THE ROLE OF ASYMMETRIC INFORMATION AMONG INVESTORS IN THE FOREIGN EXCHANGE MARKET

Transcription

1 INTERNATIONAL JOURNAL OF FINANCE & ECONOMICS In. J. Fin. Econ. (2008) Published online in Wiley InerScience ( THE ROLE OF ASYMMETRIC INFORMATION AMONG INVESTORS IN THE FOREIGN EXCHANGE MARKET ESEN ONUR,y Deparmen of Economics, California Sae Universiy, Sacrameno 6000J Sree, Sacrameno, CA , USA ABSTRACT This paper posis asymmeric informaion as he missing link beween he currency demands of invesors and changes in he exchange rae. A heoreical model demonsraes ha changes in he exchange rae and currency demand are posiively correlaed for well-informed invesors and negaively correlaed for less well-informed invesors, resuls consisen wih sylized facs from he empirical lieraure. These heoreical findings are suppored empirically using a new daa se from he Israeli foreign exchange marke. The empirical analysis indicaes ha a one million dollar larger purchase han sales by well-informed financial invesors induces an increase of per cen in he Israeli Sheqel/Dollar exchange rae over a one monh period. A similar ne flow from less well-informed invesors resuls in a per cen decrease in he exchange rae. Copyrigh r 2008 John Wiley & Sons, Ld. JEL CODE: F31; D82 KEY WORDS: Foreign exchange marke; informaion heerogeneiy; marke microsrucure 1. INTRODUCTION I is well esablished in he exchange rae lieraure ha macroeconomic variables such as he money supply and GDP have very lile effec on exchange raes, especially in he shor run. Flood and Rose (1995) demonsrae his disconnec beween macroeconomic fundamenals and he exchange rae, noing ha volailiy in money and oupu does no appear o vary significanly during regimes of fixed and floaing exchange raes. Their conclusion is ha mos criical deerminans of exchange rae volailiy are no macroeconomic and ha research on his opic should concenrae on more microeconomic deails. The approach used in he curren paper, commonly referred o as marke microsrucure, emphasizes microeconomic deails in he foreign exchange marke. This sudy conribues o he lieraure on exchange raes and marke microsrucure in hree ways. Firs, he heoreical model uilizes informaional heerogeneiy among invesors and permis an analysis of he foreign exchange marke as he amoun of asymmeric informaion in he marke changes. Second, I demonsrae heoreically and empirically ha here is a correlaion beween a change in he exchange rae and he change in currency holdings of invesors, which varies wih invesor informaion. Finally, he empirical analysis in his paper is he firs sudy of disaggregaed cusomer order flow daa from he Israeli currency marke. Israel is an emerging marke ha is disinc from he predominanly developed counries examined in he lieraure. *Correspondence o: Esen Onur, Deparmen of Economics, California Sae Universiy, Sacrameno 6000J Sree, Sacrameno, CA , USA. y eonur@csus.edu Copyrigh r 2008 John Wiley & Sons, Ld.

2 E. ONUR In he following secion, I presen some background on exchange raes and heir markes, as well as a brief discussion of he relevan lieraure. Secion 3 develops a wo-counry model of asymmerically informed invesors ha is consisen wih he sylized facs. Secion 4 analyses he Israeli foreign exchange marke for empirical suppor of he heoreical model. Secion 5 concludes and discusses exensions o his research. 2. BACKGROUND AND LITERATURE The foreign exchange marke is composed of hree major players: dealers, brokers, and cusomers. Cusomers are invesors and hey are he ulimae end-users of currency. They rigger he iniial currency exchange by placing buy or sell orders wih dealers. Dealers are inermediaries in he marke and hey quoe prices, provide liquidiy, and aemp o profi (and ake risks) by holding posiions during he day. A he end of heir rading session, dealers ry o rever back o heir iniial invenory posiion and hey do his by offering lucraive prices o cusomers. The hird group of players in he marke, brokers, acs as message boards by giving dealers he opion of an opaque inerdealer rade. Order flow is a microsrucure erm used o describe he ne rades of invesors. I corresponds o he difference beween purchases and sales of invesors in he marke. Using a microsrucure approach, Evans and Lyons (2002) find ha inerdealer order flow explains 60 per cen of changes in he exchange rae. Their model akes incoming cusomer order flows as exogenous and focuses on he rades beween dealers. Since i is known ha cusomer order flows rigger he inerdealer rade in he firs place, a naural direcion for he lieraure has been oward undersanding cusomer order flows. As more and more order flow daa have become available for analysis, he imporance of cusomer rades for explaining high-frequency changes in he exchange rae has become apparen. In paricular, a specific correlaion exiss beween ne flows from differen ypes of cusomers in he marke and observed changes in he exchange rae. Various empirical sudies (Marsh and O Rourke, 2005; Bjonnes e al., 2005; Fan and Lyons, 2003) demonsrae ha, while order flow from financial cusomers has a posiive correlaion wih he direcion of change in he price of he exchange rae, order flow from non-financial cusomers has a negaive correlaion. As saed above, i is his cusomer (or invesor) heerogeneiy ha is explored heoreically and empirically in his paper. Wu (2006) uses a daa se consising all of he daily ransacions in he Brazilian foreign exchange marke spanning he four year ime period beween 1999 and As in he presen sudy, Wu (2006) invesigaes he foreign exchange marke in an emerging economy. Wu finds ha a one per cen depreciaion in he currency decreases he financial cusomer flow by $111 million and he commercial flow by $46 million. There are wo oher sudies in he lieraure, which offer heoreical models o explain he relaionship beween flows from differen cusomer ypes and changes in he exchange rae. Evans and Lyons (2006) model hree differen ypes of cusomers; long-erm invesors, shor-erm invesors, and imporers/exporers. Heerogeneiy among invesors in heir model arises mainly from he horizon of heir invesmen and also here is no hierarchical informaion se-up in heir model. In heir empirical work, he auhors use Ciibank daa o compare simulaed resuls from heir model wih empirical esimaes. They find ha cusomer flows forecas reurns because hey are correlaed wih he fuure marke-wide informaion flow ha dealers use o revise heir prices. They also find ha correlaions are higher a lower frequencies. Osler (2006) inroduces a simple model where he wo ypes of agens in he marke are invesors and imporers/exporers, bu does no model he informaion asymmery in he foreign exchange marke. Her resuls sugges ha he posiive correlaion beween financial demand and exchange raes is due o he shor-run dominance of financial shocks relaive o commercial shocks. 3. THEORETICAL MODEL 3.1. Model overview Unlike he models in he lieraure, he heoreical model presened below emphasizes he imporance of hierarchical informaion asymmery in he foreign exchange marke. 1 All invesors observe a common,

