WHERE DO BETAS COME FROM?

Transcription

1 WHERE DO BETAS COE FRO? Robn. Greenwood * Harvard Unversy rgreenw@fas.harvard.ed ahan Sosner * Harvard Unversy sosner@fas.harvard.ed arch ABSTRACT We show ha radng cases excess comovemen of sock rerns. A smple model demonsraes ha pon nclson no (deleon from) he ndex socks shold begn o co-move more (less) wh he ndex de o a change n her radng paern. The emprcal resls provde sond sppor for hese predcons: In a recen redefnon of he kke 5 ndex n Japan he daly ndex beas of 8 added secres rose by an average of.6 whle he average beas of 3 deleed socks fell by.7. The daa confrm addonal predcons for changes n R rnover and he aocorrelaon of rerns pon ndex nclson and deleon. The resls are no drven by ndsry composon or selecon bas and hold a daly weekly and b-weekly levels. Snce radng shocks are sgnfcan deermnans of he shor-rn comovemen of sock rerns OLS esmaes of CA beas wh respec o he marke are severely based. * We are graefl o alcolm Baker cholas Barbers Ken Froo Emr Kamenca Tom Knox ke Rashes Jorge Rodrgez Jeremy Sen Jeff Wrgler Tomo Voleenaho semnar parcpans a Harvard and especally John Campbell and Andre Shlefer for helpfl dscssons. We reman responsble for any errors.

2 We sdy a change n he radng paern of 55 socks reslng from he redefnon of he kke 5 sock ndex n Japan. In Aprl he rles governng ndex membershp were changed casng he replacemen of 3 socks n he kke. Ths resled n a sgnfcan change n he comovemen of rerns and rnover for sbsed socks. We measre beas of he rerns of he addons and deleons wh respec o he rerns of socks remanng n he ndex afer he redefnon. The beas of he addons rse by.6 whle he beas of he deleons fall by.7. The average R of he regressons of sock rerns on he remander ndex rerns rse from.4 o.5 for he addons and falls from.8 o.9 for he deleons. These resls are no sensve o he lengh of he esmaon wndow and hold a daly weekly and b-weekly levels. In oher words he msprcng shows lle endency o rever over longer horzons. ore mporanly he phenomenon we descrbe s no lmed o small and llqd socks he addons represen more han % of he marke capalzaon of he Tokyo Sock Exchange and he deleons whle smaller had an average marke capalzaon of Yen 3 bn (approxmaely $3 mm) a he me of redefnon. We also fnd changes n he comovemen of rnover conssen wh or vew ha radng s responsble for he shor-rn comovemen of sock rerns. A common way o measre he effecs of demand shocks has been o sdy he nclson of socks no sock ndces sch as he S& 5. Upon nclson no a sock ndex ceran nsonal nvesors are reqred o prchase he socks. Shlefer (986) Harrs and Grel (986) Wrgler and Zhravskaya () docmen excess rerns of socks pon nclson no he S& 5 ndex n he Uned Saes. The change n prce s hard o arbe o an nformaon shock snce ndex nclson s based on pas performance and does no convey new nformaon abo he fre dvdends of he sock. Kal ehrora and orck () verfy ha even rerns do no come from nformaon by sdyng rerns assocaed wh a change n he weghs and no n he membershp of a sock ndex n Canada. The redefnon of sock ndces s also an approprae seng o show ha nnformed demand cases excess comovemen of sock rerns. Barbers Shlefer and Wrgler () (hereafer BSW) consder he comovemen of sock rerns n a model where raonal rsk-averse arbragers rade agans

3 nvesors who by and sell secres based on some arbrary rle nrelaed o he nderlyng fndamenals. In he model rsky secres do no have perfec sbses andarbragers are lmed by her rsk averson n beng agans he msprcng creaed by he rraonal raders. As a resl arbragers are nable o flly accommodae rraonal demand who a change n he prce. We follow hs heorecal framework and model an even where some ndex secres are replaced by prevosly non-ndex secres. The cenral assmpon of or model s ha here s a grop of rraonal nvesors who rade only n ndex secres n proporon o ndex weghs and rrespecve of fndamenals. The model predcs ha rerns of secres added o he ndex shold begn o comove more wh he rerns of secres remanng n he ndex. We consder wo measres of comovemen: he slope coeffcen or bea n he regresson of a secry s rern on he eqally weghed rern ofsecres remanng n he ndex and he R of hs nvarae regresson. The model generaes addonal esable predcons for changes n he aocorrelaons and cross-seral correlaons of sock rerns pon ndex nclson and deleon. The model s srcred o apply drecly o he kke 5 redefnon and we se he daa o evalae he valdy of s predcons. Or emprcal resls are relaed o he fndngs of BSW and Vjh (994) who sdy he effecs of S& 5 membershp on bea. In nvarae regressons of sock rerns on he S& 5 ndex rern BSW fnd ha he beas of addons rse by.6 whle he beas of deleons fall by.5 drng he sample perod from 976 o 998. The ncrease n he beas of addons s fond o be mch sronger n he second half of he sample afer he nrodcon of S&5 fres and opons n 98 and 983 respecvely. BSW nerpre hese resls o be nconssen wh fndamenals drven comovemen b spporve of he vew ha excess comovemen comes from nvesor demand. Vjh sdes he daly marke beas of S& 5 addons and fnds ha hey ncrease by an average of.8 beween 975 and 989. However he average change n beas dffered across sb-perods rangng from -.7 n he lae 97s o an ncrease of. n he second half of he 98s. Smlar o BSW he Vjh resls ndcae ha he ncrease n bea pon ndex nclson becomes sronger followng he nrodcon of he S& 5 fres and opons. One mporan dfference beween he fndngs n BSW and Vjh and he resls n hs paper s magnde. The changes n bea wh respec o he remander ndex ha we measre are large enogh o sgges ha radng s responsble for mos of he shor-rn comovemen of sock rerns 3

