We-Hsu Kuo Asa e Pacfc al./asa Maageme Pacfc Maageme evew (005) evew 0(), (005) 3-3 0(), 3-3 Prce Volaly, Tradg Acvy ad Marke Deph: Evdece from Tawa ad Sgapore Tawa Sock Idex Fuures Markes We-Hsu Kuo a,*, Hsa Hsu b, ad Chwa-Y Chag c a Docoral Sude Deparme of Busess Admsrao, Naoal Cheg Kug Uversy, Taa, Tawa ; ad a lecurer Deparme of Face, Lg Tug College, Tachug, Tawa b Deparme of Face, Souher Tawa Uversy of Techology, Taa Couy, Tawa. c Deparme of Busess Admsrao, Naoal Cheg Kug Uversy, Taa, Tawa. Absrac Acceped March 00 Avalable ole Ths sudy emprcally vesgaes he relaos amog prce volaly, radg acvy ad marke deph for some seleced fuures coracs raded o he Tawa Fuures Exchage (TAIFEX) ad Sgapore Exchage Dervaves Tradg Dvso (SGX-DT). Two dffere mehodologes, he OLS-based ad GACH-based models, are used o es he robusess of he resul ad o oba a sesvy check. The maor fdgs of hs vesgao are as follows. Frs, he esmaes of he codoal mea fuco of he wo fuures markes are cosse wh weak-form effcecy. Secod, he evdece suggess ha volaly s hgher durg perods of hgh fuures radg volume for he TAIFEX ad SGX-DT fuures markes, supporg he mxure of dsrbuo hypohess by Clark (973). Lasly, cosse wh marke deph heores, hs sudy demosraes ha exsg marke deph does o mgae volaly he SGX-DT ad TAIFEX fuures markes. Ths resul s oeworhy because provdes evdece ha he relao bewee prce volaly ad marke deph may vary wh he marke maury. Keywords: Prce volaly; Tradg acvy; Marke deph; Sock dex fuures; GACH. Iroduco Ths sudy documes he relaos amog prce volaly, radg acvy ad marke deph for seleced fuures coracs raded o he Tawa Fuures Exchage (TAIFEX) ad Sgapore Exchage Dervaves Tradg Dvso (SGX-DT) Tawa Sock Idex Fuures markes. Ths subec has bee exesvely vesgaed for U.S. capal markes, ad also for some developed eraoal markes. However, hs ssue has bee lle examed less-developed markes. The reaso for our parcular eres emprcal work o he Tawa Sock Idex Fuures markes s ha s a rapdly expadg emergg marke ad s characerzed by hgh volaly Asa. Therefore, hs sudy provdes addoal emprcal evdece by explorg wheher he volaly paers ad corbuo of marke deph of emergg markes dffer from hose of developed markes. Tha s, we wll es he mxure of dsrbuo hypohess ha here s a posve coemporaeous correlao bewee prce volaly ad radg volume, ad he marke deph heory ha prce volaly s affeced by exsg marke deph. The ma corbuo of hs work s o prese emprcal comparsos o fll hs gap he leraure. Numerous works have examed he relao bewee radg volume ad prce volaly for eques ad fuures. Cosderable evdece exss a posve coemporaeous correlao bewee prce volaly ad radg volume. Karpoff (987) exesvely revews prevous heorecal ad emprcal research o he prce-volume relao, ad fds 8 sudes documeg he posve relao. egardg he heorecal aspec, he wo leadg models, amely he sequeal formao model of Copelad (976) ad he mxure of dsrbuo hypohess of Clark (973), expla for he posve relaoshp bewee volume ad prce volaly. As for he emprcal aspec, varous sudes such as Crouch (970), Epps ad Epps (976), Corell (98), Harrs (986), Tauche ad Ps (983), Galla, oss ad Tauche (99), Che, Frh ad u (00), ad Cer (00) demosrae he posve coemporaeous correlao bewee volaly ad volume eques ad fuures markes. The mos rece model developed by Blume, Easley, ad O Hara (99) descrbes he formaoal role of volume, ad documes whch volume coveys formao o he marke ad he mproves he accuracy of prce moveme forecass. Furhermore, hs model demosraes how volume ca affec marke be- havor, raher ha smply descrbg he corre- * Correspodg auhor. E-mal: s7988@ms6.he.e See Hsu ad L (00), L ad Hsu (003) ad L, Hsu ad Chag (00). 3
We-Hsu Kuo e al./asa Pacfc Maageme evew (005) 0(), 3-3 lao bewee radg volume ad prce movemes. Therefore, he leraure wdely uses volume as a proxy for formao arrval. Lamoureux ad Lasrapes (990) frs apply Bollerslev s (986) GACH mehodology o vesgae he prce volaly-volume relaoshp equy markes, employg daly radg volume as a measure of he formao flow (he rae of formao arrvals) based o Clark s (973) MDH. Lamoureux ad Lasrapes fd ha auoregressve codoal heeroscedascy (ACH) effecs dsappear whe radg volume s roduced o he codoal varace equao, suggesg ha usg radg volume as a proxy for he formao varable causes prce volaly ad largely explas he GACH effecs. Joes, Kaul ad Lpso (99) also oba fdgs smlar o hose of Lamoureux ad Lasrapes (990). Ulke he sudy by Lamoureux ad Lasrapes (990), Naad ad Yug (99) ad Foser (995) show ha GACH effecs rema whe curre volume s cluded he codoal varace equao. These auhors fd a posve relao bewee radg volume ad prce volaly, whch s cosse wh he heorecal models provded by Clark (973), Copelad (976) ad Blume, Easley, ad O Hara (99). The volume-volaly relaoshp frequely has bee examed, bu few works clude marke deph he volume-volaly aalyss. Kyle (985) develops a heorecal model of marke deph, ad defes marke deph as he volume of order flows requred o move prces by oe u. Hs model suggess ha marke deph chages wh radg acvy ad a deep marke helps creae marke codos ha reduce prce pressures whe radg provdes ew formao. Cosequely, marke deph heory says ha lower prce volaly frequely may exs deeper markes ha faclae radg acvy. Tha s, observed prce volaly, codoal o coemporaeous volume, s expeced o decrease wh creasg marke deph. Earler sudes measure radg acvy fuures markes based o volume aloe. ecely, varous sudes 3 have examed he relao bewee ope eres ad prce volaly developed fuures markes. Parcularly, Bessembder ad Segu (993) frs vesgae he relaos bewee prce volaly, radg acvy varables (radg volume ad ope eres) ad marke deph for egh fuures markes he U.S. As he level of ope eres s a measure of radg acvy ad reflecs he curre wllgess of fuures raders o rsk her capal he fuures poso he presece of prce volaly, ope eres The framework ha he MDH ca be represeed as GACH model s refered o Lamoureux ad Lasrapes (990). 