On he Relaionship beween Time-Varying Price dynamics of he Underlying Socks: Deregulaion Effec on he Issuance of Third-Pary Pu Warran Yi-Chen Wang * Deparmen of Financial Operaions, Naional Kaohsiung Firs Universiy of Science and Technology Yuan-Hung Hsuku Deparmen of Financial Operaions, Naional Kaohsiung Firs Universiy of Science and Technology Shih-Kuo Yeh Deparmen of Finance, Naional Chung Hsing Universiy ABSTRACT Due o regulaion consrains, hird-pary pu warran in Taiwan was launched a he day afer six year of hird-pary call warran s issuance. We presen a model which exends Engle s (2002) DCC-GARCH approach o sudy he impac of he deregulaion on Taiwan s hird-pary pu warrans lising pracice in order o realize he ime-varying price dynamics of he underlying socks. Our empirical resuls show ha even hough hird-pary pu warran launched six year afer he lising day of hird-pary call warran, he inroducory of hird-pary pu warrans ighen he ime-varying inerdependences beween price dynamics of underlying socks. The growh rae of rading volume responses more posiively o sock reurn afer he day of pu warran issuance, moreover, sock reurn responses sharply o he expeced change of implied volailiy. The resuled closely responses from one price dynamic o anoher provide a higher explanaory power in engaging profiable porfolios. JEL classificaion: G12, G14, G18 Keywords: Third-pary pu warran, mulivariae DCC-GARCH model, Time-varying condiional correlaions * Corresponding auhor: Yi-Chen Wang, 2, Juoyue Rd., Nanz Disric, Kaohsiung 811, Taiwan, R.O.C. Tel: 886-7-6011000~3115; Fax: 886-7-6011039; E-mail: yjwang@ccms.nkfus.edu.w.
I. INTRODUCTION The underlying asses on a newly opening marke may behave differenly from ohers, since hedgers, arbirager and speculaors may ener ino he marke in an incomplee marke. The bidding process of informed rading releases useful informaion for uninformed raders. Realizing he informaion release from he price dynamics 1 of he underlying asses on a newly opened marke may enhance he poenial profiabiliy of noise rading from rading cash markes. In mos counries, opening a warran marke will provide invesor an opporuniy o choose beween call and pu, which means, warran marke for boh call and pu are launched in he same ime. In Taiwan, due o regulaory consrain 2, hird-pary pu warran was launched six years lags afer hird-pary call warran s launching. This special launching pracice induced us o ask ha wheher he marke behaviors wih call and pu warran launched a he same ime is differen from he marke behaviors ha provide only call warran bu no he pu warran in heir launching. The lagged pu warran lising on Taiwan offers a unique opporuniy o realize he price dynamics of he underlying sock under he special srucure on derivaive s inroducion. Due o he deregulaion by Taiwan s auhoriies in 2003, our sudy mainly focus on he inerrelaionship beween price dynamics of he underlying socks, and address he issue ha wheher we observe a sronger/weaker correlaion beween price dynamics 1 Price dynamics is defined as he sock reurn, he growh rae of rading volume and he expeced change of implied volailiy of he underlying socks. 2 Taiwan s auhoriies agree ha Securiies Houses was allowed o issue hird-pary warrans in 1997, wih a resricion ha securiies houses need o consruc he cash posiion agains he issuance of warran. In 1997, securiies houses are resriced from shor-selling he underlying socks for any reason, herefore, he shor-selling resricion prevens securiies houses from consrucing a shor posiion as a hedge porfolio agains heir own pu warran issuance. In 2003, he auhoriies deregulaed he shor-selling consrains on securiies houses, auhoriies agree ha securiies houses may shor-sell underlying socks for hedging purposes only, bu hey can only borrow he underlying socks from small shareholders. The Securiies Borrowing and Lending (SBL) cener opened in June 2003, allows securiies houses o borrow said underlying socks from small shareholders. Third-pary pu warrans were officially inroduced o Taiwan s marke in July 2003. 2
afer he inroducion of hird-pary pu warran. We consruc a simulaneous model, i exends Engle s (2002) dynamic GARCH model, o provide a mulivariae framework in order o describe he ime-varying condiional correlaions beween price dynamics and pu warran issuing effec boh on rivariae and bivariae basis. The empirical resuls sugges ha: he ime-varying condiional correlaion beween sock reurn and he expeced change of implied volailiy is significanly negaive (consisen wih French, Schwer, and Sambaugh (1987), Campbell and Henschel (1992), ec.). However, he condiional correlaions beween growh rae of rading volume and he expeced change of volailiy is significanly negaive afer he issuance of hird-pary pu warrans, he resul is consisen wih Alkeback and Hagelin (1998). Moreover, las period s random shock on correlaions beween he growh rae of rading volume and he expeced change of volailiy is significan posiive for all samples. On he oher hand, we find no conclusive relaionship beween he growh rae of rading volume and sock reurn. Regarding hird-pary pu warran lising effec, our resul shows ha price dynamic response