Influence of he Dow reurns on he inraday Spanish sock marke behavior José Luis Miralles Marcelo, José Luis Miralles Quirós, María del Mar Miralles Quirós Deparmen of Financial Economics, Universiy of Exremadura Av. Elvas s/n 06071 Badajoz (Spain) Absrac In recen years differen sudies have analyzed he influence of he greaer equiy markes on oher markes as well as he inegraion of emerging markes or he price and volailiy spillovers beween advanced markes. This kind of sudies has been improved wih he exisence of inraday rading daa which have made feasible he sudy of inraday price behavior. This work focuses on he main objecive of analyzing he influence of he DOW on he IBEX. We expand he daabase in such a way ha 5-min inerval quoes of he IBEX hroughou each rading day are used from February, 000 o December 30, 011. Tha fac allows us o analyze a bigger inerval of ime for each hypohesis and for a longer ime. The resuls lead us o sae he exisence of a significan underreacion effec of he previous DOW dayime reurn upon he IBEX inraday dayime reurns during he firs hours of rading which urns ino an overreacion effec during he las hours of rading. Addiionally, we found he opposie o be rue of he effec of he IBEX reurn measures on he IBEX inraday reurns (overreacion a he morning and underreacion a he end of he rading day). JEL Classificaion: G10, G11, G14. Keywords: Inraday daa; Asymmeric models; Informaion Spillovers; Overreacion; Underreacion. Corresponding auhor. Tel.: +34-94-89510; Fax: +34-94-7509. E-mail address: jlmiralles@unex.es 1
Influence of he Dow reurns on he inraday Spanish sock marke behavior 1. Inroducion The analysis of linkages among equiy markes has received grea aenion from researchers following he developmen of he differen ARCH models. There are several sudies in which he influence of he greaer equiy markes on oher markes is analyzed as well as oher sudies in which he inegraion of emerging markes or he price and volailiy spillovers beween advanced markes are invesigaed. Some examples of hose lines of invesigaion are he sudies of Liu and Pan (1997), Chan-Lau and Ivaschenko (003), Lee e al. (004) and more recenly Singh e al. (010). Furhermore, he exisence of inraday rading daa makes feasible he sudy of inraday price behavior. Soll and Whaley (1990) invesigae he srucure of he marke a he opening of he New York Sock Exchange (NYSE) and conclude ha he effec of sock marke srucure on he shor-run volailiy of sock prices is complex. Susmel and Engle (1994) find ha he volailiy spillover beween New York and London equiy markes is minimal and has a duraion which lass only an hour or so. Fabozzi e al. (1995) find ha inraday reversals for socks on he NYSE and he American Sock Exchange (AMEX) during 1989 are relaed o he iniial price change. Gosnell (1995) also documens ha he proporion of reversals is low near he opening of he marke, bu rapidly increases in he firs hour of rading. Baur and Jung (006) analyze he relaionship beween he Dow Jones Indusrial Average (DJIA) and he Deusche Akienindex (DAX) finding ha foreign dayime reurns can significanly influence domesic overnigh reurns and ha here is no evidence of spillovers from he previous dayime reurns in he US o he DAX morning rading. Finally, Harju and Hussain (008) and Harju and Hussain (011) use 5-min daa from differen inernaional equiy markes o analyze he dynamics among hem finding differen conclusions. Harju and Hussain (008) find ha he US sock marke does no cause significan volailiy spillover o he European markes whereas here is significan volailiy spillover in he opposie direcion. On he oher hand, Harju and Hussain (011) consider ha he opening of he US sock marke significanly raises he level of volailiy in Europe. References o similar sudies in he Spanish sock marke are limied because hey focus heir analysis on he response of he Spanish sock marke o bad news from he Dow Jones index, see Blasco e al. (00) or Blasco e al. (005). To our knowledge he sudy of
Miralles-Marcelo e al (010) is he only one which analyzes he behavior of he main Spanish sock index, IBEX-35, hereafer IBEX, in is early and final hours of rading and he influence of he main US index, he Dow Jones Indusrial Average, hereafer DOW, upon IBEX rading and invesor behavior. They find low price movemens of he IBEX ill he opening of Wall Sree and he exisence of a quick reacion of he Spanish sock marke plus an overreacion effec in he following en minues afer he opening of he US marke. This work follows he line of Baur and Jung (006) and Miralles-Marcelo e al (010) focusing on he main objecive of analyzing he influence of he DOW on he IBEX. Some improvemens of he previous empirical evidence are proposed: firsly, he vas majoriy of he sudies which use inraday daa employ a small daabase limied o a few years. However, we expand he daabase in such a way ha 5-min inerval quoes of he IBEX hroughou each rading day are used from February, 000 o December 30, 011. Tha fac allows us o analyze a bigger inerval of ime for each hypohesis and for a longer ime. Secondly, we use asymmeric models o avoid anomalies in he conclusions when asymmeries are no aken ino accoun as several auhors sugges. Finally, we add some behavior hypohesis in order o shed some ligh on he dynamics of he Spanish sock marke. There are wo main reasons for focusing our sudy on he Spanish sock marke. Firsly, in recen years i has become a reference for he main European sock markes based on improvemens in he echnical, operaional and organizaional sysems supporing he marke which has enabled i o channel large volumes of invesmen as is repored in he 011 Annual Repor of Bolsas y Mercados Españoles (BME), he operaor of all sock markes and financial sysems in Spain, where i is poined ou ha he invesmen flows channeled hrough he sock exchange in 011 oaled 37.73 billion euros, up 35.1% from 010. This amoun ranks BME as he 4 h among he world s sock exchanges in erms of company financing. Secondly, a beer knowledge of he inraday behavior of he Spanish sock marke would lead us o a more aracive sock marke, larger amouns of invesmen flows and, herefore, he possibiliy of developing a profiable sraegy. Addiionally, in recen imes Morgan Sanley s ineres rae sraegiss have poined ou he Spain s brighening growh oulook, progress on reforms, valuaions, and he low risk ha he eurocrisis could blow up anew which could lead Spain o become he euro area s nex Germany. In our opinion, hose facs will lead o a higher ineres for he Spanish economy and, herefore, for he Spanish sock marke. The resuls show he imporance of he DOW reurns on he IBEX inraday reurns behavior. Clear evidence is provided ha he Spanish sock marke underreacs o he DOW 3
