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1 Rober M. La Follee School of Public Affairs a he Universiy of Wisconsin-Madison Working Paper Series La Follee School Working Paper No hp:// Two Essays in Inernaional Finance: Ineres Rae Pariy and he Forward Premium Puzzle Menzie D. Chinn Professor, La Follee School of Public Affairs and Deparmen of Economics a he Universiy of Wisconsin-Madison; and he Naional Bureau of Economic Research mchinn@lafollee.wisc.edu Rober M. La Follee School of Public Affairs 225 Observaory Drive, Madison, Wisconsin Phone: / Fax: info@lafollee.wisc.edu / hp:// The La Follee School akes no sand on policy issues; opinions expressed wihin hese papers reflec he views of individual researchers and auhors.

2 Two Essays in Inernaional Finance Ineres Rae Pariy and he Forward Premium Puzzle Menzie D. Chinn * The Rober M. La Follee School of Public Affairs Universiy of Wisconsin, Madison and NBER March 2007 Acknowledgmens: Enries prepared for he Princeon Encyclopedia of he World Economy, edied by Kenneh Reiner and Ramkishen Rajan, forhcoming from Princeon Universiy Press. I hank Ramkishen Rajan and an anonymous referee for commens. * Deparmen of Economics, 7470 Social Sciences Bldg., 80 Observaory Drive, Madison, WI Tel/Fax: + (608) / mchinn@lafollee.wisc.edu

3 Ineres Pariy Condiions Ineres pariy condiions are no-arbirage profi condiions for financial capial. When such condiions hold, i is infeasible for invesors o obain higher reurns by borrowing or lending. Hence, in principle, ineres pariy condiions define heoreical linkages beween ineres raes and exchange raes beween counries. The easies way o undersand pariy condiions is o consider how a ypical invesor can save in differen locaions. Suppose he home currency is a dollar, and he foreign currency is a euro. Furher assume a forward marke exiss. A forward conrac allows an invesor o ener ino an agreemen his period o exchange currencies k periods hence a a forward rae F known oday. Then he invesor can eiher save a home, receiving ineres rae i, or save abroad, convering by he exchange rae S, receiving he foreign ineres rae i*, and hen convering back o home currency by he forward rae F obaining a ime for a rade a ime +. ( + i) versus ( + i * ) F S, + If he gross reurn on he lef is greaer han ha on he righ, hen invesors will place heir capial in he home counry; if i is less, hen invesors will place heir capial abroad. Wih infinie amouns of capial moving in search of he highes reurn (and in his example, here is no risk in nominal erms), hese reurns will be equalized. F i i *, + ( + ) = ( + ) () S Afer manipulaion, ( i ( F * i ), = + * + i ) S S (2)

4 This condiion is called covered ineres rae pariy, reflecing he fac ha invesors are covered agains nominal uncerainy by way of he forward marke. If he forward rae is equal o he fuure spo rae (see Forward premium ), such ha e F, + S, + = hen (2) becomes: ( i ( S * e i ), = + * + i ) S S (3) where he e superscrip denoes expeced. Equaion (3) is ermed uncovered ineres rae pariy. This expression holds when invesors do no require compensaion for he uncerainy associaed wih rading currencies in he fuure. I saes ha expeced nominal reurns are equalized across borders in common currency erms. When ineres raes are low, he following log approximaions are ofen used for equaions (2) and (3). ( i s (2 ) i * ) = f, + ( i s (3 ) e i * ) = s, + Jeffrey Frankel (99) has labeled condiion (2) holding as characerizing perfec capial mobiliy, while condiion (3) is associaed wih perfec capial subsiuabiliy. These erms arise from he view ha if (2) does no hold, here mus be some sor of impedimen capial conrols or he hrea hereof o he free flow of financial capial. Bu even if capial is free o move, invesors may sill respond o risk; ha response o risk migh drive a wedge beween he expeced spo and forward rae. When invesors are risk-neural in nominal erms, hen invesors will rea capial (say deb insrumens issued in differen currencies) as perfecly subsiuable. The above condiions perain o financial capial. In order o consider he mobiliy of physical capial, one has o bring ino play he prices of commodiies. Inegraion of goods 2

