Return and Volatility Spillovers Between Large and Small Stocks in the UK

Transcription

1 eurn and Vlailiy Spillvers Beween Large and Small Scks in he UK ichard D. F. Harris Xfi Cenre fr Finance and Invesmen Universiy f Exeer, UK Aniru Pisedasalasai Deparmen f Accuning, Finance and Infrmain Sysems Universiy f Canerbury, New Zealand Augus 005 Paper Number: 06/09 Absrac This paper invesigaes reurn and vlailiy spillver effecs beween he FTSE 100, FTSE 50 and FTSE Small Cap equiy indices using he mulivariae GACH framewrk. We find ha reurn and vlailiy ransmissin mechanisms beween large and small scks in he UK are asymmeric. In paricular, here are significan spillver effecs in bh reurns and vlailiy frm he prflis f larger scks he prflis f smaller scks. Fr vlailiy, here is als evidence f limied feedback frm he prflis f smaller scks he prflis f larger scks, alhugh sub-perid analysis suggess ha his is sme exen perid-specific. Simulain evidence shws ha nn-synchrnus rading penially explains sme, bu n all, f he spillver effecs in reurns, and ha i explains nne f he spillver effecs in vlailiy. These resuls are cnsisen wih a marke in which infrmain is firs incrpraed in he prices f large scks befre being impunded in he prices f small scks. KEYWODS: eurn and vlailiy spillvers; Mulivariae GACH; FTSE indices. Address fr Crrespndence: ichard D.F. Harris, Xfi Cenre fr Finance and Invesmen, Universiy f Exeer, Exeer EX4 4ST, UK. .D.F.Harris@exeer.ac.uk. 1

2 1. Inrducin Transmissin mechanisms beween he reurns and vlailiies f differen scks are impran fr a number f reasns. Firsly, ransmissin mechanisms ell us smehing abu marke efficiency. In an efficien marke, and in he absence f ime-varying risk premia, i shuld n be pssible frecas he reurns f ne sck using he lagged reurns f anher sck. The finding ha here are spillver effecs in reurns implies he exisence f an expliable rading sraegy and, if rading sraegy prfis exceed ransacin css, penially represens evidence agains marke efficiency. Secndly, ransmissin mechanisms may be useful fr prfli managemen, where knwledge f reurn spillver effecs may be useful fr asse allcain r sck selecin. Thirdly, infrmain abu vlailiy spillver effecs may be useful fr applicains in finance ha rely n esimaes f cndiinal vlailiy, such as pin pricing, prfli pimizain, value a risk and hedging. Many previus sudies have dcumened ha he reurns f large and small scks in he US sck marke are crss-crrelaed. 1 Mrever, a number f hese sudies shw ha hese crss-crrelains are asymmeric: he reurns f small sck prflis end be crrelaed wih he lagged reurns f large sck prflis, while he reurns f large sck prflis end be uncrrelaed wih he lagged reurns f small sck prflis. L and MacKinlay (1990a, 1990b) rule u nn-synchrnus rading as an explanain since implausible levels f nn-synchrnus rading are required generae he size f he crss-crrelains ha exis in pracice. A number f her explanains have herefre been prpsed. Mech (1993) suggess ha asymmery in he crss-crrelain beween reurns n large and small scks is due ransacin css, and shws ha he speed f price adjusmen is assciaed wih he sandard deviain f reurns and he bid-ask spread. Chan (1993) suggess ha differences in signal qualiy beween large and small scks induce asymmery in heir crsscrrelains. In paricular, if he signal qualiy f large scks is assumed be beer han ha f small scks, he cvariance f he curren reurns f small scks wih he lagged reurns f large scks is larger han he cvariance f he curren reurns f 1 See, fr example, L and MacKinlay (1990a, 1990b), Budukh, ichardsn and Whielaw (1994), Mech (1993), Badrinah, Kale and Ne (1995), McQueen, Pinegar and Thrley (1996) and Campbell, L and MacKinlay (1997, pages 74-78).

3 large scks wih he lagged reurns f small scks. Sme sudies (fr example, Grinbla, Timan, and Wermers, 1995; Keim and Madhavan, 1995) argue ha asymmeric spillver effecs in he reurns f large and small scks are relaed asymmeric rading paerns and he behavir f insiuinal invesrs. Cnrad, Gulekin and Kaul (1991) shw ha he same asymmery ha exiss in he ransmissin f shr hrizn reurns beween large and small scks in he US als exiss in he ransmissin f vlailiy. They find ha vlailiy shcks large scks are impran fr he fuure vlailiy f small scks, bu ha vlailiy shcks smaller scks have lile r n impac n he fuure vlailiy f large scks. As wih he resuls fr reurn spillvers, simulain evidence suggess ha he bserved spillver effecs in vlailiy are n caused by nn-synchrnus rading. Cnrad Gulekin and Kaul (1991) ne ha since sck price vlailiy is direcly relaed he rae f flw f infrmain he marke (see ss, 1989), he asymmery in vlailiy spillvers beween large and small scks is cnsisen wih a marke in which he prices f large scks respnd new infrmain immediaely, bu he prices f small scks respnd wih a lag. This explanain is suppred by McQueen, Pinegar and Thrley (1996), wh shw ha small scks display a delayed reacin cmpared large scks when news reaches he marke. Using lnger hrizn reurns, Hasan and Francis (1998) als find ha here are vlailiy spillvers beween small and large scks in he US, bu in cnras wih Cnrad Gulekin and Kaul (1991), hey find ha hese spillvers are apprximaely symmeric, acing bh frm large scks small scks, and frm small scks large scks. This paper invesigaes he reurn and vlailiy ransmissin mechanisms beween large and small scks in he UK sck marke using daily daa n he FTSE 100, FTSE 50 and FTSE Small Cap equiy indices. We invesigae hese ransmissin mechanisms using he cnsan crrelain mulivariae GACH mdel f Bllerslev (1990). We mdel he spillver effecs by inrducing in he mean and variance equain fr each index, he lagged shcks he reurns and vlailiies f he her w indices. T ensure ha ur resuls are rbus, we include dummy variables capure uliers, calendar effecs and he asymmeric respnse f vlailiy gd and bad news. T furher es he rbusness f ur resuls, we cnduc he analysis using bh he full sample and w sub-samples. Our resuls shw ha here are srng 3

