BANK OF FINLAND DISCUSSION PAPERS

Transcription

1 BANK OF FINLAND DISCUSSION PAPERS 4/2000 Financial Marks Dparmn Informd Trading, Shor Sals Consrains and Fuurs Pricing

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3 BANK OF FINLAND DISCUSSION PAPERS Financial Marks Dparmn Informd Trading, Shor Sals Consrains and Fuurs Pricing Th viws xprssd ar hos of h auhors and do no ncssarily corrspond o h viws of h Bank of Finland * Dparmn of Financ, INSEAD. Insad, Boulvard d Consanc, 77305, Fonainblau Cdx, Franc. pkka.hiala@insad.fr, Tl: , Fax: ** Financial Marks Dparmn, Bank of Finland. P.O.Box 60, FIN-000 Hlsinki, Finland. sa.jokivuoll@bof.fi, Tl: , Fax: *** Corrsponding auhor. Dparmn of Financ, Sockholm School of Economics, P.O.Box 650, S-3 83 Sockholm, Swdn. yrjo.koskinn@hhs.s, Tl: , Fax:

4 ISBN ISSN (prin) ISBN ISSN (onlin) Suomn Pankin monisuskskus Hlsinki 2000

5 Informd Trading, Shor Sals Consrains and Fuurs Pricing Bank of Finland Discussion Paprs 4/2000 Pkka Hiala Esa Jokivuoll Yrjö Koskinn Financial Marks Dparmn Absrac Th purpos of his papr is o provid an xplanaion for rlaiv pricing of fuurs conracs wih rspc o undrlying socks using a modl incorporaing shor sals consrains and informaional lags bwn h wo marks. In his modl socks and fuurs ar prfc subsius, xcp for h fac ha shor sals ar only allowd in fuurs marks. Th fuurs pric is mor informaiv han h sock pric, bcaus h xisnc of shor sals consrains in h sock mark prohibis rading in som sas of h world. If an informd radr wih no iniial ndowmn in socks rcivs ngaiv informaion abou h common fuur valu of socks and fuurs, h is only abl o sll fuurs. Uninformd radrs also fac a similar shor sals consrain in h sock mark. As a rsul of h shor sals consrain, h sock pric is lss informaiv han h fuurs pric vn if h informd radr has rcivd posiiv informaion. Socks can b undr- and ovrpricd in comparison wih fuurs, providd ha mark makrs in socks and fuurs only obsrv h ordr flow in h ohr mark wih a lag. Our hory implis ha: ) h basis is posiivly associad wih h conmporanous fuurs rurns; 2) h basis is ngaivly associad wih h conmporanous sock rurn; 3) fuurs rurns lad sock rurns; 4) sock rurns also lad fuurs rurns, bu o a lssr xn; and 5) h rading in h sock mark is posiivly associad wih h conmporanous sock rurn. Th modl is sd using daily daa from h Finnish indx fuurs marks. Finland provids a good nvironmn for sing our hory, sinc shor sals wr no allowd during h priod for which w hav daa (27 May May 994). W find srong mpirical suppor for h implicaions of our hory. Kywords: Fuurs marks, shor sals consrains, asymmric informaion 3

6 Informaaio, osakkidn lyhyksimyynnin rajoiuks ja rmiinin hinnoilu Suomn Pankin kskuslualoiia 4/2000 Pkka Hiala Esa Jokivuoll Yrjö Koskinn Rahoiusmarkkinaosaso Tiivislmä Tukimuksn arkoiuksna on arjoa sliys osakrmiinin hinnoilullsllaisn mallin pruslla, jossa osa sijoiajisa saa parmmin informaaioa kuin ois ja jossa osakkidn lyhyksimyyni (sim. osaklainauksn avulla) i ol mahdollisa. Mallissa osakk ja rmiini ova muun idnisiä, mua ainoasaan rmiinissä lyhy posiio ova mahdollisia. Trmiinin hina nnusaa osakkn ja rmiinin yhisä ulvaa arvoa parmmin kuin osakkn hina, koska lyhyksimyynnin rajoius sää kaupankäynnin osakmarkkinoilla iyissä ilanissa. Lisädllyyksnä on, ä osak- ja rmiinimarkkinoidn markkinaakaaja havaisva oisnsa markkinoidn oso- ja myynimääräyks viiväsymän jälkn. Trmiini voi siis olla nännäissi joko yli- ai alihinainn suhssa osakksn. Mallin mukaan ) rmiinin ja osakkn hinnan rous li korrloi posiiivissi rmiinin samanaikaisn hinnanmuuoksn kanssa, 2) basis korrloi ngaiivissi osakkn samanaikaisn hinnanmuuoksn kanssa, 3) rmiinin hinnanmuuos nnusaa osakkn ulvaa hinnanmuuosa lyhyllä aikavälillä, 4) myös osakkn hinnanmuuos nnusaa rmiinin ulvaa hinnanmuuosa, mua hikommin, ja 5) osakkn kaupankäynnin määrä korrloi posiiivissi osakkn samanaikaisn hinnanmuuoksn kanssa. Mallia saaan käyän suomalaisn osakindksirmiinin markkinoidn päiväainisoa. Tsiaslma on riyisn kiinnosava, koska arkasluajanjaksona, , osakkidn lyhyksimyyni i ollu Suomssa mahdollisa. Empiiris uloks ukva siyä orisa mallia varsin hyvin Asiasana: rmiinimarkkina, lyhyksimyyni, päsymmrinn informaaio 4

7 Conns Absrac... 3 Inroducion Th modl Th s-up Trading a Prics in h fuurs mark a Prics in h sock mark a Implicaions for prics and rading s Prics a Implicaions for lad-lag Empirical rsuls Conclusions Endnos... 2 Rfrncs Appndix A