4 n Japan. Snce Japan s he second larges sock marke n he world or resls sgges ha demand shocks may be pervasve deermnans of sock rerns no only n emergng markes 3 b also n flly fnconal and hghly lqd markes. Second snce we sdy a sngle even over a relavely shor perod s less lkely ha changng fndamenal rsk drves he resls. Togeher wh evdence ha he comovemen of rnover changes followng he kke 5 redefnon s hard o connec or resls wh fndamenals. In he daa ndex demand appears o be a sgnfcan deermnan of shor-rn sock rerns. Ths rases he sspcon ha OLS esmaes of CA bea obaned sng shor-rn rerns may sffer from an omed varable bas. Snce demand shocks o ndex socks case emporary msprcng of boh he ndvdal socks and he marke porfolo he OLS esmaor of marke bea obaned hrogh regressng sock rerns on a broad vale-weghed marke rern s a based esmaor of he re loadng on he marke rsk facor. 4 The bas may depend on he samplng of rerns snce he effecs of demand shocks on he comovemen of rerns depend on he horzon over whch rerns are measred. We explore he bas n OLS esmaes of CA bea by sdyng mlvarae regressons of sock rerns on ndex rerns and marke rerns. Resls of he mlvarae regressons exend beyond he basc heorecal predcons consdered n hs paper as hey demonsrae a changng paern of comovemen wh respec o socks osde of he ndex. The mlvarae resls allow esmaon of he bas n CA bea cased by he omsson of demand relaed varable from he nvarae CA regresson. The bas ha we measre s srong a boh daly and weekly levels and as expeced s especally srong for ndex socks. For example nvarae CA bea esmaes for he deleons before he even are pward based by as mch as.75. To smmarze alhogh he Aprl kke even nvolves oo few secres and oo shor rern horzons for or resls o be consdered a rejecon of he CA hey clearly sgges ha demand and no fndamenal rsk domnaes shor rn varaon n sock prces. The nex secon olnes he predcons of a smple model of comovemen. Secon II descrbes he kke 5 redefnon. Secon III ess he predcons of he model on he comovemen aocorrelaon and cross-seral correlaon of sock rerns and he comovemen of rnover. Secon IV 4

5 examnes robsness sses. Secon V descrbes how omed demand shocks bas OLS esmaes of CA bea. Secon VI concldes. I. A ODEL OF COOVEET Ths secon presens a model ha llsraes he effecs of ndex radng on secry rerns. The model s developed whn he heorecal framework p forward n BSW. Wh he nrodcon of some mnor changes he BSW sep s drecly applcable o he effecs of he kke 5 redefnon on sock rerns and radng volme. Becase of he smlary beween or model and ha orgnally presened n BSW we lm or dscsson o he basc assmpons and esable hypoheses and leave he echncal exposon for he appendx. We assme a capal marke ha conans a rsk-free secry n perfecly elasc spply and +K rsky secres n fxed spply payng nceran lqdang dvdends. of hese secres compose an eqally-weghed secry ndex correspondng o he mehodology employed by hon Keza Shmbn n he consrcon of he kke 5. Two ypes of agens operae n he marke ndex raders and arbragers. Arbragers are myopc nvesors wh exponenal ly of wealh. Index raders nves n he capal marke n response o exogenos shocks o her wealh b prchase only secres n he ndex fnd n proporon o ndex weghs. Snce arbragers are dencal all radng volme comes from neracons beween ndex raders and arbragers. In each perod a new pece of nformaon abo he lqdang dvdend becomes avalable o nvesors. The nformaon shocks are descrbed by a wo-facor model conssng of a marke and an dosyncrac facor. The covarance srcre derved from he wo facor model s referred o as he fndamenal covarance. Imporanly here s no fndamenal facor common o only ndex secres. In oher words here s no fndamenal reason for ndex secry rerns o be more correlaed han nonndex secry rerns. Capal marke eqlbrm s obaned hrogh he marke clearng of secry demands of ndex raders and arbragers. Snce ndex rader demand s exogenos prce levels are deermned by he 5

6 wllngness of arbragers o absorb. In order o oban an analycal solon for rern processes we assme ha he economy s n a covarance saonary eqlbrm where arbragers conjecre correcly he condonal covarance marx of fre sock rerns. Under hs assmpon rerns are a lnear fncon of he news abo fndamenals and he ndex demand shock. The frs proposon esablshes he properes of he varances and he covarances of he secry rerns. roposon () The varance of ndex secry rerns s hgher han he varance of non-ndex secry rerns and boh are hgher han he fndamenal varance. () The covarance beween any wo ndex secry rerns s hgher han he covarance beween an ndex and a non-ndex secry rerns whch s n rn hgher han he covarance beween any wo non-ndex secry rerns and all hree are hgher han he fndamenal covarance. The frs par roposon esablshes ha ndex radng ndces excess volaly of secry rerns beyond fndamenal volaly. Excess volaly of he ndex secry rerns s qe nve ndex radng shocks are no flly dversfed away by rsk averse arbragers and case secry prces o flcae more han can be jsfed by news abo fndamenals. A more sble resl s ha non-ndex secres exhb excess volaly as well. Ths arses becase arbragers se all secres n he marke o dversfy dosyncrac rsks. Therefore when an ndex radng shock occrs he prces of he nonndex secres are affeced hrogh he dversfcaon sraeges of he arbragers makng her rerns more volale han can be explaned by fndamenals. The second par shows ha ndex radng shocks also ndce excess covarance beween any wo secres. Ths s broadly conssen wh Harrs (989) ha he nrodcon of S& fres ncreased he volaly of S& 5 socks relave o he volaly of smlar socks osde he ndex. Usng he resls of roposon we can show ha alhogh boh ndex and non-ndex secry rerns respond o ndex demand shocks hese shocks have a sronger effec on he ndex secry rerns. Ths s becase ndex radng shocks affec he rerns of ndex secres drecly. 6

7 To sdy changes n comovemen of asse rerns followng redefnon of he kke 5 we consder an even n whch ndex secres are replaced. We defne he remander ndex rern as he eqally-weghed rern of all secres whch were n he ndex before he redefnon and remaned n he ndex afer he even RE j j roposon saes how he beas of secres ha are added and deleed from he ndex wh respec o he remander ndex shold be affeced by he redefnon even. roposon. Consder a lnear regresson model where rern on a rsky secry j s regressed on he remander ndex j RE j RE j Afer redefnon () The OLS esmae of RE j shold ncrease for he secres added o he ndex and decrease for he secres deleed from he ndex. () The R of hs regresson shold ncrease for he addons and decrease for he deleons. The change n bea s ncreasng n he coeffcen of rsk averson and he varance of ndex shocks. Ths resl s very nve arbragers are less wllng o be agans he msprcng when hey are more rsk averse and/or when he demand shocks sronger. In addon o changes n conemporaneos correlaons of rerns he model predcs ha he aocorrelaon and cross-correlaon of rerns shold also be affeced by ndex nclson and deleon. Snce fndamenals are no serally correlaed he only sorce of correlaon s ndex rader demand. Demand s..d over me and so a hgh demand shock oday mples ha omorrow s demand shock wll on average be lower and vce versa. Ths ndces negave frs-order seral and cross-seral correlaon of rerns. roposon 3. 7