3 See Bessembder ad Segu (99, 993), Harrs ad avv (993), Bessembder, Cha ad Segu (996), aguaha ad Peker (997), Waaabe (00), Fug ad Paerso (999), Ferrs, Park ad Park (00) ad Grma ad Mougoue (00). appears o serve as a good proxy for he order flow cocep ha relaes drecly o marke deph. Therefore, Bessembder ad Segu (993) use expeced ope eres as a proxy for marke deph sce reflecs order flow of he fuures rasacos ad wllgess of raders o rsk her capal. Cosse wh earler sudes, Bessembder ad Segu (993) defy a srog posve relao bewee coemporaeous prce volaly ad radg volume, bu uexpeced volume shocks fluece prce volaly more ha expeced volume shocks. Addoally, Bessembder ad Segu fd ha expeced ope eres s egavely relaed o prce volaly all egh fuures markes, dcag ha creased deph (larger expeced ope eres) mgaes prce volaly ad supporg marke deph heory. Followg he mehod developed by Bessembder ad Segu (993), aguaha ad Peker (997), Waaabe (00) ad Fug ad Paerso (999) all vesgae he relaoshps bewee prce volaly, radg acvy ad marke deph he Ausrala fuures marke, he Japaese sock dex fuures marke ad he USA fuures marke, respecvely. Ther emprcal resuls resemble hose of Bessembder ad Segu (993) despe dffereces sample daa. The purpose of hs work exeds prevous research ad furher exames he relaoshps bewee prce volaly, radg acvy ad marke deph TAIFEX ad SGX-DT Tawa Sock Idex Fuures markes usg wo dffere mehodologes for esg he robusess of our resuls. Ths paper provdes sghs o he dffere mehodologes specfed. Frs, hs work adops he mehodology of Bessembder ad Segu (993), whch he codoal mea ad volaly equaos are esmaed sequeally usg OLS. Secod, raher ha selecg a OLS-based volaly esmao framework, we also geeralze he mehodology of Bessembder ad Segu (99, 993) o a GACH-based framework followg Gule ad Mayhew (000). The codoal mea ad volaly equaos are oly esmaed umercally by maxmzg he lkelhood fuco (MLE) GACH-based model. Overall, he fdgs of hs sudy dcae ha, wh he excepo of slgh dffereces he esmao resuls of Moday effec, expeced volume ad uexpeced ope eres varables, he esmao resuls of he remag varables for he wo models are smlar for boh he TAIFEX ad SGX-DT fuures markes. Furher comparsos wh developed markes are as follows. Frs, lke Bessembder ad Segu (993), aguaha ad Peker (997), Gule ad Mayhew (000) ad Waaabe (00), he resuls of hs sudy show ha he TAIFEX ad SGX-DT fuures markes are cosse wh weak-form effcecy ad suppor he mxure of dsrbuo hypohess by Clark (973). Secod, hs sudy ess he marke 3
We-Hsu Kuo e al./asa Pacfc Maageme evew (005) 0(), 3-3 deph heory ad fds ha exsg marke deph does o mgae prce volaly he TAIFEX ad SGX-DT fuures markes. Tha s, he fdg of hs vesgao s cosse wh marke deph heory. Ths evdece corass wh he fdgs of developed markes by Bessembder ad Segu (993) ad Waaabe (00), who fd ha large expeced ope eres (e.g. marke deph) mgaes volaly. Therefore, hs sudy cocludes ha marke maury affecs prce volaly. The remader of hs paper s orgazed as follows. Seco revews he leraure o he relaoshp bewee prce volaly, radg acvy ad marke deph. Seco 3 he descrbes our daa se ad he emprcal mehodology. Subsequely, seco preses he emprcal resuls. Fally, seco 5 makes cocludg remarks.. Leraure evew The mxure of dsrbuos hypohess (MDH) by Clark (973) posulaes ha prce volaly ad volume oly ad smulaeously respod o he commo (mxg) drecg varable, whch s erpreed as he rae of formao flow o he marke. Based o he MDH, prce volaly ad radg volume should be posvely correlaed. Copelad (976) cosrucs a sequeal arrval of formao model whch he sequeal arrval of ew formao o he marke causes boh volume ad prce movemes hrough umerous formao shocks ad a fal equlbrum s esablshed. The model of sequeal formao arrval dcaes a posve relaoshp bewee volume ad prce volaly ad suggess ha prce volaly poeally s predcable based o radg volume kowledge. Blume, Easley ad O Hara (99) develop a model ha raders ca use o lear valuable formao regardg a secury by observg pas prce ad volume formao. The model demosraes how volume affecs marke behavor ad argues ha volume provdes daa o he qualy or precso of abou pas prce moveme formao. Numerous sudes such as Crouch (970), Epps ad Epps (976), Corell (98), Harrs (986), Galla, oss ad Tauche (99), Che, Frh ad u (00), ad Cer (00) use equy ad fuures marke daa o vesgae he prce-volume relaoshp. These emprcal resuls suppor a almos posve relaoshp bewee prce volaly ad volume, cosse wh he heorecal models developed by Clark (973), Copelad (976) ad Blume, Easley, ad O Hara (99). Lamoureux ad Lasrapes (990) vesgae he effcacy of he GACH effecs GACH specfcao equy markes whe he formao varable (e.g., radg volume) s corporaed o he codoal varace equao based o Clark s (973) MDH. The cocluso dcaes ha radg volume used as a proxy for he formao varable explas much of he GACH effecs, supporg he formao-based varace srucure. ecely, some researchers have suded he relao bewee prce volaly ad radg acvy measured by radg volume ad ope eres fuures markes. Usg ope eres as a proxy for marke deph, Bessembder ad Segu (993) frs vesgae he relaos bewee prce volaly, radg acvy varables (radg volume ad ope eres) ad marke deph egh fuures markes he USA. Bessembder ad Segu fd a srog posve relao bewee coemporaeous prce volaly ad radg volume, supporg he mxure of dsrbuo hypohess by Clark (973). Besdes, he fdgs of Bessembder ad Segu also suppor he marke deph hypohess, amely ha expeced ope eres s posvely relaed o umber of raders or oal capal dedcaed o a marke a he begg of a radg sesso, ad ha a crease he umber of raders or amou of capal volved a marke ehaces marke deph ad hus lesses volaly. aguaha ad Peker (997) vesgae he aure of he relaoshp bewee volumes, prce varably ad marke deph for four fuures coracs raded o he Sydey Fuures Exchage, ad oba aalycal resuls ha cofrm he emprcal fdgs of Bessembder ad Segu (993). Waaabe (00) exames he relao bewee prce volaly, radg volume ad ope eres for he Nkke 5 sock dex fuures raded o he Osaka Secures Exchage (OSE). The OSE gradually chages regulaos such as marg requremes, prce rage ad me erval updag quoao several mes. The regulaos were relaxed begg February, 99. Therefore, he samples pror o ad begg February, 99 are examed separaely. The resuls obaed by Waaabe for he perod begg February, 99 resemble he fdgs of Bessembder ad Segu (993). However, o relaoshp bewee prce volaly, volume ad ope eres s foud for he perod before February, 99. Ths aalycal resul shows ha he relao bewee prce volaly, volume ad ope eres may vary wh he regulaos. Fug ad Paerso (999) also vesgae he relaoshp bewee prce volaly, radg volume ad marke deph for seve U.S. fuures markes. 5 Fug ad Paerso defy a srog, posve relao bewee volume ad prce volaly. Furhermore, Fug ad Paerso also fd a egave relaoshp bewee marke deph ad volaly, suggesg ha creased deph reduces prce The framework whch he MDH ca be represeed as GACH model s refered o Lamoureux ad Lasrapes (990). 5 The fuures daa were obaed from he Fuures Idusry Isue ad coss of fve currecy fuures prces ad wo eres-rae fuures prces. 33
