КОНСОРЦИУМ ЭКОНОМИЧЕСКИХ ИССЛЕДОВАНИЙ И ОБРАЗОВАНИЯ - РОССИЯ И СНГ ECOOMICS EDUCATIO AD RESEARCH COSORTIUM RUSSIA AD CIS G. Kolodyazhny and A. Medvedev Microsrucure of Russian sock marke and rofiabiliy of marke making Final reor 2002
Absrac In his aer we sudy wo differen issues relaed o he microsrucure of Russian sock marke: rofiabiliy of marke making (major one) and relaionshi beween brokers and heir cliens. We use daa on all he ransacions in Moscow Inerbank Currency Exchange or a eriod of more hen one year. Our main conclusion is ha here are no cosless ooruniies o ge beer chances of rofiing by engaging in marke making. We also found saisically significan relaionshi beween marke aciviy of differen cusomers of he same broker as comared o oher aricians. We suosed ha yical financial firm ends o hide is invesmens by carrying ou marke aciviy via affiliaed comanies, which naurally become is cusomers. Inroducion This aer focuses on he microsrucure of Russian sock marke. The research was iniially moivaed by he availabiliy of high frequency daa ha auhors colleced while working in he Cenral Bank of Russian Federaion. Our daa cover all he ransacions ha were carried ou in he leading Moscow sock exchange (MICEX) over a eriod of more hen one year. I would be cerainly imossible wihin one rojec o ake full use of he unique informaion we ossess, so we focused on he issues ha have no been exensively sudied in he emirical lieraure so far. Russian sock marke is raher narrow financial marke wih one securiy srongly dominaing he ohers in rade volume. This securiy, which is he common share of Russian energy monoolis RAO UES, accouns for abou 85% of all ransacions in MICEX. This makes he daa even more aracive since acual marke resembles single securiy marke widely assumed in heoreical modeling and measuremen issues become less roblemaic. Firs issue ha we sudy in he aer and which is he major one is funcioning of marke makers. In he heoreical lieraure on marke microsrucure i is common o assume ha marke makers comee and do no receive excess rofis from heir aciviy. This is quesionable if we hink of realiy. In his aer we analyze he rofi ooruniies of marke makers in MICEX. Our main conclusion is ha here are no cosless ooruniies o ge beer chances of rofiing by engaging in marke making in MICEX. Anoher issue ha we ouch uon in he aer is he relaionshi beween brokers and heir cliens. This is searae issue, which is no relaed o he firs one, bu ineresing on is own. The fac ha, on average, a broker acs on behalf of only abou 9 cliens during rading session suggess ha mos brokers are no exacly brokers in a sense ha hey erform brokerage services for mulile cliens. We found saisically significan relaionshi beween marke aciviy of differen cusomers of he same broker as comared o
cusomers of oher brokers. This oins ou o exisence of he relaionshi beween broker and heir cliens. We concluded ha yical financial firm ends o hide is invesmens by carrying ou marke aciviy via affiliaed comanies, which naurally become is cusomers. The res of he aer is organized as follows. In he nex secion we give a brief focused descriion of he lieraure on marke microsrucure. Then we rovide a descriion of daabase we have and he way i was consruced. We also rovide useful comarison of sock exchanges and shares raded, which seems o be ineresing er se. Then we resen some reliminary observaions and he emirical analysis of he rofiabiliy of marke making. Finally, we describe he resuls of he es on he relaionshi beween brokers and heir cliens. Marke microsrucure: a brief review of he lieraure Sudy of marke microsrucure is an aem o look inside he black box of rice formaion. Tradiional aroach in economics is o assume ha markes are cleared. The way he equilibrium is achieved is negleced and he main focus is on he equilibrium quaniies. Marke microsrucure lieraure is concerned wih he rocess of rading, behavior of raders and imlicaions. ice review of he lieraure is given in he book O Hara (995) and here we give a brief accoun of he main feaures wih he aim o rovide a icure of academic view on he funcioning of he financial markes. The erminology used in he lieraure is no uniform and varies across aers. everheless, we can rovide some commonly used definiions. A dealer is a marke arician who acs (rades) on his own. A broker is a marke arician who acs on behalf of is cusomers. Broker can also be dealer ha is he can rade wih his own money. A marke maker or secialis is a marke arician who inermediaes beween buyers and sellers. Marke makers rovide bid/ask quoes on raded asses and by doing his hey mainain he liquidiy of he marke. One of imoran uroses of marke makers is o solve he roblem of ime mismaching beween order flows. Marke makers can be assigned official saus like in he case of Russian T-bills marke, where only seleced number of dealers were echnically able o se long-sanding sell and buy orders. Such a marke is called secialis marke. Each ransacion involved a marke maker as a couner ary. Alernaively, a marke can be organized in such a way ha every dealer can se orders ha are recorded in he order book if no immediaely execued. In such a marke, rading occurs as a resul of maching of sell and buy order
flows wihou involving redeermined marke makers. Russian sock exchanges are examles of his ye of he marke. Alhough here is no marke makers de juro, hey exis de faco. These are hose marke aricians ha acively rade in he marke having on average no long and shor osiions in raded securiies. Glosen and Milgrom (985), Easley and O Hara (987) were among firs who rovided realisic models of marke makers behavior. These models belong o so called informaion-based models of marke microsrucure. The main feaure of heses models is he exisence of informed and uninformed (liquidiy) raders. If marke maker rades agains informed rader hen he loses. This loss should be comensaed by gains from rades wih uninformed raders. Marke maker knows ha some share of aggregae buy/sell flows is generaed by informed invesors. The oher share is due o uninformed raders who may rade, for examle, for liquidiy reasons (no relaed o fundamenal informaion). This allows him o learn some fundamenal informaion from he aggregae order flow he observes. Kyle (985) furher enriched he model by allowing informed raders o fully exlore heir advanage. The model hen akes form of sraegic game beween marke makers and informed invesors. Theoreical models of marke making assume ha marke makers make zero execed rofi (under risk neuraliy) due o comeiion. In his aer we will be mainly concerned wih evaluaing rofiabiliy of marke making in he leading Moscow sock exchange. Daa Our daabase covers all he ransacions ha were being execued in Moscow Inerbank Foreign Exchange (MICEX) beween Augus 4, 2000 and Ocober 24, 200. I conains slighly less hen 6 million rows and has he size of 825 MB. Before we go over o he descriion of he daabase we resen a brief descriion of Russian sock marke and he role of MICEX. Russian sock marke is divided ino organized and unorganized segmens, and also ADR marke. Organized marke consiss of a number of sock exchanges, of which wo of hem (RTS and MICEX) accoun for more hen 95% of oal rade urnover. The share of RTS has been seadily declining during recen ime for several reasons. Currenly MICEX accouns for almos 85% of rade urnover in he organized marke. The oal value of ransacions carried ou in MICEX reached RUR 72bn (USD 7bn) in 2000, which is six imes as much as in 999.
