In: Lqudty, Interest Rates and Bankng ISBN: 978-1-60692-775-5 Edtors: J. Morrey and A. Guyton, pp. 139-167 2009 Nova Scence Publshers, Inc. Chapter 7 AN ANALYSIS OF LIQUIDITY ACROSS MARKETS: EXECUTION COSTS ON THE NYSE VERSUS ELECTRONIC MARKETS Mchael A. Goldsten 1,a, Gang Hu 1,b and J. Gnger Meng 2,c 1 Babson College 2 Stonehll College Abstract We examne lqudty across dfferent types of markets by usng executon costs as a proxy for lqudty. We conduct a thorough analyss of executon costs on the NYSE versus a varety of electronc NASD market centers whch also trade NYSE-lsted stocks ( Electronc Markets ). We adopt a varety of technques attemptng to correct for the selecton bas problem. Unlke current lterature, we fnd that the Electronc Markets offer lower executon costs even after controllng for selecton bases. In addton to controllng for selecton bases at the sample average level of order dffculty, we also carry out our analyss at dfferent levels of order dffculty, measured by a vector of control varables. Our results are robust under dfferent model specfcatons. Fnally, our what-f analyss shows that the Electronc Markets (the NYSE s) orders would have been worse (better) off, had they been executed by the NYSE (Electronc Markets). Overall, our results hghlght the superorty of the Electronc Markets lqudty and executon qualty. 1. Introducton It s a world-wde trend that the stock exchanges are changng ther tradtonal tradng mechansms, largely attrbuted to the competton among exchanges. For example, the a E-mal address: goldsten@babson.edu. Professor of Fnance, Babson College, 223 Tomasso Hall, Babson Park, MA 02457. Phone: 781-239-4402. Fax: 781-239-5004. b Assstant Professor of Fnance, Babson College, 121 Tomasso Hall, Babson Park, MA 02457. Phone: 781-239- 4946. Fax: 781-239-5004. E-mal address: ghu@babson.edu. c Assstant Professor of Fnance, Department of Busness Admnstraton, Stonehll College, 320 Washngton Street, Easton, MA 02357. Phone: 508-565-1986, E-mal address: gmeng@stonehll.edu.
140 Mchael A. Goldsten, Gang Hu and J. Gnger Meng modernzaton of European stock markets snce the md-eghtes, ncludng the swtch to contnuous tradng and electronc markets, was spurred by the compettve pressure of London. Electronc markets contnue to evolve and mprove. Pagano and Schwartz (2003) provde a detaled analyss of one of such mprovements: the ntroducton of electronc closng call auctons at Euronext Pars that lowered executon costs for ndvdual partcpants and sharpened prce dscovery for the broad market. In the Unted States, lqudty n NYSE stocks s movng away from the floor of the NYSE towards electronc markets. From the second half of 2003 untl the end of 2005, n the 18 months, the percentage of NYSE-lsted shares executed electroncally ncreased from 2.4% to almost 10%. As Regulaton NMS s mplemented, ths percentage wll lkely ncrease substantally. In the lterature, evdence on the relatve advantage of the NYSE versus electronc markets s mxed. For example, Kalay and Portnaguna (2001) document the frst voluntary swtch of a NYSE frm (Aeroflex) to NASDAQ, and fnd that the swtch announcement resulted n a sgnfcantly postve abnormal return, subsequent narrowng of the daly bd-ask spread, and sgnfcant ncrease of the daly volume. In contrast, Prutt, Van Ness, and Van Ness (2002) fnd that Aeroflex s swtch resulted n economcally and statstcally sgnfcant degradatons n key tradng metrcs such as the bd-ask spread and the number of equty trades. Prutt, Van Ness, and Van Ness (2002) dd not fnd any observed mprovements n tradng or quotng behavor as a result of the swtch. On December 20, 2005, Charles Schwab (SCHW) effectvely dropped ts dual lstng and decded to lst only on the NASDAQ. At the same tme, the NYSE s takng a seres of actons to move fast from floorng tradng to electronc tradng, for example, ts IPO through the merger wth the ARCA Exchange (an electronc exchange that used to be an ECN), and the new Hybrd Market system. 1 Tradng costs and lstng fees are the man determnants for the exchanges to attract frms nterested n lstng and for nvestors. NASDAQ offers lower fees; however, many prevous studes fnd that the NYSE offers lower executon costs over the years. Researchers such as Chrste and Schultz (1994) and Chung, Van Ness, and Van Ness (2001) attrbute mplct colluson among NASDAQ dealers as the cause. On the other hand, there s another strand of lterature showng that electronc markets executon costs have been declnng over the years. 2 Van Ness, Van Ness, and Warr (2005) document that NASDAQ spreads steadly declned from 1993 to 2002. Bessembnder (2003) fnd that the executon costs on electronc markets are actually lower than the NYSE for market orders. However, researchers attrbute ths dfference to order dffculty dfferences,.e., the NYSE have been recevng more dffcult orders to execute. In ths paper, we conduct a thorough analyss comparng executon costs between the NYSE and electronc NASD market centers whch also trade NYSE-lsted stocks ( Electronc Markets ), adoptng a varety of technques attemptng to correct for the selecton bas problem. Conventonally, the pont comparson of executon costs s conducted at each market s own average, whch s wdely crtczed because of the selecton bas problem,.e., the dffcultes of the orders routed to the two markets could be dfferent. Several recent 1 See Davs, Pagano, and Schwartz (2006) for a descrpton and dscusson of the new NYSE Hybrd Market. 2 The term Electronc Markets or Electronc Market Center refers to the combnaton of NASDAQ book avalable to brokers and market makers who are members of NASD, the ECN books avalable to all brokers, market makers and nvestors sponsored by brokers. All these electronc markets are voluntarly nterconnected. See Goldsten, Shklko, Van Ness, and Van Ness (2008) for a recent study on competton n these markets durng a smlar perod across market makers and three major ECNs n NASDAQ stocks.
