Bid-ask Spread and Order Size in the Foreign Exchange Market: An Empirical Investigation

Transcription

1 Bid-ask Spread and Order Size in he Foreign Exchange Marke: An Empirical Invesigaion Liang Ding* Deparmen of Economics, Macaleser College, 1600 Grand Avenue, S. Paul, MN55105, U.S.A. Shor Tile: Bid-ask Spread and Order Size in he FX marke Absrac: This aricle empirically examines he relaionship beween order sizes and spreads in he foreign exchange marke based on a FX dealer s quoes. I is found ha spreads are independen of order sizes in he iner-dealer marke, bu hey are negaively correlaed in he cusomer marke. JEL classificaion: F31; G14 Keywords: bid-ask spread; order size; foreign exchange marke; iner-dealer marke; cusomer marke. * Corresponding auhor: Liang Ding, Phone: , Fax: address: ding@macaleser.edu. 1

2 Non-echnical summary: In he pas wo decades, an increasing body of lieraure has been devoed o he deerminaion of bid-ask spreads in he foreign exchange marke. Theoreically, economiss have recognized four deerminans of spreads: exchange rae volailiy (marke uncerainy), rading volume, number of dealers (marke compeiion), and order sizes. Accordingly, many sudies made empirical invesigaions abou he relaionships beween he spreads and deerminans menioned above. Among hese sudies, however, an empirical examinaion of spread and order size, a deerminan indicaed consanly by heoreical models, can hardly be found. This aricle empirically examines he relaionship beween order size and spread in he foreign exchange marke. A new daa se has been colleced from an online foreign exchange dealer who reveals boh cusomer and iner-dealer bid-ask quoes in response o each rading reques. Then he daa are esed by an economeric model o find ou he relaionship beween order size and spread. I is found ha spreads are independen of order sizes in he iner-dealer marke, while hey are negaively correlaed in he cusomer marke. None of he curren models can explain his finding alone, so new models need o be creaed o provide more convincing heoreical reasoning. One possible direcion for fuure research would be he combinaion of all facors ha have been discussed in lieraure. Following his rack, spreads are independen of order sizes in he iner-dealer marke probably because posiive facors are offse by negaive ones, while he negaive correlaion beween order sizes and spreads in he cusomer marke migh be due o he dominance of negaive facors.

3 Bid-ask Spread and Order Size in he Foreign Exchange Marke: An Empirical Invesigaion Keywords: bid-ask spread; order size; foreign exchange marke; iner-dealer marke; cusomer marke. 1. Inroducion The relaionship beween order size and bid-ask spread in he foreign exchange (FX) marke remains unseled. On he heoreical level, exising models give mixed predicions abou he impac of order size on spread. 1 Processing cos models conend ha order size and spread should be negaively relaed, while invenory holding risk and informaion cos models boh sugges ha order size and spread should be posiively relaed. On he empirical level, economiss have found mixed resuls. Lyons (1995) showed ha order size and spread were posiively relaed for a paricular iner-bank dealer during a week in 199, while Yao (1998) and Bjønnes and Rime (005) concluded ha currency spread bears lile or no relaion o order size. The empirical evidence for he papers menioned above is based on iner-dealer daa only, while he relaionship in he cusomer FX marke has rarely been discussed. Several quesions need o be addressed. Wha is he impac of order size on spread? Is he impac differen in he iner-dealer and cusomer markes? Which heoreical model can explain he findings? If none of he curren models is consisen wih he empirical realiy, how should fuure research be direced? This paper inspecs he impac of order size on spread in boh he iner-dealer and cusomer FX markes using new daa. The daa were colleced from an online foreign exchange dealer who displayed boh cusomer and iner-dealer bid-ask quoes in response o each rading reques. The 1 Secion provides a deailed discussion of his issue. Osler e al. (006) did examine he impac of order size on spread in he cusomer FX marke. However, his paper was sared before heir resuls were available publicly. 1