sharper o ohers afer ha lising day of hird-pary pu warran. Time-varying pair-wise correlaion beween price dynamics shif closely oward +1 and -1 3 by he inroducion of pu warrans; he relaionship among sock reurn, growh rae of rading volume and he expeced change of implied volailiy is more relaed. By knowing he hree highly closed relaionships beween price dynamics, los of invesors expec o realize an upward or downward rend on warranable socks 4 afer he issuance dae of warran. When los of invesors expec an increase in price on 3 If he correlaion among sock price, rading volume, and implied volailiy is negaive for he before-pu-warran period, hen he coefficien is more negaive o one on he afer-pu-warran period. If he correlaion among sock price, rading volume, and implied volailiy is posiive for he before-pu-warran period, hen he coefficien is more posiive o one for he afer-pu-warran period 4 The warranable sock is defined as he underlying sock of a single-name warran. 3
warranable socks on he lising dae of warran, longing he underlying socks on he day before warran lising by invesors may generae posiive profis. Therefore, he igher ineracions wihin a securiy s price dynamics increase he probabiliy of engaging in a profiable rading sraegy since hey induce he explanaory power of he price dynamics. The remainder of his sudy is organized wih he nex wo secions describing he empirical mehodology and sampling daa used in his sudy. The secion following ha presens he empirical findings of he DCC-GARCH model and our sudy ends wih concluding remarks. II. METHODOLOGY DCC-GARCH Model We firs presens Engle s (2002) mulivariae dynamic condiional correlaion GARCH (DCC-GARCH) model, which esimaes condiional correlaion coefficiens simulaneously wih he condiional variance-covariance marix. By allowing condiional correlaions o vary over ime, his specificaion is viewed as a generalizaion of he Consan Condiional Correlaion model (CCC model, Bollerslev (1990)). To illusrae he dynamic condiional correlaion model for our purposes, le be a 3 1 vecor conaining he reurn, volume, and implied volailiy series in a condiional mean equaion as: x μ + ε =, where ε Ω ~ N( 0, Η ) 1, (1) x where μ = E [ x Ω 1] is he condiional expecaion of given he pas informaion Ω 1, and ε is a vecor of errors in he auoregression AR(1). Term ε is assumed o be condiional mulivariae normally disribued, wih means of zero and x 4
variance-covariance marix { h }. Η Under he assumpion ha he reurn, volume, and implied volailiy series x are deermined by he informaion se available a ime -1, he model may be esimaed using maximum likelihood mehods, subjec o he requiremen ha he condiional covariance marix, Η, be posiive definie for all values of ε in he sample. We also assume ha condiional mean μ i, has he following formaion as: μ 1 = Φ + Φ x, i, 0 1 i, i. (2) Here, Φ 1 measures he auoregression effec in daa series. In he radiional mulivariae GARCH framework, he condiional variance-covariance marix can be wrien as: Η = G R G where G = diag{ }, (3) h i where h i is he esimaed condiional variance from he individual sandard univariae GARCH(1,1) models in he following manner: h i ω i. (4) 2 = i + α iε i, 1 + β ihi, 1 We see now ha R is he ime-varying condiional correlaion coefficien marix. According o he specificaion in equaion (4), he variance of price dynamics is modeled as a funcion of he consan, he square of he lag own residuals 2 ε i, 1, and is previous period s condiional variance h i, 1. Afer he above basic consrucion, he dynamic correlaion coefficien marix of he DCC model can be denoed furher as: R 1 [ ( )] 1 diag Q 2 Q [ diag ( Q )] 2 = ( ) Q = q, 5
[ diag( Q )] = diag 1 1 1 1 2 q 11,, q 22,, q 33,. (5) In order o sandardize he residual error erm, Engle ses z 1 = G ε, where G is a 3 3 diagonal marix of condiional sandard deviaions. Term z is he sandardized residuals vecor wih mean zero and variance one. Engle also suggess esimaing he following ime-varying correlaion process as: q, ρ, =, qii, q jj, where q, = ρ + a = ( z z ρ ) + b( q ρ ) i, 1 j, 1, 1 ( 1 a b ) ρ + a zi, 1z j, 1 + b q, 1 (6) The ime-varying correlaion coefficiens in he DCC-GARCH model can be divided ino wo pars. The firs par indicaed on he righ-hand side of equaion (6), ρ, represens he uncondiional correlaion coefficien. The second par indicaed on he righ-hand side of equaion (6), a zi, 1z j, 1 + b q, 1, shows he condiional ime-varying covariance. Comparing he radiional GARCH (1,1) model in equaion (4) wih he DCC-GARCH model in equaion (6), we can show ha he DCC-GARCH model sandardizes he residual error erm ino a sandard normal disribuion, and he consan erm in he DCC-GARCH model represens he uncondiional dynamic correlaion beween error erms, oher han Bollerslev (1990) s CCC consan correlaion seing. The DCC-GARCH model conribues o he parameers esimaion process in wo pars. The firs is ha he condiional correlaion defined in he DCC-GARCH can be 6
