PROFITS AND POSITION CONTROL: A WEEK OF FX DEALING Richard K. Lyon U.C. Berkeley and NBER Thi verion: June 1997 Abrac Thi paper examine foreign exchange rading a he dealer level. The dealer we rack average $100,000 in profi per day on volume of $1 billion per day (or one bai poin). The half-life of he dealer poiion i only en minue, providing rong uppor for invenory model. A mehodological innovaion allow u o idenify hi peculaive poiion over ime. Thi peculaive poiion deermine he hare of profi deriving from peculaion veru inermediaion: inermediaion i much more imporan. Forhcoming, Journal of Inernaional Money & Finance. Correpondence Profeor Richard K. Lyon Haa School of Buine, U.C. Berkeley Berkeley, CA 94720-1900 Tel: 510-642-1059, Fax: 510-642-4700 E-mail: lyon@haa.berkeley.edu * I hank he following for helpful commen: Jeff Bohn, Frank Diebold, Bernard Duma, Mark Flood, Dick Meee, Mark Ready, Andrew Roe, Parik Säfvenblad, Ma Spiegel, Avanidhar Subrahmanyam, and eminar paricipan a Berkeley, UCLA, he Federal Reerve Board, he Federal Reerve Bank of New York, he NBER, and he Sockholm School of Economic. I alo hank Jeff Bohn for valuable reearch aiance. Par of hi paper were wrien while viiing he IIES a Sockholm Univeriy and I hank hem for heir hopialiy. Financial aiance from he Naional Science Foundaion and he Berkeley Program in Finance i graefully acknowledged.
PROFITS AND POSITION CONTROL: A WEEK OF FX DEALING Empirical work on FX microrucure i ill in i early age. The earlie work ued fuure daa ince ha wa available a high frequencie. 1 In FX, however, he fuure marke i boh much maller han po and ighly linked o po hrough arbirage. Moreover, early daa e did no have ufficien granulariy o capure agen heerogeneiy, he hallmark of he microrucure approach. Work on he po marke ielf grew in he early 90 wih he availabiliy of quoe on an inraday bai (pecifically, he indicaive quoe from Reuer called FXFX). 2 Thee quoe provide a quie accurae picure of price dynamic. More imporan, hey alo peak o heerogeneiy iue ince he name and locaion of he quoing bank are alo included. A number of inereing queion could hu be addreed ha earlier daa did no permi. The FXFX daa did no, however, leave much room for direc eing of heory ince hey provide no direc meaure of quaniy (order flow) and quaniy role in deermining price i cenral o microrucure heory. A quaniy daa became available, more direc e became poible. 3 Thi paper exend earlier work by anwering a number of key quaniy-dependen queion. Anwering ome of hee i raher raighforward. For example, how profiable i dealing in FX? And how rapidly do FX dealer dipoe of riky invenory compared o, ay, NYSE equiy peciali? Oher queion are le raighforward, requiring ome mehodological progre. For example, wha hare of dealer profi come from peculaion veru inermediaion? To anwer hi, one need a mehod for meauring dealer peculaion over ime. Thi paper inroduce a mehod for doing hi. Our anwer o he more raighforward queion are riking. Fir conider dealer profi: he dealer we rack average $100,000 profi per day (on volume of $1 billion per day). By comparion, equiy dealer average abou $10,000 profi per day (on volume of roughly $10 1 See for example Grammaiko and Saunder (1986). 2 See Goodhar and Figliuoli (1991) and Bollerlev and Domowiz (1993), among many oher. A he daily frequency, early work include Glaman (1987) and Boaer and Hillion (1991). 3 See Lyon (1995), Goodhar, Io, and Payne (1996), and Yao (1996). For an emerging experimenal lieraure ee Flood e al. (1996). For work on informaion nework embedded in FX rading echnologie ee Zaheer and Zaheer (1995). 1
million per day). 4 Nex, conider he pace of invenory managemen: he half-life for he dealer we rack i only 10 minue. Thi i remarkably hor relaive o half-live for equiy peciali of one week [Madhavan and Smid (1993)]. Invenory heory i clearly eenial o underanding rading in hi marke. Though riking, hee reul alo preen a challenge: Why do equiy and FX marke look o differen in hee dimenion? Tha i a iue hi paper raie, bu doe no reolve. A aed above, addreing ome of he le raighforward queion e.g., he hare of profi from peculaion require ome mehodological progre. For perpecive we urn o he relevan heory. Noe ha microrucure heory i compoed of wo diinc branche. The earlier branch of invenory model began in he 1970. 5 The laer branch of informaion model developed in he 1980. 6 Underlying aumpion kep hee branche diinc: invenory model include no informaion aymmerie, and informaion model include no invenory co (e.g., no rik averion). Conequenly, a dealer poiion in invenory model i purely nonpeculaive, while in informaion model i i purely peculaive. In he daa, of coure, poiion include boh peculaive and nonpeculaive componen. Dienangling hem i an imporan ep for empirical work ince heory i clear ha he repecive driving force are differen. The mehodological progre we make here i our mean of dienangling peculaive and nonpeculaive poiion. We are cerainly no he fir o effec hi decompoiion. The difference i ha our approach draw from economic raher han being purely aiical [ee Madhavan and Smid (1993) and Habrouck and Sofiano (1993)]. Specifically, our mehod idenifie he dealer peculaive poiion by projecing hi oal poiion on an informaion e, one ha conain non-public informaion ueful