Dynamic Relations between Order Imbalance, Volatility and Return of Top Losers

Transcription

1 Dynamic Relaions beween Order Imbalance, Volailiy and Reurn of Top Losers Yong-Chern Su*, HanChing Huang, Po-Hsin Kuo and Peiwen Chen Absrac Recenly, many researches show ha order imbalances have a significan relaionship wih sock reurns, especially in speculaive socks. In his paper, we examine he relaions beween order imbalances, volailiy and sock reurns of op losers. Then, we develop a rading sraegy based on he relaions. Firs, we apply GARCH (1,1) model wih and wihou volailiy o es wheher i can fi our inraday daa. We find ha GARCH (1,1) explains he inraday price behaviors of speculaive socks in boh cases. Then, we use muli-regression model o examine wheher conemporaneous and lagged order imbalances have significan influences on sock reurns. We find conemporaneous order imbalances have posiive effec and lagged one order imbalances have negaive effec on sock reurns. While conrolling for conemporaneous order imbalances, only lagged- one order imbalances have a significanly negaive effec on reurn. We also find ha order imbalance and marke capializaion have an insignificanly posiive relaion. We develop a rading sraegy based on he previous findings o make profi. We shor sell when order imbalance is negaive and buy back when order imbalance is posiive. The empirical resuls show ha if we don runcae he volume disribuion, we can find abnormal reurns. However, if we sif our daa from rading volume, ha is, above 99% volume, we documen a significan profi based on our rading sraegy. In order o explain he significan profi based on dynamic relaions beween order imbalance and reurn of speculaive op gainers, we examine he causaliy relaionship beween reurn and order imbalance. We find ha order imbalance is a unidirecional indicaor for predicing fuure reurns. Especially, order imbalance is an exraordinary good indicaor for price discovery in small firm size quarile. Key words: order imbalance, informaion asymmery, volailiy, causaliy relaionship * Corresponding auhor, ycsu@ccms.nu.edu.w, Address: 50 Lane 144 Sec. 4, Keelung Road, Taipei, Taiwan, Tel: , Fax:

2 1. Inroducion For many years, rading volume has provided he linkage beween rading aciviy and reurns. Invesors are always seeking and finding reliable useful indicaors o predic he movemens of heir holding socks. Among many possible indicaors, i has been showed ha rading aciviy can be a grea proxy o imply some privae informaion. Jus as researches of Lo and Wang (2000) and Karpoff (1987), hey find he associaion of rading aciviies and sock reurns. If no-informed invesors can find a good indicaor and use i o rade, hey may earn abnormal profis even wihou privae informaion. Therefore, he objecive of his sudy is o shed furher ligh on he dynamic relaions beween rading aciviies, volailiy and sock reurns. There are many ypes of rading volume: rading number, rading shares and rading dollars. In Chordia, Roll and Subrahmanyam s paper (2002), hey find ha rading volume have he mos efficien effec on sock reurns. They also use he indicaor, order imbalance, o sand for he rading volume and hey hink ha rading volume can reveal some privae informaion behind he marke markers and he big-deal raders. According o Lee and Ready (2000), order imbalance judges he direcion of each rading volume. Tha s an ineresing hing ha we can observe he invenory siuaion by he adjusmen of bid-ask quoes of marke makers. If marke makers don have enough invenories on hand, hey may adjus he quoes by increasing he ask price o reflec his invenory level. However, in he meanwhile, hey also can do he same behavior by jus cheaing and misleading invesors. Therefore, besides observing he order imbalances, invesors also need o guess wha he marke makers siuaions are and how hey hink. We examine wheher rading volume have significan influence on sock reurns and how long his effec lass for. Based on Jiang Wang (2002), invesors rade for wo reasons: hedging for heir sock holdings or speculaing on heir privae informaion. They find ha when invesors rade socks for hedging heir posiions wih large rading volume, he paerns of sock reurns will reverse in following periods bu if he accompanying rading volume is small, i jus refers o whie noise. However, when invesors rade socks because of his privae informaion, he paerns of sock reurns will coninue in following periods. Tha s he so-called momenum effec and once i works, hen we can buy he socks and predic he movemen of heir sock prices. Therefore, we wan o find he speculaive socks and observe he resuls of our research mehod. If i does really work, 2

3 hen we may ake his finding o develop a rading sraegy and expec o earn profis. In his sudy, we firs apply he GARCH (1,1) model o es he inraday ransacion daa of NASDAQ from TAQ. We use op losers o examine he model and see wheher he order imbalances can really have grea influence on sock reurns. Second, afer examining he original model, we are ineresed in examining he relaions beween volailiy and order imbalances. Since invesors always care more abou he reurns bu ignore he appending risks. Third, we wan o know wheher conemporaneous and lagged order imbalances do have significan influence on sock reurns. According o Chordia and Subrahmanyam (2004), we ran muliple regressions o es wheher his relaionship exiss. If we can prove he lagged order imbalances have explanaory power on curren sock reurns, hen we can use prior order imbalances o predic he paerns of sock prices. Fourh, we are curious abou wheher here exis some characerisics of our sample socks. We invesigae he small firm effec by esing wheher he order imbalances of small firms have more influence on sock reurns han large firms do. If he answer is yes, hen invesors shall choose small firms insead of large firms o make abnormal reurns. Fifh, we ry o develop a rading sraegy from he above findings. We have keen ineres in observing he following acions: o shor sell he socks when he firs seller-iniiaed order imbalance appeared and o buy back when he order imbalances become buyer-iniiaed. All our ransacions ignore he ransacion coss and axes. Then we sieve ou he volume wih 50%, 90%, 99% respecively. Afer we rim off small volume and leave he large volume in our sraegy, we wan o know wheher he rading sraegy can bea he original individual sock reurns. Finally, we develop a sory of dynamic lead-lag relaionship o explain he abnormal reurn from our sraegy. According o Chen and Wu (1999), we define five groups of dynamic relaionship, including independency, he conemporaneous relaionship, unidirecional relaionship and feedback relaionship. To deermine a specific causal relaionship, we use a sysemaic muliple hypoheses esing mehod. Unlike he radiional hypohesis esing, his esing mehod avoids he poenial bias induced by resricing he causal relaionship o a single alernaive hypohesis. 2. Daa We collec our sample socks daa from he Cener for Research in Securiy Prices (CRSP) and he NYSE Trades and Auomaed Quoaions (TAQ) daabases. We firs 3

