How Fast Do Tokyo and New York Stock Exchanges. Respond to Each Other?: An Analysis with. High-Frequency Data

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1 Discussion Paper No.10 How Fas Do Tokyo and New York Sock Exchanges Respond o Each Oher?: An Analysis wih High-Frequency Daa Yoshiro Tsusui and Kenjiro Hirayama Ocober 2008 GCOE Secrearia Graduae School of Economics OSAKA UNIVERSITY 1-7 Machikaneyama, Toyonaka, Osaka, , Japan

2 How Fas Do Tokyo and New York Sock Exchanges Respond o Each Oher?: An Analysis wih High-Frequency Daa * Yoshiro Tsusui Osaka Universiy Kenjiro Hirayama Kwansei Gakuin Universiy Absrac This paper uses one-minue reurns on he TOPIX and S&P500 o examine he efficiency of he Tokyo and New York Sock Exchanges. Our major finding is ha Tokyo complees reacions o New York wihin six minues, bu New York reacs wihin foureen minues. Dividing he sample period ino hree subperiods, we found ha he response ime has shorened and he magniude of reacion has become larger over he period in boh markes. The magniude of response in New York o a fall in Tokyo is roughly double ha of a rise. JEL Classificaion Numbers: G14, G15, F36 Keywords: inernaional linkage, sock prices, marke efficiency, high frequency daa Correspondence: Yoshiro Tsusui Kenjiro Hirayama Graduae School of Economics School of Economics Osaka Universiy Kwansei Gakuin Universiy 1-7 Machikane-yama, Toyonaka Uegahara, Nishinomiya-shi Japan Japan Phone: Phone: Fax: Fax: * We are especially graeful o he anonymous referee of his journal for many consrucive commens which led o subsanial improvemens. An earlier version of his paper was presened a MEW (he Moneary Economics Workshop), he 11h annual convenion of he Nippon Finance Associaion, and he Spring Meeing of Japan Economic Associaion. The auhors are graeful for helpful commens by Masayuki Ikeda, Hideaki Kao, Toshio Seria, and paricipans a he workshop.

3 1. Inroducion Sock prices of major economies are well known o be inerdependen, and here is an exensive lieraure on inernaional sock price linkage (Eun and Shim 1989, Jeon and von Fursenberg 1990, Mahur and Subrahmanyam,1990, Jeon and Chiang 1991, Chan e al. 1992, Kasa 1992, Corhay e al. 1993, Blackman e al. 1994, Chung and Liu 1994, Choudhry 1994, 1997, and Hirayama and Tsusui, 1998a, 1998b), including a few research papers which invesigae he possible causes of he linkage (Tsusui 2002, Tsusui and Hirayama 2004b, 2005). One of he findings in his lieraure is ha a counry s sock prices end o advance when a neighboring marke, closing jus before ha of he counry s marke, has advanced (Tsusui and Hirayama 2004a). Therefore, one can predic he course of he sock price index of he Tokyo sock marke, such as he TOPIX or he Nikkei 225, by observing wheher he sock price indices of he New York sock marke, such as he S&P500 and he New York Dow Jones Indusrial Average (henceforh known as NYDJ), have advanced or declined. This predicabiliy migh seem o conradic he marke efficiency hypohesis, bu such is no he case. When he New York Sock Exchange (NYSE) is open for rading, he Tokyo Sock Exchange (TSE) is closed due o ime differences. Consequenly, one mus wai for he opening of he TSE o execue ransacions based on he new informaion from New York. If he Tokyo sock marke is efficien, he TOPIX reacs fully o he informaion of he S&P500 on he previous day a he opening bu is no influenced hereafer. Using daily opening and closing values, Tsusui (2002) found ha he Nikkei 225 reacs o a large change (over 1.5%) of NYDJ by he closing ime of he nex day, and he Nikkei 225 does no show a significan change beyond he following day. Thus, he Tokyo sock marke is efficien over he daily ime span. Alhough he sudies above use daily observaions a bes, here is a body of lieraure ha uilizes 1

4 1 observaions of high frequency. The markes for foreign exchange and ineres rae fuures seem o reac exremely rapidly o macroeconomic news announcemens, e.g., wihin fory seconds according o Ederingon and Lee (1995) and Almeida e al. (1998). However, equiy markes respond more slowly o earnings and dividend announcemens, requiring en o fifeen minues (Paell and Wolfson 1984). The response of he S&P500 index o unexpeced changes in he money supply and Consumer Price Index (CPI) is compleed wihin one hour (Jain 1988). In his paper, we will employ one-minue reurns on he TOPIX and he S&P500 o analyze he speed of reacions of each sock exchange o he oher. The only work hus far, o our knowledge, using inraday daa in a sudy of he price linkage beween he U.S. and Japanese sock markes is ha of Becker e al. (1992). They used hourly daa for he S&P500 and Nikkei 225 Indices from Ocober 5, 1985 o December 31, They calculaed he correlaions beween hourly reurns of one counry wih he oher counry s daily reurn of he previous day. 2 They found ha he effec of he previous day s Nikkei reurn on he subsequen S&P500 reurns is absorbed wihin he firs half hour afer opening in New York, while he effec of he previous day s S&P500 reurn on he subsequen Nikkei reurns is absorbed wihin he firs hour of rading in Tokyo, and ha he effec of he lagged S&P500 reurns on he subsequen Nikkei reurns is larger han he reverse effec. Thus, he sock markes in Tokyo and New York seem o absorb he effecs from he oher sock exchange raher rapidly. However, due o he hourly observaions ha hey used we canno infer how speedily he effecs are absorbed. This paper uses high-frequency daa o examine how fas he Tokyo and New York sock markes respond o each oher. We obained he ick daa for he S&P500 from Tickdaa.com and he TOPIX daa a one-minue inervals from he Tokyo Sock Exchange. 3 Our daa sared earlier, bu o avoid he 1 For an overall inroducion o high-frequency finance, see Dacorogna e al. (2001). Goodhar and O Hara (1997) is also a good review and companion papers in he same Journal of Empirical Finance, vol. 4, no. 2-3 are research resuls wih high-frequency daa. 2 Since he New York Sock Exchange opens a 09:30 EST, he firs US reurn of he day is a half-hour reurn from 09:30 o 10:00. 3 The TOPIX is a capializaion-weighed index of all he socks lised on he Tokyo Sock Exchange. 2

