Invesmen Managemen and Fnancal Innovaons, Volume 5, Issue 4, 008 Guner Gursoy (Turkey), Asl Yuksel (Turkey), Aydn Yuksel (Turkey) Tradng volume and sock marke volaly: evdence from emergng sock markes Absrac Based on he mxure of dsrbuon hyohess, hs aer nvesgaes he relaonsh beween radng volume and condonal volaly of reurns by usng 1 emergng sock marke ndces over he erod beween January 000 and Augus 006. The resuls show ha when oal radng volume s ncluded n he condonal volaly euaon as a roxy for nformaon flow, a moderae level of declne n volaly erssence was observed only for wo sock markes. In four sock markes he declne n condonal volaly erssence s very small. On he oher hand, for he remanng markes, oal radng volume s a oor roxy for nformaon flow. The fndngs are conssen wh he fndngs of ror research, whch sugges ha volume may be a good roxy for sock-level analyss, bu no for markelevel analyss. Furhermore, followng Wagner and Marsh (005) and Arago and Neo (005) he relaonsh beween unexeced radng volume (surrse radng volume as an alernave roxy for nformaon flow) and condonal volaly s analyzed. The fndngs llusrae ha for mos of he markes, he relaonsh beween surrse volume and condonal volaly s sascally sgnfcan. Keywords: volaly erssence, nformaon flow, GARCH models, emergng sock markes. JEL Classfcaon: G14, G15. Inroducon Two sylzed facs abou he emrcal dsrbuon of sock reurns, condonal me varyng volaly and volaly erssence have long araced academc neres n he leraure. One of he argumens used o exlan condonal me varyng volaly s based on he dea ha reurns on fnancal asses are generaed from a mxure of dsrbuons (MDH) n whch he sochasc mxng varable s consdered o be he rae of arrval of nformaon flow no he marke 1. The MDH mles ha reurn volaly s rooronal o he rae of nformaon arrval, hus offerng an exlanaon for he observed heeroskedascy n reurns. Engle's (198) auoregressve condonal heeroskedascy rocess and s exenson, Bollerslev s (1986) generalzed auoregressve condonal heeroskedascy (GARCH) rocess have been oular models of volaly erssence. Even hough hese models ossessed good exlanaory ower, hey dd no offer an economc exlanaon for hs emrcal henomenon. An exlanaon for volaly erssence was offered laer on n Lamoureux and Lasraes (1990). They relae he observaon of erssen reurn volaly o he mxure of dsrbuons hyohess and sugges ha condonal volaly erssence n sock reurns (he GARCH effecs) may reflec seral correlaon n he rae of nformaon arrval. For a samle of US common socks, Lamoureux and Lasraes (1990) found ha n he generalzed auoregressve condonal heeroskedascy model, GARCH effecs vanshed when conemoraneous volume was added o he condonal varance euaon. Guner Gursoy, Asl Yuksel, Aydn Yuksel, 008. 1 The mxure of dsrbuon hyohess was develoed o model sock reurns by Clark (1973), Es and Es (1976) and Tauchen and Ps (1983). 00 The dea roosed by Lamoureux and Lasraes (1990) has been aled n he leraure o boh ndvdual socks and sock marke ndces. Whle sudes ha rely on ndvdual sock daa n general suor Lamoureux and Lasraes (1990) fndng, reored resuls are much weaker for sudes ha use sock marke ndces. These fndngs sugges ha volume may be a good roxy for sock-level analyss, bu no for marke-level analyss. One noable asec of he leraure s ha he vas maory of sudes erformng a marke-level analyss examned develoed markes and we have lmed evdence from emergng markes on hs ssue. Ye, as Bekaer and Harvey (00) dscuss, emergng markes research s valuable because of dfferen nsuonal, legal and regulaory envronmens n hese markes. Based on hs observaon, he urose of hs aer s o rovde addonal evdence from emergng markes on he relaon beween condonal volaly and radng volume. I accordngly exlores sock markes ndces of 1 emergng markes over he erod of 000-006. Ths wll allow for a crossseconal check of he robusness of he above fndng for develoed markes ha radng volume seems o be a oor roxy for marke-level analyss. In he analyss he aenon s ad o he redcably of radng volume. Whle mos of he sudes have used oal radng volume as a roxy for nformaon flow, recen sudes decomose oal volume n s redcable and unredcable comonens before examnng s effec on condonal volaly by argung ha unexeced radng volume s a beer sgn of new nformaon. To make our resuls comarable o hose of recen sudes, we reor our fndngs wh and whou hs decomoson. I s found ha, regardng hese wo ssues, he evdence rovded by earler sudes ha examned
