The Probability of Informed Trading and the Performance of Stock in an OrderDriven Market


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1 AsaPacfc Journal of Fnancal Studes (2007) v36 n6 pp The Probablty of Informed Tradng and the Performance of Stock n an OrderDrven Market Ta Ma * Natonal Sun YatSen Unversty, Tawan Mnghua Hseh Natonal Chengch Unversty, Tawan Janhung Chen Natonal Sun YatSen Unversty, Tawan Receved 26 February 2007; Accepted 07 November 2007 Abstract We estmate the probablty of nformed tradng (P) n an orderdrven stock market and perform a comprehensve analyss on the nterrelatons among P and three common performance ndcators: lqudty, volatlty, and effcency. We fnd that unnformed traders exhbt prce chasng behavor, and prce volatlty attracts unnformed traders. Usng 3SLS whch consders the endogenety of P and the lqudty, volatlty and effcency measures, we fnd that P and the volatlty and lqudty are smultaneously determned. Hgher P leads to lower lqudty and hgher volatlty, and vce versa. Frms wth larger sze, hgher ownershp concentraton, and lower turnover have hgher P. Keywords: Probablty of Informed Tradng; Lqudty; Effcency; Volatlty; Order Drven Market * Correspondng Author. Address: Correspondng author: Ta Ma, Department of Fnance, Natonal Sun Yatsen Unversty, 70 Len Ha Rd, Kaohsung, Tawan; Emal: nsysu.edu.tw; Tel: ext 4810;. Fax:
2 The Probablty of Informed Tradng and the Performance of Stock n an OrderDrven Market 1. Introducton The exstence of nformaton asymmetry among market partcpants makes nformed tradng a very mportant ssue from many respects. Unnformed traders would want to learn from the nformed about the true value of the asset, regulators are nterested n the evdence of nsder tradng, and the academcs are nterested n the behavor of the market partcpants and the process by whch prvate nformaton s ncorporated nto prces. A most challengng queston s how can we tell the probablty of nformed tradng for each stock from publcly avalable data? Hasbrouck (1991a) ponts out that the magntude of the prce effect of nformaton depends on a postve functon of the proporton of potentally nformed traders, the probablty of a prvate nformaton sgnal, and the precson of the prvate nformaton. However, the probablty of nformed tradng s not drectly observable and must be estmated from observable trade data such as quotes, transacton prces, and volumes. Past studes n ths area may be roughly categorzed nto three groups: (1) works that are related to the estmaton of the magntude of the prce mpact of nformaton or trade nformatveness, such as Hasbrouck (1991a, 1991b), and Madhavan and Smdt (1991); (2) studes that use some proxy varables to measure nformaton asymmetry, most notably, the bd ask spread. Bagehot (1971) s the frst to suggest that the bd ask spread can reflect the adverse selecton problem facng the market maker. Numerous studes later use the bd ask spread as a measure for nformaton asymmetry (see, for example, Jaffe and Wnkler, 1976; McInsh and Wood, 1992; Foster and Vswanathan, 1990, 1993a, 1993b; and Chang and Venkatesh, 1988, among others). 1) Other measures of nformed tradng nclude the proporton of nsders ownershp (e.g., Chang and Venkatesh, 1988), frm sze (e.g., Hasbrouck, 1991b), the number of trades (Jones et al., 1994), trade volume and trade sze (e.g., Kem and Madhavan, 1996; Easley, Kefer and O Hara, 1997b). 2) The thrd group s (3) sequental trade models that descrbe the tradng process and decode the probablty of nformed 1) A number of studes explore the components of bd ask spreads and estmate the adverse selecton component of spreads, e.g., Glosten (1987), Glosten and Harrs (1988), Stoll (1989) and George et al. (1991). 2) Whle most studes confrm the negatve relaton between frm sze and the probablty of nformed tradng, the emprcal evdence on the relaton between trade sze and nformed tradng s mxed. Easley, Kefer and O Hara (1997b) show that larger trade sze tends to have hgher nformaton content. Kem and Madhavan (1996) fnd that block prce mpacts are a concave functon of order sze. Barclay and Warner (1993) on the other hand fnd nformed traders are more lkely to concentrate on medumsze orders. 872
3 AsaPacfc Journal of Fnancal Studes (2007) v36 n6 tradng by econometrcally examnng ts manfestaton on observable trade data usng specfc statstcal technque such as maxmum lkelhood estmaton (e.g., Easley et al., 1996) or GMM (Handa, Schwartz and Twar, 2003). All these studes, among others, analyze the ssue of nformaton content from one pont or another, but only a few of them deal wth the drect estmaton of the probablty of nformed tradng. Easley, Kefer, O'Hara and Paperman (1996) (EKOP hereafter) and Easley, Kefer and O Hara (1997a, 1997b) poneer a seres of studes on estmatng the probablty of nformed tradng. In ther models, an nformaton event s assumed to occur once per day and the maxmum lkelhood estmaton technque s used to estmate the relevant parameters, ncludng the probablty of nformed tradng, gven actual numbers of buys and sells. One major dfference n Easley, Kefer and O Hara (1997b) from ther prevous papers s that they ncorporate trade sze nto the trade process and allow for hstory dependence n nose traders decson, and they assume nose trader s decson at tme t depends on the buy and sell decson at tme t1. They fnd that the probablty of nformatonbased tradng s lower for hgh volume stocks, and large trade tends to have hgher nformaton content. However, the concluson s obtaned by a smple comparson between subsamples wthout controllng for other factors. Although the EKOP model has some lmtatons, numerous papers have appled the EKOP model to estmate nformatonbased tradng (e.g., Brockman and Chung, 2000, Chung, L and McInsh, 2005). In ths paper, we are nterested n measurng the probablty of nformed tradng. Whle almost all studes n nformaton tradng concentrate on quotedrven markets, 3) we modfy Easley et al. s (1997b) trade model and estmate the probablty of nformed tradng n an orderdrven market. As an ncreasng number of major markets have adopted the orderdrven tradng mechansm, t would be nterestng to see whether the same result apples n such market where ndvdual nvestors submt competng bd and ask orders on the automatc lmt order book. Our study s dfferent from prevous ones n three aspects: frst of all, unlke the EKOP model whch assumes one event per day, we allow for ntra day event. Secondly, we use the opton prcng model and other smpler technque to estmate the probablty of nformed tradng, rather than more complcated MLE or GMM technques. Hence, our model 3) Handa et al. (2003) and Chou and Handa (2000) are rare examples of studes on the orderdrven market, however, ther focus was n the estmaton of spread components rather than the probablty of nformed tradng. 873