5 markes are ofen defined as relaive purchasing power pariy holding (see Purchasing power pariy). Ex ane relaive PPP can be wrien as: s e * e * + s = ( p, + p ) ( p, + p ) (4) e, where p is he log price level. Equaion 4 saes ha expeced depreciaion equals he expeced inflaion differenial. Combining (4) wih he uncovered ineres rae pariy condiion (3 ) leads o real ineres pariy. i e * * e * ( p, + p ) = i ( p, + p ) (5) This says he expeced rae of reurn on capial, expressed in physical unis, is equalized across borders. To he exen ha in neoclassical models he marginal produc of capial equals he real ineres rae, his condiion is equivalen o he equalizaion of marginal produc of capial equalized across borders. Covered Ineres Pariy Assessed For developed economies since he dismanling of capial conrols, covered ineres pariy holds fairly well. I should be noed ha mos ess are conduced using offshore raes, in which case (2) is someimes ermed closed ineres pariy, alhough covered ineres pariy is ofen used as a erm encompassing his concep. Early ess were conduced by Jacob Frenkel and Richard Levich (975). They found ha, afer accouning for ransacions coss, covered ineres pariy held for 3 monh horizons. Offshore raes someimes diverge from onshore raes, so ha he findings of covered ineres pariy are somewha weaker. The quesion of wheher covered ineres pariy holds for longer horizons is an open one. Helen Popper (993) concludes ha covered ineres differenials a long mauriies are no 3

6 appreciably greaer han hose for shor (up o one year) mauriies. This is a surprising resul given ha here are likely a number of regulaory impedimens ha would end o inroduce fricions ino he arbirage process. Prior o he dismanling of capial conrols, and in many emerging markes oday, covered ineres pariy is unlikely o hold. In oher words, covered ineres differenials could be inerpreed as poliical risk, associaed wih he possibiliy of governmenal auhoriies placing resricions on deposis locaed in differen jurisdicions (clearly his is somehing ha is no relevan when all he deposis are offshore). Rober Aliber (973) is credied wih his inerpreaion, while Michael Dooley and Peer Isard (980) provided empirical esimaes for he DM/dollar rae. The Empirical Evidence for Uncovered Ineres Pariy Uncovered ineres pariy is a more difficul condiion o es, essenially because expeced exchange rae changes are unobservable. In he lieraure, mos ess of UIP are acually join ess of UIP and he raional expecaions hypohesis, i.e., ha ex pos realizaions of he e exchange rae are a unbiased measure of he ex ane exchange rae, viz., s =, + E( s+ I ). This assumpion combined wih equaion (2 ) yields his sandard regression equaion, someimes called he Fama equaion (Fama, 984): s + s = 0 + β( f, + s ) + υ+ β (6) Or by virue of covered ineres pariy holding, s * + s = 0 + β( i i ) + υ+ β (7) where under he join null hypohesis υ + is a mean zero error unpredicable using pas informaion, and β =. 4