develoed markes holds n emergng markes. Secfcally, radng volume seems o be a oor roxy for marke-level analyss. There s some evdence ha unexeced radng volume s a roxy for he arrval of new nformaon n he conex of mxure of dsrbuons hyohess. The remander of he aer s organzed as follows. The nex secon lss exsng fndngs n he leraure. The second secon nroduces he daa and mehodology used n he sudy. The hrd secon conans he emrcal resuls. The las secon rovdes he concludng remarks. 1. Leraure Lamoureux and Lasraes (1990) dea has found wde alcaon n he leraure. The fndngs of hese subseuen sudes are arcularly moran for wo reasons. Frs, hey sugges ha, whle esng sock marke effcency, he heeroskedascy of he reurns mus be aken no consderaon (Lo and MacKnlay, 1989; Islam and Khaled, 005). Second, hey sugges ha esmaed reurn varance s one of he moran facors n he oon rcng model (Black and Scholes, 197). One of he early sudes s Bralsford (1996). I ess he relaonsh beween oal radng volume and condonal volaly usng he Ausralan sock marke ndex over he erod from 1989 o 1993. They conclude ha ncludng oal radng volume n he condonal volaly model reduces he GARCH effec noably; ndcang ha oal radng volume s a suable roxy for nformaon flow. Phylaks e al. (1996) examne he relaonsh beween oal radng volume and condonal volaly n he Ahens Sock Exchange over he erod from 1988 o 1993. They dvde he samle erod no wo sub-erods wh resec o sze of he marke o examne and comare he relaonsh beween oal radng volume and condonal volaly. They fnd ha oal radng volume s a good roxy for nformaon flow, snce he GARCH effec declne afer oal radng volume s ncluded n he model. Comarng he resuls for he wo erods, Phylaks e al. (1996) fnd ha, as he sze of he marke ncreases, he nformaon conen of radng volume also ncreases. Sharma e al. (1996) examne he NYSE ndex over he erod beween 1986 and 1989. They fnd ha he ncluson of volume n he condonal volaly model gves rse o a noable reducon bu no o a comlee dsaearance of he GARCH effecs. Ther resuls are weaker han hose of Lamoureux and Lasraes (1990). Sharma e al. (1996) arbue hs o volume beng a oor roxy for he news arrval ha conrbues condonal heeroskedascy o Invesmen Managemen and Fnancal Innovaons, Volume 5, Issue 4, 008 marke-wde reurns. Ther argumen s based on he dfference beween an ndvdual sock and a marke orfolo regardng he exen o whch sysemac and frm-secfc facors affec her volume and reurn volaly. Boh facors affec boh volume and reurn volaly for ndvdual socks. Whle boh facors affec marke volume, only sysemac facors affec marke ndex volaly. Pyun e al. (000) rovde frm-level evdence usng 15 ndvdual socks lsed n he Korean Sock Marke from 1990 o 1994. Ther aer analyzes he relaonsh beween volaly sllover and nformaon flow for frms wh dfferen szes. The auhors reor ha oal radng volume reduces he GARCH effec and volaly sllover occurs only from large o small frms, no vce versa. Emloyng he same mehod and samle erod as Lamoureux and Lasraes (1990), Omran and McKenze (000) analyze he relaonsh beween oal radng volume and volaly erssence for 50 UK socks. Even hough her resuls are conssen wh Lamoureux and Lasraes (1990), dagnosc ess show ha her GARCH model canno fully caure he volaly erssence n her daa. Myakosh (00) nvesgaes he effecs of oal radng volume on condonal volaly erssence for boh ndvdual socks and he marke ndex of he Tokyo Sock Exchange. The resuls show ha radng volume reduces he GARCH effec, boh for ndvdual socks and he marke ndex. The resuls are conssen wh he vew ha oal radng volume s a good roxy for nformaon flow. Bohl and Henke (003) analyze he relaonsh for 0 Polsh socks beween January 4, 1999 and Ocober 31, 000. They observe a declne n condonal volaly erssence afer ncludng oal radng volume n he model. They argue ha her resuls are conssen wh he revous sudes done n develoed sock markes. Fnally, Wang e al. (005) examne he relaonsh beween oal radng volume and volaly for boh Chnese ndvdual socks and he sock marke ndex. They fnd ha radng volume can be a roxy for nformaon flow for ndvdual socks, bu no for he marke ndces. The reason for hs s asynchronous nformaon arrvals for each frm lsed n he ndex. Unlke he revous sudes oulned above, Wagner and Marsh (005) and Arago and Neo (005) use unexeced radng volume (surrse volume) as a roxy for nformaon flow and examne s relaonsh wh condonal volaly for develoed sock markes. 01
Invesmen Managemen and Fnancal Innovaons, Volume 5, Issue 4, 008 Wagner and Marsh (005) analyze he relaonsh by usng seven maor sock marke ndces (hose of France, Germany, Holland, Hong Kong, Jaan, he UK, and US) over he erod beween 1988 and 1997. They fnd ha here s a sgnfcan osve relaonsh beween surrse radng volume and condonal volaly, and ha ncludng surrse radng volume n he model gves rse o a moderae decrease n volaly erssence. Moreover, hey observe ha here s an asymmerc relaonsh beween surrse volume and condonal volaly, meanng ha comared o negave surrse volume osve surrse volume has a sgnfcanly greaer effec on condonal volaly. Arago and Neo (005) also use unexeced radng volume as a roxy for he nformaon flow o nvesgae he changes n condonal volaly erssence by usng seven maor sock marke ndces (hose of France, Germany, he UK, he US, Ialy, Jaan, San, and Swzerland) beween 1995 and 000. However, Arago and Neo s resuls conflc wh Wagner and Marsh s. The ncluson of neher oal volume nor s redcable and unredcable comonens leads o a consderable reducon n volaly erssence. The evdence regardng he adeuacy of radng volume as a roxy for nformaon arrval as reored by sudes ha erformed a sock-level analyss