5 exreme effecs of Black Monday, we discarded daa before December The las day for our sample was November 27, Since our sample period is considerably longer han ha used in Becker e al. (1992), we can also examine wheher here was a change in his reacion ime during he sample period. In his paper we measure how quickly he reacion o he oher marke a he opening dissipaes. However, he shor reacion ime does no necessarily imply he marke efficiency when one uses high-frequency daa. For example, he marke microsrucure may explain he difference in reacion ime. Specifically, he TSE acceps buy and sell orders for one hour prior o he marke opening and he opening price is deermined by he bach process known as iayose. 4 The NYSE, on he oher hand, does no accep orders before he marke opening and he prices are formed by coninuous aucion. This difference in rading rules apparenly leads o differen reacion ime. Anoher microsrucure effec arises due o nonsynchronous rading. 5 I is known ha nonsynchronous rading resuls in serially correlaed sock reurns (Lo and MacKinlay 1990). 6 The lengh of reacion ime is, hus, affeced by such microsrucure effecs. If he preceding US (Japan) closing price affecs he opening price in Japan (he US) sysemaically and significanly, he reurn volailiy a he beginning of daily rading ends o be larger. Indeed, i is well-known ha he inraday reurn volailiy is W-shaped in Japan (Andersen, Bollerslev, and Cai 2000) and U-shaped in he US (Andersen and Bollerslev 1997), boh of which imply high volailiy a he opening. Thus, his sudy also consiues an analysis of microsrucure of he sylized fac of high 4 Opening and closing prices of he morning and afernoon session of he Tokyo Sock Exchange are formed by a bach process, called iayose, while oher rades during he day are carried ou by coninuous rading, called zaraba. Amihud and Mendelson (1991) analyze iayose sysem and argue ha his difference in he wo price formaion processes, iayose and zaraba, may produce differences in prices and rading volumes. 5 The bid-ask bounces are also known o affec auocorrelaion in sock reurns (Roll 1984). However, hey resul in negaive auocorrelaion while we are concerned wih posiive auocorrelaion in sock price index reurns such as S&P500 or TOPIX. 6 They proved ha he degree of auocorrelaion becomes sronger, he higher he probabiliy of nonrading for a given ime inerval. Tsusui, e al. (2007) repor ha his probabiliy of nonrading is greaer in he NYSE han in he TSE. 3

6 volailiy a he beginning of NYSE and TSE. The res of he paper is organized as follows. In Secion 2 we discuss inraday paerns of one-minue sock reurns in Tokyo and New York. Secion 3 analyzes he speed of reacion o he oher marke changes and Secion 4 presens analyses wih subperiods. In Secion 5 we focus on posiive and negaive marke changes and analyze wheher here is an asymmery in reacion. Secion 6 concludes he paper. 2. Inraday paerns of one-minue sock reurns 2.1 Inraday paerns of TOPIX reurns We obained he TOPIX daa a one-minue inervals from 09:01 o 15:00 JST (Japan Sandard Time) from May 23, 1987 o November 27, 2003 from he Tokyo Sock Exchange. There was a wo-hour lunch break beween 11:00 and 13:00 unil April 26, 1991 and a 90 minue lunch break beween 11:00 and 12:30 afer April 30, Alhough he acual saring dae of our daase is May 23, 1987, we deleed observaions up o he end of 1987 in order o avoid overwhelming influence of he Black Monday. One-minue reurns of he TOPIX are compued as: TOPIX a TOPIX a 1 RJ = 100, (1) TOPIX a 1 where is a four-digi number denoing he hours and minues in Japan Sandard Time and 1 refers o he ime one minue before. I akes on values from 0901 o 1100 for he morning session and from 1231 o 1500 for he afernoon session. 7 The noaion, , means 0959, bu refers o 1500 of he previous day. Therefore, noe ha RJ0901 is acually an overnigh reurn from he previous day s close a 15:00. Likewise, is acually 1100, because here is a lunch break. Hence, RJ1231 is a 90-minue reurn from 11:00 o 12:31. 7 Due o a longer lunch break, sars a 1301 and ends a 1500 for he afernoon session unil April 26,

7 These TOPIX reurns, RJ0901,, RJ1500, are averaged across days during he sixeen-year period (January 1988 o November 2003), and hese means are ploed in Figure 1 along wih 95% confidence bands based on he null of a zero mean. We observe he following five characerisics of inraday one-minue sock reurns in Tokyo. 1) The firs four minues immediaely following a day s opening exhibi significanly posiive reurns. 2) There are significanly posiive reurns for abou six minues before a day s closing. 3) There are significanly negaive reurns for abou en minues afer he opening (12:31) of he afernoon session. 4) One-minue reurns end o be negaive afer he firs eigh minues of he day s opening. Ou of 52 one-minue reurns from RJ0909 o RJ1000, here are 25 significanly negaive values a a 95% level. 5) Mos reurns oher han he above are saisically no differen from zero during he day. There are only six cases of significan non-zero means for 60 one-minue reurns during 10:01 and 11:00. For he inerval beween 12:41 and 14:54, here are 11 such means ou of 134 one-minue reurns. Using five-minue reurns of he Nikkei 225 Index, Andersen e al. (2000) examined heir volailiy during he period from 1994 o The mean reurns averaged across days are ploed in heir Figure 1A and hese conform o poins 2, 3, and 5 above. Alhough he firs observaion of he morning session in heir paper exhibis a negaive reurn, his is due o heir deleion of he daily iniial observaion (from 9:00 o 9:05). 8 Table 1 liss summary saisics of seleced daily TOPIX reurns. To es for serial correlaion up o he fifh order, we use Diebold s heeroscedasiciy-adjused Ljung-Box saisic (Diebold 1986, Silverpulle and Evans 1998), because sock reurns are widely known o have ARCH effecs. The serial correlaion hus measured is significan a or immediaely following he opening of eiher morning or afernoon session and reurns for a longer ime period such as RJCC or RJOC. Bu mos of oher 8 Normaliy ess are no shown here, because he Jarque Bera measure indicaes overwhelming rejecion of normaliy in every variable. 5

