The Choce of Drect Dealng or Electronc Brokerage n Foregn Exchange Tradng Mchael Melvn* Arzona State Unversty And Ln Wen** Unversty of Redlands Abstract Central bank surveys ndcate that the use of electronc brokerage systems account for the great majorty of nter-dealer spot foregn exchange market trade executon. Ths share has grown from zero n the early 1990s and s up sharply from that reported n the surveys taken n 1998. Whle the surveys pont out the rapd growth of electronc brokers as an mportant FX nsttuton, there has been no research on the mcrostructure ssues that lead traders to choose electronc brokerage (EB) over the hstorcally domnant, and stll qute relevant, nsttuton of drect dealng where blateral conversatons (ether telephone or electronc) occur between two FX traders and a deal s struck. We provde theory and emprcal analyss to further our understandng of the choce of tradng venue n foregn exchange. Our theoretcal model analyzes the choce of tradng venue for large and small traders. The theory llustrates the mportance of asymmetrc nformaton, transacton costs, and speed of executon. The most lkely outcome has drect dealng used for large trades whle the EB s used for small trades. The emprcal analyss utlzes data on orders submtted to the Reuters 2000-2 EB system. We focus on the duraton of tme between order submsson and fndng a match for trade executon. An autoregressve condtonal duraton (ACD) model s specfed usng the Burr dstrbuton. Gven the prce compettveness of an order, duraton s ncreasng n order sze. Because of ths longer duraton for large orders on the EB, large traders wll prefer the drect dealng market to the brokerage. We also fnd that the greater the depth of the market, the shorter the duraton of orders of all szes. Ths result s consstent wth traders clusterng n tme to submt orders so as to ncrease the probablty of fndng a match. *W.P. Carey School of Busness, Arzona State Unversty, Tempe, AZ 85287-3806, mmelvn@asu.edu **Department of Busness Admnstraton, Unversty of Redlands, Redlands, CA 92373-0999, ln_wen@redlands.edu We have benefted from the helpful suggestons of John Carlson, Hector Chade, Joachm Grammg, and Rchard Lyons, and from comments receved from semnar partcpants at Arzona State Unversty, Unversty of St. Gallen, and the Stockholm Conference on FX Mcrostructure. December 2004
1. INTRODUCTION One of the most dramatc shfts n the market structure of nternatonal fnancal markets has been the rse n the use of electronc brokerages to trade currences. In the last trennal survey of foregn exchange tradng taken n Aprl 2001, the Federal Reserve Bank of New York (2001) reports that the use of electronc brokerage systems such as EBS or Reuters 2002 accounts for 54 percent of total turnover n U.S. nter-dealer spot foregn exchange market tradng. Ths s up from less than a thrd of total spot market turnover n 1998. Pror to the 1998 survey, electronc brokerage volume was qute small. Smlarly, the Bank of England (2001) reports that over 2/3 of U.K. nter-dealer spot tradng volume s now conducted usng electronc brokers, compared to about 30 percent n 1998; and the Bank of Japan (2001) reports that electronc brokers account for 48 percent of Japanese nter-dealer spot volume today compared to 37 percent n 1998. In all cases, the electronc brokers have grown to ther current popularty whle startng from a base of zero wth ther ntroducton n 1992. 1 Whle the recent survey ponts out the mportance of electronc brokers as an nsttuton, there has been very lttle research to date on the mcrostructure ssues that lead traders to choose electronc brokerage over the hstorcally domnant, and stll qute relevant, nsttuton of drect dealng where blateral conversatons (ether telephone or electronc) occur between two traders and a deal s struck. We seek to provde theory and emprcal analyss of the ssue n order to further our understandng regardng the choce of tradng venue n foregn exchange. In equty 1 A comprehensve revew of electronc currency brokers s provded by Rme (2003). In Aprl 2004, a new global survey was taken but the data on electronc brokng were not fully avalable at the tme of ths draft. 1
tradng, a lterature has developed that addresses the choce of tradng through a specalst or on an electronc crossng network (ECN). 2 There are sgnfcant dfferences between the equty tradng envronment and that for foregn exchange. The crossng networks for equty tradng are part of a larger market wth a great deal of transparency as trades are publc nformaton. However, the foregn exchange market, broadly speakng, s characterzed by low transparency as the drect-dealng market generates propretary nformaton and the rest of the market does not know prces or quanttes traded. The greater transparency provded by the foregn exchange electronc brokerages s one of the attractons of ther use. To our knowledge, there has been no study that provdes a theoretcal model for the choce of nter-dealer foregn exchange tradng venue and provdes related emprcal analyss. 3 The paper s dvded nto four parts. Followng the ntroducton, a theoretcal model s developed n Secton 2 that analyzes the choce of tradng venue for large and small traders. The most lkely optmal decson rule of the model has large traders usng drect dealng whle small traders utlze the electronc brokerage. Secton 3 presents an emprcal analyss utlzng data from the Reuters 2000-2 electronc brokerage system. The analyss focuses on the duraton of the tme between submttng an order and fndng a match and a trade. An autoregressve condtonal duraton (ACD) model s specfed usng the Burr dstrbuton rather than the usual exponental dstrbuton assumed for the resdual. The gan s that of movng from a flat, constant hazard functon of the 2 For examples see Katz & Shapro (1985), Pagano (1989), Chowdhry & Nanda (1991), Glosten (1994), Parlour & Sepp (1998), and Hendershott & Mendelson (2000). 3 Vswanathan and Wang (2000) compare theoretcal models of a tradtonal dealer market and a multstage tradng mechansm smlar to an electronc lmt order book and show that the adverse selecton problem s lowered wth the order book. Ths s analogous to an advantage assocated wth the electronc brokerage n foregn exchange and may be related to the popularty of tradng on ths platform. 2