can be summarzed as follows. Afer ncludng oal radng volume n he model, n general, here s: (1) eher a consderable or comlee reducon n Garch effecs (US, Polsh and Korean socks), () a consderable reducon n Garch effecs (Chnese socks), (3) a moderae reducon n Garch effecs (Jaanese socks). On he oher hand, he evdence from sudes ha erformed a marke-level analyss can be summarzed as follows. Afer ncludng oal radng volume n he model, here are: (1) consderable reducon n Garch effecs (sock marke ndex of Greece), () lle or no reducon n Garch effecs (sock marke ndces of: Ausrala, Chna, France, Germany, Holland, Hong Kong, Ialy, Jaan, San, Swzerland, UK, US). As can be seen from he summary above, ou of 1 markes for whch a marke-level analyss has been done, only wo are emergng one (Chna and Greece). Moreover, he evdence ndcaes ha volume may be a good roxy for sock-level analyss, bu no for marke-level analyss. Noe ha he evdence from Jaan and Chna, he wo markes for whch we have boh sock and marke-level analyses, s n lne wh he concluson above. Among oher hngs, hs summary ndcaes he need for more evdence from emergng markes. 0. Daa and mehodology The daa se for 1 emergng sock markes was gahered from Daasream. Ou of hese markes, four are Lan Amercan (Colomba, Mexco, Peru and Venezuela), wo Easern Euroean (Czech Reublc, and Hungary), one Afrcan (Souh Afrca), and fve Asan (Indonesa, Souh Korea, Sngaore, Sr Lanka, and Tawan) 1. The varables n he daa se are Daasream s daly sock marke ndces and daly radng volumes for he erod from January 3, 000 o Augus 15, 006. The sock marke ndces are adused for he caal ncreases, dvdend aymens and sock sls. The daly marke reurns, R, are calculaed as he logarhmc frs dfferences of he daly closng values of he sock ndces. Toal radng volume, V, s he logarhm of radng volume, as measured by he number of shares raded daly. The unexeced radng volume s calculaed as n Arago and Neo (005) by akng he dfferences beween oal and execed radng volumes o be used as a roxy for new nformaon flow. In order o be able o esmae execed radng volume, V,ex, he followng ARMA(, ) model s used: V h1 h V h 1 DUM, (1) where V, oal radng volume on day ; resdual on day ; DUM dummy varables used o elmnae day of he week effec: = 1,,,5 and = 1,,,5. For each ndex, oal radng volume daa durng he frs 10 days (aroxmaely unl 06/30/000) are used o choose he omal ARMA(,) model. Afer choosng he omal and values for each marke ndex, execed radng volume s esmaed usng a rollng wndow whch dros he frs observaon and adds one more observaon o he samle. Thus, he daa se for he execed radng volume, V,ex, and he unexeced radng volume, V,unex, (whch s he dfference beween oal radng volume, V, and execed radng volume, V,ex ) covers he erod beween July 1, 000 and Augus 15, 006 3. Descrve sascs for reurn, oal radng volume, execed radng volume and unexeced radng volume are resened n Table 1 4. 1 These markes are characarzed as emergng by ISI Emergng Markes. To choose he omal model ( and values) for each ndex, Akake Informaon Crera (AIC) were emloyed. 3 Due o ublc holdays, he exac dae for he begnnng of he samle erod was dfferen for each marke ndex. 4 Saonary of he seres s esed usng he Augmened Dckey-Fuller (ADF) ess and he resuls show ha he seres are saonary.
Invesmen Managemen and Fnancal Innovaons, Volume 5, Issue 4, 008 Table 1. Descrve sascs Mean Sd. dev Skewness Kuross Jarue-Bera Q(1) Observaon number Lan Amerca Reurn 0.001 0.0110-0.163 0.6777 19444.4 *** 108.14 *** 1493 Colomba Toal radng volume.9387.1339-0.51.134 59.43 *** 10730.00 *** Unexeced radng volume 0.0364 1.0818 0.077 7.77 11.58 *** 16.4 Reurn 0.0006 0.0107-0.1034 5.4447 388.75 *** 41.74 *** 1550 Mexco Toal radng volume 5.1106 0.5197-1.0065 6.6786 1135.67 *** 170.10 *** Unexeced radng volume 0.009 0.4483-0.8510 8.8064 364.43 *** 17.53 Reurn 0.0005 0.008-1.38 16.951 1859.47 *** 9.81 *** 1530 Peru Toal radng volume 1.8076 0.9054 0.4516 4.088 16.76 *** 178.90 *** Unexeced radng volume -0.0018 0.7750 0.7381 5.3006 476.34 *** 1.88 Reurn 0.0008 0.011 0.4790 11.4760 4398.97 *** 90.49 *** 1451 Venezuela Toal radng volume.3691 1.488-0.1036 3.780 34.64 *** 1846.90 *** Unexeced radng volume -0.0064 1.1064 0.1801 3.8565 5.19 *** 16.17 Easern Euroe Reurn 0.0007 0.015-0.319 5.6489 464.35 *** 8.77 1541 Czech Reublc Toal radng volume 1.6573 0.7406-0.1568 3.4310 18.4 *** 47.90 *** Unexeced radng volume 0.0167 0.5369-0.5081 4.9101 300.55 *** 18.70 Reurn 0.0004 0.0134-0.1019 4.4417 135.95 *** 19.69 * 1539 Hungary Toal radng volume 1.9561 0.568-0.365 3.501 44.69 *** 1860.80 *** Unexeced radng volume 0.0087 0.4606-0.19 4.0980 89.63 *** 9.56 Asa Reurn 0.0005 0.0155-0.6435 7.949 1608.61 *** 7.88 *** 1490 Indonesa Toal radng volume 6.609 0.7867 0.05.4666 17.8 *** 60.50 *** Unexeced radng volume 0.0144 0.5134 0.1874 3.641 13.05 *** 18.33 Reurn 0.0003 0.0185-0.3736 5.9789 593.44 *** 13.76 1510 Souh Korea Toal radng volume 5.7084 0.7104 0.7195 3.0351 130.37 *** 10314.00 *** Unexeced radng volume 0.0007 0.3619 0.0879 6.7417 88.78 *** 17.13 Reurn 0.0001 0.0101-0.1895 5.345 356.38 *** 4.34 *** 154 Sngaore Toal radng volume 5.9580 0.505-0.1850.7518 1.75 *** 708.80 *** Unexeced radng volume 0.0056 0.303 0.3568 4.8161 44.61 *** 10.8 Reurn 0.0008 0.0155-0.1499 39.348 80494.6 *** 55.55 *** 1464 Sr Lanka Toal radng volume 1.3565 1.588-0.3308.97 7.07 *** 5608.90 *** Unexeced radng volume -0.0111 0.9038 0.5411 4.1456 151.48 *** 17.6 Reurn -0.000 0.0168-0.0664 5.3934 36.73 *** 0.6 * 1515 Tawan Toal radng volume 7.905 0.4353 0.0831.9979 1.75 6783.50 *** Unexeced radng volume -0.0007 0.705 0.344 3.8865 79.53 *** 18.5 03
