Volume-Return Relationship in ETF Markets: A Reexamination of the Costly Short-Sale Hypothesis

Transcription

1 Journal of Applied Finance & Banking, vol., no. 6,, -4 ISSN: (prin version), (online) Scienpress Ld, Volume-Reurn Relaionship in ETF Markes: A Reexaminaion of he Cosly Shor-Sale Hypohesis Jung-Chu Lin Absrac This sudy aims o invesigae wheher he cosly shor-sale heory is responsible for he volume-reurn relaionship in Taiwan s ETF marke. Through a model specificaion, we demonsrae ha rading volume and reurns for ETFs and heir underlying asses exhibi an asymmeric relaionship wih significanly larger volume associaed wih negaive reurns han wih non-negaive reurns, a finding ha verifies he predicion of he cosly shor-sale hypohesis. Using quanile regression, we also find ha he magniudes of he volume-reurn correlaions and subsequen asymmeric effecs vary wih he ETF volume levels. The asymmeric effecs are more obvious a he volume quaniles ha are higher han he median level and a he exrema quaniles. Noably, ha he sronges asymmeric relaionship occurs a he exrema quaniles for boh ETFs may sem largely from he sharp increases in he correlaions beween volume and negaive underlying index reurns for he exrema quaniles. We ry o use he hybrid effecs, complemenary and subsiue effecs for boh ETF and spo invesors, o explain his phenomenon. JEL classificaion numbers: G, G Keywords: ETF, Cosly shor-sale hypohesis, Asymmeric volume-reurn relaionship, Quanile regression Inroducion The relaionship beween rading volume and reurns in various financial markes coninues o be of excepional imporance and ineres for invesors seeking o undersand informaion dynamics and efficiency. The pas lieraure has focused heir aenion on he volume-reurn (V-R) relaionship in equiy or fuures markes. This paper examines he V-R relaionship for exchange-raded funds (ETFs) and heir underlying markes. There are wo main hypoheses relaed o V-R behavior ha were invesigaed in early lieraure, Associae Professor, Takming Universiy of Science and Technology. Aricle Info: Received : Sepember 7,. Revised : Sepember,. Published online : November,

2 Jung-Chu Lin he sequenial informaion model (SIM) (Copeland, 976; Jennings e al., 98) and he mixure of disribuion hypohesis (MDH) (Clark, 97; Epps and Epps, 976; Tauchen and Pis, 98; Harris, 986). The SIM implies a posiive correlaion beween volume and absolue price changes. As Harris (986) demonsraed, he MDH also suggess a posiive relaionship beween volume and price changes. In he subsequen lieraure, he V-R linkage has coninued o be debaed (e.g., Gallan e al., 99; Campbell e al., 99; Blume e al., 994; Wang, 994; Assogbavi e al., 995; Kocagil and Shachmurov, 998; Chordia and Swaminahan, ; Suominen, ; Acker and Ahanassakos, 5; Chuang e al., 9.) The sudies of he V-R relaionship have mosly examined he inra-marke associaions of differen reurn ypes wih rading volume, and have discovered ha a srong relaionship exiss beween volume and absolue or signed reurns in equiy markes bu ha no significan correlaion exiss beween volume and signed reurns (V-SR) in fuures markes. More specifically, mos of he empirical resuls for equiy markes have documened an asymmeric V-R relaionship. This, as argued by Karpoff (987), implies one of he following: a significan posiive V-SR correlaion or a significan posiive volume and non-negaive reurns (V-R + ) correlaion ogeher wih a significan negaive volume and negaive reurns (V-R - ) correlaion in which he magniudes of he wo correlaions are differen. Eiher of he wo above would consiue an asymmeric V-R relaionship. In general, in equiy markes, he V-R + correlaion is greaer han he V-R - correlaion (or he posiive V-SR correlaion), which means ha a significanly greaer volume will accrue from a price increase as compared o a price decrease. To explain his asymmeric relaionship, Jennings e al. (98) firs proposed he cosly shor-sale hypohesis, which aribues he asymmery o he higher ransacion coss associaed wih shor posiions as compared o long posiions. Tha is, o he exen he cosly shor-sale resricions (which are prevalen in mos markes) consrain he use of shor posiions, he volume associaed wih a price decrease may be smaller han ha associaed wih a price increase. Furher ess of he cosly shor-sale hypohesis have been conduced o examine if his heory also predics or explains he V-R relaionship in fuures markes. Since he coss associaed wih long and shor posiions are idenical in fuures markes, he cosly shor-sale hypohesis would predic a zero V-SR correlaion or a symmeric V-R relaionship in fuures markes. In fac, a series of empirical evidences regarding he V-R relaionship in various fuures markes did no indicae he exisence of an asymmeric effec (e.g., Karpoff, 988; McCarhy and Najand, 99; Kocagil and Schachmurove, 998); raher, hey suggesed ha a symmeric V-R relaionship should exis as prediced by he hypohesis. Puri and Philippaos (8), however, observed he iner-marke V-R relaionship and provided evidence agains cosly shor-sale hypohesis. They chose ineres rae and currency fuures raded on he London Inernaional Financial Fuures and Opions Exchange (LIFFE) as he subjec of heir sudy since neiher hese fuures nor heir underlying asses have shor-sale resricions ha would generae differen ransacion coss for long and shor posiions. Thus, if he cosly shor-sale hypohesis is rue, he volume and reurns for hese fuures and heir underlying asses should no exhibi an asymmeric relaionship. However, Puri and Philippaos (8) found a srong See Karpoff (987) for a survey up o 987. See Puri and Philippaos (8) for a concise summary of he lieraure.