for peculaion. A econd, crucial ingredien i ha hi informaion e i eleced uch ha i conen are orhogonal o he dealer nonpeculaive poiion. Thi inrumenal-variable approach provide he idenificaion we need. In general, he informaion driving peculaive poiion come from wo key ource: incoming order and incoming quoe. To drive peculaion, i i imporan ha hi informaion no be public informaion, which i i no in hi cae: quaniy and price informaion from FX 4 We ue he number from Hanch e al. (1994) for he London Sock Exchange becaue, unlike he NYSE, hi i a pure dealerhip marke and herefore more comparable o FX. They find dealer average a profi of roughly 10 bai poin on each ranacion. Though he auhor do no provide an average urnover by dealer, hey do provide daa ha allow a rough eimae. The average daily urnover for FTSE-100 ock i abou $10 million ( 6.9 million). Thi oal urnover i divided among dealer, bu acive dealer make marke in many ock. Given he marke hare he auhor repor for he more acive dealer, and given he number of ock in which each make marke, he eimaed average urnover of $10 million per dealer i abou righ. 5 See Garman (1976), Amihud and Mendelon (1980), Ho and Soll (1983), and O'Hara and Oldfield (1986), among oher. 6 See Copeland and Galai (1983), Kyle (1985), Gloen and Milgrom (1985), and Admai and Pfleiderer (1988), among oher. 2
dealer rade are no available o he marke a large. [For more on hi ee Lyon (1996).] The fir of hee wo ource, incoming order, i he andard ource of dealer informaion in informaion model. The econd ource, incoming quoe, i a pecial feaure of muliple-dealer marke [ee Leach and Madhavan (1993)]. 7 In fac, our poiion decompoiion would no be poible wihou hi feaure: in ingle-dealer model here i ypically a ingle deerminan of boh peculaive and nonpeculaive poiion namely order flow and a ingle deerminan canno erve a an inrumen for dienangling hee wo poiion componen; wih mulipledealer, however, incoming quoe provide a econd deerminan of peculaive poiion, one ha may be uncorrelaed wih non-peculaive poiion, and can herefore erve a an inrumen. Performing he decompoiion allow u o pin down he degree o which profi i due o inermediaion (i.e., he pread) veru peculaive gain. We find ha inermediaion, a lea for he dealer we rack, i much more imporan, accouning for roughly 90 percen of hi profi. To hi we hould add, however, ha our dealer i decribed by hi peer a a liquidiy machine, by which hey mean ha hi yle focue on high volume a compeiive price. In addiion, more ha 90 percen of our dealer rading i wih oher dealer (a oppoed o non-dealer cuomer), wherea he average inerdealer hare i cloer o 80 percen. Thu, in erm of he ource of hi profi, our dealer hould no be viewed a repreenaive of all dealer in hi marke. 8 Though many empirical paper addre dealer behavior, wo are epecially relevan here due o heir focu on quaniy daa. Each examine implicaion of microrucure model uing daa on equiy peciali invenorie. Madhavan and Smid (1993) ue heir invenory daa o e wheher invenorie rever oward a arge (a prediced by he heory). Their model of he arge o which invenory rever i aiical, baed on yemaic paern in reidual. They find ha allowing he arge o vary inenifie mean reverion. Neverhele, he hore half-life hey eimae i one week. Habrouck and Sofiano (1993) alo focu on he invenory erie ielf. And heir model of arge invenory i alo aiical, in hi cae driven by invenory imeerie properie. 9 Like Madhavan and Smid (1993), hey find allowing he arge o vary help accoun for earlier finding ha invenory conrol i weak. Before proceeding we wan o clarify our erm, in paricular our ue of poiion 7 I could be argued ha limi order play a imilar role wihin peciali marke. 8 See, for example, Yao (1996), who chronicle he rading of a commercial bank dealer who receive much more cuomer order flow han our dealer. 9 The hree ime-erie properie of invenory highlighed by Habrouck and Sofiano (1993) are hor-erm variaion, dicree long-erm variaion, and mooh long-erm variaion (page 1570). Their view i ha he hor-erm variaion reflec claic dealer behavior (nonpeculaion) wherea long-erm variaion of boh ype reflec invemen holding (peculaion). The poiion erie for an FX dealer diplay only hor-erm variaion by heir andard ince in general he daily cloing poiion i zero. Thu, by heir logic our poiion erie mu be devoid of any peculaive componen. Our dicuion wih FX dealer convince u oherwie. 3
conrol. Here poiion conrol refer o managemen of boh peculaive and nonpeculaive poiion. The more radiional erm invenory conrol i narrower, referring only o managemen of nonpeculaive poiion. Since hi paper cope pan boh, we adop a more flexible erminology. The paper i organized a follow: The nex ecion ouline our mehod for dienangling peculaive and nonpeculaive poiion; Secion II decribe he daa; Secion III dienangle he poiion componen and eimae dealer profi; Secion IV conclude. 4
