INTERNATIONAL PARITY CONDITIONS AND MARKET RISK

Transcription

1 INTERNATIONAL PARITY CONDITIONS AND MARKET RISK Thomas C. Chiang, Ph.D. Marshall M. Ausin Profssor of Financ Dparmn of Financ, LBow Collg of Businss, Drxl Univrsiy 34 Chsnu Sr, Philadlphia, Pa. 94, USA Tl: (25) Kywords: Inrnaional Ass Pricing, Purchasing-Powr Pariy, Uncovrd-Inrs Pariy, Exchang-Ra Risk, Equiy Prmiums, Ral Inrs-Ra Pariy, Unbiasd Forward Ra Hypohsis, Fishr Equaion, Spo Exchang Ra, Forward Exchang Ra

2 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 2 ABSTRACT This aricl prsns a s of inrnaional pariy condiions basd on consisn fficinmark bhavior. W hypohsiz ha dviaions from pariy condiions in inrnaional bond, sock, and commodiy marks ar aribuabl mainly o rlaiv quiy prmiums and ral inrs-ra diffrnials. Tsing his hypohsis agains four Europan marks for h rcn floaing currncy priod, w gain supporiv vidnc. Morovr, h dviaions of uncovrd-inrs ra pariy, inrnaional sock-rurn pariy, and purchasing-powr pariy ar no indpndn; h vidnc suggss ha dviaions from h hr pariis ar drivn by wo common facors: quiy-prmium diffrnial and ral inrs-ra diffrnial.

3 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 3. INTRODUCTION In h pas hr dcads of floaing xchang ras, a subsanial amoun of rsarch has bn dvod o idnifying linkags in inrnaional marks. Th mos prominn among hs linkags ar h uncovrd-inrs pariy (UIP), purchasingpowr pariy (PPP), and inrnaional sock-rurn pariy (ISP). Th imporanc of hs condiions sms no only from hir significanc as building blocks for inrnaional financ hory, bu also from hir applicaion in guiding rsourc allocaion in inrnaional mony, capial, and goods marks. Along wih horical advancmns, a larg volum of mpirical rsarch has bn spawnd an xaminaion of h validiy of hs pariis as applid o various mark daa. Hodrick (987), Froo and Thalr (99), Bkar and Hodrick (993), Lohian and Taylor (997a, 997b), Engl (996), and Rogoff (996) provid summaris for various yps of mark bhavior. A gnral consnsus drivd from hs sudis is ha mark imprfcions, ransacion coss, risk prmiums, masurmn rrors, xpcaions rrors, and h lack of mor powrful saisical chniqus ar h main facors ha frusra pariy condiions. I is no our purpos o ngag in an xhausiv rviw of all h pariy condiions, nor is i our innion o provid a horough mpirical s. Rahr, our goal is o provid a simpl horical framwork wihin which various ass-rurn rlaionships can b illusrad and rasond by sablishd financ horis. From his framwork, w ar abl o idnify wo common facors ha conribu o dviaions of

4 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 4 h hr pariy condiions: quiy-prmium diffrnial and ral inrs-ra diffrnial. Th vidnc basd on daa drivd from four major Europan marks validas our argumns. Following his inroducory scion, Scion 2 provids simpl y consisn mark bhavior o achiv h hr pariy condiions in h vin of a spculaiv fficin framwork (Roll, 979). Scion 3 offrs som mpirical vidnc for ach pariy condiion. Scion 4 provids a horical framwork ha rlas dviaions of h pariy condiions o quiy prmiums and ral inrs-ra diffrnials and hn rpors h mpirical vidnc. Scion 5 concluds h sudy. Furhr mpirical vidnc for addiional pariy condiions is offrd in an appndix. 2. INTERNATIONAL PARITY CONDITIONS Earlir conribuions by Solnik (978), Roll and Solnik (979), and Roll (979) laid a firm foundaion for consolidaing inrnaional pariy condiions. Basd on a fw radiional assumpions, including h prmiss ha boh goods and financial marks ar prfc and ha hr is an absnc of ransacional coss and barrirs o rad, h law of on pric implis ha homognous goods or asss ar xpcd o rad a h sam xchang-adjusd pric in any wo counris. Thus, inrnaional pariy holds if xpcd ass rurns claimd by invsors ar qual rgardlss of whhr invsmns occur in domsic or forign mark. Considr an conomic agn ngaging in a on-priod invsmn who xpcs o claim x in domsic currncy whn h conrac maurs in h fuur. Th agn hn

5 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 5 facs wo opions: invs in h domsic mark or invs in h forign mark. Th prsn valus of hs wo invsmns ar: pv x j, = + R j, () pv j, = x, (2) ( + R j, )( + s ) + + whr R j, + and R j, ar xpcd rurns in domsic and forign marks for ass j, rspcivly; an asrisk dnos a forign variabl and a suprscrip rfrs o an xpcaion opraor; s + > dnos h xpcd ra of apprciaion of h forign currncy; s is h spo xchang ra a im, xprssd as unis of domsic currncy pr uni of forign currncy; and pv sands for h prsn valu. An quilibrium condiion lads o: (+ R j, + ) = (+ R j, )( + s ). (3) Applying h law of on pric and aggrgaing ovr h nir mark by aking naural logarihms hroughou h quaion allows us o wri a gnral xprssion of an inrnaional pariy rlaionship as:

6 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 6 R + = R s +, (4) whr ln(+ R + ) R +. Noic ha h variabl x + may b alrnaivly dnod by E( x I ), indicaing an xpcd valu condiional on informaion availabl a im. By dfining ha R + = p + - p and s + = s + - s, whr p +, p, s + and s ar xprssd in naural logarihms, h xpcd rurn, R +, in his conomy is simplifid by h pric apprciaion of asss or goods. 2 Applying h indics of + and p o p bond, quiy, and commodiy marks, Equaion (4) implis hr principal opn-pariy condiions as: r = r s + + (5) Rm, + = Rm, s + (6) p p + = +, (7) s + whr r is h shor-rm inrs ra from im o ; Rm, + dnos h xpcd rurn on h sock mark; and p + rprsns h xpcd inflaion ra. Th lf-sid variabls of hs quaions ar domsic xpcd rurns, whil h righ-sid variabls

7 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 7 ar xpcd rurns in forign insrumns plus xpcd apprciaion of currncy in h forign counry o ngag invsmns. Th condiion in Equaion (5) is rfrrd o as h uncovrd inrs-ra pariy (UIP), which says ha h risk-fr rurn from a local invsmn is qual o h comparabl rurn in a forign insrumn plus an xpcd apprciaion ra of h forign currncy. Sinc h oucom of h fuur spo ra is uncrain, an invsor wih risk avrsion nds o sll h oal procds (principl plus inrss arnd) in h forward mark o hdg h risk. As a rsul, a covrd vrsion of inrs-ra pariy is achivd as follows: r = r + ( f s ), (8) whr f is h naural logarihm of h forward-xchang ra wih a mauriy ha machs ha of h insrumns of r and r. This quaion sas ha a rlaivly highr inrs ra in h domsic mark mus b offs by is currncy discoun in h forward mark. Sinc all h paramrs in Equaion (8) ar dircly assssabl, his condiion usually holds unlss h financial mark is imprfc or hr ar masurmn rrors for h daa. Th pariy in Equaion (6) may b calld h inrnaional sock-rurn pariy condiion (ISP) - h rurn in h domsic quiy mark is xpcd o b qual o h

8 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 8 xchang-ra-adjusd rurn in h forign mark. 3 For insanc, an indx rurn in h UK mark is %, whil h comparabl indx rurn in h US mark is 8%; h xcss 2% rurn in h UK mark will b offs by h sam magniud of dollar apprciaion. This condiion is mor complicad han ha of UIP sinc i involvs xpcaions for boh sock rurns and xchang-ra changs. Th xpcaions formaion for sock rurns and xchang ras ar govrnd mainly by diffrn ss of conomic fundamnals and invsor sophisicaion (Albuqurqu, Baur, and Schnidr, 24), alhough hy migh shar som common facors. Th volail bhavior of sock rurns adds an addiional risk o h pariy condiion. Th hird condiion, xprssd in Equaion (7), is h rlaiv purchasing-powr pary, which sas ha h xpcd rurn spculad on domsic goods is qual o h xpcd rurn on h forign goods mark plus an xpcd forign-currncy gain. Alrnaivly, w can hink abou h fac ha h spculaiv ral rurn o h domsic conomic agn can b achivd by dflaing h forign nominal rurn ( p + ) s + wih h domsic inflaion ra ( p p + ); ha is, ( + s + ) - p +. This xprssion is a diffrncd form of h ral xchang ra. In an fficin mark, according o Roll (979), such an xcss rurn from ffciv spculaion mus b zro. In ohr words, p ( + s + ) - p + =. A common faur shard by hs hr principal pariis is ha linkags bwn domsic rurns and forign-mark rurns all go hrough h channl of h forign-

9 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 9 xchang mark. As a rsul, a shock in h currncy mark will cra an xchangra risk, affcing hr marks (goods, bonds, and socks) simulanously. Morovr, if w viw h xchang ra as an ndognous variabl, h chang in an xchang ra is sn o b associad wih changs in rlaiv rurns, as rflcd in h rlaiv-inflaion diffrnial, inrs-ra diffrnial, and sock-rurn diffrnial. Ths rlaiv-rurn variabls will b drmind furhr by undrlying supply and dmand condiions in a gnral quilibrium framwork. ( r and No ha h rlaionships bwn pair-wis variabls such as ( and r ) and Rm p +, + ) ar wll documnd in h liraur. Firs, h xpcd inflaion ra in h goods mark is linkd o h rurn in h bond mark hrough h Fishr quaion. Formally w wri: r r + + p = and (9) r = r p, () + whr r + and r ar xpcd ral inrs ras for h domsic and forign counris, rspcivly. If boh PPP and UIP hold, h ral inrs-ra pariy mus b sablishd. Tha is,

10 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ r = r +. () Th ral inrs-ra pariy implis ha h ral rurn on capial mus b qual. I is of inrs o poin ou ha his condiion holds indpndnly of any xchang-ra facors. Anohr implicaion of his pariy condiion is ha p + p + = r r ; ha is, h inrs-ra diffrnial rflcs h xpcd inflaion-ra diffrnial as infrrd by Fama s fficin inrs-ra hypohsis (Fama, 975). Du o h vry naur of h informaion conn involvd in hs marks, Marson (997) obsrvs ha inrnaional-pariy condiions, rprsnd by a sysm formd by Equaion (5), Equaion (7), and Equaion (), ar inrrlad sinc hir dviaions from pariy ar drivn by h sam s of informaion, such as h inrs-ra diffrnial and inflaion-ra diffrnial. In paricular: r r = + ( r + s )] [ [ r p + ( p + + s + )] () This quaion sas ha an x an ral inrs-ra diffrnial is associad wih dviaions of UIP and PPP; 4 i rvals no dirc conncion wih sock-rurn diffrnials. Scond, h rurn in h bond mark is linkd o h rurn in h sock mark hrough h Capial Ass Pricing Modl (CAPM) and rm-srucur rlaionship