We-Hsu Kuo e al./asa Pacfc Maageme evew (005) 0(), 3-3 volaly.. Fuures Exchage. Uderlyg asse 3.Corac sze.corac moh 5.Tradg Hours 6.Las Tradg Day 7.Tck sze Table. Feaures of Sampled Fuures Coracs TX TF TE M-TX MSCITX TAIFEX TAIFEX TAIFEX TAIFEX SGX-DT Tawa Capalzao Tawa Bakg & Tawa Elecroc Secor Tawa Capalzao MSCI Tawa Idex Weghed Idex Isurace Secor Idex Idex Weghed Idex TWD 00 TX dex TWD 000 TF dex TWD 000 TE dex TWD 50 TX dex USD00 TMSCI dex Spo moh, he ex Spo moh, he ex Spo moh, he ex caledar Spo moh, he ex March, Jue, Sepember, moh, ad he ex caledar moh, ad he caledar moh, ad he caledar moh, ad he December ad wo eares ex hree quarer ex hree quarer hree quarer mohs ex hree quarer seral mohs mohs mohs mohs 8:5am-: 5pm 8:5am-: 5pm 8:5am-: 5pm 8:5am-: 5pm 8:5am-: 5pm :5pm-9:00pm The hrd Wedesday of The hrd Wedesday of The hrd Wedesday of he The hrd Wedesday of Secod las busess day of he delvery moh of he delvery moh of delvery moh of each he delvery moh of he corac moh each corac each corac corac each corac 0. dex po dex po 0. dex po 0.05 dex po dex po The fdgs of hese sudes sugges ha a verse relaoshp exss bewee marke deph ad he prce volaly. However, prevous sudes have egleced he relaos bewee prce volaly, radg acvy ad marke deph emergg fuures markes. Ths work addresses hs defcecy ad provdes a addoal evdece by emprcally assessg he TAIFEX ad SGX-DT Tawa Sock Idex fuures markes. 3. Daa ad Mehodology 3. Daa The Sgapore Exchage Dervaves Tradg Lmed Dvso (SGX-DT) ad Tawa Fuures Exchage (TAIFEX) roduce fuures coracs of he Tawa sock dex o Jauary 9, 997 ad July, 998, respecvely. The SGX-DT offers Morga Saley Capal Ieraoal Tawa Sock Idex Fuures (MSCITX), whch coas 77 large capalzao socks o he Tawa sock exchage. Moreover, he TAIFEX offers he Tawa Sock Exchage Capalzao Weghed Sock Idex Fuures (TX), whch cludes all of he socks 6 lsed o he Tawa Sock Exchage (TSE). Subsequely, TAIFEX also successvely lauched Tawa Sock Exchage Elecroc Secor Idex Fuures (TE), Tawa Sock Exchage Bakg ad Isurace Secor Idex Fuures (TF) ad M Tawa Sock Exchage Capalzao Weghed Sock Idex Fuures (M-TX). The daly closg prces, radg volumes, ad ope eress of TX, TF, TE, M-TX ad MSCITX are obaed from he TAIFEX ad he SGX-DT, respecvely. The sample perod for TX, TF, TE, ad MSCITX exeds 6 The TSE Weghed Idex does o clude full-delvery socks, preferred socks, ad ewly lsed sock, whch are lsed for less ha oe caledar moh. from Jauary 00 o March 003. Sce he M-TX s o roduced ul Aprl 9, 00, s sample perod rus from Aprl 9, 00 o March 003. Followg Bessembder ad Segu (993), he dex fuures prces are ake from he earby fuures coracs o oba a represeave fuures prce seres, sce he earby fuures coracs usually are mos acvely raded. The reur s compued usg he aural logarhmc dfferece he prce levels. Tha s, = l( P / P ) where P deoes he closg prce of he earby corac o day. Addoally, radg vol- ume ad ope eres are summed across all ousadg maures o oba a aggregae measure of acvy for each fuures corac. Table deals he specfcaos of he fve fuures coracs vesgaed here. Table lss some basc descrpve sascs of he reurs, absolue reurs, radg volume ad ope eres for each fuures corac examed here. The mos volale fuures corac s TE, wh daly reurs sadard devao of approxmaely.598% per day. I coras, he leas volale fuures corac s TX, whch has daly sadard devao reurs of.5%. The paral auocorrelaos of reurs a all lags are sascally sgfca, mplyg ha o evdece exss predcably of reurs. MSCITX s he mos acve fuures corac, measured erms of volume ad ope eres, whle he leas acve s TF. Frs order auocorrelao coeffces are sgfca for every radg volume ad ope eres, showg ha hgh auocorrelao exss volumes ad ope eress. The presece of u roos volume ad ope seres s esed usg he Augmeed Dckey-Fuller (ADF) ess. The emprcal fdgs of he ess frmly reec he ull hypohess of a u roo a he 5% sgfcace level for all volume seres ad ope eres seres, mplyg ha he seres eed o be dffereced o acheve saoary, a codo ecessary o 3
We-Hsu Kuo e al./asa Pacfc Maageme evew (005) 0(), 3-3 avod spurous regressos. Table. Summarzed Sascs of Fuures eurs, Volume ad Ope Ieres Corac Mea Sadard Paral Auocorrelao a Lag Devao 3 5 U oo Tes Sasc TX eur (%) Absolue eur (%) Volume Ope Ieres TF eur (%) Absolue eur (%) Volume Ope Ieres TE eur (%) Absolue eur (%) Volume Ope Ieres M-TX eur (%) Absolue eur (%) Volume Ope Ieres MSCITX eur (%) Absolue eur (%) Volume Ope Ieres -0.0.585 06 699-0.0058.638 79 77-0.050.9 375 35-0.089.588 359 37-0.063.899 55.5.399 59 305.56.83 330 7.5977.75 86 6.5.56 50 39.07.56 53 707-0.060-0.06 0.705** 0.968** -0.0 0.5** 0.86** 0.98** -0.06-0.007 0.65** 0.975** -0.079-0.03 0.7** 0.966** -0.05-0.056 0.5** 0.70** 0.05 0.098** 0.360** -0.08** 0.05 0.69** 0.53** -0.03** 0.08 0.07 0.330** 0.0 0.06 0.0** 0.369** -0.06 0.07 0.060 0.089 0.009 0.05 0.03** 0.73** 0.000 0.066 0.057 0.99** 0.0 0.07 0.9** 0.7** -0.035 0.056 0.06** 0.06** -0.035 0.073 0.009 0.09 0.7** 0.069 0.06 0.38** -0.030-0.00 0.06 0.057-0.05 0.07 0.0 0.75** -0.03 0.08 0.098** 0.** 0.03-0.035-0.065 0.0 0.079-0.037 0.03 0.00** -0.07-0.0 0.09 0.0 0.05-0.008 0.039 0.6** 0.037-0.09 0.0 0.69**. To es for he saoary of he volume ad ope eres seres, we use he augmeed Dckey ad Fuller (98) es o perform he u roo es. We 0.06-0.08 0.075 0.09 0.06 -.** -.69** -.3** -3.7** -3.8** -3.8** -3.77** -5.00** -6.65** -8.57** employ he Akake Iformao Crero (AIC) o deerme he approprae lag srucure ADF es. The crcal value for ADF es a he 5% s 3.. H 0 : u roo, H A : o u roo..** dcae sascally sgfca a 5% level. 3. Measureme of Tradg Acvy Varables ad Marke Deph Followg prevous sudes, 7 hs work uses radg volume ad ope eres as proxes for radg acvy fuures markes. Employg a echque smlar o ha of Bessembder ad Segu (99, 993), he radg acvy seres are decomposed o expeced ad uexpeced compoes. Frs, he expeced radg acvy seres s he fed value from he uvarae AMA model, whle he uexpeced radg acvy seres s defed as εˆ, whch s he acual radg acvy seres mus expeced radg acvy. Ths sep yelds e seres of forecas errors, εˆ, { acvy acvy, } ˆ ε = acvy E, τ τ =,..., () for acvy = radg volume or ope eres = TX, TF, TE, M-TX, MSCITX Addoally, o capure he evdece 8 ha pas volales ca predc volumes, he forecas errors are regressed agas lags volaly, volume, ad ope eres. Fally, he followg equao s used o esmae he expeced ad uexpeced radg acvy varables: µ moi, m = k= m= ρ ˆ σ, λkvol, k ˆ ε = ϕ ν () where Vol ad OI deoe he radg volume ad ope eres of fuures corac, respecvely. Ths sudy ulzes he Akake formao crero (AIC) o deerme he approprae lag srucure Eqs. () ad (). Therefore, hs sudy employs a dffere model for each me seres. The resduals νˆ from he Eq. () serve as he uexpeced compoe of each radg volume ad ope eres seres, whle he expeced compoe s defed as he dfferece bewee he acual radg acvy seres ad he uexpeced compoe, acvy -νˆ. 7 Bessembder ad Segu (99, 993), aguaha ad Peker (997), Waaabe (00) ad Fug ad Paerso (999). 8 See Schwer (990), Galla, oss ad Tauche (99).
