W sar, firs, running q. (9) bwn U.S. and EMU ($/ ) o forcas h E ( i i ). W gnra, ID = ( i i ) and h rsuls of his rgrssion ar prsnd in foono. Th compur is giving o us h IDF E ID = E ( i i ) from h abov quaion. Wih his forcasing inrs diffrnial IDF, w run q. (8) and h rsuls shows ha (saisically 7

14 insignifican boh cofficins) and =.965 (saisically significan a h % lvl). Thus, h xchang ra mark for ($/ ) is fficin and h unanicipad vns ( nws ) hav no ffc on spo xchang ra (hy ar anicipad). W coninu wih U.S. and U.K. ($/ ), running q. (9) o forcas h E ( i i ) and h rsuls of his rgrssion ar givn in foono. Th compur is giving o us h IDF E ID = E ( i i ) from h abov quaion. Wih his forcasing inrs diffrnial shows ha (saisically significan a 5% and % IDF, w run q. (8) and h rsuls Tabl 4: Exchang Ra Prdicabiliy, Eq. (4) s = + ( m m ) β( y y ) + γ ( i i ) + δ E ( s+ s ) + ε Variabls s ($/ ) s ($/ ) s ($/ ) s ($/ ) s ( /$) s ( /$) c (.6) (.7) (.4) (.98) (.95) (.) m m (.59) (.) (.55) (.7) (.5) (.44) y y (.36) (.3) (.33) (.87) (.4) (.9) i i (.) (.) (.) (.) (.) (.) s s (.7) (.3) (.63) (.4) (.84) (.9) s (.38) s (.38) ε (.98) (.56) ε (.8) (.3) ε (.49) (.7) R SSR F 7.644, , , D W N No: S, Tabl ; m = ln of mony supply, y = ln of incom, i = shor-rm inrs ra, and an asrisk ( ) on a variabl dnos h forign variabl. Sourc: S, Tabl. lvl); hn, diffrn han zro boh cofficins and =.97 (saisically significan a h % lvl). Thus, h xchang ra mark for ($/ ) is infficin and h changs in his 8

15 xchang ra ar unanicipad (dpnd on nws ). Now, w coninu wih U.S. and Japan ( /$), running q. (9) o forcas h E ( i i ). W gnra, ID = ( i i ) and h rsuls of his rgrssion ar prsnd in foono 3. Th compur is giving o us h IDF E ID = E ( i i ) from h abov quaion. Wih his forcasing inrs diffrnial IDF, w run q. (8) and h rsuls shows ha, (h consan rm is saisically significan a % lvl, hn, diffrn han zro; h is saisically insignifican, hn zro) and =.979 (saisically significan a h % lvl). Thus, h xchang ra mark for ( /$) is no vry fficin, bu h nws do no affc i, hy ar anicipad. Tabl 5: Exchang Ra Expcaions and Nws, Eq. (8) s = + f + [( i i ) E ( i i )] + ε if and R SSR F D W N $/ (.7) (.3) (.) $/ , (.5) (.) (.3) /$ , (.39) (.8) (.) No: S, Tabl. Sourc: S, Tabl. VI. Diagnosic Tss and Policy Implicaions Th xchang ras do no hav a consan man and xhibi phass of rlaiv ranquiliy followd by priods of high volailiy (no consan varianc). 3 W wan o s and xamin ID = s +.77 s.73 f.68 f ID.66 ID (.69) (.85) (.73) (.45) (.9) (.9) (.89) R =.845, SSR = 5.737, F =., D W =.963, N = 3, RMSE =.67 ID = s s +.78 f.538 f ID.75 ID (.86) (.94) (.99) (.53) (.39) (.59) (.58) R =.977, SSR =.6, F =,85.8, D W =.99, N = 3, RMSE =.5464 ID = s s 7.5 f +.35 f ID +.9 ID (3.77) (.54) (45.99) (35.89) (4.643) (.63) (.63) R =.6, SSR =,96.9, F =.6, D W =.6, N = 59, RMSE =