4 The Probablty of Informed Tradng and the Performance of Stock n an OrderDrven Market does not need the ndependence assumpton across days as n the EKOPtype model. 4) Fnally, we assume a nose trader s decson at tme t depends on the prce movement n perod t1, rather than the buy and sell decson at t1 as assumed n Easley et al. Our assumpton s consstent wth the trend chasng behavor of nose traders observed n many studes, e.g., Andreassen and Kraus (1988), Frankel and Froot (1989), and DeLong et al. (1990), among others, and the emprcal result also confrms our assumpton on nose traders prce chasng behavor. In addton to estmatng the probablty of nformed tradng, we are also nterested n explorng the relatonshps between nformed tradng and market performance. The sgnfcance of the probablty of nformed tradng can be best manfested through ts nteracton wth the effcency, lqudty and volatlty of the market. Although a plethora of researches has explored the theoretcal mplcaton between nformed tradng and lqudty or effcency, 5) surprsngly lttle emprcal work can be found for a comprehensve analyss on the nterrelatons between the probablty of nformed tradng and varous stock performance measures. For example, there s lttle emprcal study thus far on the relaton between effcency (or volatlty) and the estmated probablty of nformed tradng, although t s one of the key propostons n market mcrostructure theores that nformed tradng enhances effcency. Easley et al. (1996) frst explore the relaton between lqudty and the probablty of nformed tradng; however, only smple comparson of means was presented n ther study. Brockman and Chung (2000) and Chung and L (2003) adopt the EKOP model and examne the relatonshp between the probablty of nformed tradng and lqudty n Hong Kong and other markets. The crosssectonal OLS regresson s appled n ther study where lqudty s treated as the dependent varable. However, the OLS s not an approprate estmaton method when lqudty and the probablty of nformed tradng are endogenously determned. In fact, theores on nformed tradng suggest that the order strategy of nformed traders depends on the lqudty, volatlty as well as effcency of the stock, and these performance measures n turn are a result of the 4) In order to estmate the lkelhood functon n EKOPtype model, one needs the assumpton of ndependence across days. Although Easley et al. argue that n an earler 1993 paper they have tested the ndependence of nformaton events across days and can not reject the ndependence assumpton, we fnd t hard to justfy that number of buys and sells are not dependent over tme. 5) For example, Kyle (1985), Grossman (1988), Holden and Subramanyam (1992), Foster and Vswananthan (1990, 1993a) and Admat and Pflederer (1988) dscuss the theoretcal mplcatons between nformed traders, lqudty and effcency, whle Cornell and Srr (1992) and Kabr and Vermaelen (1996) emprcally examne the relaton between nsder tradngs and lqudty. 874
5 AsaPacfc Journal of Fnancal Studes (2007) v36 n6 endogenously determned tradng of the nformed and unnformed. 6) The second purpose of ths study s to do a comprehensve nvestgaton on the nteracton between the probablty of nformed tradng and the lqudty, effcency as well as volatlty of stocks. Unlke prevous studes, structural models of the above varables are bult and estmated usng three stage least squares. To the best of our knowledge, ths s the frst study that emprcally explores the nteractons among the probablty of nformed tradng and all of the key performance measures (.e., lqudty, volatlty and effcency), whle adoptng a system of equatons approach whch takes nto consderaton the endogenety of the varables. Our emprcal estmaton of the probablty structure reveals two nterestng fndngs about the behavor of the unnformed traders. Unnformed traders exhbtng a prce chasng behavor, even over a very short nterval, tend to buy when the prce n the prevous tradng perod goes up and sell when the prce n the prevous tradng perod declnes. We also fnd that volatlty n prces attracts nose traders to trade. Unnformed traders are more lkely to trade when prce moves n the prevous tradng nterval. The results of the threestages least squares (3SLS) regressons ndcate that the probablty of nformed tradng and two popular performance measures,.e., lqudty and volatlty, are smultaneously determned. Hgher probablty of nformed tradng leads to lower lqudty and hgher volatlty, and vce versa. Ths fndng does not support Admat and Pflederer (1988) s proposton that nformed traders wll follow the tradng pattern of the unnformed whose trades tend to cluster together (.e., lqudty attracts nformed tradng), snce we do not fnd that lqudty nduces nformed tradng. Rather, our fndng s consstent wth Foster and Vswanathan s (1990) argument that lqudty s lower when the probablty of nformed tradng s hgh. On the other hand, the probablty of nformed tradng and the effcency measure do not appear to be smultaneously determned. Specfcally, hgher effcency leads to hgher probablty of nformed tradng, whle there s no evdence that hgher probablty of nformed tradng leads to hgher effcency. One possble explanaton of the somewhat surprsng fndng that nformed tradng does not enhance effcency s that the samples n ths study are frms lsted n the Tawan Gre Ta Exchange, where the average frm sze s smaller, and the tradng volumes are also lower than 6) For example, Kyle (1985), Admat and Pflederer (1988) both propose that lqudty attracts nformed traders to trade. 875