Invesmen Managemen and Fnancal Innovaons, Volume 5, Issue 4, 008 Table 1 (con.). Descrve sascs Mean Sd. dev Skewness Kuross Jarue-Bera Q(1) Observaon number Afrca Reurn 0.0006 0.0105-0.618 5.8441 534.18 *** 3.74 ** 1533 Souh Afrca Toal radng volume 4.9139 0.3947-0.5549 5.8690 604.45 *** 1409.40 *** 04 Unexeced radng volume 0.0085 0.367-0.0599 6.4180 747.16 *** 13.45 Noes: In he able, Reurn refers o daly logarhmc reurn of sock marke ndces. Toal radng volume s calculaed as he logarhm of he number of shares raded n a day. Unexeced radng volume s calculaed as he dfference beween oal radng volume and execed radng volume. Q(1), Lung-Box sasc u o 1 lags measures seral correlaon n seres. *, **, and *** refer o 10, 5, and 1 ercen sascal sgnfcance levels resecvely. Table 1 shows ha he mean of daly reurns ranges beween -0.0% (sock marke ndex of Tawan) and 0.1% (sock marke ndex of Colomba), and he sandard devaon beween 0.8% (sock marke ndex of Peru) and 1.85% (Korean sock marke ndex). The Jarue-Bera (1980) normaly es shows ha all reurn dsrbuons are non-normal. Fnally, Lung-Box sascs u o 1 lags (Q(1)) ndcaes ha all of he oal radng volume seres dslay seral correlaon. We selec GARCH (,) (Bollerslev, 1986) ye models 1, as suggesed by Lamoureux and Lasraes (1990), o nvesgae he relaonsh beween radng volume and volaly. In he frs model (Model I), erssence n condonal volaly s examned wh he followng euaons: Model I: R c R 1, () 1 I 1 1 1, (3) where R Logarhmc reurn on day ; condonal sandard devaon on day ; resdual erm n he mean euaon; dummy varable, I1 eual o 1 f 1 0, and 0 oherwse. The mean euaon conans a consan, an AR(1) erm, and he conemoraneous condonal sandard devaon. The AR(1) erm accouns for he me deendence n reurn due o nonsynchronous radng (Naand and Yung, 1991; Sharma e al., 1996; and Myakosh, 00). The condonal sandard devaon s also ncluded o allow me-varyng rsk remum (Engle e al., 1987; Gennoe and Marsh, 1993). In he condonal volaly euaon, and refer o he coeffcens of suared resduals lagged by erod(s) and condonal varance lagged by e- 1 For he sock marke ndex of Sngaore, he GARCH(1,1) model could no elmnae auocorrelaon n he resduals. For ha reason, GARCH (,) models wh and values greaer han 1 were used. rod(s), resecvely. A secal ye of GARCH model develoed by Glosen e al. (1993) (GARCH-GJR(,)) s used o allow asymmerc effecs of good and bad news on condonal varance. In model I, f s greaer han zero, hen bad news ncreases volaly more han good news (leverage effec). To measure he effecs of oal radng volume on condonal volaly erssence, he frs model s modfed by addng oal radng volume no he condonal varance euaon. Thus he second model s characerzed by he followng condonal varance euaon: Model II: 1I 1 V. (4) 1 1 Fnally, snce some of he sudes n he leraure (such as Bessembnder and Segun, 1993; and Wagner and Marsh, 005) suor he use of unexeced radng volume (surrse volume) raher han oal radng volume as a roxy for new nformaon flow, boh execed radng volume (V,ex ) and unexeced radng volume (V,unex ) are ncluded no he hrd model (Model III) as exlanaory varables. A dummy varable (D ) s also added o he model o rea oenal asymmery (Bessembnder and Segun, 1993; and Wagner and Marsh, 005). Ths akes on he value of one when he unexeced radng volume s osve and zero oherwse. If here s an asymmery n radng volume, he effec of osve volume shocks on he condonal volaly euaon s execed o be greaer han he effec of he negave ones ( 0). Model III: 1 1 1I V,ex V,un ex 1 D, (5)
The models are esmaed by he mehod of he maxmum lkelhood wh he Maruard omzaon algorhm. I s assumed ha he condonal dsrbuon of he error erm has Generalzed Error Dsrbuon (GED). 