3 Volume-Reurn Relaionship in ETF Markes: A Cosly Shor-Sale Hypohesis asymmeric V-R relaionship, saing ha he volume associaed wih negaive reurns was significanly larger han ha associaed wih non-negaive reurns. The cosly shor-sale hypohesis was, herefore, rejeced. Inspired by Puri and Philippaos (8), we make use of he curren saus ha he resricions on shor sales and he associaed coss for Taiwan ETFs and heir underlying markes are differen, puing he hypohesis o a es again. In Taiwan, ETFs have lower resricions on shor sales and lower associaed ransacion coss han heir underlying asses 4 ; exra rading in ETFs should occur when he marke is on a decline as raders will wish o avoid he addiional coss and resricions associaed wih he underlying marke. Under he cosly shor-sale hypohesis, we predic an asymmeric V-R relaionship for Taiwan ETFs, wih significanly larger volume associaed wih negaive reurns han wih non-negaive reurns. ETFs are known as one of he mos successful financial innovaions of he 99s; hey decrease selecion and allocaion effors, make i possible o diversify risk effecively, efficienly rack cerain indexes wihou incurring high ransacion coss, and are raded convenienly like socks on exchanges. Invesors can inves in index porfolios indirecly by holding beneficiary cerificaes or deposiary receips issued by ETFs; ETFs are raded on sock exchanges afer he issuance. The Taiwan Sock Exchange Corporaion (TWSE) launched is firs ETF, he Taiwan Top 5 Tracker Fund (Taiwan 5 ETF), on June,, and he second ETF, he Polaris Taiwan Mid-Cap Tracker Fund (Mid-Cap ETF), on Augus, 6. The wo ETFs wih relaively higher rading volume conain much more informaion and hence are used as he main samples of his sudy. The marke capializaion and he number of lisings ha Taiwan ETFs have achieved during he las eigh years, ogeher wih heir reduced resricions on shor sales and lower associaed coss, making hem an appropriae focus for he presen sudy. Anoher reason o consider Taiwan ETFs is ha he V-R relaionship has no been sudied in his conex. This sudy is disinc in four ways. Firs, whereas earlier papers mosly examined he inra-marke V-R relaionship, we observe he iner-marke V-R relaionship for he underlying and derivaive markes. Second, whereas previous papers primarily used reurns as he dependen variable in examining he V-R relaionship, we use ETF volume as he dependen variable o deermine is connecion o he lagged reurns of he underlying asses. Such arrangemen allows us o avoid disored resuls ha occur, especially a he exremis reurn quaniles due o he price limis in Taiwan s markes. 5 Third, whereas oher papers mosly used signed reurns direcly or divided reurns ino wo groups, negaive or non-negaive, o deermine he V-R relaionship, we follow he model seing of Puri and Philipaos (8) o disinguish beween non-negaive and negaive reurns. More specifically, Puri and Philipaos (8) inroduced a dummy o disinguish negaive reurns from non-negaive reurns and compared he slope coefficiens of hem o measure he asymmeric V-R relaionship. Finally, whereas earlier papers mosly examined he average V-R relaionship hrough linear regression (ordinary leas square, OLS, mehod), we analyze he V-R relaionship across quaniles 4 The rading ax while selling is.% for ETFs and.% for heir underlying asses. In addiion, ETFs are exemped from he ban on shor selling socks whose prices are below heir closing prices of he previous rading day (which requires ha shor sales ake place a no lower han he closing price for he previous rading day.) 5 Refer o Chuang and Kuan (5).

4 4 Jung-Chu Lin using quanile regression. The combinaion of he paricular model seing and he usage of quanile regression allow us o deermine no only how ETF volume is relaed o he upward or downward movemens of he underlying index (ha is, if exiss asymmeric relaionship), bu also how such connecions vary across various volume quaniles. Accordingly, his paper no only conribues o he undersanding of he cosly shor-sale hypohesis, bu also helps furher undersanding of he V-R relaionship in ETFs and he hybrid links beween he ETFs and heir underlying asses. The resuls indicae a srong and unique asymmeric V-R relaionship in ETFs, mosly consisen wih wha he cosly shor-sale hypohesis predics. The asymmery is sronger for Taiwan 5 ETF in he quaniles ha are higher han he median level and he exrema quaniles; similarly, i is also sronger for he Mid-Cap ETF in he exrema quaniles. The posiive, concave relaionship ha reflecs he effec of non-negaive index reurns on ETF volume is differen from he V-shaped V-R + relaionship ha exiss in he American and Briish equiy markes (Chuang e al., 9); and he effec of sensiiviy o negaive reurns on ETFs volume becomes more powerful a exrema quaniles, especially he s, 5 h, 5 h, 95 h and 99 h quaniles. Boh effecs hus joinly bring ou he unique asymmery in V-R relaionship for ETFs and heir underlying asses. We argue ha invesors regard ETFs as complemens when he spo (underlying) marke is on a rise bu regard hem as legiimae subsiues when he spo marke is on a decline; he hybrid of he wo effecs, he complemenary and subsiue effecs, leads o he formaion of he asymmery. The remainder of his paper will proceed as follows. Secion describes he deails of he model, including he quanile regression and he seing of he empirical model. Secion describes he daa source, he summary saisics, he empirical resuls and heir implicaions. Finally, he concluding secion summarizes he findings and analysis. Mehodology We employ quanile regression o observe he V-R relaionship across differen volume levels. In addiion, o disinguish beween negaive and non-negaive reurns and o make a direc comparison beween he slope coefficiens associaed wih negaive and non-negaive reurns, we use he model seing proposed by Puri and Philipaos (8). The empirical mehod and model specificaion are described as below.. Quanile Regression Koenker and Basse (978) and Koenker and Hallock () proposed he quanile regression model. Quanile regression generalizes he concep of an uncondiional quanile o a quanile ha is condiional on one or more covariaes. This mehod esimaes condiional quanile (percenile) funcions by minimizing he weighed absolue deviaions of he quanile regression model. Unlike classical OLS, quanile regression can be used no jus o esimae he average relaionship of variables, bu also o provide more complee informaion on he relaionship of variables regarding any poin in he disribuion of he dependen variable. Through employing quanile regression and regarding ETF volume as he dependen variable, we can obain a clearer V-R relaionship across he disribuion of he ETF rading volume. Quanile regression minimizes he weighed sum of he absolue residuals raher han he