4 daa were hen esed by an economeric model o deermine he relaionship beween order size and spread, revealing ha spread is independen of order size in he iner-dealer marke and negaively correlaed in he cusomer marke. Since none of he curren models alone can explain hese findings, an inuiive explanaion will be offered. The remainder of he paper is organized as follows: Secion summarizes he curren lieraure abou he relaionship beween order size and spread; Secion 3 examines his relaionship empirically and displays resuls; and Secion 4 concludes.. Lieraure review Financial heory has idenified hree basic sources of bid-ask spreads: order processing coss, invenory holding risks, and informaion coss of marke making. Processing cos models claim ha spread is he compensaion for dealers who offer immediacy while bearing some fixed coss of marke making. Such coss may include subscripions o elecronic informaion, connecion o he dealing sysem, and adminisraive expense. In he earlies lieraure on spread deerminaion, Demsez (1968) presened he firs formal model for he sock marke bid-ask spread. Finding ha buy and sell orders generally do no reach he marke a he same ime, Demsez assumed a separae class of marke paricipans who provide immediacy by sanding ready o buy and sell. To cover he cos of sanding ready, hese providers of immediacy mus, on average, sell shares a a higher price han hey buy shares. The difference beween he selling (ask) and buying (bid) prices is he spread. Soll (1978) and Harmann (1998 and 1999) also buil spread deerminaion models from his perspecive. Since order processing cos is relaively sable in he shor run, he compensaion for each uni of ransacion ends o be smaller if he rading volume is larger. Thus, his line of models usually predics ha he spread should be negaively affeced by he order size.

5 Invenory risk models generally argue ha spread is he compensaion for dealers who provide immediacy and assume risk by holding invenory a he same ime. These models usually view dealers as risk aversion agens who provide liquidiy and opimize heir own securiies porfolios. In hese models, dealers choose bid-ask prices o maximize heir expeced uiliy. Afer analyzing a cenralized securiy marke wih risk aversion dealers, Ho and Soll (1981) showed ha he spread is a posiive funcion of single ransacion size (order size), he dealer s degree of risk aversion, and he securiy reurn variance. Oher similar models include Soll (1978) and Biais (1993). Apparenly, he risk of holding invenory is higher if he price of an asse is more volaile. To compensae for his risk, spread is shown o be posiively correlaed wih marke uncerainy. Given he same marke uncerainy, he ransacion wih a larger order size is more likely o change he invenory level unexpecedly and raise he dealer s risk. Thus, his line of models suggess ha he spread should be posiively affeced by he order size. Informaion cos models also known as asymmeric informaion or adverse selecion models mainain ha spread is he compensaion for dealers who migh lose money when rading wih beer-informed agens. If some invesors are beer informed han ohers, he person who places a firm quoe will lose o invesors wih superior informaion. To cover he possible loss caused by rading wih beer-informed agens, dealers quoe higher selling prices and lower buying prices. Bageho (1971) firs noed ha he losses o informed raders mus be offse by profis from uninformed raders if dealers are o say in business. Glosen and Milgrom (1985), Kyle (1985) and Admai and Pfleiderer (1988) can also be pu ino his caegory. The asymmeric informaion model suggess ha as a rade grows larger wih someone who is beer informed, a dealer s poenial loss also grows larger. Therefore, a dealer would widen he spread o deer such ransacions. Thus, his line of models usually claims ha order size and spread should have a posiive relaionship. 3

