The Mauriy Srucure of Volailiy and Trading Aciviy in he KOSPI200 Fuures Marke Jong In Yoon Division of Business and Commerce Baekseok Univerisy Republic of Korea Email: jiyoon@bu.ac.kr Received Sepember 16, Revised November 2, Acceped December 26 ABSTRACT This sudy examines he effecs of rading aciviies on he mauriy srucure of he volailiy in he KOSPI200 fuures marke. I involves esimaion of a varian of he E-GARCH(1,1) model of fuures reurns. The empirical resuls sugges ha he KOSPI200 fuures marke ends o be volaile righ before and righ afer he neares conrac expires. High volailiy immediaely prior o mauriy can be explained wihin he framework of he well-known Samuelson hypohesis. However, i is no easy o explain why volailiy increases righ afer he neares conrac expires. To do so, we esimae he volailiy equaion by using expeced and unexpeced rading volume relaive o open ineres as explanaory variables. The resuls show ha he observed U-shaped mauriy volailiy srucure reflecs he rading aciviy righ before and righ afer he expiry, and, o be noeworhy, in paricular, is ha volailiy increases immediaely afer he neares conrac reaches 19
mauriy, due o he high unexpeced rading volume relaive o open ineres. The rading aciviy in he KOSPI200 fuures marke is ypically heavily concenraed on he neares conrac, which is indicaive of low levels of marke deph in he nex-o-neares conrac. This, in urn, suggess ha here has been a emporary marke hinness righ before and afer he replacemen of he neares conrac. The KOSPI200 fuures reurns display a U-shaped mauriy srucure of volailiy, due mainly o he emporary marke hinness a he ime of he expiry. Keywords: Samuelson hypohesis, mauriy srucure of volailiy, rading volume, open ineres, E-GARCH JEL Classificaion code: G13, C50 INTRODUCTION Since he inroducion of he KOSPI200 fuures conrac in May 1996, he KOSPI200 fuures marke has seen enormous growh, wih 4.7 billion conracs raded in 2006 alone, and i has become he fifh larges in he world s sock index fuures markes. As such, is impressive growh has drawn much aenion over he pas several years. We hereby examine he effecs of rading aciviies on he mauriy srucure of he volailiy in he KOSPI200 fuures marke. In his seminal aricle, Samuelson (1967) formulaed a model where he volailiy of fuures reurns ends o increase as he conrac approaches mauriy. As a resul, reurns of fuures conracs close o expiraion reac more srongly o new informaion abou he underlying asse han reurns of more disan fuures conracs. This is known as he Samuelson effec 20
ha is jus a price elasiciy effec. Wha follows are alernaive approaches o ackling limiaions inheren o he Samuelson hypohesis. To begin wih, he sae variable hypohesis proposed by Richard and Sundaresan (1981), and by Anderson and Danhine (1983) argues ha heerogeneous informaion flows lead o violaions of he Samuelson effec. In addiion, he speculaive hypohesis argues agains he Samuelson effec, basing iself on he asymmeric informaion of raders, and on he assumpion of homogeneous informaion flow. Much empirical research has been conduced ino volailiy in he fuures markes, bu i remains conroversial wheher he ime-o-mauriy paern of volailiy is monoonic or no [Casello and Francis(1982), Galloway and Kolb(1996), Keynon e.al(1987), and Khoury and Yourougou(1993)]. In his sudy, he mauriy srucure of volailiy in he KOSPI 200 fuures marke is analyzed. Ineresingly enough, i urns ou ha he volailiy of he KOSPI200 fuures reurns follows a U-shaped curve as a funcion of days o expiry. 1 The focus of his paper, in shor, is how he rading aciviy in he KOSPI200 fuures marke ineracs o produce a U-shaped ime-o-mauriy volailiy paern. I is well known ha rading aciviy has effecs on marke volailiy [Kyle(1985), and Bessembinder and Seguin(1993)]. Many researchers have been using rading volume and open ineres as a proxy for rading aciviy. When rading volume increases, or open ineres decreases, he fuures marke ends o be more volaile, and his proposiion has been widely acceped. As an alernaive, we propose he rading volume relaive o open 1 In addiion, he realized volailiy in he KOSPI200 fuures reurns urned ou o have a U-shaped ime-o-mauriy srucure, hough i is no deal wih in his paper. 21