We-Hsu Kuo e al./asa Pacfc Maageme evew (005) 0(), 3-3 Accordg o marke deph heory by Kyle (985), Bessembder ad Segu (993) argue ha marke deph vares wh rece radg acvy, whch s proxed by edogeously deermed ope eres. As he level of ope eres s a measure of radg acvy ad reflecs he curre wllgess of fuures raders o rsk her capal he fuures poso he presece of prce volaly, expeced ope eres s a good proxy for marke deph. Therefore, hs sudy also uses expeced ope eres as a proxy for marke deph. We wll es he marke deph heory ha observed volaly, codoal o coemporaeous volume, s expeced o decrease wh creasg marke deph (larger expeced ope eres) TAIFEX ad SGX-DT Tawa sock dex fuures markes. 3.3 Measureme of Prce Volaly-Emprcal Model Specfcao To mprove sudy robusess, wo commoly used prce volaly measures, he OLS-based ad GACHbased models, are employed o exame he relaoshp bewee prce volaly, radg acvy ad marke deph for seleced fuures coracs raded o he TAIFEX ad he SGX-DT. 3.3. Model (OLS-Based Volaly Esmae) Frs, hs sudy measures he ubased esmae of daly fuures prce volaly usg he same procedure as Davda ad Carroll (987) ad Bessembder ad Segu (99, 993). The procedure volves erao bewee he followg wo equaos: a codoal mea Eq. (3) ad a codoal volaly Eq. (), γ ρ d π σˆ = = = = α U (3) m ω U ˆ η d µ Ak β ˆ σ = = k= = ˆ σ = δ e () where deoes fuures reur o day, d (=,..., ) represes four dummy varables 9 whch capures dffereces mea ad volaly for he h day of he week ad U (resduals) s uexpeced reurs from Eq. (3). σˆ s he codoal sadard devao, whch s called prce volaly hs paper. The mehod for esmag σˆ wll be explaed below. Ak are he radg acvy varables, whch are dvded o expeced ad uexpeced compoes, ad dcae how radg acvy varables affec prce volaly Eq. (). Lagged uexpeced reurs are cluded Eq. () o capure hs possble asymmery (e.g., leverage effec 0 ) he relao bewee reurs ad volaly. Tha s, egave uexpeced reur shocks mpac volaly more ha posve uexpeced reur shocks. The lagged volaly varables are cluded Eq. () o measure ad accommodae he effec of perssece prce volaly, a pheomeo called volaly-cluserg. Accordg o Bessembder ad Segu (99, 993), esmaes of daly sadard devaos are obaed usg he followg rasformao. σˆ = Uˆ π / (5) Davda ad Carroll (987) recommed ha Eqs. (3) ad () are esmaed sequeally. Equao (3) frs s esmaed whou he lagged volaly esmaes by usg OLS. The obaed resduals he are rasformed o he volaly esmaes usg Eq. (5), ad subsequely Eq. () s esmaed. Fed values calculaed from Eq. () are used as regressors reesmag Eq. (3). Equao () s fally reesmaed usg he resduals from Eq. (3). To deerme he exsece of a asymmery effec, amely, he effecs of uexpeced chages radg acvy varables o prce volaly varyg accordg o shock sg, dummy varables are defed as 0 for a egave shock (lower ha expeced radg acves) ad for a posve shock (hgher ha expeced radg acves). The produc of he dummy varable ad he uexpeced radg acvy varable hus s creaed. Cosequely, he esmaed equao s expressed as follows, σˆ = δ Uˆ d A 0 ω η µ β σˆ k = = k = = δ U exp Voldum m δ U exp OIdum e where UexpVoldum represes he produc erm of he uexpeced volume ad he dummy varable, whch s for a posve shock o day ad 0 oherwse, ad UexpOIdum represes he produc erm of he uexpeced ope eres ad he dummy varable, whch s for a posve shock ad 0 oherwse. 3.3. Model (GACH-Based Volaly Esmae) Secod, usg a procedure spred by Gule ad Mayhew (000), hs sudy rasforms Eqs. (3) ad () o he Geeralzed Auoregressve Codoal Heeroskedascy (GACH) model proposed by Bollerslev (986). I coras o he regresso Eqs. (3) ad () esmaed by OLS, he GACH model emprcally has bee demosraed o capure reasoably well he me-varyg volaly of facal daa reurs. The esmaed GACH(p, q) specfcao ca be expressed as below, = a cd = = b (6) ε, ε Ω ~ N 0, h ) (7) ( 9 d akes oe whe day s Moday ad oherwse akes zero; d akes oe whe day s ad oherwse akes zero, ad so o. 0 See Black (976), Chrse (98), Nelso (99). The leverage effec meas a reduco sock prce creases he deb/equy rao (or leverage) ad hus rases equy reurs volaly. See Bollerslev (986), Frech,Schwer ad Sambaugh (987), Nelso (99), Bollerslev,Chou ad Kroer (99). 36
We-Hsu Kuo e al./asa Pacfc Maageme evew (005) 0(), 3-3 h p = α 0 α ε β h η d = = ω U exp Vol ω 3 ExpOI ω U exp OI q = ω ExpVol where deoes fuures reur o day, d (=,, ) repre- ses four dummy varables whch capures dffereces mea ad volaly for he h day of he week, ε (resduals) s uexpeced reurs from Eq. (7), ExpVol ad UexpVol represe he expeced ad uexpeced volume, ad ExpOI ad UexpOI are he expeced ad uexpeced ope eres, respecvely. The codoal mea equao provded Eq. (7) ca be expressed as a fuco of exogeous varables wh a error erm. The h s he oe- perod ahead forecas varace based o pas formao ( Ω ), ad s called he codoal varace, whch deoes prce volaly hs paper. The codoal varace equao specfcao Eq. (8) s a lear fuco of lagged squared resduals ad lagged resdual codoal varace. Furhermore, Equao (8) ca be exeded o perm he cluso of exogeous depede varables such as daly dummes ad radg acves hs vesgao. Addoally, o deerme wheher a asymmery volume ad ope eres shocks exss, he UexpVoldum ad UexpOIdum erms are cluded Eq. (8). Equao (9), gve below, shows ha he allowed varao he effecs of uexpeced chages volume ad ope eres wh shock sg s reesmaed. p q h = α0 αε β h ηd ωexpvol ωu expvol = = = ω3expoi ωu expoi ω5u expvoldum ω6u expoidum However, he GACH s a symmerc volaly model ad s codoal varace depeds o he magude raher ha he sg of he uexpeced dsurbace erm. Thus, GACH fals o capure he leverage effec. The EGACH model proposed by Nelso (99) overcomes hs problem. The codoal varace he model depeds o boh he sg ad magude of he uexpeced reurs, ad hus s asymmerc s respose o posve ad egave uexpeced reurs. Ths sudy desgs a more rgorous model ha s used o vesgae he relaoshp bewee prce volaly, radg acvy ad marke deph for he TAIFEX ad SGX-DT Tawa Sock Idex Fuures uder he framework of EGACH specfcao. The EGACH (,) specfcao replaces Eq. (9) wh he followg Eq. (0). ε ε log h = ω 0 φ log h α γ h π h = ω ExpVol ω U exp Vol ω 3 ExpOI ω U exp OI ω 5U exp Voldum ω 6U exp OIdum d akes oe whe day s Moday ad oherwse akes zero, d akes oe whe day s