4 sough for he op losers of daily ransacions wihin CRSP during December 2005, hen mach he corresponding inraday rading daa on TAQ. We collec 61 socks from he daabases. Fify socks of our daa are lised in NASDAQ marke, while hree socks in AMEX marke and eigh socks in NYSE marke and all he socks are able o be raded in he NASDAQ marke. Socks are included and excluded depending on he following crieria: 1. The sample shall be included in boh he Cener for Research in Securiy Prices (CRSP) and he NYSE Trades and Auomaed Quoaions (TAQ). 2. Among all he op losers, in order o avoid he manipulaion, we exclude he daa whose prices are below $2 and he daily rading number below 30 ransacions. 3. For hose socks wih negaive bid-ask spread quoaions, ransacion prices, and he exreme quoes (e.g. he price is higher han 1,000) were excluded. 4. Since he sock rading characerisics differ from cerificaes, American Deposiory Receips, shares of beneficial ineres, companies incorporaed ouside he U.S, closed-end funds, preferred socks and REITS. Therefore, we exclude hese kinds of securiies. 5. If here are sock splis, reverse splis, sock dividends, repurchase on he socks during he sample period, we also eliminae hem from our sample. Our sample period are from December 1 s, 2005 o December 31 s, Moreover, our observaion period each day is from 9:30 A.M. o 4:00 P.M. Since he rading behavior during marke ime and afer marke ime is quie differen, we use he regular hour rading daa. The average order imbalance volume of our daa is -203,483 shares everyday; he average buyer-iniiaed order imbalance volume is 666,273 shares while average seller-iniiaed order imbalance volume is -869,756 shares; he average mean of order imbalance volume is -120 shares everyday; he average sandard deviaion of he order imbalance volume is really high, reaching for 2,124 shares. We find ha he seller-iniiaed order imbalance is larger han he buyer-iniiaed order imbalance. I is self-explained ha we choose our daa by selecing op losers and negaive order imbalances push sock prices move downward. 3. Mehodology We employ wo differen GARCH model o examine dynamic relaions of reurn-order 4

5 imbalance and volailiy-order imbalance Dynamic reurn-order imbalance GARCH(1,1) model: α β OI R + + ε ε = * (1) Ω 1 N (, h ) ~ 0 h A B h C = + + 1ε Where R is he reurn in period, defined as ln(p/p-1) OI is he explanaory variable, Order Imbalance on sock reurns β is he coefficien of he impac of Order Imbalance on sock reurns ε means he residual of he sock reurn in period h is he condiional variance in period Ω -1 is he informaion se in period -1 α, A 1, B 1, C 1 are coefficiens We use an order imbalance coefficien in our condiional mean equaion. The β coefficien represens he impac of order imbalance on sock reurn Dynamic volailiy-order imbalance GARCH(1,1) model: Since invesors always care more abou he reurns bu ignore he appending risks, we have an ineres o examine he dynamic relaion beween volailiy and order imbalance. α R + ε ε = (3) Ω 1 N (, h ) ~ 0 h A B h C D 2 = ε 1 1 OI Where R is he reurn in period, defined as ln(p/p-1) OI is he explanaory variable, Order Imbalance on sock reurns ε means he residual of he sock reurn in period h is he condiional variance in period Ω -1 is he informaion se in period -1 α, A 1, B 1, C 1, D 1 are coefficiens 5

6 We use an order imbalance coefficien in our condiional volailiy equaion. The coefficien represens he impac of order imbalance on sock volailiy. 3.3 Dynamic causal relaion beween reurn and order imbalance In order o clarify he dynamic lead-lag relaionship, we employ a nesed causaliy o explore he dynamic causal relaion beween reurn and order imbalance. According o Chen and Wu (1999), we define four relaionship beween wo random variables, x 1 and x 2, in erms of consrains on he condiional variances of x 1(T+1) and x 2(T+1) based on various available informaion ses, where x i =( x i1, x i2,..., x it), i=1, 2, are vecors of observaions up o ime period T. Definiion 1: Independency, x 1 x 2 : x 1 and x 2 are independen if Var ( x x ) Var( x x, x ) Var( x x, x, x ) (9) and 1 ( T = + 1) 1( 1) 2( 1) ~ 1 1( T = + 1) ~ 1 ~ 2 T + ~ 1 ~ 2 T + ~ Var ( x x ) Var( x x, x ) Var( x x, x, x ) (10) 2 ( T = + 1) 2( 1) 1( 1) ~ 2 2( T = + 1) ~ 1 ~ 2 T + ~ 1 ~ 2 T + ~ Definiion 2: Conemporaneous relaionship, x 1 <-> x 2 : x 1 and x 2 are conemporaneously relaed if Var( x + 1) x1) = Var( x1( T 1) x1, 2 ) (11) 1( T + x ~ ~ ~ and Var ( x x, x ) Var( x x, x, x ) (12) 1 ( T > + 1) 1( 1) 2( 1) ~ 1 ~ 2 T + ~ 1 ~ 2 T + ~ and Var( x + x ) = Var( x T x, ) (13) 2( T 1) 2 2( + 1) 1 x2 ~ ~ ~ Var ( x x, x ) Var( x x, x, x ) (14) 2 ( T > + 1) 2( 1) 1( 1) ~ 1 ~ 2 T + ~ 1 ~ 2 T + ~ Definiion 3: Unidirecional relaionship, x 1 =>x 2 : There is a unidirecional relaionship from x 1 o x 2 if Var( x Var( x + x ) = Var( x T x, ) (15) 1( T 1) 1 1( + 1) 1 x2 ~ ~ ~ + x ) > Var( x T x, ) (16) 2( T 1) 2 2( + 1) 1 x2 ~ ~ ~ 6