ineres (VTOI) as an explanaory variable. Convenionally, absolue measures involving he use of rading volume and/or open ineres hemselves have been used. However, he proposed VTOI is deemed appropriae as a relaive measure of rading aciviy o properly capure a se of characerisics of he KOSPI200 fuures marke. On op of ha, we examine he ime-o-mauriy volailiy srucure from a shor-erm perspecive where less han hree monhs are lef o mauriy. In he KOSPI200 fuures marke, rading aciviy is heavily concenraed on he neares conrac. Accordingly, we reckon ha he U-shaped mauriy volailiy srucure may reflec he exreme concenraion on he neares conrac. The remainder of his paper is organized as follows. Secion 2 deals wih he daa se of he KOSPI200 fuures marke and wih how o adjus price and rading volume series. In Secion 3, he empirical mehodologies are described. The empirical resuls and heir inerpreaions are given in Secion 4, wih Secion 5 concluding he paper. DATA AND FEATURES OF TRADING ACTIVITY The KOSPI200 fuures conrac is lised on he Korea Exchange. Is underlying asse is KOSPI200, which is he index consising of op 200 socks. The delivery monhs are March, June, Sepember, and December each year, so he neares conrac is replaced wih he nex-o-neares one every hree monhs. All he daa used in his sudy are colleced from he Korea Exchange daabase spanning he period from May 5, 1996 o March 30, 2007. More specifically, he daa include daily closing prices, daily rading volume, and daily open ineres. Trading 22
volume and open ineres are measured in erms of conracs. However, he daa used in his paper is only limied o he neares and nex-o-neaes conracs due o he negligibiliy of he rading aciviy relevan o oher conracs. There are a number of ways o calculae fuures prices. Usually, price series are consruced by splicing ogeher conracs near mauriy; for he mos par, he price series of he neares conrac are used. However, o avoid problems associaed wih expiraion effecs, he price series of he neares conrac in he delivery monh are excluded. Insead, he price of he nex-oneares conrac in ha period is used. Noneheless, here remains he possibiliy of he expiraion effecs occurring: Righ before and righ afer he replacemen of he conrac, volailiy may be overesimaed. In order o minimize he effecs arising hereof, some adjusmen is made o he raw price series according o Rougier (1996). He suggess he opimal fuures price index ha is designed o change proporionally as he underlying spo price. The following opimal fuures price index is defined as he weighed average of he prices of he neares and nex-o-neares conracs. (1) * m F = k F ' + m 1 k '' F * ' where F is he opimal fuures price index, F he price of '' he neares conrac, and F he price of he nex-o-neares conrac. k is he difference beween he mauriy daes of wo conracs, and m refers o he number of days lef o he expiraion of he neares conrac. When he neares conrac is 23
disan from mauriy, he weighs of he price of he neares conrac are large, and vice versa. I should be noed ha he opimal fuures price index changes proporionally as he underlying spo price. This allows us o obain a consan coinegraing vecor, regardless of how many days are lef o he expiry. I is likely ha srong seasonaliy in rading volume series arises from he rolling over of posiions from he neares conrac o he nex-o-neares conrac. As a resul, rading volume increases drasically jus before he conrac reaches mauriy. Given ha he increase in rading volume is aribuable only o he replacemen of he neares conrac wih he nex-o-neares one, i is deemed no suiable o use rading volume as a proxy for informaion arrival. In order o minimize he effecs resuling from he replacemen of he neares conrac wih he nex-o-neares one, we adjus he rading volume series according o he approach proposed by Holmes and Rougier(2005). Firs, he rolloverinduced volume is calculaed as follows: (2) 0 r min ( v 2 1 ' ' ' 1 '' ' oi ), ( v oi ) 2 ' where r is he rollover-induced rading volume, v he volume '' of he neares conrac, and v he volume of he nex-o-neares ' conrac. In addiion, oi refers o changes in he open ineres of '' he neares conrac, and oi o changes in he open ineres of he nex-o-neares conrac. 24