8 () Aocorrelaons shold become more negave for socks added o he ndex and less negave for socks deleed from he ndex. () Beas wh respec o he leadng and lagged remander ndex shold become more negave for he addons and less negave for he deleons. Of corse or smple model does no capre he whole rchness of seral correlaon paerns. For example f cross-seral correlaons are posve and sffcenly hgh hen he aocorrelaon of porfolo rerns may be posve whle he aocorrelaon of ndvdal secry rerns s negave (see Lo and acknlay (99)). In prncple one cold generae complex me seres paerns of hs sor by nrodcng addonal ypes of nvesors who reac rraonally o pas rerns or cash flow news. One sch model s descrbed n Barbers and Shlefer () where syle nvesors swch beween syles n response o pas performance of he syles generang seral correlaon paerns ha change wh horzon 5. However as we dscss below n or daa boh ndvdal secry rerns and ndex porfolo rerns are weakly negave correlaed. 6 Snce hese negave aocorrelaons are conssen wh he predcons of he model we resrc he emprcal analyss o hs smple framework. In addon o predcons relaed o rern processes he model yelds smple mplcaons for changes n he levels and correlaons of radng volme of addons and deleons. roposon 4. () () The volme of a secry shold ncrease pon nclson and fall pon deleon. Addons (deleons) o he ndex shold experence ncrease (decrease) n he correlaon of her volme wh remander ndex volme. We examne he emprcal evdence for roposons o 4 n secon III. II. THE EVET: IKKEI 5 REDEFIITIO The kke 5 s he mos wdely followed sock ndex n Japan. The newspaper hon Keza Shmbn (kke) has mananed he ndex snce 97 followng he dsconnaon of he Tokyo Sock 8

9 Exchange Adjsed Sock rce Average. The ndex ncldes 5 socks seleced accordng o composon crera se by kke. Alhogh he ndex gdelnes are src changes o ndex composon pror o he even we sdy were nfreqen ypcally one or wo socks per year. 7 Snce he composon of he ndex had remaned relavely fxed whle he ndsral composon of he sock marke was changng he kke had become less correlaed wh he marke over me fallng from a daly rern correlaon of 95% n 998 o 84% n he frs qarer of. Wh he am of revvng he relevance of he ndex on Aprl 4 kke annonced ha changes n he ndsral and nvesmen envronmens necessaed revson of rles coverng selecon of ndex componens. 8 The change n crera resled n he sbson of 3 smaller sses wh 3 large ew Economy socks. The revson became effecve a he sar of radng on Aprl 4. The new ndex was n fac more represenave of he marke as s correlaon wh he marke ncreased o 95% followng he even. The one-me redefnon cased an enormos amon of radng drng he week beween he annoncemen and mplemenaon. Ths radng can be approxmaely smmarzed as follows. The addons became a larger share (n Yen erms) of he new ndex han he deleons had aken n he old ndex. Accordngly he weghs of he socks remanng n he ndex fell. The resl was ha nvesors rackng he ndex had o by he addons and sell boh he deleons and some fracon of he socks remanng n he ndex. Drng he week afer he annoncemen many addons had rerns exceedng % and many deleons fell by more han 3%. Ths s evden n Fgre where we plo rerns srrondng he redefnon. Greenwood () sdes he cross-secon of even rerns n deph. The vale of he kke 5 s deermned by addng he ex-rghs prces ( ) dvded by face vale ( FV ) mes a consan dvdng he oal by he ndex dvsor ( D ) kke 5 ( FV D / 5) os socks have a face vale of 5 hogh some have face vales of 5 or 5. The ndex dvsor s adjsed daly o accon for sock spls capal changes or sock bybacks 9. Ths oher han some dsperson n face vale he ndex s eqally weghed. As a resl he ndex rern s a prce weghed 9

10 average of ndex sock rerns. Denong rerns of sock j n perod as wren as R kke kke kke kke D D 5 5 j j ( FV / 5) ( FV / 5) R j he ndex rern can be D Snce ndex rerns are proporonal o ndvdal sock rerns wh weghs gven by prce D over face vale. In shor socks wh hgh prces dsproporonaely affec he ndex rern. To preven he resls from beng drven by he rerns of socks wh hgh prces n he sbseqen analyss we sdy he eqally weghed rern. In fac he resls hold rrespecve of whch ndex we se. Alhogh we gnore ndex rern weghs for he res of he analyss s sefl o brefly descrbe he ndex weghs and marke vales of he addons and deleons. Frs he deleons are mch smaller han he addons he medan marke capalzaon s Yen 5bn (abo US $4mm) compared wh Yen 978bn for he addons. Second boh addons and deleons had larger represenaon (.e. ndex rern wegh) n he kke 5 han hey wold have had n a marke vale weghed ndex. Dfferences beween addons and deleons are no lmed o marke vale. Snce he redefnon was nended o change he ndsral composon of he ndex he addons conan more elecroncs and fnancal frms whle he deleons conan more chemcals and meal frms. Alhogh he dfferences beween addons and deleons are sgnfcan we laer verfy ha hese dfferences do no drve he man resl. In or analyss we focs on he rerns and rnover of 8 addons and 3 deleons. We drop wo addons he Indsral Bank of Japan and Toka bank becase of a sbseqen akeover and delsng respecvely. Fnally when formng he remander rern ndex we drop 9 of he 95 remanng socks becase of delsng ndex removal or becase hey were no n he ndex for long enogh (more han one year) pror o he even. R j III. RESULTS