7 Definiion 4: Feedback relaionship, x 1 <=>x 2 : There is a feedback relaionship beween x 1 and x 2 if and Var( x + x ) > Var( x T x, ) (17) 1( T 1) 1 1( + 1) 1 x2 ~ ~ ~ Var( x + x ) > Var( x T x, ) (18) 2( T 1) 2 2( + 1) 1 x2 ~ ~ ~ To explore he dynamic relaionship of a bi-variae sysem, we form he five saisical hypoheses in he Figure 7 where he necessary and sufficien condiions corresponding o each hypohesis are given in erms of consrains on he parameer values of he VAR model. To deermine a specific causal relaionship, we use a sysemaic muliple hypoheses esing mehod. Unlike he radiional pair-wise hypohesis esing, his esing mehod avoids he poenial bias induced by resricing he causal relaionship o a single alernaive hypohesis. To implemen his mehod, we employ resuls of several pair-wise hypohesis ess. For insance, in order o conclude ha x 1 =>x 2, we need o esablish ha x 1 < x 2 and o rejec ha x 1 >x 2. To conclude ha x 1 <->x 2, we need o esablish ha x 1 < x 2 as well as x 1 >x 2 and also o rejec x 1 x 2. In oher words, i is necessary o examine all five hypoheses in a sysemaic way before we draw a conclusion of dynamic relaionship. The following presens an inference procedure ha sars from a pair of he mos general alernaive hypoheses. Our inference procedure for exploring dynamic relaionship is based on he principle ha a hypohesis should no be rejeced unless here is sufficien evidence agains i. In he causaliy lieraure, mos ess inend o discriminae beween independency and an alernaive hypohesis. The primary purpose of he lieraure cied above is o rejec he independency hypohesis. On he conrary, we inend o idenify he naure of he relaionship beween wo financial series. The procedure consiss of four esing sequences, which implemen a oal of six ess (denoed as (a) o (f)), where each es examines a pair of hypoheses. The four esing sequences and six ess are summarized in a decision-ree flow char in Figure 8. The inference procedure sars from execuing ess (a) and (b), which resul in one of he four possible oucomes, E 1,., or E 4. The hree oucomes, E 1, E 2, and E 3, ha lead o he conclusions of x 1 <=>x 2, x 1 =>x 2, and x 1 <=x 2, respecively, will sop he procedure a he end of he firs sep. Noneheless, when oucome E 4 is realized, ess (c) 7

8 and (d) will be implemened. There again one of he four possible oucomes, E 5,..., or E 8, will be realized. The realizaion of oucomes E 5 and E 6, which respecively indicaes x 1 <=x 2, and x 1 =>x 2, will sop he procedure a he end of Sep 2. On he oher hand, he realizaion of oucome E 7 would lead o es (e) in Sep 3, which has he consequence of eiher oucome E 9 or oucome E 10. Oucome E 9 implies x 1 <=>x 2 and he procedure will sop. Eiher oucome E 8 from Sep 2 or oucome E 10 from Sep 3 will lead o es (f) in Sep 4. This las sep may generae wo possible resuls, E 11 and E 12, which imply x 1 <- >x 2 and x 1 x 2, respecively. 4. Empirical Resuls 4.1 Dynamic relaions beween order imbalances and reurns We examine he dynamic relaions beween order imbalances and sock reurns. Table l exhibis he empirical resuls. We find ha mean of he coefficiens of order imbalances is 7.39E-05, wih a variance of he coefficiens of order imbalances is 2.15E-07. From Panel A approximaely 70% of he values of order imbalances are significanly posiive relaion wih he sock reurns under 90%, 95% and 99% confidence level. This resul is consisen wih he daily resuls of previous sudies. We documen ha in our inraday sudy wih ime varying model, order imbalance has a significanly posiive relaionship wih sock reurn. We also draw he disribuion of he coefficiens of he order imbalances, rying o find some characerisics of his proxy. In Panel B, we find an ineresing phenomenon ha abou 95% coefficiens of our 61 sample socks are disribued in one ail. We aribue his siuaion o he propery of our sample socks. Since we selec he daily op losers, he empirical resuls are self-explained. 4.2 Dynamic relaions beween order imbalances and volailiy We also have ineresed in examining he relaion beween volailiy and order imbalances. We expec ha high order imbalances are accompanied by large volailiy. The empirical resuls are exhibied in Table 2. I is inuiively ha higher order imbalances cause higher volailiy. Therefore, we expec o see a significanly posiive relaion beween volailiy and order imbalances. However, in Panel A of Table 2, we find abou half of our samples have negaive relaion beween volailiy and order imbalances. We have wo poenial explanaions: 8

