World Economy - Forward Premium Puzzle 1 Forward Premium Puzzle Definiions and Relaed Conceps The forward premium puzzle is closely relaed o he failure of uncovered ineres pariy o hold, and he phenomenon of forward rae bias. The puzzle is he finding ha he forward premium usually poins in he wrong direcion for he ex pos movemen in he spo exchange rae. Uncovered ineres pariy saes ha, if covered ineres pariy holds, hen he forward discoun and hence he ineres differenial, should be an unbiased predicor of he ex pos change in he spo rae, assuming raional expecaions. The forward rae bias puzzle is given by he fac ha he forward rae does no provide an unbiased forecas of he fuure spo rae. ime as To fix conceps and erms, define he forward rae a ime for a rade o occur a F and he spo rae a ime as S. Furher, le he subjecive expecaion of he spo rae a ime +, based upon ime informaion, be defined as ε ). Assume ( S + for he momen raional expecaions, viz., E + ). Then one should expec: ( S = (1) S + F + u+ Where he error erm is an expecaional error. In realiy, regression esimaes do no find a regression coefficien of uniy, alhough he poin esimae is ofen no saisically significanly far from he posied value. A more problemaic aspec of such regressions is ha he esimaed regression error erm ofen exhibis serial correlaion, violaing he raional expecaions hypohesis. 1
World Economy - Forward Premium Puzzle 2 The forward premium puzzle can be idenified by assuming ha he error erm is log normally disribued, so ha (1) can be rewrien as: s + 0 + β 1 f + u+ = β ~ (2) Where under he null hypohesis, β = 1 1, and β0 is allowed o equal some consan impounding some Jensens Inequaliy erms. Noice ha one can subrac he curren log spo rae s from boh sides, since under he null β = 1 1. This yields: s + s = 0 + β 1 ( f s ) + u+ 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 β1 are no only differen from he value of uniy, and saisically significanly so, bu also ha he coefficien esimaes are ypically negaive. This issue is lined up o uncovered ineres pariy in he following sense. If covered ineres pariy holds, hen: ( f * s ) = ( i i ) (4) Subsiuing his no arbirage profis condiion ino (3), one finds ha (3) can be rewrien as: β ( ) ~ (5) * s + s = 0 + β 1 i i + u+ Which 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 2
World Economy - Forward Premium Puzzle 3 equaion (5) is equivalen o he finding of a negaive slope coefficien in (3), for insances where covered ineres pariy holds. There are several reasons why he forward premium puzzle migh exis, even when capial is perfecly mobile according o he covered ineres pariy crierion: (1) he invalidiy of he raional expecaions hypohesis; (2) issues of economeric implemenaion; and (3) he exisence of an exchange ris premium. As discussed a greaer lengh in he enry on Ineres Rae Pariy, esimaes of equaion (5) using values for ha range up o one year ypically rejec he unbiasedness resricion on he slope parameer. For insance, he survey by Froo and Thaler (1990), for insance, finds an average esimae for β of -0.88. Chinn and Meredih (2004) documen ha his resul holds for more recen periods exending up o 2000. They also show ha he bias ends o decrease a longer horizons. The Validiy of he Raional Expecaions Hypohesis 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 (1). Of course, reliance upon he assumpion of mean zero expecaional errors is by no means unconroversial. In a number of papers, Froo and Franel (1989) 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 ris premium, hereby lending credence o UIP. 3
World Economy - Forward Premium Puzzle 4 Chinn and Franel (1994, 2002) documen he fac ha i is difficul o rejec UIP for a broader se of currencies, when using forecass provided by he Currency Forecasers Diges (CFD), alhough here is some evidence of a ris premium a he 12 monh horizon. Chinn and Franel inerpre he differing resuls as arising from a wider se of currencies hey examine 17 currencies as opposed o he 5 or so examined by Franel and Froo (1987) where he assumpion of perfec subsiuabiliy of deb insrumens is less liely 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. Models incorporaing Bayesian learning includes Lewis (1989). More recenly, Bacchea and van Wincoop (2006) have inroduced incomplee informaion processing essenially a ransacions coss raionale for infrequen porfolio rebalancing as a reason for why he forward premium puzzle exiss. (Lyons (2001) appeal o insiuional and microsrucural facors o explain he presence of excess reurns is a relaed, bu disinc, approach.) Economeric Issues Chinn and Meredih (2004) explain he divergence in shor and long-horizon resuls by McCallum (1994) appealed o a moneary reacion funcion ha responds o exchange rae changes, hereby maing ineres raes endogenous in an economic sense. This argumen can be reinerpreed in an economeric framewor following Moore (1994) and Villanueva (2005). However, i is unclear wheher such approaches can explain he negaive coefficiens obained. 4