6 The Probablty of Informed Tradng and the Performance of Stock n an OrderDrven Market those lsted n the Tawan Stock Exchange. Therefore, nformed traders n these stocks are much less compettve. As suggested by Kyle (1985), when there s a monopolstc nformed trader, the prce dscovery process wll be slower gven the proft maxmzng behavor of the monopolstc nformed trader. 7) Our fndng that hgher probablty of nformed tradng does not lead to more effcent prcng for stocks lsted n Tawan Gre Ta Exchange llustrates the mportance of competton to market effcency, that s, nformed tradng alone does not lead to effcency. Fnally, we fnd that frms wth larger sze, hgher ownershp concentraton and lower turnover have hgher probablty of nformed tradng. It s nterestng to compare our result wth that of Hasbrouck (1991b) or Easley et al. (1996) who fnd that largerszed frms have lower probablty of nformed tradng. We fnd that, after controllng for other factors, larger frms have hgher probablty of nformed tradng. It s also nterestng to see that turnover s negatvely related wth nformed tradng n our study. Turnover ratos n Tawan stock market are commonly regarded as an ndex for nose traders; hgh turnover s assocated wth more nose tradng. The negatve relaton between the turnover rato and the probablty of nformed tradng supports the vewpont that the turnover rato s a nose tradng sgnal n Tawan, rather than a proxy for nformed tradng as suggested by some of the studes n the U.S. 2. The Trade Model of Orderdrven Market The stock exchange n Tawan s a purely orderdrven market where orders are accumulated and matched aganst each other va the automated central lmt order book at frequent call ntervals (less than one mnute between calls). There s no offcal market maker provdng bd and ask quotatons. Onlne market report on the latest transacton prces, market bd and ask quotes, and volumes for each stock s avalable to all nvestors. The bd and ask quotatons of the market are the best prces n the lmt order book provded by varous traders. From ths respect, we may thnk that there are numerous compettve market makers and that the expected 7) Another possble explanaton s heterogenety of nformatonback, Cao and Wllard (2000) show that f the correlaton of nformaton among traders s low, the relatonshp between market effcency and nformed tradng s more complcated. 876
7 AsaPacfc Journal of Fnancal Studes (2007) v36 n6 proft s zero. 8) We assume two types of traders n our trade model: nformed traders and nose (unnformed) traders. Both types of traders trade n the market over t = 1,, T ntraday tradng perods. The percentage of each type of traders s fxed. We denote P the percentage of nformed traders, and Pu = 1 P the percentage of unnformed traders n the market. For each tradng perod, an nformaton event occurs ndependently wth probabltyα. These events are good news wth probablty δ, or bad news wth probablty 1δ. The value of nformaton events s fully realzed at the end of the tradng perod. Informed traders trade stocks at each tradng perod t accordng to the nformaton event occurrng at that perod, and the correspondng acton s smply to buy (B) f the event s good news, to sell (S) f the event s bad news, and no acton s taken (N) f there s no event. In other words, n nonevent perods all transactons come from the unnformed. Therefore, P can be regarded as a measure for the probablty of nformaton tradng. Snce we assume that the nformaton arrves over tme ndependently, the decsons of the nformed traders are also ndependent over tme. Unlke nformed traders whose decsons are ndependent across tme, we assume that the behavor of the nose traders often exhbts a postve feedback pattern. 9) In order to reflect ths evdence of dependency n tradng behavor over tme, we allow for hstory dependence n the decsons of the unnformed traders. However, unlke Easley et al. (1997b) who assume that the unnformed trader chooses a specfc trade decson at tme t gven the buy or sell trade type at tme t1, we beleve the unnformed trader s more nfluenced by the drecton of the prce movement n the prevous perod rather than by trade types. Unnformed traders are more lkely to buy when the prce rses n the prevous tradng nterval, but they do not necessarly follow the prevous buy acton f the prce goes down n the prevous perod,.e., the unnformed tend to buy on uptrend and sell on downtrend n our model. These behavors of the unnformed can be captured by assgnng approprate probabltes of tradng and buyng decsons for the unnformed. If the prce change n the prevous tradng perod s an up movement (U), a nose trader chooses to trade wth probablty β(u) and not to trade 8) The sample n ths study are frms lsted n the Tawan OTC Exchange, whch s a lqud market for smaller frms (though there are some large frms lsted too), otherwse the tradng mechansm s the same as the Tawan Stock Exchange. 9) See Sentana and Wadhwan (1992) for emprcal evdence on the postve feedback behavor. 877
8 The Probablty of Informed Tradng and the Performance of Stock n an OrderDrven Market wth probablty 1  β(u); and f he decdes to trade n ths case, he wll choose to buy wth probablty γ (U) and to sell wth probablty 1  γ (U). Smlarly, f no prce change (M) s realzed n the prevous tradng perod, the probablty that a nose trader wll trade s β(m) and 1  β(m) f not; and f he does trade he wll choose to buy wth probablty γ (M) and to sell wth probablty 1  γ (M). Fnally, f the stock prce n the prevous tradng perod goes down (D), a nose trader chooses to trade wth probablty β(d) and not to trade wth probablty 1  β(d), and gven the decson to trade, he wll choose to buy wth probablty γ (D) and to sell wth probablty 1  γ (D). In addton, the decsons only depend on the prce movement of prevous tradng perod. That s, nose traders trade stocks accordng to a statonary polcy (to be shown below) assocated wth a Markov decson process, e.g. see Hller and Leberman (2005), that are parameterzed by the prce movement of the stock n the prevous tradng perod. Although these are smplfed assumptons, t does capture the sprt of the buyhgh, selllow behavor of a typcal ndvdual nvestor n the Tawanese stock market. Our emprcal results also ndcate that these assumptons are a reasonable smplfcaton of the market structure. In sum, the nose traders behavor can be modeled by a Markov decson process havng state space {U, M, D}, decson space {B, N, S} and followng the statonary polcy: B N S U β (U) γ (U) 1 β (U) β (U)(1 γ (U)) M β (M) γ (M) 1 β (M) β (M)(1 γ (M)) D β (D) γ (D) 1 β (D) β (D)(1 γ (D)) And the nformed traders behavors can be modeled by a Markov decson process havng state space {g, n, b}, decson space {B, N, S} and followng the statonary polcy: B N S g n b