11 A. Changes n ndex bea afer redefnon We measre comovemen as he ndex bea and R of a nvarae regresson of log sock rerns on he ndex rern. Ideally he fndamenal characerscs of he ndex are no affeced by he redefnon. The composon of he kke 5 changed afer he even hs casng a change n s fndamenal properes as well as a mechancal change n he bea of all socks wh respec o he kke. We can ge closer o he deal expermen by consrcng an ndex ha ncldes only he socks ha were n he kke 5 before he even and remaned n afer he even. We assme ha he fndamenal rsk (eqvalenly he srcre of rsk facors) of he remanders does no change arond he even. We hen analyze comovemen by sdyng he bea and R of addons and deleons wh respec o an eqally-weghed ndex of socks remanng n he ndex and no wh respec o he kke self. Fgre shows he dramac change n comovemen of addons and deleons wh he oher socks. anel A shows he resls for daly rerns. We defne a rollng wndow of days and esmae regressons of log rern of sock on he remander ndex log rern r r RE RE () For each -day wndow we oban separae bea esmaes for each of he addons and deleons hen average separaely across grops. We plo he me seres of hese grop means. Hgh even rerns of addons and deleons case shor-erm rends n beas afer he even. In Fgre he me seres of beas exhb sharp spkes drng he even week. However he shor-erm rends n beas dsappear once he rollng wndow leaves he even day. The doed lne n anels A corresponds o he day on whch he esmaon wndow moves beyond he even day. From ha day on mean beas reman farly sable. oably he mean bea of he addons ncreases by han more han.5 and he mean bea of deleons drops by more han.6 when compared o average bea before he redefnon. oreover mean beas show no sgn of reverson on he conrary he mean bea of addons connes o ncrease and he mean bea of deleons connes o decrease.

12 anel B of Fgre repeas he above exercse wh weekly rerns and a 3-week esmaon wndow. Beyond he fac ha he change n beas s more prononced for he deleons han for he addons he resls a he weekly level are essenally he same as a he daly level. Are hese changes n bea sascally sgnfcan? Table I shows basc ess of sgnfcance of he change n beas of addons and deleons. For each sock we esmae wo beas wh respec o he remander ndex one for a wndow before he even and one for a wndow of eqal lengh afer he even. Then as prevosly we average beas across addons and deleons. In anel A he pre-even wndow ncldes rerns from radng days beween ovember and Aprl 3. The pos-even wndow ncldes rerns from radng days beween ay and Sepember 5. The resls are agan very srong. On average he mean bea esmae of he addons goes p by.6 approxmaely a wo-fold ncrease from s pre-even level. The mean bea of deleons goes down by.7. Boh he ncrease n he beas of addons and he decrease n he beas of deleons are sascally sgnfcan a percen confdence level. The calclaon of sandard errors deserves specal aenon. The rerns of addons and deleons exhb a hgh degree of cross-seconal correlaon. As a resl bea esmaes are also cross-seconally correlaed. We se Seemngly Unrelaed Regresson mehod o correc he -sasc for hs cross-seconal correlaon n beas. Fnally n order o verfy ha a few olers do no drve he observed changes n average beas for each grop we calclae he nmber and percenage of socks whose bea goes p. We fnd ha 86 percen of he addons (4 o of 8) experence ncrease n bea whle 93 percen (8 o of 3) of he deleons experence declnes n bea. We esmae he p-vale on he hypohess ha beas were eqally lkely o go p as go down. For boh addons and deleons we rejec hs hypohess a a percen confdence level. anel B of Table I repors he change n bea measred sng 5-day esmaon wndows before and afer he even. The resls presened n anel A srvve he longer esmaon wndow. The average bea of he addons ncreases by.46 whle he average bea of he deleons decreases by.6. Boh changes are sgnfcan a percen confdence level. A hs horzon 7 percen ( o of 8) of he beas of he addons go p whle 97 percen (9 o of 3) of he beas of he deleons go down.

13 In order o make sre ha he changes n comovemen are no merely he resl of some radng frcons on a daly level we ncrease he rern horzon o weekly and b-weekly. 3 anel C shows ha he change n average bea a he weekly level s commensrae wh he changes a he daly level: beas of he addons go p by.55 whle hose of he deleons declne by.4. As shown n anel D he bweekly resls are also very smlar. Ths ndcaes ha he change n comovemen persss a leas a he b-weekly level and ha here s lle evdence of prce correcon n he shor-rn. B. Changes n ndex R roposon () saes ha followng nclson no an ndex he R of he nvarae regresson of rerns on he remander ndex rern shold go p. Fgre 3 plos he rollng R from he regressons n () averaged separaely across addons and deleons. The resls are even more srkng han hose obaned wh beas as here s a sharp drop n he R of deleons as soon as even rerns leave he esmaon wndow. The same s re for he addons where R ncreases by a leas percen when he even rerns are no longer nclded n he esmaon wndow. For boh he addons and deleons appears ha abo half of her R can be arbed o ndex membershp. anel B repeas he analyss sng 3 weeks of weekly rerns. The resls appear sronger for he deleons b less prononced for he addons. Wha s he economc mporance of he changes n R? The explanaory power of nvarae regressons rples pon nclson no he ndex and drops by half followng deleon from he ndex. These resls drecly address Roll s crqe (988) ha even ex-pos fnancal economss have been nsccessfl a explanng sock rerns. Inclson of demand shocks conrbes sbsanally o or ably o explan ndvdal sock rerns and herefore sggess ha demand accons for a large poron of he R. In oher sengs he absence of hs explanaory varable may sgnfcanly redce he R of rern regressons. We follow he same mehodology as sed n Table I and repor average R on he nvarae regresson specfed n () sng esmaon wndows of eqal lengh before and afer he even. In anel A of Table II he average R rses from 4 o 5 percen for he addons and falls from 8 o 9 percen for he deleons. Agan he calclaon of sandard errors deserves specal aenon as 3