An Analyss of Lqudty across Markets 141 papers attempt to account for the selecton bas problem. For example, Lpson (2005) fnds that once we account for the dfference n order flow dffculty, the NYSE s no more costly than other exchanges and much less costly than many. Unlke current lterature, we fnd that after controllng for the selecton bas problem, the Electronc Markets stll offer lower executon costs. We also shed lght on what mpact dfferent factors have on executon costs. The results are robust under dfferent model specfcatons. We make use of a sample of 1,138 NYSE-lsted stocks whch are traded on both the NYSE and the Electronc Markets. We start wth the conventonal smple mean comparson as well as share-weghted mean comparson of executon costs, measured by effectve spreads. The unvarate results show that the effectve spreads on the Electronc Markets are lower than those on the NYSE. We then proceed to OLS regresson analyss controllng for order dffculty. We study a wde range of potental explanatory varables and eventually reach a model wth a set of sgnfcant explanatory varables explanng effectve spreads. The model s cross-sectonal and s set up wth two dummy varables ndcatng whether the order s executed on the NYSE or the Electronc Markets. The explanatory varables are all constructed as the devaton from the n-sample mean, so that the coeffcents of the two dummy ndcators may be nterpreted as the condtonal mean effectve spreads at the mean of the explanatory varables vector. The results confrm that executon costs are lower on the Electronc Markets than on the NYSE. Next we adopted the two-stage procedure advocated by Heckman (1979) and Maddala (1983). Ths method nvolves frst estmatng a Probt model for the choce of venues, generatng two new varables from the Probt estmaton, and then ncludng these two new varables n an OLS regresson model as controls for selecton bas. Our results based on ths two-stage procedure confrm the superorty of the Electronc Markets executon. We conduct several robustness checks of our results. Snce the above OLS and two-stage analyss s effectvely a pont comparson at the sample mean of control varables, t s worthwhle to check whether the results hold at other locatons of the sample doman. To do that, we splt our sample nto two sub-samples accordng to the ftted values, whch s a measure of order dffculty, and repeat our OLS and two-stage selecton analyss n both dffculty sub-samples. The results are smlar. As another extenson and robustness check, we try to answer the followng queston: f the NYSE executed the Electronc Markets orders, wll these orders receve better or worse executon? Smlarly, what f the Electronc Markets executed the NYSE s orders? In order to answer the former queston, we frst estmate a model for the NYSE s orders alone. Then we plug n explanatory varables of the Electronc Markets orders nto the NYSE model. The ftted values represent as-f NYSE executon costs of the Electronc Markets orders. The latter queston s smlarly answered by frst estmatng the Electronc Markets model, and then pluggng n explanatory varables of the NYSE s orders. Results of the above whatf analyss suggest that the Electronc Markets (the NYSE s) orders would have been worse (better) off, had they been executed by the NYSE (Electronc Markets). Therefore, our results clearly show that the Electronc Markets offer better executon qualty than the NYSE. Gven our results of lower executon costs on the Electronc Markets, one mght fnd t puzzlng that the NYSE s stll domnant n the market place even though t s not fully electronc. We note that although executon costs and lstng fees are mportant consderatons n a frm s lstng decson, they are by no means the only factors a frm mght
142 Mchael A. Goldsten, Gang Hu and J. Gnger Meng consder. Chemmanur and Fulgher (2006) develop a theoretcal model of frms lstng decsons n an envronment of competton and co-operaton among exchanges wth endogenous lstng standards. In ther model, reputaton, asymmetrc nformaton, and nvestors ablty to produce nformaton are the man concerns n a frm s lstng decson makng process. Our results are thus consstent wth ther theoretcal analyss: executon costs alone do not drve a frm s lstng decson. The rest of the paper s organzed as follows. Secton 2 descrbes the data and sample selecton procedures. Secton 3 presents unvarate analyss. Secton 4 presents OLS and two-stage selecton model analyss. Secton 5 presents dffculty sub-sample analyss. Secton 6 contans an extenson answerng the what-f queston. Secton 7 concludes. 2. Data and Sample Selecton 2.1. Data Executon costs are often computed based on trade level data such as Trade and Quote database (TAQ), dssemnated by the NYSE. The drawback s that order drecton, order sze, and order arrval tme are not observable and must be estmated usng approxmaton methods. On November 17, 2000, the SEC adopted Exchange Act Rule 11Ac1-5 (the Dash- 5 reports ). Regardng the purpose of complng Dash-5 reports, the SEC states one of the prmary objectves of the Rule s to generate statstcal measures of executon qualty that provdes a far and useful bass for comparsons among dfferent market centers. The man advantages of the Dash-5 reports are that the order drecton s known, the benchmark prce s the best quote at order recept tme, the tme between order recept and executon s reported, and they provde order volume and executon qualty for all market centers ndvdually. Dash-5 reports have drawbacks as well. For example, they only report aggregate monthly averages. Due to the advantages of Dash-5 reports, several recent academc studes use Dash- 5 data to answer related research questons (see, e.g., Bessembnder (2003), Lpson (2005), and Nguyen, Van Ness, and Van Ness (2005)). The Dash-5 reports provde the most relevant publcly avalable data for our analyss. Our Dash-5 data are from Transacton Audt Group, Inc (www.tagaudt.com). Exchange Act Rule 11Ac1-5 mandates that all markets n the Unted States report order data and regular-way executon data receved for all stock orders of less than 10,000 shares from both ndvdual and nsttutonal nvestors. Dash-5 reports do not nclude any order for whch the customer requests specal handlng, such as orders to be executed at the market openng prce or closng prce, orders submtted wth stop prces, orders to be executed only at ther full sze, orders to be executed on a partcular type of tck or bd, orders submtted on a not held bass, orders for other than regular settlement, and orders to be executed at prces unrelated to the market prce of the securty at the tme of executon. Dash-5 reports provde data by order sze/order type/securty/market center/month/partcpant. The orders are dvded nto four sze categores: 100 to 499 shares, 500 to 1999 shares, 2000 to 4999 shares, and 5000 or greater shares. Order sze can be vewed as a measure of order dffculty. Executons for large orders are generally expected to be more costly than for small orders. Dash 5 reports nclude market orders and marketable lmt orders. We follow Boehmer (2005) and focus on market orders only. As ponted out by Boehmer (2005), results for
