Market Overreaction and Under reaction for Currency Futures Prices. Stephen J. Larson *, Associate Professor of Finance Ramapo College of New Jersey

Transcription

1 Marke Overreacion and Under reacion for Currency Fuures Prices Sephen J. Larson *, Associae Professor of Finance Ramapo College of New Jersey Sephen E. Wilcox, Professor of Finance Minnesoa Sae Universiy, Mankao ABSTRACT This paper examines exreme, one day price changes in currency fuures in an aemp o documen over and under reacion. We find repeaed evidence of coinegraion among he currency fuures price, he spo exchange rae, and ineres raes. We hen assess wheher he marke overreaced or under reaced o new informaion by comparing he acual fuures price change o he change prediced by an error correcion model. The ype of underlying informaion associaed wih each exreme, one day price change is gahered from Lexis/Nexis and used o idenify he siuaions where currency fuures prices are mos likely o over and under reac o new informaion. JEL Classificaions: G13, G14, G15 Key Words: Marke Anomalies, Currency Fuures Prices, Overreacion INTRODUCTION AND LITERATURE REVIEW Research has documened overreacion and under reacion in many markes including he sock marke and he foreign currency spo marke. This paper addresses marke over and underreacion for foreign currency fuures conracs. The daa se consiss of daily observaions of fuures prices, spo exchange raes, and Eurocurrency LIBOR for he Briish Pound, Japanese Yen, and Swiss Franc from January 2, 1991 o December 31, Using a 5 year moving window mehod and he foreign currency fuures pricing model of Amin and Jarrow (1991), we find repeaed evidence of coinegraion among he fuures price, he spo exchange rae, and ineres raes over en differen esimaion periods. We hen use an error correcion model o develop a series of prediced fuures price changes. We assess he degree of each exreme, one day price change by comparing he acual fuures price change o he change prediced by he error correcion model. We define a loser as an exreme, one day decline in he fuures price and a winner as an exreme, one day increase in he fuures price. For each even (exreme, one day price change), Lexis Nexis is accessed o deermine if news services offered an explanaion. An informed even (winner or loser) refers o an exreme currency fuures price change ha corresponds wih an explanaion in Lexis/Nexis. The informed winner and informed loser samples are each broken down according o wheher he announcemen is economic or poliical in naure. Uninformed winners and uninformed losers are exreme, one day fuures price changes ha do no correspond o Lexis/Nexis news announcemens. Our resuls sugges he ype of underlying announcemen is useful in pinpoining when he marke over and under reacs o new informaion peraining o foreign currency fuures prices. For winners here is srong evidence he marke overreacs o poliical news and news ha is no formally publicized. There is weak evidence he marke under reacs o economic news. * Conac auhor is Sephen J. Larson, and his is slarson1@ramapo.edu.

2 For losers here is srong evidence he marke under reacs o poliical news and weak evidence ha i overreacs o news ha is no formally publicized. Our main finding is he marke is apparenly oo opimisic a he poin poliical news is released; pos even price changes are negaive for boh poliical winners and poliical losers. In heir influenial paper, DeBond and Thaler (1985) were he firs o formally sudy overreacion in he sock marke. Using a hree year period, DeBond and Thaler formed en porfolios of socks based on performance. During he subsequen hree year period, he lowes decile of socks ou performed he highes decile of socks by 24.6% (saisically significan). Many sudies followed such as Akins and Dyl (1990) and Bremer and Sweeney (1991) where evidence suggess he sock marke overreacs o news a he ime i is released and subsequenly correcs iself over he nex few rading days. Larson and Madura (2003) examined sock price overreacion for winners and losers while conrolling for he underlying informaion releases. They conrolled for he informaion ha was released a he ime of he exreme price changes. Informed evens were associaed wih underlying informaion releases while uninformed evens were no. Their resuls sugges conrolling for he underlying informaion is useful when aemping o pinpoin when he marke over and under reacs. Specifically, heir uninformed winners are associaed wih an overreacion phenomenon, bu heir informed winners are no. This suggess he marke overreacs o informaion when rading of privae informaion, bu efficienly reacs o publicized informaion. This may be relaed o invesor self aribuion bias as discussed by Daniel, Hirshleifer, and Subrahmanyam (1998); hey posulae ha marke paricipans are more prone o overreac when rading on non publicized informaion. Using an even sudy mehod, Larson and Madura (2001) also examined overreacion and under reacion for spo currency exchange raes. For emerging currencies, hese auhors found evidence suggesing he marke overreacs, bu for indusrial currencies, hese auhors found evidence suggesing he marke under reacs. These auhors also found evidence ha conrolling for he underlying informaion releases helps pinpoin over and under reacion. Wang and Yu (2004) find srong evidence of weekly reurn reversals in 24 U.S. fuures markes. The auhors show ha fuures reurn predicabiliy is more pronounced if ineracing beween pas reurns and lagged changes in boh volume and open ineres. Their resuls sugges ha fuures marke overreacion exiss, and boh pas prices and rading aciviy conain useful informaion abou fuure marke movemens. Wilcox and Gepper (2007) used a five year moving window mehodology and found coinegraion beween he foreign currency spread, marke ineres raes and spo exchange raes; hey broke heir sample down ino en separae esimaion periods. They creaed a rading sraegy using he predicions of heir model and found ha i generaes significan rading profis. Rosenberg and Traub (2008) develop an order flow measure for Chicago Mercanile Exchange pi raders. They provide evidence ha order flow influences boh foreign currency fuures and spo prices and is a useful predicor of price reversals. Their resuls sugges ha overreacion frequenly occurs in boh he spo and fuures currencies markes. Tornell and Yuan (2009) find he fuures rading aciviies of speculaors and hedgers are useful predicors of currency spo raes bu are less correlaed wih currency fuures price movemens. Speculaive posiion measures usually forecas price coninuaion and hedging posiion measures frequenly forecas price reversals.