3. Resuls The resuls for he benchmark model (Model I) are resened n Table. They show ha volaly erssence, as measured by he sum of all Invesmen Managemen and Fnancal Innovaons, Volume 5, Issue 4, 008 GARCH coeffcens ( 1 1 ), s hgh for all marke ndces and akes values of more han 0.70 and even 1.0 for he sock markes of Colomba and Peru. A smlar fndng s reored n Phylaks e al. (1996). Ths fndng mles no only hgh volaly erssence bu also nonsaonary n he varance of sock marke ndex reurns for Colomba and Peru. Table. Resuls of esmang GARCH-GJR(,) model (Model I). In he able, 1,, 1, and reresen esmaed arameers of Model I: 1 I 1 1 1 1 1 1 1 1 1 Lan Amerca Colomba 0.394(5.30) *** 0.394 0.614(13.55) *** 0.614 1.008-0.060(0.7) Mexco 0.007(0.4) 0.007 0.884(37.83) *** 0.884 0.891 0.143(4.91) *** Peru 0.063(4.66) *** 0.063 0.948(95.47) *** 0.948 1.011 0.063(4.66) *** Venezuela 0.434(4.18) *** 0.434 0.95(3.8) *** 0.95 0.78-0.443(4.0) *** Easern Euroe Czech Reublc 0.036(1.6) 0.036 0.850(3.6)*** 0.850 0.885 0.036(1.6) Hungary 0.046(.91)*** 0.046 0.884(38.71)*** 0.884 0.930 0.046(.91)*** Asa Indonesa 0.060(.08)** 0.060 0.759(15.1)*** 0.759 0.819 0.136(3.9)*** Souh Korea 0.015(1.04) 0.015 0.935(6.47)*** 0.935 0.950 0.076(4.40)*** Sngaore 0.01(0.96) 0.069(.5)** 0.113 0.50(4.6)*** 0.38(.10)** 0.859 0.97 0.105(4.37)*** Sr Lanka 0.409(5.16)*** 0.409 0.556(10.98)*** 0.556 0.965 0.03(0.) Tawan 0.04(1.97)** 0.04 0.947(83.5)*** 0.947 0.971 0.051(3.07)*** Afrca Souh Afrca 0.00(1.1) 0.00 0.874(44.14)*** 0.874 0.894 0.140(5.34)*** Noes: In he condonal volaly euaon, and refer o he coeffcens of he suared resduals lagged by erod(s) and he condonal varance lagged by erod(s) resecvely. I - -1 s a dummy varable, whch s eual o one f -1 s negave and zero oherwse. -sascs are n arenheses. *, **, and *** refer o 10, 5, and 1 ercen sascal sgnfcance levels resecvely. For he sock marke ndex of Sngaore, snce > and >, only 1,, 1 and coeffcens are lsed. As execed, here s a leverage effec (>0) n egh ou of he 1 marke ndces (Mexco, Peru, Hungary, Indonesa, Souh Korea, Sngaore, Tawan and Souh Afrca). Ths resul s conssen wh Wagner e al. (005) and Arago and Neo (005), whch fnd a leverage effec n almos all of he sock marke ndces ncluded n her daa ses. Surrsngly, negave leverage effec s observed n he sock marke ndex of Venezuela, whch means ha bad news generaes less volaly han good news. There s no leverage effec n he remanng hree marke ndces. 05
Invesmen Managemen and Fnancal Innovaons, Volume 5, Issue 4, 008 Table 3. Resuls of esmang GARCH-GJR(,)-Toal Tradng Volume Model (Model II). In he able, 1,, 1,,, and reresen esmaed arameers of Model II: I 1 1 1 1 V 1 1 1 1 1 1 Lan Amerca Colomba 0.371(5.00) *** 0.371 0.573(10.69) *** 0.573 0.945 0.371(5.00) *** 0.011(.35) ** Mexco 0.004(0.4) 0.004 0.893(41.93) *** 0.893 0.897 0.141(5.08) *** 0.030(.93) *** Peru 0.060(3.93) *** 0.060 0.937(69.17) *** 0.937 0.997 0.060(3.93) *** 0.007(1.80) * Venezuela 0.187(4.18) *** 0.187 0.77(16.06) *** 0.77 0.959-0.189(4.11) *** -0.008(0.59) Easern Euroe Czech Reublc 0.034(1.47) 0.034 0.84(30.56)*** 0.84 0.876 0.034(1.47) 0.00(1.63) Hungary 0.00(0.84) 0.00 0.731(18.39)*** 0.731 0.75 0.00(0.84) 0.60(7.17)*** Asa Indonesa 0.060(.05)** 0.060 0.768(14.87)*** 0.768 0.87 0.130(0.00) -0.01(0.71) Souh Korea 0.003(0.7) 0.003 0.907(44.88)*** 0.907 0.910 0.108(4.44)*** 0.111(3.9)*** Sngaore 0.010(0.35) 0.059(1.) 0.069 0.59(0.95) 0.834(1.68)* 0.874 0.943 0.083(.00)** -0.001(0.45) Sr Lanka 0.184(4.14)*** 0.184 0.60(17.8)*** 0.60 0.787 0.050(1.16) 0.197(163.11)*** Tawan 0.01(1.04) 0.01 0.947(81.89)*** 0.947 0.959 0.07(4.33)*** 0.040(9.13)*** Afrca Souh Afrca 0.03(1.80)* 0.03 0.847(44.66)*** 0.847 0.879 0.03(1.80)* -0.009(1.96)*** Noes: and are he coeffcens of he suared resduals lagged by erod(s) and he condonal varance lagged by erod(s) resecvely. I - -1 s a dummy varable whch s eual o one f -1 s negave, and zero oherwse. V refers o oal radng volume, whch s he logarhm of radng volume as measured by he number of shares raded durng he day. -sascs are rovded n arenheses. *, **, *** reresen 10, 5, and 1 ercen sgnfcance levels, resecvely. For he sock marke ndex of Sngaore, snce > and >, only 1,, 1 and coeffcens are lsed. Table 3 reors he esmaon resuls of he second model (Model II), where oal radng volume s used as a roxy for nformaon flow. They show ha oal radng volume has a sascally sgnfcan osve effec on he condonal volaly of seven ou of 1 emergng marke ndces (Columba, Mexco, Peru, Hungary, Souh Korea, Sr Lanka, and Tawan). The GARCH coeffcens are sll sascally sgnfcan and for all he markes volaly erssence s more han 0.70. The ncluson of radng volume roduces a moderae reducon n volaly erssence for Hungary and Sr Lanka. For he remanng markes he change s small. For four sock marke ndces (Venezuela, Czech Reublc, Indonesa, and Sngaore), he coeffcen esmae of oal radng volume s nsgnfcan and hus evdence from hese markes does no suor even he mxure of dsrbuons hyohess, namely 06 he sac relaon beween nformaon arrval and volaly. Furhermore, surrsngly, here s a sgnfcan negave relaonsh beween oal radng volume and condonal volaly for he sock marke ndex of Souh Afrca. Regardng he leverage effec he resuls from Model II are very smlar o hose from Model I. Overall, he resuls n Table 3 show ha he ncluson of oal radng volume hels n exlanng condonal volaly erssence o a moderae exen for wo markes and o a small exen for four markes. For he remanng markes oal radng volume as a roxy for nformaon flow canno exlan even he condonal heeroskedascy n marke reurns. These fndngs are conssen wh hose n Sharma e al. (1996) and hus gve suor o her argumen ha volume may be a good roxy for sock-level analyss, bu no for marke-level analyss.