World Economy - Forward Premium Puzzle 5 A wide variey of differen economeric issues have also been invesigaed. Baillie and Bollerslev (2000) argue 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 liely o poin in he righ direcion. When he forward discoun is small, i is liely o poin in he wrong direcion, perhaps because ransacions coss are large relaive o poenial gains. Maynard and Phillips (2001) argue ha imposing a uni coefficien on he relaionship by subracing he spo rae from boh sides of equaion (2) can induce disorions ino he disribuion for he slope parameer when he regressor and regressand are boh highly persisen. However, follow-up wor by Maynard (2003) indicaes ha he negaive slope coefficien canno be enirely explained by he ime series characerisics of he variables. A Ris Premium Inerpreaion Perhaps he mos naural explanaion for why he forward premium predics he wrong direcion of exchange rae movemens is ha a ris premium drives a wedge beween expeced changes and acual changes. How o model he ris premium is he challenge; Engel (1996) provides a survey. The porfolio balance approach, which focuses on socs of ouside asses, was he framewor firs adoped in he modeling of he ris premium. However, he widespread failure o find any lin beween socs of ouside asses (such as governmen bonds) and he ex pos ris premium (Franel and Engel, 1984) ended his avenue of research. 5
World Economy - Forward Premium Puzzle 6 Oher ris-based explanaions have been forwarded. One se of explanaions rely upon he presence of sicy prices in general equilibrium models. Engel (1999) discusses he ris ha arises due o he covariaion of consumpion and exchange raes in such models wih nominal rigidiies. Oher rigidiies have been inroduced in order o induce ris premia. One such se of models incorporaes limied paricipaion on he par of agens. Households only ener ino arbirage when he benefis exceed he coss sufficienly. See for insance Alvarez, e al. (2002). The consumpion based ris premium approach has also been resurreced by appealing o more exoic preferences. Beaer, Hodric and Marshall (1997) conclude ha while inroducing firs order ris aversion can produce negaive slope coefficiens, he relaive magniudes of exchange rae changes and ris premia canno be mached. More recenly, Verdelhan (2006) has forwarded a model wherein ad hoc exernal habi preferences, combined wih rade coss, which can lead o quaniaively large ris premia. A he same ime, he is able o mach he variance of real exchange changes. Moore and Roche (2006) also relies upon exernal habi preferences, bu imbeds hese ino a moneary model. The combinaion of muliple coss or rigidiies appears o be a fruiful approach for explaining why he forward discoun ypically poins in he wrong direcion for he ex pos exchange rae change. Menzie D. Chinn (1/2/07) Professor of Public Affairs and Economics Universiy of Wisconsin 6
World Economy - Forward Premium Puzzle 7 References Alvarez, F., Aeson, A. and Kehoe, P.J., 2002, Money, ineres raes, and exchange raes in endogenously segmened mares, Journal of Poliical Economy 110 (1): 73-112 Baillie, R. T. and T. Bollerslev, 2000, The Forward Premium Anomaly Is No As Bad As You Thin, Journal of Inernaional Money and Finance 19: 471-488. Beaer, G., R.J. Hodric, and D.A. Marshall, 1997, The Implicaions of Firs-Order Ris Aversion for Asse Mare Ris Premiums, Journal of Moneary Economics 40: 3 39. Chinn, M.D. and J.A. Franel, 2002, Survey Daa on Exchange Rae Expecaions: More Currencies, More Horizons, More Tess, in W. Allen and D. Dicinson (ediors), Moneary Policy, Capial Flows and Financial Mare Developmens in he Era of Financial Globalisaion: Essays in Honour of Max Fry (London: Rouledge, 2002): pp. 145-167. Chinn, M.D. and J.A. Franel, 1994, Paerns in Exchange Rae Forecass for 25 Currencies, Journal of Money, Credi and Baning 26 (4) (November): 759-770. Chinn, M.D. and G. Meredih, 2004, Moneary Policy and Long Horizon Uncovered Ineres Pariy, IMF Saff Papers 51(3) (November): 409-430. Engel, C., 1999, On he Foreign Exchange Ris Premium in Sicy-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. 71-85. Engel, C., 1996, The Forward Discoun Anomaly and he Ris Premium: A Survey of Recen Evidence, Journal of Empirical Finance 3 (June): 123-92. Franel, J.A. and C.M. Engel, 1984, Do Asse Demands Opimize over he Mean and Variance of Reurns? A Six Currency Tes, Journal of Inernaional Economics. 17: 309-323. Franel, J.A. and K.A. Froo, 1987,"Using Survey Daa o Tes Sandard Proposiions Regarding Exchange Rae Expecaions," American Economic Review. 77(1) (March): 133-153. Froo, K.A. and J.A. Franel, 1989,"Forward Discoun Bias: Is I an Exchange Ris Premium?" Quarerly Journal of Economics 104(1) (February): 139-161. Froo, K.A. and R.H. Thaler, 1990, Foreign Exchange, Journal of Economic Perspecives 4(3) (Summer): 179-192. 7
World Economy - Forward Premium Puzzle 8 Lewis, K.K., 1989, Changing Beliefs and Sysemaic Raional Forecas Errors wih Evidence from Foreign Exchange, American Economic Review 79(4): 621-636. Lyons, Richard, 2001, The Microsrucure Approach o Exchange Raes (Cambridge and London: MIT Press). McCallum, B.T., 1994, A Reconsideraion of he Uncovered Ineres Pariy Relaionship, Journal of Moneary Economics 33: 105-132. Maynard, A. and P.C.B. Phillips, 2001, "Rehining an Old Empirical Puzzle: Economeric Evidence on he Forward Discoun Anomaly", Journal of Applied Economerics, 16(6): 671-708. Maynard, A., 2003, Tesing for Forward-rae Unbiasedness on Regression in Levels and in Reurns, Review of Economics and Saisics 85(2): 313 327. Moore, M.J., 1994, Tesing for Unbiasedness in Forward Mares, The Mancheser School 62 (Supplemen): 67-78 Moore, M.J. and M.J. Roche, 2006, Solving Exchange Rae Puzzles wihou Sicy Prices nor Trade Coss, mimeo (Queens Universiy Belfas, Ocober). Verdelhan, A., 2006, A Habi-Based Explanaion of he Exchange Rae Ris Premium, mimeo (Boson Universiy, Augus). Villanueva, O. Miguel, 2005, FX Dynamics, Limied Paricipaion, and he Forward Bias Anomaly, The Financial Review 40: 67-93. 8