5 Volume-Reurn Relaionship in ETF Markes: A Cosly Shor-Sale Hypohesis 5 sum of he squared residuals. T min k y bjx j, b j j Where k () j y is he dependen variable a observaion, j, x is he j h independen variable a observaion, bj are esimaes of he model s j h regression coefficiens, and T is he oal observaions. The weigh is described as q if he residual of he h observaion is posiive or as q if he residual of he h observaion is negaive or zero. The variable q is he quanile o be esimaed, and he value of q lies in beween and. For example, he median regression ( q =.5) uses symmeric weighs, and all oher quaniles regressions (e.g., q =.,., ) use asymmeric weighs. We employ boosrapping o esimae he sandard errors of he coefficien esimaes following Gould (99, 99). The boosrapping echnique is less sensiive o heeroskedasiciy (Rogers, 99).. Model Specificaions This paper invesigaes asymmeric V-R linkages in Taiwan s ETF marke under he cosly shor-sale hypohesis. As he prior secion has described, we uniquely use he ETF volume as he dependen variable o regress i agains he reurn of he underlying index. We also follow Puri and Philippaos (8) o disinguish beween non-negaive and negaive reurns and use quanile regression o examine he V-R relaionship across quaniles. By doing so, we no only idenify wheher here is any asymmeric effec of negaive and non-negaive reurns on volume bu also deermine he V-R correlaion across various levels of volume, and hus can compare hese findings o he condiional mean relaionship found in previous sudies. The V-R relaionship associaed wih period is expressed as 6 EV = + SR - + DUMMY -+ (DUMMY- SR - )+ ε () where EV denoes he volume variables for he ETFs, including he naural log of he rading share ( EVOL ), and he naural log of he rading value ( EVAL ) a period. This sudy defines he logarihmic reurn of he underlying index a period as SR (ln S ln S-), where S is he underlying index a period. DUMMY denoes he dummy variable, which equals uniy for negaive reurns for he - underlying index and zero for non-negaive reurns a period. ε is he error erm 6 We also regressed he ETF rading volume agains he conemporary underlying index reurns and agains he reurns wih wo-period lag for robus checks. However, he resuls are similar o hose presened in his paper.

6 6 Jung-Chu Lin a period. Therefore,,,, and are he esimaed parameers of he regression. This specificaion enables us o inspec he asymmeric relaionship beween ETF volume and lagged underlying index reurns of a differen direcion as measured by he slope coefficiens for he non-negaive, and ( + ) for he negaive reurns, respecively. If and are boh significan, he asymmeric V-R correlaion exiss, and he cosly shor-sale hypohesis is confirmed. Empirical Resuls and Analysis. Daa Descripion and Summary Saisics This paper uses daily daa o analyze he relaionship beween ETF volume and he underlying index reurns in Taiwan. Two ETFs, he Taiwan 5 ETF and he Mid-Cap ETF are examined; heir underlying indexes are he Taiwan 5 Index and he Taiwan Mid-Cap Index (Mid-Cap index), respecively. Again, hese wo ETFs feaure relaively higher rading volume and considerably more informaion are available abou hem; hese daa will reveal he characerisics of he V-R relaionships and illusrae more fundamenal linkages in he Taiwan ETF marke; hence hey are used as he main samples in his sudy. The Taiwan 5 ETF and Mid-Cap ETF were launched on June, and Augus, 6, respecively. Therefore, he sample daa for he Taiwan 5 ETF and is underlying index are from he period of June, hrough December,, which provides a oal of, observaions. Correspondingly, he sample daa for he Mid-Cap ETF and is underlying index are from he period of Augus, 6 o December,, which provides a oal of, observaions. All of he daily daa for he ETFs and he underlying indexes are aken from he Taiwan Economic Journal (TEJ) daabase. For he price series, daily reurns are defined as he logarihm difference in he prices on rading days and. Two ypes of rading volume are calculaed using he naural log of rading shares and rading value. The basic saisical characerisics of he Taiwan 5 ETF, Mid-Cap ETF, Taiwan 5 index, and Mid-Cap index reurn and rading volume series for he sample period are summarized in Table. The means for he Taiwan 5 ETF, Mid-Cap ETF, Taiwan 5 index, and Mid-Cap index reurns are.9.566,.9.8, , and , respecively. We observe ha he Taiwan 5 ETF and is underlying index have more similar means and lower sandard deviaions han he Mid-Cap ETF and is underlying index. These findings imply ha a closer relaionship exiss beween he Taiwan 5 ETF and is underlying index in erms of boh reurns and risks. The mean and maximum saisics for ETF rading volume and value show ha he Taiwan 5 ETF is raded consisenly more acively han he Mid-Cap ETF. Hence, we can infer ha he informaion ransmission efficiency is beer in he Taiwan 5 ETF marke han in Mid-Cap ETF marke because he volume and associaed prices can convey a lo of hings o he marke (Blume e al., 994). The descripive saisics in Table also indicae ha all reurn series are lef skewed and ha boh of he reurn series for he ETFs are lepokuric. The rading volume series of he underlying indexes are more lepokuric han hose of he ETFs. The JB normaliy ess

