Nonlnear ACD Model and Informed Tradng: Evdence from Shangha Stock Exchange Woon K Wong, Dun Tan and Yxang Tan Paper IMRU 080402
Nonlnear ACD Model and Informed Tradng: Evdence from Shangha Stock Exchange Woon K. Wong * Investment Management Research Unt Cardff Busness School Dun Tan School of Management Unversty of Electronc Scence and Technology Yxang Tan School of Management Unversty of Electronc Scence and Technology 28 January 2008 * Correspondng author: Aberconway Buldng, Colum Drve, Cardff, CF0 3EU, Unted Kngdom. Tel: +44 29 20875079; Fax: +44 29 2087449; Emal: wongwk3@cardff.ac.uk
Nonlnear ACD Model and Informed Tradng: Evdence from Shangha Stock Exchange Abstract Dufour and Engle (J. Fnance (2000) 2467) fnd evdence of an ncreased presence of nformed traders when the NYSE markets are most actve. No such evdence, however, can be found by Manganell (J. Fnancal Markets (2005) 377) for the nfrequently traded stocks. In ths paper, we ft a nonlnear log-acd model to stocks lsted on Shangha Stock Exchange. When tradng volume s hgh, emprcal fndngs suggest presence of nformed tradng n both lqud and llqud stocks. When volume s low, market actvty s lkely due to lqudty tradng. Fnally, for the actvely traded stocks, our results support the prce formaton model of Foster and Vswanathan (Rev. Fnancal Studes (990) 593). Keywords: Informed tradng, qudty tradng, Duraton, Volume, Volatlty JE Classfcaton: G, G4, G5
. Introducton Due to the avalablty of hgh frequency ntraday trade data, there have been ncreasng emprcal nterests n the role of duraton, tme between trades, n conveyng nformaton to market partcpants. The theoretcal motvatons for the study on the role of tme between transactons can be traced back to Damond and Verreccha (987) and Easley and O ara (992). Accordng to Damond and Verreccha, long duratons are lkely to be assocated wth bad news because nformed traders wll always trade unless they do not own the stock and short-sale constrants exst. On the other hand, n the model studed by Easley and O ara, nformed traders can always trade as soon as there s a sgnal or news. As a result, long duratons are lkely to be assocated wth no news. Generally speakng, nformed traders, for fear of newly receved nformaton becomng worthless, tend to trade as quckly as possble and as much as possble. owever, as ponted out by Easley and O ara (987), nformed traders may be recognsed by ther large volume tradng and ther proft opportuntes would not be maxmsed. Therefore, nformed traders may choose to break up large volume trades, thereby generatng a large number of nformaton-based trades, whch results n hgher tradng rates. Ths analyss s not only consstent wth the emprcal fndngs by Chakravarty (200) that medum-sze trades by (nformed) nsttutons cause dsproportonately large stock prces changes, but also suggests that the varatons n tradng rates n Easley and O ara (992) are assocated wth changng numbers of nformed traders. Clearly, above lteratures suggest that duraton conveys nformaton. Usng asbrouck s (99) vector autoregressve model for prces and trades, Recently, lterature suggests that nsttutons are relatvely more nformed; see, e.g., ee and Radhakrshna (2000) and Anand, Chakravarty and Martell (2005).
Dufour and Engle (2000) study emprcally the role played by duraton n the process of prce formaton. Dufour and Engle fnd that hgh tradng ntensty (short duraton) s assocated wth larger prce mpact of trades and faster prce adustment to trade-related nformaton, suggestng an ncreased level of nformaton present n the market. Manganell (2005) presents a framework that models duraton, volume and volatlty smultaneously, ncorporatng causal and feedback effects among the varables. Manganell apples the methodology to two groups of NYSE stocks, classfed accordng to trade ntensty or lqudty. Fndngs smlar to that of Dufour and Engle are obtaned for the frequently traded stocks. For the nfrequently traded stocks, both lagged volumes and squared returns hardly affect the duratons at all. Contrary to the fndngs for the Amercan markets, Celler (2003) apples Manganell s model to the Pars Bourse to fnd sgnfcantly postve relatonshp between duraton and past volatlty, mplyng that larger prce varatons tend to be assocated wth lower trade ntensty. Attrbutng the results to the dfferent learnng process n the purely order-drven Pars Bourse, Celler clams hs fndngs as evdence that the French stock market s domnated by lqudty tradng. In ths paper, we use a nonlnear (pecewse lnear) log Autoregressve Condtonal Duraton (ACD) model to study the relatonshps among the duraton, volume and volatlty for the stocks lsted on Shangha Stock Exchange (SSE). Motvated by lteratures ndcatng that volume could be used as a proxy for nformaton flow, we consder a pecewse lnear log-acd model accordng to the sze of tradng volume. Whle our fndngs are consstent wth those of Dufour and Engle (2000) and Manganell (2005), they contrbute to the lterature n the followng ways. Frst, n the case of Manganell s study, tmes of greater actvty concde wth a hgher presence of nformed traders only for the frequently traded