6 In summary, various models provide mixed predicaions of he relaionship beween spread and order size. Which candidae model is correc? How is order size relaed o spread in he real world? The empirical esing in he following secion will provide some answers. 3. Empirical esing 3.1. Daa collecion and descripion The daa used in his paper were colleced from an online foreign exchange dealer. 3 This dealer displayed boh cusomer and iner-bank bid-ask quoes for several major currencies on is quoes window in response o individual quoe requess randomly generaed by a compuer program. The dealer s responses is bid-ask quoes become par of my daase. I focused on he rae of he US dollar versus he Euro (USD/EUR), currenly he mos frequenly raded currency pair in he world. 4 To obain quoes for large, medium and small orders, he program seleced order size based on he normal disribuion around $5,000,000, $500,000, and $10,000 respecively. The sample generally conained similar numbers of large, medium and small sizes. I used each order size for five imes a he inerval of one minue. Every five-minues, I swiched o a differen order size. 5 The 970 observaions in my sample were colleced during he period of July 7 hrough July 15, 004, wih weekend days excluded due o low ransacion volume. Abou hree hours each day were spen collecing daa (usually 9:00 a.m. o noon local ime, hough o be he busies rading ime each weekday). The cusomer quoes colleced are all for individuals and no for wholesale cusomers, such as financial insiuions. Alhough no obained hrough real ransacions, he prices 3 The daase, as well as deails regarding daa sources, are available upon reques. 4 Supporing evidence can be found in he BIS s riennial survey of foreign exchange and derivaive marke aciviy. According o he mos recen survey conduced in April 004, he USD/EUR currency pair accouns for 8% of oal foreign exchange aciviy and is he mos heavily raded currency pair in he world. The resuls of he survey can be accessed from he BIS s websie (hp:// 5 The daa were colleced in his manner because I waned o see wheher spread was affeced significanly by oher facors oher han jus he order size. I found ha he spreads in my sample were sable wihin he fiveminue period for he same order size. 4

7 received from he dealer were firm quoes i.e. hey were no proposed prices subjec o laer change. Compared o he daa used in prior lieraure, he mos imporan feaure of his paper s daase is ha i conains order sizes and maching spreads. Table 1 gives descripive saisics of he variables conained in his daase, showing he mean value of cusomer spreads as significanly wider han ha of iner-dealer spreads. This paern can be explained by marke power heory, which suggess ha he spread should be wider if he cos is higher o find he bes deal in he marke. I is generally hough ha such cos is significanly less for dealers han cusomers due o he elecronic iner-dealer rading sysem. In an empirical research sudy, such as his projec, he qualiy of he daa criically affecs he reliabiliy of he conclusions. A major consideraion here is he ypicaliy of he dealer and is quoes. Given he nearly perfec capial mobiliy beween indusrialized counries and he dominance of he elecronic rading sysem in oday s FX marke (which is coninuously raded 4/7), non-spread ransacion coss become ignorable. Thus, neiher ime nor geography should lead o significan differences among he quoes of various dealers. Meanwhile, wih he rise of online rading, fierce compeiion among he dealers drives heir quoes even closer o prevailing marke raes. Moreover, I compared he midpoin of bid-ask quoes obained from he dealer wih marke raes from oher sources. The raes were similar and he direcional changes exacly he same. Therefore, I believe ha he quoes obained from his paricular dealer can represen he marke. Finally, no special evens occurred in he ime period when he daa were colleced. 5

8 3.. Esimaion model and economeric mehodologies In his economeric model he dependen variable is spread, while he independen variables are order size and exchange rae volailiy. 6 Since many sudies have demonsraed ha he volailiy of spo exchange raes can be modeled as a GARCH process, his paper esimaes he volailiy hrough a MA (1)-GARCH (1,1) specificaion: 10,000 M σ ε M, M, = ϖ + αε I 1 = µ + θε M, 1 ~ N (0, σ where M sands for he spo exchange rae and M, ) M, 1 + βσ + ε M, 1, M, M is he change of he rae. I represens he informaion se, and µ, θ, ϖ, α, β are he parameers o be esimaed. The ime subscrip refers o he place in he order of he series of quoes, so ha ˆ σ provides an esimae of he exchange rae volailiy. Since he magniude of mid-quoe flucuaions is very small wihin he 1-minue window, he exchange rae change M is muliplied by 10,000 o enlarge he effecs of dependen variables so ha esimaed parameers will no be oo small. In his esimaion model, he observaion of he exchange rae is measured as he logarihm of he mid-quoe of bid-ask prices. Given ha a and b denoe he ask and bid prices respecively, M is compued by he following formula: M, M a = log( + b ) Please noe ha he daa are no coninuous in erms of ime because hey were no colleced 4/7. To allow rading and weekend breaks in he esimaion, I esimaed he GARCH model for each day separaely. Afer obaining he exchange rae volailiy, a simple linear model was applied o esimae he impac of order size on spread: S = γ 0 + γ 1 ˆ σ + γ O + ε ~ N (0, σ ε ), = 1,..., T. ε (1) 6 Marke compeiion is anoher major spread componen menioned in lieraure, bu is omied in his research because of he unlikelihood of changing significanly over he course of a one-week sample. 6