I. Decompoing Speculaive and Nonpeculaive Poiion Componen I.A. Linking Targe Poiion o Informaion Conider he equaion ued by Madhavan and Smid (1993) o eimae mean reverion in dealer poiion (our appendix keche he opimizing model underlying i): (1) I + I ( I I ) = β + ε 1 + 1 where I i he dealer' oal poiion, and I i he dealer' arge poiion, boh a ime. The poiion diurbance ε +1 i realized a +1 and i uncorrelaed wih I - I (a propery deriving from he aumpion ha quoe are regre-free in he ene of Gloen and Milgrom (1985)). The difficuly in eimaing β come from he unobervabiliy of I. Since mo model pecify order flow a he only ource of variaion in boh I and I, i i impoible o idenify I on he bai of order flow alone, hence he pa reliance on aiical model of I. We need o be precie abou he erm arge poiion. The dealer' arge poiion can be decompoed ino a peculaive demand componen I and a nonpeculaive componen I n. (2) I = I + I n n For an FX dealer, i i reaonable o preume ha I equal zero. In paricular, i i unclear why a non-zero nonpeculaive poiion would aid a major-marke FX dealer in he proviion of immediacy (e.g., an FX dealer doe no worry abou ock-ou a he migh in a le liquid marke). Alo upporive i he fac ha FX dealer generally cloe each day wih a poiion of zero n (unlike NYSE peciali). Under he aumpion ha I equal zero, we can herefore wrie: (3) I I ( I I ) = β + ε + 1 + 1 Noe ha we are no auming he nonpeculaive componen of oal poiion I i zero, only ha he nonpeculaive componen of he arge poiion i zero. Accordingly, we decompoe he oal poiion a any ime ino peculaive and nonpeculaive componen: 5
(4) I = I + I n where I n denoe he ime nonpeculaive componen. The peculaive componen i he dealer' peculaive demand which we model in he uual way [ee O Hara (1995), page 156-158)]. The demand for he riky ae in a compeiive wo-ae economy, one rikle and one riky, wih uiliy defined over end-of-period wealh i: (5) I = θe[ P+ 1 P Ω ] where P i he price of he riky ae (FX) a ime, Ω i he dealer' informaion e a ime, and θ i a conan. The conan θ depend on he coefficien of abolue rik averion and he condiional variance of he riky ae price. For now, we aume a conan condiional variance, hough we reurn o hi iue below. I.B.. Conien Eimaion of β The uual difficuly in exracing I from I i due o he correlaion beween I and I n. To ee hi, conider he canonical peciali who draw inference abou he riky ae' value from he incoming order flow. In hi conex, incoming order flow i driving boh I n and I, he laer due o order flow informaion conen. Conequenly, order flow alone i inufficien for dienangling hee wo componen of I. Inrumen are needed for I : variable correlaed wih I bu uncorrelaed wih I n. A richer pecificaion of Ω provide he needed inrumen. Pariion Ω ino hree componen: (i) a e of public ignal Ω P, (ii) a e of non-public ignal correlaed wih I n, or Ω N, and (iii) a e of non-public ignal orhogonal o I n, or Ω N : P N N (6) Ω = { Ω, Ω, Ω } The lea-quare projecion of I on Ω N i hu purged of any correlaion wih invenory change due o I n. Le $ I denoe hi projecion. We can hen conienly eimae he half-life of he nonpeculaive poiion componen from: 6
(7) I I β( I I$ ) = + ε + 1 + 1 ince $ I i by conrucion orhogonal o ε +1. Thi i he mean reverion we aociae wih invenory conrol in he claic model. I.C. A Conien Covariance Marix of $ β Though an OLS eimae of from Eq. (7) i conien, he OLS andard error are incorrec. To ee hi, define he projecion error of $ I a η. (8) I $ I = +η If we denoe he variance of he diurbance from Eq. (3) a σ ε 2, hen he variance of he diurbance in Eq. (7) i σ + β σ. The probabiliy limi of he OLS eimae of he reidual 2 2 2 ε η covariance marix from Eq. (7) i σ 2 ε, which clearly underae he aympoic andard error. Pagan (1984) how ha Two-Sage Lea Square (2SLS) produce a conien eimaor of he variance of $ β. Thi i he eimaor we ue o calculae andard error for eimae of Eq. (7). II. Daa The daae i an augmened verion of ha ued in Lyon (1995), he principal addiion being he non-deal quoe we ue o idenify he dealer peculaive poiion. Here we provide a broad overview, wih deail only where neceary o augmen ha in Lyon (1995). The daae coni of wo linked par, each covering he aciviy of a DM/$ dealer a a major New York bank. The ample pan he five rading day of he week Augu 3-7, 1992. Each of he five rading day begin a 8:30 A.M. and end on average a 1:30 P.M., Eaern Sandard Time. The fir par comprie he dealer' poiion card. Hi poiion card include all hi rade, wih ranacion quaniie and price. The econd par i narrower bu deeper: narrower becaue i conain only a ube of hi rade, hi direc (meaning non-brokered) iner- 7
dealer rade; deeper becaue i conain all hi direc quoe, irrepecive of wheher deal. Figure 1 provide a diagram of he daa flow hrough ime. II.A. Dealer Daa: Poiion Card Becaue he poiion card include all of he dealer' ranacion, hey are ufficien for conrucing he dealer' poiion I hrough ime. An average day coni of approximaely 20 card, each wih abou 15 ranacion enrie. Each card include he following informaion for every rade: (1) he igned quaniy raded (which deermine I ) (2) he ranacion price (3) he counerpary, including wheher brokered. Noe ha he bid/ak quoe a he ime of he ranacion are no included on he poiion hee. Noe alo ha each enry i no ime-amped, hough he dealer doe record he ime a he oue of every card (o he minue), and occaionally wihin he card oo. Thi par of he daae include 1720 ranacion amouning o $7.0 billion. Figure 2 provide a diagram of he poiion hee' rucure. The only dimenion of an acual poiion hee ha i no in he diagram i he name of he counerparie. Counerpary name are conidered highly confidenial o hi dealer' iniuion. II.B. Dealer Daa: Direc Quoe and Trade The econd par of he daae include he quoe, ranacion quaniie, and ranacion price for all he non-brokered inerdealer ineracion. Thee daa derive from bank dealing record from he Reuer Dealing 2000-1 yem. Thi yem i differen from he yem ha produce he Reuer FXFX indicaion ued elewhere in he lieraure [ee, for example, Goodhar and Figliuoli (1991)]. I allow dealer o communicae quoe and rade bilaerally via compuer raher han verbally over he elephone. Thi dealer ue Dealing 2000-1 for more han 99% of hi non-brokered inerdealer rade. 8