11 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ (Campbll, 987). In h inrnaional conx, h coxisnc of an uncovrd inrspariy and inrnaional sock-rurn pariy mus lad o h quiy-prmium pariy as: R m, r = Rm, r +. (2) I suggss ha xcss rurns in inrnaional quiy marks mus b qual. Again, xchang-ra variaions play no xplici rol in xplaining h quiy-prmium diffrnial unlss w wan o considr h ral rm. Th inrnaional CAPM implis ha any divrgnc in h quiy-prmium diffrnial mus rflc h risk diffrnial (bas) associad wih wo marks. To dcompos h quiy prmium diffrnial, w yild: ( R + r ) ( Rm, r ) = [ R m, ( Rm, + s )] [ r ( r + s )]. (3) m, This quaion sas ha h dispariy in h quiy prmiums bwn wo marks is associad wih dviaions of h sock-rurn pariy and h uncovrd-inrs pariy and has no dirc conncion wih h inflaion-ra diffrnial. 5 Bfor w mov o h nx scion, i is usful o summariz h argumns ha w hav dvlopd o his poin. Basd on consisn mark bhavior, w consruc a global financial-mark sysm in which inrnaional marks ar linkd hrough h PPP, UIP,

12 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 2 and ISP for goods, bonds, and socks; whil h domsic goods mark is linkd o bond marks hrough h Fishr quaion by a ral inrs ra, and h bond mark is linkd o h sock mark via h CAPM by quiy prmiums. Any shocks o h sysm could dircly or indircly disurb h quilibrium condiions in h goods, bonds, or socks marks hrough changs in rlaiv ass rurns. Ths changs, in urn, could alr quiy-prmium diffrnials and ral inrs-ra diffrnials, causing inrnaional capial movmns and rad flows. As a rsul, w obsrv ha dviaions of pariy condiions ar associad wih xcss-rurn diffrnials. Chcking ino h facors bhind h xcss-rurn diffrnials, w prciv ha xcss rurns rflc mainly compnsaion for xcss risk associad wih sock rurns, inflaion, and xchang ra variaions. 3. EMPIRICAL EVIDENCE 3.. Daa Alhough a considrabl amoun of mpirical rsarch has bn conducd in xamining inrnaional pariy condiions, h approachs uilizd hav varid in rms of counris, im priods, frquncy, modl spcificaions, and undrlying horis, among ohr facors. To obain a consisn comparison, w shall provid a unifid approach by using a consisn daa s o xamin four major Europan counris, consising of h Unid Kingdom (UK), Grmany (GM), Franc (FR), and Swizrland (SW) and mploying h Unid Sas (US) as a rfrnc counry (wih an asrisk in our noaion).

13 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 3 In h mpirical simaions, w ra h US mark as a pric makr du o is rlaivly dominan siz and ffcivnss in informaion procssing. As such, i allows us o xamin h impac of h US mark on ach of h four Europan marks. This sudy uss nd-of-h-monh spo and on-monh forward xchang ras, wih h xchang ras xprssd as prics of h local currncy pr uni of h US dollar. Shorrm inrs ras ar masurd by h on-monh Eurocurrncy dposi ras for ach counry. Ths Eurocurrncy dposi ras hav bn widly usd in mpirical sudis du o hir homognous faurs and hir convninc in comparing across marks. Th sock-pric indxs for h fiv marks ar h FTSE (Unid Kingdom), CAC 4 (Franc), Dax 3 (Grmany), Swiss Mark Pric (Swizrland), and S&P 5 Indx (Unid Sas). Inflaion ras ar masurd by h naural log diffrnc of consumrpric indics for h counris undr invsigaion. All h ras ar masurd on a monhly basis, as dicad by h fac ha consumr-pric indics ar availabl on only a monhly basis. In h manim, mploying monhly obsrvaions allows us o consruc variabls such as forward-xchang ras and shor-rm inrs ras having h sam mauriy wihou xprincing a daa ovrlap problm. Sinc sock indics for Franc and Swizrland ar availabl only from la 988 and h Basl Accord was ffciv a abou h sam im priod, our mpirical analysis is confind o h sampl priod from January 989 hrough Dcmbr 2. 6 all h daa wr akn from Daa Sram Inrnaional.

14 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ Evidnc on h Pariy Condiions Th goal of h mpirical xrcis in his scion is o highligh h main faurs of ach pariy condiion and o prsn h findings in a consisn fashion. As nod by Roll (979), inrnaional pariy condiions provid no spcific guidanc o h dircion and xn of causaion bwn rlaiv rurns and xchang ra changs. Placing h dpndn and indpndn variabls on ach sid of h s quaion varis among diffrn rsarchrs. In his scion w shall kp h simad quaion consisn wih h modl forms xprssd by Equaion (5) hrough Equaion (7). In ordr o achiv a consisn simaor, Whi (98) and Nwy and Ws (987) procdurs hav bn usd in simaing h following s of rgrssions: uncovrd Inrs-Ra Pariy: r = β + β ( r + s ) + ε, (4) inrnaional Sock-Rurn Pariy: R m, = β + β ( R m, + s ) + ε, (5) purchasing-powr Pariy: p = β + β ( p + s ) + ε, (6) whr β and β ar consan cofficins andε is an rror rm. Sinc xpcaions ar no dircly masurabl, w impos a raional xpcaions framwork by using ralizaions of h variabls as proxy. 7 Bcaus our main concrn is o xamin a pariy