Invesmen Managemen and Fnancal Innovaons, Volume 5, Issue 4, 008 Table 4. Resuls of esmang GARCH-GJR(,)-Unexeced Tradng Volume Model (Model III). In he able, 1,, 1,,,,, and reresen esmaed arameers of Model III: 1 1 1 I 1 V,ex V, un ex D 1 1 1 1 = 1 1 Lan Amerca Colomba 0.356 (5.5) *** 0.356 0.580 (11.16)*** 0.580 0.936-0.0 (0.7) 0.016-0.07 0.033 (.95) *** (.05) ** (1.09) 9.949( 0.00) *** Mexco 0.001 (0.06) 0.001 0.878 (38.7) *** 0.878 0.879 0.159 0.010 (5.45) * (0.6) 0.041 (1.31) 0.036 (0.96) 0.65 (0.4) Peru 0.043 (.6) *** 0.043 0.98 (49.34)*** 0.98 0.971-0.03 (1.6) 0.004 (0.8) 0.009 (0.46) 0.036 (1.7) 0.060 (0.81) Venezuela 0.410 (4.0) *** 0.410 0.35 (.66)*** 0.35 0.645-0.419-0.100 0.138-0.015 (4.00) *** (.50) ** (.78) *** (0.1) 1.886 (0.00) *** Easern Euroe Czech Reublc 0.05 (.04)** 0.05 0.78 (.45) *** 0.78 0.834 0.148-0.043 0.174 0.098 (3.53) *** (.48) ** (3.) *** (1.54) 11.8 (0.00) *** Hungary 0.014 (0.7) 0.014 0.791 (5.36) *** 0.791 0.805 0.014 (0.7) 0.157 0.31 0.183 0.738 (3.56) *** (3.35) *** (.13) ** (0.39) Asa Indonesa 0.008 (0.7) 0.008 0.535 (8.85) *** 0.535 0.543 0.008 (0.7) -0.079 (1.6) 0.735 0.190 (5.39) *** (0.98) 50.391 (0.00) *** Souh Korea 0.015 (1.17) 0.015 0.97 (51.5) *** 0.97 0.94 0.106 0.090 0.179 (4.99) *** (3.71) *** (1.04) 0.145 (1.51) 0.67 (0.61) Sngaore 0.018 (0.88) 0.078 (.8)** 0.9 0.16 (1.69) 0.18 (1.3) 0.543 0.835 0.065 (1.64) -0.15 0.304 0.16 4.677 (4.5) *** (3.91) *** (.0) ** (0.00) *** Sr Lanka 0.33 (4.9)*** 0.33 0.440 (8.58) *** 0.440 0.763 0.14 (1.34) 0.040 0.045 (1.95) * (1.) 0.39 (3.95) *** 0.010 (0.9) Tawan 0.00 6(0.47) 0.006 0.937 (69.1) *** 0.937 0.943 0.096 0.019 (4.37) *** (1.0) 0.34-0.015 (.49) *** (0.0) 5.76 (0.01) *** Afrca Souh Afrca 0.019 (1.1) 0.019 0.875 (46.08) *** 0.875 0.894 0.019 (1.1) -0.037 (1.44) 0.076 (1.47) 0.000 (0.00) 3.345 (0.07) * Noes: and are he coeffcens of he suared resduals lagged by erod(s) and he condonal varance lagged by erod(s) resecvely. I - -1 s a dummy varable, whch s eual o one f -1 s negave, and zero oherwse. V,ex refers o execed radng volume. V,unex s unexeced radng volume, whch s he dfference beween oal radng volume and execed radng volume. D s a dummy varable, whch s eual o one f unexeced radng volume s osve, and zero oherwse. Exce for he las column (=), n all of he columns -sascs are n arenheses. In he las column, Wald es resuls for he hyohess of = are resened and -values are n arenheses. *, **, *** reresen 10, 5, and 1 ercen sgnfcance levels, resecvely. For he sock marke ndex of Sngaore, snce > and >, only 1,, 1 and coeffcens are lsed. In he fnal model (Model III), condonal volaly euaon ncludes boh execed and unexeced radng volumes. As Table 4 shows, he esmaed coeffcen on unexeced radng volume s sascally sgnfcan for mos of he sock markes n he samle (seven ou of 1). Exce for he Colomban Sock Marke, he drecon of relaonsh beween unexeced radng volume and condonal volaly s osve n hose markes. Moreover, here s some evdence regardng he exsence of an asymmerc relaonsh beween unexeced radng volume and condonal volaly. For hree marke ndces (Hungary, Sngaore, and Sr Lanka) osve unexeced radng volume generaes more volaly han negave 07
Invesmen Managemen and Fnancal Innovaons, Volume 5, Issue 4, 008 unexeced radng volume ( 0). However, for he remanng ndces, hs erm s nsgnfcan. For hree of he marke ndces (Mexco, Peru, and Souh Afrca), he coeffcen esmae on neher execed radng volume nor unexeced radng volume s sascally sgnfcan, meanng ha execed radng volume and unexeced radng volume canno exlan condonal volaly. For all of he markes (exce Colomba) he coeffcen on unexeced radng volume s greaer han ha on execed radng volume. As reored n he able, he Wald es reecs he null hyohess of he eualy of coeffcens on execed and unexeced radng volume for seven sock markes. Overall, he resuls n Table 4 sugges ha for he sx markes where he coeffcen on unexeced volume s sgnfcanly osve, unexeced volume ndeed aears o be a