Each record from he Dealing 2000-1 yem include he fir 5 of he following 7 variable. The la wo are included only if a rade ake place. (1) The ime he communicaion i iniiaed (o he minue, wih no lag) (2) which of he wo dealer i requeing he quoe (3) he quoe quaniy (4) he bid quoe (5) he ak quoe (6) he quaniy raded (7) he ranacion price. Thi par of he daae include 952 ranacion amouning o $4.1 billion. Though i doe no include he dealer' brokered ranacion, i ha wo key advanage over he daa from he poiion card: i provide quoe raher han ju ranacion price and i idenifie which counerpary i he aggreor. I alo provide a mean of error-checking he daa from he poiion card. Perhap mo imporan for our purpoe, hi par of he daae provide he incoming quoe ha did no generae a rade. We ue hee non-deal quoe o idenify he dealer peculaive poiion. Over our ample week, only 5 percen of incoming quoe generaed a rade. (In conra, 34 percen of ougoing quoe generaed a rade, an indicaion ha our dealer i no he average dealer in hi repec.) II.C. The Reuling Poiion Serie Figure 3 provide a plo of he dealer' poiion over he ample' five rading day. Mean reverion i eviden. Noe oo he range of he poiion: rarely did open poiion rie above $40 million ($40 million i well below he inraday poiion limi impoed on enior dealer a major bank, ypically in he $100-$150 million range). Each of he five day he dealer cloed hi rading day wih a poiion of zero. (A common overnigh limi i abou $75 million; mo dealer, however, cloe heir day a zero. Two common raionale for cloing a zero are ha (1) carrying an open poiion require monioring i hrough he evening and (2) a dealer compara- 9
ive advanage in peculaion i when he i eaed a her dek oberving order flow and quoe.) The relaive widh of he day i a reflecion of he relaive rading aciviy. Monday and Friday are he highe volume day. III. Reul: Profi and Poiion Componen III.A. Dealer Profi A ummary of he dealer' profiabiliy over he week appear in Table 1. Noe ha he daily volume i well over $1 billion each day. Profi for he week oal $507,929, Friday being he mo profiable day. Friday i alo he highe volume day. Of coure, if profi derive primarily from peculaive poiion, hen volailiy i more imporan han volume. Friday alo ha he highe volailiy in he five-day ample. We urn now o he queion of wheher profi end o come from inermediaion or peculaion. A a fir ep, we impue he inermediaion componen of profi uing an aumpion ha he dealer himelf fel i reaonable. Specifically, we aume ha he co of laying off an incoming order i one-hird of he dealer bid-ak pread. For example, if he dealer quoe hi median pread of hree pip a DM 1.4750/$ - DM 1.4753/$ and he incoming order i a purchae of dollar a DM 1.4753/$, hen on average he dealer mu provide price improvemen on he bid ide of DM 1.4751 o induce an offeing cuomer ale. Thi ranlae ino an average profi of one pip on every ranacion. The reul appear in he Profi: Spread column of Table 1. The profi impued o inermediaion correpond quie cloely o oal profi: he wo differ by le han 10 percen. Given he dealer himelf feel he aumpion driving hi comparion i reaonable, inermediaion appear o be a much more imporan ource of profi. Sill, o ge a more complee picure, we need o examine wheher hi peculaive poiion are profiable. III.B. Poiion Decompoiion Per ecion I, dienangling he peculaive and nonpeculaive poiion componen require inrumen ha are correlaed wih he peculaive componen bu uncorrelaed wih he nonpeculaive componen. The inrumen e we conider rely excluively on non-deal, 10
incoming quoe (pecifically, lagged change). 10 Thee quoe are no public informaion, o hey are arguably relevan for peculaive poiion aking. On he oher hand, hey are do no produce a ranacion, o here i no direc relaion o he nonpeculaive componen of our dealer poiion. Of coure, no direc relaion doe no rule ou an indirec relaion. One raionale for ruling ou even an indirec relaion i embedded in he model of Lyon (1997). In ha model, pa price change i orhogonal o nonpeculaive poiion becaue dealer being rik avere e price o avoid nonpeculaive poiion; hough nonpeculaive poiion ill arie, opimal ue of pa informaion bring he correlaion wih price o zero. Neverhele, incoming quoe change canno idenify he peculaive componen I if hey are uncorrelaed wih he dealer' oal poiion. Column wo of able 2 (row 2-4) verifie ha hee inrumen are indeed correlaed wih I. 11 The R 2 ' indicae ha $ I, which i he projecion of I on he informaion e Ω, accoun for abou one-quarer of he variaion in he dealer' oal poiion. Pu differenly, Ω conain informaion ueful o he dealer in deermining hi peculaive demand. The fir row of he able i included a a benchmark. Wih an empy informaion e, i i equivalen o auming ha arge poiion $ I equal zero. (Hence, here i no fir age projecion, and he R 2 i no applicable.) Table 2 alo preen eimae of he half-life of nonpeculaive poiion. 