ad oherwse akes zero, ad so o. (8) η d (9) (0) If he asymmerc erm,, s egave ad sascally dffere from 0, he egave uexpeced reur shocks mpac volaly more ha posve uexpeced reur shocks. Tradg acvy varables also are decomposed o expeced ad uexpeced compoes, ad he are sered o he EGACH codoal volaly equao as addoal explaaory varables.. Emprcal esuls Table 3 preses he esmaed resuls of he codoal mea Eq. (3) for each of he fve fuures coracs. The fdgs of hs sudy are cosse wh hose of Bessembder ad Segu (993) ad aguaha ad Peker (997). The larges adused s.39% for TF. Moreover, oe of he day-of-he-week dummes are sgfca across all coracs. Lagged reurs do o have sgfca explaaory power for all coracs. Ths evdece ca be arbued o weak-form effcecy, dcag ha pas reurs are of lmed use predcg prese reurs. Neverheless, lagged volales for TE, M-TX ad MSCITX are posve ad sascally sgfca a he 0% level. Table repors he esmao resuls of he codoal volaly Eq. (). Moday dummy exhbs sgfca day-of-he-week effec across all coracs. Moreover, all e coeffce esmaes for expeced ad uexpeced volume are posve. However, magudes ad sascal sgfcace levels show ha expeced ad uexpeced volume has heerogeeous effecs o volaly. The esmaed coeffce o expeced volume s sgfca a he 0% level for wo of fve coracs, whle he esmaed coeffce o uexpeced volume s sgfca a he 5 % level for all fve coracs. Furhermore, he coeffces of uexpeced volume are larger ha expeced volume. The rao of uexpeced volume o expeced volume vared from for he TF o for he M-TX, dcag ha uexpeced volume mpacs volaly more ha expeced volume. Ths aalycal resul s cosse wh he fdgs of Bessembder ad Segu (993), aguaha ad Peker (997) ad Waaabe (00). Excep for TF, he coeffce esmaes for expeced ope eres are egave ad sascally sgfca. Ths measureme resul corass wh he fdgs of Bessembder ad Segu (993) ad Waaabe (00), who fd ha all coeffces relag expeced ope eres o volaly are egave ad sgfca. Bessembder ad Segu (993) oe ha a sgfca egave coeffce for he effec of expeced ope eres o volaly s cosse wh he marke deph hypohess ha expeced ope eres s posvely relaed o he umber of raders or amou of capal dedcaed o a marke a he begg of a radg sesso, ad moreover creasg he umber of raders or amou of capal volved a marke mproves marke deph ad hus reduces volaly. Accordgly, cosse wh heores of marke deph, hs sudy does o 37
We-Hsu Kuo e al./asa Pacfc Maageme evew (005) 0(), 3-3 Table 3. Esmao esuls of he Auoregressve Model for Daly Fuures eurs = α γ ρ d π σˆ = = = U Fuures coracs TX TF TE M-TX MSCITX Iercep Daly dummes Moday Wedesday Sum of lagged volales Sum of lagged reurs -0.0036 (-0.8585) -0.0089 (-0.6359) -0.0056 (-0.8608) 0.0007 (0.39) -0.0009 (-0.06338) 0.08 (.005) 0.0563 (0.3388) 0.00065 (0.77) -0.003 (-0.7853) -0.003 (-.90) -0.0059 (-0.856) 0.00337 (.76) 0.003 (0.0005) 0.033 (0.306) -0.0060 (-.36766) -0.003 (-0.66) -0.0075 (-0.976) 0.00 (0.378) -0.0053 (-0.360) 0.58 (.8)* 0.0035 (0.097) -0.0000 (-.5935) 0.00009 (0.090) -0.003 (-0.675) 0.0057 (0.50080) -0.00063 (-0.9907) 0.95 (3.30876)* 0.068 (0.03786) -0.0538 (-.89779) -0.0038 (-.095) 0.0003 (0.0968) 0.00069 (0.837) 0.007 (0.6670) 0.683 (3.6075)* 0.037 (0.005) Lug-Box Q ().87 3.809 7.793 8.3059 6.976 Lug-Box Q () 38.997**.39** 5.607**.85** 0.60* Adused -0.003 0.039 0.07 0.0075 0.008753 egresso F-sasc 0.957.5309.85095*.67.3075. Tes sascs pareheses for dvdual coeffces are sascs. Tes sascs pareheses for lagged coeffces are F sascs for he hypohess ha he sum of he lagged coeffces s zero.. Lug-Box Q (k) sasc ess he o sgfcace of he auocorrelaos of he daly reur seres up o he k-h order. Lug-Box Q (k) sasc ess he o sgfcace of he auocorrelaos of he squared daly reur seres up o he k-h order. 3. * ad ** dcae sascally sgfca a he 0% ad 5% level, respecvely.. The approprae lag-legh specfcao of each equao s deermed usg Akake s Iformao Crero (AIC). fd ay evdece ha hgher levels of expeced ope eres sgfcaly mgae volaly. Four of he fve esmaed coeffces relag uexpeced ope eres o volaly are egave ad sgfca. Ths aalycal resul resembles ha of Bessembder ad Segu (993), mplyg ha a crease ope eres durg he radg day lesses he fluece of a volume shock o volaly. The sum of he esmaed coeffces o he lags of he volaly seres s posve ad sgfca for all coracs, dsplayg sgfca perssece volaly facal markes. The sum of esmaed coeffces o lagged uexpeced reurs s egave ad sgfca for TE ad MSCITX, dcag ha egave reur shocks have a larger effec o subseque volaly ha posve reur shocks do, oherwse kow as he leverage effec. Table 5 repors he esmao resuls of Eq. (6) ha allow he effecs of uexpeced chages volume ad ope eres o vary wh he shock sg. The coeffces assocaed wh he UexpVoldum ad UexpOIdum are o sascally sgfca for all coracs, dcag o asymmeres for uexpeced volume ad ope eres. Ths fdg s cosse wh he fdgs by Bessembder ad Segu (993) ad Waaabe (00), who fd posve uexpeced volume shocks fluece volaly more ha egave uexpeced volume shocks. Ths sudy repors Lug-Box es sascs for he h order seral correlao cludg boh he resduals ad squared resduals Table 3. The Lug-Box es sascs for he resdual levels are sgfca a he 5% level, revealg ha o seral auocorrelao remas he fve fuures coracs. However, he Lug-Box es sascs for he squared resduals are hghly sgfca for all coracs, dcag he exsece of me-varyg dex reurs volaly. Furhermore, Tables ad 5 also demosrae ha he sum of esmaed coeffces o he lags of he volaly seres s posve ad sgfca for all coracs. Therefore, hese aalycal resuls dcae he volaly-cluserg pheomeo observed he prese volaly seres. Ths sudy Addoally, he ad coeffces for he perssece of volaly measures are sascally posve for all coracs whe curre volume ad ope eres are cluded he codoal varace equao smulaeously. Therefore, curre volume ad ope eres do o remove he ACH effecs he SGX-DT ad TAIFEX fuures. Ths fdg s cosse wh he fdgs of Naad ad Yug (99) ad Foser (995), bu dffers from hose of 38