3 This paper should benefi academics and praciioners who are ineresed in marke anomalies. The resuls sugges marke paricipans can pinpoin over and under reacion in he foreign currency fuures marke by examining he underlying informaion releases ha cause exreme, one day price changes. HYPOTHESES Larson and Madura (2001) examined spo exchange raes and heir resuls sugges he marke under reacs o news abou indusrial currency. Since spo and fuures prices ypically move in phase, i seems reasonable o assume he currency fuures marke also under reacs o newly released informaion. Our firs hypohesis is formally saed below: Hypohesis One: Exreme, one day changes in foreign currency fuures prices are expeced o be followed by price changes in he same direcion. The nex wo hypoheses address he underlying informaion releases a he ime of he exreme one day price changes. Following Larson and Madura (2001), we expec he marke will be prone o overreac when he underlying informaion causing an exreme price change is associaed wih a high degree of uncerainy or invesor self aribuion bias. There is more uncerainy surrounding he impac of poliical evens on foreign currency prices. For example, i should be more difficul for he marke o assess he impac of a surprise elecion oucome on he exchange rae han i is for i o assess he impac of a surprise inflaion repor. The relaionship relaing o inflaion and exchange raes is fairly rudimenary; given wo counies wih differen raes of inflaion, he counry wih he higher rae is expeced o experience currency depreciaion, holding oher facors consan. The relaionship beween poliical evens and exchange raes is no as ransparen. There is some evidence [Larson and Madura (1998)] wih spo exchange raes ha suggess poliical evens are associaed wih a sronger degree of overreacion han oher evens, namely economic evens (e.g. he release of an inflaion repor). This leads us o our second hypohesis, which is saed formally below: Hypohesis Two: Poliical evens are expeced o be associaed wih reversals. Uninformed evens are no associaed wih corresponding even day explanaions on Lexis/Nexis. Here i seems reasonable o assume he marke did no rade on formal news announcemens, bu on privae informaion. Research by Daniel, Hirshleifer, and Subrahmanyam (1998) suggess marke paricipans overreac more when rading on privae informaion. They aribue his o invesor selfaribuion bias. Larson and Madura (2001) found evidence supporing his hypohesis for spo exchange raes. Our hird hypohesis is saed formally below: Hypohesis Three: Uniformed evens are expeced o be associaed wih reversals. MODEL DEVELOPMENT In heir seminal paper, Engle and Granger (1987) inroduced he heory of coinegraed processes as a means of esing long run heories among non saionary variables. Because many financial ime series conain sochasic rends, much aenion in he financial lieraure has been devoed o he possibiliy of wo or more asses being coinegraed, ha is, sharing a common sochasic rend. Examples of coinegraion among equiies can be found in Bossaers (1988), Cerchi and Havenner (1998), and Kasa (1992). Coinegraion has also frequenly been found among foreign exchange raes and Baillie and Bollerslev (1989) find ha seven currencies are coinegraed. Coinegraion has been found in many commodiy markes. For example, Bachmeier and Griffin (2006) use a coinegraion mehod o evaluae he inegraion beween and wihin he markes for coal, naural gas and crude oil. They find ha he markes for crude oil are highly inegraed and can be viewed