An Analyss of Lqudty across Markets 143 marketable lmt orders based on Dash-5 reports are hard to nterpret for at least the followng four reasons. Frst, because Dash 5 reports do not nclude nformaton on the opportunty cost of non-executon, ex post executon costs for marketable lmts understate ther true cost. Consequently, estmates for marketable lmts would not be comparable to those n SEC (2001), whch uses an ex post adjustment for unflled marketable lmts. Ths analyss cannot be replcated usng Dash 5 data, because they nclude only monthly aggregates. Second, the tme-to-executon for ths order type s censored, because cancelled and expred orders are not consdered n the computaton. Thrd, summary statstcs on speed are domnated by orders that happen to be submtted as the market moves away and, therefore, do not execute mmedately. Fnally, usage of marketable lmt orders dffers systematcally across markets. All NYSE specalsts accept market orders, but some Nasdaq market centers do not. For example, some marketable lmts reported by Island, whch does not accept market orders, are probably functonally equvalent to market orders. See Peterson and Srr (2002) for an analyss of the two order types. 2.2. Sample Selecton The Center for Research n Securty Prces (CRSP) database s used to construct the sample of stocks and several control varables based on stock characterstcs, such as prce, volume, shares outstandng, and return. We select NYSE-lsted stocks from the CRSP database. The sample selecton crtera are smlar to those used n SEC (2001). Our Dash-5 data are from January to December 2003. We start wth all the 2,557 NYSE lsted securtes as of December 31, 2002. From ths lst, we elmnated dual classes, foregn-ncorporated securtes, ADRS, REITS, Certfcates, SNIs, Unts, Closed End Funds, etc., leavng us wth 1,329 NYSE common stocks. Ths lst was further reduced to 1,138 NYSE securtes after removng securtes whose daly tradng volume was less than $20,000, whose average closng prce was less than $3, whch swtched exchanges, or whch had mssng data, or for whch data was not avalable n Dash-5 reports. The detaled sample selecton procedure s shown n the Appendx, Table A1. The sample was then merged wth Dash-5 reports data. We further apply a flter to exclude outlers: we exclude orders where the effectve spread or the quoted spread s equal to or larger than half of the tradng prce. In our data, there are 7 NYSE specalst frms and 32 electronc market centers. The lst of market centers are n the Appendx, Table A2. 3. Unvarate Analyss 3.1. Measures of Executon Costs The quoted spread s defned as the bd ask dfference, whch reflects market and order flow condtons at the tme of order arrval. The effectve spread, frst developed by Blume and Goldsten (1992) and Petersen and Falkowsk (1994), s defned, for buy orders, as double the amount of the dfference between the executon prce and the mdpont of the consoldated best bd and offer at the tme of order recept and, for sell orders, as double the amount of dfference between the mdpont of the consoldated best bd and offer at the tme of order
144 Mchael A. Goldsten, Gang Hu and J. Gnger Meng recept and the executon prce. Dash-5 data calculate at a record level, the share-weghted average of effectve spreads for order executons n the month. The realzed spread s defned, for buy orders, as double the amount of dfference between the executon prce and the mdpont of the consoldated best bd and offer fve mnutes after the tme of order executon and, for sell orders, and double the amount of dfference between the mdpont of the consoldated best bd and offer fve mnutes after the tme of order executon and the executon prce. As noted n Blume and Goldsten (1992) and Petersen and Falkowsk (1994), effectve spreads are a better measure of executon costs than quoted spreads, because orders do not always execute exactly at the bd or offer prce. The effectve spread takes ths nto account by ncorporatng any prce mprovement or ds-mprovement that an order may receve. The effectve spread calculates how much above the mdpont prce you pad on a buy order and how much below the mdpont prce you receved on a sell order. Whle prce mprovement s a good tool for measurng executon qualty, effectve spread captures both how often, and also by how much, a broker-dealer prce mproves trades. Therefore, the effectve spread can be nterpreted as the total prce mpact of the trade, a measure of the non-commsson, out-ofpocket cost of a trader. Effectve spreads can be decomposed nto two parts: realzed spread and the nformaton component or prce mpact, whch s the dfference of the bd-ask mdpont fve mnutes later and that at the tme of order recept. The nformaton component can measure the extent to whch nformed and unnformed orders are routed to dfferent market centers. Informed orders are those submtted by persons wth better nformaton than s generally avalable n the market. They therefore represent a substantal rsk to lqudty provders that take the other sde of these nformed trades. In contrast, order submtted by persons wthout an nformaton advantage (often small orders) present less rsk to lqudty provders and n theory should receve the most favorable effectve spreads avalable n the market. The smaller the average realzed spread, the more market prces have moved adversely to the market cent s lqudty provders after the order was executed, whch shrnks the spread realzed by the lqudty provders. In other words, a low average realzed spread ndcates that the market center was provdng lqudty even though prces where movng aganst t for reasons such as news or market volatlty. Spreads are not the perfect measure of tradng costs. However, they are smple to measure, readly avalable, and are usually reasonable ndcators of actual tradng costs. 3.2. Unvarate Results Table 1 presents summary statstcs of executon qualty measures n the two markets, the NYSE and the Electronc Markets. It reports the medan, smple average, as well as shareweghted average (aggregated across all stocks traded at each market over the 12 month perod) of the effectve spread, quoted spread, realzed spread, nformaton component (effectve spread less realzed spread), and executon speed. Statstcs are averaged across all categores and aggregated up to the markets level (ether the NYSE or the Electronc Markets (EM)). Ths method, whle smple, may be dstorted by varatons n executed volume among market centers. Share-weghted average statstcs are also provde to account for share volume dfferences. We also report monthly shares ordered, shares executed, and number of
An Analyss of Lqudty across Markets 145 orders. We further examne the above varables n four order sze categores: very small (100~499 shares), small (500~1,999 shares), medum (2,000~4,999 shares) and large (5,000~9,999 shares).