12 A half-life of en minue i exremely hor relaive o he poiion half-live eimaed in equiy marke; for example, he lowe eimae for equiy peciali in Madhavan and Smid (1993) i 7 day. Our finding of en minue i clear evidence of aggreive invenory conrol. Of coure, he FX marke i no he NYSE. Why hey rade o differenly, however, i ill an open queion. Reul like hi reinforce he fac ha he FX marke i diincive a he microrucural level. 10 In our daa e, ypically incoming quoe do no elici a ranacion: more han 80 percen of incoming quoe lape wihou a deal. Thi large hare of non-deal quoe ugge ha dealer gaher quoe becaue hey are informaive, no imply becaue hey provide immediacy. For lack of daa, previou work ha had o idenify no-rade even a he elaping of a given amoun of ime wihou a ranacion [e.g., five minue in Ealey, Kiefer, and O Hara (1997)]. An imporan rengh of our daa e i ha i include non-deal even explicily. 11 The la of he hree informaion e row 4 of Table 2 include a quared lagged price change in addiion o he igned lagged price change. Though hi can only improve he fir-age fi, he orhogonaliy of hi variable i more difficul o defend on heoreical ground. 12 Noe ha hee regreion are eimaed in ranacion ime raher han real ime. For a dicuion of hi iue in he conex of he FX marke ee Lyon (1995), page 345-346. 11
III.C. Regreion Diagnoic Some regreion diagnoic are in order. Fir, here i no evidence of erial correlaion (Durbin-Waon and Ljung-Box Q e) or heerokedaiciy (Whie e). A naural nex ep i o examine rucural abiliy, in paricular, wih repec o ime-of-day. To do o, we pli he ample ino wo ubample, early and lae, where early i defined a all obervaion occurring before he midpoin of he rading day (median ranacion ime). A Wald e of he equaliy of $β acro he wo ubample i rejeced a he one percen level. Clearly, ime-of-day i relaed o invenory conrol, which i no urpriing given he dealer ar and end each day wih a zero ne poiion. To capure hi ime-of-day effec, we include an addiional erm in he model of Eq. (1): 13 (9) I I ( I I$ ) (% Day)( I I$ ) = β + β + ε + 1 1 2 + 1 where he proxy %Day i defined over each day a (obervaion #, day n) divided by (oal # obervaion, day n), wih n=1,...,5. 14 The reul appear in Table 3. Noe ha he imeindependen componen of mean reverion i inignificanly differen from zero ( $ β 1 ). In conra, he ime-dependen componen, $ β 2, now doe all he work. The eimae imply ha he imedependen componen of mean reverion move from zero a he ar of each day o abou -0.3 a he end. The implied half-live a hree poin wihin he dealer' day appear in he la column. On he whole, hi ime profile quare nicely wih he fac ha FX dealer ypically cloe heir poiion a he end of each rading day. Anoher imporan conideraion i he impac of price volailiy on he pace of mean reverion. I i no a priori clear, however, how volailiy hould affec mean reverion. On one hand, he higher volailiy, he greaer he benefi of invenory conrol. On he oher hand, he higher volailiy, he greaer he co of invenory conrol (pread a broker widen, a do direc pread quoed by oher dealer; for ome evidence from indicaive quoe, ee Beembinder 13 Noe ha while Eq. (1) i derived from an opimizing model, he ame canno be aid of our adjumen o i. The echnical challenge of doing o i formidable, and he payoff, in our judgmen, marginal. 14 We refer o hi a a proxy becaue he denominaor oal ranacion for he day i no known o he dealer in advance. 12
(1994) and Bollerlev and Melvin (1994)). To capure hi, we eimae he following linear model: (10) I I (% Day )( I I$ ) ( HighVol)( % Day)( I I$ ) = β + β + ε + 1 1 2 + 1 2 where he dummy variable HighVol i equal o one if ( P 1 ) i above i median, zero oherwie. The fir regreor i he ame a he econd regreor in he model of Eq. (9) (recall ha he fir regreor in Eq. (9) produced an inignifican coefficien). The reul appear in Table 4. The coefficien $ β 2 i ignifican a he five percen level bu no a one percen. The ize and ign of $ β 2 imply ha mean reverion i lower when volailiy i high. Thi ugge ha when volailiy increae, he added co of invenory conrol dominae he added benefi. The implied half-live a high and low volailiy appear in he la column (calculaed a %Day=50%). The half-life i abou wice a long wih high volailiy han wih low volailiy. III.D. Profi From Speculaive Componen Though ecion III.A. provide eimae of profi from inermediaion, our meaure of he dealer peculaive poiion allow u o eimae peculaive profi direcly. We proceed in wo age. Fir, we deermine wheher he dealer peculaive poiion foreca fuure price change. In paricular, we e wheher peculaive poiion Granger caue price change. Though no a ufficien condiion for profiable peculaion, he reul provide ueful perpecive. Then, in age wo, we mark he peculaive poiion o marke uing he midpoin of he incoming quoe cloe o he meaured peculaive poiion change. The accumulaed change in ne value provide an eimae of peculaive profi. (Unlike our exac meaure of oal profi in Table 1, i i no poible o calculae peculaive profi exacly ince our meaured change in peculaive poiion are no linked one-for-one wih marke ranacion.) On boh coun, our reul do no evince peculaive profi. We find no evidence of Granger caualiy running from peculaive poiion o price. Furher, even uing quoe midpoin, he peculaive poiion doe no generae profi; in fac, over he week he dealer uffered negligible loe on he peculaive poiion. I i imporan o keep in mind, however, 13