modeled individually as a univariae GARCH process. The second par is ha he uncondiional expecaions ρ of he residual errors can be esimaed separaely by hisorical daa. Exend DCC-GARCH Model GARCH models are well acceped in relaed fields, because hey capure many sylized facs such as volailiy clusering and hick-ailed reurns. However, since he condiional variance is a funcion of he magniudes of he las period s error erms, i involves he esimaion of a se of parameers. Those parameers are assumed o be consan over he sample period. In his sense, a flexible esimaion srucure on he condiional volailiy and correlaion is incorporaed ino models in order o capure he change in price dynamics afer he issuance of hird-pary warrans. Our sampling period sars from he hird-pary call warran s lising day, and ends on he hird-pary pu warran s closing day. In order o capure he pu warran issuing effec, we use a dummy variable ( I ) in equaion (7) o represen he periods for he afer-call-before-pu warran issuance and afer-pu warran issuance. Afer adding he pu warran issuing effec ino he DCC-GARCH model, he esimaed condiional variance h i from GARCH(1,1) is rewrien as: h i = ω + α ε η i. (7) i i 2 i, 1 + βihi, 1 + ii * * Term represens he pu warran s issue day, and denoes a dummy variable of I * pu issuing effec. Term is equal o 1 if, which represens he rading I * * period s afer-pu warran issuance, and is equal o zero if, which I * * represens he rading period s afer-call-before-pu warran issuance. 7
We use he same conceps o inroduce a pu warran issuing effec ino he condiional correlaion as well as he condiional variance process. Therefore, we also specify he following ime-varying correlaion wih he process of he pu warran issuing effecs as: q, ρ, =, qii, q jj, where q ( + δ I )[ ρ + a ( z z ρ ) + b( q ρ )], = * i, 1 j, 1, 1 1. (8) Term * represens he pu warrans availabiliy day, and indicaor I denoes a dummy variable indicaing he pu warran s issuing day. The coefficien δ is used o capure he changing propery on condiional covariance and condiional correlaion. If he marke s compleeness can be improved by he inroducion of hird-pary pu warrans, hen he inerdependencies beween rading volume, sock price, and volailiy will be more relaed. We hen expec o observe a igher inerrelaionship beween hose price dynamics. Therefore, he coefficien δ is expeced o be posiive if hird-pary pu warrans are inroduced o he marke. III. DATA Sampling Crierions In order o realize he lagged hird-pary pu warran lising effec only, we exclude he hird-pary call warran lising effec. Hence, he sampling period is focused on he afer-call-before-pu warran and afer-pu warran periods. Since we are concerning abou he warran lising effec on firs issuance, our ineres focus on he hird-pary pu warran which issued in 2003. As of Ocober 2005, here were a oal of 74 issues of pu 8
warrans lised from 2003 o 2005. The numbers of pu warran issuances in Taiwan were 42, 8, and 24 for he years 2003, 2004, and 2005, respecively. Almos 60% (42 of 74) of pu warrans were inroduced in year 2003. If warranable socks are no coninuous being he underlying asse of he hird-pary warran, he daa propery could be disored by collecing disconinuous daa ogeher, herefore, we omi he issues where warranable sock is no coninuous being he underlying of he warran. Take Taiwan Semiconducor Corporaion (TSMC) issue as an example, as of Ocober 2005, here were a oal of four hird-pary pu warrans issued on TSMC. The hird issue sared on 14 January 2004 and ended on 9 July 2004, bu he fourh issue did no sar unil 8 July 2005. This means ha TSMC sock canno be hough of as a warranable sock from 9 July 2004 o 8 July 2005. In order o sudy he lising effec on hird-pary pu warran, daa series of he TSMC issue omi he rading days beween 9 July 2004 and 8 July 2005, and rea he observaions on 9 July 2004 and 8 July 2005 as a coninuous ime series. The exclusion of rading days before and afer pu warran issuance ha are far from approximaely equivalen is represened as he hird sampling sandard. Trading days for he before-pu warrans period are calculaed from he firs issuance dae of he call warran on he underlying sock o he firs issuance dae of he pu warran. I is imporan o noe ha rading days before call warran lising are excluded from he daa. This is done o eliminae he effecs of inroducing call warrans. Take CMC Magneics Corporaion issue as an example, he rading daes before-pu and afer-pu warran issuance are 1381 and 281, respecively. The number of rading days before-pu warran is much larger han he afer-pu warran period, he impac on days before-pu warran issuance may dominae he impac on days afer-pu warran issuance in DCC-GARCH 9