8 one-minue reurns are no serially correlaed. In Table 1 RJ0901 is acually he daily close-o-open overnigh reurn, he mean of which is posiive, whereas he daily open-o-close reurn (RJOC) is negaive. There is a endency for he TOPIX o rise during he nigh bu o decline during he rading hours (Tsusui 2003). The morning reurn beween 09:01 and 12:31 (RJMN) ends o be negaive, bu he afernoon reurn beween 12:31 and 15:00 (RJAN) posiive. The volailiy as measured by he sandard deviaion is higher a he opening of eiher he morning or he afernoon session and a he closing of he day. However, he very high sandard deviaion of RJ0901 can be regarded as a naural resul of a long ime period for his overnigh reurn. RJ0901 is observed on a 1,080-minue inerval (18 hours from 3 pm o 9 am he following morning). One may have o adjus for his long inerval depending on heir purpose of he sudy. If one wans o assess he magniude of informaion flow, he or she will compare he sandard deviaion per minue, which is during nigh. 9 We nex urn o he issue of inraday paern of volailiy. To measure volailiy in sock prices, we compued and graphed he mean of absolue TOPIX one-minue reurns (Fig. 2). Volailiy is high a he opening and closing of he morning and afernoon sessions (see also sandard deviaions in Table 1). The inraday volailiy has hree peaks, giving rise o a W-shaped paern, which is also repored for five-minue TOPIX absolue reurns by Andersen, Bollerslev, and Cai (2000). A he ime of marke opening, here is an accumulaed sock of new informaion which may resul in higher volailiy. This is wha we focus on in his paper, bu i does no explain he W-shaped paern enirely. The TSE 9 The logged sock price is known o follow a random walk model fairly well (or a Wiener process in coninuous ime) which has a propery ha he variance is proporional o he number of periods (or he duraion of he elapsed ime). Then, he sandard deviaion is proporional o he square roo of he observaion duraion. The ime lengh for RJ0901 is 1,080 imes he oher one-minue reurns. Thus, is sandard deviaion may be divided by he square roo of 1,080 o give (= 0.30 / 1080 ). The magniude of his looks small compared wih sandard deviaions of oher one-minue reurns which ypically have values around 0.03, signifying ha he informaion flow during non-rading hours is smaller ha ha during rading hours. However, in order o analyze he impac of he whole informaion accumulaed during non-rading hours, his per-minue sandardizaion does no seem appropriae. Indeed, he subsequen one-minue reurns, RJ0902 and RJ0903, have a sandard deviaion of and respecively, which is much larger han he per-minue value for RJ

9 deermines opening and closing prices of wo daily sessions by iayose mehod (TSE 2004, pp ) which coincides wih he hree peaks in volailiy, suggesing ha iayose is one of he causes for high volailiy (Amihud and Mendelson 1991). Since iayose reas all he ousanding orders as arriving a he same ime, he likelihood of successful ransacions is higher han during he normal zaraba aucioning. As a resul, more orders are accumulaed for he iayose aucion because of he reduced risk of non-execuion. This conribues o higher volume and volailiy a he opening and he closing of he wo sessions, giving a parial explanaion for hree peaks during a day. 2.2 Why does he TOPIX decline a he opening of he afernoon session? Wha abou he apparen endency of sock prices o decline a he opening of he afernoon session (poin 3 above)? Our conjecure is ha invesors give a second hough o rising prices a he opening. This may also be behind he endency of declining prices during 09:15 and 10:00 (poin 4 above). Correlaion coefficiens beween he overnigh reurn (RJ0901), he reurn during he lunch break (RJ1231), and he 45-min. reurn from 09:15 o 10:00 (denoed by RJ45M1000) are presened in Table 2. RJ0901 is negaively correlaed wih boh RJ1231 and RJ45M1000, which seems o suppor our view ha advances a he opening are correced aferwards. 10 Since correlaion coefficiens measure pair-wise relaionships only, we also ran some regressions o explain he negaive reurn a he opening of he afernoon session. We regressed he over-lunch reurn (RJ1231) on a consan, he overnigh reurn (RJ0901), five one-minue reurns immediaely preceding he lunch break, and he dependen variable lagged by one day. 11 The resul is shown under equaion (i) in Table 3. The coefficien on RJ0901 is negaive a a 15% significance level and he RJ1100 variable has also a highly significanly negaive effec on he dependen variable. 12 RJ1231 lagged one day has a 10 There is, however, sensiiviy o he choice of duraion. The 50-min. reurn from 09:10 o 10:00 (RJ50M1000) is posiively correlaed wih RJ See he nex secion for he deails of his regression specificaion. 12 In his paper Whie s robus sandard error is used o evaluae he significance in regressions. This 7

10 significanly posiive effec. Overall his regression gives an adequae explanaion of RJ1231. Before inroducing he 45-min. reurn, RJ45M1000, o he regression for RJ1231, le us consider wha effecs i may have on RJ1231. There are wo views. Firs, suppose ha he size of correcion o an over-reacion a 09:01 is deermined firs and ha i is divided ino RJ45M1000 and RJ1231. Then, if sufficien second hough is given during he 45-min. inerval up o 10:00, he exen of correcive reacion a 12:31 mus be small, making he coefficien on RJ45M1000 negaive. Second, suppose ha he size of correcion is no immediaely known bu is gradually revealed during he acual rading session. Then, if a relaively large adjusmen occurred in RJ45M1000, i would lead o a furher adjusmen afer lunch. In his insance, he coefficien on RJ45M1000 in a regression for RJ1231 ends o be significanly posiive, indicaing a furher, srenghened correcion afer lunch. In any case, he lunch break gives invesors furher ime o reconsider he excessive rise a he opening of he day. Equaion (ii) of Table 3 is he resul of regressing RJ1231 on a consan, he overnigh reurn a he opening (RJ0901), and he 45-min. reurn o 10:00 (RJ45M1000). The coefficien on RJ0901 is negaive a a 15% significance level and ha on RJ45M1000 is posiive a a 0.3% level. This resul implies he second view above is appropriae. We added five lagged one-minue reurns and one-day lag of he dependen variable o he righ-hand side and he basic resul is he same in his equaion (iii) of Table 3. These resuls imply ha he mean negaive reurn a he opening of he afernoon session is a reacion o he mean posiive reurn a he opening of he morning session. Having lunch gives invesors reflecive ime o diges he excessive rise a he day s opening. 2.3 Inraday paerns of S&P500 reurns For he U.S. sock prices we obained ick daa on S&P500 from January 2, 1987 o November 27, procedure adjuss for serial correlaion and heeroscedasiciy. 8