exponental ACD to a non-monotonc hazard of the Burr ACD that allows the hazard to vary wth duraton tme. The estmaton results support the Burr functonal form over the more common exponental or less common Webull ACD models. In terms of the testable hypotheses suggested by the theory of Secton 2, we fnd that t s mportant to condton nference on prce compettveness of orders. Gven the prce compettveness of an order, duraton s ncreasng n order sze and decreasng n market depth. Fnally, Secton 4 offers a summary and concludng dscusson. 3
2. CHOICE OF TRADING VENUE: THEORY The drect dealershp market and the electronc brokerage provde two tradng venues competng for order flow n the nter-dealer foregn exchange market. An mportant beneft provded by the electronc brokerage s the lower transacton cost relatve to the market-makng dealer s bd-ask spread. A dsadvantage s the lack of assurance of an mmedate executon of transactons. So the transacton cost and mmedacy of executon are the two key ssues to be taken nto account when a trader decdes where to trade. In ths secton, we develop a model to descrbe the mult-market tradng opportuntes and the assocated trader s choce problem. By examnng the optmal decson rule, we can relate the model results to some of the stylzed facts of foregn exchange tradng. 2.a. Model Specfcaton We begn by assumng that there are two competng venues where currency can be traded: the drect dealng market where one trades wth a market-maker (DD) and the electronc brokerage (EB). We construct a theoretcal model of the market by specfyng the players, the costs they face, avalable strateges, probabltes of order executon, and the equlbrum as follows: 2.a.1. Players: The nter-bank foregn exchange market s made up of many traders assocated wth large fnancal nsttutons around the world. We abstract from the real world wth assumptons that account for the realty that there are large and small players n ths market. We assume that there are a large number of small traders who trade only one unt of the 4
currency, as well as a larger trader who trades a large amount λ l. Each trader receves a value from tradng one unt of u. In general, u may be determned by a trader s lqudty preference, rsk averson, or other factors that determne a trader s demand for mmedacy or urgency to trade. 2.a.2. Transacton Cost: The cost of tradng ncludes commssons, fees, taxes, the bd-ask spread, the prce mpact of a trade, and the cost assocated wth prce movements f a trade cannot be executed mmedately. Traders need to pay s per unt of currency for trades wth a market-makng dealer to have ther orders executed wth certanty. On the EB, traders trade among themselves wthout the nterventon of market makers and pay a transacton cost per unt of c (c<s). Our focus s on lmt orders submtted to the EB so that the duraton between order submsson and executon s an mportant consderaton. 4 Traders would take nto account the potental delay untl a match s found on the EB by dscountng the value of tradng by a factor δ. So the net value of tradng u c multpled by δ reflects the value of tradng on the EB adjusted for expected tme to fnd a matchng order. The determnaton of δ wll be specfed next. 2.a.3. Accountng for expected duraton of orders on the electronc brokerage After a trader submts hs order to the EB, t may take some tme to fnd a match. Duraton s used to measure the watng tme on the EB and s the tme between order submsson and order executon for a flled order. For a faled order, t s the tme between order entry and order removal. We specfy duraton as follows. Let β represent 4 Whle market orders are executed mmedately at the best prce, there are related ssues nvolvng large and small orders for market order strategy. A large trade s lkely to exhaust the lmt orders wth prorty so that the order then trades at worse prces as the order s flled down the order book. So whle market orders provde mmedacy, snce traders do not know what les behnd the best prce, large market orders face prce uncertanty relatve to small market orders. 5
the common dscount factor of the traders (0<β<1). Let t s ( t l ) be the (random) number of perods t takes for a small (large) trader to fnd a match on the EB. The effectve dscount rate for large traders s then δl = Eβ t l whle for small traders t s δs = Eβ t s. Assume that t s s dstrbuted accordng to a cumulatve dstrbuton functon F(t) s = P(ts t) and t l s dstrbuted accordng to F(t) l = P(t l t). Furthermore, assume that for any value t, F(t) l F s(t) or F l domnates F s n terms of frst-order stochastc domnance. Ths mples that Etl Ets and Eβ t l Eβ t s. Then the expected payoff for a small trader submttng an order s E β ts(u c) = (u c)e β ts = (u c) δ s (1) and the expected payoff for a large trader submttng an order s E β tl(u c) λ (u c) E t l = λ l β l = (u c) λ lδ l. (2) The model just presented proposes that the duraton for small traders, t s, s less than the duraton for large traders, t l. We wll test ths proposton n the emprcal secton below. In partcular, we estmate the condtonal hazard functon as a functon of order sze. Condtonal on all avalable past nformaton (all past duraton tmes), the condtonal hazard functon measures the rate at whch order duratons are completed (matches are found and trades executed) after t 1, gven that the order exsts at other words, the condtonal hazard functon gves the expected number of trades n the next tme nterval greater than t 1 t 1 gven that orders have been submtted to the EB at t 1. Snce t takes several small orders on the other sde of the market to fll one large. In 6