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9 Inroducion Th purpos of his papr is o provid an xplanaion for som sylizd facs rgarding h pricing of fuurs conracs wih rspc o socks and h rading s in h wo marks. Th wll-known mpirical obsrvaions ha his modl can accoun for ar.) ha fuurs rurns lad sock indx rurns vn afr h ffcs of non-synchronous rading ar akn ino accoun (Chan 992), 2.) ha hr is a posiiv conmporanous corrlaion bwn rading s and rurns in h sock mark (Karpoff 987) and 3.) ha h rading and rurns ar no rlad in h fuurs mark (Kocagil and Shachmurov 998). Th modl prsnd hr is basd on shor sals consrains and informaional lags bwn diffrn marks. In his modl socks and fuurs ar prfc subsius, xcp ha shor sals ar only allowd in fuurs marks. Th fuurs pric is mor informaiv han h sock pric, bcaus h xisnc of shor sals consrains in h sock mark prohibis rading in som sas of h world. If an informd radr wih no iniial ndowmn in socks gs a ngaiv signal abou h common fuur valu of socks and fuurs, sh is only abl o sll fuurs. In addiion uninformd radrs also fac shor sals consrain in h sock mark. Ths consrains can b binding irrspciv of h informaion ha h informd radrs possss. As a rsul, h sock pric is lss informaiv han h fuurs pric vn if h informd radr has rcivd posiiv informaion abou h common valu of h scuriis, bcaus uninformd radrs migh no b abl o rad. In h modl prsnd in his papr socks can b undr- and ovrpricd compard o fuurs, providd ha mark makrs in socks and fuurs only obsrv wih a lag h prics in h ohr mark. Th modl implis ha.) h basis is posiivly associad wih h conmporanous fuurs rurns, 2.) h basis is ngaivly associad wih h conmporanous sock rurn, 3.) fuurs rurns lad sock rurns, 4.) sock rurns also lad fuurs rurns, bu o lss xn and 5.) h rading in h sock mark is posiivly associad wih h conmporanous sock rurn. Th modl is sd using daily daa from h Finnish indx fuurs marks. Finland provids a good nvironmn for sing his hory, sinc shor sals wr no allowd during h im priod sudid in his papr (May 27, May 3, 994). Th implicaions of h hory ar wll suppord by h mpirical vidnc. This modl shars h faur of imprfc informaional ingraion bwn diffrn marks wih Chan (993) and Kumar and Sppi (994). Chan modls h obsrvd posiiv cross-auocorrlaion bwn diffrn socks wih mark makrs, who pric individual socks basd on signals praining o ha spcic sock wihou accss o informaion in ohr marks. Sock rurns bcom posiivly cross-auocorrlad whn mark makrs upda hir prics afr having sn h prvious pric informaion in ohr marks. Th issu in Kumar and Sppi is h voluion of fuurs basis in a dynamic larning gam. Mark makrs rciv a signal abou h ru valu of fuurs or socks wihou immdialy bing abl o obsrv h dvlopmns in ohr marks. Arbiragurs ar abl o obsrv sock and fuurs prics across marks wih lss of a lag han mark makrs and hus bn from hir informaional advanag. Subrahmanyam (99) dvlops an 7

10 advrs slcion modl for h xisnc and populariy of bask of scuriis lik h fuurs conrac basd on a sock indx. In his modl, liquidiy radrs prfr o rad in h fuurs conrac bcaus of a smallr dangr of bing a counrpary o an informd radr. Svral ohr paprs also dal wih h inracion bwn fuurs and sock marks in an quilibrium sing, bu mphasiz h risk sharing aspcs of h wo marks. Holdn (995) xplains h xisnc of arbirag bwn socks and fuurs in an quilibrium modl as arising from h risk avrsion of mark makrs and indpndn liquidiy shocks o fuurs and sock marks. In Frmaul (99), diffrn radrs hav unqual accss o sock and fuurs marks. In hr modl, only arbiragurs hav accss o all marks. Th rol of arbiragurs is mainly basd on rallocaing risk, alhough sh also briy considrs informaional issus. Chn, Cuny, and Haugn (995) hav prsnd an quilibrium modl of sock indx fuurs basis bhavior, whr fuurs conracs ar no prfc subsius for socks bcaus hy lack cusomizaion valu of sock porfolios. In hir modl whn mark volailiy incrass currn sock holdrs sll fuurs o hdg agains h incrasing risk of hir cusomizd sock porfolios dcrasing h basis. As a rsul of incrasd hdging h fuurs opn inrs incrass oo. Shor sals consrains hav for som rason bn qui nglcd ara of rsarch. Th noabl xcpion is of cours Diamond and Vrrchia (987). Lik in our modl, prohibiing shor sals rducs h informaivnss of scuriy prics, simply bcaus som informaiv rads ar no possibl. Unlik in h modl prsnd in his papr, in Diamond and Vrrchia his ffc is mor pronouncd for bad nws. Diamond and Vrrchia also show h posiiv associaion bwn rading s and rurns. Th mpirical liraur on lad-lag rlaionship bwn fuurs and sock indics is qui larg (s for xampl Kawallr al. (987), Soll and Whaly (990) and Chan (992) for U.S. vidnc and Yadav and Pop (990) for inrnaional vidnc). This modl basd on shor sals consrains in h sock mark also hlps o xplain why fuurs rurns lad mor sock rurns han vic vrsa and why his rlaionship is robus vn if h ffcs of non-synchronous radingarakninoaccoun 2. Harris (989) sudis h crash of 987 and h bhavior of fuurs basis around ha im. H nds ha non-synchronous rading in h sock mark xplains som, bu no all, of h larg ngaiv fuurs basis and h lad-lag rlaionship bwn fuurs and socks. This mpirical vidnc s our argumn wll: in xrm siuaions lik Ocobr 987, shor sals in socks ar difcul and cosly o xcu. This would imply ha h ordr ow in fuurs marks is much mor informaiv and as a rsul, fuurs rurns would lad sock rurns and h basis would b larg. In h Finnish conx, shor sals consrains and fuurs pricing hav bn prviously dal wih in an informal way by Puonn and Marikainn (99) and Puonn (993). In hir analysis, h shor sals rsricions in h sock mark ar usd o raionaliz h undrpricing of fuurs conracs wih rspc o undrlying socks. Conrary o ha analysis, his papr shows ha shor sals consrains also xplain h ovrpricing of fuurs conracs 3. 8