11 2003. As noed above, we discard observaions up o he end of We compue one-minue reurns of S&P500 as: S & P500 a S & P500 a 1 RU = 100. (2) S & P500 a 1 Since he New York Sock Exchange opens a 09:30 and closes a 16:00, akes on values from 0931 o Unlike Tokyo, he NYSE has no lunch break and rades shares coninuously for six and a half hours every day. The ime difference beween Tokyo and New York is foureen hours (hireen hours during he Dayligh Saving Time period). Expressed in Greenwich Mean Time, he rading hours are from 0:00 o 6:00 GMT in Tokyo and from 14:30 o 21:00 GMT in New York. Thus, he wo markes are never synchronously open. Mean one-minue reurns of S&P500 are ploed in Figure 3 along wih 95% confidence bands based on he null of a zero mean. We observe he following feaures from his Figure similar o hose of TOPIX one-minue reurns: 1) The firs seven minues afer he day s opening end o exhibi significanly posiive reurns. However, heir absolue magniude is smaller han ha of Tokyo. 2) The las four minues before he day s closing are also significanly posiive, bu heir absolue magniude is smaller han in Tokyo or he firs few minues afer opening. 3) Some of he reurns end o be negaive beween 9:51 and 10:13. Ou of 23 one-minue reurns during his inerval, nine are significanly negaive. 4) Excep for hese inervals noed above, mos of he mean reurns are saisically no differen from zero. Ou of 343 one-minue reurns during 10:13 and 15:56, only 28 are significan a a 5% level. The correlaion coefficien beween he overnigh reurn a he opening (RU0931) and he 45-min. reurn from 09:45 o 10:30 is wih a -saisic of 2.54, he p-value of which is 1.1%, indicaing a significanly negaive correlaion. As in Tokyo, his may also imply ha he invesors in he NYSE give a second hough o he rise a and immediaely afer he day s opening. 9

12 13 Table 4 gives summary saisics for hese and oher daily reurns. Again he normaliy is overwhelmingly rejeced, hus no shown herein. Unlike he TOPIX, he S&P500 ends o rise during he rading hours (significanly posiive open-o-close reurn, RUOC). Mos of his rise during he dayime occurs in he afernoon (significanly posiive afernoon reurn from 13:01 o 16:00, RUAN). The volailiy is high when he marke opens, as indicaed by a high sandard deviaion of RU0931, bu i declines gradually over ime. 14 Unlike Tokyo, here is no increase in volailiy oward he end of he day. Serial correlaion is also presen a and immediaely following he opening or for daily reurns such as RUCC. Mean absolue one-minue reurns are ploed in Figure 4 o check for volailiy. I is very high a he marke opening, bu i dissipaes very rapidly and hen gradually decline oward he middle and hen again very slowly increases oward he closing of he marke. The graph does no show a ypical U-shaped paern, bu i is more like reverse J-shaped which is also poined ou by Goodhar and O Hara (1997, p. 86). 3. How quickly does one marke reac o he oher? 3.1 Correlaion coefficiens Since i is well known ha he wo sock markes affec each oher, our primary focus here is on deermining how rapidly his influence is absorbed afer he opening of a marke. As a preliminary 13 There is a sligh discrepancy in he daa for S&P500. The S&P500 price level a 16:00 is no precisely equal o he closing value as repored by he TickWrie, sofware provided by he daa vendor (TickDaa) o rerieve daa poins a desired frequency. I urns ou ha he original ick daa conain values a a few minues afer 16:00. The las value for he day is repored as he closing price. A similar discrepancy occurs wih he opening price. If wo or more daa poins exis beween 09:30 and 09:31, he las value is repored as he price a 09:31, bu he very firs value is repored as he opening price on a daily frequency. In empirical analyses below, he daily close-o-close or open-o-close reurns (RUCC and RUOC) and he like are based on rue opening and closing values. However, he difference is exremely small and he resuls are almos idenical even if he values a 09:31 and 16:00 are reaed as he opening and closing prices. 14 If he lengh of he overnigh nonrading is aken ino accoun, he sandard deviaion of RU0901 becomes ( = / 1050) and his appears o be oo small compared wih he following one-minue reurns. 10

13 invesigaion, we compue correlaion coefficiens beween he previous day s daily reurn in New York and each one-minue reurn in Tokyo. We denoe by RUCC he daily close-o-close reurn in New York on he previous day. 15 These correlaion coefficiens are displayed wih 95% confidence bands derived from he null of zero correlaion in Figure 5. They are posiive and of no small magniude unil 09:21. Namely, correlaions wih preceding RUCC 1 persis for abou weny minues afer he opening of he TSE. There are spikes a 09:01, 09:06, 09:11, 09:16 and 09:21, bu hey disappear when he sample period is resriced o before March Thus, hese spikes are mos likely relaed o five-minue periodiciy in auocorrelaion coefficiens which Tsusui e al. (2007) ascribe o he auomaic updaing of special quoes. 16 Afer 09:21 correlaion coefficiens are roughly close o zero, excep a and for several minues afer 12:31 (opening of he afernoon session) when hey are significanly negaive. Thus far, he paern is similar o ha of mean reurns of Figure 1. A noable difference exiss oward he end of he day. While mean reurns indicae ha sock prices rise oward he end of he day, hey are oally uncorrelaed wih previous day s movemens in New York. Nex we reverse he direcion and compue correlaion coefficiens beween each one-minue S&P500 reurn and he preceding daily close-o-close reurn observed in Tokyo (RJCC). In his insance, he daily reurn in Tokyo is he one observed on he same calendar dae as New York because he close of Tokyo a 15:00 JST is 01:00 EST (Easern Sandard Time) in New York and he NYSE opens is rading eigh and a half hours laer on he same day. These coefficiens are ploed in Figure 6. There are significanly posiive correlaions in he firs fifeen minues (unil 09:45), bu heir magniude is far less 15 Alhough his daily close-o-close reurn in New York is recorded on he previous calendar dae, i is observed only hree hours before he opening of he Tokyo marke since 16:00 in New York is 06:00 he nex day in Tokyo. 16 Special quoes are arranged by he TSE and issued whenever he nex equilibrium price is likely o exceed a cerain prescribed limi in order o bring marke paricipans aenion o a likely jump in sock price. If an announcemen of a special quoe fails o cause a successful rade, he nex special quoe a a one-noch higher or lower price is announced auomaically a a five-minue inerval, which seems o cause a serial correlaion in sock price index a hese inervals. 11