order, we may expect the hazard rate for a large order, wth duraton t l, to be lower than that for small orders, wth duraton t s. However, ths s really an emprcal queston as t s possble to observe hazard functons under reasonable parameterzatons where the value of the hazard functon s ncreasng n duraton for a certan range. 5 Such hazard functons have the hazard ncreasng n small duratons and decreasng n large duratons. Gven the possblty of such a hazard for trade on the EB, t s not possble to state, a pror, that large orders wll have a smaller hazard than small orders. So even f large and small traders face the same hazard functons, the ncdence of expected trades for large orders n the next tme perod could, theoretcally, be smaller or larger than that for small orders. Our emprcal work below wll yeld evdence on ths ssue. 2.a.4. Strateges: Consder a smple stuaton where traders submt ther orders to only one of the two markets. At ths pont the strategy set ncludes: 1) Go to DD, 2) Go to EB, or 3) Don t trade. The trader s decson depends on the expected payoff from tradng on each market. The payoff from a drect-dealng transacton s u s, whle the expected payoff from the EB s: (u c)δ. In general, one goes to the market wth the hgher payoff from tradng. If no postve payoff s attanable at any market, one may smply choose not to trade at all. Assume that the dscount rate, δ, s the same for a group of traders. If a trader wth u goes to the DD, t s easly shown that all the other traders n the group wth a hgher valuaton of trade would go to the DD. On the other hand, f a trader wth u goes 5 Grammg and Maurer (2000) found that the hazard functons for 5 large stocks traded on the New York Stock Exchange were ncreasng n duraton as duraton ncreased from zero and then were decreasng n duraton over the remander of duraton values. Based upon ths fndng, they argue that flexble hazard functon specfcaton s crtcal n successful duraton models of fnancal markets. 7
to the EB, we know that all the traders wth a lower valuaton of trade would go to the EB. Cutoff values can be calculated by settng the payoffs at the two markets equal. 2.a.5. Optmal Decson Rules: Frst we ll study the smplest verson of the model by assumng value from tradng, u, s the same among ndvdual traders. Here we ll study optmal decson rules where gven all the other traders strategy, a trader would have no ncentve to swtch from one market to the other. Optmal Strateges: For any trader, at equlbrum he would: Trade va DD, f (u s) > (u c)δ and u s>0 Trade va the EB, f u s < (u c)δ and (u c) δ > 0 Be ndfferent between the two markets, f u s = (u c) δ > 0 Decde not to trade, f (u c) δ < 0 and (u s) < 0. Dfferent outcomes obtan for dfferent values of u. 1) u< c, a trval case snce no one would trade. 2) c< u< s, exclusve EB tradng. 3) u> s, the most nterestng case because traders have to compare the payoffs from two compettve tradng venues. We just focus on strateges when the drect-dealng market coexsts wth the EB because t s close to what we see n the FX market. Snce all small traders have the same value from tradng, ther decsons would be the same. They wll ether all go to drect deals or else submt orders electroncally all 8
together. Then we have two possble decson rules when the two tradng venues coexst. ) Decson Rule 1: The large trader trades drectly wth market-makng dealers and small traders go to the EB. For the large trader, we may expect that the payoff from drect dealng exceeds that on the EB. The condton under whch large traders trade exclusvely va drectdealng s: (u s) (u c) λl > λδ l l, or δl δl Smlarly small traders trade exclusvely va the EB f: u > (s c)/(1 ). (3) (u s) < (u c)δ s, or u < (s δsc)/(1 δs ). (4) ) Decson Rule 2: The large trader trades on the EB and small traders trade drectly wth market-makng dealers. Ths outcome can be easly ruled out snce t requres the followng condton: (s δsc)/(1 δs ) < u < (s δlc)/(1 δl ). (5) If δs > δl, then ths condton cannot be met. So from the analyss above, we can see that the drect-dealng market and the electronc brokerage would coexst sde by sde when the valuaton from trade u falls between (s c)/(1 ) δl δl and δs δs (s c)/(1 ). Snce we expect the value of the hazard functon facng the large traders to be lower than that facng the small traders, we then also expect δl < δs. The emprcal analyss below wll ndcate whether the data support 9
ths belef. In ths most lkely strategy, the large trader chooses to trade va DD whle the small traders go to the EB. 6 2.b. Stylzed Facts 2.b.1. Sze Effect The decson rule expected s consstent wth the stylzed fact n foregn exchange that large traders tend to trade wth market-makng dealers whle small traders go to the EB. Wthn the framework developed above, we now dscuss ths fact. Value from tradng As we have shown earler, traders wth hgher valuatons are more lkely to trade va DD. Why mght large traders have a hgher trade valuaton? Survey evdence has suggested that large traders are thought to possess prvate nformaton about the value of the underlyng asset, whch, n terms of our model, would yeld a hgher value from tradng. 7 Or t could be that the large trader s more rsk averse so that a quck trade s strongly preferred to the uncertanty of the EB. Snce our theoretcal model has a common trade valuaton for all traders, we wll not devote our attenton to ths explanaton. Probablty of executon As we have argued above, the probablty of executon s lkely to be dfferent for the small traders and the large trader. Ths s smply because t s more dffcult for a large order to fnd a match on the EB. Snce the expected payoff on the EB s (u c)δ, and we 6 Note that the dstrbuton of duratons s not determned endogenously, as t would be n a general equlbrum model n whch duraton depends on the number of traders that go to the EB. However, the smplfed model presented here s ntended to shed lght on the crucal trade-off that traders face. 7 Cheung and Chnn (2001) report that surveyed foregn exchange dealers dentfy a compettve advantage to large traders stemmng from ther large customer base whch provdes better nformaton on the order flow n the market. Gehrg and Menkhoff (forthcomng) also provde survey evdence on the role of order flow whle Lyons (2001) provdes a good overvew of the topc and ponts out that large orders may have persstent prce effects due to a portfolo-balance effect assocated wth the less than perfect substtutablty across assets wth dfferent currency denomnatons (p. 32). A rapdly growng lterature on order flow ncludes Bjonnes and Rme (2001), Evans and Lyons (2001), and Klleen, Lyons, and Moore (2002). 10