11 Scion wo prsns a simpl modl of basis formaion and rading s in sock and fuurs marks. Scion hr prsns mpirical vidnc from h Finnish marks for h modl prsnd hr. Scion four concluds. 2 Th Modl Th srucur of h mark is lik in Kyl (985) 4. Thr ar hr yps of invsors: informd spculaors, mark makrs and nois radrs. Thr ar wo risky scuriis ha ar prfc subsius, xcp ha shor posiions ar allowd only in on of h scuriis. Tha scuriy is calld h fuurs conrac. Th scuriy wih no shor sals is calld h sock 5. Th risky scuriis hav a valu of ihr or. For simpliciy w assum ha and. For clariy w mainain somims h and noaion. Thr ar hr das, and. A h risk-nural informd radrs rciv a prfc signal abou h valu of h risky scuriis. Wih probabiliy h signal is and wih probabiliy h signal is 2 2 A, h informd and nois radrs submi hir ordrs o mark makrs and h wo risky scuriis ar radd for cash. Thr is only on round of rading. Th inrs ra in h cash mark is assumd o b zro. Nois radrs rad only for xognous rasons. On way of hinking abou nois rading is ha h rading aks plac bcaus of consumpion (in h sock mark) or hdging (in h fuurs mark) rasons ha ar no xplicily modlld 6.Soa bfor h rading sars h nois radrs rciv a consumpion or hdging shock ha can b ihr ngaiv or posiiv. W assum ha h shock is posiiv wih probabiliy and ngaiv wih probabiliy Th shock is assumd o b 2 2 uncorrlad bwn h wo marks and also uncorrlad wih h informaion ha h informd radrs hav. If h consumpion or hdging shock is posiiv, h nois radrs would lik o buy risky scuriis and if h shock is ngaiv, hy would lik o sll scuriis. Th mark makrs ar assumd b risk-nural and compiiv. A h mark makrs obsrv h ordrs in hir rspciv marks: h mark makrs in h sock mark obsrv h ordrs in h sock mark and mark makrs in h fuurs mark obsrv h ordrs a h fuurs mark. Basd on hs ordrs, h mark makrs s hir prics in hir rspciv marks. A h mark makrs obsrv h prics ha wr quod in h ohr mark and hn hy upda hir prics basd on ha nw informaion. No ha no nw rading aks plac a f is h pric of boh socks and fuurs a bfor h rading sars. Th prics in h sock and fuurs marks ar dnod by r and s rspcivly a, and h rading s in h wo marks ar dnod by and Th prics a ar dnod by 2. Informd spculaors rad boh in h fuurs mark and in h sock mark. In h fuurs mark hy ar abl o rad wih ou any rsricions according o hir 9

12 informaion. In h sock mark hy migh fac a shor sals consrain. So whn h informd radrs rciv a ngaiv signal, hy can always sll fuurs conracs. In h sock mark h informd radrs ar only abl o sll if hy own h sock. W assum ha hr ar wo kinds of informd radrs: wih probabiliy hy own h sock and hnc can always sll in boh marks, and wih probabiliy hy don own h sock and slling is impossibl in h sock mark. Naurally hr is no diffrnc in informd radrs abiliy o buy ihr h sock or h fuurs conrac. Th nois radrs fac h sam problm as informd radrs. In h fuurs mark hy can always rad according h hir hdging nds, bu in h sock mark hy can only sll if hy own h sock. For simpliciy i is assumd ha h shor sals consrain is binding for h nois radrs wih h sam probabiliy as wih h informd radrs: wih probabiliy h consrain is binding and wih probabiliy h nois radrs own h sock and ar abl o sll if ndd 7. Nois radrs ordrs ar normalizd o b of on uni in boh marks. So nois radrs always buy on sock or a fuurs conrac whn hy rciv a posiiv consumpion or hdging shock. In h fuurs mark, hy always sll on conrac afr a ngaiv shock. In h sock mark hy sll a sock afr a ngaiv shock wih probabiliy and wih probabiliy hy don rad a all. Thr ar spara mark makrs for boh marks. I is assumd ha mark makrs in boh marks ar abl o obsrv only h buy and sll ordrs in hir own marks a, so ha h prics in h ohr mark ar iniially unobsrvabl o h mark makr in h ohr mark. Th sam srucur is also in Chan (993), whr h purpos is o xplain cross-auocorrlaion bwn diffrn socks. This assumpion of simulanous unobsrvabiliy of h ohr mark s prics is crucial o h rsuls of his papr. Wihou his assumpion hr wouldn b any pric diffrncs bwn h wo marks. In a dynamic sing his can b hough of as informaional lag bwn h wo marks: h mark makrs don obsrv h prsn ordr ow in h ohr mark, bu could obsrv h pas prics in h ohr mark. In addiion o obsrving h buy and sll ordrs sparaly in hir own marks, h mark makrs know h probabiliis of informaion signals, consumpion shocks and binding shor sals consrain, bu hy don of cours obsrv h ralizaions of hs variabls. Th mark makrs upda hir blifs in Baysian fashion abou h liklihood of high and low signals afr rciving boh buy and sll ordrs and hn s prics. Th prics ar s so ha on xpcd rms h mark makrs braks vn and ha h marks clar. Informd radrs buy and sll using h sam ordr sizs as nois radrs. Informd radrs ar abl o mak limi ordrs. In mos Kyl (985) yp modls h informd radrs ar assumd o b abl o mak only mark ordrs. Hr h sragy spac of informd radrs is nlargd by nabling hm o mak ordrs condiional on h pric ha would prvail if hy wr o plac a buy or sll ordr. Limi ordrs ar a mor ralisic way of modlling informd radrs bhavior. A convnin way of modlling limi ordrs is o us h rsuls from Roch and Vila (994). Thy show ha h Kyl (989) modl, whr limi ordrs ar possibl for h informd radr, is quivaln o h Kyl (985) modl, whr h informd radr only placs mark ordrs, if in h lar i is assumd ha h informd 0

13 radr obsrvs h amoun ha nois radrs ar rading. Following Roch and Vila (994) i is assumd ha h informd radrs obsrv nois radrs ordrs bfor buying or slling. Howvr, i is imporan o mphasiz ha his assumpion is mrly a convnin way of modlling limi ordrs. Placing an ordr wih h mark makr coss h an amoun in boh marks. I is assumd ha 3b 32b This cos is small nough o allow proabl rading whnvr prics do no fully rc h informaion ha informd radrs hav, bu prohibis ordrs whn h pro form rading is zro. Whn h informd radr has rcivd a high signal, sh has o mak h dcision whhr o buy a fuurs conrac or no. Sh is abl o mak a limi ordr: dpnding on nois radr dmand, h informd radr will ihr buy on fuurs conrac or do nohing. This is quivaln o placing an ordr condiional on a crain pric. So if h nois radr buys on conrac, h informd radr will no do anyhing. If sh bough on conrac as wll, h mark makr would know ha informd radr is buying and hnc h signal mus hav bn high. As a rsul sh would los h amoun This will happn wih probabiliy As a rsul, on buy ordr indicas ha a high signal has occurrd. Similarly, if h signal has bn low and h nois radrs sll on fuurs conrac, h informd radr again will do nohing: wo sll ordrs would indica o h mark makr ha a ngaiv signal has occurrd wih crainy. So on sll ordr indicas ha a low signal has occurrd. Whn h signal has bn high, bu h nois radr is slling, hn h informd radr can buy. Convrsly, in h cas of a low signal and nois radr is buying, h informd radr can now sll. As a rsul, whn vr h mark makr ss on buy ordr and on sll ordr, h is no abl o chang his blifs abou h liklihood of a good signal, sinc boh ngaiv and posiiv signals ar qually likly. High + 0 High - + Low + - Low - 0 Now h prics for fuurs conracs, kping in mind ha a high signal is normalizd o b on and a low signal is normalizd o b zro, can b simply sad as h condiional probabiliy ha h high signal has occurrd givn h obsrvd ordrs: s () s s