Table 1. Summary Statstcs Ths table presents summary statstcs from Dash-5 database for the 1,138 selected securtes. Summary statstcs are computed separately for the NYSE and the Electronc Markets (EM), and are further dvded nto four sze categores: very small (100~499 shares), small (500~1,999 shares), medum (2,000~4,999 shares), and large (5,000~9,999 shares). Monthly shares ordered, monthly shares executed, and monthly number of orders are reported n mllons. Average effectve spread (AES), average quoted spread (AQS), average realzed spread (ARS), and average nformaton component (INFO, the dfference of AES and ARS) are reported n cents. Average speed (SPEED) s also reported, n seconds. Medan, mean, and share-weghted mean are reported for the above varables. NYSE Electronc Markets (EM) All Very Small Small Medum Large All Very Small Small Medum Large Shares Ordered (M) 5,517.10 1,620.73 2,188.51 1,150.60 557.27 769.94 185.81 332.42 171.74 79.97 Shares Executed(M) 5,455.13 1,602.38 2,161.68 1,139.94 551.13 743.28 181.71 324.45 163.37 73.74 Number of Orders (M) 11.98 8.83 2.63 0.42 0.09 1.43 0.95 0.40 0.07 0.01 AES (cents) AQS (cents) ARS (cents) INFO (cents) SPEED Medan 3.53 2.39 3.36 6.12 8.76 2.33 1.84 2.33 3.41 2.39 Mean 5.95 2.80 4.70 8.31 11.63 3.94 2.30 3.36 6.13 2.80 Wtd. Mean 3.03 2.38 2.83 3.58 4.59 2.16 1.47 1.85 2.80 2.38 Medan 8.04 6.62 7.57 10.33 13.03 5.04 4.59 5.00 5.98 6.20 Mean 10.81 8.02 9.51 12.96 16.18 9.47 8.31 8.76 11.54 12.39 Wtd. Mean 7.28 6.70 7.16 7.65 8.65 5.88 4.78 5.63 6.74 7.81 Medan 1.00 0.40 0.79 2.04 3.49 1.27 1.20 1.15 1.56 1.95 Mean 2.52 1.09 2.52 2.84 5.11 1.69 1.23 1.25 2.59 3.18 Wtd. Mean 10.40 6.53 20.40 1.07 1.76 1.07 0.97 0.85 1.33 1.73 Medan 2.71 1.97 2.68 3.92 4.57 1.00 0.51 1.11 2.00 2.18 Mean 3.43 1.72 2.18 5.46 6.51 2.25 1.07 2.11 3.54 4.72 Wtd. Mean -7.37-4.14-17.58 2.51 2.82 1.09 0.50 1.00 1.47 2.07 Medan 17.05 14.33 15.51 19.33 23.80 13.21 7.91 12.00 19.70 28.80 Mean 19.43 16.40 17.33 21.41 27.26 31.07 21.73 24.26 38.55 76.50 Wtd. Mean 17.14 16.03 16.61 18.02 20.66 14.37 5.51 9.92 22.88 36.96
An Analyss of Lqudty across Markets 147 NYSE orders seem to have hgher average effectve and quoted spreads. The overall effectve spread reported by the Electronc Markets has a smple mean of 3.94 cents versus 5.95 cents for the NYSE, and a share-weghted mean of 2.16 cents versus 3.03 cents. In addton, the Electronc Markets effectve spread s lower across all four sze categores. One explanaton for why the Electronc Markets can offer lower effectve spreads than the NYSE for the same NYSE stocks s that the Electronc Markets compete and attract easy orders. Ths selecton bas could cause the dfference n effectve spreads. Before formally accountng for ths selecton bas n a multvarate selecton model framework, we frst sort the data on quoted spread, an mportant varable snce t reflects the market condton at the tme of the order. We segment the data nto 8 ranges of quoted spread. Then we calculate the share-weghted effectve spread for all the NYSE records n each of the 8 quoted spread ranges. We do the same for all records n the Electronc Markets. The results are shown n Table 2. The Electronc Markets offer lower average effectve spreads n 7 out of the 8 ranges of quoted spreads. The NYSE only offers margnally lower effectve spreads n the lowest quoted spread range (0~4 cents), 1.17 cent for the NYSE versus 1.23 for the Electronc Markets. Note that ths range also contans relatvely less number of symbols and shares executed. In summary, results n Table 2 suggest that the Electronc Markets seem to be able to offer lower effectve spreads than the NYSE even after controllng for the dfferences n quoted spreads across these two markets. Table 2. Quoted Spread Bns Ths table presents results by splttng the data accordng to quoted spread bns. The number of symbols, shares executed n mllons, and share-weghted effectve spreads n each range for the NYSE versus the Electronc Markets (EM) are reported. Number of Symbols Shares Executed (M) AES (cents) Quoted Spread NYSE EM NYSE EM NYSE EM 0~4 cents 16 39 4,800 2,695 1.17 1.23 4~6 cents 130 212 17,053 3,318 1.94 1.74 6~8 cents 276 228 23,871 1,556 2.82 2.53 8~10 cents 260 204 10,850 701 3.90 3.69 10~12 cents 181 126 5,642 220 4.91 4.73 12~14 cents 114 108 2,221 180 6.14 5.09 14~16 cents 59 80 614 130 7.29 5.54 >= 16 cents 102 141 423 132 10.07 7.72 4. Regresson and Selecton Model Analyss 4.1. Factors Affectng Executon Costs We consder a wde range of varables explanng executon costs based on related mcrostructure lterature. Many of these varables have been used n one or more of prevous studes, such as Bessembnder (2003), Boehmer (2005), Lpson (2005), and Nguyen, Van
148 Mchael A. Goldsten, Gang Hu and J. Gnger Meng Ness, and Van Ness (2005). Some of these varables are cost-based, whle others are only reflectve. For example, the quoted spread drectly represents the fnancal loss a trader ncurs from a partcular transacton. On the other hand, though the tradng volume ndcates whether a partcular stock s lqud or not, t does not show us how costly t s to actually trade the stock. The explanatory varables can be classfed nto two groups: order-specfc measures and stock-specfc measures. Order-specfc measures capture the nature and dffculty of dfferent orders, whle stock-specfc measures capture the characterstcs of stocks traded and are the same across dfferent orders wthn the same stock. We further dvde the stockspecfc measures nto lqudty measures and volatlty measures. The detaled defntons of these varables are as follows: Order-specfc Measures: Log(num.ord): The natural logarthm of the number of orders. AQS: Average quoted spread. Ths varable s ncluded as a measure of market condtons at order tme. It can be vewed as a cost-based lqudty measure because t examnes the fnancal loss a trader ncurs from a partcular transacton. It s hghly correlated wth the average effectve spread. INFO: It s defned as the dfference between the effectve spread and the realzed spread. Therefore t s the mrror mage of realzed spread. The smaller the average