9 AsaPacfc Journal of Fnancal Studes (2007) v36 n6 3. Estmaton of The Model Parameters The model parameters to be estmated are P, α, δ, β () and γ (), { U, M, D}, whch wll be estmated from the actual transactonal data. The data set for the emprcal estmaton contans the 5mnute transactonal data of the bd, the ask and the transacton prces as well as the correspondng volumes for stocks traded n the Tawan OTC Stock Exchange from the begnnng of January to the end of December n We deleted those frms that had been lsted for less than a year n the study perod, a total of 107 stocks and over 960,000 observatons are ncluded. We estmate these model parameters n three steps. The frst step s to estmate the probabltes of nformaton events (α and δ ). We assume that the prce process follows a geometrc Brownan moton. Thus we can approxmate the geometrc Brownan moton by a trnomal tree. The trnomal trees are very accurate approxmatons for the geometrc Brownan moton n our problem settng, because the tradng nterval s very short (.e., 5mnute). Gven the hstory of past prces of a stock, t s straghtforward to estmate the up factor (u), down factor (d), and assocatng branchng probabltes (p, q) for a trnomal tree; see Hull (2006), for example. We assume that an upmovement n prce s due to good news and that a downmovement n prce s by bad news. Thus, we can equate the followng two equatons by matchng the probablty of up (down) movement wth the probablty of good news (bad news). αδ = p α ( 1 δ) = q (1) Solvngα, δ n terms of p and q, we can obtan estmates for the probablty of an nformaton event (α ), and the probablty that the event s good news ( δ ). The second step s to estmate γ (), { U, M, D}. To do so, we need to assgn the type of the events (.e., g, b, or n) for each tradng perod of the data. The event type for each tradng perod was assgned accordng to the rato of the volume of buy orders to the sum of the volumes of buy and sell orders at each tradng perod. If ths rato s greater than an upper threshold (λg), we assgn good news as the event type. If ths varable s less than a lower threshold (λb), we assgn bad news as the event type. 879
10 The Probablty of Informed Tradng and the Performance of Stock n an OrderDrven Market Otherwse we assgn no event as the event type. Recall that nformed traders buy (sell) only when there s good (bad) news, and on nonevent perods all trades come from nose traders. Therefore, f the event type s judged correctly, the sell (buy) orders n good (bad) event perods should come from the same unnformed populaton as the sell (buy) orders n nonevent perods. Smlarly, the total tradng volume n bad event perods should come from the same populaton as the total tradng volume n good event perods. Therefore, the two thresholds were determned numercally by mnmzng the sum of varances of (Bb  Bn), (Sg  Sn) and [(Bg + Sg)  (Bb + Sb)]. Table 1 shows the thresholds estmated for each stock. The ranges of λg and λb are computed to be between 0.61 to 0.85, and 0.15 to 0.36, respectvely. After the event type for each tradng perod s dentfed, the data set s parttoned nto 9 parts. Each part has a dfferent combnaton of event type (n, g, b) and prce movements (U, M, D). For example, the three parts correspondng to nonevent perods are (n, U), (n, M), and (n, D). Snce n nonevent perods all trades come from unnformed traders, transactons n the nonevent data set provde drect estmates for γ (), { U, M, D}. For example, let k be the number of elements n the set (n, U), Bt be the volume of buy orders, and St be the volume of sell orders n a nonevent perod t, then 1 k Bt k t = 0 Bt + St s a natural estmate of γ (U), the probablty of a decson to buy for an unnformed trader when prce moves up n the prevous tradng nterval. Smlarly, we can estmate γ (M) and γ (D). Summary Statstcs for the estmated Table 1. λ g and λ b of 107 stocks, where λg s the thresholds for good news, and λ b s the thresholds for bad news. Summary statstcs nclude the crosssectonal (107 stocks) mean, standard devaton (Std), medan, maxmum (Max), mnmum (Mn) and the 25 th /75 th percentle) The estmaton procedure s descrbed n Secton 3. Mean Std Max Mn Medan 25 th percentle 75 th percentle λ g λ b
11 AsaPacfc Journal of Fnancal Studes (2007) v36 n6 The fnal step s to estmate P and β (), { U, M, D}. The probablty to trade for an unnformed trader at t, gven the prce movement n t1, s as ( o 1) ( ) ( ˆ t St Bt PT u ) β = +, (2) where ot 1 represents the event type n the prevous nterval, T ˆ denotes the average tradng volume of the tradng nterval t, so β ( ) s the rato of the actual volume for o t 1 o t 1 trade to the expected tradng volume of the unnformed trader at tme t. Snce Pu s unknown, we cannot solve β ( o t 1) by equaton (2) alone. However, we wll be able to solve β ( ) as well as the probablty of nformed tradng, P, numercally by equatons (2), (7) and equatons (8). Let V be the true stock prce, and let V, V, and * V be the value of the stock condtoned on bad news, good news, and no event, respectvely. We can regard the ask prce as the expectaton of V condtoned on a buy decson. That s, Ask = EV [ B ] = V ( ) PV B +V ( ) PV B + * PV * B. (3) V ( ) By Bayes formula, we have PV ( B ) = ( = ) ( = ) PV V P BV V P V V P B V V P V V P B V V P V V P B V V ( = ) ( = ) + ( = ) ( = ) + ( = * ) ( = * ) (4) where P( B V V) * =, P( B V = V), P( B V V ) = denote the condtonal probabltes of a buy decson gven the correspondng event type. Accordng to the trade model, t s easy to be shown ( = V) = α ( 1 δ ) P B V ( V) P B V *, PV ( = V) = αδ, PV ( V ) * = = b, P( B V V ) where b = Pu β ( ) ( ) o t 1 = =1 α = = b, PBV ( = V) = b+ P (5) γ. o t 1 Substtutng (5) nto (4), we have PV ( B ) = ( ) α ( 1 δ) b α 1 δ b+ αδ ( b+ P) + (1 α) b α = (1 δ ) b b+ α P (6) 881