14 Pricing of h sock is mor complicad han h pricing of h fuurs conrac bcaus of h ponially binding shor sals consrain ha ihr h informd or h nois radr facs. Firs h cas whn h signal is posiiv is considrd.. Whn h nois radr dmand is posiiv, h informd radr can ihr buy on sock or do nohing. If sh bough a sock, hn h mark makr would know ha h signal has bn posiiv wih crainy. Thn h informd radr would loos h cos So sh is br off doing nohing. If h nois radr slls on sock, h informd radr can ponially buy on sock, bcaus his ordr ow migh occur also wih a ngaiv signal. Finally, if h nois radr is unabl o rad bcaus of h shor sals consrain, h informd radr migh b abl o buy a sock proably dpnding on wha happns whn h signal is ngaiv. As a summary h dmands from h informd and nois radrs oghr wih h join probabiliy of h vn occurring can b summarizd as follows: No + 0 b No - + b Ys for NT + 0 3b Ys for NT 0 + 3b Whn h informaion rcivd by h informd radrs is ngaiv and h shor sals consrain is no binding, h dmands of h radrs ar xacly lik in h fuurs mark: if h nois radr buys, h informd radrs will sll on sock and if h nois radr slls, hn h informd radr is br off by doing nohing. If h informd radr canno rad bcaus of h shor sals consrain, h ordr ow is drmind by h nois rading aciviy: ihr on buy or on sll ordr is obsrvd by h mark makr. If h nois radr is consraind by h binding shor sals consrain, h informd radr will sll on sock if h nois radr buys and will do nohing if h nois radr dos nohing. In h lar cas if h informd radr rid o sll, h mark makr would know wih crainy ha h signal has bn low. Whn h shor sals consrain is binding for boh sids, hn h informd radr canno do anyhing and mark makr ss only h ordrs of h nois radr. This can b summarizd as follows: 2 b No b No E3bb Ys for IT + 0 E3bb Ys for IT - 0 E3bb Ys for NT + - E3bb Ys for NT 0 0 Ys for boh + 0 Ys for boh 0 0 E3b 2 E3b 2

15 Now w ar abl o calcula h prics for h sock givn h ordr ow. Baysian updaing yilds h following prics for h sock: r (2) r r r I is worh noing ha no rading is bad nws for h sock s pric. In his simpl modl no rading lads o full rvlaion: no rading mans ha a good signal hasn occurrd, ohrwis sombody would hav placd a buy ordr. Now i is possibl o calcula h racions in boh marks whn informd radrs rciv ihr h high or low signals. Th prics givn by h quaions and 2 ar muliplid by h probabiliy of obsrving ha ordr ow givn h signal. Th xpcd pric for h fuurs conrac givn h high or low signal is hus: s (3) s Similarly h xpcd prics in h sock mark ar calculad givn ihr h high or low signal: r r (4) Now i is possibl o sa h following wo rsuls ha sablish ha h fuurs prics ar mor informaiv han h sock prics: s r Firs no ha if hn r.also if hn r Now i sufcs o show ha _.E rƒm for Th drivaiv is _b _.E rƒm 3, which is always ngaiv. _b E32b 2 3

16 This rsul is vry inuiiv, sinc a shor sals consrain diminishs h opporuniis for rading in h sock mark, bu no in h fuurs mark afr h informd radr has rcivd ngaiv informaion. No ha h shor sals consrain dosn acually hav o b binding, i is nough ha h consrain is xpcd o b binding for som radrs. Th nx rsul is lss inuiiv a a rs glanc: s r Firs no ha if hn r 2.Also if hn r Now i sufcs o show ha _.E rƒm for Th drivaiv _b is _.E rƒm, which is always posiiv. _b E32b 2 Th rason bhind his rsul is ha h shor sals consrains h informd and nois radrs fac afr a low signal cra lss informaion rvlaion in h sock mark vn afr a good signal. Of cours h shor sals consrain is no binding for an informd radr afr a posiiv signal: sh is always abl o buy a sock jus lik sh is always abl o buy a fuurs conrac. Howvr, h ordr ow is now lss informaiv in h sock mark han in h fuurs mark. If h mark makr obsrvs on buy ordr in h sock mark, h dosn know whhr ha rsuld from a good signal or simply from h inabiliy of h informd radr o sll afr a low signal. Th wo abov rsuls concrning h informaivnss of fuurs and sock prics ar no dircly mpirically sabl. Hnc, w sablish h following rlaionships ha can b dircly sd. s r s f Th covarianc can b wrin as s r s f, sinc h xpcd fuurs rurn is zro. Using ha dniion, h covarianc can b wrin as 3b 23b,whichsimplis o b 3b S 32b 32b S 32b This proposiion sablishs ha whn h fuurs pric changs, h sock pric changs o h sam dircion, bu by lss of an amoun. s r r f Th covarianc can b wrin as s r r f, sinc h xpcd sock rurn is zro. Using ha dniion, h covarianc can b wrin as 3b 23b 2 H 32b 2E32b 2E32b 23b 3b, which simplis o 32b 2E32b b 32b b

17 According o his proposiion whn h sock pric changs, h fuurs pric changs o h sam dircion, bu by a smallr amoun. No, howvr, ha h basis is mor srongly rlad o h conmporanous fuurs rurns han o h conmporanous sock rurn, sinc 3b 32b for. Only if h shor S 32b 2 32b sals consrain is nvr binding hr is no diffrnc in magniud. No only h xpcd prics, bu also h xpcd rading s should diffr in h sock mark dpnding on h informaion ha h informd radrs rciv. If h signal is ngaiv and if h shor sals consrain is binding for h informd radr, hn naurally h xpcd rading should b lowr compard o h if h signal is posiiv. 7 f Th covarianc can b wrin as r f, sinc h xpcd sock rurn is zro. Using ha dniion, h covarianc can b wrin as H b H 3b H Th wo mpirical implicaions abou h pricing rror and fuurs and sock rurns could b rsuls of a larning procss bwn wo marks ha hav informaional lags bwn hm (s Chan (993)), bu wihou shor sals consrains hr wouldn b any rlaionship bwn h rading and rurns. 8 f I is sraighforward o show ha h covarianc is always zro. A h markr makrs obsrvd h ordr ow in hir own marks. Afr h rading has akn plac, h mark makrs ar abl o obsrv wha has happnd in h ohr mark. Basd on h prics a in h wo marks, h mark makrs upda hir quos using h Bays rul. Th following prics prvail a 2 s r 2 s r (5) 2 s r 2 s r 2 s r 2 s r 2 s r 5