roxy for new nformaon arrval conssen wh he mxure of dsrbuons hyohess. Table 5. Dagnosc ess for Model I, Model II and Model III. Snce has no seral correlaon by consrucon, canno exlan GARCH effecs. Fnally, n order o check he robusness of our fndngs, a seres of dagnosc ess are also carred ou. The resuls are resened n Table 5. For he hree models, he null hyohess of no auocorrelaon s esed by Lung-Box ess on he level and suared resdual seres wh 1 lags (Q(1) and Q (1), resecvely). These resuls show ha exce for he level resduals of he Sr Lanka sock marke n Model II, he null hyohess of no auocorrelaon on he level and suared resduals canno be reeced a he fve ercen sgnfcance level for all models and emergng marke ndces. The Lagrange muller es (LM(5)) s used o es for he exsence of he ARCH effec. The resuls reveal ha here s no ARCH effec n he resduals a he fve ercen sgnfcance level eher. Q(1), Q (1) are Lung-box ess on he level and suared resduals seres wh 1 lags. They are dsrbued wh a (1) under he null of no auocorrelaon; LM(5) s he Engle s (198) Lagrange mullers es for he exsence of ARCH effecs. I s dsrbued wh a (5) under he null of no auocorrelaon. P- values are n arenheses. R c R 1 Model I: Model II: I 1 1 1 1 I 1 1 1 1 V Model III: 1 1 1 I 1 V,ex V, un ex D MODEL I MODEL II MODEL III Q(1) Q (1) LM(5) Q(1) Q (1) LM(5) Q(1) Q (1) LM(5) Lan Amerca Colomba 17.917 (0.08) 6.894 (0.81) 0.786 (0.56) 15.87 (0.15) 5.79 (0.9) 0.68 (0.68) 17.00 (0.10) 5.134 (0.9) 0.659 (0.65) Mexco 1.479 (0.33) 11.733 (0.38) 0.774 (0.57) 1.584 (0.3) 1.988 (0.9) 0.697 (0.63) 13.547 (0.6) 1.801 (0.31) 0.77 (0.6) Peru 16.710 (0.1) 14.77 (0.19) 1.96 (0.08) 16.544 (0.1) 1.319 (0.34) 1.596 (0.16) 15.39 (0.17) 9.646 (0.56) 1.70 (0.7) Venezuela 14.76 (0.) 9.87 (0.55) 0.18 (0.95) 10.736 (0.47) 3.53 (0.98) 0.417 (0.84) 1.557 (0.3) 1.085 (0.36) 0.30 (0.95) Easern Euroe Czech Reublc 7.396 (0.77) 10.53 (0.48) 1.430 (0.1) 7.419 (0.76) 10.116 (0.5) 1.405 (0.) 7.665 (0.74) 11.58 (0.4) 1.58 (0.16) Hungary 13.551 (0.6) 5.86 (0.89) 0.714 (0.61) 1.995 (0.9) 18.10 (0.08) 1.067 (0.38) 1.441 (0.33) 15.993 (0.14) 1.97 (0.6) 08
Invesmen Managemen and Fnancal Innovaons, Volume 5, Issue 4, 008 Table 5 (con.). Dagnosc ess for Model I, Model II and Model III MODEL I MODEL II MODEL III Q(1) Q (1) LM(5) Q(1) Q (1) LM(5) Q(1) Q (1) LM(5) Asa Indonesa 8.53 (0.67) 8.874 (0.63) 0.184 (0.97) 8.477 (0.67) 8.714 (0.65) 0.183 (0.97) 13.918 (0.4) 17.131 (0.10) 0.73 (0.60) Souh Korea 10.851 (0.46) 10.851 (0.46) 0.541 (0.75) 1.684 (0.3) 1.448 (0.33) 0.661 (0.65) 1.051 (0.36) 11.336 (0.4) 0.63 (0.68) Sngaore 15.6 (0.17) 5.05 (0.9) 0.51 (0.77) 15.513 (0.16) 5.17 (0.9) 0.486 (0.79) 16.767 (0.1) 4.785 (0.94) 0.59 (0.75) Sr Lanka 10.535 (0.48) 1.786 (1.00) 0.116 (0.99) 51.94 (0.00) 1.817 (1.00) 0.6 (0.95) 11.565 (0.40) 1.887 (1.00) 0.093 (0.99) Tawan 8.37 (0.69) 11.486 (0.40) 1.693 (0.13) 7.489 (0.76) 10.407 (0.49) 1.04 (0.30) 7.71 (0.74) 11.789 (0.38) 1.393 (0.) Afrca Souh Afrca 13.030 (0.9) 1.405 (0.33) 1.17 (0.34) 1.69 (0.3) 1.983 (0.9) 1.067 (0.38) 1.83 (0.31) 11.559 (0.40) 0.960 (0.44) Concluson Ths sudy nvesgaes he effec of radng volume on he condonal volaly erssence of 1 emergng sock marke ndex reurns beween January 3, 000 and Augus 15, 006 by usng Lamoureux and Lasraes (1990) mehodology. The resuls reveal he followng: All sock markes ndces n he samle dslay a hgh degree of volaly erssence. When radng volume s ncluded n he condonal varance euaon, as a roxy for nformaon flow, some small o moderae level reducon s observed n he volaly erssence of sx sock marke ndces. Ths fndng s conssen wh he argumen n Sharma e al. References (1996) ha volume may be a good roxy for socklevel analyss, bu no for marke-level analyss. The use of unexeced and execed volume nsead of oal volume n he condonal varance euaon gves some suor o he argumen ha unexeced volume acs as a roxy for new nformaon arrval conssen wh he mxure of dsrbuons hyohess. Snce unexeced volume has no seral correlaon by consrucon, canno be execed o exlan GARCH effecs n ndex reurns. Fnally, wo effecs documened earler by research on develoed markes, namely he leverage effec and he exsence of asymmery n he conemoraneous relaon beween radng volume and volaly, are confrmed n emergng markes. 