9 1. The invesors behavior From he perspecive of Kahneman and Tversky(1979), i explains how people make choices in siuaions where hey have o decide beween alernaives ha involving risk. Given he same variaion in value, here is a bigger impac of losses han ha of gains. Therefore, invesors end o hold heir socks when sock price going up, bu end o overreac and sell hem in panic. As a resul, he negaive relaion beween volailiy and order imbalances of he half socks may be aribued o he invesors irraional behaviors. 2. The leverage effec According o Chrisie (1982), he leverage effec refers o he well-esablished relaionship beween sock reurns and boh implied and realized volailiy: volailiy increases when he sock price falls. A sandard explanaion ies he phenomenon o he effec ha a change in marke valuaion of a firm's equiy has on he degree of leverage in is capial srucure, wih an increase in leverage producing an increase in sock volailiy. Tha is, when sock price declines, hen he marke capializaion of a company drops off and he deb o equiy raio increases. Since he leverage ges highly geared, volailiy has negaive relaionship wih order imbalances Condiional conemporaneous reurn-order imbalance relaion From above, we know ha curren order imbalances do really have a significan impac on he sock reurns. We wan o know wheher he previous order imbalances can also have influence on curren sock reurns, and if he answer is yes, how long do his previous order imbalances las for? In Panel A of Table 3, we find ha mos of he conemporaneous order imbalances (above 80%) have posiive influences on curren sock reurns and above 80% of lagged one order imbalances have negaive effec on curren sock reurns. The inercep, lagged wo o four order imbalances don have such significan influences on curren sock reurns. This resul is consisen wih Chordia and Subrahmanyam (2004). We can add anoher addiional informaion in our inraday sudy. The conemporaneous relaion beween order imbalances and reurns is consisen wih boh he invenory and asymmery informaion sories of price formaion. The negaive coefficiens of lagged-one imbalances are aribued o he reason ha he mos informaion on curren sock reurns is explained by conemporaneous order imbalance and auo-correlaed lagged order imbalances cause reverse impacs on curren sock 9

10 reurns. We compare he Panel B of Table 1 wih Panel B of Table 3. The frequencies of he coefficiens of conemporaneous order imbalances of hese wo models are similar. They boh are concenraed in one ail. Again, he characerisics of our op loser socks explain he empirical resuls Uncondiional lagged reurn-order imbalance relaion In his secion, we ry o conrol he conemporaneous order imbalances and include he lagged-five order imbalances in his muliple regression model. We wan o es wheher lagged order imbalances have impacs on he curren sock reurns. If he relaion beween sock reurns and lagged order imbalances is significan, hen we can use his resul o develop rading sraegy. In Panel A of Table 4, we find ha only lagged-one order imbalances have significan effec on curren sock reurns and he relaionship beween hese wo variables is negaive. This resuls is differen from he findings of Chordia and Subrahmanyam (2004). They argue ha abou 77% of he coefficiens on firs lag of order imbalances are posiive and significan. Their resul indicaes a predicive relaion beween lagged-one order imbalances and curren sock reurns. However, our resul is quie differen. I implies ha conrolling for he curren period order imbalances, lagged-one order imbalances is negaively relaed o curren reurns and he price pressure reverse. We aribue his siuaion o hree reasons as follows: 1. The daa which Chordia employed in his empirical ess is daily daa, while our daa here is inraday daa. I is inuiional ha since he ime lag inerval in inraday daa is much shorer han ha in he daily daa. Every period of inraday daa is oo shor o reveal informaion imely. 2. Since we selec daa by choosing op losers in daily rades and op losers are speculaive socks. There is a momenum effec on he speculaive socks, based on Llorene, Michaely, Saar and Wang(2002). Speculaive rades end o coninue hemselves. Therefore, when order imbalances are posiive and large, hen he price will go up again. When price goes up, hen he rae of reurn will decrease. As a resul, he relaion beween order imbalances and sock reurns is negaive and significan. 3. There goes anoher possible explanaion. Marke makers have he responsibiliy o conrol and mainain he sabiliy of sock markes. Therefore, when marke makers 10

11 observed a huge posiive order, hey hough his rade had privae informaion and will keep he bid-ask quoe down o preven discreionary raders from manipulaing he sock price. However, if bid-ask price is pressed lower, raders have a good opporuniy o buy socks wih a lower price and he invenories of marke makers will be reduced. I is quie dangerous ha marke makers have no invenories on hand because hey have a good chance o be cornered. Once marke makers were cornered, discreionary raders won and he sock price coninued o go up. This is he unique characerisic of speculaive socks. Apparenly, our sample socks are op losers and hey are speculaive. However, he sample daa which Chordia and Subrahmanyam employ include all socks 4.5. Small firm effec I is plausible ha invenory pressures from discreionary raders are differen among big and small caps. We expeced a significanly negaive relaionship beween marke capializaion and order imbalances, namely a small firm effec. Inuiively, small caps end o be easier manipulaed han big caps. Panel A of Table 5 shows ha he coefficien is slighly posiive and no significan under 90%, 95% and 99% confidence level. We can no conclude ha here exiss a small firm effec beween reurn and order imbalance. Insead of using original marke capializaion, we subsiue logged marke cap for our independen variable. Since logged variables can give he regression more economic meanings. In Panel B of Table 5, we find ha alhough he value is larger. The relaionship is sill insignifican. 4.6 Trading Sraegy based on reurn-order imbalance relaion Since here is evidence ha conemporaneous order imbalances and curren sock reurns have posiive relaionship. A naive quesion has been raised wheher we can develop a profiable rading sraegy based on his resul. We firs calculae he average reurn of our sample socks. The average reurn of our 61 op losers is %. Then, we form wo kinds of rading sraegies, including a rading price basis and a bid-ask quoe basis. In our rading sraegy, we ignore he ransacion coss and axes. We shor sell he socks when he firs corresponding negaive order imbalances appeared and buy back he socks when he firs corresponding posiive order imbalance show up. We rade his sraegy based on four scenarios: no runcaion, 50% runcaion, 90% runcaion and 99% runcaion. In Panel A of Table 6, we show he average reurn of each order imbalance runcaion 11