models, hus, his kind of underlying sock is omied. For ime series sudies, he larger he daase is, he more accurae he GARCH esimaor is. In order o generae reliable empirical resuls, he pu issues whose mauriy is less han six monhs are no included in he sample. Our sudy uses daily sock reurns, growh rae of rading volumes, and expeced change of implied volailiy o invesigae he issuing effec of pu warrans. Daa are gahered from he Taiwan Economic Journal (TEJ). Daa series for China Seel Corporaion (CSC hereafer) is from 8/19/2002 o 6/17/2004, which represens 450 daa poins; for Acer Inc. (Acer hereafer) he daa is colleced from 9/5/2002 o 6/1/2004, represens 423 daa poins; for SYNNEX Corporaion (SYNNEX hereafer) he sampling daa is gahered from 12/11/2002 o 8/18/2004 represens 420 daa poins; as for Hon Hai Precision Indusry Company Ld. (Hon-Hai hereafer), daa is range from 11/14/2002 o 7/22/2004 represens 416 daa poins. The relaive change of all daa series are analyze in his sudy. We analysis he relaive change o sock price, relaive change o rading volume, and relaive change o implied volailiy, in sead of sock price, rading volume, and implied volailiy iself. Table 1 shows ha eigh pu warrans are seleced. These represen four underlying socks wih pu issues ha saisfy our selecion crieria. I is shown ha here is more han one hird-pary pu warran ousanding a he same rading day on he warranable sock. As we can see from Table 1, he pu warran issues around he sampling period for CSC, Acer, SYNNEX, and Hon-Hai are 4, 2, 1, and 1, respecively. In one rading day, here may be several warrans ousanding on he marke, bu since we need one daapoin for one rading day. If here are four pu issues ousanding on he same day, hen he implied volailiy of each pu warran is differen in size owing o heir rading 10
frequency. To avoid he liquidiy risk implici in he warran marke, we choose he sampling daa wih he larges rading volume on ha sampling day. The choice of he mos liquid pu avoids he liquidiy risk implici in warran reurn and volailiy. Therefore, he implici volailiy from he mos liquid pu warran is seleced according o he liquidiy concern. <INSERT TABLE 1 ABOUT HERE> IV. EMPIRICAL FINDINGS Table 2 summarizes he reurn, growh rae of rading volume, and expeced change of implied volailiy saisics for he underlying socks of hird-pary pu warrans. The Ljung-Box Q saisics is implemened in order o es he heeroskedasic propery which underlies he GARCH family. As repored in Table 2, he heeroskedasic phenomenon appears in all sampling socks and jusifies he implemenaion of GARCH model o Taiwan s sock marke. <INSERT TABLE 2 ABOUT HERE> We also implemen Jarque-Bera es for he normaliy in he sampling socks, as shown in Table 2, he Jarque-Bera coefficiens are significan a he 1% level, which indicaes ha he sock reurn, growh rae of rading volume, and he expeced change of implied volailiy series are generally no normally disribued. Since ARCH residuals are observed in all ime series, an AR(1) framework is implemened o capure he auocorrelaion effec in he mean equaion. The coefficien Φ 1 in Table 3 reveals he 11
auoregressive effec in mean equaion parameers for price dynamics. The growh rae of rading volume reveals a negaive auocorrelaion effec, while he expeced change of implied volailiy shows a posiive auocorrelaion effec. Afer considering he auocorrelaion effec wih our empirical framework, he Ljung-Box Q saisics (Q 2 (8) and Q 2 (24)) in Table 3 are no longer significan a he 5% level for all series suggesing ha ARCH residuals are eliminaed by considering he AR(1) process. <INSERT TABLE 3 ABOUT HERE> The coefficien Φ 0 in Table 3 reveals he long-erm mean of price dynamics. The long-erm mean of he growh rae of rading volume is significanly posiive a he 1% level for all sampling socks. In addiion, he long-erm mean of he expeced change of implied volailiy is significanly posiive for CSC, Acer, and SYNNEX, and is significanly negaive for Hon-Hai. By incorporaing non-normaliy properies ino ime series daa, we adop he mulivariae GARCH model o invesigae he changes in ime-varying condiional volailiy in he even of pu warran issuance. Bivariae Time-Varying Condiional Correlaions The corresponding inerrelaionship beween price dynamics is invesigaed by he bivariae GARCH framework, his framework is conduced o see wheher corresponding correlaions beween sock reurn, growh rae of rading volume, and he expeced change of implied volailiy are significanly increased afer pu warran issuance. When we observed igher correlaions beween price dynamics, he formaion of a profiable rading sraegy regarding a pu warran issuance even can be 12
realized. We firsly provide he inerdependences beween price dynamics, as we can see, sock reurn is significanly posiively correlaed wih he growh rae of rading volume for SYNNEX and Hon-Hai a he 1% level. In conras, sock reurn is significanly negaive wih regard o he growh rae of rading volume for CSC and Acer a he 1% level. Therefore, our empirical resuls sugges no conclusive findings on he relaionship beween sock reurn and he growh rae of rading volume. <INSERT TABLE 4 ABOUT HERE> The coefficien b in Table 4 shows he persisence beween price dynamics of underlying socks. The persisence beween sock reurn and he expeced change of implied volailiy, and beween he growh rae of rading volume and he expeced change of implied volailiy are significanly, negaively relaed wih each oher for all sampling socks a he 1% level, our resul is consisen wih French, Schwer, and Sambaugh (1987), Campbell and Hensschel (1992), and Alkeback and Hagelin (1998). Moreover, he correlaion effec of las period s random shock is measured by he coefficien a in Equaion (6), i shows ha he condiion correlaion beween growh rae of rading volume and he expeced change of implied volailiy is significanly, posiively affeced by las period s random shock a he 1% level, which is consisen wih Karpoff (1987) and Schwer (1989) s sudy. Pu Warran Lising Effec on Bivariae Correlaion Coefficien δ in Table 4 indicaes he pu warran lising effec. Significanly posiive 13