4 reurn and vlailiy ransmissin mechanisms beween small and large scks in he UK sck marke. Furhermre, cnsisen wih he resuls f her sudies fr he US, we find ha hese reurn spillver effecs are asymmeric. In paricular, here are very significan reurn spillvers frm he prflis f large scks he prflis f small scks. Fr vlailiy, here are again psiive spillvers frm he prflis f large scks he prflis f small scks, alhugh here is als evidence f feedback frm he prflis f smaller scks he prflis f larger scks, and in ne case, his feedback effec is negaive. Hwever, fr he sub-samples, he paern f vlailiy spillvers is very similar ha fr reurn spillvers, wih nly limied psiive feedback frm small sck prflis large sck prflis. In rder analyse he effec f nn-synchrnus rading n ur resuls, we underake a Mne Carl simulain experimen in which daa are simulaed fr prflis f small, medium and large scks. The individual scks in he hree prflis are characerised by varying prbabiliies f nn-rading, which are esimaed using he empirical nn-rading frequencies fr he hree FTSE indices. The simulain resuls sugges ha nn-synchrnus rading leads spillver effecs in reurns, alhugh he simulaed spillver effecs are n as large as hse ha are bserved empirically. Similarly, he simulain evidence suggess ha nn-synchrnus rading cann explain he bserved paern f spillver effecs in vlailiy. We herefre cnclude ha ur empirical resuls are cnsisen wih a marke in which infrmain is firs incrpraed in he prices f large scks befre being impunded in he prices f small scks. The remainder f he paper is rganized as fllws. The fllwing secin describes he daa ha we use in he sudy. Secin 3 gives deails f he empirical mehdlgy. Secin 4 reprs he resuls. Secin 5 presens he resuls f he Mne Carl simulain. Secin 6 ffers a summary and cnclusin.. Daa Descripin The empirical analysis uses cninuusly cmpunded daily sck reurns fr he FTSE 100, FTSE 50 and FTSE Small Cap indices frm 1 January December 00, bained frm Daasream (a al f 4,435 bservains). The FTSE 4

5 100, FTSE 50 and FTSE Small Cap indices are marke-weighed indices ha accun fr apprximaely 85 percen, 1 percen and 3 percen f he FTSE All Share index, respecively, a he end f 00. We use shr hrizn reurns because we wan analyse spillver effecs in bh he mean and vlailiy f he hree series, bu ime series variain in cndiinal vlailiy ends be much weaker fr lnger hrizn reurns. Fr he sub-perid analysis, we spli he full sample in w equal subperids. The firs sub-sample is frm 1 January June 1994, while he secnd sub-sample is frm 1 July December 00. Table 1 reprs summary saisics fr he hree reurn series fr he full sample. Panel A reprs he mean, sandard errr, skewness and excess kursis cefficiens and he Jarque-Bera saisic es he null hyphesis ha reurns are nrmally disribued. All hree series are negaively skewed and highly lepkuric, and he Jarque-Bera saisic rejecs he null hyphesis f nrmaliy very srngly. Panel B f Table 1 reprs he firs fur aucrrelain cefficiens fr reurns and squared reurns fr each index, geher wih Ljung-Bx prmaneau saisics. Fr all hree indices, reurns are serially crrelaed, alhugh he magniude f he serial crrelain decreases wih capialisain. Squared reurns are highly serially crrelaed fr all hree series, indicaing he presence f vlailiy clusering. In cnras wih he paern f serial crrelain in reurns, he magniude f he serial crrelain in squared reurns increases wih capialisain, implying ha ACH effecs are srnger fr large scks han fr small scks. [Table 1] 3. Mehdlgy 3.1 Mdelling he eurns and Vlailiies f he Indices As a benchmark, we firs mdel he dynamic prperies f he reurns and vlailiies f he FTSE 100, FTSE 50 and FTSE Small Cap reurn series wihu spillver effecs. We use he fllwing mulivariae A-GJ-GACH-M mdel fr he hree indices i, j=1,, 3 5

6 4 i = α 0 + n= 1, α + γ h + c OCT 87 + c ASIA 97 + c 3 JAN n + c 4 n MON i ii, + ε 1 (1) h i = β 0 + β 1 i 1 + β ε 1 + λi 1ε d 3 JAN h + d 4 MON I d OCT d ASIA () h ( h h ) = ρ (3) ij, ij ii, jj, where, is he reurn f prfli i in perid, ψ N ( 0, H ) i ε, ψ 1 is he se f 1 all infrmain available a ime 1 and H = ] is he cndiinal cvariance [ h ij, marix. I i 1 is a dummy variable ha is equal ne if he lagged shck reurns, 1, ε is negaive, and zer herwise. OCT87 is a dummy variable ha is equal ne fr bservains beween 19/10/87 and 4/11/87 and zer herwise. ASIA97 is a dummy variables ha is equal ne fr bservains beween 3/10/97 and 8/10/97 and zer herwise. JAN is a dummy variable ha is equal ne fr he firs week in January and zer herwise. Mndays and zer herwise. MON is a dummy variable ha is equal ne fr The A(4) specificain fr he mean equain (1) was chsen n he basis f he Schwarz Bayesian Crierin (SBC) frm a general AMA(p,q) specificain, alhugh he mdel seleced by he Akaike Infrmain Crierin (AIC) led bradly similar empirical resuls. We have specified a GACH-in-mean erm, wih he cndiinal variance f each index included as an explanary variable in he respecive mean equain. This is expli as much infrmain in esimaing expeced reurns, raher han impse a paricular asse pricing resricin, and is cmmn in he lieraure. See, fr example, Hama, Masulis and Ng (1990), Cnrad, Gulekin and Kaul (1991), Ng, Chang and Chu (1991) and Thedssiu and Lee (1993). 6