18 No ha no nw rading is ndd o achiv his updaing o nw prics. I is also worh obsrving ha boh marks conribu o his larning procss: h common pric h prvails a is always h sam as h pric ha dviad h mos from f, irrspciv of h mark. In paricular, if ihr on of h 2 prics is fully rvaling a,hnbohofhpricsarfullyrvalinga Now i is possibl o calcula h lad-lag rlaionships bwn h wo marks. Th following wo proposiions can b sablishd: 2 r s f Th covarianc bwn scond priod sock rurn and rs priod fuurs rurn can b wrin as 2 r s f, sinc h xpcd fuurs rurn is zro. Using ha dniion, h covarianc can b wrin as 3b 23b,whichsimplis o 3b S 32b 32b S 32b 2 s r f Th covarianc bwn scond priod fuurs rurn and rs priod sock rurn can b wrin as s r r f, sinc h xpcd sock rurn is zro. Using ha dniion, h covarianc can b wrin as 2 H 2E32b,whichsimplis o 32b 2 32b Ths wo proposiions ar ssnially h sam as h proposiions bwn h basis and h conmporanous fuurs rurn and basis and h conmporanous sock rurn. I can b also sad ha h fuurs rurn lads h sock rurn mor han h ohr way around, sinc 3b 32b for all. Only if hr is S 32b 2 32b no shor sals consrains h lad-lag rlaionship is qually signican boh ways. 3 Empirical rsuls 8 Daily closing valus ar usd for boh h fuurs conrac and h undrlying sock indx, calld h FOX indx, from h Finnish Opions Mark (FOM) o s h implicaions of his modl. Th sampl conains daa virually from h sar of h Finnish indx fuurs mark, May 27, 988, unil May 3, Th Finnish mark provids a good nvironmn for sing our hory, sinc shor sals wr no allowd during h im of sudy. Morovr, hr hav bn larg dviaions bwn sock and fuurs prics (s Figur ). Sinc w s a modl of asymmric informaion using a sock indx and indx fuurs prics, a crucial qusion is whhr hr rally is asymmric informaion among h invsors concrning h valu of an nir sock indx. I can b argud ha priva informaion is mosly rm-spcic, h ffc of which should b largly 6

19 divrsid away in an indx. W argu, howvr, ha his is no h cas wih h FOX indx. I consiss of h 25 mos acivly radd socks in h Hlsinki Sock Exchang. As a valu-wighd indx only h fw largs socks domina i in pracis 0. Hnc priva informaion rgarding hs fw socks should also b rcd in h whol indx. Thrfor h implicaions of our modl of informd spculaiv rading should also b rlvan o h drivaivs mark basd on h FOX indx. Anohr inrsing faur of h Finnish mark is ha in h sock mark a brokr has o idnify hrslf whn doing rads, whras in h indx fuurs and opions mark sh dos no hav o. This radily givs anohr moiv for br informd radrs in Finland o us h drivaivs mark. On a hin mark lik Finland hr is a ponial problm of infrqun rading of socks ha would induc spurious posiiv auocorrlaion ino h sock indx rurns. Indd, h daily logdiffrncs of h FOX indx do xhibi larg posiiv auocorrlaion (s Tabl I). Th indx fuurs prics could hus lad h sock indx valu mrly by aking ino accoun h posiiv auocorrlaion xhibid by h obsrvd indx rurns. Thrfor i is ncssary o rs purg h indx rurns from h auocorrlaion, for ohrwis i is impossibl o ll whhr a lad-lag rlaionship bwn h fuurs and h sock mark is rally du o h shor sals consrains or du o h spurious auocorrlaion. For his purpos w us h mhod of Jokivuoll (995) ha allows h compuaion of h sock indx valu - in lvls as wll as in rurns - basd on an ARMA(p,q) spcicaion of h obsrvd indx rurn procss 2. Thn h ru indx valu and rurns ar usd o conrol for h auocorrlaion of h FOX indx in our mpirical ss. Hrafr, whnvr w rfr o an indx valu, rurn, or h fuurs basis (involving h indx valu), w man h ru indx valu, if no nod ohrwis 3. Of h wo fuurs conracs ha wr simulanously availabl in h Finnish mark during our sampl priod, w us h on wih h shorr im-o-mauriy. Th longr conrac always has a im-o-mauriy of wo monhs plus h mauriy of h shorr conrac. A nw conrac rplacs h old on a wk bfor h xpiraion day. Th main rason for using h shorr conrac for h mpirical analysis is is highr liquidiy. Th fuurs basis is compud as h prcnag diffrnc bwn h fuurs mark pric and is horical bnchmark valu according o h cos-of-carry rlaionship 4 Tha in urn is compud using h 3-monh Hlsinki Inrbank Offrd Ra (Hlibor), and h acual dividnds paid on h undrlying sock porfolio during h fuurs rmaining im-o-mauriy. Tha is scj sc6 sc6 (6) whr scj is h obsrvd indx fuurs pric a im, and sc6 W A is h horical indx fuurs pric a im. W is h ru indx valu a im, is h xpiraion priod of h fuurs conrac, and A is h prsn valu a im of h dividnds bwn and. Thriskfrrais dnod by. 7