stocks. 2 The results obtaned by our nonlnear log-acd model ndcate otherwse. Specfcally, when the volume s hgh, greater tradng actvty s found to be assocated wth larger prce varatons for both frequently and nfrequently traded stocks. Snce there s no reason to exclude nformed traders from tradng n the less lqud stocks, our fndng s more plausble. Second, Dufour and Engle (2000) reect Admat and Pflederer s (988) model n favour of Foster and Vswanathan s (990) on the ground that both the prce mpact of trades and the speed of prce adustment to trade-related nformaton ncrease as the tme duraton between trades decreases. Ths vew of Dufour and Engle may be understood by consderng the work of Sepp (997) who assocates market lqudty to the temporary or non-nformatonal prce mpact of market orders of dfferent szes. Accordngly, Dufour and Engle nterpret large prce mpacts of trades and fast prce adustment to new nformaton as sgns of a market wth reduced lqudty, a consequence of an ncreased presence of nformed traders. Strctly speakng, t s dffcult to dfferentate the two mcrostructure models of Admat and Pflederer and Foster and Vswanathan n that the former also has an ncreased presence of nformed traders (albet along wth unnformed lqudty traders) whose tradng would also make prce more nformatve. Fortunately, the emprcal work of Foster and Vswanathan (993) llustrates a way to substantate the clam made by Dufour and Engle. Foster and Vswanathan postulate that the presence of nformed traders would deter dscretonary lqudty traders from tradng, especally when the publc nformaton to be released proxy well the prvate nformaton. Accordngly, they fnd for actvely traded stocks (thus wth plenty of publc news), tradng volume on Monday s on average lower than other weekdays. The reason s that a large number nformed traders wth prvate nformaton 2 All the stocks studed by Dufour and Engle (2000) are also hghly actve stocks.
accumulated over the weekend are keen to trade to maxmze ther profts on the frst day of tradng, thereby dscouragng dscretonary lqudty traders from tradng and thus resultng n a lower volume. Consstent wth the model of Foster and Vswanathan, we fnd for the frequently traded stocks n our sample low duraton (or hgh tradng actvty) concdes wth low tradng volume. Thrd, we observe that when tradng volume s low, market actvty on the stocks s essentally lqudty motvated. Our conecture s consstent wth the noton of lqudty as defned by Sepp (997) and Dufour and Engle (2000). 3 Accordng to them, lqudty can be regarded as a measure of market qualty n whch trades have a lower mpact on prces, and new trade-related nformaton takes longer to be fully ncorporated nto prces. Therefore, our fndng of a postve assocaton between duraton and prce varaton (when the tradng volume s low) mples that lttle new nformaton s mpounded on prce when the prce varaton s small. On the other hand, f there s sgnfcant new nformaton to be ncorporated, prce adustment takes a longer duraton to do so. Fnally, our emprcal results also suggest that a nonlnear (or pecewse lnear) model s preferable to descrbe the complcated relatonshp between duraton, volume and volatlty. Ths remark s substantated by two observatons. One s the fact that, as noted above, Manganell s (2005) lnear VAR system fals to uncover sgns of nformed tradng n the nfrequently traded stocks though there s no reason why nformed traders should not explot ther nformaton advantage n the llqud stocks. The other observaton s the (ncorrect) nference mpled by Celler s (2003) model estmates for the Pars Bourse. ke the Pars Bourse, Shangha stock market s also a purely order-drven market. It s nterestng to observe that when a lnear 3 See also Grossman and Mller (988), arrs (990) and Brennan and Subrahmanyam (996) for more expostons on the defnton of lqudty.