reurns in he firs hours of rading bu overreacs during he las wo hours (afer he opening of he US markes). Addiionally, he resuls also show ha he Spanish sock marke overweighs he mos recen informaion as opposed o he older informaion, ha is he DOW reurns face o he IBEX reurns. The remainder of his paper is organized as follows. Secion describes he mehodology and presens he daa. Secion 3 shows he principal resuls and Secion 4 provides he main conclusions.. Daa and Mehodology In order o analyze he inraday ransmission of sock reurns and volailiy from he DOW o he IBEX we have iniially compiled IBEX-35 index inraday daa for he period from February, 000 o December 30, 011 (a oal of 3010 rading sessions) saring from he opening quoe a 9:00 local ime and a 5-minue inervals unil he end of each session a 17:30. Considering ha here is no a subsanial overlapping period of rading beween he NYSE and he Spanish sock marke, jus wo hours from 3:30 pm o 5:30 pm (CET ime), i is no necessary o use inraday daa from he DOW. For ha reason we jus use opening and closing prices for he DOW which reflec all he relevan informaion we need o analyze he relaionship beween hese wo markes. Using ha daa we calculae hree differen inraday reurns for he IBEX. Inraday overnigh reurns, IBEXIDNR are calculaed saring a he previous closing price of he IBEX and ending a he price of he nex day a 9:05 AM. Subsequenly, he lengh is increased in 5-min inervals unil open-plus-3 hours is reached (reporing 36 differen overnigh reurns). We calculae he inraday dayime reurns, IBEXIDDRA, iniially as he logarihm difference beween he price a 9:05 AM and he opening price. Furher dayime reurns are calculaed by increasing he lengh in 5-min inervals unil 17:30 (a oal of 10 differen dayime reurns) 1. The second inraday dayime reurns, IBEXIDDRB, are calculaed iniially as he difference beween he price a 15:35 and he price a 15:30 and hen increase he lengh in 5-min inervals unil 17:30 (giving us 4 differen dayime reurns). Basic saisics of he inraday overnigh and dayime reurns are shown in Tables 1 o 3. 1 Tha means ha he second dayime reurn is calculaed as he logarihm difference beween he price a 9:10 AM and he opening price and so on. From hese ables unil he end of he paper we show jus some of he reurns or he esimaions we carried ou in order o save space. The res of hem can be provided upon reques. 4
Table 1: Descripive saisics for IBEX overnigh reurns (IBEXIDNR, Previous close o he marked hour price) 09:05 09:15 09:30 09:45 10:00 10:15 10:30 10:45 11:00 11:15 11:30 11:45 1:00 Mean 9.15 10-6 3.7 10-5 -4.07 10-5 4.00 10-7 -5.50 10-5 -0.000113-0.000144-0.00014-0.000153-0.000175-0.000195-0.0004-0.0005 Median 0.00047 0.000403 0.000460 0.000474 0.00070 0.000307 0.000305 0.00056 0.000188 0.000375 0.000448 0.000367 0.000317 Maximum 0.049685 0.06648 0.065010 0.100001 0.09951 0.096565 0.105756 0.099081 0.106750 0.1077 0.11443 0.11506 0.113681 Minimum -0.071756-0.070960-0.077010-0.07084-0.070650-0.059560-0.065085-0.06345-0.064751-0.070488-0.06961-0.090116-0.08994 Sd. Dev. 0.0081 0.008461 0.00881 0.009303 0.009660 0.00996 0.010159 0.010346 0.010535 0.010759 0.011006 0.01138 0.011315 Skewness -0.37679-0.40480-0.45680 0.165898 0.131890 0.175037 0.66147 0.1417 0.176643 0.080401 0.085706-0.139095-0.083370 Kurosis 9.8497 10.7689 10.64680 1.41585 11.38405 9.873114 10.6401 9.688888 10.81 9.919906 10.51 11.4639 11.9648 Jarque-Bera 5908.496 7567.66 7361.400 1119.3 881.65 5938.04 7357.46 5617.157 6664.191 6006.837 6595.91 8535.563 8633.46 Probabiliy 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Sum 0.07541 0.111815-0.1553 0.00103-0.165359-0.34091-0.43300-0.45916-0.461063-0.56165-0.587814-0.79116-0.67886 Sum Sq. Dev. 0.198434 0.1534 0.33568 0.60341 0.80714 0.98515 0.310470 0.3001 0.333859 0.348170 0.364371 0.379906 0.385087 Observaions 3009 3009 3009 3009 3009 3009 3009 3009 3009 3009 3009 3009 3009 5
Table : Descripive saisics for IBEX dayime reurns (IBEXIDDR, Open o he marked hour price) 09:05 09:15 09:30 10:00 11:00 1:00 13:00 14:00 15:00 15:30 16:00 17:00 17:30 Mean -0.00053-0.0006-0.000303-0.000318-0.000418-0.000488-0.000543-0.000600-0.000631-0.000574-0.000736-0.000753-0.00038 Median -0.000134 -.09 10-5 -6.03 10-5 -7.4 10-5 -0.000163-0.00010-9.9 10-5 -0.000137-0.000159-9.60 10-5 -0.000166-0.000197 0.00014 Maximum 0.016401 0.04685 0.04901 0.097804 0.105303 0.1134 0.109477 0.119597 0.10350 0.11858 0.10399 0.11661 0.133389 Minimum -0.0413-0.05036-0.0499-0.0436-0.03375-0.054806-0.057989-0.05007-0.055587-0.059941-0.065585-0.071907-0.08094 Sd. Dev. 0.00555 0.003850 0.004897 0.006408 0.007594 0.008551 0.00914 0.009616 0.010589 0.011015 0.011107 0.01550 0.013588 Skewness -0.588601 0.18456 0.159418 1.9470 0.886946 0.45376 0.314941 0.40698 0.7797 0.15991 0.103956 0.081710 0.107596 Kurosis 9.73391 16.35480 16.3613 6.8789 18.50780 15.67798 1.94339 13.55973 10.86011 9.749771 9.94350 8.44416 8.70791 Jarque-Bera 5860.909 385.4 405.47 7353.88 30556.34 061.45 1449.84 14068.03 7787.169 576.739 6018.77 370.636 4091.98 Probabiliy 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Sum -0.76056-0.679884-0.91931-0.957361-1.57316-1.468838-1.633315-1.806336-1.900695-1.78146 -.13986 -.65086-1.149760 Sum Sq. Dev. 0.019646 0.044606 0.07166 0.13574 0.173506 0.004 0.51485 0.7856 0.337400 0.365071 0.371199 0.473900 0.555550 Observaions 3010 3010 3010 3010 3010 3010 3010 3010 3010 3010 3010 3010 3010 6
Table 3: Descripive saisics for IBEX dayime reurns (IBEXIDDRB, Price a 15:30 o he marked hour price) 15:35 15:40 15:45 15:50 15:55 16:00 16:10 16:15 16:30 16:45 17:00 17:15 17:30 Mean -4.40 10-5 -5.7 10-5 -9.68 10-5 -0.000147-0.000164-0.00018-0.000176-0.00000-0.000154-0.000151-0.000198-0.0006 0.00017 Median -3.33 10-5 -4.50 10-5 -3.3 10-5 -0.00010-0.00019-8.96 10-5 -9.16 10-5 -0.00010-6.70 10-5 -9.60 10-5 -3.41 10-5 0.000106 0.000468 Maximum 0.01384 0.014769 0.01447 0.016761 0.01568 0.03353 0.04096 0.043 0.06436 0.041896 0.0415 0.047736 0.044180 Minimum -0.0554-0.07679-0.0064-0.03078-0.0455-0.05357-0.04483-0.038368-0.04153-0.053015-0.04654-0.038003-0.039617 Sd. Dev. 0.001554 0.00053 0.00448 0.00819 0.003137 0.003353 0.0045 0.004381 0.004933 0.005890 0.006379 0.00690 0.007597 Skewness -1.309816-0.390986-0.14155-0.564677-0.3011-0.361890-0.3393-0.161579-0.401393-0.355843-0.136-0.4046-0.084386 Kurosis 31.93641 18.0353 9.171816 1.66445 10.4609 11.10496 1.7036 10.81177 8.118449 9.978941 7.571018 6.849766 6.11497 Jarque-Bera 105874.0 8384.0 4787.43 11874.08 7007.955 8304.361 11877.14 7666.484 3366.558 617.00 645.056 1883.944 15.601 Probabiliy 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Sum -0.1334-0.158766-0.91435-0.44101-0.49447-0.54636-0.58965-0.601087-0.46978-0.45391-0.59746-0.787749 0.517864 Sum Sq. Dev. 0.00763 0.01685 0.018033 0.03916 0.09615 0.03389 0.054394 0.057765 0.073 0.104373 0.144 0.143337 0.17368 Observaions 3010 3010 3010 3010 3010 3010 3010 3010 3010 3010 3010 3010 3010 7