3 ROLE OF ASYMMETRIC INFORMATION AMONG INVESTORS noisy (public) signal abou he fuure value of fundamenals, such as money supply. A porion of hese invesors are informed in he sense ha hey also receive a noisy privae signal abou fuure fundamenals in addiion o heir public signal. Every period invesors decide how much o inves in domesic bonds, foreign bonds, and heir non-asse income. I assume ha his non-asse income depends on exchange raes, hus creaing some hedging demand in he foreign exchange marke. Invesors also make use of he exchange rae as a signal since i carries informaion abou fuure fundamenals, bu his is an imperfec signal due o unobserved hedge rades in he marke. When here is a posiive shock o fuure fundamenals, informed invesors observe his informaion hrough heir privae signal and increase heir currency holdings. The counerpar of his rade is aken by less-informed invesors. Since beer fuure fundamenals cause an increase in he exchange rae, he model generaes a posiive correlaion beween he change in currency holdings of financial (informed) invesors and he change in exchange rae, as well as a negaive correlaion for he change in currency holdings of non-financial (less-informed) invesors Model deail The hree building blocks of a wo-counry moneary model of exchange rae deerminaion are money marke equilibrium, purchasing power pariy, and ineres rae pariy. I begin by assuming ha purchasing power pariy holds using p ¼ p þ s ð1þ where p is he log of he price level in he counry and s is he exchange rae. Foreign counry variables are indicaed wih an aserisk. There is a coninuum of invesors in boh counries and hey are disribued on he inerval ½0; 1Š. I assume a myopic agen se-up where agens live for wo periods and make only one invesmen decision. This overlapping generaions design simplifies he soluion subsanially. Invesors are idenical in he sense ha hey have he same uiliy funcion and hey know ha he exchange rae depends on expecaions of fuure fundamenals. Differences among invesors arise from he signals ha hey receive abou he value of fuure fundamenals. All invesors receive a common public signal abou he value of fuure fundamenals, bu a proporion of hese invesors also receive a privae signal abou his value. Before I inroduce informaion asymmery ino he model, I describe he general soluion of invesors demand for foreign currency. Invesors in boh counries can inves in money of heir own counry, bonds of he home counry for a reurn of i, bonds of he foreign counry for a reurn of i, and in some ype of producion wih a fixed reurn. I assume ha he home counry is large and he foreign counry is infiniesimally small. This allows he bond marke equilibrium o be enirely deermined by invesors in he large home counry. I is also assumed ha money supply in he home counry is consan, whereas money supply in he foreign counry is sochasic. For ease, I assume a consan price level in he home counry so ha he ineres rae in he home counry is consan. A ime, invesor i is given a fixed endowmen w i. A ime þ 1, his invesor receives he reurn on his invesmens, as well as non-asse income from invesing in producion. This producion is assumed o depend on he exchange rae as well as on real money holdings of invesor i, m i. Thus, he producion funcion is expressed as f ðm i Þ¼ki s þ1 m i ðln ðmi Þ 1Þ=a for a40. The coefficien ki is he exchange rae exposure variable. Since invesor i s producion depends on he exchange rae, he invesor will wan o hedge himself, and his hedge agains non-asse income adds o he demand in he foreign exchange marke. An invesor s hedge demand changes every period and i is only known by he individual invesor. Invesors rade compeiively in he marke based on heir informaion. They have consan absolue risk aversion preferences denoed wih Arrow Pra coefficien of absolue risk aversion, g. Agen i maximizes his expeced discouned fuure uiliy condiional on informaion known a, F i, and his budge consrain.

4 E. ONUR The maximizaion problem can be expressed as max E ½e gci þ1 jf i Š s: : c i þ1 ¼ð1 þ i Þw i þðs þ1 s þ i i ÞB i i m i þ f ðmi Þ ð2þ where w i is wealh a he sar of period, Bi is he amoun invesed in foreign bonds, and s þ1 s þ i i is he log-linearized excess reurn on invesing in foreign bonds. Invesor i maximizes his þ 1 consumpion by invesing in domesic and foreign bonds, as well as by choosing how much o inves in his non-asse income. The consan absolue risk aversion assumpion enables invesors o se heir maximizaion decisions independen of heir wealh. Assuming ha he exchange rae is normally disribued, his implies ha he equilibrium exchange rae is independen of he wealh disribuion of invesors as well as he level of aggregae wealh. Invesor i chooses he opimal amoun of foreign bonds o hold and he firs-order condiion is s ¼ E i ðs þ1 Þ i þ i gs2 ;i ðbi þ bi Þ where s 2 ;i ¼ varðs þ1þ is he condiional variance of nex period s exchange rae and b i is he hedge due o he exchange rae exposure of non-asse income, b i ¼ ki. In addiion o opimal bond holdings, he firs-order condiions from boh domesic and foreign invesors opimal money holdings are m p ¼ ai m p ¼ ai ð4þ where m and i are logs of money supply and ineres rae, respecively. These equaions coupled wih purchasing power pariy relae he exchange rae o marke fundamenals. I specify he ineres differenial in erms of he exchange rae and fundamenals o obain i i ¼ 1=aðs f Þ, where he fundamenals are defined as f ¼ðm m Þ. Combining equaions (3) and (4), invesor i s foreign bond demand can be expressed as ð3þ B i ¼ Ei ðs þ1 Þ s þ i i gs 2 ;i b i ð5þ where he firs erm is he invesmen demand ha depends on excess reurn on invesing in foreign bonds as well as risk aversion in he denominaor. The second erm represens he hedging demand agains currency exposure in he invesor s non-asse income. Hedging demand emerging from he exchange rae exposure variable is assumed o be composed of an average erm and an idiosyncraic erm, b i ¼ b þ E i. I assume ha, even hough every invesor observes heir own exposure erm, he average hedging demand is unobservable o any of he invesors. By adding an unobservable noisy erm o he exchange rae equaion, his assumpion prevens he exchange rae from revealing all he informaion in he marke o he invesors. Even hough invesors do no observe he average erm, I assume ha hey know he auoregressive process i follows, b ¼ r b b 1 þ E b, where E b Nð0; s2 b Þ. Since invesors are he end-users in he marke, he aggregae foreign bond demand of he raders in he model should sum o zero. Thus, he condiion ha characerizes he marke equilibrium is R B i di ¼ 0. Applying his marke equilibrium condiion o (5) yields E ðs þ1 Þ s ¼ i i þ gb s 2 ð6þ where E is he average expecaion across all invesors. Noe ha he idiosyncraic erms are zero when inegraed ou over all invesors and he risk-premium erm, gb s 2, depends on he average hedging demand as well as he average condiional variance, represened by s 2. Since invesors are risk averse, hey require a premium o hold foreign bonds when hey do no have perfec informaion abou omorrow s