15 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 5 condiion, a join s o invsiga h null hypohsis ha ( β β ) = ( ) will also b rpord. If h null canno b rjcd by h daa, a pariy condiion holds. Th simas for hr primary inrnaional-pariy condiions ar rpord in Panls A, B, and C of Tabl. Consisn wih xising vidnc (Solnik, 982; Mishkin, 984), non of h s quaions gains much suppor from h daa. Th join ss suggs ha h null hypohsis of ( β β ) = ( ) is rjcd uniformly. In paricular, h simad slops of h inrs-ra pariy in Panl A ar ngligibl and saisically insignifican. Ths rsuls, oghr wih h low R-squars of h s quaions, rndr no supporiv vidnc for h qualiy of h wo xchang-ra adjusd inrs ras. Th rsuls for simaing h inrnaional sock-rurn pariy ar prsnd in Panl B. Th simad cofficins indica ha corrlaions wih h US mark ar posiiv and saisically significan. 8 Th valus of h cofficins vary wihin a vry narrow rang, from.625 o.685 across h diffrn Europan marks, supporing h fficin aspc of comovmns of inrnaional sock rurns. Howvr, h s rsuls ar sill unabl o provid supporing vidnc for h null hypohsis ( β β ) = ( ). Th rjcion of h null implis h violaion of inrnaional sock-rurn pariy. This is undrsandabl sinc, in addiion o prfrnc diffrncs and possibl asymmrical informaion ( Frankl and Schmuklr, 2), h indx composiion varis among h

16 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 6 Tabl. Esimas of Inrnaional Pariy Condiions 2 Counry β β R DW Join Ts A. Uncovrd Inrs-Ra Pariy: r = β + β ( r + s ) + ε UK (28.96) (.69) (.) FR (27.56) (.923) (.) GM (29.42) (.9) (.) SW (9.7) (.5) (.) B. Inrnaional Sock-Rurn Pariy: R m, = β + β ( R m, + s ) + UK (.29) (2.) (.) FR (.22) (.49) (.) GM (.395) (7.837) (.) SW (.94) (9.222) (.) C. Purchasing-Powr Pariy: p = β + β ( p + ε s ) + UK (7.46) (.448) (.) FR (8.435) (.555) (.) GM (7.87) (.589) (.) SW (6.776) (.2) (.) a. Th indicas saisically significan diffrnc from zro a h % lvl. b. Th numbrs in parnhss ar absolu valus of h -saisics. c. DW dnos h Durbin-Wason saisic. d. Th join s is o s ( β β ) = ( ) ; h join s is h simad saisic 2 of χ (2) disribuion wih 2 dgrs of frdom and h numbrs in parnhss ar h significanc lvls. ε

17 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 7 naions and h undrlying indusris ar subjc o hir inhrn, diffrn volailiy and pric/inrs ra snsibiliy (Roll, 992). Panl C rpors simas of purchasing-powr pariy rlaiv o h Unid Sas. Again, h simad slops ar far from uniy. Non of h R-squars xcds h 2% lvl. This rsul is vry comparabl o hos rpord by Krugman (978), Roll (979), Frnkl (98), Solnik (982), and Mishkin (984), among ohrs. 9 This finding is no surprising sinc our daa sampl priod is rlaivly shor, whil mos of h vidnc in favor of h PPP mploys much longr daa spans. For xampl, Abuaf and Jorion (99), Lohian and Taylor (997b), Jorion and Swny (996), Chung and Lai (993, 998), Flissig and Srauss (2), and Baum, Barkoulas, and Caglayan (2) ar abl o find vidnc of man-rvrsion in dviaions from purchasing-powr pariy. Th failur of PPP in h shor run is prcivabl sinc, in h vry naur of pric bhavior, commodiy prics ar rlaivly sicky and xchang ras bhav mor or lss lik ass prics. Thus, h chang in xchang ras as hy adjus o nws appars o b mor snsiiv and ffciv han ha of commodiy prics. In addiion, failur o achiv PPP in h shor run may rsul also from variaion in h composiion of consumr-pric indics across diffrn counris (Pal, 99), diffring produciviy shocks (Fishr and Park, 99), and masurmn rrors in prics from aggrgaion (Talor, 988; Chung and Lai, 993).

18 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 8 4. DEVIATIONS FROM PARITY CONDITIONS AND RISK 4.. Sourcs of Dviaions Th analysis in Scion 2 convys wo imporan mssags: inrnaional-pariy condiions ar inrrlad and dparur from pariy condiions is commonly associad wih ral inrs-ra diffrnials and quiy-prmium diffrnials. Alhough som arlir rsarchrs (Korajczyk, 985; Lvin, 989; Huang, 99; Chiang, 99; Korajczyk and Viall, 992) rcogniz hs ky lmns, hir sudis mrly focus on a singl pariy (Hodrick, 987) or a smallr s of pariy condiions (Mishkin, 984; Marson, 997); an xplici rol of inrnaional sock marks is xcludd from hir analyss. Th currn sudy xnds prvious rsarch by incorporaing h linkag of sock marks ino an ingrad financial sysm. This rsarch is bound o provid mor insigh ino a muli-mark analysis of inrnaional ass allocaion, offring a broadr spcrum of porfolio bhavior in a gnral quilibrium framwork. To illusra, assuming ha xpcd changs in spo xchang ras can b prdicd by a linar rlaion of h xpcd inflaion-ra diffrnial, shor-rm inrs-ra diffrnial, and xpcd naional sock-rurn diffrnial as implid by h hr pariy condiions, w wri: = α ( p p ) + η( r r ) + γ ( R R ). (7) s m, m,

19 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 9 Th argumns on h righ sid of Equaion (7) ar considrd o b h ky variabls ha affc inrnaional ransacions involving a naion s balanc of paymns. In paricular, h variabl of h xpcd inflaion diffrnial dicas rad flows in a counry s currn accoun, whil h ohr wo argumns govrn capial flows involving bonds and socks in h capial accouns. Th wigh of ach componn will b rflcd, rspcivly, in h paramrs α, η, and γ ; h rsricion α + η + γ = is consraind by h sum of componns of h balanc of paymns. Subracing ( r ) 2, 3, from boh sids of Equaion (7) and rarranging h variabls yilds: r s ( r r ) = γ [( Rm r ) ( Rm r )] + α[( p r ) ( p r )](8),, An imporan mssag mrging from Equaion (8) is ha h dviaion from UIP is du ssnially o h xcss rlaiv rurns prvailing in sock and goods marks as compard wih h risk-fr ra in h bond marks. A sudy by Giovannini and Jorion (987) finds vidnc ha forign xchang-risk prmiums ar corrlad wih inrs ras. In fac, h informaion from quaion (8) indicas ha h sourcs of uncrainy com from h sochasic naur of discoun facors associad wih sock rurns and inflaion ras rlaiv o inrs ras. Using Equaion (9) and Equaion () and dfining δ = s ( r r ), w obain: + δ = γ[( r ) ( R r )] α( r r ). (9) R m, m,