We observe a common behavior in all cases which is characerized by increasing negaive mean values and volailiies in he course of each ime period. Focusing aenion on he values of he dayime reurns which are repored in Table (IBEXIDDR, from open o he marked hour price) we see ha here is a significan difference in heir mean and volailiy values since boh are much greaer in he laer hours of he rading day coinciding wih he opening and he firs hours of rading in New York. Therefore, we can poin ou he fac ha while he mean dayime reurn in Table a 09:05 AM akes he value of -0.00053, he same one a 15:30 when he DOW opens is -0.000574, reaching a minimum of -0.000753 a 17:00, one and a half hours afer he opening of he DOW. A he same hours he sandard deviaions of hose variables are 0.00555; 0.011015 and 0.01550 respecively. These resuls lead us o conclude ha he aciviy of he Spanish sock is concenraed in he las hours of rading in order o evaluae and incorporae ino he marke all he informaion generaed by he DOW. The inraday seasonal volailiy paern, defined by he average absolue reurns, is depiced in Figure 1. I displays a ypical U-shaped paern where large posiive mean reurns a he beginning of he rading day are followed by a decreasing rend unil mid-session. From ha momen, i sars a big upward rend unil he end of he rading day. These resuls are consisen wih he findings of Andersen and Bollerslev (1997) and Cai e al (004) among ohers for he US and UK equiy markes. Figure 1: Average Absolue Reurns for he IBEX-35 8
Addiionally, we show in Figure he average inraday volume which also exhibis a U- shaped paern in accordance wih he findings of Hussain (011). In boh figures we find significan peaks a 14:30 and 15:30 similar o hose found by Harju and Hussain (011). They associae hem wih he scheduled US macroeconomic news announcemens and he opening of he New York Sock Exchange, hereafer he NYSE, a 14:30 and 15:30 respecively. Figure : Mean Inraday Volume We have also calculaed reurns of IBEX, IBEXR, and DOW, DOWR, as he differences in logarihms of wo consecuive closing prices. However, boh of hem can also be calculaed as he sum of overnigh reurns, 3 IBEXNR and DOWNR respecively, and dayime reurns, 4 IBEXDR and DOWDR respecively. From he basic saisics of hose reurns which are repored in Table 4 we can observe he firs insighs ino reurn ransmissions. In ha sense, we deec ha posiive DOW dayime reurn is accompanied by a posiive IBEX overnigh reurn and, conversely, a negaive DOW overnigh reurn is followed by a negaive IBEX dayime reurn. 3 4 Overnigh reurns are calculaed as he difference in logarihms beween he previous closing and he opening prices of each sock marke. In his case dayime reurns are calculaed as he difference in logarihms beween he opening and he closing prices of each sock marke. 9
Table 4: Descripive saisics of daily, overnigh and dayime reurns IBEXR IBEXNR IBEXDR DOWR DOWNR DOWDR Mean -8. 10-5 0.00061-0.000343 3.67 10-5 -4.10 10-5 7.77 10-5 Median 0.000664 0.000499 0.0003 0.000308-4.36 10-5 0.000519 Maximum 0.134836 0.060546 0.133389 0.105083 0.0740 0.103756 Minimum -0.095859-0.061991-0.08094-0.08005-0.037389-0.08109 Sd. Dev. 0.01556 0.007740 0.013593 0.01884 0.00188 0.01805 Skewness 0.119813 0.043339 0.103101-0.0683-0.3934-0.0400 Kurosis 8.330108 1.49077 8.704650 10.37 99.0470 10.13654 Jarque-Bera 3569.110 1194.07 4085.413 6541.877 1160466. 6385.667 Probabiliy 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000 Sum -0.4738 0.785696-1.03304 0.110400-0.13436 0.33836 Sum Sq. Dev. 0.78481 0.18001 0.555776 0.499313 0.01440 0.4937 Observaions 3009 3009 3009 3009 3009 3009 The ime line of he marke rading hours of he IBEX and he DOW is shown in Figure 3. From is scruiny, various ineracions can be consruced wih he aim of asceraining he naure of conemporaneous and lead-lag relaionships beween he markes. Firsly, we can consider ha overnigh reurns from he DOW (defined as DOWNR ) can influence hose inraday reurns of he IBEX we have defined as IBEXIDDRB. 5 Secondly, we observe ha dayime reurns of he DOW on he previous day (DOWDR -1 ) and one-day lagged reurns of he DOW (DOWR -1 ) 6 can impac on he overnigh reurns of he IBEX he following day (IBEXNR ), bu also on he inraday reurns of he IBEX (IBEXDR ). Wih respec o he influence of he IBEX on he DOW we find some relaionship opions. In ha sense, DOW dayime reurns (DOWDR) can be influenced by he IBEX dayime reurn from 9:00 o 15:30, he IBEX dayime reurn (from open o close, IBEXDR) and he IBEX reurn (from previous close o close, IBEXR ). Likewise, here could be a conemporaneous influence of he IBEX reurns (IBEXR ) over he DOW reurns (DOWR ). 5 6 Those reurns from he opening of he DOW a 15:30 CET ime ill he end of he rading session in he Spanish sock marke a 17:30. Calculaed as he difference in logarihms beween wo consecuive closing prices, bu also he sum of overnigh and day reurns. 10
Figure 3: Time line of he marke rading hours of he IBEX and he DOW CET Time 0 3 6 9 1 15 18 1 4 3 6 9 1 15 18 1 4 IBEX IBEXNR IBEXDR IBEXNR IBEXDR IBEXNR 9:00 17:30 9:00 17:30 DOW DOWNR DOWDR DOWNR DOWDR 15:30 :00 15:30 :00 OVERLAPPING PERIOD 15:30-17:30 OVERLAPPING PERIOD 15:30-17:30 11
Following Lee e al. (004) or Kim (005) among ohers, we have performed Granger causaliy ess in order o assess hose informaion flows beween he IBEX and he DOW. From he resuls of hose causaliy ess, which are shown in Table 5, we find ha here is a clear unidirecional reurns ransmission from he DOW o he IBEX. In all cases we rejec he null ha he differen DOW s reurns do no cause IBEX s reurns. However, ha null canno be rejeced when IBEX reurns causaliies over he DOW are esed. Table 5: Granger causaliy ess DOW causes IBEX F-sa Probabiliy IBEX causes DOW F-sa Probabiliy DOWNR IBEXIDDRB 3.31639 0.0364 IBEXDR (15:30) DOWDR 0.1446 0.8830 RDOW -1 IBEXNR 9.5478 10-13 IBEXDR DOWDR 1.78844 0.1676 RDOW -1 IBEXDR 4.58636 0.0103 RIBEX DOWDR 1.00819 0.3650 DOWDR -1 IBEXNR 34.871 10-15 RIBEX RDOW 1.16066 0.3134 DOWDR -1 IBEXDR 4.00615 0.0183 Noe: IBEXIDDRB and IBEXDR (15:30) represen he dayime reurn from 15:30 o Close and he dayime reurn from Open o 15:30 respecively. The sandard frameworks in he empirical evidence o analyze he reurn and volailiy ransmission beween wo or more markes are based in he GARCH model due o is abiliy o ake ino accoun he condiional heeroskedasiciy inheren in financial ime series. 7 However, several auhors sugges ha hese volailiy models could be erroneous if we do no ake ino accoun asymmeries in variance. In his sense, Black (1976) and Chrisie (198) demonsraed he exisence of asymmeric effecs, also known as leverage effecs, on he condiional variance whereby negaive equiy reurns are usually followed by larger increases in volailiy han is he case wih equally large posiive reurns. In order o accommodae his asymmeric response we adap he aggregae-shock model proposed by Lin e al. (1994), which was also used by Baur and Jung (006), o a Threshold GARCH (TGARCH) aggregae model The TGARCH model, proposed by Glosen e al (1993) and Zakoian (1994), bu also used by Chan-Lau and Ivaschenko (003), Hughes e al (007), Jaleel and Samarakoon 7 See French e al. (1987), Akgiray (1989), Conolly (1989), Baillie and DeGennaro (1990), Bollerslev e al. (199), Kyriacou and Sarno (1999), Gonzalez e al. (003), Franses e al. (004), Baur and Jung (006) and Miralles e al (010) among ohers, who applied he GARCH models o sock indexes showing ha hey are useful in modeling he dynamic behavior of sock reurns. 1