7 The mdel fr he cndiinal cvariance marix, given by () and (3), is based n he cnsan crrelain (CCO) specificain f he mulivariae GACH mdel f Bllerslev (1990). The mdel specifies he cndiinal variance f each index as a univariae GACH mdel, wih he cndiinal cvariance f any w series i and j deermined by he cndiinal variances, h ii, and h jj,, and he cnsan crrelain cefficien, ρ ij. While here are several mulivariae GACH mdels chse frm, he CCO mdel has he advanage f being parsimnius and hence grealy reduces he cmpuainal effr required esimae he mdel, generally leading mre reliable parameer esimaes. 3 This is paricularly impran in he presen case wing he large number f parameers be esimaed. The GACH(1,1) specificain fr he cndiinal variance in equain () was chsen fr he sake f parsimny. In rder ensure he rbusness f ur resuls, we mdify he CCO mdel in several ways. Firsly, i is well dcumened ha vlailiy respnds asymmerically gd and bad news and, mrever, ha vlailiy spillvers can be significanly undersaed if his asymmeric effec is ignred. 4 T capure he asymmeric effec f news n vlailiy, we use he GJ specificain f he mulivariae GACH mdel and include a dummy variable fr negaive reurn shcks (see Glsen, Jagannahan and unkle, 1993). Secndly, allw fr uliers in he daa, we include dummy variables in bh he reurn and vlailiy equains fr perids f exreme marke mvemens. The large negaive reurns in inernainal equiy markes during he week fllwing he sck marke crash f 19 Ocber 1987 are well dcumened. S is he increase in he cndiinal vlailiy f reurns. 5 Fllwing Aggarwal, Inclan and Leal (1999), we include in he full sample and he firs sub-sample, a dummy variable fr he w weeks fllwing he sck marke crash f We als allw fr he 1997 Asian financial crisis by including in he full sample and he secnd subsample, a dummy variable fr he week ha marked he sar f he crisis (see Wang, u and Firh, 00). Lasly, we als include dummy variables in bh he mean equain and he variance equain fr he well-knwn January and Mnday effecs. Many sudies have shwn ha reurns are sysemaically higher during he firs week 3 See Engle and Krner (1995), Krner and Ng (1998). 4 See Glsen, Jagannahan and unkle (1993), Engle and Ng (1993), Bae and Karlyi (1994), Wang, ui and Firh (00) and Hung, Lee and S (003). 7

8 f January han in her mnhs f he year, and lwer n Mndays han n her days f he week. 6 A number f sudies, including Cnrad, Gulekin and Kaul (1991), have als fund ha here are similar calendar effecs in he vlailiy f reurns. 3. Mdelling Spillver Effecs Beween he Indices T analyse he reurn and vlailiy spillvers beween he FTSE 100, FTSE 50 and FTSE Small Cap indices, we mdify he A-GJ-GACH-M mdel given by (1)-(3) include in he mean and variance equains fr each index, he lagged shcks he means and vlailiies f he her w indices. Specifically, capure spillver effecs in he mean equain fr index we include he firs lag f he reurns f each f he indices i j. T capure spillver effecs in he vlailiy equain fr index we include he firs lag f he squared reurn shcks f each f he indices mdel including spillvers fr indices i, j= 1,, 3 is herefre given by i j. The, = α + α + γ h + c OCT 87 + c ASIA 97 i + c n= 1 MON n + n 3 w j= 1, j i j i ii, j, 1 + ε 1 + c 3 JAN (4) h i = β 0 + β 1hi 1 + β ε 1 + λi I 1ε 1 + d 1OCT87 + d ASIA97 + d 3 JAN + d 4 MON + 3 z j j= 1, j i ε j, 1 (5) h ( h h ) = ρ (6) ij, ij ii, jj, The parameer w i, j measures he parial impac n he reurns f index i f pas reurn shcks f he w remaining indices, while he parameer z, measures he parial i j impac n he vlailiy f index i f pas vlailiy shcks he w remaining indices. We esimae he mulivariae GACH mdel, bh wih and wihu spillver 5 See ll (1988), Schwer (1990), Aggarwal, Inclan and Leal (1999). 6 Fr evidence f he January effec, see, fr example, Tinic and Wes (1984), Laknishk and Smid (1988) and Draper and Paudyal (1997). 8

9 effecs, by quasi-maximum likelihd wih a nrmal cndiinal disribuin (see Bllerslev and Wlridge, 199). We use he BFGS algrihm wih a cnvergence crierin f applied he funcin value. bus errrs are cmpued ha are valid under nn-nrmaliy (see Whie, 198). 4. Empirical esuls 4.1 Mulivariae A(4)-GJ GACH(1,1)-M esuls Table reprs he esimaed parameers f he mulivariae A(4)-GJ- GACH(1,1)-M mdel fr each he hree indices, given by equains (1), () and (3), geher wih Ljung-Bx es saisics fr he sandardized residuals (LB(4)) and he squared sandardized residuals (LB (4)). Fr all hree indices, he sum f he esimaed GACH parameers, β 1 + β, suggess ha vlailiy is sainary bu highly persisen. In paricular, he half-life f vlailiy fr he FTSE 100, FTSE 50 and FTSE Small Cap indices is 0.88 days, 9.74 days and days, respecively. 7 The GACH-in-mean cefficien, γ i, is significanly psiive fr all hree indices, implying ha higher vlailiy is assciaed wih higher expeced reurns, which is cnsisen wih risk aversin. The cefficien f he asymmery erm, λ i, is significanly psiive fr he FTSE 100 index, implying ha bad news has a larger impac n he vlailiy f he FTSE 100 index han gd news des. The asymmery erm is als psiive fr he FTSE 50 and FTSE Small Cap indices, bu n saisically significan. As expeced, he esimaed crrelain cefficiens, amng he hree indices are psiive and highly significan. ρ ij, There is srng evidence f he effec f he Ocber 1987 crash n he reurns and cndiinal variances f he hree indices. In paricular, reurns are very significanly negaive during he crash, and fr he FTSE 50 and FTSE Small Cap indices, vlailiy is significanly higher. The Asian crisis had a significan negaive impac n reurns all hree indices, and a marginally significan psiive impac n vlailiy. The 7 The half-life is cmpued as hi = ln( 1/ ) / ln( β 1 + β + λi / ) under he assumpin ha he reurn disribuin is symmeric. 9