log-acd model s used, we arrve at the same concluson as Celler. owever, lkelhood rato tests reect a lnear specfcaton, and the nference that hgh tradng actvty s due to lqudty tradng contradcts both exstng theoretcal predctons and emprcal fndngs. Therefore, we conclude that a lnear relatonshp fals to descrbe the complex dynamcs of duraton, volume and prce varaton. The rest of the paper s organsed as follows. Secton 2 provdes nformaton on the nsttuton background of SSE. Secton 3 descrbes the econometrc models whereas Secton 4 presents the emprcal results. Fnally, Secton 5 concludes. 2. Insttutonal background Chna has the largest fast growng economy n the world. In US dollar term, the sze of ts economy stands at $2.7 trllon n 2006, ranked after US, Japan and Germany. In parallel wth the fast growng economy, the combned market captalzaton of ts two domestc stock exchanges, the Shangha Stock Exchange (SSE) and the Shenzhen Stock Exchange (SZSE), have grown to $3.7 trllon n 2007. In partcular, SSE s one of the most actvely traded stock exchanges. By the end of 2004, ts 837 lsted companes have already reached an annual share turnover of 288.7%. Market structure wse, SSE s a purely order-drven market wthout desgnated market makers. It runs an electronc automated tradng system and opens from Monday to Frday wth three sessons: 095-0925 for call aucton, 0930-30 and 300-500 for contnuous tradng double aucton. Only lmt orders are allowed n SSE. Orders are vald for one day and are stored n the lmt order book, of whch the best fve bd and ask prces and the correspondng depths of the book are revealed contnuously to publc nvestors. The tck sze (mnmum prce varaton unt) s 0.0
RMB whle the mnmum tradng quanttes unt s 00 shares (one lot). In the pre-tradng call aucton, submtted orders are batched for executon, resultng n an equlbrum openng prce that maxmzes the total tradng volume; see also Xu (2000). In the subsequent tradng sessons, submtted buy and sell lmt orders are matched contnuously based on the prce and tme prorty rules. Whle the matched orders result n a trade, the unmatched orders reman n the order queues n the lmt order book, watng for future executons. Tradng on SSE s domnated by ndvdual nvestors: 99.5% of the 68.8 mllon domestc nvestor accounts n 2002 are held by ndvdual nvestors. 4 Short sellng s absolutely prohbted n SSE. Also, to dampen extreme prce movements and to provde a cool-off perod n the events of overreacton, SSE currently sets the daly prce lmt at 0%. Due to the growng mportance of Chna economy and ts fnancal markets, there s an ncreasng research on Chna stock markets; see, e.g., Feng and Seasholes (2004), Chan, Menkveld and Yang (2007) and Ng and Wu (2007). 3. Econometrc Models 3. A lnear log-acd model The Autoregressve Condtonal Duraton (ACD) model of Engle and Russell (998) forms the bass for varous models of rregularly spaced transacton data; see, e.g., the Ultra-gh-Frequency GARC model by Engle (2000), the log-acd model by Bauwens and Got (2000), the nonlnear ACD model by Zhang, Russell and Tsay (200), and the stochastc volatlty duraton models by Ghysels, Goureroux and Jasak (2004). The ACD model employs a marked pont process to descrbe the dynamcs of transacton duraton, whch may be wrtten as follows: 4 See the Chnese Securtes Depostory & Clearng Co. td.
x = ϕ z, () p ) = µ + κ x + = ϕ = E( x Ω η ϕ. (2) q = ere, th x s the duraton, and ϕ s the condtonal mean of x ; µ, κ and η are coeffcents; Ω s the nformaton set at the tme ; and { z } s an d nnovaton process. Dstrbuton of { z } can be ether Exponental, Webull or Gama wth E ( ) = and Var z ) = δ. To ensure a postve duraton, we consder a z ( smple log-acd model proposed by Bauwens and Got (2000) wth p = q = as gven below. x = e, (3) ϕ z = E( x Ω ) = µ + κ ln( x ) + ηϕ ϕ. (4) As mentoned above, Dufour and Engle (2000) fnd that duraton plays an mportant role n the process of prce formaton. They dscover that as duraton decreases, the prce mpact of trades and the speed of prce adustment to trade-related nformaton ncrease, suggestng an ncreased presence of nformed traders. Buldng on the results of Dufour and Engle, we analyze the nfluence of volume and volatlty on duraton. Our approach s a log-acd model augmented wth volume and prce volatlty, so Equaton (4) above s replaced by = E( x Ω ) = µ + κ ln( x ) + ηϕ + ξvolume + γ u ϕ, (5) where Volume s the tradng volume seres and u s the proxy for volatlty. 5 Above augmented log-acd model s dentcal wth the duraton equaton of the VAR system of duraton, volume and volatlty proposed by Manganell (2005) to 5 u n (5) s obtaned as the resduals of an MA() process: r + = µ + ρu u. That s, u s the resdual seres after removng the mcrostructure effect of the orgnal prce return seres; see Dacorogna, Gencay and Muller (2000). We have also used u n place of u, and essentally smlar results are obtaned. 2
study NYSE stocks. Accordng to Admat and Pflederer (988), Dufour and Engle (2000), Manganell (2005) and others, f the hgh tradng ntensty s attrbuted to nformed tradng, then prce volatlty s hgh. 6 That s, volatlty s postvely related wth tradng ntensty and negatvely assocated wth duraton, so γ n Equaton (5) s expected to be negatve. Otherwse, f the hgh tradng ntensty s related to lqudty tradng, γ s expected to be postve. Smlar argument holds for volume. For example, olden and Subrahmanyam (992) generalze Kyle (985) model to ncorporate competton among multple rsk-averse nsders and demonstrate that competton among nsders s assocated wth hgh tradng volume and rapd revelaton of prvate nformaton. Generally speakng, analyses of Easley and O ara (992), O ara (995), and Easley, Kefer and O ara (997) suggest there s some mpled nformaton n the tradng volume that may not be reflected n the prce process tmely. All these studes share the same concluson that there s a postve relatonshp between volumes and nformed tradng. Therefore, the volume coeffcent ξ n (5) s expected to be negatve n the presence of nformed traders. 3.2 A nonlnear log-acd model In addton to the above mcrostructure lteratures on the assocaton of volume and nformed tradng, numerous studes have documented the mportance of volume as a proxy for nformaton. For example, amoureux and astrapes (990) fnd that augmentng the varance functon wth tradng volume for an ndvdual stock removes evdence of GARC effects; Andersen (996) n a stochastc volatlty framework regards the varaton n tradng volume as the nformaton arrval process. Therefore, snce the dynamcs of nformed tradng s lkely to dffer from those of 6 In asbrouck (99), the trade-correlated component of varance of changes n the effcent prce s regarded as a measure of prvate nformaton mpounded on the market through tradng.