14 rerns and hence R are lkely o exhb cross-seconal correlaon. We se a paramerc boosrap 4 o compe sandard errors and fnd ha for boh addons and deleons he change n R s sgnfcan a a percen confdence level. ovaed by he concern ha he resls are drven by a few olers we also repor he fracon of socks whn each sample whose R go p ogeher wh he p-vale on he nll hypohess ha R was eqally lkely o go p as go down. anel A also shows ha 86 percen (4 o of 8) of he R sascs of he addons go p whle 8 percen (4 o of 3) of he R sascs of he deleons go down. anel B of Table II repors he change n R measred sng 5-day esmaon wndows before and afer he even. 5 The resls presened n anel A agan srvve he longer esmaon wndow and are n fac sronger. The average R of he addons ncreases by 5 percen whle he average R of he deleons decreases by percen. Boh changes are sgnfcan percen confdence level. We agan check ha hese resls are no drven by a few secres and fnd ha ndeed 89 percen (5 o of 8) of he beas of he addons go p whle 97 percen (9 o of 3) of he beas of he deleons go down. anel C and anel D repor he change n R measred sng weekly and b-weekly rerns. The resls reman srong for addons whle weakenng for he deleons a he weekly level. Usng bweekly rerns here s 6 percen ncrease n R for he addons and 5 percen decrease for he deleons wh boh changes sgnfcan a he percen confdence level. So far we have verfed he wo key predcons of he model namely ha he beas and R of socks nclded n (deleed from) a sock ndex rse (fall) wh respec o he socks n he ndex and secondly ha he R of hs regresson goes p. The nex par addresses he me seres properes of rerns. C. The me-seres properes of rerns and non-synchronos radng In he model fndamenal cash flows are ndependenly dsrbed over me so he only sorce of seral correlaon of rerns s he seral correlaon of demand shocks. We showed earler ha..d. ndex demand generaes negavely aocorrelaed demand shocks and hence negavely aocorrelaed 4

15 rerns. I follows ha he aocorrelaon of rerns shold become more negave for ndex nclsons and less negave for deleons. Table III explores hs predcon by calclang he varance rao sascs for daly and weekly rerns. These sascs compare one perod rerns o rerns measred over longer horzons. They are gven by VR ( q) T q q s qr T T q T q q T r r r s where q s he aggregaon vale T s he sample sze and r s he average rern of sock. 6 Vales lower han one ndcae negave aocorrelaon of rerns. Lo and acknlay (999 p.54) provde an nve represenaon of he varance rao For example VR q q q ˆ ˆ q q q... ˆ q VR n Table III s approxmaely one pls he frs order aocorrelaon of rerns. We esmae he varance rao sasc before and afer he even sng 5 day wndows. In order o elmnae he effec of he pos-even abnormal rerns on he aocorrelaons we ncrease he even wndow by 4 days. 7 The pos-even perod hs begns on Jne 6. The resls are conssen wh or basc predcons: he seral correlaon of rerns becomes more negave for addons and less negave for deleons. For he addons he frs-order aocorrelaon decreases by 4 percen a he daly level and by percen a he weekly level. Whle he former change s sascally sgnfcan he laer s no. For he deleons he frs- order aocorrelaon ncreases by percen a he daly level and by 5 percen a he weekly level boh are hghly sascally sgnfcan. 8 The larger ncrease n he varance raos of he deleons for hgher aggregaon vales ndcaes ha hgher order aocorrelaons of he deleons have also become less negave. For he addons a he weekly level he second order aocorrelaon ncreases b hgher order aocorrelaons become more negave conssen wh he vew ha hey become exposed o negavely correlaed ndex demand shocks. However none of he weekly resls are sgnfcan. A he daly level hgher order aocorrelaons become more posve b hese changes are agan small and nsgnfcan. 5

16 In or dscsson so far we nerpreed he changes n aocorrelaons whn he framework of or model brngng n neffcen markes argmens. Can hese changes be explaned whn he effcen markes paradgm? In heory here s a possbly ha when secres are no connosly raded her esmaed aocorrelaons are affeced by a non-radng bas. In pracce however we fnd nlkely ha he observed changes n he aocorrelaons of he addons and deleons resl from a me varyng non-synchronos radng bas. Frs Lo and acknlay (999) demonsrae negave aocorrelaons generaed by non-synchronos radng are very small. For plasble changes n radng freqency one can expec changes n aocorrelaon sbsanally lower han percen. Second nder he assmpon ha radng freqency shold ncrease for addons and decrease for deleons he aocorrelaons shold become less negave for addons and more negave for deleons whch s precsely he oppose of wha we observe. Whle non-synchronos radng canno explan he changes n he aocorrelaons ndex demand shocks can. Informaon shocks have permanen effecs on secry prces whle demand shocks are sbseqenly revered by arbragers. Therefore as he magnde of demand shocks relave o nformaon shocks ncreases secres wll exhb hgher negave aocorrelaon. Ths s exacly wha appears n he daa. Whle effcen marke argmens sch as non-synchronos radng canno explan he changes n aocorrelaon can hey explan some of he changes n bea? If rerns sed o esmae sock beas are measred a a hgh freqency OLS bea may no be a conssen esmae of he re bea de o a nonsynchronos radng bas. If he redefnon cases enogh change n he freqency of rade hen changes n he esmaed beas of addons and deleons may be merely he resl of a non-synchronos radng bas. Scholes and Wllams (977) show ha de o varaon n radng freqency or non-synchronos radng he esmaed beas of socks raded very freqenly or very nfreqenly wll be based downward whle he esmaed beas of socks wh medm radng freqency wll be based pward. In hs respec f radng freqency of a sock s affeced by ndex membershp hen addon o or deleon from he ndex wll affec he non-synchronos radng bas and herefore he esmaed OLS bea. If ndex socks are raded more freqenly han non-ndex socks hen OLS beas esmaed wh respec o he ndex shold ncrease pon addon and decrease pon deleon. Snce hs scenaro seems plasble becomes an emprcal qeson how mch affecs he man resls. 6

17 Scholes and Wllams derve an nsrmenal varables (IV) esmaor whch correcs for he nonsynchronos radng bas n beas. They show ha f non-synchronos radng effecs are mporan a a one-day horzon he conssen esmaor of he re bea s gven by ˆ RE. b OLS b OLS ˆ b RE OLS where b OLS s he OLS bea wh respec o he lagged ndex rern OLS b s he convenonal (and based) OLS bea esmae b OLS s he OLS bea wh respec o he lead ndex rern and RE ˆ s he esmae of he frs order aocorrelaon coeffcen of he marke rern n or case he remander ndex rern. Correced Scholes-Wllams esmaes of bea are gven n Table IV. Wh daly rerns he decrease n bea esmaes of deleons goes down by almos half. Conssen wh he hypohess ha socks become less freqenly raded pon ndex deleon he OLS bea esmaes for deleons are almos dencal o he Scholes-Wllams IV esmaes before he even b sffer from a sbsanal downward bas afer he even. Alhogh he Scholes-Wllams correcon weakens he resls does no come close o flly explanng he decrease n he beas of deleons. o srprsngly he non-synchronos radng bas seems o maer only when rerns are measred a a daly freqency. Wh he weekly daa here s very lle change n he esmaed beas afer he correcon. Boh he pre- and pos-even OLS beas of deleons esmaed wh weekly rerns are somewha downward based and here s lle change n he bas afer he even. There s no ndcaon ha a non-synchronos radng bas affecs he addons. Usng a -day esmaon wndow he ncrease n beas of he addons s no affeced by he correcon and wh a 5-day esmaon wndow he correcon acally ncreases he measred change n bea. A he weekly level he ncrease n he bea esmaes of addons s somewha smaller afer he correcon. However snce he non-synchronos radng effecs are ndeecable a he daly level we dob ha non-synchronos radng s responsble for he resl emergng a he weekly horzon. Fnally he beas wh respec o he lagged and he leadng ndex rerns reqre some nerpreaon. They ndcae eher a change n radng freqency or a change n he exposre o demand shocks. In he frs case lead and lag beas resl from msmeasremen of rerns de o non-radng and 7