The leading osiion of MICEX is o a large exen due o echnological advanages ha enable members of he exchange o esablish remoe rading desks for heir cliens. By he mid of 200 abou 30 brokers esablished remoe rading desks and he share of rades made via Inerne has already reached 40% in money value and 60% in unis. I is cerain ha MICEX is a leader in he organized marke wih maximum number of ransacions (u o 55 000 a day) and ha he larges share of domesic and foreign invesors rade in MICEX. The asse srucure is also fairly non-uniform. The unambiguous leaders are common shares of RAO UES he energy monoolis, which accouns for more hen 80% of rade urnover (see able ). Leading Russian oil comany Lukoil holds only 5% of marke urnover. Table. Leading socks: urnover srucure RAO UES Lukoil Surgunefegaz Roselecom Sberbank 2000 January 82.2.8.22 0.39 3.94 February 8.2 8.36 0.66.2 2.99 March 76.82 8.5.26.8 3.07 Aril 79.59 4.69.96 3.5 3.7 May 83.07 6.49 2.52 2.43.6 June 89.89 4.26.24.7 0.99 July 87.8 4.3.5 2.69.69 Augus 87.35 3.9.07 2.56.3 Seember 84.8 5.49.38 2.7 0.59 Ocober 85.36 3.47 2.48 2.24 0.52 ovember 76.95 8.3 2.3.82 0.35 December 84.4 3.08 2.57.43 0.84 Toal 83.45 5.7.66 2.04.6 200 January 8.65 7.46 2.9.29 0.5 February 89.85 2.79 2.44 0.99 0.4 March 89.99 2.03.92 0.9 0.8 Aril 90.63 2.3.55.65 0.63 May 8.36 5.4 3.45 2.38 0.62 June 7.9 8.99 4.49 3.29 0.93 Toal 84.62 4.58 2.62.7 0.64 The auhors had colleced he daa when working as economis in he Cenral Bank of Russian Federaion. Iniially, daa were sored in ex files. For each rading day in he samle we had a file conaining informaion on all he ransacions and a file conaining all he orders submied during rading session. The oal number of files was abou 500 and he size of he collecion of files was abou 2 GB. Each ransacion was reresened by a row in a file wih he following informaion:
Transacion number; Time (wih he recision of one second); ame of a sock (For examle, RAO EES) Trade regime (socks of ier, socks of ier 2, ou-of-lising socks, regime of negoiaed ransacions); ID of he sock (for examle, for RAO EES RU000892662); Direcion of he ransacion (B buy, S sell); Broker s accoun; ame of he broker; Price of he ransacion; umber of los of securiies (For RAO EES lo = 00 socks); Volume of he ransacion; ID of he broker of he couner ary; ame of he broker of he couner ary; A Remark Tex forma is no suiable for calculaions so he rogram has been wrien o conver ex files ino MS Access forma. In fac, ha was he mos difficul ar of he research. Firs, i required develoing sofware o rocess ex files, second, rocessing was quie ime consuming. For examle, conversion of one-monh daa required a coule of days. The major roblem ha is encounered by many researchers is ha sock daa do no allow disinguishing beween differen invesors. Financial insiuions yically oerae boh as invesmen funds ha arac and manage caial and as brokers ha rovided inermediaion services. Tyically sock exchange daa allow searaing brokers from heir cliens bu no one clien from anoher one. Forunaely, our daa rovide means o overcome his roblem. This became ossible due o he resence of so called remarks in he ransacion saisics. Brokers end o use remarks in he order window o deermine which clien sen he reques. These remarks canno be classified since hey are made on discreion, which, however, is no necessary o do in order o disinguish cliens.