expect δl < δs, then wth u the same, the large trader gets a smaller expected payoff value from tradng on the EB than small traders. A corollary s that the transacton cost on the EB has to be lower to attract a large trader than to attract a small trader. 2.b.2. Falure of EB n hgh volatlty perods Another stylzed fact about foregn exchange tradng s that drect dealng seems to be preferred when exchange rate volatlty s hgh. One strkng result of the Federal Reserve Bank of New York survey on the mpact of electronc brokng n foregn exchange was the chef dealers belef that mantanng a vable nterbank drect dealng market was prudent to ensure suffcent lqudty to handle large trades durng perods of stress (Federal Reserve Bank of New York, 1997, p. 6). The survey ndcated that electronc brokng systems were much less satsfactory for tradng durng perods of hgh volatlty. In some extreme stuatons the EB may fal to attract a suffcent number of traders, so that t dres up n tmes of great uncertanty assocated wth hgh volatlty. Prce volatlty mght affect several varables n our model, such as the dscount factor and transacton costs at both markets, thus changng the traders behavor at the equlbrum. Snce a long hstorcal database of electronc brokerage actvty s unavalable at ths tme, volatlty effects are beyond the scope of ths paper. However, as longer data sets, encompassng hgh volatlty events, become avalable we hope to be able to address ths ssue. Snce t takes tme for orders on the EB to be executed, there s a potental loss caused by prce movement durng the duraton that an order sts wthout a match. Ths potental loss s due to an unfavorable exchange rate movement between the tme an order s entered and the tme the order s flled f the agent s unable to cancel the order 11
before executon. Ths s a type of wnner s curse, where a lmt order s pcked-off at a now-stale prce n a fast-changng market. In tmes of hgh volatlty, there s a hgher probablty of such an outcome. The theoretcal model presented above has traders accountng for the delay on the EB by dscountng the value of tradng by a factor δ. 3. EMPIRICAL ANALYSIS The theoretcal model ntroduced n the prevous secton s used to motvate the emprcal work that follows. In partcular, the model generates testable hypotheses regardng the duraton tme of submtted orders on the EB and the probablty of executon. We frst descrbe the data set used for analyss and then turn to a descrpton of the econometrc methods employed before presentng estmaton results. 3.a. Data Descrpton The data analyzed are Reuters D2000-2 electronc brokerage data on the Mark/Dollar exchange rate. The data set covers one week: October 6-10, 1997, and contans nformaton on 130,535 orders. 8 The data nclude both lmt orders and market orders. The followng nformaton about an order s avalable: type of order (market or lmt); order date, entry and ext tme; order removal codes for flled and cancelled orders; prce; quantty ordered; and quantty dealt. Reuters D2000-2 operates as an electronc lmt order book wth lqudty supply va lmt order and lqudty demand va market order. Our data contan nformaton not avalable to market partcpants snce we can observe unexecuted orders submtted to the system. Partcpants just see the nsde spread quotes but not the lmt order book. Table1 8 The data are descrbed and analyzed n detal n Danelsson and Payne (2002). 12
provdes some descrptve statstcs for the orgnal data. Table 1.a shows that the average prce of an order was 1.75144 marks per dollar and the average order sze was 2.283058 mllon dollars. The average quantty dealt was 0.883633 mllon, reflectng the fact that many orders are not flled and are wthdrawn wth no matchng counterparty or are only partally flled. Tables 1.d and 1.e provde addtonal nformaton n that 63,517 orders were successful n fndng a counterparty and 67,018 were wthdrawn before a match was found. In the emprcal work below, we wll document the role of compettve quotes n determnng the probablty of fndng a match. If an agent submts a quote that s away from the current market prce, that quote lkely goes unflled. Tables 1.b and 1.c show that there were 21,783 market orders, where orders are submtted for mmedate executon at the best avalable prce, and 108,752 lmt orders, where quantty s accompaned by a reservaton prce whch must be met for the order to be flled. 3.b. Duraton Tme of Orders 3.b.1. Defnton and Constructon In order to examne the lqudty of the EB and the effcency of ts operaton, we construct a varable (Duraton), whch measures the tme from the entry of an order untl ts removal. Snce Duraton s computed as the tme dfference between the entry tme and the removal tme of an order, t provdes a drect measure of the delay n a transacton on the EB. Table 2 provdes descrptve statstcs on Duraton. We break down the sample nto dfferent categores, for example, lmt orders, market orders, cancelled orders, and the sample of lmt orders used for estmaton. Comparng all lmt orders to all market orders, the noteworthy dfference s the speed wth whch market orders are executed. 13
The average lmt order duraton s 2.855 mnutes whle the average market order duraton s 0.0012 mnutes. Snce market orders are executed at the best avalable prce, they are essentally executed mmedately. However lmt orders may st n the order book for prolonged tmes and may be cancelled at any tme. Note that the mean duraton for cancelled orders s 3.5742 mnutes. Some orders are cancelled n seconds after submsson whle others st n the order book for hours before cancellaton. Snce our theoretcal model focuses on duraton of successful lmt orders, we construct a data set of completely flled lmt orders. As wll be dscussed below, there s a pronounced ntradaly pattern of actvty n the Reuters EB. As a result, we focus on the actve perod of 8:00 to 17:00 London tme. The data are then fltered to dentfy any extreme observatons that would be unrepresentatve of the market and would bas the analyss. We deleted any observatons wth a duraton exceedng 80 mnutes (61 observatons). Ths leaves a sample of 29,740 orders wth a mean duraton of 1.2631 mnutes. Ths s the data set used for estmaton. 3.b.2. Tme of Day Effect As wth all fnancal markets, we expect an ntradaly pattern of duraton tme as markets tend to be deeper at certan tmes of day than at others. To llustrate the ntradaly pattern, we average duraton of the offers submtted to the network for each hour of the tradng day over the fve days n our sample. Table 3 reports the 24 average duraton tmes and the number of orders submtted for each hour of the day. Traders have to wat longer on the network when the tradng actvty s low, as durng hours 21-0 GMT, when North Amercan tradng has stopped and major Asan tradng has not yet begun. Note the very low level of orders submtted durng ths tme and the relatvely 14