14 han ha of Tokyo. Afer he iniial responses, coefficiens seem o be random around zero. In boh Tokyo and New York, he responses o he oher s daily movemens dissipae wihin he firs fifeen o weny minues of daily rades. Thus, informaion from he oher marke seems o be raher quickly absorbed. 3.2 Regression analysis: effec of New York on Tokyo The main purpose of his paper is o deermine how he oher marke affecs one-minue reurns of he day and especially how rapidly he effecs are dissipaed a he opening of daily rades. In order o invesigae his effec, regression analysis aking ino accoun oher effecs on he sock reurns may be more appropriae han compuing simple correlaion coefficiens. One-minue reurns averaged across days as ploed in Figures 1 and 3 exhibi non random behavior immediaely afer he opening and oward he closing of he day. In Tokyo, he reurns are significanly negaive a and afer he opening of he afernoon session. This paern may be evidence of serial correlaion ha persiss for a few minues. In addiion, as discussed above, reurns are correlaed wih he same values of he previous day, indicaing a daily periodiciy. A model of his influence should ake ino accoun boh shor-run serial correlaion and daily periodiciy. Thus, our model of one-minue TOPIX reurns is specified as follows: 5 i RJ = α + β RJ ( i) + γ RJ 1 + δ RUCC 1 + u i= 1, (3) where refers o a ime of he day in hours and minues and i indicaes he ime i minues prior o. In he case of TOPIX reurns, akes he values from 0901 and 1100 for he morning session and from 1231 o 1500 for he afernoon session (from 1301 o 1500 before April 26, 1991 due o a longer lunch break). Therefore, (1000 3) refers o 09:57. However, (0901 1) and (0901 2) indicae 15:00 and 14:59 of he previous day respecively. Likewise, (1231 1) denoes 11:00 12

15 due o he lunch break. The subscrip denoes a dae during our sample. The second erm on he righ-hand side of equaion (3), RJ ( i), capures serial correlaion ha lass a few minues. Due o he five-minue periodiciy repored in Tsusui, e al. (2007), he lag order is se a five for his erm. The hird erm RJ, 1 is insered o accoun for daily periodiciy. RUCC 1 is he explanaory variable ha is he focus of his exercise and is a daily close-o-close S&P500 reurn observed jus prior o he opening of daily rades in Tokyo. δ capures he effec of he previous day s close-o-close reurn in New York on each one-minue reurn in Tokyo. Since he Tokyo Sock Exchange is open for four and a half hours each day, here are 270 one-minue reurns every day, and we ran 270 regressions for each reurn and obained as many coefficien esimaes for δ. The sample period is from January 5, 1988 o November 27, 2003, and he number of observaions is 2,374 for reurns from 12:31 o 13:00 and 3,001 o 3,034 for ohers. 17 Esimaion resuls of equaion (3) a 9:01, 12:31, and 14:00 are presened in Table 5. The resul for 14:00 (RJ1400) is given as a ypical example of all oher regressions. Figure 7 plos 270 regression esimaes of δ ogeher wih heir 95% confidence bands. I shows ha δ 0901 is abou 0.18 and ha he coefficiens decline rapidly. Mos of he coefficiens afer 09:06 are rifling in magniude and are no significanly differen from zero. In oher words, he Tokyo Sock Exchange reacs o he previous day s movemens in New York wihin he firs six minues afer opening. This reacion speed is much faser han ha indicaed by he correlaion coefficiens of Figure 5 which exhibi posiive correlaion wih RUCC 1 up o around 09:21. These correlaion coefficiens only capure he pairwise relaion beween each one-minue reurn and RUCC 1, hence hey do no accoun for he lagged effecs of immediae pas reurns. However, he regression equaion akes serial correlaion ino accoun by adding lagged one-minue reurns (he second erm on he righ-hand side of equaion (3)). In fac, hese lagged series 17 The sligh difference in he number of observaions is due o: 1. a few missing values, 2. a peculiar convenion in he TSE whereby only morning sessions are held on he las and firs day of he year, 3. during he earlier par of he sample period (before February 1989), wo or hree Saurdays per monh were open for rading, bu were only for he morning session. 13

16 are significanly posiive in mos regression equaions. Anoher ineresing finding from he regressions is ha, while reurns in he pas few minues usually have a posiive effec on he subsequen reurns (see righ columns of Table 5), he las reurn of he day (RJ1500) has a significanly negaive effec on RJ0901 (see lef columns of Table 5). Is coefficien is wih a p-value of %. Anoher remarkable fac shown in he middle columns of Table 5 is ha he coefficien for RUCC 1 is significanly negaive in a regression for RJ1231, which means ha he opening price of he afernoon session reverses he reacion a he opening of he morning session. Furhermore, jus as RJ0901 reacs negaively o he previous day s closing (RJ ), RJ1231 reacs negaively o he closing of he morning session (RJ1100). The coefficien on RJ1100 in a regression for RJ1231 is wih a p-value of %. Jus one example of all oher mundane resuls is given by he regression for RJ1400, in which RUCC 1 is no significan. Three ou of five lagged one-minue reurns are significan, bu he independen variable lagged one day is no. One may wonder wheher our resuls are valid, when inraday seasonaliy is removed. Indeed, seasonal adjusmen on he firs momen does no change he resuls a all excep for he consan erm as far as he seasonal facors are consan during he season, because our regression equaion (3) essenially has daily frequency, which is esimaed for every minue. 18 We did run regressions wih seasonally- 18 Suppose we use a regression approach o achieve his. We firs run a regression of a long one-minue sock reurn series on 270 dummy variables each of which represens a specific ime during he day. A dummy variable for 09:01 is equal o uniy a his ime of day, bu is zero for all oher minues. A 09:02 dummy akes he value of uniy a 09:02, bu is zero oherwise, ec. One can easily ascerain ha he esimaed coefficien on each dummy is equal o he average of associaed one-minue reurn across days. Hence, denoing such a mean by μ, he deseasonalized series is simply RJ μ, which implies he adjused series has a zero mean. Therefore, he above equaion (3) now becomes, 5 i μ = α + β [ RJ ( i) μ i ] + ( RJ 1 ) + γ μ δ RUCC 1 u, bu, his RJ + i = 1 simplifies o i [ ].This RJ μ = α + β RJ( i) μ + γ ( RJ μ + δ RUCC + u 5 i 1 ) i=