5 ROLE OF ASYMMETRIC INFORMATION AMONG INVESTORS exchange rae. Using equaion (6) and he definiion of fundamenals, he equilibrium exchange rae is given by s ¼ X1 a k E k 1 þ a ðf þk ags 2 þk b þkþ ð7þ k¼0 where E k are expecaions of order k41, defined as E k ðs þkþ ¼ R 1 0 Ei ðek 1 ðs þk 1 ÞÞ di wih E 1 ðs þ1þ ¼ E ðs þ1 Þ and E 0 ðs Þ¼s. Equaion (7) indicaes haheexchangeraeaime depends on he fundamenals a ime, heaverage expecaion of fuure fundamenals, and fuure risk premia. Noe ha wih dispersed informaion, he law of ieraed expecaions does no apply o average expecaions and E E þ1 ðs þ2 Þ 6¼ E ðs þ2 Þ. The expecaion of oher invesors expecaions maer. By focusing on a myopic se-up, I circumven his infinie regress problem Informaion srucure In addiion o observing all pas and curren values of fundamenals, all invesors in he marke receive a noisy public signal abou he fuure value of fundamenals. Asymmeric informaion arises from he fac ha a proporion of invesors also receive a privae signal abou he fuure value of fundamenals. Boh signals are noisy; hey do no fully disclose he fuure value of he fundamenals. I use o o denoe he proporion of invesors who are (relaively) uninformed because hey receive only he public signal. The remaining proporion of invesors, 1 o, are classified as informed invesors. Noe ha changing he raio of informed invesors o uninformed invesors in he economy is equivalen o choosing how much privae informaion exiss in he marke. When o ¼ 1, every invesor in he economy is receiving only he public signal so all are uninformed, and when o ¼ 0, every invesors is receiving boh of he signals so all of hem are informed. Assume ha he fundamenals in he economy are governed by he process f ¼ DðLÞE f, where E f Nð0; s 2 f Þ and DðLÞ ¼d 1 þ d 2 L þ d 3 L 2 þ. I denoe he noisy public signal received by all invesors as z and he noisy privae signal received by informed invesor i as n i. These signals carry informaion abou he value of he fundamenal T periods ahead, f þt. Le u denoe he fuure value of fundamenals in he economy, u ¼ f þt. This noaion makes i easier o compare he wo separae effecs of curren and fuure fundamenals on he exchange rae. In he economy, le he noisy public signal be composed of wo pieces: z ¼ u þ w z, where wz ¼ r zw z 1 þ Ez and E z Nð0; s2 zþ. The firs erm is he acual value of fuure fundamenals and he second, w z, is a persisen erm ha I assume follows an auoregressive process wih r z o1. 2 The error erm, E z, is independen from he value of fuure fundamenals and i is unknown o invesors a ime. In his se-up, he public signal does no reveal he exac value of fuure fundamenals o he invesors. The srucure of he noisy privae signal is given by n i ¼ u þ E ni, where Eni Nð0; s 2 nþ and he error erm of he signal is independen of u and oher invesors signals. By he law of large numbers, he average signal received by informed invesors is u, namely R 1 1 o ni di ¼ u. As menioned previously, here are wo ypes of invesors in he economy ha differ in he amoun of informaion hey possess. Le F in ¼fs ; f ; z ; n i : o þ 1g be he informed invesors informaion se a ime and F un ¼fs ; f ; z : o þ 1g be he uninformed invesors informaion se a ime. Given his informaion srucure, observing he equilibrium exchange rae, s, and curren fundamenals, f, does no reveal independen realizaions of fuure fundamenals, u, and he average hedge demand, b, o he invesors. They learn abou only a combinaion of hose sae variables, so ha here is no perfec informaion revelaion The equilibrium exchange rae Using i i ¼ð1=aÞðs f Þ, equaion (6) can be rewrien o show ha he equilibrium exchange rae depends on he firs-order average marke expecaion as well as on curren fundamenals and non-fundamenals: s ¼ 1 1 þ a f þ a 1 þ a E ðs þ1 Þ a 1 þ a gb s 2 ð8þ

6 In order o demonsrae he model s resuls in an analyical and more racable fashion, I analyse he myopic case where only ime þ 1 variables maer and values of fundamenals from ime þ 2 onward do no ener he equaion. The soluion o he more general model resuls in he loss of racabiliy of equilibrium equaions. Since cusomer order flow is also high frequency in naure, he inclusion of longerperiod analysis is no as beneficial as racabiliy o he model. In he myopic case, only omorrow s fundamenals maer, which implies u ¼ f þ1. Thus, fundamenals of laer daes do no ener he exchange rae equaion. Using equaion (7), he exchange rae formed by he one-period ahead expecaion of he invesors is given by s ¼ 1 1 þ a ½f ags 2 b Šþ 1 1 þ a a 1 þ a E. ONUR E ½f þ1 ags 2 þ1 b þ1š ð9þ In wha follows, I assume b and f o be i.i.d. and r z ¼ 0. 3 This makes he analysis more racable wihou alering he resuls. The firs sep in solving he model is o analyse individual invesor decisions by informaion ype, which is hen used o deermine he average expecaion of omorrow s fundamenals, E ðf þ1 Þ. Since average expecaion of omorrow s fundamenals will be deermined by he signals received by invesors in he economy, I conjecure ha he equilibrium exchange rae will depend on oday s fundamenals, public signal in he economy, omorrow s fundamenals and he oal hedge demand in he economy: s ¼ 1 1 þ a f þ l u u þ l z z l b b ð10þ I make use of he mehod of undeermined coefficiens o solve for he coefficiens of fuure fundamenals, public signal and aggregae hedge demand in equilibrium. Expecaions of invesors All of he uninformed invesors have he same informaion se. There are hree possible sources of heir informaion abou fuure fundamenals: he common public signal, he knowledge of disribuion of fundamenals, and he observed exchange rae. Uninformed invesors expecaions of omorrow s fundamenals are a weighed average of all of hese signals. Rewriing he conjecure saed above, I show wha he uninformed invesors learn from observing he exchange rae signal: s þ a f l z z l u ¼ u þ l b l u b where he lef-hand side of equaion (11) is wha is observed by he invesors (he signal), and he righ-hand 2s 2 side is no direcly observed. The variance of he error erm of he exchange rae signal is l b =l u b. This also means ha precision of he exchange rae signal depends on l b =l u, which is endogenous in he model. For an uninformed invesor, he weighed average of he hree signals can be expressed as b s 1 E i ðu l u s 1 1þa f l z z þ b z z Þ¼ ð12þ d where he b s capure he precision of he corresponding signals, ha is, b z ¼ 1=s 2 z, bu ¼ 1=s 2 f and b s ¼ 1=ðl b =l u Þ 2 s 2 b. Every signal is weighed by dividing is own precision by he overall precision for he uninformed invesors, namely d ¼ 1=varðu Þ¼b z þ b u þ b s. For an informed invesor, he weighed average of he signals has an addiional erm since every informed invesor receives heir own privae signal: b s 1 E i ðu l u s 1 1þa f l z z þ b z z þ b n n i Þ¼ ð13þ D ð11þ