16 h bhavior of hs im sris, hr, and o modl h condiional hroskdasiciy (ARCH or GARCH). 4 By graphing h following hr xchang ras: /$, /$, and /$, 5 w s ha hs sris ar no saionary; hir mans do no appar o b consan and hr is a srong hroskdasiciy. Thy hav im-varying mans (hy ar no saionary). Ths xchang ras show ha hy go hrough susaind priods of apprciaion and hn dprciaion wih no ndncy o rvr o a long-run man. This yp of random walk bhavior is ypical of nonsaionary sris. 6 Enormous shocks wr h cnral banks arg ras prsisnc wih a violnly vry low valu (closd o zro) for svn or mor yars. Also, h volailiy of many macro-variabls was no consan ovr im. Globalizaion has mad h macro-variabls in h four counris and conomis (U.S., Euro-zon, U.K., and Japan) o shar co-movmns ( ρ > ). m, m Th hisorical daa 7 show ha: () S =. 8 $/, σ S =. 33; h xpcd s f = rp =.449 and σ =. 763 ; h acual S F 3 = RP = rp +, σ RP = ; and ln of h acual s f 3 = rp =. 5453, σ rp = () S =.76 $/, σ S =. 9468; rp + =. 4, σ = ; RP =. 3693, σ RP =. 5566; and rp =. 63, σ rp = (3) S = /$, σ S 3 = 5, ; rp + =. 77, σ = ; RP =. 69, σ 3.87, and rp =. 455, σ Ths xising risk prmia show RP = rp = rp + ha h forign xchang mark is no vry fficin. W ar in an informaional disquilibrium or an informaional discord ha has crad normous social cos and disrss in modrn ims. Acually, a disribuion of walh from on normal invsor o h ohr invsor (spculaor) and ransfrring of risk from h spculaor o h hard working savr. Th public forms is xpcaions by using I insad of Π and damags h conomy. Th rol of acadmics is o ach h public, bu poliically corrcnss and libralism do no allow i o ak plac; h rol of public policy is o s and achiv social objcivs hrough rgulaions and a fair ax sysm. Th idal siuaion for h Fd would b o hav compl knowldg of h conomy s srucur and of all h random vns ha migh impac i. If h Fd had an aainabl objciv, i could s is policis rp + 3 If h varianc of a sochasic variabl is no consan [ E ( ε σ ], i is calld hroskdasic. 4 ARCH = Auorgrssiv Condiional Hroskdasic modl and GARCH = Grnralizd Auorgrssiv Condiional Hroskdasiciy. In Saisics, a collcion of random variabls is hroscdasic [or hroskdasic ; from Ancin Grk ἕτερον (hro = diffrn ) and σκέδσις (skdasis = disprsion )] if hr ar sub-populaions ha hav diffrn variabiliis from ohrs. Hr variabiliy could b quanifid by h varianc or any ohr masur of saisical disprsion. Bcaus hroskdasiciy concrns xpcaions of h scond momn of h rrors, is prsnc is rfrrd o as misspcificaion of h scond ordr. 5 Graphs, Figurs, and many Tabls ar omid, hr, du o spac consrains, bu hy ar availabl from h auhor upon rqus. 6 Th s of saionary (Augmnd Dicky-Fullr Uni Roo Ts) shows: () Indirc quos for h U.S. dollar: S ( /$): -.47 I(); D(S ): I(). S ( /$): I(); D(S ): I(). S 3 ( /$): I(); D(S 3 ): I(). () Dirc quos for h U.S. dollar: S ($/ ): -.54 I(); D(S ): I(). S ($/ ): I(); D(S ): I(). S 3 ($/ ): -.75 I(); D(S 3 ): I(). [I() = sris conain zro uni roos (saionary), I() = sris conains on uni roo (ingrad ordr on, nonsaionary), D(S) = variabl in s diffrncs, significan a h % lvl, significan a h 5% lvl, and significan a h % lvl]. 7 S, Kallianiois (6b). )

17 accordingly and achiv ha goal. Som popl bliv ha Fdral Rsrv officials hav a sor of scond sigh ha hy us o forll h fuur. Bu h ruh is ha h bs conomic forcasing is scond ra whn compard o h public s xpcaion. No on undrsands h conomy s srucur wih nough prcision o kp i prpually humming along in balanc and a op spd. Unforunaly, policymakrs ncssarily rly on scond-bs soluions. 