20 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 2 Th x an xcss dprciaion of a naional currncy byond is inrs-ra pariy condiion, whr δ is posiiv, is sn o b associad wih rlaivly highr risk in sock rurns and/or inflaion variaions, rflcd in a rlaivly highr quiy prmium and/or lowr xpcd ral inrs-ra diffrnial. Thos paramrs ar h main facors ha caus inrnaional capial flows. Thus, violaions of UIP corrspond o inrnaional capial flows. Comparing Equaion (9) wih xising liraur, i is asy o s ha h ral inrs-ra diffrnial hypohsis proposd by Korajczyk (985) is quivaln o rquiring ha γ =, whil h quiy-prmium diffrnial hypohsis suggsd by Chiang (99) is o impos h rsricion ha α =. Of cours, h UIP holds whn α = γ =. Nx, l us considr h dviaion of h inrnaional sock-rurn pariy, dfind as φ = ( R R ). This xprssion can b furhr dcomposd as: s m, m, φ = [ s ( r r )] [( R r ) ( R r )] m, m,. Using h informaion in Equaion (8), w hn driv: φ = ( γ )[( r ) ( R r )] α ( r r ). (2) R m, m,

21 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 2 Equaion (2) indicas ha h dviaion of h ISP is aribuabl o h quiyprmium diffrnial and ral inrs-ra diffrnial. By h sam okn, i can b shown ha: θ = γ [( r ) ( R r )] + ( α )( r r ), (2) R m, m, whrθ = ( p p ), which dnos h x an valu of h dviaion of h s rlaiv purchasing-powr pariy. By chcking h righ-hand-sid variabls of Equaion (9) hrough Equaion (2), w obsrv ha dparurs from pariy condiions ar all aribuabl o h sam facors: h quiy-prmium diffrnial and h ral inrs-ra diffrnial. 4 This is quivaln o saying ha h following condiions mus b saisfid in ordr o hav hs pariy condiions hold: xpcd ral rurns on bonds ar qual across marks, and xpcd xcss rurns in naional quiy marks ar qual across rading counris. Th mphasis on h ral inrs-ra pariy o xplain h dparur of h hr pariis has bn wll documnd (Mishkin, 984; Marson, 997). Howvr, our analysis idnifis an addiional facor, h quiy-prmium diffrnial, in inrpring h dviaions of h hr pariis. Anohr faur of our modl is ha dviaions from pariy condiions for h hr marks ar no indpndn. Th inrdpndncy among hm is rood ssnially in h inrdpndncy of financial marks; dynamic adjusmns ar snsiiv o

22 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 22 diffrncs in rlaiv ass rurns in an ingrad and unid financial sysm. From a policy poin of viw, a paramric chang in inrs ras mad by monary auhoriis will cra a gap in boh h quiy-prmium diffrnial and h ral inrs-ra diffrnial. Ths would caus invsors o ralloca hir porfolios, inducing capial and rad flows and hnc disurbing h pariy condiions Evidnc for Dviaions from Pariy Condiions In his scion, w prsn vidnc for simaing dviaions from h hr inrnaional pariy condiions. Th simad quaion is wrin in h following rgrssion form: y = + β[( Rm, r ) ( Rm, r )] + β 2 ( r + r + ) + ε β, (22) whr y applis o δ, φ, or θ ; β is an inrcp rm; β and β 2 ar consan paramrs; and ε is h random rror rm. Th rsricions of β and β 2 for ach pariy condiion follow h cofficins conaind in Equaion (9) hrough Equaion (2). Uilizing h sam s of daa prsnd in Scion 2.2, h consisn simas for h four Europan marks ar rpord in Tabl 2. As h hory prdics, all h simad cofficins hav h anicipad signs and ar saisically significan. Th only xcpion is h variabl of h ral inrs-ra diffrnial in PPP for h Unid Kingdom, whr h cofficin is no significan. In rms of xplanaory powr, h s quaions

23 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 23 prform rasonably wll. Th avrag valus of R 2 ar: %, 3%, and 56% for PPP, UIP, and ISP condiions, rspcivly. Th Durbin-Wason saisics in Tabl 2 do no indica firs-ordr srial corrlaion. Taking hs saisics oghr, h null hypohsis ha dviaions from pariy condiions ar indpndn of h quiy-prmium diffrnial and ral inrs-ra diffrnial ar dcisivly rjcd. Th rsuls also show ha, as h hory prdics, h simad cofficin of h ral inrs-ra diffrnial, β 2, producs an idnical simad valu for boh h UIP and ISP quaions; i also holds ru for h simad cofficin of h quiy-prmium diffrnial, β, in h UIP and PPP quaions. Th vidnc hus suggss ha dviaions for h hr pariy condiions no only ar inrdpndn, bu also shar h sam s of informaion. Th rsuls ar consisn wih h vidnc providd by Mishkin (984) and Marson (997). Howvr, h informaion bing usd in our mpirical sudy is drivd dircly from h hory. A spcial faur of his sudy is ha, in addiion o ral inrs-ra diffrnials, dparurs from pariy condiions ar found o b drivn by quiy-prmium diffrnials. I can b concludd ha h ffc of h risk prmium no only prsns in pricing domsic quiy risk, bu also is usd in pricing rlaiv risk, and hus is dicaing inrnaional capial flows.