7 where he addiional precision erm is defined as b n ¼ 1=s 2 n and D ¼ 1=varðu Þ¼b n þ b z þ b u þ b s is he overall precision of informed invesors signals. The coefficiens I inegrae he expecaions above over he coninuum of invesors o find he average expecaion of omorrow s fundamenals: 1 l u b s s 1 1þa f l z z E ðu Þ¼ð1 oþ D b z z þ bs l u s 1 1þa f l z z þ b z z þ bn u D ð1 oþ þo d I is apparen from equaion (14) ha he expecaion of omorrow s fundamenals depends on he raio of informed o uninformed invesors in he marke. Also noe ha he errors of he privae signals sum o zero when inegraed over a coninuum of informed invesors, which is how he acual value of fuure fundamenals eners he exchange rae in equilibrium. Subsiuing his average expecaion back ino equaion (9) solves for he coefficiens of he conjecured exchange rae equaion above: where s ¼ 1 1 þ a f þ l u u þ l z z l b b ð15þ l u ¼ a ð1 þ aþ 2 o d þ 1 o D b s þ 1 o D a o l z ¼ ð1 þ aþ 2 d þ 1 o b z D l b ¼ a 1 þ a gs2 1 þ o d þ 1 o D D ROLE OF ASYMMETRIC INFORMATION AMONG INVESTORS 1 o b n b s b n Since l b =l u is decided endogenously in his sysem of equaions, I solve a fixed poin problem o reach he acual values of he coefficiens. Looking a each coefficien closely, i is observed ha all he l s are influenced by he weighed raio of informed o uninformed invesors, o=d þð1 oþ=d. One of he primary conribuions of his heoreical model is ha i allows for he analysis of how informaion asymmery in he economy affecs he equilibrium exchange rae. Figures 1 3 show how he coefficiens change wih respec o he informaion raio in he economy. 4 Figure 1 shows ha as o! 1, he privae informaion in he economy disappears and, hus, he effec of he public signal shocks, l z, moves oward is maximum. When I invesigae he coefficien of he fuure fundamenals, l u, Figure 2 shows ha he effec of he acual fuure fundamenals on he exchange rae peaks because almos all of he invesors are receiving a privae informaion signal as o! 0. The mos ineresing resul comes from he coefficien on hedge demands, l b. There is sill confusion abou he cause of he change in he economy when o ¼ 0 and, hus, he hedge demand coefficien is effecive. Since invesors do no necessarily know if a change in he exchange rae oday is a resul of a change in hedge demand or a change in omorrow s fundamenals, hey misakenly (bu raionally) assign weigh o boh sources. Finally, Figure 3 reveals ha he coefficien increases slighly as here is less privae informaion in he economy, bu i peaks as he raio of informed o uninformed invesors in he marke diminishes. As o! 1, every invesor acquires he same public signal in he economy and, as a resul, all invesors can easily deduc he magniude of he hedge demand afer observing he foreign exchange price. This means here is no confusion and everyone has perfec informaion. Invesors do no know he rue value of he fuure fundamenals, bu hey know ha rue fundamenals do no influence he price of he exchange rae, only signals do. This is why he value of l b drops o is minimum level as no invesor in he economy receives any privae informaion signal. 5 ð14þ

8 E. ONUR Figure 1. Coefficien of public signal. Figure 2. Coefficien of fuure fundamenals. Figure 3. Coefficien of hedge demand. When l u, l z, and l b are analysed all ogeher, he coefficien on he privae informaion signal, l u, peaks when every invesor in he economy has privae informaion, whereas he public informaion coefficien is a is minimum level, and he magniude of he hedge demand coefficien is also weak compared wih mos of he oher informaion raio cases. As he privae informaion in he economy diminishes, he imporance of he public informaion coefficien picks up slowly, and so does he imporance of he bond supply coefficien. When he economy is close o he no privae informaion case, he imporance of he public

9 informaion coefficien rises sharply, bu he bond supply becomes ransparen and is coefficiens falls o is minimum level. Even in his myopic case, he amoun by which each coefficien affecs he exchange rae differs according o he disribuion of informaion in he economy. A cerain levels of informaion asymmery, a public informaion signal can cause a larger change in he exchange rae han fuure fundamenals. I have also shown ha here exis informaion levels where a shock o he aggregae hedge demand resuls in a large change in he exchange rae and, for a differen amoun of informaion, he effec of his shock o he foreign bond supply is relaively small Currency demand of invesors As discussed above, asymmeric informaion is imporan in deerminaion of he equilibrium exchange rae. An equally imporan quesion is how his informaion srucure affecs he currency demand of invesors in he marke. Making use of he soluion o he general model and he ideniy i i ¼ðf s Þ1=a, he demand for any invesor i in he marke is expressed as B i ¼ Ei ðs þ1þ s þðf s Þ 1 a gs 2 b i ð16þ Uilizing he fac ha E iðs þ1þ ¼1=ð1 þ aþe iðu Þ and he definiions of disinc expecaions of fuure fundamenals for informed and uninformed invesors, he currency demand by boh ypes of invesors in he economy is characerized below. Currency demand for uninformed invesors Making use of equaions (12) and (16), he currency demand for an uninformed invesor i, B un,is expressed as B un ¼ ð 1 lu bs s 1þa 1 f l z z Þþb z z d gs 2 ROLE OF ASYMMETRIC INFORMATION AMONG INVESTORS s þðf s Þ 1 a b i Subsiuing he definiion for l u from equaion (15) and rewriing equaion (17) yields B un f 1 þ a ¼ 1 þ a s 1 a gs 2 1 bs f D b n þ 1 z ð1 oþ d 1 þ a dgs 2 fb z b i ð18þ where f represens he reciprocal of he muliplicaion facor, which is he magnificaion of shocks o equilibrium exchange rae due o asymmeric informaion. The muliplicaion facor is equal o 1 f ¼ 1 þ 1 o D þ o b s D d b n ð19þ ð1 oþ Aggregaing over all of he demand coming from uninformed invesors, Z o B un f 1 þ a di ¼ 0 1 þ a s 1 a gs 2 o 1 þ f 1 þ bs b n þ o ð20þ z 1 þ a dgs 2 fb z ob I find ha currency demand has hree componens. The firs wo pieces capure he limi orders ha are dependen on he exchange rae and common informaion (including he public signal). Noe ha asymmeric informaion in he economy eners his par hrough many variables such as he proporion of uninformed invesors in he marke, he precision of he exchange rae signal, and he reciprocal of he muliplicaion facor, which are hemselves dependen on o. The hird piece is he privae informaion and i is he hedge demand averaged over uninformed invesors. Because of he law of large numbers, he privae informaion porion can be expressed as he average hedge demand in he economy scaled by he percenage of uninformed invesors in he marke. ð17þ