9 where S denoes spread, O denoes order size, and obained from he GARCH esimaion. γ 0, γ 1, γ following normal disribuion wih a zero mean. The variable σˆ represens he exchange rae volailiy are consan parameers, andε is an error iem O is aken as he logarihm of he original order sizes. The spreads are compued as he logarihm of he spread measured in pips 8 such ha: S log[( a b ) 10000] () = The choice of esimaion mehod is deermined by he naure of he spread daa. I is well known ha high frequency financial daa such as exchange rae spreads usually exhibi nonnormaliy and high auocorrelaion. Therefore, OLS or Maximum Likelihood Esimaion migh be inefficien o esimae he model. The saisical assumpions required by GMM for hypohesis esing are quie weak and neiher auocorrelaion of he daa nor non-normaliy of he residuals jeopardizes is esimaion. γ denoes he vecor of parameers in he model, and M (λ) is he vecor of momen condiions. Given a weighing marix W, GMM chooses he parameers, which minimize he quadraic funcion J (γˆ ) as below: J ( ˆ) γ = M ( γ )' WM ( γ ) (3) The weighing marix W can be esimaed by several approaches ha can accoun for various forms of heeroskedasiciy and/or serial correlaion. In his paper, Newey-Wes (N-W), Whie and Gallan weighing marixes are applied for he purpose of robusness. Meanwhile, insrumen variables are chosen from he explanaory variables hemselves. The firs insrumen marix 8 Since order sizes are much larger han spreads in erms of magniude, esimaed parameers would be very small if he model was esimaed by he original daa. To balance he magniude of variables on boh sides of he equaion, spreads measured in pips are used in he esimaion. 7

10 employs he square of explanaory variables (GMM1), while he oher is a one period lag of explanaory variables (GMM). A regular -es and a likelihood raio (LR) are used o es he significance of order size in he model. A Wald es is used o check he significance of coefficiens joinly by esing he resricion formed as R γ = r, where R is he parameer vecor of resricion condiions, γ is he coefficien vecor, and r is a consan o be esed. R=[0,0,1] and r=0 since our concern is wheher he order size coefficien γ is posiive, negaive or zero. Believing ha he momen condiions and residual iem (ε ) are orhogonal, he asympoic disribuion of he objecive funcion, LR saisic, and Wald saisic all follow he Chi-square disribuion allowing an accepance or rejecion decision o be made according o criical values compued from he Chi-square disribuion Esimaion resuls Much of he following discussion will focus on γ, he order size coefficien, which should be eiher negaive according o he processing cos model or posiive according o boh he invenory risk and asymmeric informaion models. The discussion will also exend o he esimae of γ, he 1 exchange rae volailiy coefficien, which should be posiive according o heoreical models. Table repors he resuls of he volailiy esimaion for each day. None of he parameers is significanly differen from zero excep for he consan iem in he innovaion equaion. This suggess ha he volailiy of spo exchange raes is fairly sable and does no possess he feaures of auocorrelaion and heeroskedasiciy perhaps because he sample includes only he hours from 9:00 a.m. o noon for seven workdays. Volailiy is sufficienly srongly auocorrelaed ha i probably did no vary much from day o day. Also, he ime inerval chosen may have had lile inraday variaion in volailiy. 8