4 as a single global marke. In conras, while he US coal indusry is coinegraed across regions, i shows less inegraion han he oil indusry as indicaed by he slow speeds of adjusmen in he error correcion represenaion. Finally, he marke for naural gas is only weakly relaed o he oher wo sources of energy. Based on heir analysis, he auhors conclude ha a single energy complex does no exis. Warrel (2006) uses he Engle Granger wo sage coinegraion mehod o analyze inernaional inegraion in he coal indusry. She finds coinegraion and inerpres his as evidence of a global coal marke. She concludes ha marke concenraion concerns for mergers in he coal indusry may be exaggeraed because he relevan reference region is he enire global marke. In he case of fuures markes, raders agree o receive or deliver a given spo marke commodiy a a cerain ime in he fuure for a price ha is deermined oday. In such circumsances, i is no surprising ha a long run relaionship beween fuures prices and spo prices may prevail. Coinegraion in fuures markes does no necessarily occur in every insance, bu, under many circumsances, coinegraion beween spo and fuures prices would be expeced on heoreical grounds and has been documened empirically. The heoreical argumens for coinegraion beween spo and fuures prices are ypically based on marke efficiency, price convergence, and/or he saionariy of he cos of carry. Hakkio and Rush (1989) and Shen and Wang (1990) demonsrae ha coinegraion beween spo and fuures prices is a necessary condiion for marke efficiency if here is no risk premium. Chowdhury (1991) and Lai and Lai (1991) argue ha price convergence a mauriy will lead o coinegraion beween he spo and fuures prices. Lien and Luo (1993) discuss he relaionship beween coinegraion and he cos of carry and argue ha a saionary cos of carry should exis for shor mauriy conracs, paricularly if ineres raes are low. For longer mauriy conracs, coinegraion may sill apply if he cos of carry is near zero due o a rade off beween he convenience yield and sorage coss. Empirically, Chowdhury (1991) finds evidence of coinegraion beween cerain spo and fuures prices in meal markes. Wahab and Lashgari (1993) and Ghosh (1993) find coinegraion beween he S&P 500 spo index and fuures conracs. Quan (1992) and Sereis and Banack (1990) discover coinegraion in crude oil markes. In currency markes, Baillie and Bollerslev (1989), Hakkio and Rush (1989), Kroner and Sulan (1993), Ghosh (1993), and Lien and Luo (1993) find coinegraion beween foreign exchange fuures and spo markes. More recenly, error correcion mehods have been used o invesigae marke inegraion and o forecas commodiy prices, paricularly in he energy complex. In he elecriciy and naural gas fuures markes, Emery and Liu (2002) find ha he mean reversion in heir rading rule simulaion is boh saisically and economically significan. Girma and Paulson (1999) find ha risk arbirage opporuniies exis in he crack spread (crude oil, heaing oil and unleaded gasoline) complex for he period 1983 o Lanza e al. (2005) build an error correcion model for he dynamics of en grades of crude oil and foureen differen refinery producs. They compare he ou of sample forecasing performance of he error correcion models wih a naïve auoregressive model which lacks he coinegraion consrains. They find ha imposing he coinegraing consrain marginally improves some of heir forecass. Ewing e al. (2006) apply a varian of an error correcion model, he momenum hreshold auoregression (M TAR), o he gasoline, heaing oil and crude oil markes. Their model is beer able o accommodae asymmeric responses o shocks in hese markes. They emphasize ha modeling he ineracions beween he spo and fuures markes is imporan for proper hedging and forecasing. In he foreign currency markes, Sequeira, e al (1999) find coinegraing relaionships beween he Ausralian dollar spo and fuures prices, and U.S. and Ausralian risk free raes of ineres. These coinegraing relaionships sugges an error correcion represenaion for he cos of carry model which, wih zero resricions, yields he error correcion formulaion for he unbiased expecaions hypohesis. The auhors find he cos of carry model o be empirically superior o he unbiased expecaions hypohesis for he four sample ses considered.