10 January effec is insignifican fr reurns, bu has a psiive impac n vlailiy, which is significan fr he FTSE 50 index, and marginally significan fr he FTSE 100 and FTSE Small Cap indices. The Mnday effec is significanly negaive fr FTSE 100 and FTSE 50 reurns, and marginally significanly negaive fr FTSE Small Cap reurns. Fr vlailiy, he Mnday dummy is significanly negaive fr he FTSE 50 index, and negaive wih marginal significance fr he FTSE 100 index. The LB (4) saisics sugges ha he mulivariae GACH(1,1) specificain successfully capures he serial crrelain in squared reurns fr each f he hree indices. The LB(4) saisics shw ha here is significan serial crrelain in he residuals fr he hree indices. Hwever, i will be seen belw ha his serial crrelain is significanly reduced nce we include reurn and vlailiy spillvers in he mdel. Alernaive AMA specificains f he mean equain (paricularly hse seleced by he AIC, which generally include lnger lags f bh he A and MA cmpnens) failed eliminae his serial crrelain. [Table ] Table 3 reprs he esimaed parameers f he mulivariae A(4)-GJ GACH(1,1)-M mdel wih spillver effecs fr each he hree indices, given by equains (4), (5) and (6). Cmparing Table and Table 3, i can be seen ha he inrducin f he spillver effecs in he mdel generally has nly a small effec n he esimaed parameer values fr he mean and variance equains f he hree indices. Mrever, he inrducin f spillver effecs significanly reduces he serial crrelain in he residuals. The LB(4) saisic is nw insignifican fr he FTSE Small Cap Index, and cnsiderably reduced fr he FTSE 100 and FTSE 50 indices. Again, alernaive AMA specificains f he mean equain failed cmpleely eliminae he remaining serial crrelain. Hwever, he chice f mdel fr he mean reurn fr hese series des n significanly affec he resuls n mean and vlailiy spillvers ha are repred belw, and alers nne f he qualiaive cnclusins. 8 8 esuls bained using alernaive specificains f he mean equain are available frm he auhrs. 10

11 Table 3 shws ha here are very significan reurn and vlailiy spillvers beween he FTSE 100, FTSE 50 and FTSE Small Cap indices. Mrever, hese spillver effecs are highly asymmeric. In paricular, here are significan psiive spillver effecs in reurns frm he FTSE 100 index he FTSE 50 and FTSE Small Cap indices. There is als a marginally significan psiive spillver frm he FTSE 50 index he FTSE Small Cap index. In cnras, here are n saisically significan spillver effecs frm he prflis f smaller scks he prflis f larger scks. Cnsisen wih he findings f previus sudies fr he US cied abve, we herefre find ha here are very significan asymmeric spillver effecs frm he reurns f large scks he reurns f small scks. Fr cndiinal vlailiy, he spillver effecs are mre cmplex. We again find ha here are significan spillver effecs frm he FTSE 100 index bh he FTSE 50 index and he FTSE Small Cap index and frm he FTSE 50 index he FTSE Small Cap index. These findings are cnsisen wih hse f Cnrad, Gulekin and Kaul (1991) fr he US. Hwever, we als find ha here is evidence f feedback in vlailiy frm smaller scks larger scks, wih a significan negaive spillver beween he FTSE 50 index and he FTSE 100 index, implying ha an increase in he vlailiy f he FTSE 50 index is assciaed wih a subsequen decrease in he vlailiy f he FTSE 100 index. There is als a psiive spillver in vlailiy frm he FTSE Small Cap index he FTSE 100 index, and a marginally significan psiive spillver frm he FTSE Small Cap index he FTSE 50 index. In rder shed mre ligh n he bserved spillver paerns, we cnduc he same analysis using each f he w sub-samples. [Table 3] 4. Sub-Perid Analysis Table 4 presens he resuls fr he firs sub-sample, while Table 5 presens he resuls fr he secnd sub-sample. The paern f reurn spillvers fr bh sub-samples are very similar hse repred fr he full sample. We again find ha he spillver effecs in reurns are highly asymmeric in bh sub-samples. There are highly significan psiive spillver effecs in reurns frm he FTSE 100 index bh he 11