17 adjused daa, and we confirmed he above proposiion. How abou seasonal adjusmen for he second momen? The price volailiy in he beginning of a marke is well known o be high, as was confirmed in Figure 2. One of he causes for his is he revelaions of new informaion during he nonrading hours and he closing price a he NYSE is probably he single mos imporan facor. 19 If we make seasonal adjusmen for he variance, e.g. applying he mehod of Andersen and Bollerslev (1997), o ge rid of he high volailiy, i will dampen he effec of New York s closing price on he NIKKEI a he beginning. 20 We are rying o deermine he cause of high volailiy a he marke opening, and herefore, adjusing he seasonaliy in inraday volailiy is incompaible wih wha we are rying o esimae in he sense ha he magniude of he response of Tokyo o New York is alered. However, since he -value of he esimaed coefficien does no change, how fas Tokyo absorbs he effec of New York s closing price is no alered. The imporance of New York o Tokyo s marke opening can be shown by simple arihmeic. The sandard deviaion of RJ0901 is 0.30 (Table 1). The regression of RJ0901 on RUCC gives an esimaed coefficien of (Table 5). When we muliply he sandard deviaion of RUCC (=1.04 according o Table 4) by his coefficien, he produc becomes 0.18 approximaely. More han half of he sandard equaion differs from (3) only in he consan erm. Oher explanaory variables are exacly he same as in (3). 19 The imporance of New York o Tokyo s marke opening can be shown by simple arihmeic. The sandard deviaion of RJ0901 is 0.30 (Table 1). The regression of RJ0901 on RUCC gives an esimaed coefficien of (Table 5). When we muliply he sandard deviaion of RUCC (=1.04 according o Table 4) by his coefficien, he produc becomes 0.18 approximaely. More han half of he sandard deviaion of RJ0901 is explained by he effec of RUCC. 20 Andersen and Bollerslev (1997) analyze inraday seasonaliy in volailiy as follows. The high-frequency / 2 reurn on day, period n is denoed by R and hey assume a decomposiion, R 1 where N,, n = N σ s n Z, n, n is he number of periods per day, σ is he volailiy level for a specific day, s n is he seasonal inraday volailiy componen, and Z, n is an i.i.d. mean zero, uni variance error erm. Inraday seasonal volailiy is esimaed by applying he flexible Fourier form and he original reurn series is divided by esimaed ŝ n o give a seasonal-volailiy adjused series. If we applied his adjusmen o our one-minue reurns, he esimaed coefficien in equaion (3) would be divided by his facor, ŝ n. However, because he sandard error is also divided by his facor, he -value is unaffeced. 15

18 deviaion of RJ0901 is explained by he effec of RUCC. All his shows he imporance of New York s closing price in explaining a high volailiy a he marke open in Tokyo. Inraday seasonaliy in sock price volailiy is parly a resul of influences from New York. 3.3 Regression analysis: effec of Tokyo on New York Nex, we examine he effecs of he Tokyo sock marke on New York. We regress each of RU (one-minue reurns of S&P500 a each minue of he day ) on a consan, lagged one-minue reurns of he preceding hree minues, he reurn a he same ime he day before, and a daily close-o-close reurn observed in Tokyo prior o he opening of he NYSE: 3 i RU = α + β RU ( i) + γ RU 1 + δ RJCC + u i= 1, (4) where RJCC is he daily close-o-close reurn of he TOPIX observed eigh and a half hours before he opening of he New York sock marke. As in equaion (3), we include lagged one-minue reurns (he second erm on he righ-hand side of (4)), bu he lag order is hree, which seems o be enough o capure he very shor-run serial correlaion in RU. Esimaion resuls a 09:31 and 15:00 are presened in lef and middle columns of Table 6. When he NYSE opens in he morning, RJCC has a significanly posiive and he lagged dependen variable (RU ) a significanly negaive effec on RU0931. Bu he previous day s final one-minue reurn a he closing has no effec. The resul for RU1500 is displayed as a ypical example of all oher regressions, where RJCC has no effec. Of he hree lagged one-minue reurns, only ha of one minue previously is significan. The dependen variable lagged one day is no significan eiher. The esimaed coefficiens on δ are presened in Figure 8. Comparing Figure 8 wih Figure 7, we iniially noice ha he firs several coefficiens in Figure 6 are significan bu ha hey are much 16

19 smaller in magniude han hose in Figure 7. Thus, he effec of he Tokyo sock marke on he New York marke is far weaker han he reverse effec. There are possibly wo reasons for he small effec of Tokyo on New York. Firs, he U.S. economy is apparenly more imporan o he Japanese economy han he oher way round. In fac, he dominan effec of he U.S. sock prices on oher counries sock prices is well documened in many sudies (e.g., Eun and Shim 1989). Second, alhough New York is he neares predecessor o Tokyo, closing righ before Tokyo opens, he NYSE opens eigh and a half hours afer he TSE closes. In he meanime Frankfur and London sar heir daily rading before New York. Tsusui and Hirayama (2004a) analyze hese four counries using daily closing prices and repor a finding ha he marke which closes immediaely before one marke has he larges effec. In ligh of his finding, i would be naural o have a small effec of Tokyo on New York due o he inervening effecs of Frankfur and London. To accoun for hese effecs, we include he daily close-o-close reurn in FAZ Index of Frankfur Sock Exchange (RGCC ) in he regression equaion: RU = α + 3 i= 1 + γ β i RU( i) RU 1 + δ RJCC + ε RGCC + u, (5) where ε capures he effec of Frankfur on New York. The effec of London s daily closing canno be incorporaed, because London s closing ime is laer han he opening of he NYSE. London closes is daily rading a 16:30 GMT, which is 11:30 EST in New York. Namely, when New York opens a 09:30 local ime, London s closing value is no ye known. Thus, we had o drop London s daily close-o-close reurn variable. 21 The Frankfur Sock Exchange, on he oher hand, is open for rading beween 10:30 and 13:30 local ime. This closing ime is wo hours before opening of New York. Frankfur s daily close-o-close reurn is known o New York, he effec of which is capured by ε 21 If we had inra-day daa of London, we could compue a reurn up o he ime of New York s opening o capure he effec of London on New York. Unforunaely we could obain only daily closing prices for London and Frankfur, which compelled us o disregard his effec of London. 17