10 Currency demand for informed invesors Making use of equaions (13) and (16), he currency demand for an informed invesor i, B in, is expressed as B in o ¼ 1 l b s ðs 1 u 1þa f l z z Þþb z z þb n n d gs 2 s þðf s Þ 1 a b i Aggregaing over all of he demand of he informed invesors, Z 1 B in f 1 þ a di ¼ 1 þ a s 1 1 o f bs a b n ð1 oþ þ 1 þ a z Dgs 2 gs 2 fb z ð1 oþ þ 1 þ a 1 Dgs 2 ðb n u Þ ð1 oþb I find ha currency demand has four componens. The porion ha capures he limi orders in equaion (22) is similar o he firs porion of equaion (20) bu weighed differenly due o differen invesor raios. The hird and he fourh pieces of equaion (22) are boh privae informaion, bu i is he hird piece of equaion (22) ha is he demand arising from informaion received from privae signals of he invesors. This hird piece is naurally missing in uninformed invesor s demand since hey do no receive privae signals. The fourh erm, similar o he las erm in he uninformed invesors case, is equal o he average hedge demand in he economy scaled by he percenage of informed invesors in he marke Change in currency demand of invesors Using equaions (20) and (22), i is possible o express he change in currency demand of boh ypes of invesors in erms of shocks o he economy. Firs, I rewrie equaion (20) as Z o B un o ¼ B un di ¼ o z 0 1 þ a dgs 2 fb z ob ð23þ 1 þ a 1 þð l u u l z z þ l b b Þ o 1 þ f 1 þ bs a b n gs 2 using B un o o indicae oal currency demand of uninformed invesors. Afer gahering he coefficiens of he equaion ogeher, i is possible o represen he hedge demand, public signal, and fuure fundamenals in erms of error erms: where B un o ¼ coefun l z þ o fb z 1 þ a dgs 2 E z þðl b coef un oþe b þ coef un l z þ o fb z 1 þ a dgs 2 þ l u coef un E f þ1 coef un ¼ 1 þ a 1 o 1 þ f 1 þ bs a b n gs 2 In he same manner, he aggregae bond demand for informed invesors can also be represened in erms of error erms: Z 1 B in o ¼ B in di ¼ coef in l z þ 1 o fb z o 1 þ a Dgs 2 E z þðl b coef in ð1 oþþe b þ coef in l z þ o þ 1 o E f þ1 1 þ a 1 þ a fb z dgs 2 E. ONUR fb n Dgs 2 þ l u coef in ð21þ ð22þ ð24þ

11 where coef in ¼ 1 þ a 1 1 o f bs a b n gs 2 and B in o represens oal currency demand of informed invesors. This represenaion permis he analysis of individual shocks and heir affec on he conemporaneous currency demand by invesors. Under he assumpions ha he sandard deviaions of error erms are equal o 0.1 and, a ¼ 10; g ¼ 50, and T ¼ 1, 6 he coefficien of E z is equal o for uninformed invesors and for informed invesors. For uninformed invesors, he coefficien of E f þ1 becomes and he same coefficien becomes for informed invesors. Finally, he coefficien of E b is for uninformed invesors and for informed invesors. These coefficiens inform us abou how individual shock affecs he currency demand of differen invesors in he model. For example, a posiive shock o fuure fundamenals causes an increase in he aggregae bond demand of informed invesors. A similar shock causes a decrease in ha of uninformed invesors. On he oher hand, a shock o public signal increases aggregae bond demand of uninformed invesors and decreases ha of informed ones. Making use of equaions (24) and (25), i is also possible o compue he correlaion coefficien beween he change in he exchange rae and he change in aggregae bond demand of invesors for all hree differen shocks. Le D denoe he change in a variable beween ime and 1 and covðds ; DB un oþ denoe he relevan covariance beween a change in exchange rae and a change in foreign bond holdings of uninformed invesors. To find he correlaion for each shock, I se all he oher shocks equal o zero and single ou he effec of each one in ha manner. For he public signal, he correlaion becomes corr l z DE z ; coefun l z þ o fb z 1 þ a dgs 2 ROLE OF ASYMMETRIC INFORMATION AMONG INVESTORS DE z 2l z coef un l z þ o fb z 1þa s 2 dgs ¼ 2 z pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi varðdb un ÞvarðDs Þ which is equal o under he paramerizaion repored above. A similar correlaion for hedge demand shock is equal o and he correlaion for fuure fundamenal shock is equal o The correlaion coefficien beween he change in he exchange rae and he change in aggregae bond demand of uninformed invesors is Conducing a similar analysis for he informed invesor, I arrive a he following values for conribuions of he public signal, hedge demand, and fuure fundamenal shocks, respecively, o he correlaion: , , The correlaion coefficien wih all shocks is for informed invesors holdings. When I analyse he correlaion of a change in currency demand wih a change in exchange raes, a posiive shock o fuure fundamenals resuls in a posiive correlaion beween change in currency demand for informed invesors and he exchange rae. Tha correlaion is negaive and of he same magniude for uninformed invesors. This suggess ha when here is a posiive shock o fuure fundamenals, informed invesors will increase heir currency demand and uninformed invesors will be he suppliers, offering evidence for he explanaion of why financial invesors are said o push he marke (Bjonnes e al., 2004). Beer fuure fundamenals also cause he exchange rae o appreciae, which is consisen wih sylized facs from he lieraure. When he error erm of he public signal is posiive, uninformed invesors ake some of ha change for increase in fuure fundamenals and heir currency holdings increase. Since informed invesors do no see a change in fuure fundamenals hrough heir privae signal, hey have a more precise belief ha rue value of fuure fundamenals is no changing and hey would be willing o sell currency o uninformed invesors. Similarly, a posiive shock o hedging demand in he economy is more likely o be misaken by uninformed invesors as an increase in fuure fundamenals so hey would increase heir currency holdings. Since informed invesors have a more precise esimae abou fuure fundamenals, hey would be willing o sell currency in he marke believing ha he signal hey saw can be aribued o he change in average hedging demand raher han fuure fundamenals.