7 Volume-Reurn Relaionship in ETF Markes: A Cosly Shor-Sale Hypohesis 7 significanly rejec he hypohesis of normaliy for all he variables. Table shows he correlaions beween he variables. The findings indicae ha a negaive or approximaely zero correlaion exiss beween ETF volume and he underlying index reurns. This, in urn, implies ha some invesors, who originally raded in spo markes, ransfer heir invesmens o he ETF marke when he spo marke is on a decline. Finally, he graphs of he daily rading volume and reurns for he wo ETFs are illusraed in Figure. Table : Summary saisics Variables Mean Sd. Max. Min. Skewness Kurosis JB. Taiwan 5 ETF: Taiwan Top 5 Tracker Fund (June, o December, ) ER *** *** *** EVOL *** *** EVAL *** ***. Taiwan 5 Index: Taiwan 5 Index (June, o December, ) SR ***.559 *** *** SVOL ***.49 *** *** SVAL *** 6.48 ***. Mid-Cap ETF: Polaris Taiwan Mid-Cap Tracker Fund (Augus, 6 o December, ) ER ***.99 *** *** EVOL ***.8 *.877 *** EVAL *** *** 4. Mid-Cap Index: Taiwan Mid-Cap Index (Augus, 6 o December, ) SR ***.649 ***.765 *** SVOL ***.47 *** 5.8 *** SVAL ***.959 *** *** Noes:. *, ** and *** denoe significance a he %, 5% and % levels, respecively.. The Kurosis presens he coefficien of excess kurosis.. JB represens he saisics for he normal disribuion es developed by Jarque-Bera. 4. ER, EVOL,and EVAL are he reurns, he naural log of he rading share, and he naural log of he rading value for ETFs; SR, SVOL,and SVAL are he reurns, he naural log of he rading share, and he naural log of he rading value for he underlying index, respecively. 5. The unis for ER and SR are percenages; he unis for EVOL and SVOL are housands of shares; he unis for EVAL and SVAL are housands of dollars.

8 8 Jung-Chu Lin Taiwan 5 ETF & Taiwan 5 Index ER. Table : Correlaion analysis EVOL -.. ER EVOL EVAL SR SVOL SVAL EVAL SR SVOL SVAL Mid-Cap ETF & Mid-Cap Index ER. EVOL.57. ER EVOL EVAL SR SVOL SVAL EVAL SR SVOL SVAL Noes:. ER, EVOL,and EVAL are he reurns, he naural log of he rading share, and he naural log of he rading value for ETFs; SR, SVOL,and SVAL are he reurns, he naural log of he rading share, and he naural log of he rading value for he underlying index, respecively.. The unis for ER and SR are percenages; he unis for EVOL and SVOL are housands of shares; he unis for EVAL and SVAL are housands of dollars. Figure : Volume and reurns of he wo ETFs. Quanile Regression Analysis of he ETF V-R Correlaion Tables o 6 deail he coefficiens for he quanile regression models when he ETF volume variables are regressed agains he reurns for he underlying indexes. To deermine he V-R relaionship across quaniles, we esimae weny-one quanile regressions, including quaniles =.,.5,.,, and.99, using STATA sofware.