As i was oined ou, common socks of RAO UES accoun for abou 85% of all he ransacions. This means ha if we resric our analysis o ransacions wih his leading sock, we will no loose much informaion abou marke microsrucure. However he gain will be subsanial, since i always easy o deal wih one sock and one rice hen wih a range of socks and rices. All he analysis ha will be resened in following secions is comued on he basis of daa ha corresond only o common socks of RAO UES. Preliminary observaions In his secion we resen some reliminary findings ha will rovide a general icure abou he microsrucure of he sock marke under consideraion. As i was already menioned in he revious secion, we will focus on single comany RAO UES ha accouns for more hen 85% of all ransacions in MICEX boh wih resec o he number and he volume. On racice, i is difficul o classify raders ino marke makers, informed and uninformed. Wha we observe in realiy is number of shares bough and sold by every rader during a day. By definiion, a marke maker says neural on average, ha is he sells and buys equal number of shares on average. This feaure rovides us wih he means o in down marke makers using daa on ransacions. This aroach seems o be roblemaic in our case for number of reasons. The main difficuly is ha here are no ure marke makers ha rofi solely from inermediaion beween buyers and sellers. Second, i is raher difficul o access heir rofis if hey are no erfecly neural on he daily basis. In his aer we will ake a simlified aroach by considering only raders ha remained erfecly neural (sold and bough he same number of shares) during a day as marker makers. This definiion, as well as he oher ones inroduced below, is day-deenden meaning ha an invesor can be classified as marke maker in one day and be classified as, for examle, buyer in he oher day. An invesor is called buyer (seller) if he number of shares he bough exceeded he number of shares he sold. An invesor is called ure buyer (ure seller) if he was only buying (selling) shares in a given day. The immediae criicism of our classificaion is ha we could ossibly enlarge he ool of marke makers by including hose who were almos neural during a day. This oion has been analyzed and we find no saisfacory way o define he noion of almos. More imoranly, he definiion of marke maker is subjec o oenial selecion bias. Indeed, an invesor migh no be willing o sell all he shares he bough
during a day if i leads o realized losses. To defend our classificaion, we noe ha marke makers we cover in our classificaion are robably hose ha exensively use leveraged borrowing o increase he scale of oenial rofis. For hem, he only way o ay ou is o close heir osiion in he end of he day whaever ne effec is. Below we rovide some emirical facs ha sugges absence of selecion bias. Pic. and 2 summarize he average daily srucure of marke aricians according o our classificaion by number of invesors and volumes of ransacions (urnover): Pic. Srucure of marke aricians (number of daily ransacions) Ohers 37% Marke makers 6% Pure buyers&selles 47% Pic. 2 Srucure of marke aricians (volume of daily rade) Ohers 35% Marke makers 24% Pure buyers&selles 4% As i follows from hese diagrams, on average, 6% of marke aricians are comrised of marke makers (as we defined hem) wih abou 50% being ure buyers or sellers. In volume erms, marke makers accoun for almos quarer of he oal urnover. This figure is no so imressive as one would exec from he role of marke makers in he marke. This is an obvious draw back of our classificaion.
everheless, even given quie resricive definiion of marke makers, we are lef wih significan share of he rade hey accoun for. From our daa, we are able o esimae he ex-os erformance of marke makers. The samle disribuion of he daily rae of reurn of marke making is shown in ic. 3. As a benchmark, we draw he disribuion of daily reurn from he simles (myoic) sraegy of buying in he beginning and selling in he end of a rading day (ic. 4). Pic. 3 Daily rae of reurn from marke making 0.20 0.8 0.6 0.4 0.2 0.0 0.08 0.06 0.04 0.02 0.00-0.09-0.08-0.07-0.06-0.05-0.04-0.03-0.02-0.0 0.00 0.0 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 Samle mean: 0.8%; sandard deviaion: 0.99 ercenage oins. Pic. 4 Daily reurn from he myoic sraegy 0.20 0.8 0.6 0.4 0.2 0.0 0.08 0.06 0.04 0.02 0.00-0.09-0.08-0.07-0.06-0.05-0.04-0.03-0.02-0.0 0.00 0.0 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 More Samle mean: -0.02%, sandard deviaion: 3.28 ercenage oins We could consider jus oosie sraegy bu i would lead us o he same conclusions.
The reurn from he myoic sraegy is, in fac, he marke reurn. Therefore, judging from he esimaes of wo firs momens for boh disribuions, we conclude ha marke making resuls in excess reurn (even of higher order in ercenage erms) wih lower associaed risk. This observaion suggess ha here are rofiable ooruniies for marke making in he Russian sock marke. Le us evaluae he rofiabiliy of marke making wih single arameer, which is he average robabiliy of success of a reresenaive marke maker over he eriod of observaions. Firs we calculae he share of marke makers ha made rofi in a given day, and hen we ake an average over he whole eriod. I is sraighforward o classify marke making beween rofiable and non-rofiable by he difference beween he value of shares sold and he value of shares bough. Recall, ha according o our classificaion marke makers buy and sell equal number of shares in a given day. This rocedure gives an esimae of he arihmeic average of daily robabiliies. Due o sufficien degree of aggregaion i has aroximaely normal disribuion wih variance ha we can esimae he following way. Denoe as π he rue (underlying) robabiliy of success in day. Le: π = T π Then if we observe seculaors hen he variance of esimae of π is equal o: ( ) V ( ~ π π π ) = and he variance of he esimae of he average robabiliy is: V ( ~ π ) = 2 T π ( π ) This variance can be evaluaed by subsiuion of rue robabiliies by heir esimaes. As a resul we obained π=0.657±0.002. For comarison, he esimaed robabiliy of success from myoic sraegy is only 0.508. I should be noed ha i is no erfecly correc o use his characerisic as a reliable indicaor of suerioriy of one disribuion over anoher. Indeed, i may be he case ha robabiliy of success is greaer bu he execed uiliy, which deermines correc ordering, is lower. In fac, i is also no sric o