12 E. ONUR When none of he shocks are se o zero, a posiive correlaion of is observed beween he change in exchange rae and he change in currency holdings of informed invesors. The resuls sugges ha he effec of fuure fundamenals shocks dominaes he effec of oher shocks in overall correlaion calculaions and his is primarily due o he coefficien of fuure fundamenals in he equilibrium exchange rae dominaing oher coefficiens. Similarly, his causes a negaive overall correlaion beween he change in exchange rae and he currency holdings of uninformed invesors. The magniude of correlaions repored here are close o empirical observaions from he Israeli foreign exchange marke discussed in Secion EMPIRICAL ANALYSIS The heoreical model and calibraion analysis presened above generaes some resuls ha are empirically esable wih disaggregaed cusomer order flow daa. In line wih he assumpions of he heoreical model, he invesors in his daa se are caegorized ino informed and uninformed groups. I use his cusomer order flow daa o examine he correlaion beween a change in he exchange rae and he change in currency holdings of invesors for boh informed and uninformed invesors. Moreover, his paper is he firs sudy of disaggregaed cusomer order flow daa from he Israeli currency marke Daa The daa se I examine comes from he Foreign Currency Deparmen of he Bank of Israel (BOI). I covers all daily spo and swap ransacions in he New Israeli Sheqel (NIS)/Dollar marke beween June 2000 and June BOI collecs daa from cerain banks regarding heir daily rades of foreign currency wih cusomers as well as wih oher banks. 7 The daa include spo and swap ransacions by cusomers agains he bank, bu no forward ransacions even hough here is a perfecly funcioning marke for ha in Israel. According o he BOI s yearly publicaion analysing he developmens in Israel s currency markes (Bank of Israel, ), NIS rade agains he dollar is he bigges par of oal urnover in he NIS foreign exchange marke, accouning for per cen of oal urnover over he las five years. In erms of he imporance of he marke, Israel s foreign exchange aciviy is comparable o ha of counries such as he Czech Republic, Greece, and New Zealand. In 2004, average daily urnover was approximaely $1.65 billion for he whole marke, jus below he 2003 figure of $1.68 billion. 8 In erms of jus he spo marke, urnover was $722 million in 2004, slighly lower han he $748 million figure in Foreign currency is raded agains he sheqel beween he banks and heir cusomers in Israel and abroad, and among he banks hemselves in he inerbank marke. The curren exchange rae policy is based on a free floa of he sheqel vis-a -vis oher currencies, and for many years he BOI pursued a policy of non-inervenion in he foreign exchange marke. Cusomer order flow in he daa is classified ino hree caegories: foreign financial insiuions, oher cusomers, and domesic inerbank. The foreign financial insiuions classificaion includes foreign banks (commercial or invesmen) wih branches in Israel. BOI noes ha foreign financial insiuions drive he marke and engage in more speculaive aciviy han do domesic cusomers (Bank of Israel, ). On days of high rade urnover, he marke share of foreign financials increases significanly compared wih heir average marke share for each year. I is also noeworhy ha foreign financial insiuions consisenly hold larger open foreign exchange posiions (boh long and shor) han he Israeli cusomers. Based on his informaion from BOI, I hypohesize ha foreign financial insiuions are he cusomers who are driving he marke, similar o financial cusomers in Bjonnes e al. (2005), and ha hey are he cusomers wih speculaive moives. The second caegory of invesor in he marke, oher cusomers, is a heerogeneous group of domesic cusomers who rade foreign exchange for variey of reasons such as impors and expors, ourism, fund

13 ROLE OF ASYMMETRIC INFORMATION AMONG INVESTORS managemen, and invesmen. Inquiry ino his group of invesors wih he head of he Economic Uni a BOI yielded a descripion of his group as domesic companies and privae cusomers; by definiion, nonfinancial domesic insiuions. For he curren analysis, I ake his group of oher cusomers o be similar o non-financial cusomers in Bjonnes e al. (2005). Domesic banks are he inraday liquidiy providers and he domesic inerbank caegory of cusomer order flow covers rades beween hese banks. Purchase and sale daa for he domesic inerbank ransacions sum o zero mos of he ime. Looking a he ransacions beween domesic banks and cusomers, he ne currency holdings of cusomers do no sum o zero a he end of every day. The simple correlaion beween ne currency holdings of hese wo ypes of cusomers in he daa is approximaely 0.5, suggesing ha eiher banks hold some balances overnigh or he BOI daa do no cover he enire marke. The laer explanaion is more likely since I observe only he NIS/Dollar marke daa and i is very likely ha banks can balance heir overnigh invenories hrough rading in differen currency pairs as well Preliminary analysis Table 1 presens descripive saisics for he order flow daa in he NIS/Dollar marke spanning he whole ime series. Momens are quie balanced for boh of he cusomer ypes. Foreign financial insiuions lead in buying NIS, whereas oher cusomers lead in buying dollars. Sandard deviaions also seem o be similar wih average daily oal urnover reaching $570 million. Toal urnover average is higher (approximaely $630 million) when early years in he daa se are omied since hose are he years when he marke was sill mauring. BOI repors indicae ha he marke maured in 2002 afer several years of expansion in response o liberalizaion (Bank of Israel, ). Before examining he daa graphically, I calculae simple correlaions beween he change in exchange rae and he change in currency holdings of differen invesors. Recen lieraure using oher daa ses indicaes a posiive correlaion beween financial cusomer order flow and he change in exchange rae and a negaive correlaion beween he non-financial cusomer order flow and he change in exchange rae. This negaive correlaion associaed wih non-financial cusomers is used o idenify hem as overnigh liquidiy suppliers. In he Israel daa, his corresponds o he oher cusomers caegory and I es wheher hey are he ones supplying he liquidiy in he overnigh marke. The posiive correlaion associaed wih he foreign financials idenifies hem as pushers in he marke; hey are he speculaors who iniiae he rade. As expeced, he correlaion beween he change in currency holdings of foreign financial cusomers and he change in exchange rae is The corresponding correlaion for he oher cusomers caegory is The magniude of hese correlaion numbers increases for differen segmens of he daa, bu he signs of he correlaion coefficiens always say posiive for foreign financials and negaive for oher cusomers, which is consisen wih he lieraure. I graph he daily daa o see how ne purchases of he cusomer groups and he exchange rae move ogeher in he NIS/Dollar marke. Figures 4 6 are graphs of cumulaive ne order flows of cusomers and he exchange rae for various periods. 9 Disaggregaing he daa ino hree periods helps o demonsrae how Israel s currency marke maures over ime. Table 1. Descripive saisics: currency flows in spo marke Order flow Variables Toal urnover Financial Oher cusomers Aggregae Mean Sd. dev Minimum Maximum Noe: All values are in millions of dollars.