7 The evidence in favor of his join hypohesis of UIP and raional expecaions is quie weak. The regression of he ex pos change of he spo exchange rae on eiher he forward discoun (in equaion 6), or he ineres differenial (in equaion 7) ypically yields a slope coefficien esimae ha is no only differen from uniy, bu in fac negaive and differen from zero a convenional levels of saisical significance. This is rue for reserve currencies (he U.S. dollar, he yen, he Swiss franc, he deuschemark, he franc, or heir successor currency, he euro) a horizons up o a year. I is also rue for some emerging marke currencies (see Frankel and Poonawala, 2006). One ineresing characerisic of hese regressions is ha, alhough he coefficiens are ypically differen from zero in a saisical sense, he proporion of oal variaion explained is ypically very small. A longer horizons, (3, 5, 0 years) he evidence is more supporive of he combined UIPraional expecaions hypohesis. Menzie Chinn and Guy Meredih (2004) documen ha esimaes of he β coefficien are usually no significanly differen from he posied value of uniy a 5 and 0 year horizons. The finding ha he join hypohesis of uncovered ineres pariy and raional expecaions holds beer a long horizons han a shor appears o be robus. Noneheless, some cauion is necessary here. Consider regressions involving en year ineres differenials; by 2003, here would only be hree non-overlapping observaions available per currency. Ineresingly, Chaboud e al. (2005) find ha UIP also holds a exremely shor horizons of a few minues. Oher ineresing resuls perain o periods of exreme marke urmoil. Rober Flood and Andrew Rose (2002), following heir 996 work, find ha uncovered ineres pariy holds beer in recen imes when he sample encompasses successful aacks on currency pegs. Noneheless, he sill find los of heerogeneiy in experiences wih UIP. 5

8 A differen perspecive on uncovered ineres pariy is provided by dropping he raional expecaions hypohesis (see Forward premium puzzle). A new area of research involves invesigaion of wheher uncovered ineres pariy holds for emerging markes. Ravi Bansal and Magnus Dahlquis (2000) found ha here was a basic asymmery in wheher UIP holds. In paricular, hey find ha when he U.S. ineres rae is lower han foreign counry raes, UIP holds, while UIP fails o hold when he U.S. rae is higher. They also find ha idiosyncraic facors, such as he GDP per capia of he foreign counry, are imporan in deermining he degree of failure of UIP o hold. Using he forward discoun in sead of ineres differenials, Jeffrey Frankel and Jumana Poonawala (2006) find ha here is subsanial heerogeneiy in he resuls. Wha maers imporanly is he exchange rae regime; highly managed exchange rae regimes are associaed wih currencies ha exhibi greaer deviaions from UIP. Real Ineres Pariy Measured If uncovered ineres pariy does no seem o hold a shor horizons, i seems unlikely ha real ineres pariy, described as exac equalizaion of real ineres raes, would hold. However, one could sill es he weaker condiion ha movemens in real raes in one counry would be me by one for one real movemens in oher counries. The key difficuly wih esing his condiion, like ha of uncovered ineres pariy, is ha marke expecaions are no direcly observable. Hence, one can conduc only join ess for real ineres pariy. In Eiji Fujii and Menzie Chinn (200), real ineres raes are calculaed using a variey of proxy measures of expeced inflaion: ex pos inflaion, and inflaion prediced using lagged values of inflaion models. Boh approaches are consisen wih raional expecaions. 6

9 They find ha here real ineres pariy holds wih differen srengh a differen horizons. As in numerous previous sudies (Cumby and Obsfeld, 984; Mark, 985), he real ineres pariy (RIP) hypohesis is decisively rejeced wih shor horizon daa. A five o en-year horizons, however, he empirical evidence becomes far more supporive and in some cases he RIP hypohesis is no rejeced. In general, RIP, up o a consan, holds beer a long horizons han a shor horizons. These resuls are robus o alernaive ways of modeling expeced inflaion raes. In recen years, several counries, including he U.K., he U.S., France and Canada, have begun issuing inflaion-indexed deb securiies. These are markeable securiies whose principal is adjused by changes in he price level (usually he CPI). The principal increases wih he inflaion rae so ha he real reurn can be direcly observed. A cursory invesigaion reveals ha here is no evidence of equalizaion. Moreover, while here is some covariaion, i is no anywhere near one for one. However, he hinness of he markes and he differences in he mauriies of he relevan deb insrumens makes srong conclusions in eiher direcion difficul. Also see: Capial mobiliy, Forward premium, Peso problem, Purchasing power pariy, Exchange rae regimes, Exchange rae volailiy, Speculaion, Sovereign risk. Furher Readings Aliber, R.Z., 973, The Ineres Pariy Theorem: A Reinerpreaion, Journal of Poliical Economy 8: Bansal, R. and M. Dahlquis, 2000, The forward premium puzzle: differen ales from developed and emerging economies, Journal of Inernaional Economics, Volume 5:

10 Chaboud, A.P. and J. H. Wrigh, 2005, Uncovered Ineres Pariy: I Works, Bu No For Long, Journal of Inernaional Economics 66(2): Pages Chinn, Menzie D., 2006, The (Parial) Rehabiliaion of Ineres Rae Pariy: Longer Horizons, Alernaive Expecaions and Emerging Markes, Journal of Inernaional Money and Finance 25() (February): 7-2. Chinn, Menzie D. and Guy Meredih, 2004, Moneary Policy and Long Horizon Uncovered Ineres Pariy, IMF Saff Papers 5(3) (November): Cumby, Rober E. and M. Obsfeld (984) Inernaional Ineres Rae and Price Level Linkages under Flexible Exchange Raes: A Review of Recen Evidence, in J. F. O. Bilson and R. C. Marson (ediors) Exchange rae Theory and Pracice (Universiy of Chicago Press, Chicago, IL). Dooley, M.P. and P. Isard, 980, Capial conrols, poliical risk, and deviaions from ineresrae pariy, Journal of Poliical Economy 88(2): Fama, E.F., 984, Forward and Spo Exchange Raes, Journal of Moneary Economics 4: Flood, R.P. and A.K. Rose, 996, Fixes: Of he Forward Discoun Puzzle, Review of Economics and Saisics: Flood, R.B. and A. K. Rose, 2002, Uncovered Ineres Pariy in Crisis, Inernaional Moneary Fund Saff Papers 49: Frankel, Jeffrey and Jumana Poonawala, 2006, The Forward Marke in Emerging Currencies: Less Biased Than in Major Currencies, NBER Working Paper No (Augus). Frenkel, J.A., and R.M. Levich, 975, Covered Ineres Pariy: Unexploied Profis? Journal of Poliical Economy 83(2):

11 Froo, K.A. and J.A. Frankel, 989,"Forward Discoun Bias: Is I an Exchange Risk Premium?" Quarerly Journal of Economics 04() (February): Fujii, Eiji and Menzie D. Chinn, 200, Fin de Siècle Real Ineres Pariy, Journal of Inernaional Financial Markes, Insiuions and Money (3/4): Popper, H., 993, Long-Term Covered Ineres Pariy Evidence From Currency Swaps, Journal of Inernaional Money and Finance, Vol. 2, No. 4, pp

12 The Forward Premium Puzzle The forward premium puzzle is closely relaed o he failure of uncovered ineres pariy o hold (see Ineres rae pariy condiions), and he phenomenon of forward rae bias, he endency for he forward exchange rae o sysemaically mispredic he fuure spo exchange rae. The puzzle is he finding ha he forward premium usually poins in he wrong direcion for he subsequen acual movemen in he spo exchange rae. Uncovered ineres pariy saes ha, if he covered ineres pariy holds for pair of currencies, hen he forward discoun and hence he ineres differenial beween he wo counries, should be an unbiased predicor of he subsequen change in he spo rae, assuming ha acors make guesses abou he fuure ha are on average correc (wha is someimes ermed raional expecaions ). The puzzle is of imporance for wha i suggess abou he workings of inernaional financial markes. To he exen ha he puzzle reflecs he failure of raional expecaions o hold, hen ineres rae differenials will be poor guides o fuure exchange rae movemens. In addiion, he implied lack of marke efficiency suggess a poenial role for governmen inervenion in markes. On he oher hand, if he puzzle reflecs he presence of a premium o compensae for he riskiness of specific currencies, hen capial may no be so ready o migrae from one currency o anoher. Explaining he Forward Premium puzzle as To fix conceps and erms, define he forward rae a ime for a rade o occur a ime k k F and he spo rae a ime as S. Furher, le he subjecive expecaion of he spo rae a 0