work only wih firs wo momens of he disribuion. everheless, we believe ha robabiliy of incorrec inference is negligible if comared o he exen o which he use of single arameer simlifies analysis. Before we roceed wih he discussion of hese finding, i is imoran o assure ha here is no samle bias so ha resuls are no surious. By our classificaion, marke makers are hose invesors ha were erfecly neural by he end of he day. The main criicism is ha he samle is biased owards more successful marke makers because invesors may be unwilling o realized losses by closing u heir osiions. Le us ry o es indirecly if indeed here may exis selecion bias in our esimaes. If he sory abou invesors non-wiliness o fix losses is correc hen we exec o find ha in days wih high average robabiliy of success, he number of marke makers (according o our classificaion) is larger hen in days wih low robabiliy of success. Also we should double-check his in he following way. Since shor selling is no always available hen invesors ha do no wan o realize losses are likely o remain among buyers in a given day. Hence here should be negaive correlaion beween he number of marke makers and he number of buyers. Since we are ineresed in a shor-run correlaion hen i is reasonable o ake firs differences in daa. Insead of he number of buyers we considered he difference beween he number of buyers and he number of sellers. This was done o exclude ossible common facors ha affec marke aciviy. The resuls are resened in able 2. Table 2 Correlaion marix #marke makers %success #buyers-#sellers #marke makers.00 0.27-0.03. %success 0.27.00-0.20 #buyers-#sellers -0.03-0.20.00 According o he argumen, in bad imes more invesors face losses and migh no be willing o close u heir osiions. If bad imes are correcly measured by he average robabiliy of success hen we exec o find osiive correlaion beween he success robabiliy and he number of marke makers on one hand, and negaive correlaion beween he number of buyers and he success robabiliy on he oher
hand (due o shor-selling difficulies). Alhough he resuls are in accord wih he execaions, he correlaion of 0.27 is no very convincing. Moreover we are surrised o see no significan correlaion beween he number of buyers and he rofiabiliy of marke making. These observaions allow us o conclude ha if any, he samle bias should no be significan. Our main findings so far sugges ha here are highly rofiable ooruniies for marke making in he Russian sock marke. Does his mean ha his marke segmen is no comeiive as is always assumed in he heoreical model of marke making? This quesion is no easy o ask because we imlicily made quie unrealisic assumion ha marke makers are homogeneous. Suose ha new marke maker eners he marke. Can we claim ha he will immediaely face highly rofiable ooruniies? Our sory of marke making obviously lacks some learning asecs ha are necessary o make i realisic. Learning marke is cosly so here may be no free lunch. The disribuion of he rae of reurn from marke making (ic. ) reflecs ooruniies faced by an average (wih resec o knowledge) marke maker and here is no reason o believe ha newcomer will have he same odds. One way o enrich our analysis, which we will ursue in he nex secion, is o allow for wo yes of marke makers: so called rofessionals and amaeurs. Then our ask will be o assess ooruniies faced by reresenaive amaeur, which will give more realisic icure of how aracive is enering he business of marke making. To simlify he analysis, we will assess he araciveness by single arameer robabiliy of success, wih benchmark of 50% (aroximaely he same as in he case of myoic sraegy). We finish his secion by resening anoher ineresing iece of informaion abou marke microsrucure. MICEX is organized in such a way ha only limied number of invesors can direcly ariciae in he rade. These invesors are called brokers. In his connecion, i migh be ineresing o observe disribuion of he number of cliens er broker. The average number of brokers ha raded daily is 286, whereas he average number of ariciaing invesors is equal o 2554. This observaion suggess ha a broker has, on average, abou 9 cliens (including himself). In ic. 5 we resen he average daily disribuion of he number of cliens er broker comued for he whole eriod of observaions.
Pic. 5 Average disribuion of he number of (acive) cliens er broker 0.5 0.4 0.3 0.2 0. 0.0 (,0] (0,20] (20,50] (50,00] >00 This diagram was consruced he following way. We chose six inervals for he number of cliens er broker. Then for each day and for each inerval we couned brokers ha aced on behalf of cliens, number of which falls wihin corresonding inerval. Hence for each day we have six numbers. Then we summed hese numbers across all he days and scaled hem o have final values summing u o one. The icure suggess ha a significan share of brokers make oeraions on behalf of only one clien (mos robably hemselves). Mos of he ohers have no more hen 0 cliens. There are several brokers ha serve numerous cliens (more hen 00). I seems reasonable o exec ha brokers ha have few cliens have close relaionshi wih hem. On he oher hand, large-scaled brokers (wih resec o he number of cliens), mos robably, are no direcly relaed o heir cliens. However, one migh exec ha hey rovide exer advise o heir cliens, which we call as indirec relaionshi. The issue of he relaionshi beween cliens and brokers will be analyzed laer in he aer. Profiabiliy of marke making Preliminary findings discussed in he revious secion sugges ha here are aracive ooruniies for marke making in he Russian sock marke. We found ha marke making generaes higher order reurns wih lower associaed risk, as measured by sandard deviaion, comared o he benchmark. As i has been noed, we imlicily assumed homogeneous marke makers. Obviously, marke making involves coss of learning he marke, which should no be negleced when assessing he araciveness of marke making ooruniies. These coss canno be measured direcly. An alernaive way is o dro assumion of