12 FTSE 50 and FTSE Small Cap indices. The evidence f asymmery is even mre prnunced fr he secnd sub-sample, wih an addiinal significan psiive reurn spillver frm he FTSE 50 index he FTSE Small Cap index. There are marginally significan negaive spillvers frm he FTSE Small Cap index he FTSE 50 index in he secnd sub-sample, and frm he FTSE 50 index he FTSE 100 index in he firs sub-sample. Fr cndiinal vlailiy, he psiive spillver effecs frm he FTSE 100 index he FTSE 50 index and he FTSE Small Cap index ha are presen in he full sample are als presen in he w sub-samples. The psiive spillver frm he FTSE 50 index he FTSE Small Cap index ha is presen in he full sample is significan fr he secnd sub-sample, bu n fr he firs sub-sample. The psiive spillver effec frm he FTSE Small Cap index he FTSE 100 index ha is presen in he full sample, is marginally significan in he firs sub-sample, bu absen in he secnd subsample. Hwever, in he secnd sub-sample, here is a significanly psiive spillver frm he FTSE Small Cap index he FTSE 50 index ha is nly marginally significan in bh he full sample and he firs sub-sample. The significan negaive spillver frm he FTSE 50 index he FTSE 100 index ha is presen in he full sample is insignifican in bh sub-samples. The resuls f his secin herefre sugges ha he spillver effecs in reurns and vlailiy frm larger sck prflis smaller sck prflis are rbus wih respec he ime-perid cnsidered. The spillvers in bh reurns and vlailiy end be srnger in he secnd sub-sample han he firs sub-sample. Hwever, here remain sme marginally significan feedback effecs in vlailiy frm he prflis f smaller scks he prflis f larger scks, bu hese vary smewha wih he ime-perid cnsidered. The negaive spillver frm he FTSE 50 index he FTSE 100 index is n presen in eiher f he w sub-samples, casing dub n is rbusness and suggesing ha i culd be, sme exen, spurius. [Tables 4 and 5] 1

13 5. The Effec f Nn-synchrnus Trading n eurn and Vlailiy Spillvers Many previus sudies (fr example, L and Mackinlay, 1990a, 1990b) repr evidence ha nn-synchrnus rading can penially induce an asymmery in he ransmissin mechanisms f reurns beween large and small scks. T invesigae he penial effecs f nn-synchrnus rading n ur resuls, we emply he simulain experimens used in Cnrad, Gulekin and Kaul (1991) and Kadlec and Paersn (1999). These simulain experimens are based n he nn-synchrnus rading mdel firs develped by Schles and Williams (1977) and laer generalised by L and MacKinlay (1990a). Suppse ha he unbservable laen cninuusly cmpunded reurns mdel. i, f N securiies are generaed by he fllwing single-facr i, = α i + β i M + ε, i= 1,..., N (7) where M N(0, ) is a zer-mean cndiinally heerscedasic cmmn facr ~ h M, and ε i ~ N(0, h ) is a zer-mean idisyncraic nise erm ha is emprally and, ε crss-secinally independen a all leads and lags. When M is he reurn n he marke prfli, equain (7) represens he marke mdel f Sharpe (1964). We assume ha he cndiinal vlailiy f GACH(1,1) mdel. M is generaed by he fllwing asymmeric h ε (8) M, = a0 + a1hm, 1 + am 1 + a3i 1 M, 1 In rder calibrae his mdel, we esimae i fr he FTSE All Share index fr he full sample perid. This yields parameer esimaes ˆ a =.73*, ˆ1 = a, a ˆ = and a ˆ3 = Using hese parameer esimaes, and seing he iniial cndiinal variance, h M,, he esimaed uncndiinal variance f he FTSE All Share index, we use equain (8) generae he cndiinally heerscedasic facr reurn, M. We hen use equain (7) generae he individual sck reurns, Fr all scks, β i is se equal uniy, and α i is se equal zer. Fllwing Kadlec i. 13

14 and Paersn (1999), in rder esimae he variance f ε, we firs randmly selec 100 scks frm he FTSE All Share index a he end f 00. We regress he daily reurns f each f hese individual scks n a cnsan and he daily reurn n he FTSE All share index. We hen calculae he average variance f he residuals bained frm hese regressins and use his as an esimae f h ε. We nw inrduce nn-synchrnus rading in he simulain mdel. If securiy i rades in perid +1 bu did n rade in perid, is bserved reurn, i 1, +, a + 1 is simply he sum f is laen reurns ha perid and is laen reurns fr all pas cnsecuive perids in which i did n rade. Hence, he bserved reurn,,, is i given by he fllwing schasic prcess. = k= 0 i, X ( k) k, i= 1,..., N (9) where he randm weigh X i, ( k) is an indicar variable ha akes he value 1 when securiy i rades a ime bu has n raded in any f he k previus perids, and akes he value 0 herwise. T simulae he bserved reurn,,, we firs simulae 4435 daily laen reurns,,, i i fr 10 large, 10 medium and 10 small scks. We generae he nn-rading hisry fr each individual sck frm a Bernulli prcess, using he empirical nn-rading frequencies f he FTSE 100, he FTSE 50 and he FTSE Small Cap indices. These empirical nn-rading frequencies are , and , respecively. 9 Once he laen reurns and he nn-rading hisry f large, medium and small scks are generaed, an bserved reurn fr each individual sck is cmpued using equain (9). The daily reurns fr individual small, medium and large scks are hen aggregaed in small, medium, and large prflis respecively. As a benchmark, we als simulae he reurn and vlailiy ransmissins under he assumpin f n nn- 9 These nn-rading frequencies are cmpued frm he daily daa fr he individual scks ha cmprise each f he FTSE 100, FTSE 50 and FTSE Small Cap indices beween 1 January 1986 and 31 December