1. Arago V., L. Neo. Heeroskedascy n he Reurns of he Man World Sock Exchange Indces// Inernaonal Fnancal Markes Insuons and Money, 005. 15.. 71-84.. Bekaer G., C.R. Harvey. Research n Emergng Markes Fnance: Lookng o he Fuure// Emergng Markes Revew, 00. 3.. 49-448. 3. Bessembnder H., P.J. Segun. Prce Volaly, Tradng Volume, and Marke Deh: Evdence from he Fuures Markes// Journal of Fnancal and Quanave Analyss, 1993. 8.. 1-39. 4. Black F., S.M. Scholes. The Valuaon of Oon Conracs and a Tes of Marke Effcency// Journal of Fnance, 197. 7 ().. 399-417. 5. Bohl M.T., H. Henke. Tradng Volume and Sock Marke Volaly: The Polsh Case// Inernaonal Revew of Fnancal Analyss, 003. 1.. 513-55. 6. Bollerslev T. Generalzed Auoregressve Condonal Heeroskedascy// Journal of Economercs, 1986. 31.. 307-37. 7. Bralsford T.J. The Emrcal Relaonsh beween Tradng Volume, Reurns, and Volaly// Accounng and Fnance, 1996. 35.. 89-111. 8. Clark P. A Subordnaed Sochasc Process Model wh Fne Varances for Seculave Prces// Economerca, 1973. 41.. 135-155. 9. Engle R.F. Auoregressve Condonal Heeroskedascy wh Esmaes of he Varance of UK Inflaon// Economerca, 198. 50.. 987-1008. 09
Invesmen Managemen and Fnancal Innovaons, Volume 5, Issue 4, 008 10. Engle R.F., D.M. Llen, P.R. Robns. Esmang Tme Varyng Rsk Prema n he Term Srucure: The Arch-M Model// Economerca, 1987. 55 ().. 391-401. 11. Es T., M. Es. The Sochasc Deendence of Secury Prce Changes and Transacon Volumes: Imlcaons for he Mxure of Dsrbuon Hyohess// Economerca, 1976. 44.. 305-31. 1. Gennoe G., A.T. Marsh. Varaons n Economc Uncerany and Rsk Premums on Caal Asses// Euroean Economc Revew, 1993. 37 (5).. 101-1041. 13. Glosen L.R., R. Jagannahan, D.E. Runkle. On he Relaon Beween he Execed Value and he Volaly of he Nomnal Excess Reurn on Socks// Journal of Fnance, 1993. 48.. 1779-1801. 14. Islam A., M. Khaled. Tess of Weak-Form Effcency of he Dhaka Sock Exchange// Journal of Busness Fnance and Accounng, 005. 3.. 1613-164. 15. Jarue A., A. Bera. Effcen Tess for Normaly, Heeroskedascy and Seral Indeendence of Regresson Resduals// Economc Leers, 1980. 6.. 55-59. 16. Lamoureux C.G., W.D. Lasraes. Heeroskedascy n Sock Reurn Daa: Volume versus GARCH Effecs// Journal of Fnance, 1990. 45.. 1-9. 17. Lo A.W., A.C. MacKnlay. The Sze and Power of he Varance Rao Tes n Fne Samles// Journal of Economercs, 1989. 40.. 03-38. 18. Myakosh T. ARCH versus Informaon-Based Varances: Evdence from he Tokyo Sock Marke// Jaan and he World Economy, 00. 14 ().. 15-31. 19. Naand M., K. Yung. A GARCH Examnaon of he Relaonsh Beween Volume and Prce Varably n Fuures Markes// Journal of Fuures Markes, 1991. 11.. 613-61. 0. Omran M. F., E. McKenze. Heeroscedascy n Sock Reurns Daa Revsed: Volume versus GARCH Effecs// Aled Fnancal Economcs, 000. 10.. 553-560. 1. Phylaks K., M.G. Kavussanos, G. Manals. Sock Prces and he Flow of Informaon n he Ahens Sock Exchange// Euroean Fnancal Managemen, 1996. (1).. 113-16.. Pyun C. S., S.Y. Lee, K. Nam. Volaly and Informaon Flows n Emergng Euy Marke A Case of he Korean Sock Exchange// Inernaonal Revew of Fnancal Analyss, 000. 9.. 405-40. 3. Sharma J.L., M. Mougoue, R. Kamah. Heeroskedascy n Sock Marke Indcaor Reurn Daa: Volume versus GARCH Effecs// Aled Fnancal Economcs, 1996. 6.. 337-34. 4. Tauchen G.E., M. Ps. The Prce Varably Volume Relaonsh on Seculave Marke// Economerca, 1983. 51.. 485-505. 5. Wang P., P. Wang, A. Lu. Sock Reurn Volaly and Tradng Volume: Evdence from he Chnese Sock Marke// Journal of Chnese Economc and Busness Sudes, 005. 3 (1).. 39-54. 6. Wagner N., T.A. Marsh. Surrse Volume and Heeroskedascy n Euy Marke Reurns// Quanave Fnance, 005. 5 ().. 153-168. 10