18 changes n hese beas ndcae changes n he freqency of rade. Alernavely f ndex demand s..d. (as s assmed n he model) hen boh lead and lagged beas shold decrease for addons and ncrease for deleons. 9 Table IV sggess ha ndex membershp has a posve effec on radng freqency. For boh -day and 5-day wndows beas of addons wh respec o he lagged ndex b sbsanally decrease whle her beas wh respec o he lead ndex b OLS OLS sbsanally ncrease. For deleons n boh he -day and 5-day wndows beas wh respec o he lagged ndex ncrease sbsanally. For he -day rern wndow he bea of deleons wh respec o he lead ndex decreases whle for 5-day wndow remans essenally nchanged. Alogeher hese observaons adm possble non-synchronos radng effecs on he beas esmaed wh daly rerns. They also ndcae ha a he daly level he effec of non-synchronos radng on leadng and lagged beas domnaes he effec of he demand shocks. If he demand shocks were o drve hese beas hen boh leadng and lagged beas wold change n he same drecon. For he addons hs occrs wh weekly rerns as boh lagged and leadng beas decrease. I s conssen wh he vew ha addons become more sbjec o demand shocks snce boh her leadng and lagged beas decrease. The evdence for deleons conradcs he ndex demand vew snce leadng and lagged beas also decrease. To smmarze he aocorrelaons of rerns change n he way predced by he model. onsynchronos radng does no appear o be an sse a he weekly rern level and even a he daly rern level or man resls srvve. One addonal fac gves pase: as we dscss n he followng secon whle he rnover of he addons s vrally nchanged afer he even he rnover of he deleons goes p raher han gong down. Ths mples ha he downward bas n bea occrrng afer deleon from he kke s becase of oo freqen radng raher han oo nfreqen radng. On he oher hand he srong ncrease of he bea of deleons wh respec o he lagged ndex and decrease n her bea wh respec o he lead ndex mply ha he deleons are raded oo nfreqenly afer he even. In shor we shold be carefl wh nerpreng he Scholes-Wllams resls snce hey possbly nrodce a consderable amon of nose no he bea esmaes. ore mporanly he resls reman hghly sgnfcan afer he correcons. 8

19 D. Trnover In he model a change n he radng process of socks resls n a change n bea and R. The rerns daa srongly sppor hs hypohess. I s worhwhle o search for sppor for frher evdence n he radng daa. Ideally we wold observe he bys and sells of ndex raders drecly. However hs s no feasble and hs we sdy he mplcaons of or model on radng volme. Ths secon examnes wheher changes n he levels and comovemen of rnover before and afer he even are conssen wh he model. In he model he rnover of non-ndex secres s always zero. Once added o he ndex secres shold experence an ncrease n her rnover. Of corse he model s no mean o capre he oher reasons ha marke parcpans may rade. For nsance he model canno explan he fac ha volme as well as he sandard devaon of volme of he deleons wen p afer he even. Ths occrred as many ndex fnds began o gradally nwnd her posons n hese socks. oneheless he predcon of he model ha radng volme shold become more correlaed afer ndex nclson holds even f we add nose o he model casng radng volme n excess of ha beween arbragers and ndex raders. We follow Lo and Wang () and se rnover as a measre of volme he nmber of shares raded dvded by oal nmber of shares. They show ha rnover s well sed for sdyng he relaons beween volme and eqlbrm asse prcng models. To measre changes n he correlaon of rnover before and afer he kke redefnon we se he same mehodology ha we sed o examne he comovemen of rerns. We sdy he bea of rnover wh respec o he average rnover of he socks remanng n he ndex. Trnover s normalzed by sandard devaon o accon for heeroskedascy. Table V presens esmaes of rnover beas before and afer he ndex redefnon. For each sock we calclae he nmber of shares raded daly dvded by he oal nmber of shares normalzed by sandard devaon. The rnover ndex s defned as he eqally weghed rnover of he remanders henceforh remander rnover ndex. We se he same esmaon wndows as before and measre rnover beas on he remander rnover ndex pror o and afer he even. For each sock we esmae he regresson 9

20 Trn Rem Trn jremanders j () anel A presens he resls sng days of rnover before and afer he even. The average bea of addons rses from.74 o.5 whle he average bea of deleons falls from.8 o.6. Snce he ndependen varable s sandardzed hese beas can be nerpreed as he sensvy of sock rnover o a one sandard devaon ncrease n he rnover of ndex socks. The average R of eqaon () rses by percen for he addons and falls by 5 percen for he deleons. We correc all -sascs for crossseconal correlaon as we dd wh he rerns daa. The able shows smlar resls when he wndow s exended o 5 days or when we se weekly rnover. In shor he change n rnover followng he even ndcaes ha he changes n comovemen of rerns are smlar o he changes n comovemen of rnover. We nex ask wheher he changes n rnover beas are drven by volme relaed o kke 5 fres and opons expraons. Fres and opons on he kke 5 ndex are raded on he Osaka Sock Exchange and he expraon dae s always he second Frday of he monh. Alhogh he fres conrac s cash seled he expraon cases sgnfcan ncreases n he volme of ndex socks rnover de o lqdaon of arbrage porfolos conssng of socks and dervaves. Table VI shows he average daly rnover before and afer he redefnon for addons and deleons. Average rnover on ondays hrogh Thrsdays s vrally nchanged for he addons. However her rnover ncreases dramacally on Frday. Snce fres relaed radng on second Frdays s approxmaely doble average daly radng drng he res of he monh we verfy n anel B of Table V ha hese olers do no drve he changes n rnover beas. We esmae he same model as n anel A b exclde hree days every monh one day before hrogh one day afer fres closes. Ths redces he day wndow by 3 days for example. The resls ndcae ha he changes n rnover beas do decrease sbsanally once we elmnae hese days fallng from.4 o.3 for he addons and from.67 o.48 for he deleons. However he resls are sll economcally large and hghly sgnfcan for boh he changes n beas and n R. Smlar resls oban when we se a 5-wndow.