long duratons. Table 3 also shows the mportance of the Reuters network for mark/dollar tradng whch s domnated by European and U.S. tradng. The market s seen to be relatvely thn durng Asan tradng hours. Ths reflects the fact that, whle Hong Kong and Sngapore both were actve market-makng centers for the mark (and now the euro), the rval electronc brokerage system offered by EBS s more popular for Asan tradng. In addton, Tokyo tradng s domnated by yen/dollar relatve to any other currency par. 9 In contrast to the thn market durng Asan tradng hours, note the depth of the market and assocated short duraton tme durng the peak European tradng tmes from 8:00-17:00 GMT. 3.b.3. Autoregressve structure of duraton tme The data suggest that there s a clusterng of duraton over tme. Ths wll surely be affected by the regular ntradaly patterns, as well as any dosyncratc patterns that emerge due to shocks. Long duraton tme tends to be followed by long duraton and short duraton followed by short duraton tme. The duraton tme of an order submtted to the network depends on the wllngness of all other traders n the market to partcpate by contrbutng orders. As n the theoretcal model presented earler, f the market was lqud and the watng tme was short last perod, people would be more lkely to go to the EB ths perod, gven ther expectaton condtonal on past performance of the EB. To document the presence of clusterng n the duraton data, we compute the average duraton tme of orders submtted wthn every 15-mnute nterval. A sample of 459 observatons s constructed from 5 tradng days. Autocorrelaton coeffcents are computed and the results are reported n Table 4. The statstcs suggest that the duraton 9 A dscusson of Asan tradng practces n foregn exchange s provded n Ito, Lyons, and Melvn (1998) and Covrg and Melvn (2002). 15
tme s hghly autocorrelated wth large and statstcally sgnfcant coeffcents even up to the ffth order. 3.c. Estmaton of Duraton Models The theoretcal model of secton 2 suggests testable hypotheses regardng duraton and the probablty of executon on the EB. We examne the emprcal evdence regardng the followng three varables: order sze, prce compettveness, and lqudty. We wll dscuss hypotheses related to each of these varables n turn before examnng the evdence. Hypothess 1: Sze effect A stylzed fact of the foregn exchange market s that large traders are more lkely to use drect dealng than go to the EB. The ntutve explanaton s that, n general, large orders have to wat longer on the network, whch makes electronc tradng rsker and less attractve. However, f the Burr dstrbuton s a good representaton of the foregn exchange market as Grammg and Maurer (2000) found for the stock market, then there may be a non-monotonc relatonshp between duraton and the value of the hazard functon. Rather than mpose a partcular shape on the hazard functon, as s commonly done, we wll specfy a flexble functon that wll allow the data to dentfy the shape of the hazard functon. It s possble to have a hazard functon that s ncreasng n duraton for small duratons and decreasng n duraton for large duratons, so that one cannot be sure that large orders have a smaller hazard value than small orders. For nstance, n an order book t could be the case that market order submsson results n a short duraton for lmt orders wth prorty but also reduces the lqudty n the book so that followng a clusterng of market orders and short duratons there s a lengthenng of the duraton 16
process for newly submtted lmt orders as market order submsson slows whle the depth of the book s rebult. In ths case, the hazard functon could be ncreasng for very short duratons and then fall as the duratons lengthen. The evdence presented here wll allow the data to speak to ths ssue. We examne the relatonshp between duratons and order sze by ncorporatng an exogenous varable SIZE n our estmatons below. Hypothess 2: Prce Impact Submsson prce of a lmt order should affect the watng tme of the order on the EB. In general, we expect that an order wth a compettve submsson prce, for example, a relatvely hgh-prced buy order, or a relatvely low-prced sell order, should get flled more quckly than other orders where prce s farther away from the current transacton prce of orders recently flled. Ths effect s explored by ncludng n our estmaton dummy varables for prce compettveness: DummyBP, swtches to one for buy orders wth a hgher lmt order prce than the last transacton prce; DummyBN, swtches to one for buy orders wth a submtted prce lower than the last transacton prce; DummySP, swtches to one for sell orders wth a submtted prce hgher than the last transacton prce; and DummySN, swtches to one for sell orders wth a submtted prce lower than the last transacton prce. Compettve (uncompettve) quotes wth expected negatve (postve) effects on duraton are captured by DummyBP and DummySN (DummyBN and DummySP). Hypothess 3: Lqudty Effect Duraton should be negatvely correlated wth the total lqudty or depth of the market. The EB s characterzed by a postve externalty: An ncrease n the network s submtted order volume ncreases ts lqudty, beneftng all trades. The duraton should be smaller 17