20 Th fuurs rurn is compud as h indx rurn implid by h fuurs prics assuming ha h cos-of-carry rlaionship holds i.. Wc 3 Wc (7) whr Wc scj A This is don in ordr o conrol for h drminisic cos-of-carry componn of h fuurs pric changs. Th fuurs rading is masurd as h numbr of conracs radd daily. I dos no show any rnd during our priod of invsigaion, alhough hr is variaion in h daily. Th sampl avrag numbr of conracs radd daily is 62. Thr is a signican numbr of days whn hr was no fuurs rading a all. Bcaus of hs zro obsrvaions in h fuurs sris w analyz h sris in lvls as such, and do no us logarihmic ransformaions. Trading of h FOX indx on day is masurd according o h following formula: FOX indx rading (a im ) = 2D M}Å c nuj c ' 2 c whr c is h maximum ransacion pric during day of sock, c is h minimum ransacion pric during day of sock, c is h numbr of shars of sock radd during day, and 25 is h numbr of FOX indx socks. Th avrag of h daily maximum and minimum ransacion pric of ach sock was usd as h bs availabl proxy of h daily avrag pric. Th variabl o b usd in h rgrssions is h abov FOX indx rading scald by h daily closing indx valu in ordr o conrol for changs in h ovrall pric lvl. Th scald indx rading xhibis a mor cyclical parn ovr h priod undr invsigaion han h fuurs rading. A priod of high rading in was followd by a priod of low in Thn in h rapidly rachd nw highs xcding hos xprincd in W s h following v hypohss ha ar implid by h modl dvlopd in scion 2 5 :. h fuurs basis is posiivly rlad o h conmporanous fuurs rurn, 2. h fuurs basis is ngaivly rlad o h conmporanous indx rurn, 3. h laggd fuurs rurn lads h conmporanous obsrvd indx rurn, 4. h laggd obsrvd sock rurn lads h conmporanous fuurs rurn, 5. h sock indx rading is posiivly rlad o h conmporanous indx rurn, and 6. h fuurs rading has no rlaionship wih h conmporanous fuurs rurn. Tabl IIa prsns h rsuls of h OLS rgrssion sing h rs hypohsis. As h basis is rahr prsisn hr rs lags of h ndognous variabl ar includd. Th conmporanous fuurs rurn obains a highly signican cofcin wih h corrc posiiv sign. Th laggd fuurs rurn also obains a signican cofcin wih a posiiv sign. Ths rsuls ar vry sabl hroughou h v subpriods of qual lngh no rpord hr. Hnc, h daa clarly suppors our rs hypohsis. Tabl IIb conains h rsuls of h OLS rgrssion sing h scond hypohsis. As in abl IIa hr rs lags of h ndognous variabl ar includd. 8

21 Th conmporanous indx rurn obains a highly signican cofcin wih h corrc ngaiv sign. Th laggd indx rurn is posiiv and signican. This could b vidnc of ha hr is a ow of informaion also from h sock mark o h fuurs mark. W rurn o his subjc in sing h fourh hypohsis blow. Givn h rsuls of Tabl IIa i is no surprising ha h rsuls of h ladlag rgrssion, prsnd in Tabl IIIa, suppor h hird hypohsis which is basically h dynamic vrsion of h sam ffc driving h rs hypohsis. An rror-corrcion rm is includd in h rgrssion o accoun for h apparn coingraion of h sock indx and h indx fuurs (s Engl and Grangr, 987). No ha, qui in accordanc wih h hory, h laggd fuurs rurn subsums all xplanaory powr wih rspc o h currn obsrvd indx rurn, laving nohing o h laggd obsrvd indx rurn. Also noic ha hr h obsrvd indx rurns ar usd insad of h ru indx rurns, as h lad-lag sup basd on a s of Grangr-causaliy involv h laggd obsrvd indx rurns which radily srv as a conrol for h obsrvd indx rurn auocorrlaion. To compl h analysis h lad-lag rlaionship was also sd in h opposi dircion, as prsnd in Tabl IIIb. Th obsrvd indx rurn prdics h currn fuurs rurn only in is hird lag. Thrfor h ow of informaion bwn h wo marks mainly appars o go in on dircion from h fuurs mark o h sock mark. This is inconsisn wih h rsul in Tabl IIb. If h basis is ngaivly rlad o h conmporanous sock rurns, hn h laggd sock rurns should lad fuurs rurns. Ts rsuls of h fh hypohsis ar prsnd in Tabl IV whr IVa prsns a vrsion using h logdiffrnc of h indx rading as h ndognous variabl, whras IVb uss a vrsion whr h log lvl of h is h ndognous variabl. In ach cas h conmporanous indx rurn obains a highly signican posiiv sign, as is consisn wih h hory. Th im sris of h indx rading, boh in log lvls and h log diffrnc form, conains occasional vry larg obsrvaions in absolu valu. As hs ar fairly vnly disribud ovr im w nd o inrpr hm as occasional hroscdasiciy in h sris. Th ovrall OLS simaion sragy of using Whi s hroscdasiciyconsisn covarianc marix should radily accoun for his (Whi, 980). As a scond chck, alhough no rpord hr, h indx rading rgrssions using robus simaion, ha is, h las-absolu-rrors mhod (LAE, s Judg al., 988), wr carrid ou. Th cofcin simas urnd ou o b vry similar as in h OLS rgrssions. Howvr, analysis of h OLS rgrssions wih v subpriods of qual lngh rvald ha h conmporanous indx rurn obains a signican cofcin only in h las wo subpriods, whras in h hird subpriod i is barly marginally signican (wih a p-valu of 3%). Nvrhlss, h sign of h cofcin is corrc (posiiv) hroughou all h subpriods, alhough clarly no signican in h rs wo subpriods. Ovrall w conclud ha h fh mpirical hypohsis also gs suppord by h daa. Th nal hypohsis of no rlaionship bwn h fuurs rading and h conmporanous fuurs rurn is sudid in Tabl V. Consisn wih h hory h cofcin of h fuurs rurn is no signican. Howvr, i should b born in mind ha in his cas h hory s prdicion coincids wih h null hypohsis, so h fac ha h null is no rjcd should no b akn oo srongly as vidnc in 9

22 favor of h nw hory w propos. In conclusion, h ovrall mpirical rsuls suppor qui wll h prdicions of h hory. Thus, h hory of h fuurs basis bhavior and rading s basd on asymmric informaion in conjuncion wih shor sals consrains appar o provid a rasonabl xplanaion of h facs in h Finnish indx fuurs mark during h priod of h sudy. 4 Conclusions A primary moivaion for his papr is o ry o undrsand h larg dviaions of h sock indx fuurs pric from is arbirag basd cos-of-carry rlaionship in Finland. I is no saisfacory o rfr only o h apparnly larg ransacions coss in h Finnish mark inhibiing fcin arbirag, bu i is also imporan o undrsand h fuurs basis dynamics insid any arbirag-fr band inducd by ransacions coss. A modl which is basd on shor-slling rsricions of socks and spculaiv fuurs buying and slling dmand of an informd invsor is proposd as an xplanaion of h obsrvd phnomna. In h modl shor sals consrain dcrass h possibiliis for h informd radr o pro from ngaiv informaion. Morovr, shor sals consrain also maks h sock prics lss informaiv vn if h informd radr has rcivd posiiv informaion. Using h a hisory of six yars of daily daa from h Finnish indx fuurs mark from May 27, 988 unil May 3, 994, w nd srong suppor for h modl s prdicion ha h lvl of basis is posiivly rlad o h conmporanous fuurs rurn and ngaivly rlad o conmporanous sock rurns, ha h fuurs rurns lad sock rurns and ha h rading in h sock mark is posiivly rlad o h conmporanous sock rurns. 20