lqudty tradng, a nonlnear relatonshp dependent on the level of tradng volume s consdered. Another motvaton for a nonlnear model comes from the emprcal results of Manganell (2005) for the less frequently traded stocks, where most of the volatlty coeffcents γ s are found to be nsgnfcant. Snce there s no theoretcal ground to exclude nvestors wth prvate nformaton to trade on llqud stocks, we conecture that the nsgnfcant fndng of Manganell s lkely due to the possblty that a lnear model fals to uncover the presence of nformed tradng n a less lqud stock. We thus propose here a smple nonlnear (pecewse lnear) log-acd model to dfferentate the relatonshp between volatlty and duraton accordng to the sze of tradng volume as stated below, ϕ = E( x Ω = µ + κ ln( x ) ) + ηϕ + ξvolume + γ V u + γ V u. (6) V s an ndcator varable that equals to f Volume Mean(Volume), 0 otherwse. 7 The other ndcator varable s smply defned as V = V. The above nonlnear model s actually a pecewse lnear log-acd model n whch the relatonshp between duraton and volatlty s captured by γ when volume s above average ( V =, V = 0 ); when volume s below average ( V =, V = 0 ), the relatonshp s descrbed by γ. Snce t s theoretcally plausble that (dscretonary) lqudty tradng also causes concentrated tradng (see Admat and Pflederer, 988), the advantage of (6) s to allow for concentrated tradng to be caused by nformed tradng at certan perods of tme (say, when volume s hgh), as well as by lqudty tradng at other tme ntervals (when volume s low). If ths hypothess was correct, our nonlnear log-acd model would detect presence of nformed traders for both lqud and 7 Mean (Volume) s the mean value of volume over the entre sample.
llqud stocks. As t turns out, our emprcal results n the next secton shows that hgh tradng actvtes at dfferent volume state do suggest a rather dfferent economc dynamc: short duraton at hgh-volume state mples nformed tradng whereas at low-volume state, concentrated tradng s lkely due to lqudty traders. We therefore consder a step further n whch a dfferent dynamc also exsts between duraton and volume accordng to the sze of volume, as descrbed below. ϕ = E( x Ω = µ + κ ln( x ) + ( ξ Volume ) + ηϕ + γ u ) V + ( ξ Volume + γ u ) V. (7) Generally speakng, hgh tradng volume s assocated wth rapd revelaton of prvate nformaton. owever, Foster and Vswanathan (990, 993) clam that the presence of nformed traders could also deter dscretonary lqudty traders from tradng and thus resultng n a relatvely lower volume. Our nonlnear log-acd model above enables us to formally test the clam made by Foster and Vswanathan. For hghly actve stocks wth plenty of news coverage, the Foster and Vswanathan s model predcts a postve ξ ; n all other cases, ξ s should be negatve. 4. Emprcal results 4. Data We consder 0 stocks lsted on the SSE and extract ther transacton data from the CSMAR database. 8 To select the 0 stocks, we frst classfy all the stocks lsted on the SSE nto large, medum and small groups accordng to ther market value, and fve stocks wth the hghest market value n the large and small groups are 8 CSMAR stands for Chna Securtes Market and s a regstered trade mark of GTA Informaton Technology, Co. td.
selected. For our analyss, we use prce of trades, tme stamp of trades, sze (volume) of trades, and bd-ask quotes. Our sample perod begns on September 2003 and ends on 30 June 2005. As s noted before, n each tradng day, there are four tradng hours n two sessons of contnuous tradng, from 0930 to 30 and from 300 to 500, wth a noon-break n between. Smlar to Engle (2000), the effectve duraton s defned as the tme nterval between two trades wth a prce change (trades wth the same prce are aggregated). The frst trade n both the mornng as well as the afternoon sessons s deleted. Descrptve statstcs of the 0 stocks are shown n Table. Bascally, duratons and spread are smaller for large and actvely traded stocks. < Insert Table : Sample stocks > Smlar to mcrostructure varables such as spread and volume, duraton has a strong ntraday perodcty; see, e.g., Engle and Russell (998), Andersen and Bollerslev (997) and Martens (200). We apply the smoothng method of Engle and Russell to remove the ntraday perodcty of duraton and volume seres. Takng the duraton seres Dur as an example, the smoothng method s, s( t ) N = = D (ˆ a x = Dur s t ), (8) + bˆ ( t T ( ) + cˆ ( t T ) 2 + dˆ ( t T 3 ) ). (9) ere, th Dur s the duraton, s ( t ) s the perodc factor, x s the adusted duraton, N s the number of sample sectons n each tradng day, and T s the correspondng specfed tme pont of the sample secton. Snce each secton lasts for half an hour, N = 8 and T ( =,..., 8 ) refers to 0930, 000,..., 430, 500. Fnally, D s a dummy varable that attrbutes each duraton to a specfed secton th ( D = f the duraton takes place n the th secton, D = 0 otherwse), and t