5 In his effor, we make use of he foreign currency fuures pricing model derived by Amin and Jarrow (1991) wihin he framework of Heah, e al (1992) as indicaed in equaion (1). F, T is he fuures exchange rae beween a domesic currency, d, and a foreign currency, f, a ime for a fuures conrac wih mauriy T, is he spo exchange rae beween domesic currency d and foreign currency f a ime S, e is Euler s number, d i, T and f, T i are he domesic and foreign T period ineres raes a ime, respecively, and θ is an adjusmen erm for he marked o marke feaure of a fuures marke conrac., T d f ( i, T i, T ) T θ, T F, T = S e e (1) Assuming T =1 and applying he properies of he naural logarihm o boh sides of equaion (1) resuls in equaion (2). s are he naural logarihms of F and S, respecively. f, T and, T f + d f, T = s + i, T i, T θ, T (2) The marked o marke adjusmen erm is no direcly observable, bu i is reasonable o assume ha his erm is covariance saionary and can reaed as an inercep erm in an empirical model. Accordingly, he model we es for coinegraion is presened in equaion (3) where he esimaed coefficiens for β 1 and β 2 are prediced o be posiive and he esimaed coefficien for β 3 is prediced o be negaive. f = + (3) d f, T β 0 + β 1 s + β 2 i, T + β 3 i, T ε If coinegraion beween he daa series in (3) is presen, hen here exiss an error correcion model ha predics changes in f, T based on pas changes in d f s, i, T, and i, T, and deviaions in any exising coinegraing relaionships. DATA We make use of daily closing prices for he Briish pound (BP), Japanese yen (JY), and Swiss franc (SF) fuures conracs ha rade via open oucry on he Chicago Mercanile Exchange. We assume coninuous conrac pricing, so he fuures price used is ha for he nearby fuures conrac. We also make use of daily BP, JY, and SF spo exchange raes, expressed as American quoes o mach he pricing convenion of he fuures conracs. Finally, we make use of daily observaions of he 3 monh BP, JY, SF, and U.S. dollar ($) LIBOR raes for ineres rae daa. The daa se begins in 1991 and runs hrough year end Following Norbin, e al (1997), we employ a 5 year rolling window mehodology. The rolling regressions help o validae he sabiliy of he relaionship and allow us o evaluae wheher he forecasing abiliy is robus o varying ime periods. Our analysis makes use of en in sample 5 year esimaion periods from January 2, 1991 o December 31, The error correcion model for each of hese en 5 year esimaion periods is hen used o predic changes in he currency fuures exchange rae in he following 1 year ou of sample ime period. Table 1 illusraes he en in sample esimaion periods as well as he en ou of sample esing periods. UNIT ROOT TESTS The firs condiion for a se of series o be coinegraed is ha each series mus be inegraed of he same order. The augmened Dickey Fuller (ADF) [see Dickey and Fuller (1979)] and Phillips Perron

6 (PP) [see Phillips and Perron (1988)] uni roo ess can be used o es he values of all he specified daa series for nonsaionariy. The saring poin for a uni roo in ime series x is o firs consider a firsorder auoregressive process [AR(1)] such as ha in equaion (4). x = μ + ρ x + ε (4) 1 μ and ρ are parameers and he error erm, ε, is assumed o be whie noise. Tess are carried ou by esimaing equaion (5) where x 1 is subraced from boh sides of equaion (4) where α = ρ 1. Δx = μ + α x + ε (5) 1 The null hypohesis of a non saionary series [an I(1) series or series wih a uni roo] can be evaluaed by esing wheher he value of he esimaed coefficien for α, α ˆ, is zero. Because a α greaer han zero implies an explosive series ha makes lile economic sense, he hypohesis is esed agains he one sided alernaive ha α ˆ is less han zero. The simple uni roo es described above is valid only if he series is an AR(1) process. If he series is correlaed a higher order lags, he assumpion of whie noise disurbances is violaed. The ADF and PP ess use differen mehods o conrol for higher order serial correlaion in he series. The ADF approach conrols for higher order correlaion by adding lagged difference erms of he dependen variable, Δx, o he righ hand side of he regression, resuling in equaion (6). 1 Δx = μ + α x + β Δx + ε (6) 1 L i i = 1 i The lag lengh, L, is chosen o render he error erm ε whie noise. 2 If he ADF saisic for α ˆ is negaive and significan, he null hypohesis of a uni roo is rejeced and he series canno be considered non saionary. If he null hypohesis is no rejeced, hen here is no evidence ha he series is saionary and he series is assumed o be non saionary. The PP es makes use of a non parameric mehod of conrolling for higher order serial correlaion. The es regression for he PP es is he AR(1) process presened in equaion (6) above. The PP es makes a correcion o he es saisic of he α coefficien o accoun for serial correlaion in ε. The correcion is non parameric because he procedure makes use of an esimae of he specrum of ε ha is robus o heereoskedasiciy and auocorrelaion of unknown form. The asympoic disribuion of he PP saisic is he same as he ADF saisic and es resuls are inerpreed in he same manner. The Kwiakowski, Phillips, Schmid, and Shin (KPSS) es (1992) differs from he ADF and PP ess in ha he series x is assumed o be saionary under he null hypohesis. The KPSS es saisic makes use of he residuals from he OLS regression of x on he exogenous variables. The (Lagrange muliplier) KPSS es saisic is based on a cumulaive residual funcion and an esimae of he residual specrum a frequency zero. Criical values are based upon he asympoic resuls presened in KPSS. 3 1 There are acually hree possible variaions of he ADF and PP uni roo ess: (1) esimaion wih a consan and a rend erm, (2) esimaion wih a consan [see equaion (8)], and (3) esimaion wih neiher a consan nor rend erm. We have included a consan erm, μ, in our analysis because he mean change in some of he daa series was saisically differen from zero and all daa series exhibied some skewness. We did no include a deerminisic rend erm because economic heory predics none will exis in he daa series we use for his paper. 2 We choose a lag lengh ha minimizes he Schwarz Informaion Crierion for he opimal lag, L, in our ADF ess. 3 The AR specral densiy esimaor a frequency zero for he PP and KPSS ess is deermined using he Barle kernel sum of covariances. The bandwidh parameer for he kernel based esimaors is deermined using he Newey Wes (1994) procedure.