9 Volume-Reurn Relaionship in ETF Markes: A Cosly Shor-Sale Hypohesis 9 The sandard errors of he coefficien esimaes are simulaed using he boosrapping mehod wih replicaions. We also use OLS mehod o esimae he average coefficiens for V-R correlaion for comparison. Firs, Tables o 6 and Figures o 5 presen he slope coefficiens in general. is saisically significanly posiive for all quaniles excep he higher quaniles for he Mid-Cap ETF, indicaing ha a srong posiive relaionship exiss beween he ETF volume and he non-negaive underlying index reurns. However, such posiive relaionship weakens for boh ETFs as he quanile increases. Tha is he sensiiviy of ETF volume o he non-negaive index reurns decreases as he ETF rading volume increases. The posiive, concave syle ha displays he propery of he effec of non-negaive index reurns on ETFs volume is differen from he V-shaped V-R relaionship ha exiss in he American and Briish equiy markes (Chuang e al., 9). The OLS resuls for are all significanly posiive documening again he posiive relaionship beween he ETF volume and he non-negaive reurns. Nex, for he negaive index reurns for he Taiwan 5 ETF, he slope coefficien ) esimaes are negaive, and heir absolue values ( ) are usually larger ( han he slope coefficiens across almos all quaniles, indicaing ha an asymmeric effec exiss in he ETF V-R relaionship. Addiionally, he asymmeric V-R relaionship became sronger for he volume quaniles ha are above he median (quanile =.5) as indicaed by he saisically significan coefficien esimaes and. For he Mid-Cap ETF, he asymmeric effec also appears and is more obvious for he exrema (i.e., lower or higher) volume quaniles especially he higher quaniles. These oucomes can also be verified in Figures o 5 in which he asymmeric effecs are displayed by he shaded regions. Regarding he OLS resuls, all he are negaive and saisically significan while he slope coefficiens ( ) are all negaive indicaing he average negaive correlaions beween he ETF volume and non-negaive index reurns; Ye, he asymmeric effec measured by - is more significan for he Taiwan 5 ETF. The resuls of asymmeric V-R relaionship described above are consisen wih wha he cosly shor-sale hypohesis predics: an asymmeric V-R relaionship wih significanly larger volume associaed wih negaive reurns han wih non-negaive reurns, and hus lend suppor o he hypohesis for he Taiwan ETF marke. In paricular, we find ha he magniudes of he correlaions beween ETF volume and non-negaive index reurns aain heir highes level a he lower volume quaniles, and hen decrease wih he increase of he volume quanile. On he oher hand, we find ha he magniudes of he negaive correlaions beween ETF volume and negaive index reurns a he 5 h and 95 h quaniles for he Taiwan 5 ETF are much higher, as are he corresponding correlaions for he s (5 h for he Mid-Cap ETF s rading value) and 99 h quaniles for he Mid-Cap ETF, indicaing ha he correlaions beween ETF volume and he negaive reurns become sronger a he exrema quaniles. We inerpre hese oucomes by he argumen ha here are wo effecs, complemenary and subsiue effecs, for he ETFs o invesor. When he marke is on he rise, ETFs are complemens o invesors; when he marke is on a decline, on he conrary, ETFs are subsiues o invesors. The condiions ha he complemenary effec is sronger for he lower volume and hen decay wih he increase of he volume quanile, and ha he subsiue effec is

10 Jung-Chu Lin sronger for boh he lower and higher volume joinly consiue he resuls of he correlaions and he correspondingly asymmeric V-R relaionship described above. Based on he empirical resuls presened above, hree implicaions can be inferred. Firs, invesors in spo markes regard ETFs as complemens when he underlying index markes are on he rise, especially when he ETF volume is a a lower level; hus he slope coefficiens beween ETF volume and non-negaive reurns has is relaively higher value around he lower volume quaniles. Second, when he underlying index marke is on a decline, given he coss of shor-sales in he spo markes, spo invesors ransfer heir rades o similar ETF markes, especially when he ETF volume is a an exreme (higher or lower) level. ETFs are now regarded as subsiues for he underlying socks, and he cosly shor-sale hypohesis is hence confirmed. In summary, wo effecs, complemenary and subsiue effecs, influence he magniudes of he V-R correlaions and he correspondingly asymmeric V-R relaionship; ha is why we can observe ha he asymmeric V-R relaionship for he Taiwan 5 ETF became sronger for he volume quaniles ha are above he median, especially he higher quaniles, as did he corresponding relaionship for he Mid-Cap ETF for he exrema quaniles especially he higher quaniles. Third, he slope esimaes of he quanile regressions for he negaive index reurns are apparenly larger a he exrema quaniles. We ry o explain his phenomenon from wo kinds of siuaions. Firs, when he spo markes are on a decline and have lower rading volume, he complemenary effec for ETF invesors dominaes heir subsiue effec, and hus ETF invesors may reduce heir rades in he ETF markes while spo invesors sill urn heir shor selling o he ETF markes. Therefore, he volume of he ETF markes will increase a his ime poin jus due o he ransferred rades of spo invesors. Second, when he spo markes are on a decline and have higher rading volume, spo raders are no he only ones who may increase heir ETF rades; In addiion, ETFs invesors may also increase heir ETF rades if he subsiue effec for ETFs invesors dominaes he complemenary effec. Table : Esimaion resuls of quanile regression for he rading volume of Taiwan 5 ETF Dependen variable: EVOL Esimaed regression parameer Esimaed regression parameer Quanile Esimaes Quanile Esimaes *** (.48).78 *** (.97) (.46) ** (.65) *** (.9).9 *** (.87) * (.7) -.76 *** (.98).454 *** (.955).44 *** (.74) -.4 * (.9) *** (.74) *** (.69).5 *** (.79) -.57 (.97) -.6 *** (.756)

11 Volume-Reurn Relaionship in ETF Markes: A Cosly Shor-Sale Hypohesis *** (.575).76 *** (.455).9 -. (.867) -.7 *** (.69) *** (.5).74 *** (.96) (.759) *** (.46) 8.7 *** (.57).85 *** (.69) (.95) *** (.4) 8. *** (.777).86 *** (.68).75.8 (.5) *** (.44) *** (.74).965 *** (.47) (.49) -.66 *** (.68) *** (.75).759 *** (.78) (.9) *** (.7) *** (.67).7 *** (.8) (.845) -.64 *** (.4) 9.7 *** (.46).8 *** (.55) -.7 ** (.645) *** (.465) *** (.44).85 *** (.4) -.69 *** (.4) -.56 *** (.6) 9.87 *** (.47).56 *** (.76) -.9 ** (.5) -.56 *** (.4) 9.68 *** (.4).76 *** (.6) -.44 ** (.65) -.57 *** (.45) *** (.448).47 *** (.6) -.9 ** (.654) -.5 *** (.47) *** (.578).45 *** (.89) ** (.77) *** (.7) *** (.578).67 *** (.8) -.4 * (.858) *** (.8)