th s the tme at whch the duraton s takng place. The estmators of â, bˆ, ĉ, dˆ can be obtaned from regresson of equaton (9), and the ftted s t ) s used for ( duraton perodcty adustment. The emprcal ntraday patterns of duraton and volume are found to be qualtatvely smlar to those of Engle (2000) and other lterature on ntraday seasonalty. 4.2 Duraton and tradng actvty ere, we provde statstcs on volume and spread for a large stock 60009 and a small stock 600063 n order to prelmnarly assess the role played by duraton n the process of prce formaton. We frst consder the scenaros of hgh and low volume. Then for each observaton, duraton x s sorted nto short-medum-long groups and prce volatlty u s sorted nto small-medum-large groups. Relevant statstcs only for the short and long duraton groups as well as the small and large sze groups are reported n Table 2 below. < Insert Table 2: Duraton and tradng actvty > The fgures n Panel A are average number of shares per unt tme (n second) transacted between two trades that result n a prce change. It s clear that short duraton n SSE concdes wth hgh tradng ntensty, regardless of whether t s n a hgh or low volume state. Moreover, as can be seen from Panel B, the average total volume statstcs reveal that, despte ther short tme span, short duratons account for a sgnfcant porton of tradng volume. Panel C provdes fgures on the spread, defned as asks mnus bds quotes. Consstent wth exstng lterature, when duraton s short and prce s volatle, tradng s especally actve and spread s large. Spread can be decomposed nto two parts, asymmetry cost and nventory cost; see, e.g., Madahavan, Rchardson and Roomans (997). gher spread s thus often regarded
as hgher asymmetry cost, whch mples a hgher lkelhood of presence of nformed traders. Fnally, R s defned as the rato of large- u to small- u fgures. R measures the relatve ncrease n tradng ntensty when prce becomes volatle. So we can see that n the hgh-volume state, tradng actvty ntensfes consderably for both stocks when prce vares consderably. For example n Panel A, value of R s.53 for stock 600063. The correspondng R value when market s quet wth low tradng volume s only.5. Smlar pattern s also observed for stock 60009 as well as n Panel B. Though no formal nference can be made based on R statstcs, they do suggest that the tradng dynamcs durng a short duraton n the hgh-volume state can be rather dfferent from those n the low-volume state. 4.3 near log-acd estmates Throughout the paper, estmaton of log-acd parameters uses maxmum lkelhood estmaton (ME) method. We assume that the nnovaton process { z } n Equaton (3) follows an exponental dstrbuton, and the assocated lkelhood functon s gven by ( Θ) = N = x log( ϕ + ), (0) ϕ where N s the number of observatons and Θ s the vector of parameters. ere, we shall frst consder the estmates of lnear log-acd model gven by Equaton (5). Consstent wth Manganell (2005) and most lteratures, t can be seen from Table 3 that the volume coeffcent ξ s sgnfcantly negatve for all stocks except 600050. That s, large volume n SSE s assocated wth hgh tradng actvty or short duraton. The emprcal result for the volatlty coeffcent γ s rather dfferent. Except for 600900, larger prce volatltes tend to be followed by
longer duratons. Adoptng the Dufour and Engle s (2000) vew on lqudty, postve volatlty coeffcents suggest that SSE s domnated by lqudty traders. < Insert Table 3: near log-acd model > 4.4 Nonlnear log-acd estmates The above emprcal results contradct wth most lterature, notceably Dufour and Engle (2000) and Manganell (2005) who fnd for NYSE stocks concentrated tradng s assocated wth an ncreased presence of nformed traders. For the Chna stock market, Fang and Wang (2005) also fnd that nformed tradng leads to short duratons. Our proposed nonlnear log-acd models resolve ths contradcton and suggest that a lnear log-acd s lkely a model msspecfcaton. < Insert Table 4: Nonlnear log-acd model I > Table 4 provdes estmates of our frst nonlnear log-acd model specfed by (6). The most strkng dfference les n the fact that all volatlty coeffcents γ are now sgnfcantly negatve except for stock 600697. So when volume s hgh, short duraton (hgh tradng ntensty) mples a hgher number of nformed traders on the Chna stock market. When volume s low, all γ s are sgnfcantly postve. Accordng to Dufour and Engle (2000) and Sepp (997), a lqudty drven trade would normally have a lower mpact on prce, and trade-related nformaton takes longer to be fully ncorporated nto prces. That s, when market s domnated by lqudty traders, large prce change corresponds to longer duraton. Our results n Table 4 thus suggest that t s lqudty traders who account for actve tradng when market s n a low-volume state. Fnally, we remark that preference of the nonlnear model over ts lnear counterpart s supported by 9 out of 0 sgnfcant lkelhood rato statstcs. From Table 4, we can see that the volume coeffcents for less lqud stocks are
negatve, whch s consstent wth the fact that hgh volume concdes wth short duraton. For the large stocks, 4 out of 5 ξ s are postve (3 of them sgnfcant). When tradng volume s hgh, ths may be regarded as sgns supportng Foster and Vswanathan s (990) predcton that presence of nformed traders deters lqudty traders and results n lower tradng volume (at short duraton). Ths explanaton does not hold, however, when the tradng volume s below the average level. To allow for a dfferent dynamcs between volume and duraton when tradng s less actve, we estmate our second nonlnear log-acd model gven by (7). < Insert Table 5: Nonlnear log-acd model II > If Foster and Vswanathan were correct, we would expect to see a negatve relatonshp between volume and duraton when volume s low, but the relatonshp would become postve when volume s hgh. As can be seen from Table 5 above, ths ndeed turns out to be the case. Frst of all, when tradng volume s low, all low-volume coeffcents ( ξ ) are negatve. When tradng volume s hgh, 3 out of 5 large stocks have sgnfcantly postve hgh-volume coeffcents ( ξ ). Though the other two large stocks have negatve ξ, only one of them s sgnfcant. Fnally, we remark that that both the SSE and Pars Bourse are purely order drven markets. It s nterestng to see that the lnear log-acd specfed by (5) yelds smlar (ncorrect) nference as Celler (2003). The fact that the sample NYSE stocks analyzed by Dufour and Engle (2000) and Manganell (2005) are from an order drven market wth specalsts suggests that there could be a subtle dfference n the dynamcs of the two dfferent market structures. 9 The mportant pont here s that when an approprate nonlnear model s used, the underlyng economcs are found to be the same for both NYSE and SSE. 9 Specalsts at NYSE have dual broker-dealer roles. They trade as brokers for ther clents whle actng as dealers for ther own accounts; see arrs and Panchapagesan (2005) for more detals on the market structure of NYSE.