21 In sm he resls for radng volme confrm or hypohess ha demand shocks sgnfcanly affec sock rerns n he shor rn. Changes n comovemen of he rnover are clearly ndcave of changng paerns of rade. These paerns of rade are responsble for he srong ncreases n he beas of addons and decreases n he beas of deleons. IV. Robsness Tess Ths secon addresses several robsness sses. We frs ask wheher he rerns assocaed wh he characerscs of he addons and deleon drve he changes n ndex bea. We hen ask wheher non-random selecon of deleons and addons nrodces a selecon bas no or resls. A. Do sock characerscs drve he resls? A noed feare of he even was he dfference n sze and secor composon of he socks comprsng he addons and deleons. The addons were manly large socks ha had experenced hgh posve rerns drng he pas few years and moreover were prmarly n ndsres sch as bankng and elecroncs. The deleons on he oher hand were smaller socks ha had experenced low rerns and declnes n lqdy drng he years pror o he even. The dfferences n sze and secor composon of addons and deleons are mporan only o he exen ha he change n beas s drven by exposre o facors relaed o frm characerscs. The dfferences beween he wo grops observed n he daa are no capred n he model where here s only one common rsk facor affecng all secry rerns. However f n realy here s varaon n facor exposre beween grops may affec he ndex bea esmaes. We begn wh sze. The medan addon had a marke capalzaon of Yen 978 bn compared wh Yen 5 bn for he medan deleon 3 and Yen 73 bn for he medan sock n he remanders. Therefore f here s a sze facor n rerns he addons are mch more exposed o han he deleons. We oban rerns of Tokyo Sock Exchange small cap and large cap porfolos. Takng he dfference n log rerns beween hese wo ndces gves rern on a porfolo whch s long n small socks and shor n

22 large socks. We hen esmae he bea of hs porfolo rern wh respec o he remander ndex rern and fnd ha remans vrally nchanged afer he even. I s also possble o check ha whn-sample varaon n sze does no drve or resls. We spl he addons and deleons no hose above and below her respecve medan sze and repea he analyss from Table II. Usng days of daa boh sbsamples of addons and deleons experence sgnfcan changes n ndex bea. The second concern relaed o characerscs of addons and deleons s ha her respecve cash flows may be exposed o dfferen ndsry shocks. The mos common ndsres n he sample are elecroncs bankng chemcals and meals. O of 8 addons 9 are elecroncs frms whle 6 are bankng frms. Of he 3 deleons 7 are classfed nder chemcals whle 9 frms fall nder mnng ron and seel or nonferros meals. To make sre ha ndsry characerscs are no drvng or resls we frs look a he correlaon of he relevan Tokyo Sock Exchange secor ndces wh respec o he rerns of he kke remanders sng rerns from Daasream. These ndsry ndces ypcally nclde more han frms and more han n he case of he elecroncs ndex. In any case f characerscs drve or resls hen he correlaons of he chemcal ndex and he ron and seel ndex wh he remander rerns shold declne afer he even whle he correlaon of he elecroncs 4 ndex and he bankng ndex wh he remanders shold go p. We esmae correlaons on 5 days of daa before and afer he even and fnd ha n hree o of he for cases hey go n he wrong drecon. For he elecroncs however he correlaon goes p conssen wh an ncrease n ndsry rsk ech rsk drvng some of he change n bea of he addons. To es hs hypohess we om elecroncs frms from he addons and recalclae average beas. We fnd ha ndeed he change n bea declnes b remans sgnfcan. oreover of he 9 secres lef n he sample 6 experence ncreases n bea. There are also robsness sses concernng he lengh and placemen of he esmaon wndow before and afer he even. Frs as we noed earler an even rern wndow of a leas days s exclded from all calclaons snce he rerns srrondng he even are lkely o overwhelm any measres of comovemen we consrc. However Greenwood () shows ha n addon o large and sgnfcan even rerns he socks n he ndex experenced reverson of even rerns over a perod p o weeks afer he even. any arbragers ook large posons n he addons and deleons drng he

23 even. I s plasble o hnk ha mch of he reverson of prces drng he weeks followng he even may be drven by prce pressre of arbragers nwndng her posons n a correlaed manner. In hs case we mgh observe excess covarance becase of arbragers raher han n spe of hem. 5 Ths concern s easly addressed however as we can exend he blacko wndow by 4 days. Ths only srenghens he resls. The las sse we address s wheher he change n bea we observe s de o he nwndng of ndex arbrage posons drng kke 5 fres and opons expraon daes on he second Frday of every monh. In shor s he case ha a few days of rerns are drvng or resls? We elmnae a hree-day wndow srrondng hese days (he second Frday of every monh) from or daa and esmae changes n average bea for radng day wndows. The beas of he addons rse by.6 whle hose of he deleons rse by.66 agan vrally nchanged. B. Selecon bas One of he mos problemac feares of ndex redefnons s he poenal for selecon bas n he composon of he addons and deleons. In sngle even rern sdes of S& 5 sock sbsons s possble o clam ha nclson no he ndex s a cerfcaon of qaly by Sandard and oors. Clearly n he kke 5 even replacemen s hardly random: deleons were small socks and represened only a mnor fracon of ndex capalzaon whle he addons were newer companes ha had experenced hgh recen rerns and growh n marke capalzaon. The dfference n composon of hese socks s nmporan as long as he selecon crera do no drve or man resl. Hypohecally he sory goes as follows: sppose ha rerns are acally..d. b he perod of me we sdy was one n whch he kke ndex was fallng. To ncrease he relevance of he ndex he organzers drop he exreme losers and add he wnners. Ths reqres ha he prces of deleons o be fallng even more han he ndex drng hs me whle he prces of socks osde he ndex ncldng he addons were rsng. Followng he redefnon he abnormal rerns cease and prces rever o he mean. Ths sory cold accon for he changng beas of he addons and deleons boh wh respec o socks nsde and osde he ndex. 6 3