12 Jung-Chu Lin.45.5 Quanile *** (.667).669 *** (.79) (.84) *** (.4) *** (.64).58 *** (.9) OLS -.79 (.86) *** (.465) Esimaed asymmeric parameer *** (.487).566 *** (.9) -.5 ** (.659) *** (.7) 8.79 *** (.).66 *** (.) -.97 ** (.457) *** (.4) OLS Noes:. *, ** and *** denoe significance a he %, 5% and % levels, respecively.. The numbers in parenheses are he sandard errors, which are simulaed using he boosrap mehod wih replicaions.. The empirical models are expressed as follows: EV = + SR - + DUMMY -+ (DUMMY - SR - )+ ε where EV denoes he volume variables for he Taiwan ETFs, including he naural log of he rading share ( EVOL ) and he naural log of he rading value ( EVAL ) a period. SR represens he logarihmic reurns for he underlying index a period. DUMMY - denoes he dummy variable, which equals uniy for negaive reurns for he underlying index and zero for non-negaive reurns a period.

13 Volume-Reurn Relaionship in ETF Markes: A Cosly Shor-Sale Hypohesis Figure : Slope comparison and asymmeric V-R effecs for he rading volume of he Taiwan 5 ETF. The slope esimae for non-negaive reurns is, and ha for negaive reurns is. The asymmeric effec is measured by - and displayed by he shaded region. Table 4: Esimaion resuls of quanile regression for he rading value of Taiwan 5 ETF Dependen variable: EVAL Esimaed regression parameer Esimaed regression parameer Quanile Esimaes Quanile Esimaes *** (.).9 *** (.7) (.6) *** (.7).9 *** (.68).9 *** (.49) * (.97) *** (.679).65 *** (.667).998 *** (.44) (.86) *** (.68).866 *** (.55).85.6 *** (.9) 4.64 *** (.44).489 ** (.684) -.75 (.7) -.47 *** (.99).857 *** (.6).568 *** (.57) (.) *** (.675).676 *** (.46).78 *** (.) -.77 (.88) *** (.56).4968 *** (.5).8 *** (.84)

14 4 Jung-Chu Lin (.684) -.66 *** (.55).97 *** (.59).69 *** (.79) (.69) *** (.487).998 *** (.45).96 *** (.9).75.6 (.57) *** (.48).4 *** (.447).89 *** (.88) (.567) -.57 *** (.47).75 *** (.45).68 *** (.7) (.45) *** (.).54 *** (.57).479 *** (.8) ** (.65) -.56 *** (.4).669 *** (.).5 *** (.7) *** (.55) *** (.8).7459 *** (.98) OLS.6 *** (.57) -.4 * (.695) *** (.59).84 *** (.9).656 *** (.7) -.4 ** (.6) *** (.49).957 *** (.8).64 *** (.) -.58 *** (.46) *** (.6).85 *** (.89).86 *** (.8) -.9 *** (.4) *** (.75).65 *** (.69).4 *** (.7) *** (.54) -.57 *** (.88).99 *** (.84).5 *** (.94) *** (.45) -.54 *** (.88).85 *** (.8). *** (.6) -.76 ** (.7) *** (.97).675 *** (.7).79 *** (.4)

15 Volume-Reurn Relaionship in ETF Markes: A Cosly Shor-Sale Hypohesis 5 Quanile *** (.) -.54 *** (.74) Esimaed asymmeric parameer -.6 ** (.464) -.54 *** (.8) OLS Noes:. *, ** and *** denoe significance a he %, 5% and % levels, respecively.. The numbers in parenheses are he sandard errors, which are simulaed using he boosrap mehod wih replicaions.. The empirical models are expressed as follows: EV = + SR - + DUMMY -+ (DUMMY - SR - )+ ε where EV denoes he volume variables for he Taiwan ETFs, including he naural log of he rading share ( EVOL ) and he naural log of he rading value ( EVAL ) a period. SR represens he logarihmic reurns for he underlying index a period. denoes he dummy variable, which equals uniy for negaive reurns for he DUMMY - underlying index and zero for non-negaive reurns a period.