(009), Haniff and Pok (010) and Sabiruzzaman e al (010) among ohers, 8 is specified as follows: h r αε μ ε βh γε where o allow for asymmery in volailiy he sandard GARCH model is augmened by including a dummy variable, I -1, which akes he value of 1 if ε -1 is negaive and 0 (zero) oherwise. In his model, good news, ε -1 >0, and bad news, ε -1 <0, have differenial effecs in condiional variance. Good news has an impac of α while bad news has an impac of α+γ. In his model we say ha here is a leverage effec if γ>0 and is saisically significan. Taking ino consideraion no only he unidirecional reurns ransmission we found previously, bu also he ime line of he marke rading hours of he IBEX and he DOW, we propose he analysis of five differen hypoheses: Hypohesis 1: I (1) IBEXIDNR h αε μ 0 μ IBEXDR βh 1 γε I -1 μ DOWDR θdowdr -1 () The firs one analyzes he impac of he previous dayime reurns of he DOW and IBEX (DOWDR -1 and IBEXDR -1 respecively) on he inraday overnigh reurns of he Spanish sock index (IBEXIDNR ) during he firs 3 hours of rading, which means ha 36 esimaions were calculaed. Addiionally, we analyze he influence of he DOW dayime volailiy by including is squared reurn lagged one period in he variance equaion. This analysis, where he DOW index is used insead of any Asian index, makes sense from he poin of view ha using NYSE Arca i is possible o ener and execue orders from 10 AM CET o 3:30 PM CET. Therefore, here is a coninuous flow of informaion coming from he US marke ha neuralizes any news coming from he Asian markes which close a 7 AM CET approximaely. 8 There is anoher opion o capure asymmery which is he use of he Exponenial GARCH (EGARCH) model. However, Engle and Ng (1993) find ha he variabiliy of he condiional variance implied by he EGARCH model is oo high. Addiionally, beyond o he fac of he GARCH models being incapable of 13
Hypohesis : IBEXIDDRA h αε μ 0 βh μ IBEXNR 1 γε I μ DOWNR θdownr (3) The second hypohesis focuses on he behavior of he inraday dayime reurns of he IBEX during he las wo hours of rading. In his case, we analyze wheher he DOW and IBEX overnigh reurns (DOWNR and IBEXNR respecively) influence he IBEX inraday dayime reurns from Open-o-15:30 (IBEXIDDRA ) and he following ones unil he end of he rading session a 17:30. We also analyze wheher DOW overnigh volailiy, characerized by he squared overnigh reurns, conains any relevan informaion for hose dayime reurns. Hypohesis 3: IBEXIDDRB h μ 0 αε μ IBEXIDDR 1 βh γε OPEN TO15:30 I μ θdownr DOWNR (4) Hypoheses 1 and are he same as he firs wo proposed by Miralles-Marcelo e al (010). The hird one is also similar bu changing he mehodology of calculaing he endogenous variable. We boh use he 15:30 CET o close reurn, however, while Miralles- Marcelo e al (010) calculae he reurns by mainaining he closing price fixed and hen using prices a 15:30 plus en-minues ahead (wih icks of one minue), we fix he price a 15:30 CET and change he oher reference beginning by he price a 15:35 CET wih icks of 5-minues ill he end of he rading session a 17:30. Tha difference allows us o mainly analyze he effec of he DOW overnigh reurn over he cumulaive reurn of he IBEX from he opening of he US marke. Consequenly, in he hird hypohesis we consider as he endogenous variable he second inraday dayime reurn (IBEXIDDRB ) while he exogenous variables of he reurn model are he DOW overnigh (DOWNR ) reurns and he inraday dayime reurns of he Spanish index (IBEXIDDR OPEN TO 15:30 ) from Open-o-3:30 pm. Furhermore, he DOW overnigh squared reurns lagged one period are included in he volailiy equaion in order o capure he volailiy spillover from he American marke ino he Spanish marke. separaing ou he asymmeric informaion, Sabiruzzaman e al (010) provide evidence ha he TGARCH specificaion is superior o GARCH specificaion. 14
In addiion o hese hypoheses, we sugges wo more in order o analyze in deph he behavior of he Spanish sock marke. Hypohesis 4: IBEXIDDRA h μ 0 αε μ IBEXIDDR 1 βh γε I OPEN TO15:30 μ θdownr DOWNR (5) The fourh hypohesis shares wih he second hypohesis he exogenous variable relaive o he DOW (he overnigh reurns, DOWNR ) and parially he endogenous variable (because in his case he firs variable o be analyzed is he inraday dayime reurns from open o 15:35) 9. However, in conras wih he second hypohesis, we include he inraday dayime reurn of he IBEX from Open o 15:30 as an exogenous variable. This change will allow us o examine he behavior of he IBEX during he las wo hours of he rading session faced wih he conemporaneous news generaed by he IBEX and he DOW unil he opening of he laer. As well as in he second hypohesis we add he squared DOW overnigh reurn in he volailiy equaion as an exogenous variable. We also find suppor for using he DOW overnigh reurn as an exogenous variable in hypoheses o 4 from Figures 1 and. In boh cases, we find a significan increase a 15:30 CET. Following he evidence repored by Harju and Hussain (011) and Hussain (011), ha behavior could be associaed wih he opening of he New York Sock Exchange and, herefore, i mus be considered. Hypohesis 5: IBEXIDDRA h αε μ 0 βh μ IBEXR 1 γε I -1 μ DOWR θdowr -1-1 (6) The las hypohesis proposed in his paper measures in he mean equaion he effecs of he previous daily reurns of he IBEX and DOW indexes (IBEXR -1 and DOWR -1 respecively) on he inraday dayime reurn of he following day (IBEXIDDRA ). Meanwhile, in he volailiy equaion we add as an exogenous variable he squared daily reurn of he DOW lagged one period in order o analyze is effec on he condiional volailiy of he IBEX. In his case we analyze he behavior of he IBEX hrough he whole rading session which leads us o esimae 10 regressions. 9 The followers are he dayime reurns from Open o 15:40 and so on increasing he lengh in 5 min inervals. The fac ha he exogenous variable is he dayime reurn from Open o 15:30 leads us o esimae 4 regressions. 15