12 rading sraegy. The mean of no runcaion, 50%, 90%, 99% runcaions are %, %, % and 1.06%, respecively. Alhough he firs hree sraegies have negaive reurns and even he firs wo are worse han he original average reurn, we observe he rend ha when rimming he smaller order imbalances, he sraegy yield a higher average reurn. When rimming off he 99% smaller order imbalances, he average reurn even becomes posiive. This resul is amazing and we documen a successful rading sraegy ha urns daily op losers, wih an average reurn of , o a posiive reurn. In Panel A of Table 6, we replace our rading sraegy wih a bid-ask quoe basis. The Mean of no runcaion, 50%, 90%, and 99% runcaions are %, %, % and 2.59%, respecively. Again, we find ha he firs hree scenarios are worse han he reurn of using ransacion price. We aribue his resul o he bid ask spread which marke markers earned. Since invesors buy socks a ask price and sell socks a bid price, bid-ask spread is marke maker s profi. We use he paired comparisons es o see wheher he order imbalance runcaion rading sraegy is beer han no runcaion rading sraegy. We use no runcaion and 99%-runcaed sraegy in our hypohesis esing: H : 0 μ (19) H μ 1 2 μ μ : < Where μ is he mean of he no runcaion rae of reurn 1 μ 2 is he mean of he 99%-runcaed rae of reurn While he -saisic wih n-1 degree of freedom is compued as follows: d = (20) sd In he Panel B of Table 6 and Table 7, he values of one-paired es are all significan. Therefore, we conclude ha he 99%-runcaed rading sraegy earned a significan reurn han non-runcaed one. 4.7 Reurn-order imbalance causaliy relaionship in explaining he successful rading sraegy To explore he reason why a runcaed order imbalance rading sraegy earns a significan abnormal reurn, we employ a nesed causaliy approach. In order o invesigae a dynamic relaionship beween wo variables, we impose he consrains in 12

13 he upper panel of Figure 1 on he VAR model. In Table 8, we presen he empirical resuls of ess of hypoheses on he dynamic relaionship in Figure 2. Panel A presens resuls for he enire sample. In he enire sample, we show ha a unidirecional relaionship from reurns o order imbalances is 6.56% of he sample firms for he enire sample, while a unidirecional relaionship from order imbalances o reurns is 36.07%. The percenage of firms ha fall ino he independen caegory is 13.11%. Moreover, 31.15% of firms exhibi a conemporaneous relaionship beween reurns and order imbalances. Finally, 13.11% of firms show a feedback relaionship beween reurns and order imbalances. The percenage of firms carrying a unidirecional relaionship from order imbalances o reurns is almos six ime han ha from reurns o order imbalances, suggesing ha order imbalance is a good indicaor for predicing fuure reurns. I is consisen wih many aricles, which documen ha fuure daily reurns could be prediced by daily order imbalances (Brown, Walsh, and Yuen (1997); Chordia and Subrahmanyam (2004)). In addiion, he percenage of firms exhibiing a conemporaneous relaionship is over wice han ha reflecing a feedback relaionship, indicaing ha he ineracion beween reurns and order imbalances on he curren period is larger han ha over he whole period. In order o provide he evidence showing he impac on he relaion beween reurns and order imbalances, in Panels B, we divide firms ino hree groups according o he firm size. Then we es he muliple hypoheses of he relaionship beween reurns and order imbalances. The resuls in Panel B indicae ha he unidirecional relaionship from order imbalances o reurns is 40.00% in he small firm size quarile, while he corresponding number is 30.00% in he large firm size quarile during he enire sample period. The size-sraified resuls can be explained as follows. When he firm size is smaller, he percenage of firms exhibiing a unidirecional relaionship from order imbalances o reurns is larger, indicaing ha order imbalance is a beer indicaor for predicing reurns in small firm size quarile. 5. Conclusions Wih a view oward beer undersanding how sock prices move, many former researches have exensively explored he relaion beween rading aciviies and sock reurns. We use order imbalances as a proxy for rading aciviies. This sudy underakes an analysis of he relaion beween order imbalances and sock reurns. 13

14 In his sudy, we firs apply GARCH (1,1) model o examine how prices reac o order imbalances. We find ha conemporaneous order imbalances have posiively significan influences on curren sock reurns no maer wheher we add he volailiy facor in he model or no. Furher, we exend our ime inerval o a longer horizon. We find conemporaneous order imbalances are srongly relaed o conemporaneous sock reurns, bu he relaion beween he lagged wo o four order imbalances and curren sock reurns is no significan. Afer conrolling for he conemporaneous order imbalances, he posiive relaionship even disappear and only lagged-one order imbalances have significanly negaive impacs on curren sock reurns. We es he relaion beween marke capializaion and order imbalances o invesigae wheher here exiss a small firm effec. The es help us o judge wheher firms wih some specific characerisics end o have more significan order imbalances han oher socks wihou his characerisics. According o Jiang Wang (2002), small firm are easier o be influenced by informed raders. I is inuiional ha he sock prices of firms wih smaller capializaion are easier o be affeced by adjusing he rading volume of hose socks, while he sock prices of firms wih larger capializaion are more difficul o be manipulaed. However, in our empirical es, we fail o find significan relaionship beween he marke capializaion of our firms and heir curren order imbalance coefficiens. We develop a successful order imbalance runcaed rading sraegy based upon our empirical findings. Since our samples are daily op losers. Our sraegy is o shor sell when he firs negaive order imbalances appeared and buy back when he order imbalances become buyer-iniiaed. All acions ignore he ransacion coss and axes. No maer wha kinds of scenarios we choose, by rading price or by bid-ask price, we all can aain abnormal reurns by rimming 99% volumes. Our order imbalance runcaed rading sraegy yields a significan reurn. In order o explore he reason why our order imbalance runcaed rading sraegy earns a significan reurn, we furher invesigae he dynamic causaliy relaion beween reurn and order imbalance. According o he nesed causaliy empirical resuls, we find ha order imbalance is a good indicaor for predicing fuure reurns. Moreover, order imbalance is a beer indicaor for price discovery in small firm size quarile. 14