16 6 Jung-Chu Lin Figure : Slope comparison and asymmeric V-R effecs for he rading value of he Taiwan 5 ETF. The slope esimae for non-negaive reurns is, and ha for negaive reurns is. The asymmeric effec is measured by - and displayed by he shaded region. Table 5: Esimaion resuls of quanile regression for he rading volume of Mid-Cap ETF Dependen variable: EVOL Esimaed regression parameer Esimaed regression parameer Quanile Esimaes Quanile Esimaes *** (.).9 *** (.9) (.9) -.67 *** (.).9787 *** (.5).8 ** (.87) * (.66) *** (.9) 4.7 *** (.6).9 *** (.64).9 -. *** (.99) *** (.84) ***.85 (.79) *** (.9) -.6 (.59) -.7 (.874). * (.74) *** (.4) (.787) -.65 (.88). * (.778) 6.94 *** (.).8 (.595) -.88 (.479).8 (.68) 6.67 *** (.95)

17 Volume-Reurn Relaionship in ETF Markes: A Cosly Shor-Sale Hypohesis *** (.557) -.65 (.8) *** (.779) 4.56 *** (.654). *** (.47) * (.87) *** (.68) *** (.858).7 *** (.5).75.8 * (.96) *** (.64) 4.85 *** (.575).45 *** (.49) (.868) *** (.65) *** (.5).6 *** (.94) (.78) *** (.8) *** (.67).44 *** (.).6 -. (.65) -.44 *** (.5) 5.6 *** (.49).5 ** (.99) (.68) -.47 *** (.5) 5.77 *** OLS (.556).455 (.575) -.98 (.8) -.5 (.56) 6.7 *** (.875).5 * (.665) (.67) *** (.666) *** (.768).5 ** (.44) -.54 (.85) -.8 *** (.5) 5.88 *** (.54).6 *** (.94) -.97 (.) -. *** (.47) *** (.8).474 *** (.7) -. (.76) -.86 *** (.4) 5.5 *** (.58).89 *** (.6) -.5 (.) -.99 *** (.4) *** (.468). *** (.) (.89) -.84 ** (.7) *** (.5)

18 8 Jung-Chu Lin Quanile.6 *** (.5) -.74 (.846) -.95 *** (.8) Esimaed asymmeric parameer.568 *** (.5) -.6 (.785) *** (.455) OLS Noes:. *, ** and *** denoe significance a he %, 5% and % levels, respecively.. The numbers in parenheses are he sandard errors, which are simulaed using he boosrap mehod wih replicaions.. The empirical models are expressed as follows: EV = + SR - + DUMMY -+ (DUMMY - SR - )+ ε where EV denoes he volume variables for he Taiwan ETFs, including he naural log of he rading share ( EVOL ) and he naural log of he rading value ( EVAL ) a period. SR represens he logarihmic reurns for he underlying index a period. denoes he dummy variable, which equals uniy for negaive reurns for he DUMMY - underlying index and zero for non-negaive reurns a period.

19 Volume-Reurn Relaionship in ETF Markes: A Cosly Shor-Sale Hypohesis 9 Figure 4: Slope comparison and asymmeric V-R effecs for he rading volume of he Mid-Cap ETF. The slope esimae for non-negaive reurns is, and ha for negaive reurns is. The asymmeric effec is measured by - and displayed by he shaded region. Table 6: Esimaion resuls of quanile regression for he rading value of Mid-Cap ETF Dependen variable: EVAL Esimaed regression parameer Esimaed regression parameer Quanile Esimaes Quanile Esimaes *** (.455).65 *** (.69) (.86) -.48 *** (.755) 7. *** (.9).87 *** (.76) (.) -.5 *** (.584) *** (.447).665 *** (.484) *** (.7) -.88 *** (.) ***.85 (.67).87 *** (.87) -.47 (.86) -.8 (.7).4 *** (.6).65 *** (.8) -. (.8) -.69 * (.6).9 (.87).474 *** (.78) -.8 (.67).77 (.65).75 (.76).47 *** (.645)

20 Jung-Chu Lin ** (.) -.7 (.4) -.7 *** (.6) *** (.485).86 *** (.79) ** (.75) -.47 *** (.486) 8.88 *** (.6).58 *** (.) (.989) -.4 *** (.5) 8.8 *** (.794).49 *** (.96) (.4) -.7 *** (.558) 8.57 *** (.5).459 *** (.75) (.5) -.4 *** (.8) *** (.5).5 *** (.8).6 -. (.844) *** (.) *** (.54).45 ** (.97) (.76) -.74 *** (.) *** OLS (.57) -.59 (.46) -.47 (.55).7 (.5) *** (.9).574 (.6) (.9) * (.85) *** (.6).847 ** (.9) -.74 (.79) -. *** (.6) 9.88 *** (.96).6 *** (.67) -.5 (.85) *** (.48) *** (.68). *** (.46) -.45 (.85) -.54 *** (.56) 8.94 *** (.54).47 *** (.96) -.8 (.787) -.54 *** (.47) 8.88 *** (.86).4 *** (.55) -.64 (.749) *** (.78) *** (.55)

21 Volume-Reurn Relaionship in ETF Markes: A Cosly Shor-Sale Hypohesis Quanile.497 *** (.7) (.9) -.75 *** (.6) Esimaed asymmeric parameer. *** (.66) -.45 (.85) -.5 *** (.47) OLS Noes:. *, ** and *** denoe significance a he %, 5% and % levels, respecively.. The numbers in parenheses are he sandard errors, which are simulaed using he boosrap mehod wih replicaions.. The empirical models are expressed as follows: EV = + SR - + DUMMY -+ (DUMMY - SR - )+ ε where EV denoes he volume variables for he Taiwan ETFs, including he naural log of he rading share ( EVOL ) and he naural log of he rading value ( EVAL ) a period. SR represens he logarihmic reurns for he underlying index a period. denoes he dummy variable, which equals uniy for negaive reurns for he DUMMY - underlying index and zero for non-negaive reurns a period.