Second, we calculae he sum of he rading volumes of he neares and nex-o-neares conracs, and hen subrac he rollover-induced rading volume from he calculaed sum. The rollover-adjused rading volume is obained as follows: (3) vˆ = v 2 r where vˆ is he adjused rading volume, and v is he (raw) unadjused rading volume. The rollover-induced rading volume is subraced from he raw rading volume. I is well known ha here are conemporaneous relaions beween rading aciviy and price volailiy. As a proxy for informaion arrival, rading volume has posiive conemporaneous relaions wih price volailiy[bessembinder and Seguin(1992)]. According o hem, when volume is pariioned ino expeced and unexpeced componens, unexpeced volume shocks have a larger posiive effec on price volailiy. Likewise, he relaion beween price volailiy and open ineres has been examined. Open ineres is used as a proxy for marke deph [Bessembinder and Seguin(1993)], demand for hedging [Chen, Cuny and Haugen(1995)], and difference of raders opinions [Bessembinder, Chan and Seguin(1996)]. Bessembinder and Seguin(1993) sugges ha here are negaive relaions beween price volailiy and open ineres. When open ineres is pariioned ino expeced and unexpeced componens, unexpeced open ineres shocks have a larger negaive effec on price volailiy. 25
Fig.1 shows he ime-o-mauriy paern of he rading volume (a), open ineres (b), and rading volume relaive o open ineres (c) in he KOSPI200 fuures marke. All he daa are he sum of wo ses of daa on he neares and nex-o-he neares conracs. As shown in Fig. 1, he values are daily averages by less-han-120 days o mauriy. Also, he rading volume is free of he rollover-induced volume as a resul of using he mehods of Holmes and Rougier (2005). The remaining days o mauriy are on he neares conrac. On May 2007, he daily volume averaged 181,111 conracs, and he daily open ineres averaged 84,620 conracs. The daily average of he rading volume relaive o open ineres is abou 2.14. There seems o be a ime-o-mauriy paern in he daa. Here, our focus is how he rading volume relaive o open ineres (VTOI) affecs price volailiy. VTOI measures rading volume relaive o open ineres. Fig.1 (c) shows he ime-omauriy paern of VTOI by days o mauriy. VTOI is high righ before and righ afer he replacemen of he neares conrac. The reason for high VTOI is because he open ineres is low during ha period, no because he rading volume is high. I is hough, herefore, ha he ime-o-mauriy paern of price volailiy can be explained by VTOI which is a relaive measure, raher han by rading volume or open ineres. EMPIRICAL METHODOLOGIES To analyze he impac of rading aciviy on he KOSPI200 fuures marke volailiy, an E-GARCH(1,1) varian is employed in his sudy. I allows for several effecs in he reurn equaion and in he volailiy equaion. We use a model as parsimonious as 26
possible in order o minimize he number of parameers o be esimaed. Firs, he reurn equaion is he error correcion model (ECM), which is based on he coinegraion relaion beween he fuures price and he underlying spo price. The reurn equaion is given as follows: (4) ln( s ) = a ln( f ) + v (5) ln( f ) = c 0 + vˆ +, where ~ ( 0, h ) Eq. (4) is he coinegraion equaion, where ln( f ) is he log of he fuures price, and ln( s ) is he log of he underlying spo price. Also, vˆ in Eq. (5) is he esimae of he coinegraion errors in Eq. (4). The esimaed coinegraion errors are used as an explanaory variable in he volailiy equaion. Eq. (5) has no lagged variables for he fuures and spo reurns by Akaike s informaion crierion. Second, he volailiy equaion is he univariae E-GARCH (1,1) model which allows for he leverage effec, weekday effec, error correcion effec, mauriy effec, and rading aciviy effec. The volailiy equaion is expressed as follows: (6) log( h ) = 0 + 1 h + 2 log( h 1 ) + 3 1 1 h 1 1 + 1 mon+ 2 ue + 3 hu + 4 fri + 5 sa + 6 + 1 m + 2 m + 1 2 evoi + 2 uvoi vˆ + 7 2 v ˆ 27