20 in equaion (5) above. We ran a regression for his equaion and he esimaed ε 0931 is abou (see he righ columns of Table 6) which is greaer han δ = in equaion (4) (see he lef columns of Table 6). However, i is only one-quarer of he effec of New York on Tokyo (see he lef columns of Table 5 and ). The resul seems o vindicae our wo conjecures above offered as an explanaion for he small effec of Tokyo on New York. Though his smallness is parly caused by he inervening marke in Frankfur, Frankfur s effec on New York is also very small compared wih he effec of New York on Tokyo, which implies a dominan influence of New York on oher markes. We repor, in passing, he esimaed δ 0931, he coefficien on he firs one-minue reurn afer opening, in equaion (5). I is now 0.015, which is roughly half ha in equaion (4). δ 0932 is also significanly posiive, bu no afer hese firs wo minues. This reducion implies ha abou half of Tokyo s effec on New York as measured by equaion (4) is absorbed by Frankfur. Nex, in Figure 8, coefficiens up o RU0944 end o be significan, which means i akes he NYSE abou foureen minues o absorb new informaion from Tokyo. Closer inspecion reveals ha eigh ou of foureen coefficiens on RJCC are saisically significan. When we examine he effec of Frankfur on New York in equaion (5), i is significan for mos of he firs fifeen minues afer 09: Since he reacion ime is six minues in Tokyo, he reacion ime of New York is longer han ha of Tokyo. This difference in reacion ime does no necessarily reflec differences in efficiency. I may be explained by he fac ha he opening price of he Tokyo Sock Exchange is formed by a bach process (iayose, see Foonoe 4), in which rading orders are acceped during sixy minues prior o he marke opening a 09:00. However, in he New York Sock Exchange, he usual coninuous rading process deermines he opening price. Anoher reason for his difference may be due o differen degree of nonsynchronous rading. 22 This coefficien of does no change much even if RJCC is excluded from equaion (5). 23 This resul is basically unalered even if RJCC is dropped from equaion (5). 18

21 3.4 Wha reurns do he markes reac o? In he previous secion, we assume ha he markes reac o daily close-o-close reurns. Since he media, such as TV and newspapers, regularly announce his reurn, his assumpion is reasonable. In his subsecion, we will invesigae wheher he markes reac o he informaion from more specific periods han he close-o-close reurn. The close-o-close reurn of he TOPIX (RJCC) can be divided ino a close-o-open reurn (RJ0901; nonrading-hours reurn) and an open-o-close reurn (RJOC; rading-hours reurn). RJOC can furher be divided ino a morning reurn (RJMN; 9:01 o 12:31) and an afernoon reurn (RJAN; 12:31 o 15:00). Likewise, he close-o-close reurn of S&P500, RUCC, is divided ino a close-o-open reurn, RUCO, an open-o-close reurn, RUOC, a morning reurn, RUMN, and an afernoon reurn, RUAN, where morning means 9:31 o 13:00 and afernoon is 13:01 o 16: Le us firs look a correlaions beween hese reurns. While RUOC highly correlaes wih RUCC (coefficien is 0.995), he correlaion coefficien beween RUCO and RUCC is only Acually, RUOC is almos idenical o RUCC, which can also be ascerained by heir means and sandard deviaions in Table 4. This fac leads us o expec ha he Tokyo marke reacs o RUOC jus he same way as o RUCC in equaion (3). Indeed, replacing RUCC wih RUOC in regression equaion (3) yields nearly he same resul. The same applies o RJOC and RJCC in equaion (4). In order o find ou which reurn he markes reac o, we compare he explanaory power of he reurns in equaion (3) or in equaion (4). For he ease of exposiion, le us refer o equaion (3) as Model A and he equaion in which RUCC is replaced wih RUOC, RUCO, RUMN or RUAN as Model B. Consrucion of hese models requires a non-nesed es, because neiher is a subse of he oher model. 24 RUCO is he close-o-open overnigh reurn, which is slighly differen from RU0931 ha is defined as he reurn beween 16:00 in he previous day and 09:31. See Foonoe

22 In his paper we apply Deaon s F es (Deaon 1982). In his es, we compare Model A and B, and focus on he variables ha are no included in he oher model. In he es of Model A (equaion 3) vs. Model B (RUxx replaces RUCC in equaion 3), equaion (3) is run firs; hen we add he alernaive reurn variable and es he explanaory power of his variable by a sandard F es (equivalen o a es, since here is only one addiional variable). If he addiional variable is saisically significan, Model B is seleced over Model A. In he es of Model B vs. Model A, Model B is run firs; hen we add RUCC and es he explanaory power of RUCC. If RUCC is significan, Model A is seleced over Model B. Naurally, a pair of hese ess may no produce an unequivocal resul. P-values of he es for he firs seven minues of TOPIX reurns are presened in Table 7, since he firs six minues are he ime he Tokyo marke significanly reacs o New York. In he lef columns, we compare addiional explanaory power of RUOC and RUCC. When RUOC is added o equaion (3) (Model A), RUOC is significan a a 10% level for hree cases ou of seven (see he second column). 25 The hird column shows he resuls when RUCC is added o Model B. Three cases ou of seven cases are significan, implying RUOC and RUCC have almos he same explanaory power. The resul is reasonable because RUOC and RUCC are almos idenical series. Comparing RUCO and RUCC, while RUCC is significan in six cases, RUCO is significan only in wo cases. This implies ha he close-o-close reurn is more imporan and is he one focused on by Japanese invesors. Similar resuls are obained for he morning reurn (RUMN) and he afernoon reurn (RUAN). In summary, Table 7 suggess ha he Tokyo marke waches he close-o-close reurn (RUCC) more han oher reurns, probably because his is wha he media usually repors. RUOC has srong explanaory power simply because i is almos idenical o RUCC. The same procedure is applied o equaion (4) o compare he explanaory power of RJCC wih oher reurns such as RJOC and he resuls for he firs fifeen minues are shown in Table 8. In he firs 25 We also provide he number of significan cases a a 5% level in he Table, which leads o he same conclusions. 20