15 synchrnus rading. In his case, we simply repea he simulain described abve, bu wih he hree nn-rading prbabiliies se zer. The simulains are underaken using 1000 replicains. T examine he reurn ransmissin mechanisms acrss he hree prflis, we esimae he fllwing regressin fr each index i = 1,, 3. γ +, (10) = 0+ γ 11, 1+ γ, 1+ γ 33, 1 u where γ 0 is a cnsan, and γ 1, γ and γ 3 are he cefficiens f he lagged reurns f prflis f he large, medium and small sck prflis respecively. The vlailiy ransmissin mechanisms acrss all hree prflis are invesigaed by esimaing he fllwing regressin. ˆ ω ˆ ˆ ˆ ˆ + (11) u = 0 + ω1u1, 1 + ωu, 1 + ω3u3, 1 + ω4 I 1u 1 v where ω 0 is a cnsan, and ω 1, ω and ω 3 are he cefficiens f he lagged squared reurn shcks f prflis f he large, medium and small sck prflis respecively. These equains are analgus he mulivariae asymmeric GACH mdel wih spillver effecs ha is used in he empirical analysis in he previus secin. Table 6 reprs he resuls fr he reurn ransmissins. Panel A shws evidence f asymmeric reurn spillvers frm larger sck prflis smaller sck prflis when nn-synchrnus rading is allwed fr in he simulain prcess, alhugh here is ne case ha indicaes a reurn spillver frm a smaller sck prfli a larger sck prfli. This asymmery in reurn spillver effecs is cnsisen wih he empirical resuls repred in he previus secin. Hwever, he esimaed crssauregressive parameers in he simulain are cnsiderably lwer han hse bserved in he empirical analysis. When we assume n nn-synchrnus rading in he simulain prcess, hese spillver effecs disappear alms cmpleely. These resuls herefre sugges ha nn-synchrnus rading may explain a prprin f he asymmeric spillver effecs beween he FTSE 100, FTSE 50 and FTSE Small Cap indices, bu is n able accun fr all f i. This is cnsisen wih he findings f 15

16 L and MacKinlay (1990a and 1990b), wh find ha nn-synchrnus rading, while generaing significan reurn spillvers beween large and small scks, is insufficien explain he magniude f lagged crss-crrelains in sck reurns bserved in he US. [Table 6] Table 7 suggess ha nn-synchrnus rading is als unlikely fully explain he bserved spillver effecs in vlailiy beween he FTSE 100, FTSE 50 and FTSE Small Cap indices. When here is n nn-synchrnus rading, here is a symmeric paern f vlailiy spillvers beween he large, medium and small prflis (which arises frm he single facure naure f he simulain mdel). In cnras wih he simulain evidence fr reurn spillvers, he inrducin f nn-synchrnus rading has n disinguishable effec n he paern f spillvers in vlailiy. Furhermre, he esimaed lagged crss-crrelains in squared residuals bserved in he simulain wih nn-synchrnus rading are n significanly differen frm hse bserved in he simulain wih n nn-synchrnus rading. Thus, i is unlikely ha nnsynchrnus rading wuld be able accun fr he asymmeric paern f vlailiy spillvers ha is bserved in pracice. [Table 7] 6. Cnclusin In his paper, we invesigae reurn and vlailiy spillver effecs beween large and small scks in he UK sck marke using he mulivariae A-GJ GACH-M mdel. We find ha he reurns and vlailiies f large scks are impran in predicing he fuure dynamics f smaller scks, bu ha he reurns and vlailiies f smaller scks have much less impac n he fuure dynamics f large scks. Our empirical resuls sugges ha infrmain flw has an influence n he paern f he ransmissin mechanisms beween large and small scks. Marke-wide infrmain is firs incrpraed in he prices f large scks befre being impunded in he prices f small scks. In her wrds, he prices f small scks respnd wih a delay 16

17 he arrival f marke-wide infrmain. Simulain evidence suggess ha nnsynchrnus rading can accun fr sme f he spillver effecs in reurns, bu n all f i. Similarly, he simulain evidence suggess ha nn-synchrnus rading is unlikely accun fr he spillver effecs in vlailiy. The resuls are cnsisen wih previus sudies ha find a similar paern f reurn and vlailiy spillvers fr he US, and are penially useful fr a range f applicains in finance ha rely n frecass f reurns and vlailiies. 17

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19 Grinbla, M., S. Timan, and. Wermers (1995), Mmenum Invesmen Sraegies, Prfli Perfrmance, and Herding: A Sudy f Muual Fund Behavir, American Ecnmic eview, Vl. 85, pp Hama, Y.,.W. Masulis, and V.K. Ng (1990), Crrelains in Price Changes and Vlailiy acrss Inernainal Sck Markes, The eview f Financial Sudies, Vl. 3, N., pp Hasan, I., and B.B. Francis (1998), Macrecnmic Facrs and he Asymmeric Predicabiliy f Cndiinal Variances, Eurpean Financial Managemen, Vl. 4, N., pp Hung, M.W., C.F. Lee, and L.C. S (003), The Impac f Freign-lised Single Sck Fuures n he Dmesic Underlying Sck Markes, Applied Ecnmics Leers, Vl. 10, N.9, pp Kadlec, G.B., and D.M. Paersn (1999), A Transacins Daa Analysis f Nnsynchrnus Trading, The eview f Financial Sudies, Vl. 1, N. 3, pp Keim, D., and A. Madhavan (1995), Anamy f he Trading Prcess: Empirical Evidence n he Behavir f Insiuinal Traders, Jurnal f Financial Ecnmics, Vl. 37, pp Krner, K., and V.K. Ng (1998), Mdeling Asymmeric Cmvemen f Asse eurns, eview f Financial Sudies, Vl. 11, N. 4. Laknishk, J., and S. Smid (1988), Are Seasnal Anmalies eal?: A Niney Year Perspecive, eview f Financial Sudies, Vl. 1, pp L, A. W., and A. C. MacKinlay (1990a), An Ecnmeric Analysis f Nnsynchrnus Trading, Jurnal f Ecnmerics, Vl. 45, pp L, A. W., and A. C. MacKinlay (1990b), When are Cnsrarian Prfis due Shck Marke Overreacin?, eview f Financial Sudies, Vl. 3, pp McQueen, G., M. Pinegar, and S. Thrley (1996), Delayed eacin Gd News and he Crss-Aucrrelain f Prfli eurns, Jurnal f Finance, Vl. 51, N. 3, pp Mech, T. (1993), Prfli Aucrrelain, Jurnal f Financial Ecnmics, Vl. 34, pp Ng, V.K.,.P. Chang and. Chu (1991), An Examinain f he Behavir f Inernainal Sck Marke Vlailiy, in: S. Ghn hee and sia P. Chang, eds., Pacific-Basin Capial Marke esearch, Vl. (Nrh-Hlland, Amserdam), Pp ll,. (1988), The Inernainal Crash f Ocber 1987, Financial Analyss Jurnal, Sepember-Ocber, pp