15 References 1. Admai, A. and P. Pfleiderer, 1988, A Theory of Inraday Paerns: Volume and Price Variabiliy. Review of Financial Sudies, 1, Aiken, M., P. Brown. H.Y. Izan and A. Kua, 1995, An Inraday Analysis of he Probabiliy of Trading on he ASX a he Asking Price. Ausralian Journal of Managemen, 20, Barclay, M. and J. Warner, 1993, Sealh Trading and Volailiy. Journal of Financial Economics, 34, Barclay, M. J., T. Hendersho and D. T. Mccormick, 2003, Compeiion Among Trading Venues: Informaion and Trading on Elecronic Communicaions Neworks. Journal of Finance 58, Bernard, B. S., 2002, An Empirical Sudy of he Mixure of Time and Movemens in Prices. Deparmen of Finance and Saisics, Swedish School of Economics and Business Adminisraion. 6. Bessembinder, H. and M. Kaufman, 1997, A Cross-exchange Comparison of Execuion Coss and Informaion Flow for NYSE-lised Socks. Journal of Financial Economics 46, Bollerslev, T., 1986, Generalized Auoregressive Condiional Heeroskedasiciy. Journal of Economerics, 31, Campbell, J. Y., S. J. Grossman, and J. Wang, 1993, Trading Volume and Serial Correlaion in Sock Reurns. Quarerly Journal of Economics, 108, Chen C., and C. Wu, 1999, The dynamics of dividends, earnings and prices: Evidence and implicaions for dividend smoohing and signaling. Journal of Empirical Finance 6, Chordia, T., R. Roll, and A. Subrahmanyam, 2002, Order Imbalance, Liquidiy, and Marke Reurns. Journal of Financial Economics, 65, Chordia, T., R. Roll, and A. Subrahmanyam, 2003, Evidence on he Speed of Convergence o Marke Efficiency. Journal of Financial Economics, Forhcoming. 12. Chordia, T. and A. Subrahmanyam, 2004, Order Imbalance and Individual Sock Reurns: Theory and Evidence. Journal of Financial Economics, 72, Chordia, T., R. Roll, and A. Subrahmanyam, 2006, Liquidiy and Marke Efficiency. Journal of Financial Economics, Forhcoming 14. Copeland, T. E., 1976, A model of Asse Trading under he Assumpion of Sequenial Informaion Arrival. Journal of Finance, 31,

16 15. Chrisie, A. A, 1982, The Sochasic Behavior of Common Sock Variances: Value Leverage and Ineres Rae Effecs. Journal of Financial Economics, 10, Chau, M. Marke-Making when Traders Follow Dynamic Order Placemen Sraegies. Working Paper, Easley, D., Kiefer, N. and O Hara, M., 1997, The Informaion Conen of he Trading Process. Journal of Empirical Finance 4, F. A. Wang, 1998, Sraegic Trading, Asymmeric Informaion and Heerogeneous Prior Beliefs. Journal of Financial Markes, 1, Foser, D. F. and S. Viswanahan, 1994, Sraegic Trading wih Asymmeric Informed Traders and Long-Lived Informaion. Journal of Financial and Quaniaive Analysis, 29, Foser, D. F. and S. Viswanahan, 1996, Sraegic Trading When Agens Forecas he Forecass of Ohers. Journal of Finance, 51, Figlewski, S. and X. Wang, 2001, Is he "Leverage Effec" a Leverage Effec? Working Paper, Grossman, S., 1975, On he Efficiency of Compeiive Sock Markes where Trades Have Diverse Informaion. Journal of Finance, 31(2), Gallan, R., P. Rossi, and G. Tauchen, 1992, Sock Prices and Volume. Review of Financial Sudies, 5, Gaun, C. and A. Gunn, 2004, Limi Order Imbalances and Reurn Predicabiliy. EFMA 2004 Basel Meeings Paper, He, H., and J. Wang, 1995, Differenial Informaion and Dynamic Behavior of Trading Volume. Review of Financial Sudies, 8, Hong, H., and J. Wang, 2000, Trading and Reurns under Periodic Marke Closures. Journal of Finance, 55, Hirshleifer, D., A. Subrahmanyam and S. Timan, 2006, Feedback and he Success of Irraional Invesors. Journal of Financial Economics, 81, Kahneman, D. and A. Tversky, 1979, Prospec Theory: An Analysis of Decision under Risk. Economerica, 47, Karpoff, J., 1987, The Relaion beween Price Changes and Trading Volume: A Survey. Journal of Financial and Quaniaive Analysis, 22, Kyle, A., 1985, Coninuous Aucions and Insider Trading. Economerica, 53, Lamoureux, C., and W. Lasrapes, 1990, Heeroskedasiciy in Sock Reurn Daa: 16

17 Volume versus GARCH Effecs. Journal of Finance, 45, Lee, Y. T., Y.J. Liu, R. Roll and A. Subrahmanyam, 2004, Order Imbalances and Marke Efficiency: Evidence from he Taiwan Sock Exchange. Journal of Financial and Quaniaive Analysis, 39, Lin, J. C., G. C. Sanger, and G. G. Booh, 1995, Trade Size and Componens of he Bid-Ask Spread, Review of Financial Sudies, 8, Llorene, G., R. Michaely, G. Saar, and J. Wang, 2002, Dynamic Volume-Reurn Relaion of Individual Socks, Review of Financial Sudies, 15, Lo, A. and J. Wang, 2000, Trading Volume: Definiions, Daa Analysis, and Implicaions of Porfolio Theory, Review of Financial Sudies, 13, Wang, J., 1993, A Model of Ineremporal Asse Prices Under Asymmeric Informaion, Review of Economic Sudies, 60, Wang, J., 1994, A Model of Compeiive Sock Trading Volume, Journal of Poliical Economy, 102,