7 Resuls were analyzed for he uni roo ess for he naural logarihm of he Briish pound fuures exchange rae, f $/BP $/BP, he naural logarihm of he Briish pound spo exchange rae, s, he 3 monh U.S. dollar LIBOR, i $ BP, and he 3 monh Briish pound LIBOR, i. For he ADF and PP ess, he null hypohesis ha he series is non saionary is rejeced in only wo of he en 5 year ime periods esed for $/BP $/BP BP f, s, and i. The null hypohesis of non saionariy is rejeced in only one of he en 5 year ime periods esed for i $. For he KPSS ess, he null hypohesis ha he series is saionary is rejeced for all four series in all of he en 5 year ime periods a he 1 percen confidence level. Resuls were analyzed for he uni roo ess for he naural logarihm of he Japanese yen fuures exchange rae, f $/JY $/JY, he naural logarihm of he Japanese yen spo exchange rae, s, he 3 monh U.S. dollar LIBOR, i $ JY, and he 3 monh Japanese yen LIBOR, i. For he ADF and PP ess, he null hypohesis ha he series is non saionary is no rejeced in any of he en 5 year ime periods esed for $/JY f and s $/JY and is rejeced in only one of he en 5 year ime periods esed for i $. The null hypohesis of non saionariy is rejeced by boh he ADF and PP ess in hree of he en 5 year ime periods esed for i JY. For he KPSS ess, he null hypohesis ha he series is saionary is rejeced for all four series in all of he en 5 year ime periods a he 1 percen confidence level. Resuls were analyzed for he uni roo ess for he naural logarihm of he Swiss franc fuures exchange rae, f $/SF $/SF, he naural logarihm of he Swiss franc spo exchange rae, s, he 3 monh U.S. dollar LIBOR, i $ SF, and he 3 monh Swiss Franc LIBOR, i. For he ADF and PP ess, he null hypohesis ha he series is non saionary is no rejeced in any of he en 5 year ime periods esed for $/JY f and s $/JY and is rejeced in only one of he en 5 year ime periods esed for i $ SF and i. For he KPSS ess, he null hypohesis ha he series is saionary is rejeced for all four series in all of he en 5 year ime periods a he 1 percen confidence level. The resuls 4 srongly sugges ha all he individual daa series used in our model are nonsaionary and possess a uni roo. The KPSS null hypohesis of saionariy is rejeced for all series in all en 5 year ime periods esed a he 1 percen confidence level. COINTEGRATION TESTS Coinegraion resuls when a linear combinaion of a se of non saionary series is saionary. Johansen s (1991, 1995) mehod for deermining wheher non saionary series are coinegraed ess he resricions imposed by coinegraion on he unresriced vecor auoregression (VAR) involving he series. Equaion (7) represens a VAR of order ρ. ρ X = Α X + ΒY + Ε (7) i = 1 i i X is a vecor of non saionary, I(1) variables, Y is a vecor of deerminisic variables, and is a vecor of innovaions. Equaion (8) represens anoher way o wrie he VAR where Π = A I and ρ Γ =. i A j j = i + 1 ρ i = 1 i E ρ 1 ΔX = ΠX + Γ ΔX + ΒY + Ε (8) 1 i = 1 i i Assuming r represens he number of coinegraion relaions or rank, if Π has reduced rank r < k, hen here exis k r marices κ and ω each wih rank r such ha Π = κ ω and ω X is saionary. Each 4 Tables for he Uni Roo ess can be requesed: slarson1@ramapo.edu (Sephen J. Larson)