δ coefficien means he price dynamics become more relaed o each oher afer he issuance of pu warran. In able 4, he δ coefficiens in he ineracions beween price dynamics are significanly posiive for all socks. We conclude ha price dynamics of he underlying socks are ighly correlaed o each oher afer he pu warran issuing day. Since he inerdependence beween price dynamics are sharply relaed, he explanaory power of price dynamics o each oher increases afer he issuance of pu warran. Time Paerns of Bivariae Condiional Correlaions Figure 1, 2 and 3 ploed he ime-varying relaionship beween price dynamics. Figure 1 shows he ime-varying relaionship beween sock reurn and growh rae of rading volume. The ime-varying correlaion coefficiens beween sock reurn and growh rae of rading volume are more volaile and more posiively correlaed o each oher afer he pu lising day for all sampling socks. Alhough he dynamic correlaions beween sock reurn and he growh rae of rading volume for Acer are significanly higher for he pos-warran period, one observes ha he correlaion coefficiens significanly increased, hough slighly in size, and lagged in ime. <INSERT FIGURE 1 ABOUT HERE> Panel A in Figure 2 describes he dynamic correlaion coefficiens beween sock reurn and he expeced change of volailiy for CSC, he correlaion coefficiens are more volaile righ afer he issuing dae of a pu warran. Panels C and D in Figure 2 indicae he dynamic correlaions for Hon-Hai and SYNNEX, respecively. From Panel 14
C, he correlaion coefficiens for Hon-Hai are volaile and shif o show a more negaive correlaion afer he pu warran was issued. Panel D shows ha he dynamic correlaions for SYNNEX move oward o -1 righ afer he pu warran was issued. As described in Panel B, he ime-varying correlaion coefficiens ploed for Acer canno be disinguished very well afer he issuance of a pu warran for he same reason ha he δ coefficien for Acer shown in Table 4 is only 0.924. <INSERT FIGURE 2 ABOUT HERE> We nex discuss he ime-varying condiional correlaion coefficien beween growh rae of rading volume and he expeced change of implied volailiy. Panel A in Figure 3 indicaes ha he dynamic correlaions beween growh rae of rading volume and he expeced change of implied volailiy are dramaically volaile for CSC afer he day of pu issue. Moreover, he correlaion coefficiens for Hon-Hai and SYNNEX as in Panel C and Panel D become more volaile afer pu issuance. We also observe he lagged volaile effec on he ime-varying relaionship beween growh rae of rading volume and he expeced change of implied volailiy for Acer. <INSERT FIGURE 3 ABOUT HERE> As we can see from Figure 1 o 3, he ime-varying correlaion coefficiens beween price dynamics are more volaile and are more ighly relaed o each oher afer he issuance of hird-pary pu warrans. 15
Trivariae Condiional Correlaions In he bivariae DCC-GARCH framework, we realize he inerdependencies beween sock reurn, growh rae of rading volume, and he expeced change of implied volailiy. Will he unique correlaion among he hree price dynamics increase afer he pu warran s issuance day is he nex opic we would like o know. Since a unique indicaor represening he inerrelaionship among he hree price dynamics canno be available by he bivariae framework, herefore, we conduc he rivariae GARCH model o undersand wheher or no he overall correlaion among he hree price dynamics increases in he even of a pu warran issuance. The coefficien b in Table 5 shows ha he persisence of las period s condiional correlaions among sock reurn, growh rae of rading volume, and he expeced change of implied volailiy are significanly negaive for CSC, and are significanly posiive for Acer, SYNNEX, and Hon-Hai. Which means ha las period s condiional correlaions persisenly, significanly influen oday s condiional correlaion coefficiens. The inroducory effec on pu warran issuance is revealed by he coefficien δ in Table 5. In Table 5 we show ha he changes in correlaion among hree price dynamics are significanly increased afer pu warran inroducion for CSC, Acer, SYNNEX and Hon-Hai. The posiive, significan sign of δ indicaes ha he resuling correlaion among price dynamics increases by he inroducion of pu warrans. The inerdependence among price dynamics is more ighly relaed, which induces beer abiliy in forecasing he direcion and size in correlaion, and also enhances he probabiliy of diversificaion. <INSERT TABLE 5 ABOUT HERE> 16