24 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 24 Tabl 2. Esimas of Dviaions from Pariy Condiions 2 Counry β β β 2 R DW A. Dviaion from h Uncovrd Inrs-Ra Pariy UK (.24) (2.993) (2.424) GM (.) (2.9) (3.7) FR (.975) (3.542) (3.42) SW (.69) (3.642) (3.52) B. Dviaion from h Inrnaional Sock-Rurn Pariy UK (.96) (6.328) (2.336) GM (.85) (8.28) (3.729) FR (2.75) (5.52) (2.975) SW (.67) (.57) (3.494) C. Dviaion from h Rlaiv Purchasing-Powr Pariy UK (.) (2.993) (.95) GM (.64) (2.9) (2.32) FR (.975) (3.542) (.83) SW (.63) (3.642) (2.22) a. Sampl priod: January 989 Ocobr 2. b. Numbrs in parnhss ar absolu valu of h -saisics. Th,, and indica saisically significan diffrnc from zro a h %, 5%, and % lvls for h - raios, rspcivly. DW dnos h Durbin-Wason saisic.

25 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ CONCLUSION This sudy prsns a consisn mark bhavior framwork o sablish hr pariy condiions in bond, sock, and goods marks. Du o h xisnc of inflaion risk and xchang-ra risk, arlir sudis rcogniz h significanc of a ral inrs-ra diffrnial as a ky lmn in xplaining dviaions of inrs-ra pariy or purchasingpowr pariy. Howvr, h ral inrs-ra diffrnial dos no sm adqua o xplain capial movmns involving h rading of inrnaional socks. On h ohr hand, h quiy-prmium diffrnial hypohsis highlighs h rlaiv-risk facor in quiy marks; howvr, inflaion-ra uncrainy has bn ignord. In h currn modl, boh h ral inrs-ra diffrnial and h quiy-prmium diffrnial ar usd o xplain h dparurs. Th saisical rsuls drivd from h four Europan marks rlaiv o h Unid Sas valida our argumn. Th vidnc furhr suggss ha dviaions from h hr inrnaional pariy condiions ar drivn by common facors as rprsnd by h quiy-prmium diffrnials and ral inrs-ra diffrnials. Th inriguing informaional conn of hos diffrnials is ha hy rflc no only rlaiv risk across counris, bu also rlaiv risk as compard wih fixd-incom invsmn. APPENDIX This Appndix provids addiional mpirical vidnc on h popular pariy condiions prvailing in inrnaional marks. Th rgrssion modls ar:

26 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 26 A. Efficin Inrs-Ra Pariy: s ( r r ) = β + β s + ε B. Efficin Inrnaional-Sock Pariy: s ( R = Rm, m, ) β + β s + ε C. Efficin Purchasing-Powr Pariy: s ( p p ) = β + β s + ε D. Inrnaional Fama Pariy: ( p p ) = β + β ( r r ) + ε E. Ral Inrs-Ra Pariy: r = β + β r + ε F. Equiy-Prmium Pariy: Rm, r = β + β( Rm, r ) + ε G. Covrd-Inrs pariy: r - r = β + β( f s ) + H. Unbiasd Forward-Ra Hypohsis I: f ε s = β + β ( f s ) + ε ' ' I. Unbiasd Forward-Ra Hypohsis II: s s = β + β( f s ) + ' ε Modls A hrough C ar fficin vrsions of h UIP, ISP, and PPP proposd by Roll (979). An fficin mark implis ha β = and β=. Th vidnc prsnd in Panls A, B and C of Tabl A is qui consisn wih h fficin naur of h spo xchang ra, suggsing ha all informaion concrning fuur xchang ra-adjusd rurn diffrnials is incorporad ino h currn spo xchang ra. Th supporiv vidnc holds ru for all hr pariy condiions. Howvr, i should b poind ou ha spcifying h modl in his form nds o lad o no rjcing h fficin-mark hypohsis. In paricular, Roll s spcificaion is mor or lss o s spo xchang-ra fficincy rahr han o s pariy condiions. If w chck h simad quaions, h sris of rurn diffrnials is saionary and is magniud is rahr small as compard

27 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 27 wih h lvl of xchang ras. As a rsul, h dominanc of h laggd xchang-ra variabl in h s quaion givs ris o a high R-squar. Nx l us considr h fficin-mark hypohsis for US Trasury bills. Fama (975) argus ha h on-monh nominal inrs ra can b viwd as a prdicor of h inflaion ra. Applying his noion in inrnaional marks implis ha h nominal inrs-ra diffrnial can b usd o prdic h inflaion-ra diffrnial. Th vidnc in Panl D dos provid som prdiciv vidnc for h Grman and Swiss marks. Howvr, h fficin-mark hypohsis is rjcd in h inrnaional conx. This also cass doub on h validiy of ral inrs-ra pariy. Th rsuls from Panl E confirm his poin; h corrlaions of ral inrs ras for hr of h four marks ar posiiv and saisically significan, bu h pariy condiion sill fails. Th rasons advancd by Koraczyk (985) ar h xisnc of risk prmiums and mark imprfcions. In h x as wll as in financ liraur, w ar concrnd wih h rlaionship bwn sock-quiy prmiums. Th vidnc drivd from Panl F indicas ha h corrlaion for ach counry is highly significan, alhough w ar unabl o find srong suppor for h pariy condiion. If w viw h US quiy prmium as a proxy for h world-porfolio prmium, h slop cofficin for ach simad quaion can b rad virually as a ba cofficin in ligh of h CAPM framwork. 6 Panl G conains h rsuls for sing covrd inrs-ra pariy. Sinc all h variabls in his quaion ar dircly obsrvabl and radily assssd by conomic