where h is he condiional variance a ime, and 1 is he lagged value of he residual in Eq.(5). The firs line of Eq. (6) is he original form of Nelson(1991) s E-GARCH(1,1) model which allows for asymmeric responses of volailiy o news. Negaive 3 implies he leverage effec. Fig. 1. Trading aciviies observed when less han 120 days are lef o expiry (a) Trading Volume Series 160,000 140,000 120,000 100,000 80,000 60,000 40,000 20,000 0 120 106 92 78 56 42 28 14 0 (b) Open Ineres Series 70,000 60,000 50,000 40,000 30,000 20,000 10,000 0 120 106 92 78 56 42 28 14 0 28
(c) Trading Volume Relaive o Open Ineres 3.50 3.00 2.50 2.00 1.50 1.00 0.50 0.00 120 106 92 78 56 42 28 14 0 Noe) All he daa are he sum of wo ses of daa on he neares and nex-o-neares conracs. The given values are daily averages by less-han-120 days o mauriy. The rading volume is free of he rollover-induced volume. The days o mauriy are on he neares conrac. mon, ue, hu, fri, sa are he dummy variables which ake a value of one for Monday, Tuesday, Thursday, Friday, and Saurday, and which ake a value of zero oherwise. The model esed here includes he coinegraion errors vˆ for capuring he error correcion effec of he approach aken by Zhong e al.(2004). Also included are he squared values of he coinegraion errors 2 v ˆ as an explanaory variable. We conjecure ha he coinegraion errors have no only he sign effec bu also he size effec. m is he number of calendar days lef o he expiraion of he neares conrac. m and m 2 capure he mauriy srucure of volailiy, which is expressed as 2 m 2 1 ( 2 2 ). If 2 is posiive and 1 negaive, he volailiy is represened by a usual quadraic 29
form of days o mauriy. And if 0 < - 1 / ( 2 2 ) < 90, he volailiy shows a U-shaped paern for days o mauriy. evoi is he expeced rading volume relaive o open ineres, and uvoi is he unexpeced rading volume relaive o open ineres. According o he Akaike informaion crierion, he AR(17) model is employed o pariion he rading volume relaive o open ineres ino expeced and unexpeced componens. 2 Also, consan, rend, and weekday dummy variables are used in he proposed model as explanaory variables. The fied values are defined as an expeced componen and he residual as an unexpeced componen. Nelson(1991) proposes he generalized error disribuion(ged) o capure fa ail disribuions usually observed in financial ime series. The probabiliy densiy funcion of GED is given by (7) f (x) = 2 / c x / b 2 c / 2 1 2 1 c / 2 exp b where b is a scale parameer and c is a shape parameer. ( ) is he gamma funcion, and c is a posiive parameer ha governs he ail behavior of he error disribuion. b and c are esimaed as par of he MLE procedure. 2 The main resuls obained in his sudy are robus wih respec o he ARMA specificaion concerning he rading volume relaive o open ineres. As is shown in Secion 4, he raio of rading volume o open ineres is saionary. 30
Under GED, we esimae Eqs. (5) and (6) joinly using maximum likelihood esimaion. Furhermore, he Broyden- Flecher-Goldfarb-Shanno algorihm is used as a numerical opimizaion ool in his sudy. RESULTS We presen he resuls of esing he uni roo and coinegraion, and he resuls of esimaing he volailiy equaion. In addiion, we summarize he feaures of he rading aciviy in he KOSPI200 fuures marke and hereby inerpre he empirical resuls. Table 1. ADF ess for fuures prices and reurns, and raio of rading volume o open ineres raio Variables When consan is only included When consan and rend are boh included Fuures price -1.09-2.71 Fuures reurns -29.31-29.33 Raio of rading volume o open ineres -6.35-7.11 Noe) A he significance levels of 1%, 5%, and 10%, criical values are - 3.43, -2.86, -2.57, respecively when consan is only included, and -3.96, -3.41, -3.12, respecively when boh consan and rend are included. 31