12 The Probablty of Informed Tradng and the Performance of Stock n an OrderDrven Market Smlarly, we can compute ( ) equaton (3), we fnally have PV B and PV ( * ) B. Substtutng these terms nto Ask = * ( 1 ) ( ) ( 1 ) s+ α( 1 δ) P V α δ b+ V αδ b+ P + V α b (7) Wth the same argument, t can be shown that Bd = * ( 1 ) ( ) ( 1 ) Vα δ P + s + V αδ s+ V α s ( 1 δ) s+ α P (8) where s = Pu β( ot 1) ( 1 γ ( ot 1) ) Snce α, δ, γ ( ), u and d are known, V = S(1+ u), V = S(1 d ), S s the transacton o t 1 prce and β ( ) can be substtuted by equaton (2), t s then straghtforward to o t 1 solve P, the probablty of nformed tradng, by equatons(7) and equatons (8). Usng the procedures descrbed above, we estmate that P, β () and γ () form the transactonal data. The results are lsted n Table 2 ~ Table 4. It s nterestng to see from Table 2 that for most stocks n the sample, β (U) and β (D) are larger than β (M). Ths result ndcates that prce volatlty attracts nose traders to trade. In addton, β (U) s larger than β (D) for most of frms, ndcatng nose traders stronger wllngness to trade on uptrend than on down trend. One possble explanaton for ths asymmetry n tradng behavor s the restrcton to short sellng at down tck. Table 2. Summary Statstcs of β (U), β (M) and β (D), where β (U), β (M) and β (D) denote the probabltes to trade for an unnformed trader when the prce moments n the prevous tradng perod are up, no change and down, respectvely. Summary statstcs nclude the crosssectonal (107 stocks) mean, standard devaton (Std), medan, maxmum (Max), mnmum (Mn), and the 25 th /75 th percentle) The estmaton procedure s descrbed n Secton 3. Mean Std Max Mn Medan 25 th percentle 75 th percentle β (U) β (M) β (D)
13 AsaPacfc Journal of Fnancal Studes (2007) v36 n6 Table 3 shows the estmates of γ (). We can see that γ (U) s larger than 0.5 and that γ (D) s less than 0.5 for most stocks. In other words, unnformed traders are more wllng to buy (sell) when prces rse (fall) n the prevous tradng perod, whch s consstent wth the postve feedback behavor assumpton for nose traders n the model. Table 3. Summary Statstcs of γ (U), γ (M) and γ (D), where γ (U), γ (M) and γ (D) denote the probabltes to buy when a nose trader decdes to trade, gven that prce moments n the prevous tradng perod are up, no change, and down, respectvely. Summary statstcs nclude the crosssectonal (107 stocks) mean, standard devaton (Std), medan, maxmum (Max), mnmum (Mn) and the 25 th /75 th percentle) The estmaton procedure s descrbed n Secton 3. Mean Std Max Mn Medan 25 th percentle 75 th percentle γ (U) γ (M) γ (D) Table 4 reports the estmates for P for the 107 stocks n our samples. The number ranges from 0.04 to ). These estmates serve as proxes for the probabltes of nformed tradng and wll be used n the followng market performance tests. Table 4. Summary Statstcs of P, where P s the average of the P s estmated by the bd and the ask prce usng the method descrbe n Secton 3. Summary statstcs nclude the crosssectonal (107 stocks) mean, standard devaton (Std), medan, maxmum (Max), mnmum (Mn), and the 25th/75th percentle) The estmaton procedure s descrbed n Secton 3. Mean Std Max Mn Medan 25th percentle 75th percentle P Informed Tradng and Stock Performance In ths secton, we dscuss the nterrelaton between the probablty of nformed tradng and the lqudty, volatlty and effcency of the stock and establsh the structural model for our emprcal test. 10) Compared wth Easley et al. (1996), the mean arrval rate of the nformed s between to
14 The Probablty of Informed Tradng and the Performance of Stock n an OrderDrven Market 4.1 Lqudty and nformed tradng Kyle (1985) models the process by whch nformaton s ncorporated nto prces when there s a monopolstc nformed trader. In hs model, and many that follow, the nformed traders strategy s a functon of the depth of the market. Admat and Pflederer (1988) ntroduce dscretonary lqudty traders nto the prce formaton process and propose that nformed traders wll follow the tradng pattern of the unnformed traders whose trades tend to cluster together; n other words, lqudty attracts nformed tradng. Subrahmanyam (1991) ponts out that f nformed traders are rsk averse, the concluson of Admat and Pflederer may not sustan. For nstance, hgher lqudty does not necessarly lead to more nformed tradng. On the other hand, Foster and Vswananthan (1990) argue that dscretonary unnformed traders wll delay ther tradng when the probablty of nformed tradng s hgh. In other words, hgher probablty of nformed tradng wll lead to lower market lqudty. Madhavan (1992) makes a smlar concluson that depth s a negatve functon of prvate nformaton. However, emprcal studes of nsder tradng (e.g., Cornell and Srr, 1992; Kabr and Vermaelen, 1996) support a postve relaton between nsder tradng and lqudty. To sum up, proftmaxmzng nformed traders make tradng decsons based on the depth of the market, and the latter s also a result of the tradng decsons of the nformed and unnformed. Both wll be taken as endogenous varables n our model. However, the drecton of the relaton between the lqudty and nformed tradng needs to be emprcally determned. 4.2 Effcency and Informed Tradng In Kyle s (1985) model where there s a monopolstc nformed trader, nformaton s released gradually over tradng tme to maxmze the nformed trader s proft. From ths respect, hgher probablty of nformed tradng may lead to less effcent prcng. On the other hand, Holden and Subrahmanyam (1992) modfy Kyle s and demonstrate that wth compettve nformed traders, nformaton wll be quckly ncorporated nto prces. Ths case s smlar to a ratonal expectaton equlbrum. Snce the compettveness of nformed traders s not observable, the sgn of the relaton between effcency and nformed tradng can not be determned a pror and 884