8 column of ω is he coinegraing vecor and he elemens of κ are known as he adjusmen parameers in a vecor error correcion model. Johansen s mehod is o esimae he Π marix in an unresriced form, hen use a race es o es wheher he resricions implied by he reduced rank of Π can be rejeced. The race es is a likelihood raio es saisic ha is based on eigenvalues. To deermine he number of coinegraing relaions, r, he es proceeds sequenially from r = 0 o r = k 1 unil i fails o rejec. In words, he null hypohesis of no coinegraion is esed agains he alernaive hypohesis of full rank. If ha is rejeced, he null hypohesis of one coinegraing relaion is esed agains he alernaive hypohesis of full rank. The process would be repeaed unil he null hypohesis of some number of coinegraing relaions, r k 1, canno be rejeced. Criical values for he race saisic can be found in Oserwald Lenum (1992). The exac form of he Johansen coinegraion es depends on he assumpion one makes concerning he possible deerminisic componens of he sysem. From Equaion (5), he coinegraing relaion should conain a consan o accoun for he marked o marke adjusmen. Also, o allow for shor run rends in he level of he variables (paricularly he ineres raes), we specify he error correcion componen o have an inercep ( α 0 ) in Equaion (9). Tables 2A, 2B, and 2C presen he Johansen coinegraion es resuls for he BP. JY, and SF fuures exchange rae, respecively, based on he relaionship suggesed in equaion (3). The Johansen coinegraion es resuls indicae ha a coinegraing relaionship exiss in each of he en 5 year esimaion periods for all hree currencies. We rely on he race es and is 5 percen criical value o idenify he number of coinegraing relaions. 5 The number of saisically significan coinegraing equaions ranges from one o hree depending on he ime period esed. These es resuls srongly suppor he predicions of our model ha coinegraion should exis beween a foreign currency fuures exchange rae, he corresponding spo exchange rae, and shor erm ineres raes in he wo counries of exchange. 6 ERROR CORRECTION MODELS A (vecor) error correcion model is a resriced VAR designed for use wih nonsaionary series ha are known o be coinegraed. An error correcion model has coinegraion relaions buil ino he specificaion so ha i resrics he long run behavior of he endogenous variables o converge o heir coinegraing relaionships while allowing for shor run adjusmens. The error correcion model used in his paper is presened in equaion (9) where n is he number of coinegraing equaions. The Δ noaion refers o he change in he level of he variable. 7 Δf n d f, T α 0 + β j CE j + χ i Δf i, T + δ i Δs i + φ i Δi i, T + γ i Δi i, T + η j = 1 i = 1 i = 1 i = 1 i = 1 = (9) The form of he coinegraing equaion, CE j, is presened in equaion (10) where he subscrip j corresponds o he number of he coinegraing vecor and j varies from 1 o 3 across he sub ime periods. 5 The race es and he maximum eigenvalue es idenify he same number of coinegraing vecors in seven of he en sub periods. Lukepohl, e al (2001) compare he power of he race and maximum eigenvalue ess. They find ha, in general, he wo ess show similar power, alhough in some cases he race es has greaer power. Overall, hey recommend he race es be used. Because of his, we repor boh he race es and he maximum eigenvalue es and when he wo ess disagree we use he number of coinegraing vecors indicaed by he race es. 6 The number of coinegraing relaions did no appear o affec he number of observed under valuaions or observed overvaluaions. Esimaed mispricings were disribued fairly evenly hroughou he sample even hough he error correcion model used o deermine pricing errors changed wih each ou of sample esing period. 7 While we only forecas he change in he foreign currency fuures exchange rae, o avoid exogeneiy issues we esimae he coinegraing error correcion sysem using he Johansen full informaion maximum likelihood esimaion. In addiion, we resric ourselves o one day ahead forecass and, herefore, he forecass only rely on predeermined variables.

9 j 0j 1j f 1, T 2j s 1, T d 3j i 1, T f 4j i 1, T CE = Θ + Θ + Θ + Θ + Θ (10) The firs coinegraing vecor is normalized wih Θ 11 = 1. The second coinegraing vecor (when presen) is normalized wih Θ 22 = 1. Finally, he hird coinegraing vecor (when presen) is normalized wih Θ 33 = 1. The acual number of coinegraing vecors, n = 1, 2, or 3, corresponds o he Johannsen coinegraion es resuls presened in Tables 3A. 3B, and 3C. The error correcion model in equaion (9) is esimaed using five years of daily daa and hen used o forecas f, T in he following one year ou of sample esing period. Equaion (11) hen defines a pricing error, x, as he difference beween he acual change, by he model, ( f ) E, presened in equaion (9). x, T, T ( f ), T f, T, and he expeced change prediced = f E (11) A posiive x suggess he foreign currency fuures exchange rae is higher han wha is warraned given he predicions of he model. Conversely, a negaive x suggess he foreign currency fuures exchange rae is lower han wha is warraned given he predicions of he model. To conrol for volailiy differences over he differen esimaion periods, we sandardize x based on Brown and Warner s (1980) mean adjused reurns model as shown in equaion (12) where AERC is he abnormal exchange rae change. AERC x = (12) σ d / f ( f ) To idenify he exreme one day price changes, we sor from highes o lowes he enire disribuion (combining all en esimaion periods) of he abnormal exchange rae changes for each currency. We hen choose he highes 5 percen as winners and he lowes 5 percen as losers. The resul is 244 observaions of exreme one day price changes for each currency; 122 of hese observaions are defined as winners and 122 of hese observaions are defined as losers. In oal for all hree currencies, here are 732 observaions wih 366 winners and 366 losers. The saisical significance of he pricing error is deermined using he saisic in equaion (13) where n is he sample size, AERC i is he sandardized mispricing for even i on day, σ AERC is he sandard deviaion of he abnormal exchange rae changes for he 5 year pre even period. 1 AERC i Z = (13) n σ AERC The saisical significance of he average pricing error will be calculaed for day 0, day 1, day 2, and day 3. The saisical significance of he cumulaive average pricing error will also be calculaed for days 1 o 2, and days 1 o 3. The saisical significance will be repored for he full sample of winners followed by resuls for sub samples peraining o economic announcemens, poliical announcemens and uninformed announcemens. This will be repeaed for losers. RESULTS Resuls for he degree of mispricing are disclosed in Table 3. The firs column breaks down he sample of winners and he sample of losers ino sub samples based on he ype of informaion associaed wih he exreme fuures price changes. The second column shows he sample size. The nex six columns disclose he resuls of assessing he saisical significance of he mispricing on he even day (day = 0)