when the depth s large. There s a potental offsettng crowdng effect of a negatve externalty assocated wth a large number of orders. As Hendershott & Mendelson (1999) pont out, low value orders can compete wth hgher value orders on the same sde of the market and there may be a greater chance of smaller orders beng squeezed out of the queue. However the crowdng effect can only domnate the lqudty effect after the EB becomes suffcently lqud. We wll explore the effect of lqudty by ncorporatng a varable LDEPTH, whch measures the total quantty offered for purchase or sale on all actve submtted lmt orders. An addtonal measure of lqudty s a varable MORDERS, whch s the number of market orders submtted n the perod mmedately precedng a lmt order. 3.c.1. Econometrc Methodology: the ACD Model Snce we are studyng orders submtted n rregular tme ntervals, the standard econometrc technques based on fxed tme nterval are not approprate analytcal tools. If a short nterval s chosen, there wll be many ntervals wth no new nformaton and heteroskedastcty wll be ntroduced. On the other hand, the mcrostructure of the data wll be lost f a long tme nterval s pcked. Engel and Russell (1998) developed an autoregressve condtonal duraton (ACD) model to descrbe the pont process of order arrval rates that s a natural approach to estmatng the relatonshps of concern here. The ACD model belongs to the famly of self-exctng marked pont processes of Cox and Lews (1966). A pont process s descrbed as self-exctng when the past evoluton mpacts the probablty of future events. Bascally, the economc motvaton behnd the ACD and the ARCH model follows a smlar logc: due to a clusterng of 18
news, fnancal market events occur n clusters. Ths mples that the watng tme between these events exhbts sgnfcant seral correlaton. Engel and Russell (1998) proposed the standard exponental ACD (EACD) model by specfyng the observed duraton x as a mxng process x = ψ ε. ψ s the condtonal duraton defned as ψ = E( x x 1,...,x 1 ) and ε s an IID error sequence. For the EACD model, the densty of error ε s assumed to be exponental. A condtonal densty gves the forecast densty for the next observaton of order arrval condtonal on all avalable past nformaton (all past duraton tmes). Gven the current nformaton set, the condtonal hazard functon measures the rate at whch duratons are completed after duraton t, gven that they last at least untl t. Then for an EACD model, the Condtonal Densty of f s x 1 x x 1,..., x ) = exp( ) (6) ψ ψ ( x 1 and the condtonal hazard s h ( x x 1,..., x1) = 1. (7) ψ In an ACD model, the condtonal expectaton s a lnear functon of the prevous duraton and condtonal expectaton. A smple EACD (1,1) s specfed as ψ = + + ω αx 1 βψ 1. (8) Ths equaton has coeffcent constrants ω > 0, β 0, α 0, and α + β < 1. The frst three constrants ensure the postvty of the condtonal duratons and the last ensures the exstence of the uncondtonal mean of the duratons. As wll be dscussed below, when addtonal explanatory varables are added to the model, the non-negatvty 19
constrants may be overly restrctve. For ths reason, we wll specfy and estmate a log- ACD model below. Frst we wll dscuss mplcatons of the partcular dstrbutonal assumpton made for the error term. For EACD models, the hazard functons condtonal on past duraton are restrcted to be a constant. The Webull dstrbuton s more flexble n that t nests the exponental and allows a non-flat hazard functon h( x x γ 1 1,..., x1) = x γ However, the hazard functon s monotone: ncreasng f γ >1, decreasng f γ <1. As ponted out above, t s possble that the hazard functon of fnancal transactons may be ncreasng for small duratons and decreasng for long duratons. The msspecfcaton of the condtonal hazard functon can severely mpact the estmaton results. To avod such problems, the Burr-dstrbuton s proposed. Ths allows a hump shaped hazard and nests the Webull dstrbuton as a partcular case. The Burr-dstrbuton may be descrbed by frst defnng where κ and 1 (1+ ) 2 1 κ ( σ ) Γ( + 1) 2 f ( ψ ) σ = ξ = ψ, (9) 1 1 1 Γ(1 + ) Γ( ) 2 κ σ κ 2 σ are parameters, Then the condtonal densty s a Burr densty 0 < σ 2 < κ and Γ represents the gamma functon. 1 1 2 (1 + σ ξ κ κ 1 1 ( ) + 1 κ 2 σ ) κ ξ x f ( x x,..., x ; θ ) =, (10) κ x and the condtonal hazard functon s κ κ 1 κ ξ x 1,..., x1; θ ) = 2 κ κ 1+ σ ξ x h( x x. (11) 20
For σ 2 0, the Burr-ACD reduces to the Webull-ACD and f n addton κ = 1, t becomes the exponental-acd. Snce the Burr-ACD nests the Webull and exponental specfcatons, by estmatng the Burr model, we can test whch specfcaton s supported by the results. 10 Fgure 1 llustrates the shape of the hazard functon for some alternatve parameters. The monotonc functon s parameterzed as the Webull wth κ = 0.5 and 2 σ = 0. The hump-shaped hazard s a Burr wth κ = 2 and σ = 0.5. In general, for κ > 1the Burr hazard has the hump-shape. Such hazard functons have the hazard ncreasng n small duratons and decreasng n large duratons. Gven the possblty of such a hazard for trade on the EB, t s not possble to state, a pror, that large orders wll have a smaller hazard than small orders. So even f large and small traders face the same hazard functons, the ncdence of expected trades for large orders n the next tme perod could, theoretcally, be smaller or larger than that for small orders. Our emprcal work below wll yeld evdence on ths ssue. As mentoned above, n order to test hypotheses suggested by our theoretcal model, we want to nclude varables such as order sze, prce compettveness, and market depth as explanatory varables n the condtonal duraton equaton. When addtonal varables wth negatve coeffcents are added lnearly to the rght-hand sde of the equaton, condtonal duraton ψ may become negatve whch s not admssble. If workng wth a standard ACD specfcaton, we would have to mpose non-negatvty constrants on the coeffcents of the varables so that the rght-hand sde of the ACD equaton remans strctly postve. Snce non-negatvty constrants on the coeffcents 2 10 We acknowledge the generosty of Joachm Grammg n sharng hs sute of ACD GAUSS programs, whch greatly shortened the tme spent n programmng for the current study. 21