15 AsaPacfc Journal of Fnancal Studes (2007) v36 n6 needs to be done emprcally. 4.3 Volatlty and Informed Tradng It goes wthout sayng that nformaton leads to changes n prces. But the queston s whether volatlty nduces nformed traders to trade. Lterature n ARCH models ndcates that stock return volatlty exhbts clusterng phenomena. A possble explanaton s that nformed tradng causes volatlty whch n turn attracts more nformed tradng. Foster and Vswananthan (1990) suggest that when publc nformaton has some nformaton content, nformaton tradng wll be hgh on Monday whch leads to hgh volatlty on Monday. Kyle s (1985) model and others that follow all have smlar specfcaton that the tradng decson of the nformed s a functon of the volatlty of nose tradng as well as the volatlty of prces. Postve nterrelaton between volatlty and the probablty of nformed tradng s expected n our structural model. 4.4 Lqudty, Effcency and Volatlty A plethora of papers have looked nto the relatons between volume and prces or volume and volatlty (e.g., Karpoff, 1987; Jan and Joh, 1988; Gallant et al., 1992); most fnd postve relaton between the two. Admat and Pflederer (1988) also predct that volatlty and lqudty are postvely related. However, Foster and Vswananthan (1993b) fnd that for nterday data volume and volatlty are negatvely related. There are fewer studes dealng wth lqudty and effcency. Grossman and Mller (1988) establsh a model for equlbrum lqudty and predct the lower the autocorrelaton of returns (.e., more effcent), the hgher s the equlbrum level of lqudty. Amhud and Mendelson (1991) fnd a postve relaton between effcency and volumes. Others study the relaton between nformaton and volatlty (e.g., French and Roll, 1986; Jones et al., 1994). To sum up, emprcal as well as theoretcal researches provde a strong ratonale for treatng lqudty, effcency and volatlty as endogenous varables n our emprcal model. Before proceedng to the structural equatons, we need to defne the related measures used n our model. For lqudty measure, nstead of the commonly used tradng 885
16 The Probablty of Informed Tradng and the Performance of Stock n an OrderDrven Market volume, bd and ask order quanttes or the number of trades whch lead to dfferent results n many of the volatltyvolume relaton, we use the Amvest lqudty rato whch reflects one concept of depth;.e., the volume of trades needed to cause a unt change n prce. 11) ( Ptk,, Pt, 1, k) where % Δ P = tk,, P tk,, LR tk,, = N P N t,, k t,, k k = 1 N % ΔPtk,, k = 1 P tk,, : the stock prce of company at tradng perod k of day t N tk,, : the tradng volume of company at tradng perod k of day t, The larger s the LR rato, the hgher s the lqudty for stock. For volatlty measure, we use the standard devaton of returns to measure the nterday volatlty, as well as the daly prce range to measure the ntraday volatlty; the latter (SP) s as SP j N t = 1 ( H ) N = 1 ln L, jt where H and L denote the hgh and low prce for stock. N s the number of tradng perods. For effcency measure, we use Lo and MacKnlay s (1988) varance ratos. The varance ratos can be defned for any order greater than 1. In ths paper, we compute the average of the varance ratos for q = 1,, 10 and defne the effcency measure (EFF) as follows: VR q= 1 ( ) 10 1 VR q = 10 q EFF = 1 1 VR 11) Amhud, Yakov (2002), for example, used the rato to measure lqudty n ther study. 886
17 AsaPacfc Journal of Fnancal Studes (2007) v36 n6 The hgher s EFF, the more effcent s the stock. In addton to the above endogenous varables, there are several varables that are used as control varables. For example, ownershp concentraton s generally consdered to be hghly related wth probablty of nformed tradng and lqudty. Turnover ratos may reflect the degree of nformed tradng as suggested n some research, or t may represent, on the contrary, the extent of nose tradng. The sze of the frm s an mportant factor to all of the measures. The volatlty of stock s usually related wth the level of spread and the prce of stock. Fnally, due to the heat n the htech ndustry durng the study perod, a hghtech ndustry dummy s used. Now, we can defne the structural equatons as follows: PI = β 10 + β 11 EFF = β 20 + β 21 LIQ = β 30 + β 31 VAR = β 40 + β 41 EFF + β 12 PI + β 22 PI + β 32 PI + β 42 LIQ + β 13 LIQ + β 23 EFF + β 33 EFF + β 43 VAR + β 14 sze + μ 2 con + β 4 LIQ + β 44 con + β 15 sze + nd + μ 3 sze + β 45 turn + β 16 spd + β 46 sze + μ 1 prce + μ 4 where PI :the probablty of nformed tradng of stock EFF :effcency ndex measure for stock LIQ :lqudty ndex measure for stock VAR :volatlty ndex measure for stock con :ownershp concentraton turn :turnover rato sze :market captalzaton nd :ndustry type; a dummy varable = 1 for electronc ndustry, 0 otherwse prce :average stock prce spd :average spread 12) 12) Spread s endogenous n usual cases. However, durng the sample perod n our study, there was a twotck restrcton n dsclosng the best quotes. Bds and asks would not be dsclosed f they were beyond twotcks from prevous transacton prces. Therefore, the dsclosed spread was sometmes dstorted and not a good measure for endogenous lqudty. 887
18 The Probablty of Informed Tradng and the Performance of Stock n an OrderDrven Market Here, PI, EFF, LIQ and VAR are endogenous varables and con, sze, nd, turn, prce and spd are exogenous varables. μ 1, μ 2, μ 3 and μ 4 are random error terms assocated wth the structural equatons. Twostage least squares (2SLS) s frst used to estmate the coeffcents n the structural equatons. We fnd the resduals assocated wth each regresson equatons are hghly correlated. Threestage least squares method s then appled. Snce all equatons are overdentfed, there s gan n effcency n the estmaton of coeffcents usng 3SLS. 13) The emprcal results are reported n Table 6. Most coeffcents are sgnfcant wth pvalues of 0.1. Table 5 exhbts the descrptve statstcs of the probablty of nformed tradng ranked by tradng volumes and market captalzaton. The samples are dvded nto Table 5. The Descrptve Statstcs of P by Volume and Captalzaton Panel A:Rank by Volume (share). The samples (107 stocks) are frst dvded nto quntles accordng to tradng volume (n number of shares), the frst quntle beng the frms wth hghest volume or largest frm sze. The Descrptve Statstcs of P are then computed for each quntles, where P s the average of the P s estmated by the bd and the ask prce usng the method descrbe n Secton 3. The jont test (KruskalWalls Test) and the parwse test (Wlcoxon 2Sample Test and KruskalWalls Test) are sgnfcant at α = 0.01 for all comparsons, ndcatng that P s are sgnfcantly dfferent among volume quntles. 1 st quntle 3 rd quntle 5 th quntle Mean Std Mn Max Panel B:Rank by Captalzaton. The samples (107 stocks) are frst dvded nto quntles accordng to frm sze, the frst quntle beng the frms wth largest frm sze. The Descrptve Statstcs of P are then computed for each quntles, where P s the average of the P s estmated by the bd and the ask prce usng the method descrbe n Secton 3. The jont test (KruskalWalls Test) and the parwse test (Wlcoxon 2Sample Test and KruskalWalls Test) are sgnfcant at α = 0.01 for all comparsons, ndcatng that P s are sgnfcantly dfferent among volume quntles. 1 st quntle 3 rd quntle 5 th quntle Mean Std Mn Max ) See, for example, appendx of chap 12 of Pndyck and Rubnfeld (1998) for more detals. 888