V. CONCLUDING REMARKS In Taiwan, due o regulaory consrain, hird-pary pu warran was launched six years lagged afer hird-pary call warran s launching. This special launching pracice induced an issue wheher he price dynamics wih call and pu warran launched a he same ime is differen from he price dynamics wih provide only call warran bu no he pu warran. Therefore, he lagged lising on pu warran a he Taiwan sock marke offers an unique opporuniy o realize he special srucure on derivaive s inroducion, and he impacs on he underlying sock under he special srucure. In order o undersand he inroducory effec on warran s underlying asses in Taiwan s marke, we exend Engle s (2002) Mulivariae Dynamic Condiional Correlaion Generalize Auoregressive Condiional Heeroscedasiciy (DCC-GARCH) model o examine he ime-varying condiional correlaions of hese price dynamics. The empirical resuls show ha: he ineracions beween each wo of he price dynamics are more closely relaed o each oher afer he pu warrans issuing day. From his bivariae inerrelaionship, i is much easier for invesors o forecas changing direcions in sock reurns by he growh rae of rading volume and he expeced change of volailiy for he reason ha he relaionships beween each oher are much sronger. By undersanding he higher correlaion beween price dynamics, invesors may iniiae a profiable and diversifiable porfolio o gain posiive profis. From rivariae DCC-GARCH model, we produce an overall correlaion among he hree price dynamics, he overall correlaion increases afer he issuing day of a pu warran and his leads o a higher probabiliy in forming a diversifiable porfolio. 17
References Alkeback, P., and N. Hagelin, 1998, The impac of warran inroducions on he underlying socks, wih a comparison o sock opions, Journal of Fuures Markes, Vol. 18, iss. 3, 307 Bollerslev, T., 1990, Modelling he Coherence in Shor-Run Nominal Exchange Raes: A Mulivariae Generalized Arch Model, The Review of Economics and Saisics, Vol. 72, iss. 3, 498 Campbell, J.Y., and L. Henschel, 1992, No news is good news: An asymmeric model of changing volailiy in sock reurns, Journal of Financial Economics, Vol. 31, 281 Chaudhury, M., and S. Elfakhani, 1997, Lising of pu opions: Is here any volailiy effec? Review of Financial Economics, Vol.6, iss. 1, 57 Corrado, C.J., and T.W. Miller Jr., 2005, The forecas qualiy of CBOE implied volailiy indexes, Journal of Fuures Marke, Vol. 25, iss. 4, 339 Draper, P., B. Mak and G. Tang, 2001, The derivaive warran marke in Hong Kong: Relaionships wih underlying asses, Journal of Derivaives, Vol.8, iss. 4, 72 Engle, R.F., 2002, Dynamic condiional correlaion: a simple class of mulivariae generalized auoregressive condiional heeroskedasiciy models, Journal of Business and Economic Saisics, Vol. 20, 339 French, K.R., G.W. Schwer and R. Sambaugh, 1987, Expeced sock reurns and volailiy, Journal of Financial Economics, Vol. 19, 3 Karpoff, J.M., 1987, A heory of rading volume, The Journal of Finance, Vol. 41, 1069 Schwer, G.W., 1989, Why does sock marke volailiy change over ime?, The Journal of Finance, Vol. 44, 1115 18
Table 1: Daa descripion for seleced underlying sock on pu warran Underlying Socks on Pu Warran CSC Acer SYNNEX Hon-Hai Number of pu warran issuance 4 2 1 1 Issuing dae of pu warrans 7/9/2003 7/30/2003 8/21/2003 11/26/2003 Closing dae of pu warrans 6/17/2004 6/1/2004 8/18/2004 7/22/2004 Mauriy of hird-pary pu warrans (years) 0.94 0.84 0.99 0.66 Trading daes before pu warrans issuance 221 223 172 252 Trading daes afer pu warrans issuance 228 205 250 166 19
Table 2: Summary saisics CSC Acer Mean Sandard deviaion Skewness Kurosis Jarque-Bera Q(8) Q(24) Q 2 (8) Q 2 (24) Reurn 0.0016 0.0204 0.5623*** 1.7381*** 80.3582*** 20.0259** 43.6094*** 31.6196*** 67.0375*** Volume 0.1491 0.6828 2.1667*** 6.3956*** 1119.0266*** 37.6302*** 51.3949*** 5.3445 12.8680 Implied Volailiy 0.6198 0.3699 6.0846*** 44.7565*** 40335.57107*** 276.8727*** 300.6225*** 142.3258*** 148.1924*** Reurn 0.0010 0.0261-0.0302 2.2727*** 91.1035*** 8.0124 39.0044** 14.3388 25.6198 Volume 0.1792 1.0943 9.6123*** 138.6544*** 345355.5079*** 17.6792** 25.6474 0.0852 0.4014 Implied 0.6322 0.3130 4.2091*** 22.3324*** 10039.2123*** 1232.5385*** 2119.1518*** 852.1886*** 1019.7934*** Volailiy Reurn 0.0001 0.0259-0.2932** 2.5020*** 115.5707*** 13.5740* 23.3301 32.7603*** 47.9865*** Volume 0.3276 1.4989 7.0091*** 78.3466*** 110857.3187*** 19.4742** 43.1574*** 0.2612 0.7650 SYNNEX Implied 0.5945 0.2086 8.2634*** 103.7156*** 193026.2659*** 264.9687*** 454.8883*** 69.6668*** 70.0791*** Volailiy Hon-Hai Reurn 0.0003 0.0214 0.0212 1.4847*** 38.2396*** 17.4321** 36.1684** 8.1022 15.1829 Volume 0.1589 0.6829 2.1068*** 7.4531*** 1270.6040*** 45.2800*** 57.8222*** 4.2763 13.1333 Implied Volailiy 0.5897 0.3544-16.2120*** 307.2460*** 1654491.4239*** 30.1813*** 36.4508** 0.3988 0.7979 1. Daa series for CSC is from 8/19/2002 o 6/17/2004, log difference on daily daa is used, which represens 450 daa poins. 2. Daa series for Acer is from 9/5/2002 o 6/1/2004, log difference on daily daa is used, which represens 423 daa poins. 3. Daa series for SYNNEX is from 12/11/2002 o 8/18/2004, log difference on daily daa is used, which represens 420 daa poins 4. Daa series for Hon-Hai is from 11/14/2002 o 7/22/2004, log difference on daily daa is used, which represens 416 daa poins 5. ***, ** and * represen significance a he 1%, 5 % and 10% levels, respecively. 6. Q(8), Q(24), Q 2 (8) and Q 2 (24) are he Ljung-Box ess for he 8 h and 24 h order serial correlaion of sandardized residuals and sandardized squared residuals, respecively. 20