10 and he hree day period following he even day. Bold ype indicaes saisical significance a he en percen level or higher. We can assess he degree of over or under reacion by examining he signs on he degree of mispricing for he pos even period (day 1, day 2, day 3, days 1 and 2, and days 1 3). For he full sample of winners and he full sample of losers he resuls do no sugges marke paricipans under reaced or over reaced o new informaion peraining o currency fuure prices. Therefore, when assessing each full sample here is no evidence supporing hypohesis one, which suggess he marke will under reac o new informaion. Insead, i appears he marke efficienly responded o new informaion abou currency fuures conracs. By examining he sub samples we hope o pinpoin any over or under reacion ha may be relaed o he ype of informaion released on day zero. Such findings may help marke paricipans esimae when he marke is prone o err. When examining he sample of winners corresponding o economic announcemens only, here is weak evidence supporing hypohesis one ha he marke will under reac. For day wo, he sign on he sandardized mispricing variable is posiive and saisically significan suggesing he marke underreaced on he even day. For he sample of losers corresponding o economic announcemens, i appears he marke s response was efficien as none of he sandardized mispricing variables are saisically significan. When examining he degree of mispricing during he pos even period for poliical winners and losers all of he signs on he degree of mispricing are negaive and saisically significan excep for losers on day one. This suggess he marke overreaced o favorable poliical news and his suppors hypohesis wo. For poliical losers however, he resuls do no suppor hypohesis wo. Insead, i appears he marke acually under reaced o poliical news. Considering poliical winners and losers ogeher i appears ha marke paricipans were overly opimisic in response o he release of boh favorable and unfavorable poliical news. Tha is, pos even currency fuures price changes are negaive for boh winners and losers. This suggess he marke errs on he side of over opimism when confroned wih poliical news. When examining uninformed winners here is srong evidence ha he marke overreaced; his suppors hypohesis hree. All of he signs of he sandardized mispricing variables are negaive and saisically significan excep for day hree. For losers however, here is weaker evidence supporing hypohesis hree. The sandardized mispricing variable is only boh posiive and saisically significan for day hree. CONCLUSION This paper addresses marke overreacion and under reacion for foreign currency fuures conracs. Using a 5 year moving window mehod and he foreign currency fuures pricing model of Amin and Jarrow (1991), we find repeaed evidence of coinegraion among he fuures price, he spo exchange rae, and ineres raes over en differen esimaion periods. An error correcion model is hen used o develop a series of prediced fuures price changes. We compare acual price changes o prediced price changes o assess wheher he marke overreaced or under reaced o new informaion. Our resuls sugges he ype of underlying announcemen is relevan in pinpoining when he marke over and under reacs o new informaion peraining o foreign currency fuures prices. Firs, i appears he marke is overly opimisic a he ime poliical news is released; winners are associaed wih reversals while losers are associaed wih under reacion. Second, here is srong evidence ha he marke overreacs a he poin favorable unpublished informaion becomes available. There is only weak evidence ha he marke overreacs a he poin unfavorable unpublished informaion becomes available. Third, i appears he marke is nearly efficien in re pricing foreign currency fuures conracs a he poin economic news is released. There is only weak evidence in favor of under reacion for winners following economic news releases.

11 Table 1: In Sample Esimaion Periods And Ou Of Sample Tesing periods (daily daa) In Sample Esimaion Period Ou of Sample Tesing Period Noes: Our analysis makes use of a 5 year moving window mehodology which resuls in en in sample 5 year esimaion periods from January 2, 1990 o December 31, The error correcion model for each of hese en 5 year esimaion periods is hen used o predic changes in he foreign currency fuures exchange rae in he following 1 year ou of sample ime period.