23 pair, RJOC is significan in four cases a a 10% level, while RJCC is significan in six cases. RJ0901 is significan in four cases, and RJCC in eleven cases. RJMN is insignifican in all cases and RJAN is significan only in one case. RJCC is significan in eigh and seven cases in he las wo pairs of ess in Table 8. These resuls sugges he same conclusion as he Tokyo marke: he close-o-close reurn of TOPIX is wha he U.S. invesors focus on. 4. Changes in he linkage over sub-periods In order o examine wheher he response paern has changed during our sample period, we divide he whole sample ino hree subperiods and conduc he same analysis of he previous secion. We examined he daily closing prices of S&P500 and TOPIX for our sample period and divided he whole period ino he following hree subperiods 26 : Period I: January 5, 1988 o December 31, 1989 when sock prices exhibied an upward rend in boh he U.S. and Japan. Period II: January 4, 1990 o Ocober 15, 1998, when sock prices in he U.S. exhibied an upward rend, while hose in Japan fell significanly a firs and were sagnan hereafer. Period III: Ocober 16, 1998 o November 27, 2003, when sock prices in boh counries moved in a similar fashion, exhibiing an invered U-shaped paern. We regress equaion (3) by OLS and he sum of coefficiens on RUCC 1 in regressions for RJ cumulaed over each one-minue inerval is depiced in Figure 9 for he Tokyo sock marke. Thus, he graph shows cumulaive effecs of he S&P500 on he TOPIX during he course of a day s rading. Individual coefficiens are saisically significan only a he beginning of he day. Ohers are seldom significan, hus rendering he cumulaive sums saisically no very meaningful. However, even hough hey are no differen from zero saisically, whenever hey end o be posiive over 26 We should ideally search for break poins by conducing srucural break ess. However, equaion (3) consiss of 270 regression equaions and each one of hem has o be subjeced o such a es. We will hen have 270 ses of break poins. There is no esablished mehod o aggregae hose ino a single se. Namely i seems quie difficul o specify break poins uniquely wih hese ess. Hence we give hese poins exogenously. 21

24 successive minues he cumulaive sum ends o rise, which does imply ha he effec from he oher marke is cumulaively posiive. Thus, aside from sric saisical significance, we can infer a general direcion of he oher marke s influence during he day from his graph. Figure 9, which plos hese cumulaive sums for hree subperiods, reveals he following: 1)The lengh of reacion ime has decreased over he sixeen-year period. In Period I, posiive responses coninue unil around 09:30 and hereafer negaive responses follow during he morning session. In Period II, posiive responses dissipae by around 09:15 and he decline aferwards is much smaller. Period III exhibis a rapid increase afer he opening and he peak is observed a 09:06. 2) The magniude of he cumulaive reacion has become greaer, from around 0.1 for Period I o 0.3 for Period III. Two reasons can be offered. One is ha he increase reflecs inensified economic inegraion beween he U.S. and Japan. The oher is ha he relaive size of he Tokyo sock marke o he New York sock marke, as measured by annual urnover, has declined over he period. Tokyo s urnover exceeded ha of New York in 1988 and However, he Japanese sock prices have declined and sagnaed since hen, whereas he New York marke has seen a specacular rise in he 1990s. Thus, he U.S. urnover has grown remendously, dwarfing ha of Tokyo. 3) A negaive response a he opening of he afernoon session is visible in all hree subperiods. 27 Cumulaive sums of coefficiens on RJCC in regression equaion (4) for he New York sock marke are displayed in Figure 10. The speed of reacion has become greaer from Period I o Period II. Specifically, posiive responses, small in magniude, coninue for abou wo hours afer he opening in Period I, bu in Periods II and III iniial posiive responses abae in abou fifeen minues afer opening. The overall magniude of cumulaive responses is much higher in Period III han in Period I or II. However, i is much smaller han ha of Tokyo. This is probably due o he relaive imporance of he economy. 27 In Period I when he afernoon session sared a 13:00 his negaive response is observed a 13:01. 22

25 5. Is here asymmery in he reacion as he oher marke rises or falls? In order o see if here is asymmery in responses o he oher marke s rise or fall, we regress Japanese reurns on posiive RUCC 1 and on negaive RUCC 1 separaely. Alhough he regression equaion is equaion (3), we divide he observaions ino one group where RUCC is posiive and anoher where RUCC 1 is negaive. Thus, we ran wo ses of regressions. The resulan esimaes are displayed in Figure 11, in which cumulaive sums of coefficiens are shown. The cumulaive responses o he posiive and negaive RUCC 1 are remarkably similar. Likewise, esimaing equaion (4) wih posiive and negaive RJCC separaely, we compue he 1 cumulaive sums of coefficiens for he New York sock marke reacing o posiive and negaive RJCC values which are depiced in Figure 12. Unlike Tokyo, New York exhibis clear asymmery in reacion. Bad news from Japan has a considerably sronger effec on New York han good news. The magniude of he response in New York o a fall in Tokyo is roughly double ha of a rise. The response paern is also differen: when Tokyo has advanced, responses in New York are spread over a longer period, abou one and a half hours, bu when Tokyo has fallen, posiive responses swifly reach a peak wihin abou foureen minues. This asymmery in reacion o a rise or fall in Tokyo is in conras o he finding of Tokyo s symmeric responses o New York. 28 This asymmery in New York migh be srongly influenced by he rapid declines in he TOPIX during he period from January 1990 o July To check on his possibiliy, we divided he sample ino hree subperiods as above and ran he same regressions. We again obained asymmeric responses in New York o a rise or fall in Japan in all hree subperiods, indicaing asymmery hroughou he sixeen-year period. Why invesors in New York are more sensiive abou he fall in Tokyo is anoher agenda for fuure research. 28 Analyzing he daily sock price index daa from 1975 o 1995 for he U.S., he U.K., Germany, and Japan, Hirayama and Tsusui (1998b) found ha negaive large changes have a clearer effec han posiive ones. 23

Chapter 8: Regression with Lagged Explanatory Variables

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