In all cases we run several regressions using differen proxies of he inraday IBEX overnigh and dayime reurns by saring from he reference quoe in each case and exending he ime span on a 5 min basis. The main objecive of hese procedures is o analyze he behavior of he Spanish marke as more and more real-ime informaion is available. In all he regressions, maximum likelihood esimaion are obained from he Bernd-Hall-Hall- Hausman algorihm. 3. Empirical Resuls Table 6 repors he regression resuls for he firs hypohesis. The firs hree rows show he coefficiens relaive o he mean equaion which measures he impac of IBEX s and DOW s previous open-o-close reurns (IBEXDLDR -1 and DOWDLDR -1 respecively) on he inraday overnigh reurns of he Spanish sock index (IBEXIDNR ). In his case, if IBEX inraday overnigh reurns conain any informaion from DOW or IBEX and heir previous dayime reurns, hese coefficiens should be significan. The following five rows show he coefficiens relaive o he volailiy equaion where we focus our aenion on he las wo, γ and θ, which represen he coefficiens relaive o he asymmery and he DOW volailiy respecively. Some ineresing resuls emerge from he firs hree rows of coefficiens. Firsly, all of hem are significan which means ha here are significan ransmissions of informaion from he previous dayime reurns of he IBEX and he DOW o he IBEX inraday overnigh reurns, which is consisen wih he resuls of he previous empirical evidence. Secondly, he negaive values of he coefficiens relaed o he IBEX previous dayime reurns show evidence of an overreacion effec. While he posiive values of hose relaed o he DOW previous dayime reurns show evidence of an underreacion effec. Moreover, his underreacion effec is in keeping wih he firs evidence of informaion ransmission beween hese markes found in he descripive saisics where a posiive DOW dayime reurn coincides wih a posiive IBEX overnigh reurn. I is also ineresing o poin ou ha he coefficiens relaive o he previous IBEX dayime reurns are lower in absolue erms han hose relaive o he DOW. In our opinion, ha fac means ha he Spanish sock marke overweighs he informaion coming from he US marke in he firs hours of rading. Tha circumsance makes sense from he poin of view ha he informaion coming from he US marke is closer and, herefore, more valuable han he Spanish one. 16
Table 6: Reurn and volailiy spillovers from Hypohesis 1 09:05 09:15 09:30 09:45 10:00 10:15 10:30 10:45 11:00 11:15 11:30 11:45 1:00 Mean Equaion μ 0-5.54 10-5 (-0.619) μ 1-0.138 *** (-16.957) μ 0.355 *** (7.951) 3.75 10-5 (0.405) -0.131 *** (-14.670) 0.340 *** (6.96) -3.65 10-5 (-0.361) -0.13 *** (-1.886) 0.334 *** (4.668) -6.55 10-5 (-0.609) -0.143 *** (-13.98) 0.333 *** (3.139) -1.18 10-4 (-1.01) -0.150 *** (-1.95) 0.36 *** (1.473) -1.3 10-4 (-1.014) -0.143 *** (-11.933) -1.57 10-4 (-1.54) -0.139 *** (-11.619) -1.43 10-4 -1.78 10-4 (-1.114) (-1.35) -0.141 *** -0.147 *** (-11.05) (-11.09) 0.3 *** (0.390) 0.31 *** (19.944) 0.3 *** (0.13) 0.37 *** (0.185) Variance Equaion -.08 10-4 (-1.540) -0.144 *** (-10.664) 0.3 *** (19.491) -.55 10-4* (-1.763) -0.138 *** (-9.686) 0.31 *** (18.85) -.39 10-4* (-1.658) -0.133 *** (-9.341) 0.316 *** (18.95) -.39 10-4* (-1.645) -0.131 *** (-8.907) 0.31 *** (17.667) ω 3.70 10-7*** (.744) α 0.050 *** (3.18) β 0.818 *** (5.1) γ 0.10 *** (4.898) θ 0.07 *** (9.975) 4.84 10-7*** (3.419) 0.047 *** (3.38) 0.830 *** (63.710) 0.109 *** (5.748) 0.0 *** (8.44) 6.1 10-7*** (3.941) 0.039 *** (.801) 0.837 *** (69.631) 0.10 *** (6.696) 0.03 *** (8.07) 6.75 10-7*** (4.8) 0.035 *** (.81) 0.844 *** (66.559) 0.131 *** (9.10) 0.0 *** (7.053) 8.33 10-7*** (4.191) 0.037 *** (3.077) 0.844 *** (65.899) 0.13 *** (8.485) 0.0 *** (6.309) 6.89 10-7*** (3.881) 0.08 ** (.369) 0.869 *** (74.7) 0.116 *** (7.770) 0.00 *** (5.766) 7.56 10-7*** (3.777) 0.07 ** (.37) 0.867 *** (75.545) 0.11 *** (8.409) 0.03 *** (5.869) Saisics 7.63 10-7*** (3.817) 7.89 10-7*** (3.736) 0.03 *** 0.030 ** (.599) (.469) 0.111 *** 0.870 *** (8.016) (75.779) 0.870 *** 0.114 *** (77.63) (8.176) 0.01 *** 0.0 *** (5.60) (5.77) 8.13 10-7*** (3.713) 0.07 ** (.54) 0.880 *** (78.766) 0.11 *** (8.74) 0.019 *** (5.01) 1.1 10-6*** (5.499) 0.03 * (1.946) 0.879 *** (74.939) 0.106 *** (8.400) 0.0 *** (6.1) 1.0 10-6*** (4.998) 0.019 * (1.73) 0.883 *** (8.569) 0.11 *** (8.579) 0.0 *** (6.11) 1.16 10-6*** (5.143) 0.017 (1.478) 0.876 *** (75.170) 0.11 *** (8.541) 0.06 *** (6.466) LL 1141.66 1110.01 10900.13 10719.37 10541.5 10406.43 10317.73 1059.94 10195.6 1019.88 1007.18 9989.37 9960.8 LB(15) 5.1 *** 4.183 ***.367 1.658 9.17 ** 4.353 * 3.499 17.370 13.49 19.07 0.80 0.503 18.48 LBS(15) 6.7999 18.911 15.61 11.715 10.605 18.936 14.53 19.195 18.614 3.68 * 1.8 0.074 15.085 Noes: This able shows he resuls for he TGARCH model IBEXIDNR μ 0 μ 1 IBEXDR -1 μ DOWDR -1 h αε 1 βh 1 γε 1 I 1 θdowdr 1 T-saisics in parenheses. LL is he Log-likelihood saisic. LB(15) and LBS(15) are he Ljung-Box saisics for he sandardized residuals and squared residuals, respecively, wih 15 lagged values included. Significan coefficiens are denoed by ***, ** and * for 1%, 5% and 10% significance levels, respecively. 17
Relaive o he second par of Table 6 where he coefficiens of he volailiy equaion are shown, we deec a significan volailiy spillover effec from he DOW o he IBEX, which remains consan hroughou he differen esimaions. Furhermore, he posiive and significan value of he γ coefficien in all cases indicaes ha here is a leverage effec where bad news increases volailiy. Finally, he analysis of he Ljung-Box saisics for he sandardized and squared sandardized residuals shows, in mos of he cases, he inexisence of serial correlaion in he mean equaions or remaining ARCH effecs in he variance equaions. Shown in Table 7 are he resuls of he esimaions relaive o he second hypohesis where we analyze he influence of he DOW and IBEX overnigh reurns upon he IBEX inraday dayime reurns from Open-o-15:30 and he following ones unil he end of he rading session a 17:30. We find significan conemporaneous reurn spillovers form he DOW overnigh reurns o he IBEX inraday dayime reurns. However, in conras wih he resuls obained by Miralles e al (010), we find significan conemporaneous spillovers from he IBEX overnigh reurns o he IBEX inraday dayime reurns basically due o he fac ha hey use a sample of jus years while we use a sample of 1 years where spillovers among markes can change enormously. As well as in he firs hypohesis resuls, we find evidence of overreacion and underreacion effecs as a consequence of he negaive and posiive values of he IBEX and DOW coefficiens in he mean equaion. Once again, he DOW coefficiens are higher han he IBEX coefficiens and heir value decreases hroughou he rading session, bu in his case hey become no saisically significan from 17:00 onwards. In our opinion, his is evidence of he exisence of a significan Opening DOW effec in he Spanish sock marke which akes ino accoun all he informaion coming from he DOW opening and disappears gradually once he informaion is analyzed by he markes. However, besides hese iniial ineresing resuls, we also find ha even hough he asymmery coefficiens of he volailiy equaion are all significan, herefore indicaing he exisence of a leverage effec, mos of he volailiy coefficiens associaed wih he DOW overnigh volailiy are no significan. This fac, ogeher wih he significan values of he Ljung-Box saisics for he squared sandardized residuals in mos of he esimaions, leads us o consider his model as inappropriae. Table 8 repors he analysis of he spillover effecs from he DOW overnigh reurns and IBEX inraday dayime reurns from Open o 15:30 on he IBEX inraday dayime reurn from he opening of he DOW a 15:30 unil he end of he rading session. 18