homogeneous marke makers and osulae exisence of wo yes of marke makers: exerienced (rofessionals) and inexerienced (amaeurs). Then he rofi ooruniies faced by inexerienced marke makers is he righ measure of araciveness of his aciviy. In his secion we develo a saisical model ha will hen be used o esimae rofi ooruniies of wo yes of marke makers. To simlify maers we will measure rofi ooruniies by he robabiliy of success. Since he share of exerience marke makers is no known, we will obain only 95% confidence area in he wo dimensional sace wih he robabiliy of success of rofessionals and amaeurs as coordinaes. In order o ge an idea of how differen are invesors wih resec o heir success robabiliies we will make use of ime series roery of our daa. If invesors are homogeneous hen he condiional robabiliy of success of an invesor is indeenden of his resuls in he revious day. Indeed, oherwise his curren success is an informaive signal for his fuure success, which can be he case only if invesors have differen uncondiional (rior) robabiliies. Hence he reasonable aroach is o consider adjacen rading days and esimae condiional robabiliies of success. This aroach has a number of difficulies, which become eviden once we ry o imlemen i. Firs, on average, only one hird of seculaors ha ariciaed during some rading day also ariciae during he nex day. Aar from reduced coverage, we may oenially have roblems wih samling bias. Indeed, we found ha he average robabiliy of success comued over reduced samle is equal o 0.643±0.004 insead of 0.657±0.002 ha we had before. Given he esimaed sandard error, we conclude ha he samling is no erfec. This curious resul is difficul o exlain, which, in fac, is no so imoran given ha he new esimae is no (economically) significanly differen. So we will simly sick o i insead of he old one. Second, he condiional robabiliy of success of an invesor for some day given ha he ariciaed also during he nex day migh be higher hen ha for an average invesor. This bias may emerge if success in one day increases robabiliy of ariciaion in he nex day. Indeed, he esimaed mean of he robabiliy of success of an invesor condiional on his ariciaion in he revious day is 0.64 whereas condiioning on he nex day ariciaion gives 0.68. This difference is indeed significan no only from he saisical oin of view bu also economically. As i will be seen laer, under reasonable assumions his discreancy does no change formulas ha we obain for esimaion uroses.
Formal seu Le us formalize he heerogeneiy of invesors in he following formal seu. We assume ha here are wo yes of seculaors in he marke: rofessionals and amaeurs. Firs ye of invesor will be referred as high ye and he second as low ye. The share of high ye is fixed and denoed as λ. Le π be he robabiliy of success of an average invesor in day, h(l) robabiliy of success of high (low) ye. Then: π = λ + ( λ) h l Le us denoe as s s he condiional robabiliy of success of a reresenaive invesor given ha he succeeded in he revious day. Suose ha success in one day has equal mulilier on he robabiliy of coninuaion indeenden of he ye of invesor. Then he share of he high ye among all seculaors ha ariciaed oday () and yeserday (-) is always λ. I follows ha robabiliy of high ye given success yeserday is equal o: Pr( h s) = Pr( s h) Pr( h) Pr( s h) Pr( h) + Pr( s l) Pr( l) = h λ + λ h l ( λ) Similarly Pr( l s) = Pr( s l) Pr( l) Pr( s h) Pr( h) + Pr( s l) Pr( l) = h l λ + ( λ) l ( λ) And he condiional robabiliy s s is equal o: h h l l s s h l λ + ( λ) = Pr( h s) + Pr( l s) = π () Le us assume ha robabiliy of success of high ye is relaively smooh over ime ( h h - ). In oher words, he volailiy of he robabiliy of success of he average invesor is accouned for mainly by he volailiy of corresonding robabiliy for low ye (non-rofessionals). This assumion seems o be reasonable and also very useful since allows us o solve for h. Exression () can be now wrien in he following form: s h 2 l l s π ) λ + ( λ) (2) = ( Also we have:
π (3) h l = λ + ( λ) π = λ + ( λ) (4) h l The sysem of equaions (2), (3) and (4) can be easily solved o obain: π + π 2 λ π λ h s s = + ( π π π ) + 2 2 (5) This exression relaes high ye robabiliy o condiional and uncondiional robabiliies of success, which can be esimaed from he daa. The issue of esimaion is comlicaed by non-lineariy of he relaionshi. On he oher hand we seek esimaes of arihmeic averages of fundamenal robabiliies bu no heir so values: h l T T h l π T π Given sufficienly long series of daa we are able o make assumion abou normaliy of some esimaes and his will hel considerably in obaining confidence inervals. The esimaion echnique is described in Aendix. Esimaion resuls The esimaion rocedure described in he revious secion was imlemened on our daabase. Firs we found esimae of a, hen evaluaed variance of he esimae and finally deermined 95% confidence area using is definiion given by (5), (6) and (7). In he las se, we ook 00 uniformly disribued values from inervals [-2,2] and (0,) where and λ are defined and hen loed hose 0000 oins (x,y) ha saisfy condiions x and y 0. The resuling lo is shown below.
Pic. 6. The 95% confidence area for rue success robabiliies 0.7 0.6 Probabiliy (low ye) 0.5 0.4 0.3 0.2 0. 0 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95.00 Probabiliy (high ye) The minimum λ for which he confidence area for underlying robabiliies inersecs wih square [0,] 2 is abou 0.3 so we can rejec hyohesis ha seculaors are homogeneous wih resec o heir robabiliies of success. ow we are able o make judgmens abou ossible values of low ye robabiliy ha is key variable we waned o esimae. There are wo observaions in order. Firs, l is always smaller hen 0.6, which does no look such oimisic as 0.66. This is he maximum ossible value for he low ye robabiliy, which can be rue only if rofessionals make sure rofis. For examle, if some invesors maniulae he marke, hen i migh be reasonable o exec h. However, his would mean ha more hen 0% of marke makers acually maniulae he marke. This looks quie unrealisic. If here is any maniulaion, i robably haens occasionally and should no affec aggregae resuls. Second observaion is ha if we believe ha low ye invesors can succeed wih more hen 50% robabiliy (ha is benchmark) hen we will have o acce ha high ye has robabiliy of a leas 77%. This figure seems o be exceionally high, alhough, here is no sric way o jusify our belief. Success robabiliy of 77% imlies huge execed reurn from marke making rovided ha he reurn disribuion is no highly asymmeric 2. The heory ells us ha due o resence of informed raders, marke makers infer he fundamenal informaion from rades and earn on uninformed raders. Hence, he marke making rofi ooruniies deend crucially on he unequal disribuion of informaion in he marke. In his 2 Suose ha here is large robabiliy of very small rofis and small robabiliy of huge losses. Then he robabiliy of success can be high by he rofi ooruniies are no esecially favorable. This is general observaion ha use of success robabiliy o measure araciveness of aciviy is correc only if reurn disribuion is near symmeric. This is wha we observe for he whole samle of marke makers (see ic. ).