Table 2. Engle-Granger ess for he KOSPI200 Index and fuures price Model Resuls ln( f ) 1.0003 (4346.41) *** Engle-Granger es saisics -43.04 *** Noe) Criical values of he Engle-Granger es saisics are from MacKinnon(1991) s response surface regressions, and a 1%, 5%, 10% significance level are -3.90, -3.34, -3.05 respecively.. Figures in parenhesis are -values. (***), (**), and (*) represen significance a he 1%, 5%, 10% significance levels. Resuls of Uni Roo and Coinegraion Tess Firs, we es he uni roo hypohesis using an augmened Dickey-Fuller(ADF) es wherein consan is only used, or consan and rend are boh used. The resuls are repored in Table 1. The lag lengh is deermined using he Akaike informaion crierion. As is usual, log of he KOSPI200 fuures prices is I(1), and he difference of hem is I(0). Also, rading volume relaive o open ineres is I(0). Second, we es he coinegraion hypohesis for he fuures and underlying spo prices. Table 2 shows he resuls of an Engle- Granger (EG) es. Criical values of EG es saisics are from MacKinnon(1991) s response surface regressions. The EG es leads o rejecion a he 1 percen level of he hypohesis ha he fuures and underlying spo prices are no coinegraed. Because he coinegraion vecor is close o (1,-1), basis can be inerpreed as he coinegraion errors which are saionary. 32
Table 3. Esimaion of ECM and E-GARCH(1,1) for KOSPI200 fuures onracs Variables Eq. (5) When variables of rading aciviy are excluded When variables of rading aciviy are included consan 0.0018 (4.25) *** 0.0019 (4.60) *** vˆ 0.1524 (6.90) *** 0.1523 (5.86) *** Eq. (6) consan -2.2772 (-11.18) *** -2.3352 (-10.89) *** h 0.5592 (14.58) *** 0.5433 (13.06) *** 1 1 log( h 0.7497 (34.10) *** 0.7458 (33.07) *** 1) h 1 1-0.0669 (-2.22) ** -0.0660 (-2.21) ** Mon 0.1805 (1.41) 0.1627 (1.31) Tue -0.2685 (-2.19) ** -0.2778 (-2.28) ** Thu 0.0631 (0.44) 0.0552 (0.38) Fri 0.0906 (0.64) 0.0793 (0.56) Sa 0.2059 (1.15) 0.3136 (1.52) vˆ 5.6633 (7.38) *** 5.5877 (6.84) *** 2 v ˆ m 2 6.0598 (3.96) *** 6.5418 (4.08) *** -0.0038 (-1.68) * -0.0036 (-1.56) m 4 10 (1.93) * 4 10 0.3874 (1.53) 0.4739 evoi 0.0306 (1.17) uvoi 0.2201 (2.96) *** shape (c) 1.6887 (25.84) *** 1.6872 (25.95) *** likelihood 6490.0 6496.1 Noe) Figures in parenhesis are -values. (***), (**), and (*) represen significance a he 1%, 5%, 10% significance levels. 33
Esimaion Resuls of Volailiy Equaion Firs, Eqs. (5) and (6) are esimaed wihou using he rading volume relaive o open ineres as an explanaory variable in he volailiy equaion. As repored in he second column of Table 3, he resuls are mosly consisen wih he lieraure. In Eq. (5), he esimae of he error correcion erm is significan and posiive. This means ha he fuures price is no weakly exogenous o he coinegraion relaion in he conex of Johansen (1992). Nex, he volailiy equaion is esimaed, and he main resuls are described in he following way. The coefficien esimae of 1 h 1 is significan and negaive. This means he volailiy in he fuures marke displays an asymmeric response o news. The coefficien for he dummy variable for only Tuesday is also significan. In addiion, he coefficiens for he coinegraion errors and heir squared values are significan and posiive. This indicaes ha he coinegraion relaion has boh he sign effec and he size effec. The volailiy in he fuures marke could inensify when he fuures price deviaes from he long-run equilibrium relaion. 3 Noably, deviaions have a larger impac on he volailiy when he fuures conrac is overpriced. The esimae of he shape parameer (c) is abou 1.69. This implies he ails of he disribuion are hicker han a normal disribuion. Of paricular imporance is he finding ha he coefficien of m is negaive and ha of m 2 posiive. The poin esimae of m is -0.0038, while ha of 2 4 m 10 is 0.4739. These resuls suppor he quadraic mauriy effec of 2 m 2 1 ( 2 2 ). The 3 These resuls corroborae he long-run hypohesis of Zhong e al.(2004). 34