may be very restrctve, we work nstead wth a more flexble functonal form provded by the log-acd model as dscussed by Bauwens and Got (2000). In a log-acd model, duraton x s defned as the mxng process x = exp(ψ ) ε, such that ψ s the logarthm of the condtonal duraton. ε s the same random varable as n the ACD model and we specfy t as havng a Burr dstrbuton. The specfcaton of the basc Log-ACD (1,1) model s: ψ = ω + αln( x 1) + βψ 1. (12) Wth ths specfcaton, the only coeffcent restrcton s that α + β < 1 for covarance statonarty of 3.c.2. Censorng ln( x ). Estmaton proceeds va maxmum lkelhood. The data nclude orders that are completely flled and those that are only partally flled or cancelled. Estmaton usng only the completely flled orders may result n a censorng bas due to the termnaton of the other orders pror to ther full executon. Let c denote an observaton beng completely flled, c = 1, or censored, c = 0. If the pars (x,c ) are statstcally ndependent, then the lkelhood functon for the sample of data may be wrtten as: n c 1 c = = 1 F C f (x;x ) g(x;x ) f(x;x ) g(x;x ) (13) where and denote products taken over flled and censored orders, respectvely, F C and X denotes the explanatory varables on whch duraton s condtoned. The ndependence assumpton allows for the censorng mechansm to be related to past duraton or the vector of varables contaned n X. But at the tme the order s submtted, 22
the censorng decson (whch s made later) s ndependent of the condtonal duraton or the lkelhood that the order s executed. 11 We estmate the model parameters usng the lkelhood functon as gven n equaton (13). 3.c.3 Estmaton Results Estmaton s based on lmt orders. The ssue of duraton for market orders s rrelevant snce market orders get executed almost mmedately after they are posted on the EB. As shown n Table 2, the mean duraton for market orders s 0.0012 mnutes, whch s very small compared to the mean for flled lmt orders of 1.7886 mnutes. As dscussed n the pror secton, we estmate the parameters of the model for both flled lmt orders and censored orders as manfested n cancelled orders. If only the flled orders were used, based estmates may gve us naccurate nformaton on model parameters related to the dstrbuton of duraton tme. Fnally, to avod the problem of spurous results drven by thn tradng perods, we estmate usng data over the perod of peak European busness hours (8:00am 5:00pm GMT). 12 As stated above, we seek to estmate ACD models whch ncorporate the followng varables: SIZE (the quantty submtted n mllons of dollars), dummy varables for compettveness of submtted order (submsson prce last transacton prce), LDEPTH (total depth of the order book n mllons of dollars), and MDEPTH, the number of market orders submtted over the pror 5 mnutes precedng each lmt order. Before proceedng to the results, some dscusson of the prce compettveness dummes s n order. To determne the compettveness of the submsson prce, we dentfy the 11 See Lo, MacKnlay, and Zhang (2002) for a dscusson of censorng n a lmt-order settng. 12 No overnght duratons are utlzed. We start each day wth the duraton from the frst order after 8:00 GMT as our frst avalable lag for that day. 23
transacton prce of the last trade before each order s submtted and take the dfference between the submsson prce and the last-trade transacton prce. To avod the bd-ask bounce, the trade must be of the same type as the submtted order. So for a buy lmt order, the last transacton for a buy-order s found and the prce dfference between the submsson prce and the transacton prce s computed. If the submsson prce s hgher than the transacton prce, we consder t a compettve order and expect t to get flled more quckly. By the same token, for a sell order, the submsson prce of a compettve order would be lower than the transacton prce of the last flled sell-order. We constructed 4 dummy varables n order to capture the mpact of prce compettveness on duraton tme: Defne varable Prcedff = submsson prce last transacton prce, then DummyBP = 1 for buy orders wth Prcedff>0; 0 otherwse DummyBN = 1 for buy orders wth Prcedff<0; 0 otherwse DummySP = 1 for sell orders wth Prcedff>0; 0 otherwse DummySN = 1 for sell orders wth Prcedff<0; 0 otherwse. The functonal form of the Burr-log-ACD (1,1) model estmated s: ψ = ω + αln( x 1) + βψ 1+ δ1size + δ2dummybp + δ3dummybn + δ3dummysp + δ4dummysn + δ5ldepth + δ6mdepth (14) where ndexes submtted orders and orders are arranged n calendar (clock) tme. Note that there s no collnearty problem assocated wth ncludng the four dummes for prce compettveness of quotes snce about 30 percent of submtted orders have quotes equal to the last transacton prce. Prelmnary estmates ndcated that one could not reject the hypothess of equalty of coeffcents for the dummy varables for compettve bd and ask quotes and uncompettve bad and ask quotes. As a result, we constran the coeffcents for each par to be equal to reduce the number of coeffcents to be estmated. 24
Estmates of the model are reported n Table 5. The estmaton procedure employs the jont lkelhood functon for flled and unflled orders as n equaton (13). Estmates of the functon for flled orders are gven n part a) of Table 5. As expected, we get a postve sgnfcant coeffcent for SIZE. Ths suggests that the bgger the order, the longer the duraton tme. In the theory presentaton of secton 2, the effect of SIZE was uncertan due to the possblty of a hump-shaped hazard functon. However, the emprcal results ndcate that sze of trade s a reason to expect bg traders to prefer the dealer market over the EB. Whle not reported n the table, the shape and scale parameters assocated wth the Burr dstrbuton are constraned to be equal for both the 2 flled and censored samples. The estmated parameters of κ = 0.6379 and σ = 0.4652 suggest that the approprate hazard functon for the electronc foregn exchange brokerage wll have a shape lke that portrayed n Fgure 2. For these data, the hazard s monotoncally decreasng n duraton. The emprcal results for flled orders suggest no ambguty n the effect of SIZE on the value of the hazard functon. Both measures of market depth, LDEPTH and MDEPTH, have negatve and statstcally sgnfcant coeffcents n part a) of Table 5. So the greater the quantty of outstandng orders, the shorter the duraton tme and the more market orders that were submtted pror to a lmt order, the shorter the duraton of the lmt order. Wth regard to our prce mpact varables, results for the four dummes are also consstent wth our prors. The negatve coeffcents of DummyBP and DummySN ndcate that t takes less tme to fnd a match for a lmt order wth a compettve prce (a better prce than the last transacton prce). On the other hand, for buy orders wth low prces and sell orders wth hgh prces (relatve to last transactons), the results suggest longer duratons as ndcated 25