13 ime +k, based upon ime informaion, be defined as ε ). Assume for he momen raional expecaions, viz., E + ). Then one should expec: ( S k ( S + k k S + k F + u+ k = () where he error erm is an expecaional error. In realiy, regression esimaes do no obain a regression coefficien of uniy, alhough he poin esimae is ofen no saisically significanly far from he posied value.. The forward premium puzzle can be idenified by assuming ha he error erm is log normally disribued, so ha () can be rewrien as: k s + k 0 + β f + u+ k = β ~ (2) where under he null hypohesis, β =, and β0 is allowed o equal some consan impounding some Jensens Inequaliy erms (explain his). Noice ha one can subrac he curren log spo rae s from boh sides, since under he null β =. This yields: k s + k s = 0 + β ( f s ) + u+ k β ~ (3) The lef hand side of equaion (3) is ex pos depreciaion, while he erm in he parenheses is he forward discoun (or inverse of he forward premium). The puzzle is ha esimaes of β are no only differen from he value of uniy, and saisically significanly so, bu also ha he coefficien esimaes are ypically negaive. This suggess ha agens could make subsanial profis by arbiraging. To be concree, individuals could borrow in he low ineres currency and lend in he high ineres currency, in a process ermed he carry rade. This well known sraegy can be highly profiable, alhough he profis are highly vulnerable o sharp movemens in he exchange rae.

14 This issue is linked up o uncovered ineres pariy in he following sense. If covered ineres pariy holds, hen: ( f k k k* s ) = ( i i ) (4) Subsiuing his no arbirage profis condiion ino (3), one finds ha (3) can be re-wrien as: k k* s + k s = 0 + β ( i i ) + u+ k β ~ (5) The above is he regression equaion used o es he join null hypohesis of uncovered ineres pariy and raional expecaions. The finding of a negaive slope coefficien in equaion (5) is equivalen o he finding of a negaive slope coefficien in (3), for insances where covered ineres pariy holds. Reasons behind he Puzzle A number of papers have invesigaed a wide variey of differen economeric issues bu overall i appears ha he negaive slope coefficien canno be enirely explained by he ime series characerisics of he variables. Leaving aside hese economeric issues, he forward premium puzzle migh exis even when capial is perfecly mobile according o he covered ineres pariy crierion eiher because of he invalidiy of he raional expecaions hypohesis or he exisence of an exchange risk premium. As discussed a greaer lengh in he enry on Ineres Rae Pariy, esimaes of equaion (5) using values for k ha range up o one year ypically rejec he unbiasedness resricion on he slope parameer. For insance, he survey by Kenneh Froo and Rober Thaler (990), finds an average esimae for β of Menzie Chinn and Guy Meredih (2004) documen ha his resul holds for more recen periods exending up o They also show ha he bias decreases a longer horizons. 2

15 I is imporan o recall ha, in fac, uncovered ineres pariy properly defined as relaing o expeced depreciaion, is unesable. Esimaion of he sandard UIP regression equaion relies upon he raional expecaions mehodology embodied in equaion (). Of course, reliance upon he assumpion of raional expecaions is by no means unconroversial. In a number of papers, Kenneh Froo and Jeffery Frankel (989) demonsrae ha he sandard ess for UIP yield radically differen resuls when one uses survey-based measures of exchange rae depreciaion. They find ha mos of he variaion of he forward discoun appears o be relaed o expeced depreciaion, raher han a ime varying risk premium, hereby lending credence o UIP. Menzie Chinn and Jeffery Frankel (994) documen he fac ha i is difficul o rejec UIP for a broader se of currencies, alhough here is some evidence of a risk premium a he 2 monh horizon. The auhors inerpre he differing resuls as arising from a wider se of currencies hey examine 7 currencies as opposed o he 5 or so examined by Frankel and Froo (987) where he assumpion of perfec subsiuabiliy of deb insrumens is less likely o hold. As hese auhors have sressed, rejecion of he raional expecaions hypohesis does no necessarily mean one acceps he proposiion ha agens are irraional. I may be ha agens are consanly learning abou he economic environmen such ha heir forecass are biased for long sreches of ime. Perhaps he mos naural explanaion for why he forward premium predics he wrong direcion of exchange rae movemens is ha a risk premium drives a wedge beween expeced changes and acual changes. However, he modeling of he risk premium has proven quie challenging. A sandard model moivaes he risk premium as a funcion of he correlaion beween relaive reurns on asses denominaed in he wo currencies, and he raio of marginal uiliies of consumpion in he wo respecive counries. While he heory is quie 3