8 During h las global financial crisis, h monary policy (Quaniaiv Easing) wih zro inrs ra from Dcmbr 8 o Dcmbr 5 was complly inffciv and fficincy has disappard from h marks bcaus popl soppd o rus h corrupd financial mark anymor. Furhrmor, xchang ras rspond o surpriss, o nws, and o human acions du o ignoranc of Π and knowldg of I only. Bu hs surpriss ar unprdicabl. Bcaus xchang ras rspond snsiivly o h unxpcd vns ha randomly hi marks, xchang ras hmslvs also mov randomly. This is h naur of mark fficincy and has unforunaly bcom our scond naur, oo. Invsors hav no ohr choic xcp o accp h mark fficincy bcaus h spo marks ar following h fuurs marks wihou any qusions and if somon ignors h fuurs mark, h will hav normous losss and will go bankrup. W ar nslavd o h fuurs marks and for his rason, w hav o rgula hs marks. 9 VII. Conclusions In hs spcificaion modls, w sd h hypohsis ha h forign xchang mark is fficin and w argud ha h forward ra fully rflcs h limid availabl informaion (du o h lack of compl and corrc global knowldg) abou h xchang ra xpcaions and h forward ra. Thus, h forward ra is usually viwd by h mark paricipans as an unbiasd prdicor of h fuur spo ra. Th convnional s of h unbiasdnss hypohsis ha w usd was a rgrssion simaion by fiing h currn spo on h on-priod laggd spo ra, on h on-priod laggd forward ra, on h on-priod laggd spo and forward ra, h xchang ra prdicabiliy, and on h on-priod laggd forward ra and h nws. Ths ss involv h join hypohsis ha h consan rms do no diffr from zro, ha h cofficins on h on-priod laggd spo and forward ras do no significanly diffr from on, ha h sum of h cofficins of h on priod laggd spo and forward ras do no significanly diffr from on, ha h cofficin of h nws is no diffrn from zro, and ha h rror rms pass som saisical ss (srial corrlaion, normaliy, homoscdasiciy, ARCH, c.). Th mpirical rsuls show ha w canno rjc h unbiasd hypohsis for U.S.A. and Euro-zon, bu for h U.K. and Japan i is rjcd. Th rsuls imply ha w can us h forward ra as a proxy for h prdicion of h spo ra nx priod bwn dollar and uro ($/ ). Thr is som insabiliy in h paramrs of almos all h quaions of h modl, bu, from a forcasing poin of viw, his is consisn wih h las cos approach o h conomic agns, alhough i may no yild h minimum forcas rror du o inrvnions, 8 S, Economic Trnds, Fdral Rsrv Bank of Clvland, Augus 994, p.. 9 Th Commodiy Fuurs Trading Commission (CFTC) has jurisdicion o rgula h fuurs marks wih ovrsigh ovr h nir indusry. Each U.S. fuurs xchang opras as a slf-rgulaory organizaion govrning is floor brokrs, radrs and mmbr firms. Naional Fuurs Associaion rgulas vry firm or individual ha conducs fuurs rading businss wih h invsing public. S, hps:// Also, for rading forign currncy, s, hps://

18 incompl and parial knowldg (incorrc informaion), and simpliciy in modling. Th ovrall rsuls show ha h forign xchang marks for boh h U.S. and Euro-zon ar pry fficin. Briain s and Japan s mark fficincis ar qusionabl. Furhr diagnosic ss, lik hroskdasiciy, rsidual, spcificaion, and sabiliy ss ar usful o b applid for h abov modls. Rfrncs Ahmad, Rubi and Yun Mng Wong (93), Forign Exchang Marks Efficincy undr Rcn Criss: Evidnc from h Europan Marks, hp:// 3-Rading/paprs/Compl-Wong%6Ahmad.pdf Ariz, A.C., I.N. Kallianiois, al (5), Saisical Spcificaions and Divrs Tss of Efficincy in Europan Forign Exchang Marks, Inrnaional Journal of Economics and Financ, Vol. 7, No., 5, pp hp:// Bilson, John (978), Raional Expcaions and h Exchang Ra, in Th Economics of