14 E. ONUR Figure 4 graphs he flows corresponding o 2000 and The marke was sill growing during hose years and foreign invesors were slowly coming ino he currency marke in Israel. The growh rae in he marke was 54 per cen in 2000 and 58 per cen in This indicaes ha he marke may no be in equilibrium during hose years. During his ime period, foreign financials appear o be buying currency while he dollar is appreciaing, whereas oher cusomers are doing he selling. Sill, he exchange rae appears o be much more volaile han he ne flows in he marke and ha could be anoher sign of marke immauriy. As a resul, I analyse his early ime period separaely in he remainder of he paper. Figure 5 presens he flows from 2002 o The mos noiceable feaure of his graph is ha flows from foreign financials are negaively correlaed wih he flows from oher cusomers. Because he marke may sill be mauring in 2002, a beer correlaion is observed beween he flows and he exchange rae in The order flow from foreign financials appears o be posiively correlaed wih he change in he exchange rae, whereas order flow from he oher cusomer group is negaively correlaed. The correlaion coefficien beween exchange rae changes and he flows from foreign financials is 0.16 for he period and i increases o 0.27 when only 2003 daa are considered. On he oher hand, he correlaion coefficien beween exchange rae changes and he flows from oher cusomers is 0.3 for he same period. Figure 6 looks a he mos recen years of daa, A clear negaive correlaion beween he ne holdings of oher cusomers and he change in exchange rae is eviden in he graph. Even hough foreign financials appear o be in a selling rend in he marke in he laer par of he ime series, high-frequency changes in ne holdings are sill posiively correlaed wih changes in exchange rae. Figure 4. Sheqel/Dollar exchange rae, Figure 5. Sheqel/Dollar exchange rae,

15 ROLE OF ASYMMETRIC INFORMATION AMONG INVESTORS Figure 6. Sheqel/Dollar exchange rae, Empirical model and resuls I employ a simple regression model o examine he empirical relaionship beween order flows and changes in exchange rae. The dependen variable is he change in he log of he spo exchange rae and he independen variables are disaggregaed order flows by differen cusomer ypes. If order flow from differen cusomer ypes is correlaed differenly wih price due o privae informaion, hese effecs should be observable in a simple regression. To es his hypohesis, I run he following regression on he disaggregaed daa, where financial and oher cusomer ne order flow is separaed ino disinc independen variables: Ds ¼ b 0 þ b 1 x fin þ b 2 x oher þ E ð26þ Table 2 summarizes he resuls from running he regression in equaion (26) on daily disaggregaed daa. Similar o wha he heoreical model suggess, order flow from foreign financials is posiively associaed wih he change in he exchange rae, whereas oher cusomers ne order flow is negaively correlaed. All coefficiens are saisically significan wih he excepion of he coefficien on foreign financials for he period. This may be because paricipaion by foreign financials in Israel s currency marke was sill growing during hose years and he marke iself was sill mauring. R 2 saisics sugges ha approximaely 8 per cen of daily changes in he exchange rae can be explained by daily disaggregaed ne order flow from cusomers. Nex, I run he regression above using a lower-frequency daa. Lyons (2001) repors a beer fi for a similar regression model in monhly frequency raher han daily, which is consisen wih wha I find here. Table 3 summarizes he regression in equaion (26) for weekly and monhly daa during he period. Finally, I include a macroeconomic variable in his regression, he ineres rae differenial beween he US and Israel. Theoreical model shows ha curren fundamenals are an imporan par of equilibrium exchange rae and wihou a proxy for fundamenals in he regression, here is room for omied variable bias. I choose he ineres rae differenial as a proxy for macroeconomic effecs since i is known o be highly correlaed wih exchange raes in he long-run and i is easily available a any required frequency. Lowering he frequency of he daa o weekly inervals improves he R 2 saisic o approximaely 17 per cen. The signs on he coefficiens are he same as in he higher-frequency regression and hey are boh saisically significan. The resuls sugges ha a one million more dollar purchase han sales by foreign financials is associaed wih an increase of per cen in he NIS/Dollar rae over a one week period. The magniude of an average weekly ne purchase is approximaely $30 million for foreign financials, hus in a normal week, order flow from foreign financials may be associaed wih a 1.5 per cen change in he exchange rae. As expeced, his coefficien is large compared wih oher currency markes bu he NIS/ Dollar is more of a local marke and i is no as liquid as markes for more popular currency pairs (e.g.

16 E. ONUR Table 2. OLS regression resuls: daily disaggregaed daa Foreign financials Oher cusomers All daa Coefficien sa R Coefficien sa R Coefficien sa R Noe: The dependen variable is he log change in he daily exchange rae over he relevan inerval, and he explanaory variables are he disaggregaed ne cusomer order flow in he marke. Table 3. OLS regression resuls: weekly and monhly disaggregaed daa Foreign financials Oher cusomers Ineres diff. Weekly Coefficien sa R Monhly Coefficien sa R Disaggregaed Coefficien sa R Noe: The dependen variable is he log change in he exchange rae over he relevan inerval, and he explanaory variables are he disaggregaed ne cusomer order flow in he marke. The las regression also includes he ineres rae differenial beween he US and Israel. Euro/Dollar or Yen/Dollar). A similar ne flow from oher cusomers is correlaed wih a fall in he exchange rae of per cen over a one week period. The monhly order flow regression in Table 3 reurns an even beer fi wih an R 2 of 30 per cen. The model fi improves o 40 per cen when I include he ineres differenial beween counries as an addiional explanaory variable. The coefficiens are similar; a one million dollar larger purchase han sales by foreign financials is associaed wih a per cen increase in he NIS/Dollar rae over a one monh period. As before, he correlaion beween a similar ne flow from oher cusomers and he fall in exchange rae is around per cen. A brief discussion is in order abou he possibiliy of mulicollineariy in he explanaory variables. I is imporan o undersand how much he correlaion beween he disaggregaed order flows affecs he regression resuls. Even hough he correlaion coefficien beween he order flow of foreign financial insiuions and oher cusomers is no rivial (approximaely 0.50), adding each of he variables o he regression changes neiher he coefficiens nor he significance of single variable regressions by much. One way o deec mulicollineariy is o run he regression of change in exchange rae on he wo-order flow variables independenly and compare he coefficiens of hose regressions wih he mulivariae regression.