ha we are working wih only one week of daa, which may no be repreenaive wih repec o peculaive profi. To be ure, peculaive profi are much more volaile han profi from inermediaion. IV. Concluion We are able o addre a number of queion ha have no ye been examined in empirical work on FX microrucure. And our anwer o hee queion are riking. Fir he dealer we rack i quie profiable: he average $100,000 profi per day (on volume of $1 billion per day). By comparion, equiy dealer average abou $10,000 profi per day (on volume of roughly $10 million per day). Second, we alo find quie rapid invenory managemen: he half-life for he dealer we rack i only 10 minue. Thi i remarkably hor compared o half-live for equiy peciali of one week. Why do equiy and FX marke generae uch differen reul a he microrucural level? Thi i an imporan opic for fuure reearch. The paper alo make mehodological progre. Specifically, we develop a mehod for meauring peculaive poiion-aking over ime. Unlike pa purely aiical mehod for doing hi, our meaure i baed on he informaion flow ha drive peculaion. We ue hi meaure of peculaive poiion o pin down he exen o which dealer profi derive from peculaion. In he end we find ha inermediaion i much more imporan ource of profi, a lea for he dealer we rack over he week we are able o rack him. 14
Appendix Skech of Madhavan and Smid (1993) Derivaion of Eq. (1) Agen: (1) Rik neural informed rader (2) Liquidiy rader (3) Rik neural dealer, wih invenory carrying co (proporional o he variance of wealh) Preference: Marke: The dealer and informed rader maximize he expeced value of erminal wealh. Liquidiy rader preference are no modeled (heir rading can be generaed a opimizing in he conex of endowmen hock). There i a ingle riky ae ha rade in a erie of aucion. There i a conan probabiliy (1-ρ) ha a given ime τ will be he liquidaion ime. The ae' fundamenal value follow a random walk. Thi value i known by he informed rader. Noaion: ν : fundamenal value a ime µ : dealer' condiional expecaion of ν Ω : dealer' informaion e W : dealer' wealh I : dealer' poiion : price P z Q X D : exce demand, a funcion of P : demand of informed rader, a funcion of P : demand of liquidiy rader (aggregae), no a funcion of P : inercep of demand chedule, informed plu uninformed The informed rader' demand i proporional o he gap beween fundamenal value and price. (A1) Q ( v, P) = δ ( v P) I i helpful o define he inercep of he exce demand chedule a he following: (A2) D = δ v + X When divided by δ, hi variable D provide an unbiaed ignal of he fundamenal value ν (ince X i mean zero). (A3) D δ = v + X δ Now, he updaing equaion can be expreed a a weighed average of hi ignal and he dealer' prior expecaion. 15
(A4) ( D ) ( ) 1 1 µ = φ δ + φ µ Thi evoluion of he dealer' expecaion can hen be inegraed wih he dealer' ochaic programming problem. Max EW j= (A5) [ j Ω j] Pr[ τ ] P j= 1 The oluion o hi ochaic programming problem yield Eq. (1) in he ex: (1) I + I ( I I ) = β + ε 1 + 1 where he error erm in he regreion correpond o he dealer' eimae of liquidiy-rader demand X in he model: 1+ β (A6) ε + 1 ( 2 ) E[ X Ω ] 16
Reference Admai, A. and Pfleiderer, P. (1988) A heory of inraday paern: Volume and price variabiliy. Review of Financial Sudie 1, 3-40. Amihud, Y. and Mendelon, H. (1980) Dealerhip marke: Marke making wih invenory. Journal of Financial Economic 8, 31-53. Ammer, J. and Brunner, A. (1994) Are bank marke imer or marke maker? Explaining foreign exchange rading profi. Inernaional Finance Dicuion Paper #484, Board of Governor of he Federal Reerve Syem. Beembinder, H. (1994) Bid-ak pread in he inerbank foreign exchange marke. Journal of Financial Economic 35, 317-348. Bollerlev, T. and Domowiz, I. (1993) Trading paern and price in he inerbank foreign exchange marke. Journal of Finance 48, 1421-1444. Bollerlev, T. and Melvin, M. (1994) Bid-ak pread and volailiy in he foreign exchange marke: An empirical analyi. Journal of Inernaional Economic 36, 355-372. Boaer, P. and Hillion, P. (1991) Marke microrucure effec of governmen inervenion in he foreign exchange marke. Review of Financial Sudie 4, 513-541. Copeland, T. and Galai, D. (1983) Informaion effec on he bid-ak pread. Journal of Finance 38, 1457-1469. Ealey, D., Kiefer, N. and O'Hara, M. (1997) One day in he life of a very common ock. Review of Financial Sudie, forhcoming. Flood, M. (1992) Marke rucure and inefficiency in he foreign exchange marke. Journal of Inernaional Money and Finance 13, 131-158. Flood, M., Huiman, R., Koedijk, K. and Mahieu, R. (1996) Price dicovery in muliple-dealer financial marke: The effec of pre-rade ranparency. Concordia Univeriy ypecrip, December Garman, M. (1976) Marke microrucure. Journal of Financial Economic 3, 257-275. Glaman, D. (1987) Exchange rae rik and ranacion co: Evidence from bid-ak pread. Journal of Inernaional Money and Finance 6, 479-490. Gloen, L. and Milgrom, P. (1985) Bid, ak, and ranacion price in a peciali marke wih heerogeneouly informed agen. Journal of Financial Economic 14, 71-100. Goodhar, C. and Figliuoli, L. (1991) Every minue coun in financial marke. Journal of Inernaional Money and Finance 10, 23-52. 17