KOSPI200 fuures marke is highly volaile immediaely afer he replacemen of he neares conrac a he ime of abou 90 days lef o expiraion. Over ime, however, volailiy decreases. The esimaed value of 1 ( 2 2 ) is abou -40.5. Thus, he volailiy reaches is minimum when 40.5 days are lef o mauriy, and aferwards, i moves up. Once again, he KOSPI200 fuures marke becomes highly volaile immediaely prior o he replacemen of he neares conrac. As far as we know, his is he firs-ever finding on he U-shaped mauriy srucure of volailiy. Given ha volailiy is high jus prior o mauriy, he resul of his sudy suppors he Samuelson hypohesis. However, i is a puzzle ha goes beyond explanaion: Why is volailiy high immediaely afer he neares conrac reaches mauriy? In figuring ou his puzzle, rading aciviy is inroduced in he volailiy equaion. Eqs. (5) and (6) are esimaed by using explanaory variables such as expeced VTOI and unexpeced VTOI, days o expiraion, and heir squared values. The resuls are repored in he hird column of Table 3. Coefficien esimaes for oher explanaory variables are no qualiaively alered by inclusion of expeced and unexpeced VTOI, wih he excepion of m and m 2. The coefficiens of m and m 2 are no significan, whereas he coefficien of unexpeced VTOI is significan and posiive. The significance of unexpeced VTOI is also confirmed by he likelihood raio es saisics compued as wice he difference of he wo loglikelihood values in Table 3. The numbers calculaed show ha he chi-square es saisics wih wo degrees of freedom equals 12.2, and i is highly significan. Such resuls sugges ha an unexpeced increase in he rading volume relaive o open ineres, or an unexpeced decrease in he open ineres relaive o rading volume has posiive effecs on volailiy. This follows 35
he resuls obained by Bessembinder and Seguin(1993): The more unexpeced rading volume and he less unexpeced open ineres, he more volaile he fuures marke becomes. As suggesed by Bessembinder and Seguin(1993), unexpeced rading volume and unexpeced open ineres, insead of unexpeced VTOI, can be arguably included as explanaory variables. Of course, resuls no repored here sugges ha unexpeced rading volume and unexpeced open ineres are significan. In he equaion, however, he coefficiens of m and m 2 are significan. In his conex, we sugges ha unexpeced VTOI is more appropriae for explaining he U-shaped mauriy srucure of volailiy, in ligh of our empirical findings (See he nex subsecion) on he feaures of he rading aciviy observed in he KOSPI200 fuures marke. We sugges ha VTOI is more useful in describing marke deph in he fuures marke. Open ineres is a variable ha is dependen on he conrac life cycle. This is in conras o he number of shares ousanding in he sock marke. VTOI, a relaive measure, can represen dependence on he conrac life cycle which rading volume and/or open ineres hemselves canno. We expec much research ino VTOI will be conduced. In a word, he KOSPI200 fuures marke has a U-shaped volailiy paern ha can be explained by he unexpeced VTOI. From now on, we deal wih he feaures of he rading aciviy dependen on he conrac life cycle in he KOSPI200 fuures marke. Feaures of rading aciviy in he KOSPI200 fuures marke Periodically, he old neares conrac expires, and he nex-oneares conrac becomes he new neares. In he KOSPI200 fuures marke, he new neares conrac replaces he old neares 36
one a an inerval of 90 days. As shown in Fig.1 (a) and (b), he rading volume and open ineres are no large during he period when he neares conrac is replaced by he nex-o-neares conrac. Noably, open ineres is small during ha period. Tha s because in he KOSPI200 fuures marke, rading aciviy is heavily concenraed on he neares conrac; rading aciviy in he nex-o-neares conrac is relaively hin before he nexo-neares conrac becomes he neares conrac. Therefore, as shown in Fig.1 (c), afer he replacemen of he neares conrac, he rading volume relaive o open ineres begins o increase dramaically due o he decrease in open ineres raher han o he increase in rading volume. This suggess ha here is emporary marke hinness during ha period. Of more imporance is he fac ha here definiely is a huge increase in he unexpeced rading volume relaive o he open ineres, as shown in Fig.2. Fig.2 shows he ime-o-mauriy paern of unexpeced VTOI, which is he resul of Nadaraya-Wason kernel esimaion. We use Epanechnikov kernel of which he bandwidh is 0.79 IQR / 1/ 5 N, where IQR is he inerquarile range (75 percenile-25 percenile) of days o expiraion and N is number of daa poins. Jus afer he replacemen of he neares conrac, he unexpeced VTOI is exremely high. During his period, he unexpeced VTOI ranges from 0.5 o 0.8. Compared wih an average VTOI of 2, his unexpeced VTOI is relaively high. These resuls indicae ha an increase in unexpeced VTOI leads o he high volailiy occurring immediaely afer he neares conrac is replaced by he nex-oneares conrac. 37