Table 3: The condiional mean equaion in AR(1) process The condiional mean equaion as an auoregression (AR1) process is x = μ + ε, where ε Ω ~ N( 0, Η ), where 1 μ [ x Ω 1] informaion, and ε is a vecor of errors in he auoregression AR(1). We also assume ha μ has he following formaion as: 1 (2) CSC Acer SYNNEX Hon-Hai Ω Φ 0 Φ 1 Q(8) Q(24) Q 2 (8) Q 2 (24) Reurn 0.0015 (1.5692) -0.1207 (-2.1247)** 11.9651 30.2436 4.6769 4.82917 Volume 0.1421 (5.1186)*** -0.2169 (-7.2250)*** 18.4011** 33.7250* 10.4750 18.5676 Implied Volailiy 0.0237 (3.0961)*** 0.9580 (7.5893)*** 7.6751 33.2803* 10.4750 18.5676 Reurn 0.0008 (0.6917) -0.0730 (-1.3695) 2.7821 2.90097 2.51290 4.2986 Volume 0.2554 (10.3961)*** -0.6460 (-15.4798)*** 12.9097 34.4358* 2.4001 16.7108 Implied Volailiy 0.0450 (4.3686)*** 0.9127 (4.4063)*** 0.7855 2.9939 0.7855 2.9939 Reurn 0.0003 (0.3389) -0.0002 (-0.0040) 10.8750 17.1763 9.1094 20.8254 Volume 0.4909 (8.9861)*** -0.3235 (-4.4108)*** 6.0575 27.1755 0.5849 2.3880 Implied Volailiy 0.0276 (3.3185)*** 0.9490 (6.0219)*** 10.2952 24.7848 0.5849 2.3880 Reurn 0.0003 (0.3212) 0.06354 (1.1835) 14.6277* 3.68349 3.7596 13.6754 Volume 0.2040 (6.23926)*** -0.2717 (-4.7122)*** 15.2247* 33.6468* 1.8672 9.6231 Implied Volailiy -0.0190 (-3.7145)*** 1.0189 (11.1922)*** 5.8722 24.3911 1.8672 9.6231 1. Daa series for CSC is from 8/19/2002 o 6/17/2004, log difference on daily daa is used, which represens 450 daa poins. 2. Daa series for Acer is from 9/5/2002 o 6/1/2004, log difference on daily daa is used, which represens 423 daa poins. 3. Daa series for SYNNEX is from 12/11/2002 o 8/18/2004, log difference on daily daa is used, which represens 420 daa poins 4. Daa series for Hon-Hai is from 11/14/2002 o 7/22/2004, log difference on daily daa is used, which represens 416 daa poins 5. ***, ** and * represen significance a he 1%, 5 % and 10% levels, respecively. = E is he condiional expecaion of given he pas μ 1 i, = Φ0 + Φ1xi,, i. 6. Q(8), Q(24), Q 2 (8) and Q 2 (24) are he Ljung-Box ess for he 8 h and 24 h order serial correlaion of sandardized residuals and sandardized squared residuals, respecively. 7. Parenheses are T saisics. x 21
Table 4: Brivariae ime-varying condiional correlaions on DCC-GARCH model wih pu warran issuance concern The ime-varying correlaion wih pu warran issuing effecs are processed as z z i j i, 1 j, 1 +, 1 [ ] q, ρ, =, where q, = ( + δ I * ) ρ + a( zi z j ρ ) + b( q ρ ), 1, 1, 1 qii, q jj, 1. ρ represens he uncondiional expecaion of he cross produc, i.e. he uncondiional correlaion coefficien. a z z b q, shows he condiional ime-varying covariance. Indicaor I denoes a dummy variable indicaing he pu warran s issuing day. The coefficien δ is used o capure he changing propery on condiional covariance and condiional correlaion. CSC Acer SYNNEX Hon-Hai a b δ Reurn-Volume 0.0767 (12.2908)*** -0.0119 (-4.4510)*** 7.7230 (4.1913)*** Reurn-Implied Volailiy 0.0378 (26.4215)*** -0.2663 (-7.9994)*** 2.7141 (6.2010)*** Volume-Implied Volailiy 0.06697 (18.0983)*** -0.9597 (-11.6702)*** 3.0434 (22.1156)*** Reurn-Volume -0.0819 (-5.5622)*** -0.4530 (-13.5002)*** 0.9707 (23.3457)*** Reurn-Implied Volailiy 0.0117 (9.5770)*** -0.7614 (-11.8991)*** 0.9240 (5.09521*** Volume-Implied Volailiy 0.0137 (23.8579)*** -0.5323 (-6.2650)*** 0.8918 (8.7674)*** Reurn-Volume -0.0190 (-22.5025)*** 0.0778 (4.6684)*** 59.4703 (4.5388)*** Reurn-Implied Volailiy -0.0055 (-22.7769)*** -0.0026 (-7.1362)*** 11.5036 (10.9861)*** Volume-Implied Volailiy 0.0246 (7.6449)*** -0.0080 (-4.9724)*** 21.0936 (4.2552)*** Reurn-Volume 0.1047 (7.8251)*** 0.1137 (4.3681)*** 4.4029 (5.21921*** Reurn-Implied Volailiy -0.0053 (-21.0470)*** -0.3667 (-7.5308)*** 1.6493 (4.58357)*** Volume-Implied Volailiy 0.02293 (25.3045)*** -0.3258 (-10.7469)*** 1.3283 (6.8113)*** 1. Daa series for CSC is from 8/19/2002 o 6/17/2004, log difference on daily daa is used, which represens 450 daa poins. 2. Daa series for Acer is from 9/5/2002 o 6/1/2004, log difference on daily daa is used, which represens 423 daa poins. 3. Daa series for SYNNEX is from 12/11/2002 o 8/18/2004, log difference on daily daa is used, which represens 420 daa poins 4. Daa series for Hon-Hai is from 11/14/2002 o 7/22/2004, log difference on daily daa is used, which represens 416 daa poins 5. ***, ** and * represen significance a he 1%, 5 % and 10% levels, respecively. 6. Parenheses are T saisics. 22
Table5: Trivariae ime-varying condiional correlaions on DCC-GARCH model wih pu warran issuance concern The ime-varying correlaion wih pu warran issuing effecs are processed as q,, = q q q CSC ACER SYNNEX Hon-Hai z z i j i, 1 j, 1 +, 1 ρ, where, = ( + δ I * )[ ρ + a( zi, 1z j, 1 ρ ) + b( q, ρ )] ii, jj, 1. 1 ρ represens he uncondiional expecaion of he cross produc, i.e. he uncondiional correlaion coefficien. a z z b q, shows he condiional ime-varying covariance. Indicaor dummy variable indicaing he pu warran s issuing day. The coefficien δ is used o capure he changing propery on condiional covariance and condiional correlaion. Reurn Volume Implied Volailiy Reurn Volume Implied Volailiy Reurn Volume Implied Volailiy Reurn Volume Implied Volailiy a b δ 0.0120 (20.9532)*** -0.0131 (-4.3888)*** 2.0010 (3.5412)*** -0.0092 (-17.4139)*** 0.0017 (19.0534)*** 2.7133 (13.9444)*** 0.0385 (3.0111)*** 0.8717 (16.5723)*** 0.2915 (7.6792)*** 0.0348 (12.4760)*** 0.8594 (8.8729)*** 10.4620 (11.4476)*** 1. Daa series for CSC is from 8/19/2002 o 6/17/2004, log difference on daily daa is used, which represens 450 daa poins. 2. Daa series for Acer is from 9/5/2002 o 6/1/2004, log difference on daily daa is used, which represens 423 daa poins. 3. Daa series for SYNNEX is from 12/11/2002 o 8/18/2004, log difference on daily daa is used, which represens 420 daa poins 4. Daa series for Hon-Hai is from 11/14/2002 o 7/22/2004, log difference on daily daa is used, which represens 416 daa poins 5. ***, ** and * represen significance a he 1%, 5 % and 10% levels, respecively. 6. Parenheses are T saisics. I denoes a 23