20 ss, S.A. (1989), Infrmain and Vlailiy: The N-Arbirage Maringale Apprach Timing and esluin Irrelevancy, Jurnal f Finance, Vl. 44, pp Schles, M., and J. Williams (1977), Esimaing Beas frm Nnsynchrnus Daa, Jurnal f Financial Ecnmics, Vl. 5, pp Schwer, G.W. (1990), Sck Vlailiy and he Crash f 87, The eview f Financial Sudies, Vl. 3, N. 1, pp Sharpe, W.F. (Sep. 1964), Capial Asse Prices: A Thery f Marke Equilibrium under Cndiins f isk, Jurnal f Finance, pp Thedssiu, P. and U. Lee (1993), Mean and Vlailiy Spillvers acrss Majr Nainal Sck Markes: Furher Empirical Evidence, Jurnal f Financial esearch, Vl. 16, N. 4, pp Tinic, S. M. and.. Wes (1984), isk and eurn: January vs he es f he Year, Jurnal f Financial Ecnmics, Vl. 13, pp Wang, S.S., O.M. u and M. Firh (00), eurn and Vlailiy Behavir f Dually-raded Scks: he Case f Hng Kng, Jurnal f Inernainal Mney and Finance, Vl. 1, pp Whie, H., 198, Maximum Likelihd Esimain f Misspecified Mdels, Ecnmerica 50,

21 Table 1 Descripive Saisics and Aucrrelains Panel A: Descripive Saisics Index Mean S Dev Skewness Kursis JB Saisic FTSE ** FTSE ** FTSE SC ** Panel B: Aucrrelains FTSE 100 FTSE 50 FTSE SC FTSE 100 FTSE 50 FTSE SC ρ ** 0.** 0.30** 0.51** 0.35** 0.9** ρ -0.04** 0.1** 0.0** 0.9** 0.1** 0.16** ρ -0.04** 0.08** 0.18** 0.18** 0.14** 0.1** 3 ρ ** 0.14** 0.0** 0.18** 0.34** 0.5** LB(4) 30.18** ** 913.3** 1,791.39** 1,335.64** ** Nes: Panel A reprs he mean, sandard deviain and skewness and excess kursis cefficiens, and he Jarque-Bera es saisic fr nrmaliy. Panel B reprs he firs fur aucrrelains fr he reurns and squared reurns f each index and furh-rder Ljung-Bx saisics. * and ** dene saisical significance a he 5% level and he 1% level respecively. 1

22 Table The Mulivariae A(4)-GJ GACH(1,1)-M Mdel FTSE 100 FTSE 50 FTSE Small Cap Ceff -sa Ceff -sa Ceff -sa α α ** ** ** α ** ** α ** ** α ** ** γ i * * ** c ** ** ** c ** ** * c c ** ** β 0 x ** ** * β ** ** ** β ** ** ** λ i ** d 1x * * d x d 3x ** d 4x * ρ FTSE100,FTSE ** ρ FTSE100,FTSESC ** ρ FTSE50,FTSESC ** LB(4) [0.00] [0.00] [0.00] LB (4) [0.8].5457 [0.64] [0.9] Nes: The able reprs he esimain fr he mulivariae A(4)-GJ GACH(1,1)-M mdel given by 4 = α i,0 + α i, n n + γ ihii, + c1oct 87 + c ASIA 97 + ci,3jan + c4mon + ε n= 1 hi = β 0 + β1hi 1 + βε 1+ λi I 1ε 1 + d1oct87 + d ASIA97 + d3jan + d 4MON h = ρ ( h h ) ij, ij i jj, -saisics are in parenhesis. * and ** dene saisical significance a he 5% level and he 1% level respecively. LB(4) and LB (4) are he furh-rder Ljung-Bx saisics fr sandardized residuals and squared sandardized residuals, respecively. The p-values f hese saisics are repred in parenheses.

23 Table 3 The Mulivariae A(4)-GJ GACH(1,1)-M Mdel wih Spillvers FTSE 100 FTSE 50 FTSE Small Cap Ceff -sa Ceff -sa Ceff -sa α * α ** ** α ** ** α * * ** α ** ** γ i ** ** ** c ** ** ** c ** ** * c c ** w FTSE ** ** w FTSE w FTSESC β 0 x ** ** β ** ** ** β ** ** ** λ i ** d 1x d x * * d 3x * d 4x * * z FTSE ** ** z FTSE ** * z FTSESC * ρ FTSE100,FTSE ** ρ FTSE100,FTSESC ** ρ FTSE50,FTSESC ** LB(4) [0.03] [0.00] [0.17] LB (4) [0.74] 1.80 [0.87] [0.88] Nes: The able reprs he esimain fr he mulivariae A(4)-GJ GACH(1,1)-M mdel wih spillver effecs, given by 4 3 = 0 + α n n + γ ihii, + c1oct + ci, ASIA 97 + ci,3jan + ci,4mon + w j n= 1 j= 1, j i α 87 + ε 3 1hi 1 + βε 1 + λii 1ε 1 + d1oct87 + d ASIA + d3jan + d4mon + z j j= 1, j i h, = β,0 + β 97 ii h i = ρ ( h h ) ij, ij i jj, -saisics are in parenhesis. * and ** dene saisical significance a he 5% level and he 1% level respecively. LB(4) and LB (4) are he furh-rder Ljung-Bx saisics fr sandardized residuals and squared sandardized residuals, respecively. The p-values f hese saisics are repred in parenheses. j, 1 ε j, 1 3