We-Hsu Kuo e al./asa Pacfc Maageme evew (005) 0(), 3-3 Table. egressos of Fuures eurs Volaly o Expeced ad Uexpeced Tradg Acvy σ ˆ = δ m ω U ˆ η d µ Ak β σˆ = = k = = e Fuures coracs TX TF TE M-TX MSCITX Iercep 0.086 0.085 0.0098 0.07 0.03360 (3.3560)** (7.3568)** (.536)** (.0368)** (3.8)** Daly dummes Moday 0.0075 0.00389 0.0077 0.008-0.00706 (3.9979)** (.83)* (.9066)** (3.5989)** (-.6675)** 0.0000-0.0087 0.0066 0.000667 0.000 (0.009) (-.35707) (.0856) (0.980) (0.775) Wedesday 0.0033-0.000 0.00333 0.005-0.0080 (.605) (-0.65788) (.680) (0.957) (-3.0590)** -0.00056-0.003-0.0005-0.0003-0.007 (-0.6353) (-.58038) (-0.39339) (-0.589) (-.80079)* Expeced volume.57e-07 5.E-06 3.E-06 9.9E-08 3.07E-08 (.69090) (3.8056)** (.8873)* (0.08660) (0.0563) Uexpeced volume.9e-06.05e-05 7.85E-06.06E-05.08E-06 (8.58)** (9.5388)** (7.7906)** (.95)** (6.803)** Expeced ope eres -.6E-07 -.5E-06 -.E-06 -.69E-07 -.E-07 (-0.7999) (-3.586)** (-0.990) (-0.7595) (-.60) Uexpeced ope eres -.9E-06-8.60E-06 -.6E-05 -.88E-06 -.07E-07 (-5.66)** (-.5993)** (-6.665)** (-.0735)** (-0.560) Sum of lagged volales 0.38 0.87 0.35699 0.77 0.8 (3.67)** (.9785)* (.875)** (8.6696)** Sum of lagged uexpeced reurs -0.059-0.0863-0.695-0.0985 (.93938) (0.78) (6.389)** (0.58856) Adused 0.0 0.079 0.0803 0.3093 0.536 egresso F-sasc 9.890** 0.653** 5.86893**.835**.5537. * ad ** dcae sascally sgfca a he 0% ad 5% levels, respecvely. (.7563)* -0.7657 (.5889)**. Tes sascs pareheses for dvdual coeffces are sascs. Tes sascs pareheses for lagged coeffces are F sascs for he hypohess ha he sum of he lagged coeffces s zero. 3. The approprae lag-legh specfcao of each equao s deermed usg Akake s Iformao Crero (AIC). Lamoureux ad Lasrapes (990) ad Joes, Kaul ad Lpso (99), who fd ha ACH effecs o prce volaly are sgfca whe volume s cluded he codoal varace equao. Table 7 repors he esmao resuls of a sadard GACH model [Eqs. (7) ad (9)] ha allows he effecs of uexpeced volume ad ope eres shocks o volaly o vary wh shock sg by roducg he UexpVoldum ad UexpOIdum erms. The esmao resuls are almos decal regardless of he presece of dummy varables, excep ha he coeffces o he expeced volume varable for TE ad MSCITX become egave ad he coeffce o uexpeced ope eres for TE becomes sgfca. The coeffces assocaed wh UexpVoldum ad UexpOIdum are o sascally sgfca for all coracs, dcag ha eher of he uexpeced radg acvy shocks are asymmerc SGX-DT ad TAIFEX. Ths resul also s cosse wh he Schwer volaly esmaes lsed Table 5. 5. Cocluso Despe exesve research o he relaos amog radg acvy, volaly ad marke deph fuures markes, cludg ha by Bessembder ad Segu (993), aguaha ad Peker (997), Waaabe (00) ad Fug ad Paerso (999), few researchers have examed he same relaos for emergg markes. Ths sudy ams o furher exed he mehodology used by Bessembder ad Segu (993) ad mprove udersadg of he relaos amog prce volaly, radg acvy ad marke deph for seleced fuures coracs he Tawa Fuures Exchage (TAIFEX) ad Sgapore Exchage Dervaves Tradg Dvso (SGX-DT) Tawa Sock Idex Fuures markes. Ths sudy vesgaes hs ssue usg wo dffere modelg mehodologes, he OLS-based ad GACHbased models, o es he robusess of he resuls ad o oba a sesvy check. Esseally, he fdgs of hs sudy regardg he relaoshp amog volaly, volume ad ope eres are robus for dffere measures of prce volaly. Besdes slgh dffereces he esmao resuls for Moday dummy, expeced volume ad uexpeced ope eres varables, he esmao resuls of he remag varables are smlar across he wo models for he TAIFEX ad SGX-DT fuures markes. Furher comparso wh developed markes s preseed below. Frs, he resuls of codoal mea fuco of he wo models he TAIFEX ad SGX-DT fuures markes are cosse wh weak-form effcecy. The fdgs resemble hose foud for oher developed markes sudes by Bessembder ad Segu (993), aguaha ad Peker 39
We-Hsu Kuo e al./asa Pacfc Maageme evew (005) 0(), 3-3 Table 5. egressos of Fuures eurs Volaly o Tradg Acvy (Allowg for Asymmeres) m = ˆ δ ˆ d Ak ˆ 0 ω η µ β σ δ U expvoldum δ = = k = = σ U UexpOIdum e Fuures coracs TX TF TE M-TX MSCITX Iercep 0.077 0.0798 0.0097 0.0 0.0339 (3.356)** (7.9)** (.560)** (3.599)** (3.0363)** Daly dummes Moday 0.0079 0.00087 0.00765 0.00805-0.0070 (3.87)** (.9098)* (.876)** (3.60693)** (-.656)** 0.00003-0.0079 0.009 0.00058 0.0099 (0.089) (-.337) (0.9557) (0.66) (0.7667) Wedesday 0.0036-0.0033 0.0036 0.00-0.0088 (.5685) (-0.679) (.0) (0.668) (-3.368)** -0.0005-0.00333-0.00066-0.00099-0.00503 (-0.3957) (-.556) (-0.97) (-0.85) (-.9059)* Expeced volume.8e-07 5.00E-06.88E-06-6.30E-07-3.E-07 (.566) (3.7)** (.6506) (-0.5699) (0.589) Uexpeced volume.80e-06.e-05 6.E-06 7.7E-06.79E-06 (.0393)** (.30)** (.80)** (.53)** (3.690)** UexpVoldum.77E-07 -.39E-06.87E-06.09E-06 -.06E-06 (0.93) (-0.3638) (0.8) (.8395) (-.5599) Expeced ope eres -.9E-07 -.8E-06 -.36E-06 -.9E-07 -.83E-07 (-0.888) (-3.83)** (-.078) (-0.307) (-.68) Uexpeced ope eres -6.00E-06 -.7E-05 -.58E-05 -.8E-05-7.E-08 (-.030)** (-.8)** (-.7)** (-3.979)** (-0.38) UexpOIdum.3E-06 8.67E-06 7.3E-06.6E-06-8.76E-08 (0.87776) (0.8569) (0.6780) (.680) (-0.66) Sum of lagged volales 0.385 0.50 0.3876 0.785 0.385 (.857)** (3.8855)* (5.096)** (8.7858)** (3.8756)** Sum of lagged uexpeced reurs -0.033-0.05585-0.59-0.096-0.77 (.9608) (0.9808) (5.908)** (0.577) (.697)** Adused 0.866 0.073 0.37 0.387 0.569 egresso F-sasc 8.967** 9.56** 5.706** 3.3680**.98**. * ad ** dcae sascally sgfca a he 0% ad 5% levels, respecvely.. Tes sascs pareheses for dvdual coeffces are sascs. Tes sascs pareheses for lagged coeffces are F sascs for he hypohess ha he sum of he lagged coeffces s zero. 3. The approprae lag-legh specfcao of each equao s deermed usg Akake s Iformao Crero (AIC). (997), Gule ad Mayhew (000) ad Waaabe (00). Secod, as foud for he developed markes, boh models also show ha uexpeced volume flueces volaly more ha expeced volume for he TAIFEX ad SGX-DT fuures markes. Ths fdg dcaes ha volaly creases wh creasg fuures volume, bu hs behavor s drve by he uexpeced volume compoe, raher ha he expeced compoe. Ths fdg seems o suppor he mxure of dsrbuo hypohess by Clark (973). Thrd, boh models demosrae he volaly-cluserg pheomeo observed he prese volaly seres for he TAIFEX ad SGX-DT fuures markes whe curre volume ad ope eres are cluded he codoal varace equao. Ths aalycal resul s cosse wh hose of Bessembder ad Segu (993), aguaha ad Peker (997), Waaabe (00), bu s cosse wh he fdgs of Lamoureux ad Lasrapes (990). Fourh, o asymmerc relaoshp s foud bewee uexpeced radg acvy ad volaly he TAIFEX ad SGX-DT