0.7 1 0.6 0.9 0.8 0.5 0.7 0.4 0.6 0.3 0.5 0.4 0.2 0.3 0.1 0 2 0 0 2 /8 /1 9 2 0 0 2 /1 0 /1 9 2 0 0 2 /1 2 /1 9 2 0 0 3 /2 /1 9 2 0 0 3 /4 /1 9 2 0 0 3 /6 /1 9 2 0 0 3 /8 /1 9 2 0 0 3 /1 0 /1 9 2 0 0 3 /1 2 /1 9 2 0 0 4 /2 /1 9 2 0 0 4 /4 /1 9 0.2 0.1 0 2002/9/5 2002/11/5 2003/1/5 2003/3/5 2003/5/5 2003/7/5 2003/9/5 2003/11/5 2004/1/5 2004/3/5 2004/5/5 Panel A: CSC Panel B: Acer 1 0.8 0.6 0.4 0.2 0 2002/11/4 2003/1/4 2003/3/4 2003/5/4 2003/7/4 2003/9/4 2003/11/4 2004/1/4 2004/3/4 2004/5/4 2004/7/4-0.2-0.4-0.6-0.8 0.45 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 2 00 2 /12 /11 2 00 3 /2/1 1 2 00 3 /4/1 1 2 00 3 /6/1 1 2 00 3 /8/1 1 2 00 3 /10 /11 2 00 3 /12 /11 2 00 4 /2/1 1 2 00 4 /4/1 1 2 00 4 /6/1 1 2 00 4 /8/1 1-0.05-0.1 Panel C: Hon-Hai Panel D: SYNNEX Figure 1: Brivariae ime-varying condiional correlaion coefficien beween sock reurn and growh rae of rading volume The lising day of hird-pary pu warran for CSC, Acer, Hon-Hai, and SYNNEX is 7/9/2003, 7/30/2003, 8/11/2003, and 11/26/2003, respecively. The dynamic correlaions beween sock reurn and he growh rae of rading volume for CSC are posiive, which becomes much volaile afer he pu warran issuance day. Moreover, he links of reurn and rading volumes are more posiively relaed o each oher for Hon-Hai and SYNNEX afer he pu warran issuing day. However, we observe a lag volaile effec for Acer, since he changes in dynamic correlaion coefficiens beween mean and rading volume are posiively relaed and much volaile afer pu warran has issued around six monh. 24
-0.05 2002/8/19 2002/10/19 2002/12/19 2003/2/19 2003/4/19 2003/6/19 2003/8/19 2003/10/19 2003/12/19 2004/2/19 2004/4/19 0 2002/9/5 2002/11/5 2003/1/5 2003/3/5 2003/5/5 2003/7/5 2003/9/5 2003/11/5 2004/1/5 2004/3/5 2004/5/5-0.07-0.1-0.09-0.2-0.11-0.3-0.13-0.4-0.15-0.5-0.17-0.6 Panel A: CSC Panel B: Acer 0-0.1 2002/11/4 2002/12/4 2003/1/4 2003/2/4 2003/3/4 2003/4/4 2003/5/4 2003/6/4 2003/7/4 2003/8/4 2003/9/4 2003/10/4 2003/11/4 2003/12/4 2004/1/4 2004/2/4 2004/3/4 2004/4/4 2004/5/4 2004/6/4 2004/7/4 0 2002/12/11 2003/2/11 2003/4/11 2003/6/11 2003/8/11 2003/10/11 2003/12/11 2004/2/11 2004/4/11 2004/6/11 2004/8/11-0.05-0.2-0.1-0.3-0.4-0.15-0.5-0.2-0.6-0.25-0.7-0.8-0.3-0.9-0.35 Panel C: Hon-Hai Panel D: SYNNEX Figure 2: Brivariae ime-varying condiional correlaion coefficien beween sock reurn and he expeced change of implied volailiy The lising day of hird-pary pu warran for CSC, Acer, Hon-Hai, and SYNNEX is 7/9/2003, 7/30/2003, 8/11/2003, and 11/26/2003, respecively. As we can see, he ime-varying correlaions beween sock reurn and he expeced change of volailiy for CSC become much volaile afer he pu warran issuance day. On he oher hand, he relaionship beween reurn and implied volailiy for Hon-Hai and SYNNEX are more negaively relaed o each oher afer he hird-pary pu warran has issued. However, he changes in dynamic correlaion coefficiens beween reurn and implied volailiy for Acer canno be idenified by simply observaion. 25
0.4 1.2 0.2 1 0 2002/8/19 2002/10/19 2002/12/19 2003/2/19 2003/4/19 2003/6/19 2003/8/19 2003/10/19 2003/12/19 2004/2/19 2004/4/19-0.2 0.8 0.6-0.4 0.4-0.6 0.2-0.8-1 0 2 0 0 2 /9 /5 2 0 0 2 /1 1 /5 2 0 0 3 /1/5 2 0 0 3 /3 /5 2 0 0 3 /5 /5 2 0 0 3 /7 /5 2 0 0 3 /9 /5 2 0 0 3 /1 1 /5 2 0 0 4 /1/5 2 0 0 4 /3 /5 2 0 0 4 /5 /5-0.2 Panel A: CSC Panel B: Acer 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 2002/11/4 2003/1/4 2003/3/4 2003/5/4 2003/7/4 2003/9/4 2003/11/4 2004/1/4 2004/3/4 2004/5/4 2004/7/4-0.1 0.6 0.5 0.4 0.3 0.2 0.1 0 2 00 2 /12 /11 2 00 3 /2/1 1 2 00 3 /4/1 1 2 00 3 /6/1 1 2 00 3 /8/1 1 2 00 3 /10 /11 2 00 3 /12 /11 2 00 4 /2/1 1 2 00 4 /4/1 1 2 00 4 /6/1 1 2 00 4 /8/1 1-0.1-0.2-0.2-0.3-0.3-0.4 Panel C: Hon-Hai Panel D: SYNNEX Figure 3: Brivariae ime-varying condiional correlaion coefficien beween he growh rae of rading volume and he expeced change of implied volailiy The lising day of pu warran for CSC, Acer, Hon-Hai, and SYNNEX is 7/9/2003, 7/30/2003, 8/11/2003, and 11/26/2003, respecively. The ime-varying correlaions for CSC become negaively correlaed afer four monh of pu warran issuance, hen he dynamic correlaions become posiive again. Toally speaking, he ime-varying correlaion for CSC is much volaile afer he pu warran issuance day. The dynamic correlaions for Acer become much volaile afer six monh of pu warran issuance day. For he Hon-Hai and SYNNEX case, he inerdependences beween rading volume and implied volailiy are more posiively relaed and volaile. 26