aer we focus on he marke for a single sock RAO UES. The comany reresens a huge energy monoolis wih uncerain fuure and highly non-ransaren accouning. According o marke aricians, he marke has no clear undersanding of bounds for he fundamenal value of RAO UES. Under hese circumsances, he dynamics of he rice of common shares of RAO UES is mainly deermined by general oliical and economic facors raher hen comany secific ones so ha one canno exec he informaion o be unequally disribued in he marke. As a consequence, marke making should no yield huge reurns in his segmen of sock marke. As is evidenced by ic. 6, rofessionals have he robabiliy of success of a leas 66%, which is sill high. This observaion resens a uzzle ha we are no ready o fully resolve. This migh evidence ha here is robably some samle bias in he classificaion we adoed (see discussion above) ha increases all he robabiliy esimaes. This bias should no be large as is evidenced by he indirec es so ha we are inclined o believe ha 77% would sill be large even if correced for he samle bias. Consequenly, he argumen agains low ye robabiliy being greaer hen 50% remains valid. To sum u, we conclude ha robabiliy of success of amaeurs is unlikely o be beer hen 50/50 chances. Relaionshi beween brokers and heir cliens In his secion we will es for he exisence of he relaionshi beween brokers and heir cliens. As i is eviden from reliminary analysis, mos of brokers have only several cliens, which are robably direcly relaed o hem (affiliaed comanies). This kind of relaionshi we call direc relaionshi. The indirec relaionshi arises when brokers rovide marke advise o heir cliens, for examle, in he form of daily marke review. Boh yes of relaionshi should resul in a relaively similar behavior of cliens of he same broker. Hence he righ way o es he hyohesis of exisence of he relaionshi is o esimae he degree of coordinaion in acions of invesors ha use services of one broker as comared o ohers in he marke. Mehodology The saisical mehodology is adoed from he emirical lieraure on herding behavior (Lakonishok, Shleifer and Vishny (992), Wermers (999) among ohers) bu is alied o oally differen conex. The herding saisics, inroduced by Lakonishok, Shleifer and Vishny (992), measures he degree of concenraion of he rade of a grou of invesors in differen socks. Here we wan o measure somehing
very similar. amely, we would like o measure he degree of coordinaion beween acions of invesors ha are associaed wih he same broker. In case of he herding measure we have a grou of invesors being fixed and socks being varied. Here we fix he sock bu vary grous of invesors by considering differen brokers. Le index refer o some day in he samle and le i refer o a broker, who erformed oeraions on behalf of is cliens (or himself) during he day. If an invesor increased holdings of he sock during he day hen we say ha he was a buyer during his day. Similarly we define a seller. Le i be he share of buyers among all ariciaing cliens of broker i during day. Under null hyohesis i should be an unbiased measure of general roensiy o buy among all invesors during day. There is no a riory reason o believe ha i is equal o one half since invesors do no rade equal amouns. This roensiy is roxied by he acual raio of buyers among all ariciaing invesors during day. Under null hyohesis he following value is a realizaion of random variable wih zero mean: h i = E (8) i i The execaion on he righ-hand side of (8) is comued given ha i has binomial disribuion wih mean : E i = i j= C j i j ( ) ( ) i j j i Here i is he number of ariciaing cliens of he broker i in day. Le us define aggregae daily measure: H = I I i= h i (9) If he number of brokers I is sufficienly large hen under null hyohesis H is normally disribued wih zero mean. Given a series of observaions of H over he samle eriod, we may use -es o es he null hyohesis. The saisical inference can be also made wihou assuming ha H are disribued normally. Insead, we assume ha only H has normal disribuion, where
H = T H Is variance can be esimaed from he variances of h i. Under null hyohesis: V ( h i ) = E 2 2 ( ) 2 ( ) E ( ) = E ( ) i i i i Given assumion on he indeendence of esimae in ie and across brokers, which has been imlici so far, he variance of H is equal o: V ( H ) = V ( hi ) 2 2 T I ow we have an observaion of a normal random variable wih zero mean and known variance under null hyohesis. The es for he hyohesis is based on evaluaing robabiliy of his observaion. The validiy of null hyohesis can be also checked visually by means of a simulaion. In his aer we erformed several simulaions of he disribuion of H using he following mehodology. Taking as given we simulaed i assuming binomial disribuion and comued H. For each day we simulaed 00 values of H. The oal number of days in he samle is equal o 240, so each simulaion consiss of 24000 observaions of H. Esimaion resuls The value of H was calculaed in several differen ways by imosing resricions on he minimum number of acive cliens of a broker C min. These resricions were imosed o exclude noisy observaions of brokers ha raded on behalf of very small number of cliens. For each day in he samle, H was comued by averaging across only hose brokers ha erformed oeraions on behalf of a leas C min of heir cliens (robably including hemselves) during his aricular day. In able 3 we resen esimaes of H and -saisics for a range of values of C min. The es based on known normal disribuion for H also indicaed high significance.