17 ROLE OF ASYMMETRIC INFORMATION AMONG INVESTORS If mulicollineariy is paricularly problemaic, coefficiens would lose saisical significance. In he curren analysis, however, he coefficiens of mulivariae regressions are sill significan. The empirical resuls from he Israeli foreign exchange marke are consisen wih oher findings in he lieraure. Marsh and O Rourke (2005) repor ha a ne flow of one billion Euros from leveraged financial insiuions is associaed wih a 1.49 per cen rise in he value of Euro over one day, and a 1.86 per cen rise over a week. A similar flow from non-financial corporaions is associaed wih a fall in he value of he Euro of 0.68 per cen over one day and a 0.93 per cen increase over a week. 10 Lyons (2001) repors ha a similar ne flow from leveraged funds is associaed wih a 0.6 per cen appreciaion of he Euro over a one monh period. This analysis suggess ha orders from differen ypes of cusomers are correlaed differenly wih he change in exchange rae. In addiion, he consisen paern of coefficiens observed in a variey of empirical sudies suggess ha here is imporan informaion conained in cusomer order flows. If he correlaion beween flows and changes in he exchange rae was simply due o liquidiy effecs, hen here would be no difference beween equally sized orders from differen cusomer ypes. The resuls repored here, as well as hose from he lieraure, sugges ha here is a difference. Anoher similar paern observed in he lieraure is ha rades from financial cusomers have a larger price impac han ohers. The common view in he lieraure is ha his is due o superior informaion possessed by he financial invesors in he marke. 5. CONCLUSION In his paper, I offer boh a heoreical and an empirical examinaion of he informaion asymmery among invesors in he foreign exchange marke and he relaionship beween cusomer order flow and exchange raes. The heoreical model incorporaes macroeconomic fundamenals, a microsrucure approach, and hierarchical informaional asymmery. Invesmen decisions of asymmerically informed invesors generae and explain he commonly observed correlaions beween currency holdings and he exchange rae in he foreign exchange marke. While oher researchers have documened hese correlaions empirically, his paper also offers a heoreical model ha explains he mechanics behind he empirical relaionships. Addiionally, I couple he heoreical model wih empirical resuls from a marke ha has no been sudied before in erms of he microsrucure approach o foreign exchange markes. The primary findings of he heoreical model indicae ha he amoun of asymmeric informaion in he marke plays an imporan role in deermining he equilibrium exchange rae. This asymmeric informaion beween invesors also assigns informed invesors he role of marke pushers and less well-informed invesors he role of liquidiy suppliers. In a general analysis, changes in he exchange rae and currency demand are posiively correlaed for well-informed invesors and negaively correlaed for less wellinformed invesors. One scenario is ha informed invesors, afer observing hrough heir privae signals ha fuure fundamenals will be higher, increase heir demand for foreign currency and hus drive up he exchange rae. This increased exchange rae leads he less well-informed invesors o sell heir currency holdings, creaing a negaive correlaion beween heir holdings of currency and he equilibrium exchange rae. The heoreical resuls are suppored by he empirical analysis. The correlaion beween he change in currency holdings of informed invesors and he change in he exchange rae is 0.12 in he BOI daa se and in he heoreical model. The corresponding correlaion for uninformed invesors is 0.22 in he daa se and in he heoreical model. Alhough he magniude of hese correlaions differ, he model predicions beer mach he empirical correlaions when he maured years of he Israeli foreign exchange marke are analysed. These resuls offer a srong heoreical and empirical basis for believing ha he characerisics of he invesors holding currency maers a grea deal in foreign exchange markes. Finally, he empirical analysis indicaes ha a one million dollar larger purchase han sales by foreign financials is associaed wih a per cen increase in he NIS/Dollar exchange rae over a one monh period and a similar ne flow from oher cusomers is associaed wih a per cen fall in he exchange

18 E. ONUR rae. I also find ha disaggregaed order flow daa and ineres rae differenials explain 40 per cen of he change in exchange raes a monhly frequencies. ACKNOWLEDGEMENTS I am deeply graeful o he Bank of Israel for providing he daa and o Francoise Ben Zur for helping me wih my queries abou he daa. NOTES 1. This model inroduces hierarchical informaion asymmery and builds upon he model presened in Bacchea and Van Wincoop (2006). 2. The fac ha z has a persisen erm permis he public signal o be expressed in erms of is curren and pas innovaions when conjecuring he equilibrium exchange rae. 3. This is same as assuming r b ¼ 0, w z ¼ Ez and f ¼ E f. In addiion, since he model is solved for an equilibrium value of he condiional variance of nex period s exchange rae, I drop he ime subscrip on s 2 from his poin forward. 4. These graphs are drawn under he following assumpions: T ¼ 1; r b ¼ 0; w z ¼ 0; f ¼ E f. In addiion, I se a ¼ 10; g ¼ 50 and all sandard deviaions of shocks are equal o These heoreical resuls are similar o he findings of Wang (1993), who argues ha he limiing equilibrium of o! 1 can be very differen from he equilibrium when o ¼ These values are chosen o mach hose used in Bacchea and Van Wincoop (2006). 7. Unforunaely, I do no know wha percenage of he oal marke is composed of hese repored rades. 8. These figures include swaps as well as spo ransacions. 9. The figures show he cumulaive flow of foreign financials, oher cusomers, and he NIS/Dollar exchange rae for differen ime spans. The spo exchange rae is expressed on he righ-hand scale. The cumulaive cusomer flow is expressed on he lef-hand scale in millions of dollars. Horizonal axis shows he number of days corresponding o he chosen ime period. 10. Marsh and O Rourke (2005) also repor ha flow in oher markes may have much higher coefficiens. A similar ne flow in he Euro/Yen marke, for example, is associaed wih a 4 per cen increase in he Euro. REFERENCES Bacchea P, Van Wincoop E Can informaion heerogeneiy explain he exchange rae deerminaion puzzle? American Economic Review 96: Bank of Israel. Foreign Currency Deparmen Annual Repor ( ), Bank of Israel. Available a Bjonnes G, Rime D, Solheim H Liquidiy provision in he overnigh foreign exchange marke. Journal of Inernaional Money and Finance 24: Bjonnes G, Rime D, Solheim H Volume and volailiy in he foreign exchange marke: does i maer who you are? In Exchange Rae Economics: Where Do We Sand? Paul De Grauwe (ed.). MIT Press: Cambridge, MA. Evans M, Lyons RK Order flow and exchange rae dynamics. Journal of Poliical Economy 110: Evans M, Lyons RK Undersanding order flow. Inernaional Journal of Finance and Economics 11: Fan M, Lyons RK Cusomer rades and exreme evens in foreign exchange. In Essays in Honor of Charles Goodhar, Paul Mizen (ed.). Edward Elgar: Norhampon, MA. Flood P, Rose K Fixing exchange raes: a virual ques for fundamenals. Journal of Moneary Economics 36: Lyons K The Microsrucure Approach o Exchange Raes. MIT Press: Cambridge, MA. Marsh I, O Rourke C Cusomer order flow and exchange rae movemens: is here really informaion conen? Cass Business School Working Paper, London. Osler C Macro lessons from microsrucure. Inernaional Journal of Finance and Economics 11: Wang J A model of ineremporal asse prices under asymmeric informaion. Review of Economic Sudies 60: Wu T Order flow in he souh: anaomy of he brazilian FX marke. Working Paper, Universiy of California, Sana Cruz.