μ 0 -.4 10-4* (-1.654) μ 1-0.084 *** (-3.568) μ 0.331 *** (3.559) ω 9.45 10-7*** (6.657) α 0.047 *** (3.865) β 0.890 *** (9.347) γ 0.111 *** (7.846) θ 0.035 (1.15) Table 7: Reurn and volailiy spillovers from Hypohesis 15:30 15:35 15:40 15:45 15:50 16:00 16:10 16:15 16:30 16:45 17:00 17:15 17:30 -.5 10-4 (-1.639) -0.089 *** (-3.785) 0.331 *** (3.496) 9.74 10-7*** (6.415) 0.04 *** (3.594) 0.89 *** (93.310) 0.115 *** (8.79) 0.03 (0.956) -.39 10-4* (-1.738) -0.089 *** (-3.888) 0.309 *** (3.85) 1.08 10-6*** (6.61) 0.05 *** (4.139) 0.884 *** (90.883) 0.109 *** (6.966) 0.04 (1.93) -.51 10-4* (-1.8) -0.088 *** (-3.79) 0.86 *** (3.007) 1.01 10-6*** (6.85) 0.047 *** (3.960) 0.89 *** (100.383) 0.103 *** (6.948) 0.045 (1.505) -.95 10-4** (-.134) -0.093 *** (-3.89) 0.95 *** (3.048) 9.00 10-7*** (6.18) 0.036 *** (3.355) 0.904 *** (114.767) 0.099 *** (7.955) 0.055 ** (.199) -3.06 10-4** (-.176) -0.107 *** (-4.471) 0.59 *** (.66) 9.98 10-7*** (6.74) 0.09 *** (.805) 0.90 *** (104.85) 0.114 *** (9.603) 0.056 * (1.853) Mean Equaion -3.07 10-4** (-.16) -0.105 *** (-4.46) 0.19 ** (.77) Variance Equaion 8.68 10-7*** (5.976) 0.04 *** (.658) 0.91 *** (119.99) 0.111 *** (10.566) 0.019 (0.596) Saisics -3.18 10-4** (-.40) -0.113 *** (-4.513) 0.3 ** (.80) 8.59 10-7*** (5.948) 0.01 ** (.43) 0.915 *** (16.931) 0.113 *** (11.351) 0.016 (0.510) -.63 10-4* (-1.80) -0.100 *** (-3.953) 0.00 * (1.946) 9.67 10-7*** (5.73) 0.030 *** (3.445) 0.907 *** (133.768) 0.111 *** (9.419) 0.00 (0.657) -.5 10-4* (-1.693) -0.105 *** (-3.895) 0.177 * (1.654) 9.81 10-7*** (5.971) 0.018 ** (.495) 0.915 *** (141.139) 0.117 *** (11.067) 0.009 (0.61) -3.06 10-4** (-1.993) -0.094 *** (-3.316) 0.145 (1.98) 1.10 10-6*** (6.575) 0.010 (1.396) 0.9 *** (144.34) 0.10 *** (1.388) -0.007 (-0.177) -.87 10-4* (-1.790) -0.084 *** (-.998) 0.11 (1.043) 1.36 10-6*** (6.96) 0.011 * (1.79) 0.915 *** (135.95) 0.17 *** (1.868) -0.009 (-0.00) 4.6 10-5 (0.5) -0.040 (-1.336) 0.139 (1.134) 1.60 10-6*** (7.494) LL 9884.37 9854.10 9861.9 9863.7 9850.83 987.06 9734.71 9719.0 964.70 9538.49 9473.45 9380.06 933.85 0.006 (0.901) 0.915 *** (137.643) 0.136 *** (13.685) LB(15) 15.00 16.01 14.557 1.551 13.703 16.495 11.338 13.17 17.667 19.958 18.791 1.69 19.891 LBS(15) 1.859 6.803 ** 7.670 ** 5.94 ** 3.90 *.747 *.09 19.873.368 3.051 *** 35.010 *** 7.301 ** 6.804 ** Noes: This able shows he resuls for he TGARCH model IBEXIDDRA μ 0 μ 1 IBEXNR μ DOWNR h αε 1 βh 1 γε 1 I 1 θdownr T-saisics in parenheses. LL is he Log-likelihood saisic. LB(15) and LBS(15) are he Ljung-Box saisics for he sandardized residuals and squared residuals, respecively, wih 15 lagged values included. Significan coefficiens are denoed by ***, ** and * for 1%, 5% and 10% significance levels, respecively. 0.001 (0.05) 19
μ 0-5.67 10-6 (-0.307) μ 1 0.008 *** (4.730) μ -0.008 (-0.57) ω 5.45 10-9*** (3.905) α 0.070 *** (15.480) β 0.91 *** (4.48) γ 0.040 *** (4.104) θ 0.001 ** (.344) Table 8: Reurn and volailiy spillovers from Hypohesis 3 15:35 15:40 15:45 15:50 15:55 16:00 16:10 16:15 16:30 16:45 17:00 17:15 17:30-3.06 10-5 (-1.3) -0.001 (-0.07) -0.018 (-0.886) 1. 10-8*** (5.100) 0.050 *** (8.537) 0.98 *** (10.46) 0.050 *** (4.78) 0.001 * (1.715) -4.7 10-5 (-1.608) -0.008 *** (-.686) -0.039 * (-1.759).04 10-8*** (3.88) 0.066 *** (8.590) 0.911 *** (180.05) 0.047 *** (5.715) 0.004 *** (3.083) -1.06 10-4*** (-3.077) -0.011 *** (-.84) -0.054 ** (-.100) 1.57 10-8*** (3.110) 0.054 *** (9.647) 0.99 *** (38.895) 0.038 *** (4.709) 0.005 *** (3.660) -1.5 10-4*** (-3.0) -0.018 *** (-5.07) -0.065 ** (-.543) 3.14 10-8*** (4.505) 0.054 *** (6.601) 0.93 *** (48.797) 0.045 *** (3.618) 0.004 ** (.013) -1.19 10-4*** (-.865) -0.019 *** (-4.958) -0.06 * (-1.880) 3.87 10-8*** (4.537) 0.061 *** (8.415) 0.9 *** (4.094) 0.033 *** (3.03) 0.004 * (1.788) Mean Equaion -1.01 10-4** (-.01) -0.018 *** (-3.557) -0.085 ** (-.404) Variance Equaion 4.15 10-8*** (3.181) 0.061 *** (8.381) 0.93 *** (189.604) 0.037 *** (3.570) 0.004 (1.113) Saisics -1.07 10-4** (-.019) -0.019 *** (-3.515) -0.086 ** (-.186) 4.91 10-8*** (3.41) 0.05 *** (7.904) 0.96 *** (0.77) 0.045 *** (4.57) 0.007 * (1.87) -6.89 10-5 (-1.15) -0.011 * (-1.661) -0.109 ** (-.348) 7.59 10-8*** (3.807) 0.050 *** (6.901) 0.98 *** (194.389) 0.040 *** (4.786) 0.010 *** (.901) -4.09 10-5 (-0.557) -0.005 (-0.714) -0.130 ** (-.013) 1.19 10-7*** (4.19) 0.034 *** (5.59) 0.931 *** (19.875) 0.06 *** (7.99) 0.019 *** (.91) 1.74 10-4** (.057) 0.013 * (1.799) -0.15 *** (-3.635) 1.98 10-6*** (11.91) 0.169 *** (1.114) 0.755 *** (90.183) 0.049 ** (.64) -0.018 *** (-13.881) -7.91 10-5 (-0.910) 0.01 (1.314) -0.166 ** (-.08).7 10-7*** (5.3) 0.033 *** (4.5) 0.96 *** (164.530) 0.070 *** (6.343) 0.016 (1.359).3 10-4** (.444) 0.040 *** (3.703) -0.174 ** (-.78) 3.4 10-7*** (5.576) 0.09 *** (3.660) 0.91 *** (14.60) 0.086 *** (7.94) LL 15654.80 14910.59 14396.94 13943.59 13661.58 13450.06 173.9 161.70 108.67 11737.75 11413.34 1177.00 11008.10 LB(15) 13.756 1.169 13.659 4.8364 9.6468 6.9964 7.063 6.5311 13.683 16.65 16.71 4.15 * 0.838 LBS(15) 1.7557 3.1583 5.6989 3.739 5.9901 9.6714 4.570 8.6136 13.43 6.0415 13.156 6.5661 10.9 Noes: This able shows he resuls for he TGARCH model IBEXIDDRB μ 0 μ 1 IBEXIDDR OPEN TO15:30 μ DOWNR h αε 1 βh 1 γε 1 I 1 θdownr The exogenous variable IBEXIDDR represens in his hypohesis he dayime reurn from Open o 15:30. T-saisics in parenheses. LL is he Log-likelihood saisic. LB(15) and LBS(15) are he Ljung-Box saisics for he sandardized residuals and squared residuals, respecively, wih 15 lagged values included. Significan coefficiens are denoed by ***, ** and * for 1%, 5% and 10% significance levels, respecively. 0.013 (0.887) 0
Based on he value of he IBEX coefficiens, we find hree differen phases. The firs one, which akes he firs esimaion, shows evidence of a weak underreacion effec which urns ino an overreacion effec, second phase, during he following hour of rading approximaely (unil 16:30). Finally, we find a hird phase where we again observe a weak underreacion effec. We do no find a significan influence of he DOW overnigh reurn on he IBEX inraday dayime reurns unil 15:45, when an overreacion effec appears once he marke has evaluaed he informaion coming from he US. The increasing values of he coefficiens associaed wih he DOW overnigh reurns, as well as heir larger values when compared in absolue erms wih hose relaive o he IBEX reurns, show he imporance of he DOW on he IBEX developmen. Focusing on he volailiy coefficiens, we again find evidence of he exisence of a leverage effec and a significan bu weak volailiy spillover form he DOW overnigh reurn o he IBEX inraday dayime reurn from 15:35 o he end of he session. Finally, he analysis of he Ljung-Box saisics for he sandardized and squared sandardized residuals shows he adequacy of he model. The resuls of he fourh hypohesis are shown in Table 9. This hypohesis solves he problems we found in he second hypohesis relaive o he adequacy of he model for describing he condiional heeroskedasiciy of he daa. In his case, we consider ha in he mean equaion of he model i is more appropriae o relae he IBEX inraday dayime reurns during he las hours of rading wih he IBEX inraday dayime reurn from Open o 15:30 han wih he IBEX overnigh reurn. This is mainly because here is much more informaion o be considered for he Spanish sock marke a 15:30 in he former han in he laer. As prediced, he resuls for he μ 1 coefficiens associaed wih he spillover effecs from he IBEX inraday dayime reurns are all significan and much higher in absolue erms han he μ coefficiens relaed wih he DOW overnigh reurns spillovers, which are also mosly significan. This means ha he IBEX inraday dayime reurns are basically driven by he previous behavior of he Spanish marke during he session and in a minor way by he DOW s behavior. Furhermore, he signs of boh coefficiens show ha he IBEX underreacs o is previous reurns and overreacs o he DOW overnigh reurns, which is in accordance wih he resuls of he previous hypohesis. I is also ineresing o poin ou ha boh effecs increase as he rading day finishes and as more and more updaed informaion abou he markes goes o he IBEX. 1