Goodhar, C., Io, T. and Payne, R. (1996) One day in June 1993: A udy of he working of he Reuer 2000-2 elecronic foreign exchange rading yem. In The Microrucure of Foreign Exchange Marke, ed. J. Frankel, G. Galli and A. Giovannini, pp. 107-179. Univeriy of Chicago Pre, Chicago, IL. Grammaiko, T. and Saunder, A. (1986) Fuure price variabiliy: A e of mauriy and volume effec. Journal of Buine 59, 319-330. Hanch, O., Naik, N. and Viwanahan, S. (1994) Trading profi, invenory conrol and marke hare in a compeiive dealer marke. Duke Univeriy ypecrip, November. Habrouck, J. (1988) Trade, quoe, invenorie, and informaion. Journal of Financial Economic 22, 229-252. Habrouck, J. and Sofiano, G. (1993) The rade of marke maker: An empirical analyi of NYSE peciali. Journal of Finance 48, 1565-1593. Ho, T. and Soll, H. (1983) The dynamic of dealer marke under compeiion. Journal of Finance 38, 1053-1074. Kyle, P. (1985) Coninuou aucion and inider rading. Economerica 53, 1315-1335. Leach, J. and Madhavan, A. (1993) Price experimenaion and ecuriy marke rucure. Review of Financial Sudie 6, 375-404. Lyon, R. (1995) Te of microrucural hypohee in he foreign exchange marke. Journal of Financial Economic 39, 321-351. Lyon, R. (1996) Opimal ranparency in a dealer marke wih an applicaion o foreign exchange. Journal of Financial Inermediaion 5, 225-254. Lyon, R. (1997) A imulaneou rade model of he foreign exchange ho poao. Journal of Inernaional Economic 42, 275-298. Madhavan, A. and Smid, S. (1991) A bayeian model of inraday peciali pricing. Journal of Financial Economic 30, 99-134. Madhavan, A. and Smid, S. (1993) An analyi of change in peciali invenorie and quoaion. Journal of Finance 48, 1595-1628. O'Hara, M. (1995) Marke Microrucure Theory. Blackwell Buine, Cambridge MA. O'Hara, M. and Oldfield, G. (1986) The microeconomic of marke making. Journal of Financial and Quaniaive Analyi 21, 361-376. Pagan, A. (1984) Economeric iue in he analyi of regreion wih generaed regreor. Inernaional Economic Review 25, 221-247. Yao, J. (1996) Marke making in he inerbank foreign exchange marke, New York Univeriy ypecrip, December. 18
Zaheer, A. and Zaheer, S. (1995) Caching he wave: Alerne, reponivene, and marke influence in global elecronic nework. Univeriy of Minneoa ypecrip, December. 19
Table 1 Summary of DM/$ dealer' rading and profi from Monday, Augu 3 o Friday, Augu 7, 1992. The $ Profi: Spread column repor he profi he dealer would have realized if he had cleared one-hird of hi pread on every ranacion. I i calculaed a he dollar volume ime one-hird he median pread he quoed in he ample (median pread = DM 0.0003/$), divided by he average DM/$ rae over he ample (DM 1.475/$). Tranacion Volume (mil) Profi: Acual Profi: Spread Monday 333 $ 1,403 $ 124,253 $ 95,101 Tueday 301 $ 1,105 $ 39,273 $ 74,933 Wedneday 300 $ 1,157 $ 78,575 $ 78,447 Thurday 328 $ 1,338 $ 67,316 $ 90,717 Friday 458 $ 1,966 $ 198,512 $ 133,298 Toal 1,720 $ 6,969 $ 507,929 $ 472,496 20
Table 2 Mean Reverion in Dealer Poiion ( $ ) I I = β I I + ε + 1 + 1 Definiion: I +1 i he dealer' poiion following he incoming rade a ime +1, where each incoming rade in he ample define a ingle period (i.e., ranacion ime). I $ i an eimae of he dealer' peculaive poiion a ime, defined a a projecion on an informaion e Ω. The informaion e we conider appear in column one. P,5 i he cumulaive change in he nondeal quoe received by he dealer over he period panning five incoming rade prior o he incoming rade a. Noe ha he fir of he informaion e implie I $ =0. The error erm ε +1 repreen diurbance o he dealer' poiion from he proviion of immediacy. Eimaion: Fir, we eimae I $ a he OLS projecion of I on Ω. Then, we ue I $ o eimae β from he above equaion uing OLS. Column wo preen he R 2 ' from he projecion of I on Ω. In row 2-4, he -aiic in parenhee are calculaed from 2SLS andard error o accoun for he ue of a generaed regreor. The implied half-life i calculaed a he mean inerranacion ime (1.8 minue) ime he half-life in ranacion implied by $ β [defined a -ln(2)/ln(1+ $ β )]. Sample: 838 obervaion from Monday, Augu 3 o Friday, Augu 7, 1992. Informaion e R 2 of projecion $ β Implied half-life Ω= {} N.A. -0.10 (-5.63) { } Ω = P 0.24-0.12,5 (-5.73) { P,, P, } Ω = 0.26-0.12 5 5 5 (-5.64) { P, 5, P 5, 5,( P, 5) } Ω = 2 0.29-0.13 (-5.97) 12 minue 10 minue 10 minue 9 minue 21
Table 3 Time-Dependen Mean Reverion in Dealer Poiion ( $ ) (% )( $ ) I I = β I I + β Day I I + ε + 1 1 2 + 1 Definiion: I +1 i he dealer' poiion following he incoming rade a ime +1, where each incoming rade in he ample define a ingle period (i.e., ranacion ime). I $ i an eimae of he dealer' peculaive poiion a ime, defined a a projecion on an informaion e Ω. The informaion e we conider appear in column one. P,5 i he cumulaive change in he nondeal quoe received by he dealer over he period panning five incoming rade prior o he incoming rade a. The variable %Day i defined over each day a (obervaion #, day n)/(oal # obervaion, day n), n=1,...,5. The error erm ε +1 repreen diurbance o he dealer' poiion from he proviion of immediacy. Eimaion: Fir, we eimae I $ a he OLS projecion of I on Ω. Then, we ue I $ o eimae β from he above equaion uing OLS. The -aiic in parenhee are calculaed from 2SLS andard error o accoun for he ue of a generaed regreor. The hree half-life column repor he implied half-life when he dealer' day (%Day) i 25% done, 50% done, and 75% done. The implied half-life i calculaed a he mean inerranacion ime (1.8 minue), ime he half-life in ranacion implied by $ β 2 [defined a -ln(2)/ln(1+ $ β 2 )], ime %Day. Sample: 838 obervaion from Monday, Augu 3 o Friday, Augu 7, 1992. Implied half-life Informaion e $ β 1 $ β 2 25% 50% 75% { } Ω = P 0.02,5 (0.29) { P,, P, } Ω = 0.03 5 5 5 (0.46) -0.30 (-3.06) -0.32 (-3.13) 16 8 5 minue 16 7 5 minue 22