18 Figure 1. Hypoheses on he Dynamic Relaionship of a Bivariae Sysem Hypoheses The VAR es H 1 : x 1 x 2 φ 12 (L)= φ 21 (L)=0, andσ 12 =σ 21 =0 H 2 : x1<->x 2 H 3 : x1 >x 2 H * 3 : x2 >x 1 H 4 : x1<=>x 2 φ 12 (L)= φ 21 (L)=0 φ 21 (L)=0 φ 12 (L)=0 φ 12 (L)* φ 21 (L) 0 H 5 : x1 >>x 2 φ 21 (L)=0, andσ 12 =σ 21 =0 H 6 : x2 >>x 1 φ 12 (L)=0, andσ 12 =σ 21 =0 H 7 : x1<<=>>x 2 φ 12 (L)* φ 21 (L) 0, andσ 12 =σ 21 =0 The bivariae VAR model: φ11 φ 21 ( L) ( L) φ12 φ 22 ( L) ( L) 1 x x 2 1 = 2 variables. The firs and second momens of he error srucure, and E( ε ) = 0 ε for k 0 and E = Σ +k ε + k ) ~ ~ ( ~ ~ ε ε ε ~ where ε x 1 and ε x 2 are mean adjused = (, )', are ha E ) = ε, σ 11 σ 12 ε for k=0, where Σ = σ 21 σ 22 The causal relaionship are defined as follows: is independency; <-> is conemporaneous relaionship; > is negaion of a unidirecional relaionship; <=>is feedback relaionship; >> is negaion of a srong unidirecional relaionship whereσ 12 =σ 21 =0 ; and <<=>> is a srong feedback relaionship whereσ 12 =σ 21 =0 ( ~ 18

19 Figure 2. Tes Flow Char of a Muliple Hypohesis Tesing Procedure Tes Sequence I (a) H 3 vs. H 4 (b) H * 3 vs. H 4 E 4 : (a) no rejec H 3 * (b) no rejec H 3 Tes Sequence II (c) H 2 vs. H 3 * (d) H 2 vs. H 3 E 1 : (a) rejec H 3, (b) rejec H 3 * x1<=>x 2 E 2 : (a) rejec H 3, (b) no rejec H 3 * x1 x 2 E 3 : (a) no rejec H 3, (b) rejec H 3 * x1 x 2 E 5 :(c) rejec H 2, (b) no rejec H 2 x1 x 2 E 6 : (c) no rejec H 2, (b) rejec H 2 x1 x 2 E 8 :(c) no rejec H 2, (b) no rejec H 2 E 7 : (c) rejec H 2 (d) rejec H 2 Tes Sequence III Tes Sequence IV (e) H 2 vs. H 4 E 10 : (e) no rejec H 2 (f) H 1 vs. H 2 E 9 : (e) rejec H 2 E 11 :(f) rejec H 1 E 12 :(f)no rejec H 1 x1<=>x 2 x 1 x 2 x 1 x 2 Five groups of dynamic relaionship are idenified: independency ( ), he conemporaneous relaionship ( ), unidirecional relaionship ( or ) and feedback relaionship (<=>). To deermine a specific causal relaionship, we use a sysemaic muliple hypoheses esing mehod. Unlike he radiional pairwise hypohesis esing, his esing mehod avoids he poenial bias induced by resricing he causal relaionship o a single alernaive hypohesis. In implemening his mehod, we need o employ resuls of several pairwise hypohesis ess. For insance, in order o conclude ha x 1 =>x 2, we need o esablish ha x 1 < x 2 and o rejec ha x 1 >x 2. To conclude ha x 1 <->x 2, we need o esablish ha x 1 < x 2 as well as x 1 >x 2 and also o rejec x 1 x2. In oher words, i is necessary o examine all five hypoheses in a sysemaic way before a conclusion of dynamic relaionship can be drawn. 19

20 Table 1. Resuls of dynamic reurn-order imbalance relaion = α + β * OI ε ε ~ N ( 0, h ) R + h A B h C = + + 1ε Ω 1 Where R is he reurn in period, defined as ln(p/p-1) OI is he explanaory variable, Order Imbalance on sock reurns β is he coefficien of he impac of Order Imbalance on sock reurns ε means he residual of he sock reurn in period h is he condiional variance in period Ω -1 is he informaion se in period -1 α, A 1, B 1, C 1 are coefficiens Panel A. he significance es of he coefficiens of condiional variance and order imbalances Confidence Level Criical Value B(1) Spill B(1) Spill 90% > % 72% 95% > % 69% 99% > % 69% 90% < % 5% 95% < % 5% 99% < % 5% Panel B he Disribuion of he coefficiens of Conemporaneous order imbalances frequency range 20

21 Table 2. Resuls of dynamic volailiy-order imbalance relaion = α ε ( ) ε ~ N 0, h R + h A B 2 h + 1 C 1ε D Ω 1 = OI Where R is he reurn in period, defined as ln(p/p-1) OI is he explanaory variable, Order Imbalance on sock reurns ε means he residual of he sock reurn in period h is he condiional variance in period Ω -1 is he informaion se in period -1 α, A 1, B 1, C 1, D 1 are coefficiens Panel A he significance es of he coefficiens of condiional variance and order imbalances Confidence Level Criical Value B(1) Spill B(1) Spill 90% > % 43% 95% > % 41% 99% > % 39% 90% < % 43% 95% < % 41% 99% < % 39% 21