11 Panels A and B of Table 3 display he resuls of equaion (1) for boh cusomer and iner-dealer spreads. As shown in panel A, he -es, Likelihood Raio es and Wald es all sugges a significanly negaive coefficien for order size a he 5% significance level wih Whie sandard errors. The negaive coefficien for order size is also found a he 10% significance level wih Newey-Wes and Gallan sandard errors. This means ha he spreads quoed by he dealer for individual cusomers are acually negaively relaed o he order sizes. In principle, his resul is consisen wih Osler e al. (006), who also found ha larger order sizes lead o narrower spreads for boh commercial and financial cusomers. 9 Specifically, he esimae of γ suggess ha if order size increase from $1 million o $ million, he spread given by he dealer decreases abou 1 pip for individual cusomers. 10 In conras, he dealer s iner-dealer quoes display a differen scenario. No maer wha insrumens or densiy marices are used, he parameers of order size ( γ ) are very close o zero in all esimaions. More imporanly, he corresponding -saisics of he coefficien (around -0.5) and boh he Likelihood Raio and Wald saisics (less han 0.3) are far below he criical value a a 5% significance level. This suggess ha order size does no significanly impac his dealer s inerdealer spreads in our sample. In regard o he impac of exchange rae volailiy shown in Panel A of Table 3, all ess in he esimaion fail o show ha coefficien γ 1 is saisically differen from zero in he cusomer marke. For iner-dealer spreads, he resuls are similar. As shown by Panel B of Table 3, boh GMM1 and GMM obain posiive resuls, bu he values of -saisics are around 1.4 and no large enough o sugges ha exchange rae volailiy affecs spreads significanly. The mos likely reason is ha he 9 Their daase does no conain quoes for individual cusomers. Also, heir regression divides all order sizes ino hree groups (small, medium and large) and uses a dummy variable o esimae he impac of order size on spread, so only a general comparison can be made. 10 The coefficien of order size is esimaed when spreads and order sizes are measured in a logarihmic forma. This needs o be aken ino accoun when esimaing he direc impac of order size on spread. 9

12 volailiy in my sample wasn volaile a all, considering ha only he consan iem was significan in he GARCH esimaion. Thus, including volailiy in he model is similar o feeding he model wih a consan number and some whie noise Discussion Looking back a he exising models surveyed in Secion, i seems ha only he processing cos model can explain he negaive relaionship beween order size and cusomer spread. In addiion, as suggesed by Osler e. al. (006), he negaive paern can also be suppored by anoher imporan spread deerminan in he FX marke sraegic dealing. Building on abundan evidence ha order flow carries informaion (e.g., Evans and Lyons 00), he paper argues ha raional FX dealers migh sraegically vary spreads o gain informaion ha hey can hen exploi in fuure rades. Thus, FX dealers effecively subsidize spreads o arac hose larger ransacions mos likely o carry useful informaion. On he oher hand, invenory risk and adverse selecion migh no be as significan as prediced by heories in his dealer s spread deerminaion. Invenory risk is associaed wih he dealer s unexpeced invenory change. When his dealer receives such a change, i can adjus is invenory and share he risk wih oher dealers hrough iner-dealer rading quickly and easily. Wih regard o asymmeric informaion, Bjønnes and Rime (005) sugges ha insead of order size, i is only he direcion of an order ha carries informaion, and his paper presens evidence consisen wih his alernaive hypohesis. Therefore, spreads could be unrelaed o order size even under adverse selecion eiher. Overall, he dominance of processing coss and sraegic rading over invenory risk and adverse selecion explains he negaive paern in he cusomer marke. Similarly, order size has lile impac on he dealer s iner-dealer spread probably because all hese impacs offse in he iner-dealer marke. Since he order sizes used o exrac boh he iner-dealer and cusomer quoes are idenical 10