28 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 28 agns, h simad quaion is closs o h pariy condiion. I is gnrally rcognizd ha arbirag profi drivd from his quaion is vry ngligibl, if hr is any. Thus, any gap in his quaion mus rflc counry risk (Frankl and MacArhur, 988), ransacion coss (Fraianni and Wakman, 982), or simply daa rrors. Th forward prmium (or discoun) has bn commonly usd o prdic forignxchang risk prmiums as wll as currncy dprciaion as dnod by h quaions in Panls H and I. Th unbiasdnss hypohsis in Panl H rquirs ha β = β = ; ' howvr, h unbiasdnss hypohsis in Panl I implis ha β and β ' = (Hansn and Hodrick, 98; Cornll, 989; Bkar and Hodrick, 993). Fama (984) nos h complmnariy of h rgrssions in Panl H and Panl I and suggss ha β = ha β = ' β, and ha ε ε ' = = ' β,. Consisn wih h xising liraur, h vidnc prsnd in Panl H and Panl I apparnly rjcs h unbiasdnss hypohsis. 7 Howvr, h complmnary naur of h cofficins appars consisn wih Fama s argumn. Th puzzl naild in his s of quaions is ha h simad slop in h Panl I quaion is ypically ngaiv. This inrpraion has bn aribuabl o risk prmium (Fama, 984; Giovannini and Jorion, 987; Hodrick, 987; Mark, 988; and Jiang and Chiang, 2), forcas rrors (Froo and Thalr, 99), and rgim shifing (Chiang, 988; Bkar and Hodrick 993).

29 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 29 Tabl A. Esimas of Inrnaional Pariy Condiions 2 Counry β β R DW Join Ts A. Efficin Inrs-Ra Pariy: s ( ) = r r ε β + β s + UK (.553) (2.87) (.279) FR (.28) (43.4) (.459) GM (.27) (45.83) (.562) SW (.678) (4.9) (.26) B. Efficin Inrnaional-Sock Pariy: s ( R = Rm, m, ) β + β s + ε UK (.359) (2.68) (.22) FR (.77) (42.42) (.743) GM (.8) (45.37) (.76) SW (.76) (39.35) (.22)

30 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 3 C. Efficin Purchasing-Powr Pariy: s ( p p ) = β + β s + ε UK (2.22) (26.52) (.47) FR (.833) (3.59) (.59) GM (.365) (3.36) (.39) SW (.264) (28.22) (.42) D. Inrnaional Fama Pariy: ( p = β + p ) β ( r ) + ε r UK (.587) (.57) (.) FR (5.56) (.55) (.) GM (2.4) (3.6) (.) SW (.357) (3.5) (.) E. Ral Inrs-Ra Pariy: r = β + β r + ε UK (5.267) (.478) (.) FR (9.547) (2.92) (.) GM (5.44) (2.92) (.) SW (3.958) (2.672) (.)

31 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 3 F. Equiy-Prmium Pariy: Rm, r = β + β( Rm, r ) + ε UK (2.579) (3.78) (.) FR (.667) (.75) (.366) GM (.) (7.827) (.78) SW (.65) (9.6) (.726) G. Covrd-Inrs Pariy: r - r = β + β( f s ) + UK (.3) (28.52) (.4) FR (.997) (56.7) (.4) GM (.6) (28.24) (.963) SW (.24) (25.63) (.93) H. Unbiasd Forward-Ra Hypohsis I: f ε s = β + β ( f s ) + ε UK (.27) (.369) (.938) FR (.29) (.875) (.968) GM (.84) (.7) (.969) SW (.486) (.74) (.4)

32 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 32 I. Unbiasd Forward-Ra Hypohsis II: s = ( f s ) ' ' s β + β + ε UK (.287) (.372) (.644) FR (.29) (.47) (.584) GM (.84) (.75) (.594) SW (.486) (.923) (.23) a. Th numbrs in parnhss ar absolu valus of h -saisics. b. Th,, and indica saisically significan diffrnc from zro a h %, 5%, and % lvls for h -raios, rspcivly. c. DW dnos h Durbin-Wason saisic. d. Th join s is o s ( β β ) = ( ) ; h join s is h saisics of h 2 χ (2) disribuion wih 2 dgrs of frdom and h numbrs in parnhss ar h significanc lvls.

33 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 33 ENDNOTES. Ohr pariy condiions, including an unbiasd forward-ra hypohsis, covrd inrs-ra pariy, and ral inrs-ra pariy will b discussd a a lar poin. A formal drivaion of hs pariy condiions can b achivd by mploying a consumpion-basd approach in h Lucas framwork (Lucas, 982; Roll and Solnik, 979; Chiang and Trinidad, 997, Cochran, 2). 2. In ordr o simplify h analysis, w ignor h coupon paymn (c ) o h bond and h dividnd paymn (d ) o h sock by assuming c = d =. Diffrn ax ffcs ar also absracd from h calculaions. W can link h currn modl o a Lucas-Cochran framwork by sing pv j = p. Thus, p = E(m x ), whr p is h currn ass pric; m is h sochasic discoun facor; and x is h payoff a im. By sing x = p, w hav: p = R E ( ) p. 3. An quilibrium rlaionship bwn ass rurns basd on a coninuous im modl can b found in Sulz (98). 4. Frankl and MacArhur (988) furhr dcompos UIP ino wo pars: h covrd-inrs diffrnial and h currncy-risk prmium. Thus, quaion () bcoms: r ( )] + [( ) = r r f s + [( f s ) s ] + [ s + ( p p + )]. r