22 Table 3. Empirical resuls of condiional order imbalance regressions lagged 0 hrough lagged 4 Panel A Regression of Oder Imbalance (OI) on reurn---lagged 0 hrough lagged 4 α β OI β OI β OI R = Where R is he sock reurn in period, defined as ln(p/p-1) OI is he curren order imbalance in period OI -i,i=1,2,3,4 are lagged order imbalance a ime -1, -2, -3, -4 of he sock are he coefficiens of he impac of he curren and lagged order imbalances β i,i=1,2,3,4,5 ε is he residual of sock reurn in period β OI β OI ε 1. Significance es resul of conemporaneous order imbalance (in numbers) Confidence Level Criical Value inercep (OI) (OI)-1 (OI)-2 (OI)-3 (OI)-4 90% > % > % > % < % < % < Significance es of conemporaneous order imbalance (in percenage) Confidence Level Criical Value inercep (OI) (OI)-1 (OI)-2 (OI)-3 (OI)-4 90% > % 90.16% 1.64% 3.28% 3.28% 8.20% 95% > % 81.97% 1.64% 0.00% 3.28% 4.92% 99% > % 80.33% 1.64% 0.00% 1.64% 1.64% 90% < % 0.00% 88.52% 8.20% 8.20% 8.20% 95% < % 0.00% 85.25% 4.92% 3.28% 4.92% 99% < % 0.00% 80.33% 1.64% 3.28% 1.64% 22

23 Table 4. Empirical resuls of uncondiional order imbalance regressions lagged 1 hrough lagged 5 Panel A Regression of Order Imbalance (OI) on reurn---lagged 1 hrough lagged 5 α β OI β OI β OI β OI β OI R = Where R is he sock reurn in period, defined as ln(p/p-1) OI is he curren order imbalance in period OI -i,i=1,2,3,4,5 are lagged order imbalance a ime -1, -2, -3, -4, -5 of he sock β i,i=1,2,3,4,5 are he coefficiens of he impac of he curren and lagged order imbalances ε ε is he residual of sock reurn in period 1. Significance es resul of lagged order imbalance Confidence Level Criical Value inercep (OI)-1 (OI)-2 (OI)-3 (OI)-4 (OI)-5 90% > % > % > % < % < % < Significance es resul of lagged order imbalance Confidence Level Criical Value inercep (OI)-1 (OI)-2 (OI)-3 (OI)-4 (OI)-5 90% > % 1.59% 3.17% 4.76% 7.94% 3.17% 95% > % 1.59% 0.00% 1.59% 7.94% 3.17% 99% > % 1.59% 0.00% 1.59% 4.76% 3.17% 90% < % 82.54% 1.59% 3.17% 4.76% 1.59% 95% < % 79.37% 1.59% 3.17% 1.59% 0.00% 99% < % 77.05% 1.59% 0.00% 0.00% 0.00% 23

24 Table 5. Small Firm Effec Tesing resul Panel A. Relaion beween Marke Capializaion and Order Imbalance Coefficien + Marke Cap + α i θ 0 θ = 1 ( ) i ε i Where α i is he coefficiens of he order imbalances of each sock, θ 0 is he inercep θ 1 is he coefficien of he marke cap of each sock, ε i is he residual of he sock SUMMARY Regression Saisics Muliple R R Square Adjused R Square Sandard Error Observaions 61 Coefficien Sandard Error value P value Lower 95% Upper 95% Inercep E E E E-05 X E E E E-08 Panel B. Relaion beween Log Marke Capializaion and Order Imbalance Coefficien = + ln Marke Cap + α i θ 0 θ 1 ( ) i ε i Where α i is he coefficiens of he order imbalances of each sock, θ 0 is he inercep θ 1 is he coefficien of he marke cap of each sock, ε i is he residual of he sock SUMMARY Regression Saisics Muliple R R Square Adjused R Square Sandard Error Observaions 61 Coefficien Sandard Error value P value Lower 95% Upper 95% Inercep E E X E E E E-05 24

25 Table 6. Reurn from Speculaive Trading Sraegy under Truncaed Order Imbalance Disribuion (rading price basis) Panel A. Average Reurn of All Sample Socks under 0%, 50%, 90% and 99% order imbalance runcaions Average Reurn Average Daily Reurn No runcaed 50% runcaed 90% runcaed 99% runcaed % % % % 1.06% Panel B. Significan es on wih and wihou speculaive rading sraegies X1 X2 Mean Variance Numbers Pearson Correlaion Coefficien Mean Difference 0 Degree of Freedom 60 value P(T<=) one-ailed 1.35E-07 Criical Value: one-ailed P(T<=) wo-ailed 2.69E-07 Criical Value: wo-ailed

26 Table 7. Reurn from Speculaive Trading Sraegy under Truncaed Order Imbalance Disribuion (bid-ask basis) Panel A Average Reurn of All Sample Socks under 0%, 50%, 90% and 99% order imbalance runcaions Average Daily Reurn Average Reurn No runcaed 50% runcaed 90% runcaed 99% runcaed % % % % 2.59% Panel B Significan es on wih and wihou speculaive rading sraegies X1 X2 Mean Variance Numbers Pearson Correlaion Coefficien Mean Difference 0 Degree of Freedom 60 value P(T<=) one-ailed E-12 Criical Value: one-ailed P(T<=) wo-ailed E-12 Criical Value: wo-ailed

27 Table 8 Dynamic Nesed Causaliy Relaionship beween Reurns and Order Imbalances (in percenage) x 1 x 2 x1<->x 2 x1 x 2 x1 x 2 x1<=>x 2 Panel A All Trade Size Panel B: Firm Size Small Firm Size Medium Firm Size Large Firm Size The causal relaionship are defined as follows: is independency; <-> is conemporaneous relaionship; > is negaion of a unidirecional relaionship; <=>is feedback relaionship; >> is negaion of a srong unidirecional relaionship whereσ 12 =σ 21 =0 ; and <<=>> is a srong feedback relaionship whereσ 12 =σ 21 =0 27