realzed spread, the more market prces have moved adversely to the market center's lqudty provders after the order was executed, whch shrnks the spread "realzed" by the lqudty provders. In other words, a low average realzed spread ndcates that the market center was provdng lqudty even though prces were movng aganst t for reasons such as news or market volatlty. SPEED: Another dmenson of executon qualty measures beyond tradng costs. There s a trade-off between the urgency and the absolute cost. Therefore one would expect that the faster the speed, the hgher the cost. SEC (2001) used a fve-day perod n June and found that for smaller orders (orders below 5,000 shares), the NYSE executon costs are below NASDAQ costs, but NASDAQ orders generally execute faster. Boehmer (2005) extended ths part of study and found that small orders (below 2,000 shares) execute at lower cost on the NYSE, but substantally faster on NASDAQ. However ths results reverses for larger orders (between 2,000 and 9,999 shares). These execute more cheaply on NASDAQ, but faster on the NYSE. Log(Ord.Sz) and Ord.Sz/Vol: Ord.Sz/Vol s the standardzed order sze, calculated as the order sze for the securty at the specfc markets, versus ts total tradng volume n the last month of 2002. It s ntutve that larger orders should be more dffcult to execute (due to pure lqudty reasons, regardless of nformaton content) and also should contan more nformaton. We expect both reasons to cause a postve relatonshp between order sze and the effectve spread. Boehmer (2005) descrbes a specfc example for why larger NYSE orders should contan more nformaton. He reasons that traders who have ether no prvate nformaton or whose nformaton s suffcently long-lved often use floor brokers to work large orders. Ths nvolves delegatng control over the actual tradng decsons to a floor broker, who then seeks favorable (partal) executons untl the order s flled. An nformed trader wth short-lved nformaton cannot afford to use ths opton because t s slow, and the trader rsks that others dscover the same nformaton before the orders are flled. For the
An Analyss of Lqudty across Markets 149 same reason, small NYSE orders are not useful for nformed traders because they are executed sequentally. One would thus expect nformed traders (or ther agents) to submt large orders drectly to the specalst. Stock-specfc Measures: Lqudty measures: Illqudty reflects the mpact of order flow on prce: the dscount that a seller concedes or the premum that a buyer pays when executng a market order, whch results from adverse selecton costs and nventory costs. MCAP and MCAP Rank: MCAP s the market captalzaton, calculated as the product of prce and shares outstandng. MCAP Rank s the market captalzaton rank (1~20) based on Fama-French NYSE Breakponts. They are common proxes for lqudty snce a larger stock ssue has smaller prce mpact for a gven order flow and a smaller bd ask spread: large frms are more lqud. 1/PRC: The nverse of prce. The hgher ths factor, the more lqud the order. Turnover: The volume n the stock dvded by the number of shares outstandng. ADV: Average dollar volume (prce tmes share volume) n the fourth quarter of 2002. Hgh volume levels may ndcate that a partcular securty s very lqud. However, t does not tell us how costly t s to actually trade the securty. CBMA: Gbbs estmate of transacton cost, c, from Basc Market-Adjusted Model from Hasbrouck (2006). It s a daly lqudty proxy. cov( rt, rt 1) f cov( rt, rt 1) 0 CBMA = < 0 otherwse. (1) I1: Amhud s (2002) llqudty measure, calculated as the average daly rato over year of the absolute value of daly return dvded by the daly tradng volume n mllons of dollars. abs( ret) I1 = 1,000,000. (2) prc vol As can be seen from the above defnton, Amhud s llqudty measure can be nterpreted as the daly prce response (senstvty) assocated wth one dollar of tradng volume, thus servng as a rough measure of prce mpact. Amhud (2002) shows that llqud stocks are more dffcult to trade. We expect orders n more llqud stocks more lkely to be submtted to NYSE rather than the Electronc markets. PSGAMMA: Pastor-Stambaugh (2003) gamma. However, the authors cauton aganst ts use as a lqudty measure for ndvdual securtes, notng the large sample error n the ndvdual estmates. Volatlty Measures:
150 Mchael A. Goldsten, Gang Hu and J. Gnger Meng VOLA: The standard devaton of daly returns n the fourth quarter of 2002. The specfcaton of ths varable s slghtly dfferent n other papers. For example, Lpson (2005) defnes t as the standard devaton of daly trade-weghted prces.
Table 3. OLS Regressons Ths table presents OLS regresson results. The dependent varable s average effectve spread (AES). NYSE s a dummy varable that equals 1 for orders executed by the NYSE and 0 otherwse. EM s a dummy varable that equals 1 for orders executed by the Electronc Markets and 0 otherwse. There s no ntercept term snce both NYSE and EM are ncluded n the regresson. NYSE EM Log(NUM.ORD) INFO 1/PRC ORD.SZ/VOL SPEED ADV TURNOVER MCAP.RANK VOLA RR R 2 α 1 α 2 α 3 α 4 α 5 α 6 α 7 α 8 α 9 α 10 α 11 α 12 Model 1 7.65 4.92 70.45% (t-stat) 59.20 *** 37.26 *** Model 2 7.68 5.66-0.55 76.19-15.04 7.86 95.15% (t-stat) 99.61 *** 66.39 *** -14.77 *** 52.23 *** -14.72 *** 13.06 *** Model 3 7.70 5.65-0.54 76.03-15.05 7.85 0.01 95.12% (t-stat) 96.47 *** 65.92 *** -14.60 *** 51.80 *** -14.73 *** 13.04 *** 0.97 Model 4 7.24 6.03-0.20 72.75-21.69 7.67 0.01 0.01-21.17-0.14 95.26% (t-stat) 68.86 *** 57.08 *** -3.23 *** 47.61 *** -16.28 *** 12.49 *** 0.48-0.09-2.75 *** -7.87 *** Model 5 7.26 6.01-0.22 72.69-22.09 7.78 0.01 0.01-19.28-0.13-10.38 10.03 95.27% (t-stat) 67.68 *** 55.7.9 *** -3.37 *** 47.18 *** -12.92 *** 12.10 *** 0.51 0.04-2.14 ** -7.73 *** -1.25 1.17 Model 6 7.23 6.04-0.20 72.89-21.30 7.63-18.83-0.14-2.21 95.26% (t-stat) 76.27 *** 62.26 *** -3.60 *** 47.61 *** -13.69 *** 12.39 *** -2.10 ** -7.92 *** -0.49