12 Table 2A: Johansen Coinegraion Tess $/BP $/BP $ BP Model esed: f, T = β 0 + β 1 s + β 2 i, T + β 3 i, T + ε f $/BP : naural logarihm of he Briish pound fuures exchange rae s $/BP : naural logarihm of he Briish pound spo exchange rae i $ : 3 monh U.S. dollar LIBOR i BP : 3 monh Briish pound LIBOR Time Period Hypohesized Number of Coinegraing Equaions Trace Saisic Maximum Eigenvalue 1991:1995 None # *** *** A mos 1 # *** ** A mos 2 # ** * 1992:1996 None # *** *** A mos 1 # *** ** A mos * :1997 None # *** *** A mos 1 # *** *** A mos 2 # *** * 1994:1998 None # *** *** A mos 1 # *** * A mos 2 # *** * 1995:1999 None # *** *** A mos 1 # ** A mos 2 # ** * 1996:2000 None # *** *** A mos A mos :2001 None # *** *** A mos ** A mos :2002 None # *** *** A mos A mos :2003 None # *** *** A mos 1 # *** * A mos 2 # ** * 2000:2004 None # *** *** A mos 1 # *** ** A mos Criical values *** : 1% criical value, ** : 5% criical value, and * : 10% criical value. # Denoes rejecion of he specified number of coinegraing equaions based on he Trace Saisic and he 5% criical value.

13 TABLE 2B: JOHANSEN COINTEGRATION TESTS $/JY $/JY $ JY Model esed: f, T = β 0 + β 1 s + β 2 i, T + β 3 i, T + ε f $/JY : naural logarihm of he Japanese yen fuures exchange rae s $/JY : naural logarihm of he Japanese yen spo exchange rae i $ : 3 monh U.S. dollar LIBOR i JY : 3 monh Japanese yen LIBOR Time Period Hypohesized Number of Coinegraing Equaions Trace Saisic Maximum Eigenvalue 1991:1995 None # *** *** A mos A mos :1996 None # *** *** A mos A mos :1997 None # *** *** A mos 1 # ** ** A mos :1998 None # *** *** A mos 1 # *** *** A mos 2 # ** ** 1995:1999 None # *** *** A mos 1 # *** *** A mos :2000 None # *** *** A mos 1 # ** A mos :2001 None # *** *** A mos A mos :2002 None # *** *** A mos A mos :2003 None # *** *** A mos 1 # ** ** A mos :2004 None # *** *** A mos 1 # ** ** A mos Criical values *** : 1% criical value, ** : 5% criical value, and * : 10% criical value. # Denoes rejecion of he specified number of coinegraing equaions based on he Trace Saisic and he 5% criical value.

14 TABLE 2C: JOHANSEN COINTEGRATION TESTS $/SF $/SF $ SF Model esed: f, T = β 0 + β 1 s + β 2 i, T + β 3 i, T + ε f $/SF : naural logarihm of he Swiss franc fuures exchange rae s $/SF : naural logarihm of he Swiss franc spo exchange rae i $ : 3 monh U.S. dollar LIBOR i SF : 3 monh Swiss franc LIBOR Time Period Hypohesized Number of Coinegraing Equaions Trace Saisic Maximum Eigenvalue 1991:1995 None # *** *** A mos 1 # *** ** A mos 2 # *** *** 1992:1996 None # *** *** A mos 1 # *** *** A mos :1997 None # *** *** A mos A mos :1998 None # *** *** A mos 1 # *** *** A mos :1999 None # *** *** A mos * A mos :2000 None # *** *** A mos A mos :2001 None # *** *** A mos 1 # *** *** A mos :2002 None # *** *** A mos 1 # *** *** A mos :2003 None # *** *** A mos 1 # *** *** A mos 2 # ** ** 2000:2004 None # *** *** A mos 1 # *** *** A mos 2 # *** *** Criical values *** : 1% criical value, ** : 5% criical value, and * : 10% criical value. # Denoes rejecion of he specified number of coinegraing equaions based on he Trace Saisic and he 5% criical value

15 TABLE 3: Resuls for he Saisical Significance of he Sandardized Mispricing (AERC) Winners: Pound, Swiss franc, and yen N =0 =1 =2 =3 =1 o 2 =1 o 3 All *** EN *** ** PN *** *** ** *** *** *** 2.51 U *** *** *** *** *** 2.33 Losers: Pound, Swiss franc, and yen N =0 =1 =2 =3 =1 o 2 =1 o 3 All *** EN *** PN *** *** *** * *** 2.72 U *** ** Bold ype indicaes saisical significance a he 0.01 (***), 0.05 (**), or 0.10 (*) level Variable Key: = day (=0 is day of announcemen), EN = Economic announcemen on =0, PN = Poliical announcemen on =0, U = Uninformed (no news) announcemen on =0

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