23 Endnos. Similar issus ar also dal wih in Säfvnblad (997). 2. Our modl assums ha shor sals ar prohibid. This is no h cas in h U.S. marks. Howvr, shor sals ar sill mor cosly han ohr yps of rads and, morovr, shor sals ar no allowd on a down ick. 3. Puonn (993) also claims ha fuurs lad socks mor whn hr ar bad nws. Howvr, Marikainn and Puonn (994) nd no saisically signican vidnc for his, onc hroscdasiciy is akn ino accoun. 4. A similar binary Kyl-yp modl has prviously bn usd by Dow and Goron (997). Th classic xampl of a binary srucur in a rading gam is Glosn and Milgrom (985). 5. In h mpirical par w s our hory wih an indx fuurs conrac and a sock indx. 6. For h quivalnc of consumpion and hdging basd modls, s Sarkar (994). 7. Th assumpion ha informd and nois radrs hav h sam probabiliy of facing a shor sals consrain dosn affc our qualiaiv rsuls a all. This assumpion simplis h calculaions considrably. 8. S appndix for all h abls conaining h mpirical rsuls. 9. Trading in indx drivaivs basd on h FOX-indx sard in FOM on May 2, Bfor h 990 s commrcial banks had a larg wigh in h indx, bu sinc h conomic dprssion in Finland in h arly 990 s and h subsqun banking criss hir mark valu droppd dramaically. In h las half of our daa sampl Nokia Corporaion has bn h largs company masurd by mark capializaion. Ohr imporan companis ar mainly pulp and papr producrs.. Alrnaivly, vn in h absnc of infrqun rading hr can b posiiv auocorrlaion in sock indx rurns as a rsul of diffrnial informaion among sock spcic mark makrs, as shown by h modl of Chan (993). 2. S Kmpf and Korn (998) for an mpirical applicaion of h Jokivuoll (995) procdur in a similar conx. 3. Th compuaion of h ru indx valu and rurns, don in an x pos mannr, was basd on an AR(4) spcicaion of h FOX indx daily logdiffrncs (s Jokivuoll, 995, for dails). A Chow s, spliing h nir FOX indx sampl in wo halfs, did no indica a srucural brak in h sris, hrby giving som jusicaion for h shor-cu of using x pos analysis. 4. No ha h rminology hr dvias from h sandard on whr h basisisdnd as h diffrnc bwn h currn fuurs and h spo pric. Whn h risklss inrs ra is zro and hr ar no inrim dividnds, as in our modl, hn h sandard dniion of h basis and h fuurs pricing rror rlaiv o h cos-of-carry rlaionship ar h sam. 5. Throughou our mpirical analysis w ar ofn forcd o us svral lags of h ndognous variabl as xplanaory variabls o purg h modls from rsidual auocorrlaion. An xposiionally lighr alrnaiv migh hav 2

24 22 bn o us h auocorrlaion consisn simaion mhod of Nwy and Ws (987). Howvr, w do bliv h approach w hav adopd is conomrically a las as rliabl as hirs.

25 Rfrncs Black, F (976)., 3, Black, F. and Schols, M. (973)., 8, Chan, K.A. (992)., 5, Chan, K.A. (993)., 48, Chn, N.F., Cuny, C.J. and Haugn, R.A. (995).,, 50, Diamond, D.W. and Vrrchia, R.E. (987).,, 8, Dow, J. and Goron, G (997)., 05, Engl, R. and Grangr C.(987).,, 55, Frmaul, A. (99).,, 64, Glosn, L. and Milgrom, P. (985)., 4, Holdn,C.(995)., 5, Jokivuoll, E.(995).,, Spmbr Judg, G., Grifhs,W.,Hill,R.,Lukpohl,H.,andL,T.(988): 2. d. Wily. Karpoff, J. (987)., 22, Kawallr, I., Koch, P. and Koch, T. (987)., 42, Kmpf. A. and Korn, O.(998).,,7. Kocagil, A. and Shachmurov, Y.(998)., 8,

26 Kumar, P. and Sppi, D.(994)., vol. 67, Kyl, A.S. (985).,, 53, Kyl, A.S. (989)., 56, Lo, A. and MacKinly, A.C.(988).,,, Marikainn, T. and Puonn V. (994)., 8, Nwy, W. K., and Ws, K.D. (987).,, 55, Puonn, V. (993).,, 3, Puonn, V. and Marikainn, T. (99)., 37, Roch, J-C. and Vila, J-L. (994).,, 6, Sarkar, A. (994)., 3, Soll, H.R. and Whaly, R.E.(990)., 25, Subrahmanyam, A. (99)., 4, 7-5. Säfvnblad, P. (997)., working papr no. 83, Whi, H. (980).,, 48, Yadav, P. and Pop, P.(990)., 0,