13 a he same ime, he ransacion coss should no be he cause of reason ha causes he differences in he iner-dealer spread. Since spread and order size migh no be significan spread componens in our sample, he difference beween he wo markes mus be caused by sraegic rading. To be logically consisen, he effec of sraegic rading should indeed be greaer in he cusomer marke han in he iner-dealer marke. This claim seems consisen wih boh inuiion and realiy. In he FX marke, dealers firs obain informaion from cusomer order flow. This informaion hen spreads in he marke hrough iner-dealer rading. So, dealers have more incenive o reduce spread o arac large orders in he cusomer marke han in he iner-dealer marke. Therefore, he sraegic rading effec is likely sronger in he cusomer marke. 4. Conclusions This aricle empirically examines he relaionship beween order size and spread in he foreign exchange marke. Based on quoes from an individual FX dealer, spread appears o be independen of order size in he iner-dealer marke, while he wo are negaively correlaed in he cusomer marke. None of he curren models can explain his finding alone, so new models are needed o provide more convincing heoreical reasoning. As discussed in he previous secion, one possible direcion for fuure research would be he combinaion of all facors found o affec spread. Following his line of hinking, spread would be independen of order size in he iner-dealer marke probably because posiive and negaive facors offse, while he negaive paern in he cusomer marke could be due o he dominance of negaive facors over posiive ones. Alhough his paper focuses on he relaionship beween order size and spread in he foreign exchange marke, i also reveals addiional areas o be explored. Firs, his sudy focused on one individual dealer and one currency pair. Wheher he conclusions apply o oher dealers and oher 11

14 currencies deserves more research. Second, he daase used in his paper is no large. More daa need o be esed o verify wheher his aricle s finding is robus. Finally, revealing empirical facs is no difficul once daa are available. However, proposing a heory ha explains such a resul is more imporan. Alhough his paper proposes one possible soluion, more research needs o be compleed o build a saisfying heoreical model. 1

15 REFERENCES Admai AR, Pfleiderer P Selling and rading on informaion in financial markes. American Economic Review 78: Bageho W The only game in own. Financial Analyss Journal : Biais B Price formaion and equilibrium liquidiy in fragmened and cenralized markes. Journal of Finance 484: Bjønnes GH, Rime D Dealer behavior and rading sysems in foreign exchange markes. Journal of Financial Economics 75: Bollerslev T, Melvin M Bid-ask spreads and volailiy in he foreign exchange marke: an empirical analysis. Journal of Inernaional Economics 36: Cheung YW, Chinn MD, Marsh IW How do UK-based foreign exchange dealers hink heir marke operaes? Inernaional Journal of Finance and Economics 9: Demsez H The cos of ransacing. Quarerly Journal of Economics 8: Demos AA, Goodhar C The ineracion beween he frequency of marke quoaions, spread and volailiy in he foreign exchange markes. Applied Economics 8: Evans M, Lyons R. 00. Order flow and exchange-rae dynamics. Journal of Poliical Economy 110: Glosen LR, Milgrom PR Bid, ask, and ransacion prices in a specialis marke wih heerogeneously informed raders. Journal of Financial Economics 14: Harmann P Do Reuers spreads reflec currencies' differences in global rading aciviy? Journal of Inernaional Money and Finance 17: Harmann P Trading volumes and ransacion coss in he foreign exchange marke. Journal of Banking and Finance 3: Ho T, Soll H Opimal dealer pricing under ransacions and reurn uncerainy. Journal of Financial Economics 9: Huang DR, Masulis RW FX spread and dealer compeiion across he 4-Hour rading day. The Review of Financial Sudies 1: Kyle A Coninuous aucions and insider rading. Economerica 53: Lyons RK Tess of microsrucural hypoheses in he foreign exchange marke. Journal of 13

16 Financial Economics 39: Osler CL, Mende A, Menkhoff L Price Discovery in Currency Markes. Mimeo. Payne R Informed rade in spo foreign exchange markes: an empirical invesigaion. Journal of Inernaional Economics 61: Soll HR The supply of dealer services in securiies markes. Journal of Finance 33: Yao JM Marke making in he inerbank foreign exchange marke. Working paper S-98-3, Sern School of Business, New York Universiy. 14