34 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 34 Th firs rm on h righ sid of his xprssion is a dviaion of h covrd inrs ra, which is considrd a counry prmium; h scond rm is h currncy-risk prmium; and h hird rm is h chang in h ral xchang ra. Branson (988) inrprs hs hr componns as h masur of a lack of ingraion of h bond, currncy, and goods marks, rspcivly. 5. A sysmaic rlaionship bwn sock rurns and inflaion can b found in Sulz s sudy (986). 6. Th Basl Accord was a landmark rgulaory agrmn affcing inrnaional banking. Th agrmn was rachd on July 2, 988. Is goals wr o rduc h risk of h inrnaional banking sysm and o minimiz compiiv inqualiy du o diffrncs among naional banking and capial rgulaions (Wagsr, 996). 7. Using ralizaions o proxy xpcaions could gnra an rror-in-h-variabls problm. In fac, h formaion of xpcaions has long bn a challnging issu in mpirical simaions. Expcaions rang from raional xpcaions, disribud lag xpcaions, adapiv xpcaions, rgrssiv xpcaions, and random walk o xpr xpcaions basd on survy daa (Frankl and Froo, 987). 8. In h financ liraur, xpcd rurns ar rlad o risk, which can b modld by ARCH or GARCH in man (Bailli and Bollrslv, 99). Also, many rcn sudis incorpora condiional varianc and covarianc ino various modls o xamin h rlaionship bwn xcss rurns and risk (Domowiz and Hakkio, 985; Hodrick, 987; Bkar and Hodrick, 993; Hu, 997; D Sanis and Grard, 998; Jiang

35 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 35 and Chiang, 2, Cochran, 2). In his papr, w do no innd o xplor hs yps of modls. 9. Our s hr follows h radiional approach by focusing on xamining whhr h slop cofficin diffrs significanly from uniy. Rogoff (996) provids a good rviw. Rcn rsarch pays paricular anion o h sochasic propris of dynamics of adjusmns oward PPP and mploys mor powrful saisical chniqus. Chung and Lai (993, 998), Jorion and Swny (996), Lohian and Taylor (997b), and Baum al. (2) prsn vidnc in favor of PPP.. Roll s fficin simaions and ohr pariy condiions ar providd in h Appndix.. Expcd inflaion-ra diffrnials can also affc h capial accoun hrough hir ffcs on ral inrs-ra diffrnials (Frankl, 979). 2. As mniond arlir, Frankl and MacArhur (988) dcomposd UIP ino wo pars: h covrd-inrs diffrnial and h currncy-risk prmium, whil Goky (994) dcompos UIP ino a ral inrs-ra diffrnial and an x an dviaion from rlaiv PPP as: s + ( r r ) = [ s ( p p + )] + [ +. r r + ] Basically, Frankl and MacArhur s dcomposiion (988) is achivd by subracing and adding h forward prmium, f s ), ino h UIP as w showd in No 4, whil (

36 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 36 Goky s dcomposiion (994) is obaind by subracing and adding h xpcd inflaion-ra diffrnial, ( p ), ino h quaion. p + 3. Th long-rm inrs ra diffrnial can also b addd o h righ sid of Equaion (7) as an indpndn argumn. As a rsul, diffrnc in long-shor ra sprads will b shown on h righ sid of Equaion (8) o capur h informaion of rlaiv liquidiy risk as implid by h xpcaions hypohsis of h rm-srucur of inrs ras. 4. Using Equaion (9) hrough Equaion (2), w obain h following wo quaions: r + r + = θ - δ, and ( R + r ) ( Rm, r ) = δ - φ. m, 5. A prcis procss and spd of adjusmn o rsor a nw quilibrium can b vry complicad and so canno b answrd wihou having a compl spcificaion of h modl, which is byond h scop of h currn sudy. 6. Cumby (99) ss whhr ral sock rurns from four counris ar consisn wih consumpion-basd modls of inrnaional ass pricing. Th hypohsis is rjcd by including a sampl ha bgan in 974. Howvr, h null canno b rjcd whn only h 98s ar considrd. 7. Esimas of h unbiasdnss hypohsis ar basd on h sampl priod from 989. o du o unavailabiliy of FR, GM, and SW forward marks and h swich o h Euro saring in January 999.

37 Thomas C. Chiang, Inrnaional Pariy Condiions and Mark Risk, Encyclopdia of Financ 37 REFERENCES Albuqurqu, R., Baur, G., and Schnidr, M. (24) Inrnaional Equiy Flows and Rurns: A Quaniaiv Equilibrium Approach. NBER working papr. Abuaf, N. and Jorion, P. (99) Purchasing powr pariy in h long run. Journal of Financ, 45, Bailli, R.T. and Bollrslv, T. (99) A mulivaria gnralizd ARCH approach o modling risk prmia in forward forign xchang ra marks. Journal of Inrnaional Mony and Financ, 9, Baum, C. F., Barkoulas, J.T., and Caglayan, M. (2) Nonlinar adjusmn o purchasing powr pariy in h pos-bron Woods ra. Journal of Inrnaional Mony and Financ, 2, Bkar, G. and Hodrick, R.J. (993) On biass in h masurmn of forign xchang risk prmiums. Journal of Inrnaional Mony and Financ, 2, Branson, W.H. (988) Commns on poliical vs. currncy prmia in inrnaional ral inrs diffrnials: a sudy of forward ras for 24 counris, by Frankl, J.A. and MacArhur, A.T., Europan Economic Rviw, 32, Campbll, J.Y. (987) Sock rurns and h rm srucur. Journal of Financial Economics, 8, Chung, Y.W. and Lai, K.S. (993) Long-run purchasing powr pariy during h rcn floa. Journal of Inrnaional Economics, 34, Chung, Y.W. and Lai, K.S. (998) Pariy rvrsion in ral xchang ras during h pos-bron Woods priod. Journal of Inrnaional Mony and Financ, 7, Chiang, T.C. (988) Th forward ra as a prdicor of h fuur spo ra - a sochasic cofficin approach. Journal of Mony, Crdi and Banking, 2,

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