24 Table 4 The Mulivariae A(4)-GJ GACH(1,1)-M Mdel wih Spillvers ver he perid: 1 s Jan h Jun 1994 FTSE 100 FTSE 50 FTSE Small Cap Ceff -sa Ceff -sa Ceff -sa α α ** * α * * α * * ** α ** ** γ i c * ** ** c c ** ** * w FTSE ** ** w FTSE w FTSESC β 0 x ** ** * β ** ** ** β ** * * λ i d 1x * * d 3x d 4x z FTSE ** ** z FTSE z FTSESC ρ FTSE100,FTSE ** ρ FTSE100,FTSESC ** ρ FTSE50,FTSESC ** LB(4) 5.44 [0.5] [0.05] [0.03] LB (4).064 [0.7] 1.84 [0.86] [0.94] Nes: The able reprs he esimain fr he mulivariae A(4)-GJ GACH(1,1)-M mdel wih spillver effecs, given by 4 3 = α i,0 + α i, n n + γ ihii, + ci,1oct 87 + c3jan + c 4MON + wi, j j, 1 + ε i, n= 1 j= 1, j i 3 1hi 1 + βε 1 + λii 1ε 1 + d1oct + d3jan + d4mon + z j j= 1, j i hi = β0 + β 87 h = ρ ( h h ) ij, ij i jj, -saisics are in parenhesis. * and ** dene saisical significance a he 5% level and he 1% level respecively. LB(4) and LB (4) are he furh-rder Ljung-Bx saisics fr sandardized residuals and squared sandardized residuals, respecively. The p-values f hese saisics are repred in parenheses. ε j, 1 4

25 Table 5 The Mulivariae A(4)-GJ GACH(1,1)-M Mdel wih Spillvers ver he perid: 1 s Jul s Dec 00 FTSE 100 FTSE 50 FTSE Small Cap Ceff -sa Ceff -sa Ceff -sa α * α ** ** ** α ** ** ** α ** * ** α ** ** γ i * ** c ** ** * c * c w FTSE ** ** w FTSE * w FTSESC β 0 x ** ** * β ** ** ** β ** ** ** λ i ** ** d x ** ** d 3x d 4x ** ** z FTSE ** * z FTSE ** z FTSESC * - - ρ FTSE100,FTSE ** ρ FTSE100,FTSESC ** ρ FTSE50,FTSESC ** LB(4) [0.18] [0.0] [0.40] LB (4) [0.5] [0.97] [0.54] Nes: The able reprs he esimain fr he mulivariae A(4)-GJ GACH(1,1)-M mdel wih spillver effecs, given by 4 3 = α 0 + α i, n n + γ ihi + c ASIA 97 + ci,3jan + c 4MON + w j j, 1 + ε n= 1 j= 1, j i 3 1hi 1 + βε 1 + λii 1ε 1 + d ASIA + d3jan + d4mon + z j j= 1, j i hi = β0 + β 97 h = ρ ( h h ) ij, ij i jj, -saisics are in parenhesis. * and ** dene saisical significance a he 5% level and he 1% level respecively. LB(4) and LB (4) are he furh-rder Ljung-Bx saisics fr sandardized residuals and squared sandardized residuals, respecively. The p-values f hese saisics are repred in parenheses. ε j, 1 5

26 Table 6 Simulain esuls fr Nn-Synchrnus rading: eurns Panel A: Nn-synchrnus Trading, 1 1 3, 1 1, (0.81) , (-1.0) (-1.43), (14.49)** (5.30)** (4.64)** 3, (19.80)** (6.18)** (-1.1) Panel B: Synchrnus Trading, 1 1 3, 1 1, (-0.1) , (0.08) (0.47), (0.64) (-0.41) (0.18) 3, (0.73) (-0.86) (-0.51) Nes: 1,,, and are he simulaed bserved reurns f large, medium and small sck 3, prflis respecively. The able reprs he average cefficiens in he regressin = γ 0+ γ 11, 1+ γ, 1+ γ 33, 1+ u fr each index i = 1,, 3. Fr he nn-synchrnus rading case, he nn-rading prbabiliies are se he empirical nn-rading frequencies f , and Fr he synchrnus rading case, he nn-rading prbabiliies are se equal zer. The simulain is based n 1000 replicains. -saisics are repred in parenheses. * and ** dene saisical significance a he 5% level and he 1% level respecively. 6

27 Table 7 Simulain esuls fr Nn-Synchrnus Trading: Vlailiy Panel A: Nn-synchrnus Trading u ˆ1, u ˆ, u ˆ3, u ˆ1, 1 u ˆ, 1 u ˆ3, (31.31)** (4.67)** (15.5)** (34.88)** (40.94)** (15.68)** (5.96)** (34.44)** (5.41)** Panel B: Synchrnus Trading u ˆ1, u ˆ, u ˆ3, u ˆ1, 1 u ˆ, 1 u ˆ3, (31.81)** (4.06)** (15.79)** (3.99)** (43.41)** (16.0)** (5.8)** (34.05)** (11.55)** Nes: u ˆ, uˆ and u are he simulaed squared residuals f large, medium and small sck ˆ 1,, 3, u = 0 1 1, 1, 1 3 3, prflis respecively. The able reprs he average cefficiens in he regressin ˆ ω + ω uˆ + ω uˆ + ω uˆ + ω I uˆ + v fr each index i = 1,, 3. Fr he nnsynchrnus rading case, he nn-rading prbabiliies are se he empirical nn-rading frequencies f , and Fr he synchrnus rading case, he nn-rading prbabiliies are se equal zer. The simulain is based n 1000 replicains. -saisics are repred in parenheses. * and ** dene saisical significance a he 5% level and he 1% level respecively. 7