27 25 Appndix A Tabls and Figurs Figur 'DWH 7 K H ÃS U LF LQ J ÃH U U R U Ã È

28 Tabl I. Basis Obsrvd indx rurn Fuurs rurn Ln Sock rading vol. Dln Sock rading vol. Fuurs rading vol. Opn inrs #obs Man S.dv p.a..25 p.a Min Max ρ.85* (.85*).27* (.27*).09* (.09*).78* (.78*).4* (.4*).46* (.46*).97* (.97*) ρ 2.80* (.30*).02 (.0*).03 (.04).75* (.34*).07* (.29*).35* (.7*).94* (.02) ρ 3.75* (.08*).03 (.07*).02 (.03).74* (.25*).0 (.9*).33* (.5*).9* (.04) ρ 4.70* (.02).0* (.07*).04 (.04).72* (.6*).0 (.5*).27* (.06*).88* (.0) ρ 5.66* (.0).09* (.05*).07* (.07*).7* (.2*).02 (.08*).30* (.4*).85* (.02) ρ 6.62* (.00).03 (.00).0 (.02).70* (.06*).04 (.*).26* (.04).82* (.03) ρ 7.59* (.05*).03 (.02).05* (.05*).70* (.09*).02 (.07*).24* (.05*).79* (.03) ρ 8.55* (.03).06* (.03).05* (.03).69* (.06*).02 (.09*).27* (.08*).76* (.03) ρ 9.52* (.0).02 (.0).0 (.02).69* (.08*).03 (.2*).24* (.03).74* (.02) ρ 0.48* (.03).05* (.05*).0 (.00).70* (.*).07* (.02).8* (.04).7* (.0) Figurs in parnhss ar cofficins of parial auocorrlaion. * indicas saisical significanc of an individual auocorrlaion cofficin a 5 % lvl Tabl IIa. Basis( ) Basis( 2) Basis( 3) Basis( 4) Fuurs Fuurs Cons. rurn() rurn( ) coff p-valu (.000) (.000) (.003) (.35) (.000) (.05) (.00) R 2 adj..79 Q-rj s Non Q-rjcions indica h rsidual lags a which h cumulaiv Q-s for rsidual auocorrlaion up o 5 lags rjcs a h 5 % significanc lvl. I.., h rsuls displayd in h abl ar from 4 = 0 i i i+ i i= i= 0 h modl Basis α + α Basis + β Fuurs rurn + ε. 26

29 Tabl IIb. Basis( ) Basis( 2) Basis( 3) Indx Indx Indx Cons. rurn() rurn( ) rurn( 2) coff p-valu (.000) (.000) (.0) (.000) (.000) (.706) (.02) R 2 adj..76 Q-rj s Non Q-rjcions indica h rsidual lags a which h cumulaiv Q-s for rsidual auocorrlaion up o 5 lags rjcs a h 5 % significanc lvl. I.., h rsuls displayd in h abl ar from 3 2 = 0 i i i+ i i= i= 0 h modl Basis δ + δ Basis + γ Indx rurn + ε. Tabl IIIa. EC( ) Obsrvd indx rurn ( ) Obsrvd indx rurn ( 2) Obsrvd indx rurn ( 3) Fuurs rurn ( ) Fuurs rurn ( 2) Fuurs rurn ( 3) Consan Cofficin p-valu (.00) (.977) (.002) (.090) (.000) (.036) (.787) (.954) R 2 adj..5 Q-rjcions Non Q-rjcions indica h rsidual lags a which h cumulaiv Q-s for rsidual auocorrlaion up o 5 lags rjcs a h 5 % significanc lvl. I.., h rsuls displayd in h abl ar from h modl Obsrvd indx rurn 3 i= η Fuurs rurn + ε i+ i = φ 0 + φ Error Corrcion + ϕ iobsrvd indx rurn whr h rror corrcion variabl is h rsidual from rgrssing h log of h obsrvd indx on h log of h fuurs pric. 3 i= i + 27

30 Tabl IIIb. EC( ) Fuurs rurn ( ) Fuurs rurn ( 2) Fuurs rurn ( 3) Obsrvd indx rurn ( ) Obsrvd indx rurn ( 2) Obsrvd indx rurn ( 3) Consan Cofficin E5 p-valu (.90) (.433) (.897) (.724) (.37) (.92) (.042) (.982) R 2 adj..02 Q-rjcions Q-rjcions indica h rsidual lags a which h cumulaiv Q-s for rsidual auocorrlaion up o 5 lags rjcs a h 5 % significanc lvl. I.., h rsuls displayd in h abl ar from h modl Fuurs rurn 3 i= i+ = κ 0 + κ Error Corrcion + λ ifuurs rurn η Obsrvd indx rurn + ε i whr h rror corrcion variabl is h rsidual from rgrssing h log of h obsrvd indx on h log of h fuurs pric. 3 i= i + Tabl IVa. ( ) ( 2) ( 3) ( 4) ( 5) ( 6) Cofficin p-valu (.000) (.000) (.000) (.000) (.000) (.000) Indx Indx Consan ( 7) ( 8) ( 9) rurn() rurn( ) Cofficin p-valu (.000) (.000) (.000) (.000) (.000) (.932) R 2 adj..34 Q-rjcions Non Q-rjcions indica h rsidual lags a which h cumulaiv Q-s for rsidual auocorrlaion up o 5 lags rjcs a h 5 % significanc lvl. I.., h rsuls displayd in h abl ar from h modl ln( Volum ) = µ i= µ i + i= 0 ν i+ Indx rurn i + ε 28

31 Tabl IVb. ( ) ( 2) ( 3) ( 4) ( 5) ( 6) Cofficin p-valu (.000) (.000) (.000) (.04) (.036) (.748) ( 7) ( 8) ( 9) ( 0) ( ) ( 2) Cofficin p-valu (.20) (.734) (.73) (.000) (.800) (.584) Indx Consan ( 3) ( 4) ( 5) rurn() Cofficin p-valu (.503) (.8) (.035) (.000) (.000) R 2 adj..72 Q-rjcions Non Q-rjcions indica h rsidual lags a which h cumulaiv Q-s for rsidual auocorrlaion up o 5 lags rjcs a h 5 % significanc lvl. I.., h rsuls displayd in h abl ar from h modl Volum 0 5 = ϖ + ϖ Volum + θ Indx rurn i= i i + ε. Tabl V. Fuurs Volum ( ) Fuurs Volum ( 2) Fuurs Volum ( 3) Fuurs Volum ( 4) Fuurs Volum ( 5) Cofficin p-valu (.000) (.036) (.08) (.899) (.00) Fuurs Volum ( 6) Fuurs Volum ( 7) Fuurs Volum ( 8) Fuurs rurn() Consan Cofficin p-valu (.567) (.4) (.08) (.57) (.000) R 2 adj..36 Q-rjcions Non Q-rjcions indica h rsidual lags a which h cumulaiv Q-s for rsidual auocorrlaion up o 5 lags rjcs a h 5 % significanc lvl. I.., h rsuls displayd in h abl ar from h modl Fuurs Volum 0 8 = ϑ + ϑ Fuurs Volum + ς Fuurs rurn i= i + ε. 29

32 ISSN , prin; ISSN , onlin /2000 Jussi Snllman Jukka Vsala David Humphry p. ISBN , prin; ISBN , onlin. (TU) 2/2000 Esa Jokivuoll Samu Pura p. ISBN , prin; ISBN , onlin. (RM) 3/2000 Riso Hrrala p. ISBN , prin; ISBN , onlin. (TU) 4/2000 Pkka Hiala Esa Jokivuoll Yrjö Koskinn p. ISBN , prin, ISBN , onlin (RM)