152 Mchael A. Goldsten, Gang Hu and J. Gnger Meng RR: The average daly relatve prce range durng the fourth quarter of 2002. Daly relatve prce range s defned as the daly range dvded by the closng prce. Ths s an ntraday measure. Compare to the other volatlty measure VOLA, RR does not rely on statonary assumptons over the perod of tme needed to calculaton VOLA. 4.2. OLS Regressons The OLS regresson method s specfed n the followng model, across dfferent stocks: AES = α NYSE + α NON. NYSE + α X + e, (3) p 1 p 2 p 3 p p where AES p s the mean effectve spread for stocks at market p, p ( N, EM). NYSE p s a dummy varable whch equals one f the market s N, zero f the market s EM. NON.NYSE p s another dummy varable whch equals zero f the market s N, and one f the market s EM. X p s a vector of explanatory varables selected from the lst of varables dscussed prevously. All X p are measured as devatons from ther own sample cross-sectonal mean. Ths way, when the X p are excluded from the regresson, the coeffcents estmates α 1 and α 2 produce the smple cross-sectonal mean effectve spreads of the two markets. When the control varables X p are ncluded n the regresson, the coeffcent estmates on the two dummy varables reveal condtonal mean executon costs on the NYSE versus the Electronc Markets, evaluated at the mean of the varables that comprse the X p vector. We start our OLS regresson analyss wth specfcatons smlar to Bessembnder (2003), and then add other potentally related factors dscussed prevously. The results are shown n Table 3. We run dfferent specfcatons of the followng regresson model: AES = α NYSE + α EM + α log( NUM. ORD ) + α INFO p 1 p 2 p 3 4 p 1 ORD. SZ + α + α + α SPEED + α ADV + α TURNOVER p 5 6 7 p 8 9 PRC VOL + α MCAP. RANK + α VOLA + α RR + e 10 11 12 p. (4) We start by runnng an OLS regresson on the two dummy varables: one for the NYSE and one for the Electronc Markets (therefore there s no ntercept term). The coeffcents on the two dummy varables represent the uncondtonal cross-sectonal smple averages for these two markets. Specfcally, the effectve spread s 7.65 cents for the NYSE and 4.92 cents for the Electronc Markets. In other words, the effectve spread for the Electronc Markets s 2.73 cents (or 36%) lower than the NYSE. In the second model, we add four control varables, as n Bessembnder (2003): logarthm of number of orders, nformaton component, nverse prce, and standardzed order sze. We note three thngs here: frst, after addng these control varables, the effectve spread for the NYSE almost reman unchanged, at 7.68 cents. On the other hand, the effectve spread for the Electronc Markets ncreases dramatcally, from 4.92 cents to 5.66 cents, causng the dfference between the two markets to narrow to 2.02 cents (or 26%). Ths means that the
An Analyss of Lqudty across Markets 153 Electronc Markets receved relatvely easer orders than dd the NYSE, hence controllng for dffculty reduces the cost advantage shown by uncondtonal results. These results hghlght the mportance of controllng for the relatve dffculty of the orders receved by dfferent markets before drawng nferences. Second, the slope coeffcents are generally consstent wth those reported n pror research (see, e.g., Bessembnder (2003)). The average effectve spread decreases wth the tradng actvty as measured by total orders n the stock, ncreases wth average nformaton component, decreases wth the nverse share prce (or ncrease wth share prce), and ncreases wth average order sze. Each coeffcent estmate s hghly sgnfcant. Thrd, the R 2 ncreases to 95.15% from the frst regresson s 70.45%. In the thrd model, we further add SPEED to the regresson. Though t s consdered to be the other mportant dmenson of executon qualty, t does not seem to have margnal explanatory power for effectve spread. The coeffcent for SPEED s not sgnfcantly dfferent from zero. The coeffcents for the two dummy varables and the R 2 reman almost unchanged. In the fourth model we further add ADV, TURNOVER, and MCAP.RANK, tryng to capture effects of llqudty on effectve spreads. Coeffcents on TURNOVER and MCAP.RANK are sgnfcant and negatve, whch s ntutve. Hgh turnover and large market cap securtes are more lqud, and therefore should have lower executon costs. The coeffcent on ADV s not sgnfcant. The condtonal mean effectve spread for the NYSE decreases to 7.24 cents, whle that for the Electronc Markets ncreases to 6.03 cents. The ffth model s the full specfcaton. We further add two volatlty varables VOLA and RR. Nether of them turns out to be sgnfcant. The condtonal effectve spreads for the NYSE and the Electronc Markets are almost unchanged. The sxth model s our selected model, chosen manly based on the statstcal sgnfcance of dfferent factors n prevous models. It ncludes market condton factors such as number of orders, order sze; and nformaton component, securty llqudty proxes such as prce, turnover, and market cap rank, and a volatlty measure, VOLA (though t s the only nsgnfcant factor). The condtonal mean effectve spread for the NYSE s 7.23 cents, versus 6.04 cents for the Electronc Markets, whch represents a dfference of 1.19 cents or 16%. Overall, our OLS regresson results show that controllng for the above factors narrows the dfference n condtonal mean effectve spread for the NYSE versus the Electronc Markets. However, the Electronc Markets stll outperform the NYSE. 4.3. Two-Stage Selecton Model The two-stage procedure to control for selecton bas follows the work by Heckman (1979) and Maddala (1983). Effectve spreads are modeled for the NYSE (N) and the Electronc Markets (EM) as: ES ES = β ' X + ε, N, N N, = β ' X + ε, EM, EM EM, (5) where X s a vector of condtonng varables for each securty, β s a vector of parameters to be estmated, and the ε s are error terms. We assume the dfference n effectve spreads