μ 0 1.91 10-6 (0.11) μ 1 1.000 *** (538.683) μ -0.005 (-0.301) ω 5.7 10-9*** (4.561) α 0.078 *** (14.890) β 0.914 *** (184.88) γ 0.036 *** (3.360) θ 0.001 *** (3.000) Table 9: Reurn and volailiy spillovers from Hypohesis 4 15:35 15:40 15:45 15:50 15:55 16:00 16:10 16:15 16:30 16:45 17:00 17:15 17:30-1.49 10-5 (-0.690) 0.99 *** (375.598) -0.015 (-0.73) 1.56 10-8*** (5.318) 0.096 *** (10.867) 0.901 *** (131.87) 0.008 (0.680) 0.003 *** (3.858) -.99 10-5 (-1.066) 0.985 *** (315.396) -0.034 (-1.460).48 10-8*** (4.433) 0.087 *** (11.355) 0.900 *** (156.35) 0.019 ** (1.97) 0.006 *** (4.85) -9.49 10-5*** (-.87) 0.98 *** (31.195) -0.047 * (-1.791) 1.86 10-8*** (3.44) 0.076 *** (15.378) 0.90 *** (51.834) 0.008 (1.193) 0.008 *** (4.789) -1.10 10-4*** (-.89) 0.979 *** (97.787) -0.061 ** (-.190) 3.85 10-8*** (4.710) 0.077 *** (11.013) 0.911 *** (196.60) 0.03 ** (1.980) 0.006 *** (.736) -1.07 10-4*** (-.63) 0.976 *** (51.586) -0.063 * (-1.94) 4.10 10-8*** (4.468) 0.071 *** (11.703) 0.918 *** (01.487) 0.019 ** (1.981) 0.006 ** (.535) Mean Equaion -9.01 10-5* (-1.89) 0.976 *** (185.757) -0.089 ** (-.443) Variance Equaion 4.37 10-8*** (3.95) 0.060 *** (8.143) 0.93 *** (174.717) 0.037 *** (3.394) 0.007 * (1.803) Saisics -9.67 10-5* (-1.831) 0.975 *** (185.494) -0.091 ** (-.347) 5.30 10-8*** (3.401) 0.055 *** (7.519) 0.94 *** (185.940) 0.04 *** (3.848) 0.009 ** (.147) -6.40 10-5 (-1.051) 0.981 *** (145.04) -0.116 *** (-.63) 7.48 10-8*** (3.671) 0.051 *** (6.943) 0.97 *** (193.84) 0.039 *** (4.531) 0.011 *** (.81) -3.49 10-5 (-0.478) 0.986 *** (133.698) -0.131 ** (-.15) 1.17 10-7*** (4.19) 0.034 *** (5.187) 0.930 *** (15.85) 0.065 *** (7.38) 0.018 *** (.850) -7.34 10-5 (-0.956) 0.997 *** (18.953) -0.150 ** (-.353) 1.59 10-7*** (4.796) 0.031 *** (4.38) 0.98 *** (186.605) 0.076 *** (6.760) 0.010 (1.088) -6.69 10-5 (-0.776) 1.004 *** (110.07) -0.167 ** (-.185).4 10-7*** (5.175) 0.035 *** (4.456) 0.94 *** (166.605) 0.070 *** (6.440) 0.013 (1.119).44 10-4 (.576) 1.033 *** (96.195) -0.175 ** (-.317) 3.13 10-7*** (5.553) 0.09 *** (3.830) 0.9 *** (148.194) 0.084 *** (7.955) LL 16085.89 15150.08 14549.47 1404.46 13744.34 135 1767.77 1645.97 138.97 11764.15 1155.96 1190.1 1100.51 LB(15) 1.643 15.915 13.48 5.8047 11.993 1.486 1.80 11.441 15.093 16.801 16.056 4.555 * 0.607 LBS(15).9781 5.105 1.400 6.954 10.43 11.746 4.4193 8.8491 14. 7.6050 7.4617 6.745 3.67 * Noes: This able shows he resuls for he TGARCH model IBEXIDDRA μ 0 μ 1 IBEXIDDR OPEN TO15:30 μ DOWNR h αε 1 βh 1 γε 1 I 1 θdownr The endogenous variable IBEXIDDRA represens in his hypohesis he dayime reurn from Open o 15:35 and followers while he exogenous variable IBEXIDDR OPEN TO 15:30 represens in his hypohesis he dayime reurn from Open o 15:30. T-saisics in parenheses. LL is he Log-likelihood saisic. LB(15) and LBS(15) are he Ljung-Box saisics for he sandardized residuals and squared residuals, respecively, wih 15 lagged values included. Significan coefficiens are denoed by ***, ** and * for 1%, 5% and 10% significance levels, respecively. 0.010 (0.688)
Wih respec o he resuls of he coefficiens relaive o he asymmery, we observe ha mos of hem are posiive and significan. This concurs wih he resuls obained in he previous hypoheses, as well as he θ coefficiens, associaed wih he volailiy ransmission from he DOW, which are also posiive and significan in mos of he cases. Finally, we make wo more observaions, when he resuls of he Log-likelihood, and Ljung-Box saisics for he sandardized and squared sandardized residuals are compared wih hose obained in he second hypohesis (Table 7). Firsly, ha he log-likelihood sas are much higher in his case, which means ha he model is beer suied. Secondly, all of he Ljung-Box sas are no significan (wih he excepion of wo a he end of he session). Therefore his TGARCH model is clearly adequae for describing he condiional heeroskedasiciy of he daa. Table 10, while showing he resuls of he fifh hypohesis, also provides us wih a general vision of he behavior of he IBEX inraday dayime reurns hroughou he whole session. Firsly, we observe ha a 09:05 AM here are iniial overreacion and underreaion effecs in he IBEX inraday dayime reurns caused by he informaion coming from he previous daily reurns in he IBEX and DOW respecively. Secondly, here are no significan coefficiens in he mean equaion relaed wih he μ 1 and he μ erms unil 1:00 which indicaes ha afer he opening of he Spanish marke here is a period of relaive calm which is broken as he marke begins o ge ready for he opening of he DOW and he arrival of news from he US. This leads us o he hird par of he day when he IBEX inraday dayime reurns underreac o he IBEX previous reurns, which is in accordance wih he fourh hypohesis, and overreac o he DOW reurns (which is also in accordance wih he hird and fourh hypoheses). We find no differences wih respec o he previous resuls of he asymmery and volailiy coefficiens in his case since boh of hem are posiive and significan, which in reference o he asymmery coefficiens indicaes he exisence of a leverage effec. Finally, he Ljung-Box saisics show ha he serial dependence of he condiional mean and variance dependence were well capured by he proposed model. Therefore, he analysis of hese five hypoheses leads us, firsly, o confirm he exisence of reurn and volailiy spillovers from he DOW over he IBEX. Secondly, o sae ha he DOW reurns cause an underreacion effec in he IBEX firs hours of rading (from 09:05 o 1:00) and an overreacion effec in he laer hours (from 15:30 o he end of he rading day). 3