19 AsaPacfc Journal of Fnancal Studes (2007) v36 n6 quntles accordng to tradng volume (n number of shares) or frm sze, the frst quntle beng the frms wth hghest volume or largest frm sze. The smple comparson of means shows that the probablty of nformed tradng (P) decreases wth frm sze or tradng volume, and the dfferences are sgnfcant. Ths s consstent wth prevous fndngs. However, the result of the 3SLS descrbed below reveals a dfferent pcture n the relaton between frm sze and P. Table 6 reports the regresson result of the 3SLS. We fnd that P and the volatlty and lqudty of stocks are smultaneously determned. Hgher P leads to lower lqudty and hgher volatlty and vce versa. Ths fndng s consstent wth Foster and Vswananthan s (1990, 1993a) argument that nformed tradng reduces lqudty, but t does not support Admat and Pflederer s (1988) predcton that lqudty attracts nformed tradng. Our fndng also provdes support to Kyle s (1985) model that nformed tradng s a postve functon of the volatlty of nose tradng. On the other hand, P and effcency do not appear to have twoway connectons. The probablty of nformed tradng ncreases wth the effcency of the stock, whle hgher P does not lead to greater effcency. As the GreTa Exchange s a market for smaller and newer frms, the market s thnner than the Tawan Stock Exchange, and nformed tradng n that market s relatvely noncompettve. 14) The negatve emprcal result between P and effcency s consstent wth the theoretcal model of Madhavan (1996) on thnly traded markets. Our fndng also suggests that Kyle s (1985) noncompettve nformed trader model explans better the prce dscovery process n the GreTa Stock Exchange than Holden and Subrahmanyam s (1992) compettve nformed traders model does. As to the nterrelatons between lqudty, volatlty and effcency, the nterestng fndng s that lqudty can explan volatlty and effcency, whle the opposte s not true. It seems to suggest that lqudty s the domnant performance factor over the other two. In other words, our result does not support Grossman and Mller s (1988) argument that the equlbrum level of lqudty s affected by the autocorrelaton of 14) The followng table llustrates the dfference n terms of tradng volume and number of nsttutonal shareholders per frm between the top 100 TSEC lsted frms and the top 50 Gre Ta lsted frms for year Compared wth TSEC, tradngs n Gre Ta lsted frms are thnner and much less compettve n terms of nsttutonal traders. TSEC GreTa Medan number of shares traded (n mllons) per frm 2, Average percent of nsttutonal tradng 35.03% 21.68% Medan number of nsttutonal shareholders per frm
20 The Probablty of Informed Tradng and the Performance of Stock n an OrderDrven Market returns. The result also shows that effcency s negatvely related wth nterday volatlty but postvely related wth ntraday volatlty, ndcatng that more effcent stock has hgher ntraday volatlty, but nformaton s quckly ncorporated nto prces by the end of the day so that nterday volatlty s smaller for more effcent stocks. For robustness check, we used dfferent order of qs n estmatng the effcency measure, and the results are smlar. Table 6. Result of 3SLS Regresson Model Ths table reports results of 3SLS regresson for the structural equatons defned n Secton 4. PI s the probablty of nformed tradng, EFF s the effcency measure, LIQ s the lqudty measure, VAR s the volatlty measure, con s the ownershp concentraton, turn s the turnover rato, sze s the market captalzaton, nd s a dummy varable = 1 for electronc ndustry, 0 otherwse, prce s the average stock prce, spd s the average spread. PI, EFF, LIQ and VAR are endogenous varables, and con, sze, nd, turn, prce and spd are exogenous varables. Twostage least squares s frst used to estmate the coeffcents n the structural equatons. It turns out that the resduals assocated wth each regresson equatons are hghly correlated. Thus, threestage least squares regresson s then appled to gan n effcency n the estmaton of coeffcents. The coeffcents on column 3 (4) s the result when SP (standard devaton of return) s used to measure volatlty. Most coeffcents are sgnfcant wth pvalues of 0.1 ( * ndcates sgnfcant at level 0.1). Dependent varable Independent varable VAR = SP VAR = Standard devaton PI EFF * * LIQ ( ) * ( ) * VAR * con * * turn ( ) * ( ) * sze * * EFF PI LIQ * * sze LIQ PI ( ) * EFF con ( ) * ( ) * sze * * nd * VAR PI * * EFF * ( ) * LIQ * * sze ( ) * ( ) * spd * * prce ( ) * ( ) * 890
21 AsaPacfc Journal of Fnancal Studes (2007) v36 n6 In terms of the exogenous factors, we fnd that frms wth larger sze, hgher ownershp concentraton and lower turnover have hgher probablty of nformed tradng. It s nterestng to see that, after controllng for other factors, the negatve relaton between frm sze and P observed n Table 5 turns nto postve n Table 6. Ths suggests that prevous studes whch conclude a negatve relaton between frm sze and P by a smple comparson of means may be questonable. It s also nterestng to see that turnover rato s negatvely related wth nformed tradng, suggestng that the turnover rato s a nose tradng ndex n Tawan. 5. Polcy Implcatons and Conclusons In ths paper we estmate the probablty of nformed tradng P for ndvdual stock traded n the orderdrven Tawan OTC market by modfyng Easley, Kefer and O Hara s (1997b) model and usng a dfferent estmaton technque. In addton, unlke prevous emprcal studes we examne comprehensvely the nterrelatons among nformed tradng, lqudty, effcency, and volatlty usng a system of equatons approach that takes nto consderaton the endogenety of these varables. Consstent wth our trade model assumpton about the unnformed traders behavor pattern, our fndng ndcates that unnformed traders exhbt prce chasng behavor even over a very short tme nterval and that they tend to buy when the prce n the prevous tradng perod goes up and sell when the prce n the prevous tradng perod declnes. We also fnd that volatlty n prces attracts nose traders to trade. Unnformed traders are more lkely to trade when prce moves n the prevous tradng nterval. Ths fndng suggests that a temporary tradng halt mechansm may be warranted to reduce excessve tradng fed by volatlty. We also fnd that hgh P leads to lower lqudty and hgher volatlty, and vce versa. Ths fndng supports Foster and Vswananthan s (1990) argument that nformed tradng reduces lqudty but s contrary to Admat and Pflederer s (1988) predcton that lqudty attracts nformed tradng. In terms of polcy mplcaton, our fndng suggests that the popular trend n exchanges around the world to enhance pretrade transparency may actually lead to an undesrable result, that s, lower lqudty and hgher volatlty, f the market s not large enough, as pretrade trans 891