154 Mchael A. Goldsten, Gang Hu and J. Gnger Meng across the two markets s a factor that determnes the market selected by a trader for that stock. The dfference n expected effectve spreads s y* = E ES, N ES, EM X = β β X + ε ε ( ' ') N EM, N, EM = γ ' X + ζ. (6) In ths model, a trader of stock chooses to trade the order n the NYSE f y* 0,.e., the NYSE trade s expected to be less costly. The order submsson rule for a securty a traders wshes to trade s y = 1, f y* 0; y = 0, f y* > 0; (7) wth y = 1 ndcates the NYSE and y = 0 ndcates the Electronc Markets. We wll use several ndependent varables dscussed prevously to model the choce whch market to choose from n a Probt framework. Then, the probablty a trader chooses the NYSE s estmated, whch s, Pr( y = 1) =Φ ( γ ' X ), (8) where Φ s the cumulatve dstrbuton functon of the standard normal. The next step s to multply the parameter estmates from the Probt, γ, wth the complementary set of observatons, X, to estmate the probablty of choosng the NYSE (Φ(γ X)). In the second stage of ths method, the Probt probablty estmates are used to control for the selecton bas. Because an stock s traded on the NYSE only when y* 0, the error term ε,n does not have a zero mean, condtonal on beng NYSE. The condtonal expected executon costs for the NYSE and the Electronc Markets are denoted as: φ( γ ' X ) E ESN, y* 0 = βn' X+ αn, Φ( γ ' X ) φγ ( ' X ) E ESEM, y* > 0 = βem' X+ αem ; 1 Φ( γ ' X ) (9) where φ( γ ' X ) and Φ( γ ' X ) are the densty and cumulatve dstrbuton functon of the standard normal evaluated at γ ' X, respectvely. α = cov( ε, ζ ). In ths methodology, estmatng the second stage equaton by OLS provdes consstent estmates of the parameters. φ( γ ' X ) λ 1 = s the Inverse Mlls Rato. It s monotoncally decreasng n the Φ( γ ' X ) φ( γ ' X ) probablty that an order wll be routed to the NYSE. λ2 =. The Heckman 1 Φ ( γ ' X )
An Analyss of Lqudty across Markets 155 method can detect the selecton bas n a rather straghtforward fashon. Potentally, the parameters from the Heckman method can also be used to examne the trade-offs n the market selecton strateges. 4.4. Selecton Model Results The full specfcaton for the frst stage Probt regresson s as follows: Pr( NYSE = 1) = g( β + β log( MCAP) + β log( VOL ) + β log( ORD. SZ ) p 0 1 2 3 p + β Info + β AQS + β SPEED + β RR + βvola + β CBMA + β I1 4 p 5 p 6 p 7 8 9 10 + β PSGAMMA + ε ) 11 p (10) In the second stage OLS regresson correctng for selecton bas, we use the full model and the model selected prevously. The specfcaton of the full model s as follows: AES = α NYSE + α EM + α ( λ NYSE ) + α ( λ EM ) p 1 p 2 p 3 1 p 4 2 p 1 ORD. SZp + α log( NUM. ORD ) + α INFO + α + α + α SPEED VOL 5 6 p 7 8 PRC + α ADV + α TURNOVER + α MCAP. RANK + α VOLA + α RR + e 10 11 12 13 14 9 p p (11) In the lterature there appears to be some nconsstency as to whether only λ 1, or both λ 1 and λ 2 should be ncluded n the second stage regresson. We dd both. To adapt to our specfc model where the two parts of sample (the NYSE and the Electronc Markets) are combned nto one model, ndcated by two dummy varables, we create two new varables λ 1 NYSE and λ 2 EM. Note that these two varables are hghly correlated wth each other. Table 4 Panel A presents frst stage Probt regresson results. We start wth a model smlar to that n Bessembnder (2003). The ndependent varables nclude market captalzaton, order volume, order sze, nformaton component, and quoted spread. All coeffcents are sgnfcant at least at the 95% level, confrmng the presence of systematc selecton bases n order routng. The coeffcent on order volume s sgnfcantly negatve, ndcatng that actvely traded stocks are more lkely to be executed n the Electronc Markets. Coeffcents on market captalzaton, order sze, nformaton component, and quoted spread are all sgnfcantly postve, suggestng that orders for larger stocks, wth larger order szes, contanng more nformaton, and wth worse market condton, tend to be executed on the NYSE. We then further add varables ncludng SPEED, RR, VOLA, CBMA, I1 and PSGAMMA to the Probt model. These varables comprse volatlty measures and llqudty measures. Out of those new varables, the coeffcents on SPEED, RR, VOLA, and CBMA are all sgnfcant at the 99% level, and PSGAMMA s sgnfcant at the 95% level. Interestngly, many of these same varables have shown lttle explanatory power n prevous OLS regressons on effectve spreads. One explanaton s that these factors affect order routng decsons rather than executon costs drectly.
Table 4. Two-Stage Selecton Model Ths table presents selecton model results. Panel A presents the frst stage Probt regressons for the lkelhood of an order beng executed by the NYSE. Panel B presents the second stage OLS regresson of condtonal average effectve spreads. Panel A. Frst Stage Probt Regressons for the Lkelhood of an Order Beng Executed by the NYSE Log (MCAP) Log (VOL) Log (ORD.SZ) INFO AQS SPEED RR VOLA CBMA I1 PSGAMMA β 1 β 2 β 3 β 4 β 5 β 6 β 7 β 8 β 9 β 10 β 11 Pseudo R 2 Prob > χ 2 Model 1 1.04-2.29 16.99 28.56 6.67 89.57% 0.00 (z-stat) 6.87 *** -10.17 *** 17.45 *** 8.57 *** 2.34 ** Model 2 0.90-2.32 18.94 32.03 9.82-0.10-49.07 54.19-117.63 3.58-56665.03 93.10% 0.00 (z-stat) 3.14 *** -6.07 *** 12.79 *** 7.95 *** 2.62 *** -8.23 *** -2.24 *** 2.59 *** -2.39 *** 1.59-2.01 ** Panel B. Second Stage OLS Regressons of Condtonal Average Effectve Spreads NYSE EM λ 1 NYSE λ 2 EM Log(NUM. ORD) INFO 1/PRC ORD.SZ /VOL SPEED ADV TURNOVER MCAP. RANK VOLA RR R2 α 1 α 2 α 3 α 4 α 5 α 6 α 7 α 8 α 9 α 10 α 11 α 12 α 13 α 14 Model 1 7.14 4.92-0.74-0.02 72.42% (t-stat) 57.42 *** 39.68 *** -1.72 * -0.05 Model 2 7.75 4.92-1.32 70.56% (t-stat) 57.86 *** 37.32 *** -2.78 *** Model 3 7.08 4.92-0.02 72.38% (t-stat) 59.22 *** 39.66 *** -0.05 Model 4 7.25 6.02 0.11-0.22 72.82-22.09 7.74 0.01 0.01-19.66-0.13-10.42 10.01 95.27% (t-stat) 65.80 *** 55.71 *** 0.54-3.31 *** 46.75 *** -12.92 *** 11.94 *** 0.53 0.01-2.18 ** -7.74 *** -1.26 1.17 Model 5 7.22 6.04 0.10-0.20 73.01-21.30 7.59-19.18-0.14-2.27 95.26% (t-stat) 74.01 *** 62.21 *** 0.52-3.56 *** 47.16 *** -13.69 *** 12.20 *** -2.13 ** -7.93 *** -0.50