17 Table 1: Descripive Saisics of he Daa This able gives descripive saisics of he daa. All quoes are exchange rae for USD/EUR Variable Number of observaions Mean Sd. Dev. Min Max Cusomer spreads Iner-dealer spreads Order sizes

18 Table : Exchange Rae Volailiy Esimaion This able gives he esimae of exchange rae volailiy for each day in he sample (weekends 7/10 and 7/11 are excluded). The volailiy is esimaed by a GARCH specificaion as below: 10,000 M σ ε M, M, = ϖ + αε I 1 = µ + θε M, 1 ~ N(0, σ M, M, 1 + βσ where M sands for he spo exchange rae and M is he change of spo exchange rae. I represens he informaion se, and µ, θ, ϖ, α, β are he parameers o be esimaed. The ime subscrip refers o he place in he order of he series of quoes, so ha ˆ σ provides an esimae of he exchange M, rae volailiy. Since he magniude of mid-quoe flucuaions is very small wihin he 1-minue window, he exchange rae change M is muliplied by 10,000 o enlarge he effecs of dependen variables so ha esimaed parameers will no be oo small. In his esimaion model, he observaion of he exchange rae is measured as he logarihm of he mid-quoe of bid-ask prices. Given ha a and b denoe he ask and bid prices respecively, M is compued by he following formula: a + b M = log( ) ) + ε M, 1 Sandard errors are repored in parenheses, and * denoes significance a he 5% level., M, dae µ θ ϖ α β 7/7/ (0.151) * (0.1058) (1.8100) (0.0371) (36.590) 7/8/ (0.138) * (0.137) (.5600) 0.05 (0.051) (6.700) 7/9/ (0.060) * (0.1548) (1.7851) (0.1007) (3.487) 7/1/ (0.043) * (0.0594) (10.490) (0.1108) (.874) 7/13/ (0.073) * (0.0930) (1.1844) (0.0985) (0.4101) 7/14/ (0.1048) * (0.0871) (1.5680) 0.01 (0.0405) (1.351) 7/15/ (0.4155) * (0.1890) ( ) (0.1353) (0.8961) 16

19 Table 3: Tes Resuls of Spreads and Order Sizes This able gives he esimaes for he regression model: S = + γ ˆ 0 1 σ + γ γ O + ε Here, σˆ represens he exchange rae volailiy obained from he GARCH esimaion. O is he order size associaed wih each spread, and S is eiher he cusomer or iner-dealer spread calculaed based on he following formula: S = log[( a b ) 10000] where a and b denoe original ask and bid quoes given by he dealer. ε is a sandard error iem. γ, γ γ are corresponding coefficiens of explanaory variables including a consan iem. The 0 1, regression model is esimaed by GMM. Three differen densiy marix esimaion mehods are applied: Whie, Newey-Wes (N-W) and Gallan. There are wo insrumen variables: he square of explanaory variables (GMM1) and a one period lag of explanaory variables (GMM). The - saisics of esimaes are repored in parenheses. LR sands for likelihood raio, and w is for he Wald es saisic. Panel A: Cusomer Spreads GMM1 GMM Coefficien: consan iem exchange rae volailiy order size LR w consan iem exchange rae volailiy order size LR w Whie (59.96) (0.50) (-.47) (16.1) (0.10) (-.7) N-W (41.44) (0.4) (-1.80) (1.85) (0.08) (-1.90) Gallan (41.9) (0.4) (-1.83) (1.75) (0.08) (-1.95) Panel B: Iner-Dealer Spreads GMM1 GMM Coefficien: consan iem exchange rae volailiy order size LR w consan iem exchange rae volailiy order size LR w Whie.7490 (10.8) (1.33) (-0.48) (65.85) (-1.07) (-0.60) N-W.7490 (101.4) (1.44) (-0.51) (61.61) (-1.69) (-0.63) Gallan.7490 (100.3) (1.45) (-0.50) (60.04) (-1.61) (-0.61)