fuures markes. Ths fdg corass wh he fdgs of Bessembder ad Segu (993) ad Waaabe (00), amely ha posve uexpeced volume shocks mpac volaly more ha egave uexpeced volume shocks. Fally, emprcal ess of he marke deph heory demosrae ha creased levels of expeced ope eres (vewed as a proxy for marke deph) do o mgae volaly sgfcaly. Ths fdg suggess ha marke deph does o have a effec o volaly he SGX-DT ad TAIFEX fuures markes, mplyg ha exsg marke deph does o mgae prce volaly. Ths aalycal resul corass wh he fdgs of he developed markes examed by Bessembder ad Segu (993) ad Waaabe (00). Because he Tawa Sock Idex Fuures marke s a emergg marke ad characerzed by hgh volaly, hs dfferece ca be arbued o marke maury. Ths resul s oeworhy because provdes evdece ha he relao bewee prce volaly ad marke deph may vary wh he marke maury. I ca be cocluded ha marke maury affecs prce volaly. Thus, he fdgs of hs sudy have mplcaos for facal marke regulaors cocered wh how o ehace marke 0
We-Hsu Kuo e al./asa Pacfc Maageme evew (005) 0(), 3-3 deph he SGX-DT ad TAIFEX fuures markes. Table 6. Effec of Fuures Tradg Acvy o Volaly-GACH Model = a b c d = = ε, ε Ω ~ N ( 0, h ) p q h = α 0 α ε β h η d ω ExpVol ω U exp Vol ω 3ExpOI ω U exp OI = = = Pael A Codoal Mea Equao Fuures coracs TX TF TE M-TX TMSCI Iercep -0.0008-0.00069-0.00073-0.00076-0.0085 (0.7855) (0.6989) (0.8363) (0.7309) (0.3880) Daly dummes Moday -0.0009-0.007-0.0068 0.0009-0.0039 (0.6773) (0.997) (0.7039) (0.958) (0.670) -0.0093-0.003.E-05-0.0007 0.0066 (0.67) (0.) (0.993) (0.88) (0.389) Wedesday 0.0036-0.0006 0.00080 0.003 0.0088 (0.60) (0.803) (0.8570) (0.687) (0.575) 0.0007 0.0008-8.96E-05 0.00039 0.0066 (0.7763) 0.096 Sum of lagged reurs (0.8679) Pael B Codoal Varace Equao TX GACH (,).7E-05 Iercep (0.85) 0.333 (0.05)** Moday Wedesday Expeced volume Uexpeced volume Expeced ope eres Uexpeced ope eres 0.53333 (0.033)** 0.0 (0.83) 9.37E-05 (0.3083) -.5E-05 (0.737).7E-05 (0.588) -.6E-05 (0.89).67E-09 (0.799).97E-08-9.70E-0 (0.8767) -7.8E-08 (0.00)** Model Dagoscs Tes o Sadardzed esduals Lug-Box Q () Lug-Box Q () ACH (). The umber pareheses are he p-values. 5.80 (0.96) 6.78 (0.60) 5.36 (0.8) (0.706) 0.066 (0.5066) TF GACH (,) 9.0E-05 (0.0673)* 0.99 (0.000)** 0.59996 5.78E-06 (0.90) -0.0003 (0.9) -.77E-05 (0.658) -0.0006 (0.0067)**.07E-09 (0.897).65E-07 -.E-08 (0.085) -.E-07 (0.0379)**.007 (0.9830) 8.098 (0.783) 7.8705 (0.795) (0.9858) 0.09 (0.870) TE GACH (,) 0.0005 (0.08)** 0.7565 (0.00)** 0.0000 (0.68) 0.7999 (0.077)* 0.03999 (0.8975) -.80E-05 (0.933) -0.000 (0.5) -0.000 (0.05) -3.5E-05 (0.8535) 3.38E-08 (0.5678).E-07 (0.008)** -.E-08 (0.66) -.8E-07 (0.000)** 9.80 (0.667) 8.370 (0.06) 7.00 (0.8) (0.95) -0.0033 (0.973) M-TX GACH (,) 0.00036 (0.0088)** 0.5000 (0.073)* 0.0000 (0.668) 0.8000 (0.0078)** 0.0000 (0.8557) -.78E-05 (0.776) -0.0006 (0.9) -8.68E-05 (0.503) -6.E-05 (0.6330).0E-08 (0.3700).06E-07 -.5E-08 (0.908) -.3E-08 (0.06).88 (0.38).3 (0.09)** 5.050 (0.03)** (0.338) 0.070 (0.539) TMSCI GACH (,) 0.0006 (0.008)** 0.333 (0.07) 0.0 (0.5939) 0.53333-0.0008 (0.03)** 0.0000 (0.570) -0.0003 (0.09) -0.0007 (0.00)**.8E-08 (0.0069)** 3.39E-08 -.7E-09 (0.37).8E-09 (0.709) 9.85 (0.63) 7.3806 (0.) 5.958 (0.933). LB Q () ad LB Q () are he Lug-Box sascs appled o he sadardzed ad squared sadardzed resduals, respecvely. ACH () s he sascs used o es wheher sadardzed resduals exss ACH effec up o he order. 3. * ad ** dcae sascally sgfca a he 0% ad 5% levels, respecvely.
We-Hsu Kuo e al./asa Pacfc Maageme evew (005) 0(), 3-3 Table 7. Effec of Fuures Tradg Acvy o Volaly-GACH Model wh Dummy Varables = a b c d = = ε, ε Ω ~ N ( 0, h ) Pael A p q 0 αε β h ηd ωexpvol ωuexpvol ω3expoi ωuexpoi ω5uexpvoldum ω6 = = = h = α Codoal Mea Equao UexpOIdum Fuures coracs TX TF TE M-TX TMSCI Iercep -0.0005-0.00097-0.00073-0.00075-0.0080 (0.760) (0.63) (0.839) (0.87) (0.373) Daly dummes Moday -0.0003-0.005-0.0068 0.000-0.0038 (0.97) (0.5730) (0.693) (0.9577) (0.667) -0.00057-0.00309.5E-05-0.0007 0.0067 (0.8673) (0.83) (0.999) (0.9) (0.378) Wedesday 0.000-0.00063 0.00080 0.003 0.0090 (0.8908) (0.83) (0.8587) (0.7898) (0.577) 0.000 0.0007-8.9E-05 0.00039 0.0066 Sum of lagged reurs Pael B Iercep Codoal Varace Equao (0.90) 0.09 (0.87) TX GACH (,) 0.0000 (0.) 0.3333 (0.05)** 0.53333 (0.0093)** 0.0 (0.807) Moday 7.30E-05 (0.570) -8.E-05 (0.937) Wedesday -8.0E-05 (0.8) -5.96E-05 (0.376) Expeced volume 9.89E-0 (0.873) Uexpeced volume.05e-08 (0.0053)** UexpVoldum.E-08 (0.3) Expeced ope eres -9.87E-0 (0.7378) Uexpeced ope eres -.E-07 (0.08)** UexpOIdum 9.58E-08 (0.97) Model Dagoscs Tes o Sadardzed esduals Lug-Box Q () 8.963 (0.706) Lug-Box Q ().563 (0.8) ACH ().36 (0.99). The umber pareheses are he p-values. (0.7537) 0.0639 (0.507) TF GACH (,) 0.0000 (0.059) 0.985 (0.005)** 0.5999 8.07E-06 (0.933) -0.0005 (0.007)** -3.8E-05 (0.683) -0.0006 (0.039)**.5E-08 (0.7395).E-07 (0.000)** -.89E-09 (0.9869) -.97E-08 (0.30) -3.8E-07 (0.099)**.0E-07 (0.83) 3.9760 (0.980 7.395 (0.835) 7.379 (0.883) (0.9856) 0.03508 (0.780) TE GACH (,) 0.00050 (0.0335)** 0.000 (0.8) 0.0000 (0.68) 0.67999 (0.095)** 0.0000 (0.899) -.09E-05 (0.838) -7.96E-05 (0.663) -9.7E-05 (0.5798) -.67E-05 (0.8770) -3.00E-08 (0.503).6E-07 (0.0)** -.E-08 (0.856) -.77E-08 (0.655) -.5E-07 (0.509) -3.79E-07 (0.30900) 8.6695 (0.73) 9.77 (0.07) 0.396 (0.060) (0.935) -0.0069 (0.955) M-TX GACH (,) 0.00037 (0.000)** 0.000 (0.97) 0.0000 (0.696) 0.8000 (0.0)** 0.0000 (0.85) -5.9E-05 (0.6658) -0.000 (0.96) -6.3E-05 (0.5889) -7.7E-05 (0.85).9E-08 (0.3386).8E-07 5.56E-08 (0.333) -.53E-08 (0.390) -.8E-08 (0.38) -.83E-07 (0.69).90 (0.373).575 (0.03)** 3.33 (0.05)** (0.0) 0.08536 (0.758) TMSCI GACH (,) 0.00055 (0.0039) 0.3333 (0.09) 0.0 (0.69) 0.53333 (0.000)** 0.070 (0.55) -.7E-05 (0.773) 5.66E-05 (0.507) -6.77E-05 (0.08) -5.08E-05 (0.6865) -.06E-08 (0.56) 3.78E-08 (0.0037)** -.58E-08 (0.505) -3.E-09 (0.985).E-09 (0.8786) -.63E-08 (0.0) 8.98 (0.769) 0.96 (0.05) 7.505 (0.35). LB Q () ad LB Q () are he Lug-Box sascs appled o he sadardzed ad squared sadardzed resduals, respecvely. ACH () s he sascs used o es wheher sadardzed resduals exss ACH effec up o he order. 3. * ad ** dcae sascally sgfca a he 0% ad 5% levels, respecvely.