Table 4 The Impac of Volailiy on Time-Dependen Mean Reverion in Dealer Poiion (% )( $ ) ( )( % )( $ ) I I = β Day I I + β HighVol Day I I + ε + 1 1 2 + 1 Definiion: I +1 i he dealer' poiion following he incoming rade a ime +1, where each incoming rade in he ample define a ingle period (i.e., ranacion ime). I $ i an eimae of he dealer' peculaive poiion a ime, defined a a projecion on an informaion e Ω. The informaion e we conider appear in column one. P,5 i he cumulaive change in he nondeal quoe received by he dealer over he period panning five incoming rade prior o he incoming rade a. The variable %Day i defined over each day a (obervaion #, day n)/(oal # obervaion, day n), n=1,...,5. The dummy variable HighVol i equal o one if 2 ( P 1 ) i higher han i median, zero oherwie. The error erm ε +1 repreen diurbance o he dealer' poiion from he proviion of immediacy. Eimaion: Fir, we eimae I $ a he OLS projecion of I on Ω. Then, we ue I $ o eimae β from he above equaion uing OLS. The -aiic in parenhee are calculaed from 2SLS andard error o accoun for he ue of a generaed regreor. The wo half-life column repor he implied half-life when he dealer' day i 50% done and volailiy i high ( HighVol =1) and low ( HighVol =0). The implied half-life i calculaed a he mean inerranacion ime (1.8 minue), ime he half-life in ranacion implied by $ β 1 and $ β 2 [defined a -ln(2)/ln(1+ $ β ), where $ β = $ β 1 wih low volailiy and $ β = $ β 1 + $ β 2 wih high volailiy], ime 0.5 o accoun for %Day. Sample: 838 obervaion from Monday, Augu 3 o Friday, Augu 7, 1992. Implied half-life Informaion e $ β 1 $ β 2 High Vol. Low Vol. { } Ω = P -0.36,5 (-4.56) { P,, P, } Ω = -0.37 5 5 5 (-4.72) 0.21 (2.09) 0.21 (2.11) 13 6 minue 13 6 minue 23
Figure 1 Diagram of daa rucure Definiion: Q o i an ougoing inerdealer quoe (i.e., a quoe made) and, if he quoe i hi, T i i he incoming dealer rade. Q i i an incoming inerdealer quoe (i.e., a quoe received) and, if he quoe i hi, T o i he ougoing rade. T b i a brokered inerdealer rade. Brokered rade do no align verically wih a quoe becaue he daa for brokered rade come from he dealer poiion hee, and he broker-adveried quoe a he ime of he ranacion are no recorded. appear whenever a rade occur; appear whenever a non-deal quoe occur. The dijoin egmen below he op ime-line repreen he dealer' poiion over he ame inerval. The imeline a he boom clarifie he iming relevan o he regreion ubcrip; namely, period are defined over incoming ranacion. T i T b T i T o T i Q o Q o Q i Q o Q o Q i Q o Q i Q o Q o Q i Q i Q i Q o Q i poi ion level 2 1 24
Figure 2 Diagram of poiion hee rucure, fir foureen rade on Monday, Augu 3, 1992 The dealer' poiion hee provide he dealer wih a running record of hi ne poiion and he approximae co of ha poiion. Thi dealer fill i in by hand a he rade. Each hee (page) cover abou fifeen ranacion. The Poiion column accumulae he individual rade in he Trade column. Quaniie are in million of dollar. A poiive quaniy in he Trade column correpond o a purchae of dollar. A poiive quaniy in he Poiion column correpond o a ne long dollar poiion. The Trade Rae column record he exchange rae for he rade, in deuchemark per dollar. The Poiion Rae column record he dealer' eimae of he average rae a which he acquired hi poiion. The Poiion and Poiion Rae are no calculaed afer every rade due o ime conrain. The Source column repor wheher he rade i direc over he Reuer Dealing 2000-1 yem (r=reuer) or brokered (b=broker). Trade dae: 8/3 Value dae: 8/5 Poiion Poiion rae Trade Trade rae Source Time 1 1.4794 r 8:30 2 1.4797 r 3 1.4796 28 1.4795 r -10 1.4797 r -10 1.4797 b -10 1.4797 r -3 1.4797 b -2 1.4797 0.5 1.4794 r 0.75 1.4790 r 3 1.4791 r 2 1.4791-10 1.4797 r -8 1.4797 2 1.4799 b -6 1.4797 5 1.4805 b -7 1.4810 r -8 1.4808 25
Figure 3 Plo of DM/$ dealer' poiion I (in million of dollar) from Monday, Augu 3 o Friday, Augu 7, 1992. Thee poiion are conruced from he dealer' poiion hee. Shor dollar poiion correpond o long DM poiion, and vice vera. The verical line deignae he four overnigh period hrough which he dealer did no rade. The relaive widh of he day i a reflecion of he relaive rading aciviy. The wo horizonal line brackeing zero are wo andard deviaion from he mean long poiion of wo million dollar. 26
Figure 4 Plo of DM/$ dealer' oal poiion I and peculaive poiion I $ (in million of dollar) on Friday from 9AM o 12PM, Augu 7, 1992. The oal poiion I i conruced from he dealer' poiion hee. Shor dollar poiion correpond o long DM poiion, and vice vera. The peculaive componen I $ i eimaed a he projecion of I on he informaion e Ω, wih Ω = { P,5 }, where P,5 i he cumulaive change in he nondeal quoe received by he dealer over he period panning five incoming rade prior o he incoming rade a. 27