24 However plasble hs explanaon mgh be he evdence pons he oher way. Drng he days pror o he even he remanders operformed he TOIX ndex. oreover he deleons operformed no only he remanders b also he addons drng hese days. Fnally we verfy ha he ndex beas we measre are no abnormal by exendng he pre-even wndow back o Jne 997 he ndex beas of he deleons reman hgh whle hose of he addons reman low. Fnally here exss he possbly ha socks were deleed from he ndex no becase of pas rerns b becase of ndex beas. 7 There are a varey of echnqes o address hs concern. The smples s o sdy changes n comovemen for oher hgh bea socks. Ths s done as follows. For each sock n he ndex beas are esmaed wh respec o all ndex socks (.e. boh he remanders and deleons). Then a conrol grop of he 3 hghes bea socks n or sample ha dd no nclde deleons s seleced. 8 These socks have an average ndex bea of.4 before he even and.4 afer he even compared wh.53 and.87 for he deleons. In oher words he ndex beas of comparable hgh bea socks fall by only.6 less han a qarer of he.66 for he deleons. The nerpreaon of hese resls s ha alhogh addons and deleons are no randomly seleced selecon bas does no drve he man resl. V. THE BIAS I ESTIATES OF CA BETA Snce demand s sch an mporan deermnan of shor-rn secry prces s naral o ask how hese omed demand shocks affec he valdy of he CA bea obaned from nvarae regressons of sock rerns on a broad marke ndex. The evdence hs far ndcaes ha demand shocks case emporary msprcng whch s sysemac across socks. Therefore boh ndvdal socks and he marke porfolo are sbjec o correlaed msprcng. B f hs s he case hen he OLS esmaor of marke bea obaned by regresson of sock rerns on a broad vale-weghed marke rern s no a conssen esmaor of he re loadng on marke rsk facor. The magnde of he bas depends boh on how comovemen wh respec o ndex socks changes followng he redefnon and on changes n comovemen wh respec o socks osde of he ndex- hey may parally cancel o n whch case demand shocks are dversfable o some degree. 9 In or model however hese shocks do no cancel o 4

25 ndex rader shocks are ne demand shocks for all socks and hence here s a posve bas on he CA bea esmaes for ndex socks. We can easly exend hs non o sdy he effecs of ndex nclson and deleon on changes n he CA bas. Snce for addons acqre exposre o ndex radng demand shocks esmaed beas shold be more based followng ndex nclson. Eqally snce for deleons exposre o ndex radng demand shocks goes down esmaed beas shold be less based followng ndex nclson. To beer ndersand he effecs of demand shocks on CA esmaes we sdy he resls of mlvarae regressons ncldng boh he remander ndex rern and he marke rern. In hese regressons he remander ndex serves as a proxy for he demand shocks. Table VII shows he resls of hs regresson: r r r RE RE KT KT (3) In hese regressons he remander ndex rern proxes for demand shocks for ndex socks. One cavea s n place here. We fnd ha n he hree monhs pror o he redefnon he rerns of he kke 5 move n he oppose drecon of he Topx. Sch behavor of rerns s no repeaed anywhere else n he sample and s lkely o domnae or resls especally n he day wndow. To redce he effec of hese abnormally dvergen rerns drng hs perod we exend or pre-even esmaon wndow o 5 days for daly rerns and weeks for weekly rerns. The pos-even sample s 5 days and 5 weeks respecvely. Table VII provdes a nmber of observaons. Frs he coeffcen of he addons rerns on he remander ndex rern s close o zero n he pre-even regressons. Ths holds closely o or heory he remander ndex rern capres ndex demand and shold be less mporan for socks ha are no n he ndex. We see ha hs changes dramacally afer he even: he coeffcen on remander ndex rern goes from an nsgnfcan.4 o a sgnfcan.4. The dramac change n hs coeffcen demonsraes he mporance of he demand shocks for he rerns of socks n he ndex. The same paern holds wh he weekly daa. We also fnd an ncrease n R followng addon no he ndex conssen wh he model s predcon ha ndex demand becomes a more mporan deermnan of We se he Topx rern o proxy for he marke. 5

26 rerns followng nclson. Fnally we noe ha here s a declne n bea wh respec o he marke from.96 o.67. Ths ndcaes ha no only do addons begn o co-move more wh ndex socks b also hey begn o co-move less wh non-ndex socks. Ths resl holds a he daly level only. The deleons presen he same broad paerns as he addons. A boh he daly and weekly level he bea of rerns of he deleons wh respec o ndex rerns drops sbsanally (by.64) followng he even. ore neresngly her exposre o he ndex s very hgh pror o he even confrmng he mporance of demand shocks for he deleons. There s a dramac declne n R afer he even agan spporve of or clam ha demand shocks are sgnfcan deermnans of sock rerns. Fnally we noe he ncrease n marke bea followng he even. A he daly level bea rses by.9. Ths s smlar o he resl we obaned wh addons: no only do deleons begn o co-move less wh ndex socks hey co-move more wh socks osde of he ndex. The fndng ha he ndex redefnon changes he comovemen properes of addons and deleons wh respec o non-ndex socks falls osde of or model. I s however explaned by a model n whch some grops of nvesors shf resorces beween socks n dfferen syles. 3 Barbers and Shlefer () derve he properes of sock rerns when socks fall no wo syles. Ther model predcs excess negave correlaon beween socks n dfferen syles and excess posve correlaon of rerns of socks whn a syle. If here are only wo syles ndex socks and non-ndex socks hen he kke redefnon we sdy shold case deleons o co-move more wh non-ndex socks and less wh ndex socks. Addons shold begn o co-move more wh ndex socks and less wh non-ndex socks. For he deleons a leas hs seems o be re and he addons show some evdence of a syle effec a he daly rern level. However alhogh we do beleve ndex-socks may form an nvesmen syle we fnd nlkely ha non-ndex socks ogeher defne a syle. To beer ndersand he change n marke bea for he deleons we nvesgae pre- and pos-even correlaons of deleon rerns wh a nmber of dfferen syle rerns. We fnd (nrepored) ha he ncrease n marke bea afer he even s parly drven by an ncrease n her bea wh respec o oher small socks. A plasble explanaon of hs s ha he ndex redefnon cased he deleons o be reclassfed from he ndex sock caegory o he small sock caegory. 6