22 The Probablty of Informed Tradng and the Performance of Stock n an OrderDrven Market parency can amplfy the negatve mpact of P. 15) In addton, we fnd no evdence that hgher probablty of nformed tradng leads to hgher effcency. One possble explanaton s that the samples n ths study are frms lsted n the Tawan Gre Ta Exchange, where the frms szes are smaller and the tradng volumes are also lower than those lsted n the Tawan Stock Exchange. Therefore, nformed traders n these stocks are much less compettve. As suggested by Kyle (1985), when there s a monopolstc nformed trader, the prce dscovery process s slower gven the proft maxmzng behavor of the monopolstc nformed trader. Our fndng that hgh probablty of nformed tradng does not lead to more effcent prcng for stocks lsted n the Tawan Gre Ta Exchange llustrates the mportance of competton to market effcency, that s, nformed tradng alone can not ensure effcency. Unlke Hasbrouck (1991b) and Easley et al. (1996) who found that frms wth larger sze have lower P, we fnd that, after controllng for other factors, frms wth larger sze have hgher P, and that ownershp concentraton and lower turnover lead to hgher P. These results have nterestng mplcatons for unnformed traders. Hgh turnover s often attrbuted to nformed tradng n the U.S. market where nsttutonal nvestors domnate. On the contrary, our study fnds that, n a market domnated by ndvdual nvestors as n most Asan stock markets, hgh turnover mples hgh percentage of nose tradng. The unnformed would have a lower chance of tradng wth the nformed (usually the nsttutonal nvestors) by avodng large frms and frms wth low turnover ratos. 15) See Madhavan (1996) for a theoretcal dscusson on transparency and stock performance. 892
23 AsaPacfc Journal of Fnancal Studes (2007) v36 n6 References Admat, A. and P. Pflederer, 1988, A Theory of Intraday Patterns: Volume and Prce Varablty, Revew of Fnancal Studes 1, pp Amhud, Y., 2002, Illqudty and Stock Returns: Crosssecton and Tmeseres Effects, Journal of Fnancal Markets 5, pp Amhud, Y. and H. Mendelson, 1991, Volatlty, Effcency and Tradng: Evdence from the Japanese Stock Market, Journal of Fnance 46, pp Andreassen, Paul and Steven Kraus, 1988, Judgmental Predcton by Extrapolaton, Mmeo, Harvard Unversty. Back, K., C. H. Cao, and G. A. Wllard, 2000, Imperfect Competton among Informed Traders. Journal of Fnance, 55, pp Bagehot, W., The Only Game n Town. Fnancal Analysts Journal 27, pp Barclay, M. J. and J. B. Warner, 1993, Stealth Tradng and Volatlty: Whch Trades Move Prces? Journal of Fnancal Economcs 34, pp Brockman, P. and D. Y. Chung, 2000, Informed and Unnformed Tradng n an Electronc, OrderDrven Envronment, Fnancal Revew 35, pp Chang, R. and P. C. Venkatesh, 1988, Insder Holdngs and Perceptons of Informaton Asymmetry: A Note, Journal of Fnance 43, pp Chou R. K. and P. Handa, 2000, The Response of Securty Markets to Order Imbalances NYSE vs. NASDAQ, the 8th Conference on the Theores and Practces of Securtes and Fnancal Markets, Natonal Sun Yatsen Unversty. Chung, K. H. and M. L, 2003, Adverseselecton Costs and the Probablty of Informatonbased Tradng, Fnancal Revew, 38 (2). Chung, K. H., M. L and T. H. McInsh, 2005, Informatonbased Tradng, Prce Impact of Trades, and Trade Autocorrelaton, Journal of Bankng and Fnance, 29 (7), pp Cornell, B. and E. Srr, 1992, The Reacton of Investors and Stock Prces to Insder Tradng, Journal of Fnance 47, pp
24 The Probablty of Informed Tradng and the Performance of Stock n an OrderDrven Market DeLong, J. B., A. Shlefer, L. H. Summers, and R. J. Waldmann, 1990, Nose Trader Rsk n Fnancal Markets, Journal of Poltcal Economy 98, pp Easley, D., N. M. Kefer, M. O Hara, and J. B. Paperman, 1996, Lqudty, Informaton, and Infrequently Traded Stocks, Journal of Fnance 51, pp Easley, D., N. M. Kefer, and M. O Hara, 1997a, One Day n the Lfe of a Very Common Stock. Revew of Fnancal Studes 10, pp Easley, D., N. Kefer, and M. O Hara, 1997b, The Informaton Content of the Tradng Process, Journal of Emprcal Fnance 4, pp Foster, F. D. and S. Vswanathan, A Theory of Interday Varatons n Volume, Varance, and Tradng Costs n Securtes Markets. Revew of Fnancal Studes 3, pp Foster, F. D. and S. Vswanathan, 1993a, Varaton n Tradng Volume, Return Volatlty, and Tradng Costs: Evdence on Recent Prce Formaton Models, Journal of Fnance 48 (1), pp Foster, D. F. and S. Vswanathan, 1993b, The Effect of Publc Informaton and Competton on Tradng Volume and Prce Volatlty, Revew of Fnancal Studes 6, pp French, K. R. and R. Roll, 1986, Stock Return Varances: The Arrval of Informaton and the Reacton of Traders, Journal of Fnancal Economcs 17, pp Froot, K. A. and J. Frankel, 1989, Forward Dscount Bas: Is t an Exchange Rsk Premum? Quarterly Journal of Economcs 104 (416), pp Gallant, A. R., P. E. Ross and G. Tauchen, 1992, Stock Prce and Volume, Revew of Fnancal Studes, 5, pp George, T., G. Kaul, and M. Nmalendran. 1991, Estmaton of the Bdask Spread and Its Components: A New Approach, Revew of Fnancal Studes 4, pp Glosten, L. R. and L. Harrs, 1988, Estmatng the Components of the Bdask Spread, Journal of Fnancal Economcs 21, pp Glosten L. R., 1987, Components of the Bdask Spread and the Statstcal Propertes of Transacton Prces, Journal of Fnance 42 (5), pp Grossman, S. J., 1988, An analyss of the mplcatons for stock and futures: Prce 894
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