Table 3 Resuls of he es for he resence of relaionshi beween brokers and heir cliens C min 5 0 20 30 H 0.03 0.029 0.02 0.06 -saisics 29.23 23.67 7.93 4.28 Av. num. of brokers 60 29 5 2 The -saisics are highly significan, which is usual when a large number of observaions is available. The highes value of H is obained for he case of mild resricions as indicaed by he second column of he able. The value of H can be loosely inerreed as an average bias of he raio of buyers wihin one broker as comared o he oal value. Here he bias is equal o 3 ercenage oins, which does no seem o be aricularly significan from he economic oin view. One ossible exlanaion of his fac is ha we did no ake ino accoun full informaion abou invesors behavior such as volumes of heir ransacions. Insead, we used he simles classificaion ino buyers and sellers. Anoher ossible reason is ha we esed he hyohesis on high frequency daa. everheless we are able o rejec he null hyohesis saisically. As is evidenced by he las row in he able, he average number of brokers quickly decreases as resricions on minimum number of ariciaing cliens become sronger. For examle, on average only 29 brokers erformed oeraions on behalf of a leas 0 cliens during a day. This fac may also imair he validiy of he saisical inference based of -saisic. Indeed, as i was menioned in revious secion, he es relies on he normaliy assumion due o sufficien aggregaion. We double-checked he resuls by alying he es based on known normal disribuion of H. The esimaed sandard deviaion of H is around 0.0008 for all four cases. The lowes value of H we obained is 0.06, which is sufficienly differen from zero given sandard deviaion 0.0008. Anoher way o check he validiy of resuls is o see visually he difference beween acual and nullhyohesis disribuion of H, we simulaed he laer for C min = 5 and 30.
Simulaion Acual daa A: C min = 5 50 40 30 20 0 0-0.04-0.02 0.00 0.02 0.04 0.06 50 40 30 20 0 0-0.04-0.02 0.00 0.02 0.04 0.06 B: C min = 30 50 40 30 20 0 0-0.04-0.02 0.00 0.02 0.04 0.06 50 40 30 20 0 0-0.04-0.02 0.00 0.02 0.04 0.06 Our resuls sugges ha here exis a relaionshi beween brokers and heir cliens. Even for quie large number of cliens er broker (here more hen 30) we obained significan esimae of H. This means ha boh direc and indirec relaionshi exiss. As i can be execed he srengh of he relaionshi measured by H declines as a resricion on he minimum number of cliens becomes sronger, so ha he direc relaionshi is obviously sronger. Could our resuls be biased? Yes, if he choice of an invesor beween large-scaled and small-scaled brokers may be somehow relaed o he ye of sraegy he ursues. In his case he difference in behavior beween cliens of differen brokers may be observed if we aggregae H across brokers of differen size 3. In aricular, his reasoning may exlain why we observe decrease in he bias as resricions on he 3 Here by size and scale we mean average number of acive cliens. This may no be relaed o he size of he broker defined as a value of he cliens orfolio.
number of ariciaing cliens become sronger 4. To make sure ha our resul are no consisen wih his exlanaion, we erformed he es by imosing he resricion ha he number of ariciaing cliens o be no less hen 5 and no more hen 0. Under his resricion, we aggregae over relaively homogeneous brokers in erms of heir size. The resuling value of H is equal o 0.030 (-saisic 8.3). oe ha hese calculaions are based on aroximaely half of he samle used o calculae H value in he second column of able. everheless, he new value is only slighly smaller. The resuls we obained in his secion reresen an ineresing iece of informaion, which, however, is no direcly relaed o wha we did in revious secions. We esablished ha brokers and heir cusomers are somehow relaed. Our daa sugges ha brokers are no very acive dealers and volumes of heir rades are surrisingly small. All hese observaions sugges ha here is a endency o hide invesmen aciviy by firms via affiliaed comanies, which are cusomers of hese firms. This exlains he observed direc relaionshi beween brokers and heir cliens. Wha seems uzzling is he exisence of wha we call indirec relaionshi. We found ha large-scaled brokers also end o be somehow relaed o heir cliens. One ossible exlanaion is ha brokers rovide marke advice o heir cliens. Alernaively, syle of invesmen may affec he choice of a broker. Summary and conclusions This aer resens several emirical resuls on he marke microsrucure ha were obained using unique daabase covering all he ransacions in he leading Moscow sock exchange (MICEX) over a eriod of more hen one year. Two issues have been invesigaed: Profi ooruniies for marke making in he sock marke Relaionshi beween brokers and heir cliens Preliminary calculaions showed ha he marke making allows earning higher order reurns as comared o he benchmark wih lower associaed risk. The robabiliy of success of engaging in marke making was esimaed o be abou 66%, which was deemed o be high. However, careful saisical analysis showed ha invesors are no homogeneous wih some of hem having higher robabiliy of success hen he ohers. Assuming exisence of wo yes of invesors rofessionals and amaeurs we argued 4 oice ha we esimae no from he whole samle, bu from he resriced one for he urose of consisency.