Exchang Ras, Edid by J. Frnkl and H.G. Johnson, Rading MA: Addison-Wsly. Davidson, Jams Dal (5), Th Ag of Dcpion: Dcoding h Truhs Abou h U. S. Economy, Nw York: Sragic Invsmn. Dornbusch, Rudigr (978), Monary Policy undr Exchang Ra Flxibiliy, in Managd Exchang-Ra Flxibiliy: Th Rcn Exprinc, Fdral Rsrv Bank of Boson Confrnc Sris, No.. Endrs, Walr (995), Applid Economric Tim Sris, Nw York: John Wily & Sons, Inc. Fama, E. (97), Efficin Capial Marks: A Rviw of Thory and Empirical Work, Journal of Financ, 5, May, pp Frnkl, Jacob A. (984), Flxibl Exchang Ras, Prics, and h Rol of Nws : Lssons from h 97s, in Economic Inrdpndnc and Flxibl Exchang Ras, did by J. S. Bhandari and B. H. Punam, Cambridg, MA: Th MIT Prss, pp Frnkl, Jacob A. and Michal L. Mussa (98), Th Efficincy of Forign Exchang Marks and Masurs of Turbulnc, Amrican Economic Rviw, 7, pp Isard, Pr (98), Expcd and Unxpcd Changs in Exchang Ras: Th Rol of Rlaiv Pric Lvls, Balanc-of-Paymns Facors, Inrs Ras and Risk, Fdral Rsrv Board, Inrnaional Financ Discussion Paprs, No. 56. Kallianiois, I.N. (7), «Ἡ Τρέχουσ Ἑλληνική Κρίσις ἐστίν Ἔργον τῶν ηµιουργῶν τῶν υτικῶν Ἐπνστάσεων τοῦ Πρελθόντος», Απολογητικά, Fbruary 9, 7, pp. -7. hp://apologiikaa.blogspo.com.cy/7//i.hml Kallianiois, I.N. (6a). «Ἐπνστάσεις, Κρίσεις κί Ἑνώσεις», Chrisian Vivliografia, Dcmbr, 6, pp. -6. hps://chrisianvivliografia.wordprss.com/6///%%bc%9%cf%8%c%b%c %bd%c%b%cf%83%cf%84%c%ac%cf%83%c%b5%c%b9%cf%8- %c%ba%cf%8%c%af%cf%83%c%b5%c%b9%cf%8-%c%ba%c%b%c%af- %%bc%9%c%bd%cf%8%cf%83%c%b5%c%b9%cf%8/ Kallianiois, I.N. (6b), Facors Affcing h Exchang Ra Risk prmium, Journal of Applid Financ and Banking, Vol. 6, No. 6, pp hp:// Kallianiois, John N. (3a), Exchang Ras and Inrnaional Financial Economics: Hisory, Thoris, and Pracics, Nw York: Palgrav MacMillan. Kallianiois, John N. (3b), Inrnaional Financial Transacions and Exchang Ras: Trad, Invsmn, and Pariis, Nw York: Palgrav MacMillan.

19 Kallianiois, I.N. (), Th Gnraiv Moiv of Europan Union and is Las Sruggl for Survival, Inrnaional Journal of Businss and Commrc, Vol., No. 6, Fbruary, pp.-4. hp:// Mishkin, F. S. (983). A Raional Expcaions Approach o Macroconomics. Chicago: Univrsiy of Chicago Prss. Muh, J. F. (96), Raional Expcaions and h Thory of Pric Movmns, Economrica, 9, pp Samulson, P. A., and W. D. Nordhaus (985). Economics, h diion, Nw York, NY: McGraw-Hill. Wickrmasingh, Gunran B. and Ja H. Kim (8), Wak-Form Efficincy of Forign Exchang Marks of Dvloping Economis: Som Sri Lankan Evidnc, Journal of Emrging Mark Financ, Vol. 7, No., Augus, pp Auhor Dr. Ioannis N. Kallianiois Economics/Financ Dparmn, Th Arhur J. Kania School of Managmn, Univrsiy of Scranon, Scranon, USA, ioannis.kallianiois@scranon.du Acknowldgmns Economics/Financ Dparmn, Th Arhur J. Kania School of Managmn, Univrsiy of Scranon, Scranon, PA 85, U.S.A. I would lik o acknowldg h assisanc providd by Andra V. Sanz, Jrry Zoloukha, Angla J. Parry, and Janic Mcadon. This papr prsnd a h EEA 43rd Annual Confrnc in Nw York Ciy, Fbruary 3-6, 7 and I hav bnfid from confrnc paricipans. Financial suppor (profssional ravl xpnss, submission fs, c.) was providd by Provos s Offic (Faculy Travl Funds, Hnry Gorg Fund, and Faculy Dvlopmn Funds). Th usual disclaimr applis. Thn, all rmaining rrors ar min. 3