22 Jung-Chu Lin Figure 5: Slope comparison and asymmeric V-R effecs for he rading value of he Mid-Cap ETF. The slope esimae for non-negaive reurns is, and ha for negaive reurns is. The asymmeric effec is measured by - and displayed by he shaded region. 4 Concluding Remarks This paper examines he V-R relaionship beween Taiwan ETFs and heir underlying asses o re-es he cosly shor-sale hypohesis in his new conex. In addiion o he correlaion measuremens for V-R asymmery, an addiional measure of asymmery is employed in which he slope coefficiens associaed wih negaive and non-negaive reurns are compared. Furhermore, o observe he V-R relaionship across various volume levels, he quanile regression mehod is applied. The empirical resuls yield several essenial findings. Firs, he srong, posiive, bu concave relaionship beween ETF volume and he non-negaive underlying index reurns demonsraes ha spo invesors may regard ETFs as complemens when heir underlying index markes are on a rise and especially when he ETF volume is a a lower level; he weakening of he posiive relaionship ha occurs as he volume quanile increases demonsraes he decay of he complemenary effec for spo invesors. Second, he srong, negaive relaionship beween ETF volume and negaive underlying index reurns indicaes ha because of he high shor-sale coss in spo markes, spo invesors may regard ETFs as subsiues and ransfer heir rades o he ETF markes when he underlying index marke is on he decline (and especially when he ETF volume is a an exrema level.) Third, a direc comparison of he slope coefficiens associaed wih negaive and non-negaive reurns reveals ha hey are significanly differen. The slope coefficiens associaed wih negaive reurns exceeds ha associaed wih non-negaive reurns especially for he Taiwan 5 ETF a he quaniles ha are higher han he median level and for he Mid-Cap ETF a he exrema quaniles. Thus, he ETFs are found o exhibi an asymmeric V-R relaionship, and he cosly shor-sale hypohesis is confirmed. Moreover, since he negaive correlaions beween ETF volume and negaive index reurns for boh ETFs a he exrema quaniles increase sharply, we ry o include he complemenary and subsiue effecs for ETF invesors, combined wih he subsiue effec of spo raders, o explain his phenomenon.

23 Volume-Reurn Relaionship in ETF Markes: A Cosly Shor-Sale Hypohesis ACKNOWLEDGEMENTS: The auhor acknowledges he financial suppor from Naional Science Council of Republic of China (Gran No: NSC -4-H-47-8-) and he assisance provided by he research assisans. References [] T.E. Copeland, A Model of Asse Trading under he Assumpion of Sequenial Informaion Arrival, Journal of Finance,, (976), [] R.H. Jennings, L.T. Sarks and J.C. Fellingham, An Equilibrium Model of Asse Trading wih Sequenial Informaion Arrival, Journal of Finance, 6, (98), 4-6. [] P.K. Clark, A Subordinaed Sochasic Process Model wih Finie Variance for Speculaive Prices, Economerica, 4, (97), [4] T.W. Epps and M.L. Epps, The Sochasic Dependence of Securiy Price Change and Transacion Volume: Implicaions for he Mixure-of-Disribuions Hypohesis, Economerica, 44, (976), 5 -. [5] G.E. Tauchen and M. Pis, The Price Variabiliy-Volume Relaionship on Speculaive Marke, Economerica, 5, (98), [6] L. Harris, A Transacion Daa Sudy of Weekly and Inraday Paerns in Sock Reurns, Journal of Financial Economics, 6, (986), [7] A.R. Gallan, P.E. Rossi and G. Tauchen, Sock Prices and Volume, Review of Financial Sudies, 5, (99), [8] J.Y. Campbell, S.J. Grossman and J. Wang, Trading Volume and Serial-Correlaion in Sock Reurns, Quarerly Journal of Economics, 55, (99), [9] L. Blume, D. Easley and M. O Hara, Marke Saisics and Technical Analysis: The Role of Volume, Journal of Finance, 49, (994), 5-8. [] J. Wang, A Model of Compeiive Sock Trading Volume, Journal of Poliical Economy,, (994), [] T. Assogbavi, N. Khoury and P. Yourougou, Shor Ineres and he Asymmery of he Price-Volume Relaionship in he Canadian Sock Marke, Journal of Banking and Finance, 9, (995), [] A.E. Kocagil and Y. Shachmurove, Reurn-Volume Dynamics in Fuures Markes, Journal of Fuures Markes, 8, (998), [] T. Chordia and B. Swaminahan, Trading Volume and Cross-Auocorrelaions in Sock Reurns, Journal of Finance, 55, (), [4] M. Suominen, Trading Volume and Informaion Revelaion in Sock Markes, Journal of Financial and Quaniaive Analysis, 6, (), [5] L.F. Acker and G. Ahanassakos, The Relaionship beween Shor Ineres and Sock Reurns in he Canadian Marke, Journal of Banking and Finance, 9, (5), [6] C.C. Chuang, C.M. Kuan and H.Y. Lin, Causaliy in Quaniles and Dynamic Sock Reurn-Volume Relaions, Journal of Banking and Finance,, (9), 5-6. [7] J.M. Karpoff, The Relaion beween Price Changes and Trading Volume: a Survey, Journal of Financial and Quaniaive Analysis,, (987), 9-6. [8] J.M. Karpoff, Cosly Shor Sales and he Correlaion of Reurn wih Volume. Journal of Financial Research,, (988), 7-88.

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