Table 10: Reurn and volailiy spillovers from Hypohesis 5 09:05 09:15 09:30 10:00 11:00 1:00 13:00 14:00 15:00 15:30 16:00 17:00 17:30 Mean Equaion μ 0-1.31 10-4*** -4.01 10-5 -1.3 10-4** -1.8 10-4** -.5 10-4*** -3.05 10-4*** -3.97 10-4*** -3.89 10-4*** -3.11 10-4** -.50 10-4* -3.8 10-4** -3.4 10-4** 3.85 10-5 (-3.339) (-0.763) (-1.97) (-.304) (-.585) (-.67) (-3.337) (-3.19) (-.331) (-1.855) (-.357) (-.107) (0.9) μ 1-0.014 *** -0.003 0.00-0.01 0.006 0.00 * 0.0 * 0.01 * 0.07 ** 0.031 ** 0.034 ** 0.035 ** 0.037 ** (-4.654) (-0.739) (0.414) (-1.545) (0.589) (1.74) (1.836) (1.747) (1.974) (.08) (.410) (.159) (.064) μ 0.01 ** -0.00-0.01-0.016-0.00-0.035 ** -0.033 ** -0.045 *** -0.079 *** -0.089 *** -0.093 *** -0.094 *** -0.08 *** (.538) (-0.315) (-1.466) (-1.545) (-1.638) (-.397) (-.081) (-.777) (-4.345) (-4.799) (-4.916) (-4.48) (-3.63) Variance Equaion ω 1.73 10-7*** 1.73 10-7*** 3.01 10-7*** 4.38 10-7*** 6.55 10-7*** 9.76 10-7*** 1.09 10-6*** 8.98 10-7*** 8.0 10-7*** 8.5 10-7*** 9.64 10-7*** 1.10 10-6*** 1.74 10-6*** (7.930) (7.607) (4.578) (4.93) (4.767) (5.983) (5.569) (4.733) (4.678) (4.69) (4.763) (5.587) (6.843) α 0.068 *** 0.041 *** 0.113 *** 0.09 *** 0.101 *** 0.085 *** 0.103 *** 0.083 *** 0.040 *** 0.041 *** 0.09 *** 0.011 0.007 (6.515) (4.303) (8.896) (6.640) (11.168) (9.76) (10.397) (6.583) (3.19) (3.14) (.76) (1.539) (0.99) β 0.855 *** 0.855 *** 0.784 *** 0.807 *** 0.8 *** 0.83 *** 0.810 *** 0.88 *** 0.868 *** 0.865 *** 0.877 *** 0.910 *** 0.897 *** (59.981) (93.48) (65.993) (63.773) (67.57) (66.610) (60.751) (71.951) (84.67) (76.838) (85.88) (130.589) (111.550) γ -0.00 0.084 *** 0.096 *** 0.118 *** 0.07 *** 0.06 *** 0.046 ** 0.077 *** 0.113 *** 0.13 *** 0.16 *** 0.13 *** 0.148 *** (-0.144) (6.149) (6.419) (6.33) (4.370) (3.377) (.355) (3.689) (6.760) (7.743) (9.157) (11.10) (1.468) θ 0.00 *** 0.005 *** 0.010 *** 0.011 *** 0.015 *** 0.00 *** 0.03 *** 0.09 *** 0.0 *** 0.03 *** 0.018 *** 0.009 *** 0.013 *** (8.405) (9.147) (13.444) (6.870) (6.40) (7.598) (11.070) (8.738) (6.894) (6.193) (5.47) (.905) (.745) LL 14051.79 198.9 19.30 11566.88 10956.40 1059.61 10391.99 1069.94 9987.13 9897.0 9837.03 9478.48 939.64 LB(15) 3.664 *** 9.3871 14.786 10.695 9.6891 14.513 9.3964 1.783 13.693 14.536 16.945 19.713 0.607 LBS(15) 6.0988 4.598 5.3905 16.051 7.3603 5.1194 4.188 8.903 16.614 15.778 19.347 9.655 *** 3.67 * Noes: This able shows he resuls for he TGARCH model IBEXIDDRA μ 0 μ 1 IBEXR -1 μ DOWR -1 Saisics h αε 1 βh 1 γε 1 I 1 θdowr -1 T-saisics in parenheses. LL is he Log-likelihood saisic. LB(15) and LBS(15) are he Ljung-Box saisics for he sandardized residuals and squared residuals, respecively, wih 15 lagged values included. Significan coefficiens are denoed by ***, ** and * for 1%, 5% and 10% significance levels, respecively. 4
Thirdly, o sae ha he influence of he IBEX upon he IBEX inraday reurns is conrary o ha of he DOW because i causes an overreacion effec in he IBEX firs hours of rading and usually an underreacion effec when he inraday dayime reurns are considered as endogenous variables. Addiionally, i is ineresing o poin ou he fac ha he coefficiens relaed wih he DOW are usually higher in absolue erms han he IBEX coefficiens (see Tables 6, 8 and 10 relaive o hypoheses 1, 3 and 5 respecively). Considering ha ime references used o calculae he differen DOW reurns are closer o he period analyzed in each esimaion han he IBEX ones, ha fac could indicae ha he Spanish sock marke overweighs he mos recen informaion as opposed o he older informaion. In summary, hese resuls show wo differen behaviors in he Spanish sock marke. Firsly, ha a he opening of he marke, he normal lack of news during he nigh leads he Spanish marke o follow a conservaive paern. Therefore, in he firs hours of rading he Spanish sock marke follows and overweighs he previous rend of he DOW, which is supposed o conain he mos recen news abou he markes. On he oher hand, i underweighs he iniial overreacion o he previous Spanish marke rend which has older informaion. Secondly, we find he opposie behavior during he las hours of rading. In his case, afer considering he news coming from he US marke, invesors op o ake some profi from he previous rend of he marke by selling in an upward rend or by buying in a downward rend. Finally, we find in all cases significan leverage effecs on volailiy caused by bad news. These resuls are consisen wih he previous empirical evidence which shows significan ransmissions of informaion beween he US markes and differen developed and emerging markes (a few examples are Becker e al., 1990; Peiró e al., 1998; and Lee e al., 004). This overreacion behavior is consisen wih he findings of Fung e al. (000), who sugges he exisence of inraday price reversals following large price changes a he opening of he S&P 500 Fuures marke and he HIS (Hong Kong) Fuures marke; and Lo and MacKinlay (1990) who argue ha when some socks reac more quickly o informaion han ohers hey lead invesors o use a conrarian sraegy ha may produce profis. 4. Conclusions The main objecive of his paper has been he analysis of five differen hypoheses relaive o he reurn and volailiy ransmissions from he DOW and IBEX indexes upon 5
differen inraday reurns of he IBEX in order o undersand he dynamics of he Spanish sock marke during he rading session. The resuls lead us o sae hree main facs. Firsly, he exisence of a significan underreacion effec of he previous DOW dayime reurn upon he IBEX inraday dayime reurns during he firs hours of rading which urns ino an overreacion effec during he las hours of rading. Addiionally, we found he opposie o be rue of he effec of he IBEX reurn measures on he IBEX inraday reurns (overreacion a he morning and underreacion a he end of he rading day). Secondly, by analyzing he coefficien values of each exogenous variable we observed ha hose relaed wih he variable ha conains he mos recen informaion were higher. In our case, ha mosly means ha he informaion which comes from he US marke is more imporan ha he Spanish one. Finally, we found in all cases significan leverage effecs on volailiy caused by bad news. These resuls no only imply imporan informaion for building accurae asse pricing models, planning invesmen sraegies and undersanding he Spanish sock marke bu also sugges he imporance of examining he inraday behavior of sock markes in order o develop a profiable rading sraegy. References Akgiray, V., 1989. Condiional heeroskedasiciy in ime series of sock reurns: evidence and forecass. Journal of Business, 6, 55-80. Andersen, T.G., Bollerslev, T., 1997. Inraday periodiciy and volailiy persisence in financial markes. Journal of Empirical Finance, 4, 115 158. Baillie, R., DeGennaro, R., 1990. Sock reurns and volailiy, Journal of Financial and Quaniaive Analysis, 5, 03-14. Baur, D., Jung, R.C., 006. Reurn and volailiy linkages beween he US and he German sock marke. Journal of Inernaional Money and Finance, 5, 598-613. Becker KG, Finnery JE, Gupa M., 1990. The ineremporal relaion beween he U.S. and Japanese sock markes. Journal of Finance, 45, 197-1306. Black, F., 1976. Sudies of sock price volailiy changes. Proceedings of he 1976 Meeings of he American Saisical Associaion, Business and Economical Saisics Secion, 177 181. Blasco, N., Corredor, P., Sanamaría, R., 00. Is bad news cause of asymmeric volailiy response? A noe. Applied Economics, 34, 17-131. 6
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