Fig. 2.. The ime-o-mauriy paern of he raio of unexpeced rading volume o open ineres 1.0 0.8 0.6 0.4 0.2 0.0-0.2-0.4 95 84 74 63 53 42 32 21 11 0 Noe) The above graph is aken from he Nadaraya-Wason kernel esimaion using Epanechnikov kernel. The bandwidh is 1/ 5 0.79 IQR / N, where IQR is he inerquarile range (75 percenile-25 percenile) of days o expiraion, and N is he number of daa poins. In he KOSPI200 fuures marke, his phenomenon is fundamenally he resul of an inense concenraion of rading aciviy on he neares conracs. Thus, he old neares conrac canno be replaced by he new one smoohly because of he low levels of open ineres in he new neares conrac. Jus afer he replacemen of he neares conrac, he KOSPI200 fuures marke ends o experience a jump or a disconinuiy in rading aciviy. I is inerpreed as emporary marke hinness, he cause for an increase in volailiy. 38
CONCLUSIONS This paper analyzes he effecs of rading aciviies on he mauriy srucure of volailiy in he KOSPI200 fuures marke. We esimae a varian of he E-GARCH(1,1) model of fuures reurns. The empirical resuls confirm he leverage effec and he weekday effec. They also subsaniae he view ha error correcion erms have effecs on volailiy, which creaes he sign effec as well as he size effec. Mos imporanly, he U-shaped mauriy srucure of volailiy is observed. This means ha he KOSPI200 fuures marke ends o be volaile righ before and righ afer he neares conrac expires. In his respec, our observaions are in conras o hose in he exising lieraure. The high volailiy observed righ before he expiry can be explained wihin he framework of he Samuelson hypohesis, bu he high volailiy found righ afer he expiry is a mysery ha is beyond explanaion. In order o ackle he puzzling phenomenon, we esimae he volailiy equaion by using expeced and unexpeced rading volume relaive o open ineres as explanaory variables. The resuls show ha he coefficien of unexpeced rading volume relaive o open ineres is only significan and posiive. On he conrary, he coefficiens of days o expiraion and heir squared values are no significan. This leads us o conclude ha he U-shaped mauriy srucure of volailiy reflecs he rading aciviy around he expiraion dae of he neares conrac. Volailiy ends o be higher jus afer he expiry because of high unexpeced rading volume relaive o open ineres. Noably, he rading aciviy in he KOSPI200 fuures marke is heavily concenraed on he neares conrac. This is indicaive small open ineres in he nex-o-neares conrac. The open ineres in he nex-o-neares conrac is oo small so ha 39
he nex-o-neares conrac canno replace he neares one immediaely prior o he replacemen of he neares conrac. In addiion, even afer he new neares conrac has jus replaced he old neares one, small open ineres in he new neares conrac do no guaranee geing back o normal levels of marke deph; i akes much ime o achieve a sufficien level of open ineres. This, in urn, suggess ha here has been a emporary marke hinness righ before and righ afer he neares conrac is replaced by he nex-neares conrac. As is well-known, low marke deph ends o increase volailiy. The same goes for he volailiy in he KOSPI200 fuures marke which ends o increase righ before and righ afer he replacemen of he neares conrac wih he nex-neares one. The observed U- shaped mauriy srucure of he KOSPI200 fuures reurns is aribuable mainly o he emporary marke hinness before and righ afer he neares conrac expires. REFERENCES Anderson, R. W. and Danhine, J. P., The Time Paern of Hedging and he Volailiy of Fuures Prices, Review of Economic Sudies, 50, 1983, 249-266. Bessembinder, H. and Seguin, P. J., Price Volailiy, Trading Volume, and Marke Deph : Evidence from Fuures Markes, Journal of Financial and Quaniaive Analysis, 28, 1993, 21-39. Casello, M. G. and Francis, J. C., Basis Speculaion in Commodiy Fuures : The Mauriy Effec, Journal of Fuures Marke, 2, 1982, 195-206. 40
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