4.5 Robustness of results Managanell (2005) proposes a VAR framework to study duraton, volume and returns smultaneously, whch has the advantage of takng nto account feedbacks among the varables concerned. We do not carry out such analyss here, partly because our man obectve does not nclude mpulse response functon analyss, for whch feedbacks should be more rgorously dealt wth. More mportantly, smlar to Dufour and Engle (2000) who treats duraton exogenously n ther prce and trade model, we beleve our results are not affected by the ssue of smultanety and are qualtatvely vald. Ths s supported by varous analyses that have been carred out to check the robustness of the aforementoned emprcal results. Due to constrant of space, we do not report all the numercal results. 0 Overall, the followng analyses show that the fndngs of ths paper are stable and robust. The ntraday pattern of volatlty Smlar to the duraton and volume, volatlty has an -shaped ntraday pattern. To make sure that our fndngs are not spurous results due to ntraday seasonalty n volatlty, we apply the smoothng methods gven by (8) and (9) to the volatlty seres u, and re-estmate our nonlnear log-acd models. Results obtaned are qualtatvely smlar to the above fndngs. The nfluence of other factors on duraton Present theoretcal or emprcal works on duraton fnd that there are other factors that may affect the dynamcs of the duraton besdes volume and volatlty. We follow Bauwens and Got (2000) to consder more control varables n our nonlnear log-acd models. In partcular, buy-to-sell rato and spread are augmented 0 Detaled results are avalable from the authors upon request.
to (7): ϕ = E( x Ω = µ + κ ln( x ) + ( ξ Volume + θ BSraton ) + ηϕ 2 + γ u ) V + θ Spread. + ( ξ Volume + γ u ) V () In above, BSrato s the rato of buyer-ntated volume to the total volume cumulated from the frst trade after market open to the current trade. BSrato can be regarded as a proxy for the stock prce trend. Generally speakng, f BSrato s larger than 0.5, t mples that the stock prce s on an upward trend; otherwse, t s on downward trend. The other varable, Spread, can be regarded as a proxy for the presence of asymmetrc nformaton. Whle an unnformed lqudty trader may be deterred from tradng by a large spread, a competng nformed trader would be keen to trade as soon as possble before hs prvate nformaton become obsolete. So n the former case, duraton wll be lengthened, whereas n the latter case, duraton wll be shortened. Anyway, spread s an mportant varable that needs to be consdered. Agan, estmates of () reveal the same message as n the last secton. ung-box statstcs Table 6 below lsts ung-box (B) statstcs for the orgnal duraton seres (after adustment for ntraday perodcty) and ts estmated resduals usng nonlnear log-acd model gven by (7). 50 lags are used n calculatng the B statstcs. We can see that there s a huge reducton n the B statstcs after fttng the nonlnear log-acd(2,2) specfcaton. Though most of the B statstcs are sgnfcant, two remarks are made here. Frst s that ths s a common feature wth long tme seres. Engle (2000) and Manganell (2005) also face smlar data fttng problems. Indeed, our data s extremely long: the longest tme seres has 232,364 observatons, compared to 52,46 observatons n Engle (2000) and 88,97 observatons n
Manganell (2005). Second, more mportantly, our estmated auxlary models wth longer lags reveal the same conclusons. < Insert Table 6: ung-box statstcs > 5. Conclusons The emprcal evdence obtaned n ths paper on the Shangha Stock Exchange (SSE) contrbutes to the lterature on the mcrostructure of fnancal markets. The fact that both the SSE and Pars Bourse are purely order drven and that both Celler (2003) and our lnear log-acd analyss provdes smlar (ncorrect) nference suggest there s a subtle dfference n the learnng process between a centralzed purely-order-drven market and an order-drven-specalsts market such as NYSE. owever, the economcs that underle the tradng of SSE are the same: a hgher tradng actvty concdes wth an ncreased presence of nformed traders on the market. Ths observaton s made possble by usng a nonlnear log-acd model that dentfes the dfferent dynamc of nformed tradng from that of lqudty tradng. Snce an nformed trader wll be equally keen to trade on an llqud stock f there s prvate nformaton to be exploted, t s probable that the Manganell s (2005) fndngs (on the presence of nformed tradng) can be extended to less frequently traded stocks f nonlnearty s taken nto account. We also valdate the clam made by Dufour and Engle (2000) that ther fndngs support Foster and Vswanathan s (990) model. Ths s evdenced from the emprcal results of our nonlnear econometrc model: when volume s hgh, short duraton (hgh tradng ntensty) concdes wth lower volume, suggestng that the presence of nformed traders deters dscretonary lqudty traders from tradng. Both the samples of TORQ and TAQ databases used by Dufour and Engle (2000) and Manganell (2005) respectvely use NYSE transacton data.