We-Hsu Kuo e al./asa Pacfc Maageme evew (005) 0(), 3-3 efereces Bessembder, H. ad Segu, P.J. (99). Fuures radg acvy ad sock prce volaly. Joural of Face, 7, 05-03. ad. (993). Prce volaly, radg volume, ad marke deph: Evdece from fuures markes. Joural of Facal ad Quaave Aalyss, 8, 0-39., Cha, K. ad Segu, P.J. (996). A emprcal examao of formao, dffereces of opo, ad radg acvy. Joural of Facal Ecoomcs, 0, 05-3. Black, F. (976). Sudes of sock, prce volaly chage. Proceedgs of he 976 Meegs of he Busess ad Ecoomcs Sascs Seco, Amerca Sascal Assocao, 77-8. Blume, L., Easley, D. ad O Hara, M. (99). Marke sascs ad echcal aalyss: The role of volume. Joural of Face, 9, 53-8. Bollerslev, T. (986). Geeralzed auoregressve codoal heeroskedascy. Joural of Ecoomercs, 33, 307-37., Chou,.Y. ad Kroer, K.F. (99). ACH modelg face: A revew of he heory ad emprcal evdece. Joural of Ecoomercs, 5, 5-59. Che, G., Frh, M. ad u, O.M. (00). The dyamc relao bewee sock reurs, radg volume, ad volaly. The Facal evew, 38, 53-7. Chrse, A. (98). The sochasc behavor of commo sock varace: Value, leverage ad eres rae effecs. Joural of Facal Ecoomcs, 0, 07-3. Cer, C. (00). Iformao coe of volume: A vesgao of Tokyo commody fuures markes. Pacfc-Bas Face Joural, 0, 0-5. Clark, P. (973). A subordaed sochasc process model wh fe varace for speculave prces. Ecoomerca,, 35-55. Copelad, T. (976). A model of asse radg uder he assumpo of sequeal formao arrval. Joural of Face, 3, 9-68. Corell, B. (98). The relaoshp bewee volume ad prce varably fuures markes. Joural of Fuures Markes,, 303-36. Crouch,. (970). A olear es of he radom-walk hypohess. Amerca Ecoomc evew, 60, 99-0. Davda, M. ad Carroll,.J. (987). Varace fuco esmao. Joural of Amerca Sascal Assocao, 8, 079-68. Dckey, D.A. ad Fuller, W.A. (98). Lkelhood rao sascs for auoregressve me seres wh a u roo. Ecoomerca, 9, 057-07. Epps, T.W. ad Epps, M.L. (976). The sochasc depedece of secury prce chages ad rasaco volumes: Implcaos for he mxure-of-dsrbuos hypohess. Ecoomerca,, 305-35. Ferrs, S.P., Park, H.Y. ad Park, K. (00). Volaly, ope eres, volume, ad arbrage: Evdece from he S&P 500fuures marke. Appled Ecoomcs Leers, 9, 369-37. Foser, A.J. (995). Volume-volaly relaos for crude ol fuures markes. Joural of Fuures Markes, 5, 99-95. Frech,.K., Schwer, G.W. ad Sambaugh,.F. (987). Expeced sock reurs ad volaly. Joural of Facal Ecoomcs, 9, 3-9. Fug, H.G. ad Paerso, G.A. (999). The dyamc relaoshp of volaly, volume, ad marke deph currecy fuures markes. Joural of Ieraoal Facal Markes, Isuos & Moey, 9, 33-59. Galla,.A., oss, P.E. ad Tauche, G. (99). Sock prces ad volume. evew of Facal Sudes, 5, 99-. Grma, P.B. ad Mougoue, M. (00). A emprcal examao of he relao bewee fuures spreads volaly, volume, ad ope eres. The Joural of Fuures Markes,, 083-0. Gule, H. ad Mayhew, S. (000). Sock dex fuures radg ad volaly eraoal equy markes. Joural of Fuures Markes, 0, 66-685. Harrs, L. (986). Cross-secury ess of mxure of dsrbuo hypohess. Joural of Facal ad Quaave Aalyss,, 39-6. Harrs, M. ad avv, A. (993). Dffereces of opo make a horse race. evew of Facal Sudes, 6, 73-506. Hsu, H. ad L, B.J. (00). The kecs of he sock marke. Asa Pacfc Maageme evew, 7 (), -. Joes, C.M., Kaul, G. ad Lpso, M.L. (99). Trasacos, volume, ad volaly. evew of Facal Sudes, 7, 63-65. Karpoff, J.M. (987). The relaoshp bewee prce chage ad radg volume: A survey. Joural of Facal ad Quaave Aalyss,, 09-6. Kyle, A. (985). Couous aucos ad sder radg. Ecoomerca, 53, 35-335. Lamoureux, C. ad Lasrapes, W. (990). Heeroskedascy sock reur daa: Volume versus GACH effecs. Joural of Face, 5, - 9. L, C.C., Hsu, H. ad Chag, C.Y. (00). The formao rasmsso bewee wo subsues of dex fuures: The case of TAIEX ad M-TAIEX sock dex fuures. Asa Pacfc Maageme evew, forhcomg. L, C.H. ad Hsu, H. (003). The mpacs of foreg capal ad prce dscovery process bewee Tawa ad Sgapore fuures coracs. Asa Pacfc Maageme evew, 8 (), 3-6. Naad, M. ad Yug, K. (99). A GACH examao of he relaoshp bewee volume ad prce varably fuures markes. Joural of Fuures Markes,, 63-6. Nelso, D. (99). Codoal heeroscedascy asse reurs: A ew approach. Ecoomerca, 59, 37-370. aguaha, V. ad Peker, A. (997). Prce volaly, radg volume, ad marke deph: evdece from he Ausrala fuures marke. Appled Facal Ecoomcs, 7, 7-5. Schwer, G.W. (990). Sock volaly ad he Crash of 87. evew of Facal Sudes, 6, 77-0. Tauche, G.E. ad Ps, M. (983). The prce varably-volume relaoshp o speculave markes. Ecoomerca, 5, 85-505. Waaabe, T. (00). Prce volaly, radg volume, ad marke deph: Evdece from he Japaese sock dex fuures marke. Appled Facal Ecoomcs,, 65-658. 3