by the postve and sgnfcant coeffcents estmated for DummyBN and DummySP. Wthout condtonng the estmaton results on prce compettveness of quotes, one cannot properly nfer the effects of other varables, lke SIZE and LDEPTH. Our results for flled orders may be summarzed as follows: gven the prce compettveness of submtted orders, duraton s ncreasng n order sze and decreasng n market depth or lqudty. Part b) of Table 5 reports the estmated parameters assocated wth the censored sample of cancelled orders. Interestng dfferences from the flled order results nclude a negatve sze coeffcent and a postve and nsgnfcant coeffcent for the depth of the order book. The former ndcates that large orders are more lkely to be cancelled faster than small orders. Perhaps ths reflects the more careful management of large orders by partcpants. Wth regard to the proper functonal form of ACD model, as mentoned above, the Burr model nests the Webull and exponental. Referrng back to the specfcaton of the Burr ACD n Secton 3.c.1, we can test whether the Webull ACD s supported by a test of σ 2 0. The results clearly reject the hypothess that σ 2 = 0 (wth a p-value of 0.000). Snce we reject the Webull n favor of the Burr specfcaton, t s clear that the exponental s not supported (but we would also reject the addtonal restrcton assocated wth the exponental, that s κ = 1). 26
4. SUMMARY We begn by specfyng a theoretcal model of nter-dealer foregn exchange market partcpants facng a choce of tradng drectly wth other dealers or submttng orders to an electronc brokerage (EB). The optmal decson rule of the model suggests that under normal condtons, we would expect large traders to prefer the drect-dealng market where certanty of quck executon s provded. A large order may be expected to have a longer duraton on the EB n order to fnd a match. Smaller traders would prefer the EB due to lower transacton costs along wth the greater lkelhood of fndng a match for a small order. The longer the expected duraton of a submtted order, the lower the expected value from tradng. Ths result s drven by the potental cost of havng the market prce move unfavorably and a lmt order flled at an undesrable prce before an order can be wthdrawn. Snce a buldng block of the model s the longer duraton for large orders, the emprcal analyss focuses on estmatng duraton models of lmt orders submtted to the Reuters D-2000-2 electronc brokerage system. We model the tme from order submsson to order fll (Duraton) n an autoregressve condtonal duraton (ACD) framework where n addton to lagged condtonal and uncondtonal duraton, we nclude the sze of the order (SIZE), the lqudty or depth of the market (DEPTH), and prce compettveness of the quote (PRICEDIF). The latter varable s measured by the dfference between the prce of the submtted order and the last transacton prce on the same sde of the market (buy or sell). It s mportant to condton the duraton results on prce compettveness of quotes n order to make sensble nferences on other varables, 27
lke sze of order submtted. We fnd that prce compettveness has the effects expected: uncompettve quotes, as measured by relatvely low buy prces or relatvely hgh sell prces, are assocated wth longer duratons whle compettve quotes, as measured by relatvely hgh buy prces or low sell prces are assocated wth shorter duratons. Gven these effects of prce compettveness, we fnd that the larger the sze of order submtted, the longer the duraton. Pror evdence for equty trades ndcates that the hazard functon may be ncreasng n duraton for small duratons and fallng n duraton for larger duratons. In ths case, we cannot say that large orders wll have a lower value of the hazard functon than small orders. However, our evdence suggests a hazard functon that s monotoncally decreasng n duraton. So the longer duraton, the lower the value of the hazard functon and, n terms of the theory presented, the lower the value of order submsson on the electronc brokerage. The emprcal results support the theoretcal model where bg traders wll prefer the dealer market over the EB due to the longer watng tme for bg orders to fnd a match on the electronc brokerage. We also fnd that the greater the depth of the market, the shorter the duraton. Ths s the expected result, as greater depth should ncrease the probablty of fndng a match for any submtted order. Ths frst look at theory and emprcs on the choce of tradng venue for foregn exchange pays due respect to the stylzed facts of the market. The growth of electronc brokng s the number one nsttutonal FX development of the last decade and has revolutonzed the way n whch currences are traded. The popularty of ths nnovaton n tradng protocol s assocated wth lower cost of transactng and the ablty of smaller traders to compete on an equal footng wth the bg players n the market va anonymous order submsson. In the future, f longer data sets become avalable, t wll be nstructve 28
to analyze how tradng mgrates between the electronc brokng network and the drect dealng network durng tmes of stress. The theoretcal model developed here can be extended by ncludng a role for volatlty to ncrease the probablty of a regretted trade for submtted lmt orders n tmes of great volatlty. In such tmes of great prce uncertanty, a lmt order may be pcked off and executed at an unfavorable prce relatve to the fast-movng current market values. As a result, we expect the electronc brokerage network to dry up durng tmes of hgh volatlty as even small traders mgrate to the drect dealng market where mmedate executon s offered. Analyss of such volatlty effects awats the avalablty of new and longer data sets. 29
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