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Table : Sample stocks Summary statstcs for the sample stocks are provded n the table below. Prce refers to the transacted prce, duraton s the tme between transactons that result n a prce change, spread s smply asks mnus bds, and volume s the number of shares transacted n each nterval. Stock Industry Code Company name Average Prce Average Duraton Average Spread Average Volume No. of Obs. arge (lqud) stocks 60009 C65 600028 B03 600036 I0 600050 G85 600900 D0 Baoshan Iron & Steel Co., td. Chna Petroleum & Chemcal Corp. Chna Merchants Bank Co., td. Chna Unted Tele. Corp. td. Chna Yangtze Power Co., td. 6.47 34.0 0.0 59864.39 4289 4.72 32.6 0.0 723.02 54545 9.52 27. 0.02 3320.39 86765 3.56 2.8 0.00 09833.3 232364 8.84 25.9 0.0 39535.97 90278 Small (llqud) stocks 600063 C47 60072 C6 600426 C47 600697 600877 C75 Amhu Wanwe gh- Tech Mat. Ind. Co. td. enan uanghe Whrlwnd Co., td. Shandong ualu- engsheng Chem. Co. td. Chang Chun Eurasa Group Co., td. Chna Jalng Industry Co., td. (Group) 5.4 42.3 0.05 5357.67 3250 5.53 85.4 0.03 6733.03 5479.22 64.3 0.022 5760.99 72386 6.00 60.0 0.08 6582.38 28645 4.8 38. 0.06 9286.49 33663
Table 2: Duraton and tradng actvty Volume and spread statstcs are provded for stocks 60009 and 600063. At each observaton, duraton x s sorted nto short-medum-long groups; prce volatlty u s sorted nto small-medum-large groups. Relevant statstcs only for the short and long duraton groups as well as small and large prce varaton groups are reported below for the hgh and low volume scenaros. The fgures n Panel A are average number of shares per second transacted n an effectve duraton. Panel B tabulates the average volume statstcs, whereas Panel C provdes fgures on the spread, defned as asks mnus bds quotes. Fnally, R s the rato of large- u to small- u fgures. R measures the relatve ncrease n tradng ntensty when prce becomes volatle. Small 60009 600063 (arge stock) (Small stock) u arge u R Small u arge u R Panel A: Average volume per unt tme gh Short x 23046 36685.59 885 355.53 volume ong x 359 4252.8 55 52 0.95 ow Short x 477 900.29 39 60.5 volume ong x 365 363 0.99 0 0.00 Panel B: Average volume per prce change gh Short x 6083 229588.43 0646 640.52 volume ong x 20677 26066.29 3007 3655.05 ow Short x 9687 737.2 55 788.5 volume ong x 7324 2024.7 229 2343.02 Panel C: Average spread gh Short x 0.039 0.078 0.023 0.0223 volume ong x 0.005 0.05 0.028 0.089 ow Short x 0.003 0.026 0.04 0.0227 volume ong x 0.005 0.05 0.039 0.097
Table 3: near log-acd model Estmates of the lnear log-acd model gven by equaton (5), ϕ = µ + κ ln( x ) + ηϕ + ξvolume + γ u, are provded n the table below. The volume and volatlty coeffcents are hghlghted for ther relevance. The values n parentheses are p-values of the estmated coeffcents. Stock µ κ η ξ γ kelhood arge (lqud) stocks 60009 0.03 0.029 0.974-0.094.349-26995.9 600028 0.02 0.024 0.978-0.63 0.934-40739.6 600036 0.05 0.03 0.969-0.28 0.639 0.08-7546.9 600050 0.004 0.00 0.990 0.024 0.755-228673.5 600900 0.04 0.025 0.977-0.0-2.34-79604.9 Small (llqud) stocks 600063 0.046 0.068 0.922 -.954 4.475-2467.7 60072 0.044 0.059 0.934 -.668.72-4436.7 600426 0.034 0.063 0.937-0.70 2.394-58080.9 600697 0.036 0.06 0.93 -.088 3.884-22467.9 600877 0.043 0.074 0.93-0.963 3.54-27563.2