Table 5. OLS Regressons for Two Order Dffculty Sub-Samples Ths table presents OLS regresson results for the two order dffculty sub-samples. Panels A and B present results for easy and dffcult orders respectvely, where order dffculty s defned by the ftted value usng the model for the whole sample. Panel A. Sub-Sample of Easy Orders NYSE EM Log(NUM.ORD) INFO 1/PRC ORD.SZ/VOL TURNOVER MCAP.RANK VOLA R 2 α 1 α 2 α 3 α 4 α 5 α 6 α 9 α 10 α 11 Model 1 3.70 3.11 82.74% (t-stat) 51.08 *** 48.01 *** Model 2 3.82 3.01-0.18 46.87-16.35 29.34 23.96-0.04-2.60 90.84% (t-stat) 41.56 *** 39.23 *** -3.37 *** 14.55 *** -10.76 *** 10.49 *** 2.83 ** -2.00 ** -0.63 Panel B. Sub-Sample of Dffcult Orders NYSE EM Log(NUM.ORD) INFO 1/PRC ORD.SZ/VOL TURNOVER MCAP.RANK VOLA R 2 α 1 α 2 α 3 Α 4 α 5 α 6 α 9 α 10 α 11 Model 1 10.70 7.29 84.63% (t-stat) 64.88 *** 39.87 *** Model 2 6.59 4.52-0.33 70.49-28.62 6.04-56.98-0.15-4.51 96.18% (t-stat) 30.02 *** 19.50 *** -2.94 *** 31.59 *** -9.52 *** 6.89 *** -3.30 *** -5.40 *** -0.54
Table 6. Two-Stage Selecton Model for Two Order Dffculty Sub-Samples Ths table presents selecton model results for the two order dffculty sub-samples. Panels A and B present results for easy and dffcult orders respectvely, where order dffculty s defned by the ftted value usng the model for the whole sample. Log (MCAP) Panel A. Sub-Sample of Easy Orders Frst Stage Probt Regressons for the Lkelhood of an Order Beng Executed by the NYSE Log (VOL) Log (ORD.SZ) INFO AQS SPEED RR VOLA CBMA I1 PSGAMMA β 1 β 2 β 3 β 4 β 5 β 6 β 7 β 8 β 9 β 10 β 11 Pseudo R 2 Prob > χ 2 2.29-5.04 45.60 32.85 23.98-0.11-68.14 75.07 50.94 10.59-112142 95.82% 0.00 (z-stat) 3.32 *** -4.95 *** 5.70 *** 2.46 *** 1.82 * -3.78 *** -1.35 1.64 * 0.46 1.25-1.01 Second Stage OLS Regressons of Condtonal Average Effectve Spreads NYSE EM λ 1 NYSE Log(NUM. ORD) INFO 1/PRC ORD.SZ TURNOVER MCAP. /VOL RANK VOLA R2 α 1 α 2 α 3 α 5 α 6 α 7 α 8 α 11 α 12 α 13 Model 1 3.69 3.10 0.02 82.73% (t-stat) 49.48 *** 47.83 *** 0.04 Model 2 3.79 3.01 0.51-0.18 0.48-16.21 29.68 24.50-0.04-2.70 90.85% (t-stat) 40.75 *** 39.28 *** 1.48-3.29 *** 14.70 *** -10.67 *** 10.60 *** 2.90 *** -1.83 * -0.66
Log (MCAP) Panel B. Sub-Sample of Dffcult Orders Frst Stage Probt Regressons for the Lkelhood of an Order Beng Executed by the NYSE Log (VOL) Log (ORD.SZ) INFO AQS SPEED RR VOLA CBMA I1 PSGAMMA β 1 β 2 β 3 β 4 β 5 β 6 β 7 β 8 β 9 β 10 β 11 Pseudo R 2 Prob > χ 2 0.67% -1.87 14.12 26.46 4.39-0.06-104.25 91.97-82.22 0.49-37041.59 94.40% 0.00 (z-stat) 1.06-2.14 ** 7.05 *** 4.22 *** 0.68-4.36 *** -2.38 ** 2.20 ** -1.30 0.18-1.24 Second Stage OLS Regressons of Condtonal Average Effectve Spreads NYSE EM λ 1 NYSE Log(NUM. ORD) INFO 1/PRC ORD.SZ /VOL TURNOVER MCAP. RANK VOLA R2 α 1 α 2 α 3 α 5 α 6 α 7 Α 8 α 11 α 12 α 13 Model 1 10.71 7.29-0.31 84.63% (t-stat) 63.32 *** 37.85 *** -0.30 Model 2 6.63 4.50-0.47-0.35 70.36-28.56 6.04-55.27-0.15-4.82 96.18% (t-stat) 29.58 *** 19.37 *** -0.90-3.03 *** 31.45 *** -9.50 *** 6.88 *** -3.18 *** -5.41 *** -0.58
160 Mchael A. Goldsten, Gang Hu and J. Gnger Meng Table 4 Panel B presents the second stage OLS regressons. When both λ 1 NYSE and λ 2 EM are added to the model n addton to the two dummy varables, the coeffcent on λ 1 NYSE s sgnfcant only at the 90% level, whle the coeffcent on λ 2 EM s not sgnfcant. Ths could be because the two constructed varables are hghly correlated. So we also nclude λ 1 NYSE and λ 2 EM separately n second and thrd model. λ 1 NYSE becomes more sgnfcant, but λ 2 EM s stll not sgnfcant. In the fourth and ffth models, we nclude λ 1 NYSE (the Probt factor) and other control varables. The Probt factor becomes nsgnfcant. It s probably because that the constructed varable s closely lnked to varables that are known to affect executon costs, therefore contan smlar nformaton. Ths s consstent wth Bessembnder s (2003) fndng that OLS regressons seem to do a good job at controllng for order dffculty, and selecton models do not seem add ncremental explanatory power. To summarze results obtaned so far, uncondtonal mean effectve spread s hgher for the NYSE than the Electronc Markets. Controllng for stock and order characterstcs n multvarate OLS regressons decreases ths dfference, though the NYSE stll has sgnfcantly hgher condtonal effectve spread than the Electronc Markets. Selecton models do not sgnfcantly change OLS regresson results. 5. Dffculty Sub-Sample Analyss Snce the above analyss only examnes the executon cost at the n-sample mean ponts, t s worthwhle to conduct analyss for the two markets at other dffculty levels. One mght thnk that the mpact of dfferent dmensons of dffculty may change dependng on the levels of dffcultes. One mght also expect that the selecton effect could be stronger among more dffcult orders. In order to do ths, we calculate the ftted value based on our selected model α X wthout ntercept. These ftted values are estmates of order dffculty. We then sort our sample accordng to ths order dffculty measure and splt our sample to two sub-samples. The OLS analyss and selecton model analyss are reproduced for each dffculty sub-sample. Table 5 presents OLS results for the two dffculty sub-samples. Panel A s for the subsample of easy orders, whle Panel B s for the sub-sample of dffcult orders, accordng to our dffculty measure α X. We note some nterestng results here: (1) More dffcult orders show a greater cost decrease n mean effectve spreads condtonally (after ncludng varous factors n the regresson) versus uncondtonally. The NYSE condtonal mean effectve spread dropped 38.41%, from uncondtonal mean of 10.70 cents to condtonal mean of 6.59 cents. The Electronc Markets mean effectve spread dropped a smlar 38.00%, from uncondtonal mean of 7.29 cents to condtonal mean of 4.52 cents. On the other hand, the condtonal means of effectve spreads for easy orders do not change as much. (2) For easy orders, the condtonal effectve spread dfference on and off the NYSE s wder than the uncondtonal means. It means that ncludng demeaned explanatory varables ncreases dvergence. Ths result s n contrast to the common concepton that easer orders are more often sent to the Electronc Markets. (3) For dffcult orders, the condtonal effectve spread dfference on and off the NYSE s narrower, whch confrms the NYSE s asserton that they receve more dffcult orders. (4) For dffcult order sub-sample, turnover has a negatve correlaton wth the effectve spread, meanng that hgh volume orders are charged wth lower costs. However, for easy orders,