ha he robabiliy of success of he laer is a leas no higher hen 50%. This resul suggess ha wihou cosly learning here are no excessive gains from marke making. We found saisically significan relaionshi beween marke aciviy of differen cusomers of he same broker as comared o cusomers of oher brokers. This oins ou o exisence of he relaionshi beween broker and heir cliens. We classified his relaionshi as direc (case of small-sized brokers) and indirec one (case of large-sized brokers) and found evidence of boh yes of relaionshi. We suosed ha yical financial firm ends o hide is invesmens by carrying ou marke aciviy via affiliaed comanies, which naurally become is cusomers. References: Easle, D., and O Hara, 987, Price, rade size, and informaion in securiies markes, Journal of Financial Economics 9, 69-90. Glosen, L., and P. Milgrom, 985, Bid, ask, and ransacion rices in a secialis marke wih heerogeneously informed raders, Journal of financial economics 3, 7-00. O Hara, M., 995, Marke microsrucure heory, Blackwell Publishers Inc., Cambridge MA, USA. Kyle, A.S., 985, Coninuous aucions and insider rading, Economerica 53, 35-336. Lakonishok, J, A. Shleifer and R.W. Vishny, 992, The imac of insiuional rading on sock rices, Journal of Financial Economics, 32, 23-34. Wermers, R., 999, Muual fund herding and he imac on sock rices, Journal of Finance, o. 2, Aril, 58-622.
Aendix: Esimaion echnique Esimaion echnique Alhough we are no able o esimae h and l we may ry o find a subse of sace ( h, l ), where he rue robabiliies lie wih a leas 95% robabiliy given our observaions. This se is defined as a union of 95% confidence subses corresonding o all ossible values of arameer λ inerseced wih he scare [0,] 2. h π + π Le us denoe δ = 2 2, which is square of he difference beween robabiliy of success of high ye and average robabiliy of success of reresenaive invesors oday and yeserday. From (5) i follows ha: 2 λ s s π π δ = π ( π ) + (6) λ 2 Define: δ T δ Le us use he following aroximaion: h π + δ (7) oe, ha all he relaionshis so far involve only rue values for underlying arameers. ow we go over o esimaion issues. Le us firs discuss how o esimae δ for arbirary λ. In he formula (6) we ignore he second erm on he righ hand side for he reason ha i is significanly smaller hen he firs erm. Indeed, i aeared ha he unbiased esimae of he second erm in (6) is more hen 40 imes smaller hen ha of he firs erm. Taking he second erm ino accoun will significanly comlicae calculaions bu will no change our resuls noiceably. The comlicaions resul from he fac ha i is no sraighforward o consruc an unbiased esimae of his erm. Presence of several sums in he exression of he esimae of δ will creae unnecessary difficulies in comuing is variance.
We roose he following unbiased esimae for δ: ~ λ ~ s s ( ~ ~ λ δ = π ) a~ π = (8) λ λ T The absence of a bias sems from he fac ha esimaes are indeenden in ime. Variance of a can be easily esimaed he following way: V a~ ) = T ( ~ π ( ~ ~ ( ~ ~ ( ~ )) (2) s s s s s s V π )) π ( )( Cov, ) V 2 π π 2 ( π 2 T where ( ~ ( ~ s s ~ )) [ ~ 2 ] [ ~ s s ~ 2 s} s V π π = E π E π ] π ( π ) (3) Here we gain use indeendence of esimaes in ime. Exressions (2) and (3) include erms V ~ π ), ( ( ~, ~ s s Cov π ), E ~ ~ π s s 2 [ ] and 2 E ~ π ]. Le us find exlici formula for hem. [ Le ss be he number of invesors ha succeeded yeserday and oday, fs number of invesors ha failed yeserday bu succeeded oday, sf number of invesors ha succeeded oday bu failed yeserday and finally ff number of invesor ha failed boh oday and yeserday. Define s = ss + fs number of invesors ha succeeded yeserday and f = sf + ff number of invesors ha failed yeserday. By definiion ~ ss sf s s = s and f s = f ~ are wo indeenden random variables ha have means s s and s f corresondingly. The frequency of success is a linear combinaion of hem: ~π = ~ s s s s f + ~ s f + f Hence we have: Cov( ~ π, ~ s s s ) ( ~ s s = V s f + ) Assuming normaliy of esimaes, we can easily find he following exressions for variances: V ( ~ s s s s ( ) = s s s )
( ) V ( ~ π π π ) = + s f From he definiion of he variance: E ~ π ( ~ π + π 2 2 [ ] = V ) E ~ ~ π ( ~ π π ) s s 2 s s s s s s [ ] = V ) + V ) 2Cov, ) ( ( ~ ( ~ ~ π Variance V (a~ ) can be evaluaed by subsiuing rue robabiliies wih heir unbiased esimaes. In order o find confidence inervals we assume ha a ~ is normally disribued. Indeed, as i follows from (8) i is an average of random variables wih T being equal o 240. The normaliy assumion is jusified by he Cenral limi heorem. 2 Le us assume ha comued esimae of π is exac. Indeed, he sandard error of he esimae is very small (0.0035) so his assumion will no affec our resuls in a significan way. Taking ino accoun (7) we conclude ha given λ and esimae a ~, he rue value h belongs o he following inerval wih 95% robabiliy: λ λ ~ π + + V ( a ~ ) where [ 2,2] (4) λ λ ow using (4) and (4) we find ha he air of rue arameers ( h, l ) wih al leas 95% robabiliy belongs o a subse {(x,y)} of R 2 ha can be arameerized in he following way: x = π + λ ~ λ ~ a + V ( a ~ ) λ λ (5) π λx y = λ (6) [ 2,2], λ (0,), such ha (x,y) [0,] 2 (7) This se reresens wo-dimensional 95% confidence area, which is consisen wih our observaion. The dimension wo resuls from he fac ha we do no observe λ, and i is difficul o make any rior judgmen abou i.