Table 4: Nonlnear log-acd model I Estmates of the nonlnear log-acd model gven by equaton (6), ϕ = µ + κ ln( x ) + ηϕ + ξvolume + γ u V + γ u V, are provded. V ( V ) s an ndcator that equals to one f Volume s below (above) the average value. The values n parentheses are p-values of the estmated coeffcents whereas the values n square brackets are lkelhood rato (R) statstcs for model specfcaton (6) over (5). Under the null hypothess, the R statstcs are dstrbuted as Ch-squared wth 2 degree of freedom wth 5.99 (9.2) as 5% (%) crtcal value. Stock µ κ η ξ *00 γ γ kelhood arge (lqud) stocks 60009 0.009 0.028 0.974 0.084 5.075-3.05-2696.8 [58.2] 600028 0.008 0.025 0.977 0.0433 (0.00) 4.630-3.78-4065. [77.0] 600036 0.03 0.03 0.968-0.93 3.796 -.824-7537.8 [90.2] 600050 0.003 0.0 0.989 0.044.383-0.756-228632. [82.8] 600900 0.02 0.025 0.977 0.05 (0.233).94 (0.005) -6.732-79548.2 [3.4] Small (llqud) stocks 600063 0.039 0.069 0.92 -.342 8.285 -.696 (0.057) -2444.3 [46.8] 60072 0.039 0.060 0.933 -.80 6.75-6.069-44095.7 [82.0] 600426 0.03 0.064 0.936-0.500 5.790 -.525 (0.005) -58057.0 [47.8] 600697 0.035 0.062 0.930-0.984 4.684 2.898-22466.3 [3.2] 600877 0.039 0.077 0.908-0.56 7.744-4.24-27509.4 [07.6]
Table 5: Nonlnear log-acd model II Estmates of the nonlnear log-acd model gven by equaton (7), ϕ = µ + κ ln( ) + ηϕ + ( ξ Volume + γ u ) V + ( ξ Volume γ are provded. x + u ) V V ( V ) s an ndcator that equals to one f Volume s below (above) the average value. The values n parentheses are p-values of the estmated coeffcents whereas the values n square brackets are lkelhood rato (R) statstcs for model specfcaton (7) over (6). Under the null hypothess, the R statstcs are dstrbuted as Ch-squared wth 2 degree of freedom wth 5.99 (9.2) as 5% (%) crtcal value., Stock µ κ η ξ *00 ξ *00 γ γ kelhood arge (lqud) stocks 60009 0.05 0.029 0.97-3.053 0.082 5.32-3.964-2680.2 [23.3] 600028 0.02 0.025 0.974-2.453 (0.00) 0.069 4.849 (0.00) -3.903-40560.4 [8.4] 600036 0.09 0.032 0.966-3.396-0.234 4.677-2.328-75262.0 [309.8] 600050 0.004 0.0 0.988-0.623 0.045.40-0.635-228597.0 [53.0] 600900 0.08 0.026 0.974-3.68-0.005 (0.589).784 (0.489) -8.089-79328.0 [553.8] Small (llqud) stocks 600063 0.048 0.069 0.92-4.970 -.329 9.94-3.33 (0.057) -2434.5 [9.6] 60072 0.050 0.060 0.932-5.697 -.205 7.940-8.846-44069.8 [5.8] 600426 0.039 0.065 0.935-3.890-0.583 6.584-2.5 (0.005) -58036.6 [40.8] 600697 0.047 0.06 0.930-5.585 -.092 5.450.784-22450.3 [32.0] 600877 0.055 0.079 0.905-7.32-0.64 9.043-5.960-27486. [46.6]
Table 6: ung-box statstcs The table below lsts ung-box statstcs for the orgnal duraton seres (after adusted for ntraday perodcty) and ts estmated resduals usng nonlnear log-acd model gven by (7) wth varous ACD auxlary specfcatons. 50 lags are used n calculatng the ung-box statstcs. The correspondng crtcal values at 5% and % sgnfcance levels are 67.5 and 76.2 respectvely. arge (lqud) stocks 60009 600028 600036 600050 600900 Orgnal duraton 70568 74044 97774 30857 79403 ACD(,) resduals 334 2396 392 205 275 ACD(2,2) resduals 74 622 370 344 335 ACD(3,3) resduals 72 586 448 33 332 Small (llqud) stocks 600063 60072 600426 600697 600877 Orgnal duraton 62773 02426 73287 500 44999 ACD(,) resduals 79 290 75 230 207 ACD(2,2) resduals 8 282 760 230 207 ACD(3,3) resduals 5 257 653 70 79