16 sraighforward, an implausibly high degree of risk aversion is necessary o raionalize he observed volailiy of he risk premium. Also see: Capial mobiliy, Ineres pariy condiions, Moneary policy rules, Peso problem, risk premium, Sovereign risk, References Chinn, M.D. and J.A. Frankel, 994, Paerns in Exchange Rae Forecass for 25 Currencies, Journal of Money, Credi and Banking 26 (4) (November): Frankel, J.A. and C.M. Engel, 984, Do Asse Demands Opimize over he Mean and Variance of Reurns? A Six Currency Tes, Journal of Inernaional Economics. 7: Frankel, J.A. and K.A. Froo, 987,"Using Survey Daa o Tes Sandard Proposiions Regarding Exchange Rae Expecaions," American Economic Review. 77() (March): Froo, K.A. and J.A. Frankel, 989,"Forward Discoun Bias: Is I an Exchange Risk Premium?" Quarerly Journal of Economics 04() (February): Froo, K.A. and R.H. Thaler, 990, Foreign Exchange, Journal of Economic Perspecives 4(3) (Summer): Furher Readings Alvarez, F., Akeson, A. and Kehoe, P.J., 2002, Money, ineres raes, and exchange raes in endogenously segmened markes, Journal of Poliical Economy 0 (): Baillie, R. T. and T. Bollerslev, 2000, The Forward Premium Anomaly Is No As Bad As You Think, Journal of Inernaional Money and Finance 9:

17 This paper argues ha here is a nonlineariy in he relaionship beween he spo rae and he forward discoun. When he forward discoun is large in absolue value, hen he forward discoun is likely o poin in he righ direcion. When he forward discoun is small, i is likely o poin in he wrong direcion, perhaps because ransacions coss are large relaive o poenial gains. Engel, C., 999, On he Foreign Exchange Risk Premium in Sicky-Price General Equilibrium Models, Inernaional Finance and Financial Crises: Essays in Honor of Rober P. Flood, Peer Isard, Assaf Razin and Andrew Rose, eds., (IMF and Kluwer), pp Engel, C., 996, The Forward Discoun Anomaly and he Risk Premium: A Survey of Recen Evidence, Journal of Empirical Finance 3 (June): Lewis, K.K., 989, Changing Beliefs and Sysemaic Raional Forecas Errors wih Evidence from Foreign Exchange, American Economic Review 79(4): Lyons, Richard, 200, The Microsrucure Approach o Exchange Raes (Cambridge and London: MIT Press). Maynard, A. and P.C.B. Phillips, 200, "Rehinking an Old Empirical Puzzle: Economeric Evidence on he Forward Discoun Anomaly", Journal of Applied Economerics, 6(6): Maynard, A., 2003, Tesing for Forward-rae Unbiasedness on Regression in Levels and in Reurns, Review of Economics and Saisics 85(2): McCallum, B.T., 994, A Reconsideraion of he Uncovered Ineres Pariy Relaionship, Journal of Moneary Economics 33:

18 Moore, M.J., 994, Tesing for Unbiasedness in Forward Markes, The Mancheser School 62 (Supplemen): Villanueva, O. Miguel, 2005, FX Dynamics, Limied Paricipaion, and he Forward Bias Anomaly, The Financial Review 40: