Keskustelualoitteita #57 Joensuun yliopisto, Taloustieteet. Jani Saastamoinen

Transcription

1 Keskuselualoea #57 Joesuu ylopso, Talouseee Quale egesso aalyss of dspeso of sock eus - evdece of hedg? Ja Saasamoe ISBN ISSN o 57

2 QUANTILE REGRESSION ANALYSIS OF DISPERSION OF STOCK RETURNS - EVIDENCE OF HERDING? Ja Saasamoe Mach 008 Absac Numeous sudes aemp o deec hedg sock makes by measug dspeso of sock eus. I hs leaue, hedg s defed as a decease of dspeso of sock eus, o cease of dspeso a a less-ha-popooal ae wh he make eu. Thee has bee a specal ees o look fo he evdece of hedg he exeme als of sock eus dsbuo. As a depaue fom he sadad mehodology ha employs OLS ad dummy vaable models, we use quale egesso ou esmao. Ou empcal daa s fom he lage-capal compaes he Helsk Sock Exchage. We fd ha dspeso ceases a less-ha-popooal ae wh he make eu he lowe al of sock eu dsbuo. Ths mgh be he evdece of hedg, bu hs s o he coclusve poof of hedg. We also fd ha he ae of cease s olealy ceasg he uppe al of sock eu dsbuo. Ths mples ha sock eu dspeso ceases moe ha CAPM suggess he sg makes. Keywods: behavoal face, empcal face, quale egesso, hed behavo. Uvesy of Joesuu, Ecoomcs ad Busess Admsao, P.O. Box, FI-800 JOENSUU, FINLAND; e-mal: ja.saasamoe@joesuu.f.

3 . INTRODUCTION A geeal belef s ha hed behavo s pevale sock makes. Howeve, vey lle evdece of hed behavo amog vesos exss. A ceasg body of leaue has bee devoed o deec hedg sock makes by measug dspeso of sock eus. I hs leaue, deceasg dspeso of sock eus o cease of dspeso a a less-ha-popooal ae wh he make eu s epeed as he evdece of hedg (Chag e al. 000, p. 655). The cocep of hed behavo s smple. A aoal age maxmzes uly (pof) codoal o a pvae fomao se. She ca fe he pvae fomao of ohe ages by obsevg how hey behave he smla suao. Age heds whe she suppesses he ow fomao favo of he fomao she has leaed fom he ohes. Ths ca lead o cluseg of huma behavo whch has bee obseved may felds of socal sceces. Fo sace, he pheomea as dvese as fasho o evoluos ca be explaed by hed behavo (Bkchada e. al 99). I facal makes, hedg could mea ha vesos buy o sell secues egadless of he udelyg fudameals, because some sgals lauch hed behavo. Hed behavo coadcs wh aoal asse pcg whch acceuaes he mpoace of equy fudameals o sock pcg. Gve he fomao, howeve, hedg s o aoal pe se because vesos ca pof fom. I hs pape, we sudy dspeso of sock eus he Helsk Sock Exchage (OMXH). Some chaacescs of OMXH sugges ha hedg could ake place hee. Despe apd gowh adg volumes ad make capalzao dug he pas decade, OMXH cao be chaacezed as beg a paculaly effce make. Apa fom Noka ad a hadful of ohe lage copoaos, he publcly aded compaes OMXH ae small ems of make capalzao ad umbe. Fuhemoe, adg suffes fom low lqudy because a emoe sock exchage does o gae as much aeo fom eaoal vesos o secues aalyss as he majo eaoal sock makes. Fo hese easos, hee could be oom fo fomaoal asymmees ha gge hed behavo he sock exchage. Howeve, deecg hedg wh he mehods ha ae commoly used he leaue does o ecessaly pove ha vesos hed. Hed behavo s oe possble epeao fo he pheomeo, bu he explaao could be, fo example, coelaed adjusme o ew fomao (Bkchada ad Shama 00, p. 80). The mege bewee he sock exchage opeaos HEX (Flad) ad OM Goup (Swede) spawed a ew compay OMX Goup 003. OMXH wll be used efeece o he Helsk Sock Exchage.

4 We use daly eus fom he lage capal socks lsed OMXH fom July 00 ul May 007. The codoal Capal Asse Pcg Model (CAPM) s used fo aoal asse pcg. Ths pape ca be vewed as a couao o he leaue ha aemps o dsclose he evdece of hed behavo facal makes by examg sock eus. Ou sudy dffes fom he pevous eseach by he choce of mehodology. Isead of oday leas squaes (OLS) ad dummy vaable models ha ae pevale he leaue, we buld o Chag e al. (000) ad use quale egesso (QR) ou empcal aalyss. We ague ha QR s a vald aleave o he esmao of hedg models such as Huag ad Chse (995) ad Chag e al. (000). Ou fdgs clude ha dspeso ceases a less-ha-popooal ae wh he make eu he lowe al of sock eu dsbuo, whch mgh cosue he evdece of hedg as defed he leaue. O he ohe had, we fd ha he ae of cease s olealy ceasg he uppe al of eu dsbuo. The pedcos of CAPM seem o hold he mddle of eu dsbuo. The pape poceeds he followg ode. I he secod seco, we evew he pevous eseach. I he hd seco, we pese he model ha we use o measue dspeso of sock eus ad coduc he ecoomec aalyss. I he fal seco, we coclude ad compae ou esuls o he pevous eseach.. LITERATURE REVIEW The sadad ecoomc heoy s based o he assumpo ha ecoomc ages ae aoal. Raoal ages maxmze uly codoal o he fomao se. Ths assumpo s also behd aoal asse pcg models such as he Capal Asse Pcg Model (CAPM). A make s effce whe make pces eflec coecly all fomao ha s avalable o make cumbes. Cosequely, pces adjus o he fudameal values as vesos eceve ew fomao o make fudameals. Ths mples ha hee should be o eoeously pced secues he make. Gve ha he access o he make fomao s (moe o less) ufom, coelaed movemes sock pces mgh be a aoal espose fom he vesos ha shae a smla fomao se o he ew fomao, o he evdece of hedg (Bkchada ad Shama 00, p. 80). Obvously some fomaoal asymmees pess. Fo example, compay sdes ae bee fomed o a fm s facal codo ha ohe vesos. I s o ucommo ha make commeaos expla sock pce movemes as a cosequece of veso hed behavo. Fo example, flueal vesos o seasoed maages ae epoed o be

5 esposble fo he appecao of sock pces he compaes ha hey buy o ae hed o maage (Hshlefe ad Teoh 003, pp ). Ths edoseme effec s a ype of fomaoal hedg. I fomaoal hedg, ages suppess he ow fomao favo of he fomao hey fe fom he behavo of ohe ages. Hedg eed o be aoal. I ca be pefecly aoal behavo because ohe vesos may have bee fomao o he vesme decso (Bkchada ad Shama 00, p. 80). I s mos geeal fom, Deveow ad Welch (996) defe hedg as behavo paes ha ae coelaed acoss dvduals. I ca also be cosdeed a fom of socal leag, alhough he amou of leag s small a hed (Chamley 004, p. 66). Iuvely, hed behavo could be commo sock makes. Assume ha hee ae wo ypes of vesos: pofessoals ad o-pofessoals. Pofessoals ae make aalyss, pofessoal ades ad pofolo maages fo suoal vesos o muual fuds. No-pofessoals ae vesos ha ves he savgs secues fo fuue cosumpo o wh speculave moves. Boh ypes could hed. Fo example, pofessoal pofolo maages ed o follow he make cosesus he asse allocao o avod udepefomg he pees (Schafse ad Se 990). Ths ype of hedg sems fom he age-pcpal poblem (Deveow ad Welch 996, pp ). Moeove, equy aalyss may hed by akg cues fom each ohes ecommedaos whch could mea ha he make cosesus s fac based (Tuema 994, Welch 000; Behad e al. 006 fo a dsseg vew). No-pofessoals could hed because hey ae less fomed o make codos, such as macoecoomc eds, o how o value secues (Shlle 984). Theefoe, s plausble ha hey base he vesme decsos o he fomao ha hey, a leas paally, deduce fom ohe vesos. Alhough aoal asse pcg eques ew fomao fo a chage he value of a asse, s heoecally possble ha asse pces flucuae whou ew fomao (Rome 993). Foo e al. (99) show ha ude specfc ccumsaces, vesos may hed o he same fomao. Moeove, Avey ad Zemsky (998) oduce a model of sho-lved hedg by make pacpas. The aoal exubeace aoud he al publc offegs (IPOs) of echology compaes he lae-90s could be a example of hed behavo descbed Welch (99). Bkchada e al. (998) oe ha despe aoaly ad depede payoffs, he decsos ha ages make covege apdly, bu hey ae dosycac ad fagle. Fo hs easo, facal Oe ca hadly fd a moe fg phase ha aoal exubeace o descbe hedg sock makes. See Robe Shlle s defo ad ogs of he em hp:// 3

6 fezes ad pacs could be ggeed by smple obsevaoal leag mechasms. Accodg o Deveow ad Welch (996), hee obseved egulaes facal makes could esul fom hedg. Fs, meges ad IPOs dsplay waves. Secod, he make cosesus seems o be low ad o based o pvae fomao. Thd, flueal make pacpas adm ha ohe vesos fluece he vesme decsos. Vaous facos could lead o hedg facal makes. Hwag ad Salmo (004) dscuss he possbly ha macoecoomc sgals lead vesos o beleve ha he make s easy o foecas. The make eus o he CAPM equlbum, whe a uexpeced shock ales he vesos fomao se. Gleaso e al. (004) beleve ha vesos also seek comfo fom publc opo dug he peods of make sess 3. I hs case, hedg could be a cos effce way o oba fomao o he deco ha he make s headg. Wemes (999) offes some suppo o hs vew by showg ha he socks ha ae bough by heds oupefom ohe eques. He also fds ha small-capal socks ad gowh-oeed muual fuds ed o hed moe. Ths could esul fom fomaoal coss ha may ase o he uceay ove he gowh pospecs of a dvdual fm o dusal seco. As egads he fomaoal asymmey ad uceay, especally sock makes emegg ecoomes have bee suspec o dsplay hed behavo. Accodg o Bkchada ad Shama (00), hs s due o fomaoal asymmees, lqudy cosas ad suoal facos such as goveme eveo ad poo accoug legslao. Recely, hee has bee much ees o fd he empcal evdece of hedg sock makes wh ecoomec mehods. The poeeg sudy hs feld s Chse ad Huag (995) (efeed o as CH hecefoh). They pese a mehodology ha s based o he coss-secoal sadad devao (CSSD) o deec hedg dug peods of make sess. CSSD s defed as (, ) = CSSD =, () 3 Make sess s defed as a peod of lage sock pce movemes whch usually coespods wh exeme make eus. % ad 5% als of sock eus dsbuo ae commoly used hesholds fo make sess he leaue. 4

7 whee, s he eu fom a secuy ad s he aveage eu fom secues. CH also pese a model ha s based o he coss-secoal absolue devao (CSAD) o allevae poblems wh oules. The measue fo CSAD s CSAD = =,. () CH esmae a make sess model CSSD D D U L = α + γ + γ + ε. (3) The dummy vaables D, D ake he value of uy, f sock eus le he uppe (U) o lowe U L (L) al of sock eus dsbuo, ad zeo ohewse. If sock eus appoach he make ae of eu, he eus become moe coelaed, whch s epeed as he evdece of hedg 4. Wh hs mehod, howeve, CH fal o deec he evdece of hedg he majo US sock exchages. Chag e al. (000) (efeed o as CCK hecefoh) popose a aleave mehod o deec hedg. They we a expeced CSAD peod as ECSAD = [ ] = β β m E m f, (4) whee β, β ae he me-vaa bea coeffces fo a secuy ad he make especvely ad m m s he make ae of eu. If =, equaos () ad (4) ae equvale. CCK show ha m equy eu dspeso s a lea ad ceasg fuco of he make eu, because ECSAD E [ E [ m ] ECSAD m ] = = = 0. β β m > 0 (5) 4 We epo he sascally sgfca fdgs he leaue evew as hedg. 5

8 CCK ague ha f hedg akes place, he dspeso of eus ceases a a less-ha popooal-ae wh he make eu o he ae could eve be deceasg. Fo hs easo, hey esmae a olea model CSAD = α + γ + γ + ε, (6) m, m, whee a egave ad sascally sgfca γ could dcae he pesece of hed behavo. Compaed o CH, CCK ague ha hs model eques less o-leay he eu dspeso o deec hedg, whch s cosse wh aoal asse pcg models. They also show ha boh model lead o smla coclusos. CCK es he model he sock makes of he US, Japa, Hog Kog, Souh-Koea ad Tawa. They fd γ s egave ad sascally sgfca Tawa ad Souh-Koea, wheeas he coeffce s sascally sgfca he US, Japa ad Hog Kog. The subseque eseach has appled mos cases he mehods of CH ad CCK wh mo modfcaos ad coflcg esuls. Ta (005) augmes he mehod of CCK wh ollg beacoeffce esmaes. She coeds ha hs s moe covee appoach he dyamcs of exeme pce movemes. He evdece suggess ha hedg exss he Chese A-shae makes, whee domesc vesos ae allowed o ade. I coas, she epos ha o hedg akes place he Chese B-shae makes, whee eaoal vesos ade. I a fuhe vesgao o he Chese sock makes, Ta e al. (008) deec hedg pevale he boh A- ad B-shaes make. These fdgs coadc wh Deme ad Kua (006), who also exame hedg he Chese sock makes. They fd o evdece of make-wde o secoal hedg. Dffee leghs daa ses could expla hese muually coadcoy esuls. Mxed evdece of hedg s pese ohe makes as well. Heke e al. (006) do o deec hedg he Ausala sock make. Cajueo ad Tabak (007) spec he Japaese sock make, whee hey epo hedg behavo oly he exeme dow makes. Chag ad Zheg (008) dsclose he evdece of hedg he US, Japa, Hog Kog, Gemay ad he UK sock makes. Gleaso e al. (004) focus o aday hedg of seco ETFs he US. They fd o evdece of hedg, bu oe ha hee s asymmey he cease of dspeso bewee he sg ad fallg makes. The ae of cease s lowe he fallg makes, whch hey epe as weak evdece of myopc loss aveso. 6

9 As a depaue fom he mehodology of CH ad CCK, Hwag ad Salmo (004) develop a model of bea hedg ha ess he hedg hypohess agas he CAPM equlbum. They ague ha he measue fo hedg s a mpoveme ove CH ad CCK, because codos hedg o fudameals. As he poof, hey epo he evdece of hedg he US ad Souh Koea sock makes dug egula make codos. Ieesgly, he esuls dcae ha peods of make sess cause sock valuaos o eu back o fudameal valuaos as pedced by he CAPM equlbum. Thus, coceag he deeco effos o peods of he exeme pce movemes may be msplaced because hey epo advese hedg akg place he sessed makes. Hwag & Salmo (006) pese a opaamec veso of he bea hedg measue. Usg hs measue, hey epo smla fdgs he US, UK ad Souh Koea sock makes as Hwag ad Salmo (004). Whle hese esuls ae eesg, he majo shocomg hese models s ha hey cao vefy explcly ha a causal elao bewee vesos hed behavo ad he obseved deceases o oleaes equy eus dspesos exss. Hedg CH s make sess model could also esul fom chages he me-sees volaly o depede adjusme o fudameals (Hwag ad Salmo 004, p. 588). Deveow ad Welch (996) oe ha coelaed aval of fomao o depedely acg vesos could be msake fo hedg. CCK po ou ha a aleave o he hedg hypohess could be he pesece of a o-lea make model. Hshlefe ad Teoh (003) ague ha hed behavo could esul fom a combao of pefeece, epuaoal ad fomaoal effecs, dec payoff eacos ad mpefec aoaly. As a esul, deceasg dspeso o oleaes eus cao be cosdeed he coclusve evdece of hed behavo. 3. ECONOMETRIC ANALYSIS 3. Daa ad Mehodology Ou daa cosss of daly closg pce quoes fo he lage-capal compaes he OMXH. I addo o he sock pce daa, we use daly closg pces fo he geeal OMXH sock pce dex (OMXHPI) o appoxmae he eus fom a equal-weghed make pofolo. Daly quoes of he oe-moh Eubo ees ae ae used as a poxy fo he sk-fee asse. A sho-em ees ae s used o elmae empoal sks ha ase fom he log-em bod make vesmes. The u oo ess dcae ha each vaable has a saoay me-sees (see able A Appedx). 7

10 Alogehe, he daa cosss of 3 compaes wh appoxmaely 50 pce quoes pe compay a yea dug he obsevao peod fom Jue 8 h 00 ul May 3 s 007. Ths amous o oughly 00 obsevaos dug he ee obsevao peod. The begg of he obsevao peod s geeally cosdeed he me whe he bea make, whch bega alog he bus of he sock make bubble 000, boomed ou ad he bull make bega. As a esul, he daa s chaacezed by he chage he geeal make seme. Ths could be due o some ew fomao o maco-ecoomc shock ha chaged he expecaos o sock eus. Fo example, he majo ceal baks kep ees aes a he hsocally low levels a he me. Ths could be a fele ecoomc clmae fo hed fomao (Hwag ad Salmo 004, p.590). I sp of he seco aalyss of Deme ad Kua (006), we ae eesed he goup of socks, amely he lage-capal socks (lage-cap). These ae he mos acvely aded compaes OMXH. By defo, a fm s a lage-cap whe s make capalzao exceeds bllo ( ) euos 5. We coceae o hem because hey ae moe lqud ha small-capal (small-cap) o md-capal compaes (md-cap) ad have accuae daly adg daa avalable. Some small-caps, fo sace, ae o aded fo weeks. I addo, he lage-caps have moe dvese oweshp base, ad hey gae moe ees fom foeg ad domesc secues aalyss. Fo hese easos, hedg s less lkely amog he lage-caps ha amog he md-caps o small-caps. Fo smplcy, we cosde a compay o be a lage-cap fom he begg of he yea dug whch s aual facal esuls dcae ha s make capalzao exceeds bllo euos. Thee ae also wo cases whee dvesme has sgfcaly aleed he compay s make value. I hese cases, he values fo aalyss have bee calculaed fo he pae compay ad s sp-off fom he dae of he dvesme. We use CAPM o model aoal asse pcg. CAPM copoaes fomao o eus fom a sk-fee asse ad a make pofolo o gve a measue of sysemac sk fo a dvdual sock. CAPM saes ha he eu fo a sock peod s = f, + β E [( m, f, )], (7), 8

11 whee β s he bea-coeffce whch measues a equy s sesvy o he movemes of he make 6. I geeal, β s calculaed by usg daly, weekly o mohly daa o eus agg fom 6 weeks o seveal yeas. Sce he fequecy o me spa of he daa ha s used calculaos s o sadad, he value of β fo he same sock shows vaao depedg o he calculao mehod. We use daly eus fo βˆ 7. The eus fom he make pofolo, fom July s 00 o May 3 s 007 he esmaes m,, ae appoxmaed by OMXHPI daa fom he same peod. Reus fom he oe-moh Eubo ees ae seve as a poxy fo he sk-fee ae of eu,. f Equao (7) mples ha β emas cosa ove me. I facal leaue, he assumpo ha he bea-coeffce s me-vaa has me ccsm (fo example, see Blume (975), Fabozz & Facs (978)). Hwag & Salmo (004) ague ha beas could become based because of hedg. They sugges ha vesos may chage he belefs abou he pefomace of dvdual socks whch leads o covegece beas. I pacce, vesos could expec ha sock eus mach he make eus. As a cosequece, he socks ha oupefom he make wll be sold because hey ae expeced o be ove-valued, wheeas he socks ha ude-pefom ae beg bough because hey seem ude-valued. Fo hs easo, we follow Ta (005) ad use he ollg bea, whch s deoed by β,, o ake o accou vaao he bea coeffce ove me. A esmae fo ˆβ, s calculaed by usg daly eus fom he pevous 6 weeks. The ollg bea s obaed by deleg he oldes obsevao ad addg a ew obsevao ad he esmag ˆβ,. Gve aoal expecaos, he acual value of E[CSAD] s equao (4) ad a eo em ε ~ N(0, σ ). Thus, CSAD (wh he ollg bea) becomes CSAD = = ˆ β E [( m )] + ε 8,,,. (8) 6 See Appedx, Equaos (A)-(A). 7 A shoe peod s used, f a fm has o bee lsed he sock exchage houghou he obsevao peod. 8 See Appedx, Equaos (A3) (A5). 9

12 To es whehe hedg as defed by CCK exs, we esmae he followg equao wh quale egesso (QR) CSAD = α + η + η + ε, (9) m, m, Ulke CCK, we do o use absolue values fo m,, because QR eables he examao of effecs dffee pos of make eu dsbuo. If γ s egave ad sascally sgfca, dcaes ha vesos hed aoud he make ae of eu. I ohe wods, dspeso of eus deceases o ceases a a deceasg ae ad appoaches he make ae of eu, whch could be a dcao of hed behavo. 3. Quale Regesso Appoach Whle he eseaches followg CH have employed OLS wh dummy vaables, hee ae good easos o op fo quale egesso (QR) aemps o deec hedg equy makes. Fs, facal daa usually does o pass he es of omaly. QR s a sempaamec aleave o OLS. Compaed o OLS, QR may be a moe effce esmao mehod whe he dsbuo of eos s o-omal (Baes & Hughes 00, p. 5). Secod, sce he make sess models ae pevale he empcal facal hedg leaue, QR s a vesale ool aalyzg exeme quales of eu dsbuo. Howeve, Hwag ad Salmo (004) wa ha eseaches may o deec hedg because hey obseve oly he exeme als of eu dsbuo. Moeove, hey ague ghfully ha he defo of make sess s subjecve. QR solves hese poblems because povdes a mehod o esmae he effecs o he depede vaable ove he ee dsbuo. As he hd agume, CH oe ha he mehod based o CSSD s sesve o oules. Sce QR s obus o he pesece of oules, hey wll o pose a sevee hea o he elably of esuls (Koeke & Hallock 00, p. 7). QR ca be used o oba esmaes fo hedg he als of make eu dsbuo 9. Theefoe, we ca es he mpac of make sess, bu do o eque as hgh level of oleay fo deeco as CH (see CCK, pp ). By seg τ = o τ = 0. 0, we oba quale esmaes fo he exemely low eus. Smlaly, seg τ = o τ = poduces quale esmaes fo he exemely hgh eus. The egesso equao s 9 See Quale Regesso Appedx. 0

13 CSAD ( τ x) = α + η ( τ ) + η[ ( τ )] + ε. (0) m, m, As a aleave o OLS esmaes, we u meda egesso o equao (0). The esuls fo meda egesso (CSAD(0.5)) ae peseed Table. Sce η (0.535) s posve ad sascally sgfca ad η (0.03) s posve ad sascally sgfca, hee s a posve ad lea elaoshp bewee CSAD ad pcg s aoal. m,. Ths dcaes ha o a meda adg day sock Nex, we exame make sess by specg exeme quales of eu dsbuo as a aleave o he make sess models. The esuls ae epoed also Table. As CH, we use he abay % ad 5% hesholds fo make sess. Seg τ = 0. 0 coespods o he % lowe al of sock eu dsbuo (exemely low eus) ad τ = coespods o he 5% lowe al. Regesso yelds posve ad sascally sgfca η (0.5) ad egave ad sascally sgfca η (-0.805) fo CSAD(0.0). Fo he 5% heshold, whch coespods o CSAD(0.05), we oba η (0.53) ad η (-8.590), whch ae boh sascally sgfca wh compaable magude. These esuls dcae ha hee s a deceasg ae he cease of dspeso because he olea em s egave ad sascally sgfca. As a esul, he lea elao bewee cease dspeso ad he make eus dsappeas dug sock sell-offs, whch coadcs wh he pedcos of CAPM. Exemely hgh eus ae locaed he uppe al of eu dsbuo. Seg τ = ad τ = 0.99 coespod o he 5% ad % of he exemely hgh eus, especvely. The esuls ca be foud Table. Fo CSAD(0.99), boh η (0.55) ad η (7.783) ae posve ad sascally sgfca. The same cocluso apples o CSAD(0.95), fo whch he coeffces η (0.55) ad η (7.80) ae posve ad sascally sgfca. Ths mples ha dspeso ceases wh a ceasg ae he uppe al of sock eus dsbuo. Ths dcaes ha vesos place moe emphass o he equy fudameals ha CAPM suggess, whe he make poss exemely hgh eus. Cosequely, vesos do o hed.

14 Table Resuls fo meda egesso ad quale egesso fo he make sess model. CSAD(τ) α η η R CSAD(0.5) (-.79*) (58.53***) (0.3) CSAD (0.95) (5.75***) (7.34***) (3.6***) CSAD(0.05) (-4.90***) (74.6***) (-3.53***) CSAD(0.99) (6.84***) (3.90***) (4.5***) CSAD(0.0) (-5.94***) (.7***) (-4.50***) The esuls fo quale egesso o CSAD ( τ x) = α + η m, ( τ ) + η[ m, ( τ )] + ε wh vayg values fo τ. T-sascs ae epoed paeheses. * dcaes a 0% sgfcace level; ** dcaes a 5% sgfcace level; *** dcaes a % sgfcace level. Examg quale pocess povdes a moe obus vew o he effecs a dffee quales. A vsual epeseao of he esmaes wh he 95% coddece eval s peseed Fgue ad he exac coeffces ae epoed able A Appedx. Usg dffee values of τ., η emas posve ad sascally sgfca. Ths shows ha he elao bewee posve all ove dsbuo. Moe eesg s he gaph fo m, m, ad CSAD emas. I clealy shows how he ae of cease of dspeso s deceasg he lowe al, fla he mddle as aoal asse pcg suggess, ad ceasg he uppe al of dsbuo. I fac, η emas egave ad sascally sgfca up o he fs quale (5%). Afe hs, s sascally sgfca whe τ (0.5,0.70) wh he sg swchg fom egave o posve a he meda. Fally, he coeffce becomes posve ad sascally sgfca he uppe al of dsbuo. These esuls dcae ha equy eu dspeso ceases a a deceasg ae he beash make, whch defes aoal asse pcg. Ths mgh cosue he evdece of hedg, bu he cocluso cao be valdaed wh hs daa. Equy eu dspeso behaves as pedced whe eus ae wh he omal age. Whe he make us bullsh, he ae of equy eu dspeso ceases olealy. Ths mples ha vesos could place moe emphass o equy fudameals whe he make s sg oably.

15 Fgue. Quale Pocess. Q u a l e P o c e s s E s m a e s ( 9 5 % C I ) I e c e p Q u a l e Q u a l e Q u a l e 3

16 4. DISCUSSION The ma cobuo of hs pape s he applcao of quale egesso o he aalyss of dspeso of sock eus. QR s a suable ool o aalyze dspeso of eus he exeme als of sock eus dsbuo. We use mehodology of Chag e al. (000) o deec a decease o less-ha-popooae cease dspeso of sock eus. Ou empcal aalyss focuses o he lage-capal compaes OMXH. We fd ha dspeso does o decease o a aveage adg day. I hs espec, asse pcg s aoal ad vesos do o hed. Tesg make sess wh QR yelds dffee esuls. We fd ha he coeffce fo he olea em, whch ha measues he ae of cease, s egave ad sgfca he lowe al (5% o %) of sock eus dsbuo. Ths coadcs wh CAPM. O he ohe had, he coeffce s posve ad sascally sgfca he uppe al (95% ad 99%). Ths dcaes a olea cease dspeso. These esuls compae especally well wh Cajueo ad Tabak (007) who also fd deceasg dspeso he boom al of sock eus dsbuo. The esuls fom quale pocess dcae sascally sgfca egave coeffce up o he fs quale (5%) of sock eus dsbuo. Afe hs, he coeffce emas egave bu sascally sgfca almos up o he meda. A possble explaao fo hs could be ha sock sell-offs dsub he fomao se of vesos, who he cu he losses o cosoldae eags by sellg whe ohe vesos sell oo. Oe cause fo hs fdg could be he obsevao peod, whch cocdes wh a ecoomc expaso ad a bull make. As he sock make s effecvely foecasg fuue eags, he fea ha he busess cycle s ug o a dowwad ed mgh spak sell-offs. Oveall, hs mgh cosue he evdece of hedg. Howeve, hs s jus speculao because hee s o cool devce ha would mplcae hedg as he causal faco. As a fuue deco fo eseach, would be wohwhle o clude all socks lsed OMXH he aalyss. I s possble ha he devaos fom CAPM he cease of dspeso mgh be moe pome amog he smalle compaes because fomaoal asymmees could be sake ha amog he lage compaes (Gleaso e al. 004, p. 69). Moeove, cludg adg volumes o he aalyss mgh gve dffee esuls as well as ceasg he legh of he daase. Thus, ou esuls should be epeed cauously eve f oe acceps he pemse ha hese mehods dsclose hed behavo - as he obusess emas o be esed. I a boade pespecve, QR should be appled ohe sock makes as well o mpove he vew ha he make sess ad o-lea hedg models have povded he pevous eseach. 4

17 REFERENCES Baes, Mchelle L. & Hughes, Ahoy W. (00): A Quale Regesso Aalyss of he Coss Seco of Sock Make Reus, Wokg Pape, FRB Boso Sees, No. 0-, hp:// Behad, Da, Campello, Mullo & Kusoa, Edwad (006): Who Heds?, Joual of Facal Ecoomcs, Vol. 80, pp Bkchada, Sushl, Hschlefe, Davd & Welch Ivo (99): A Theoy of Fads, Cusom ad Culual Chage as Ifomao Cascades, Joual of Polcal Ecoomy, Vol.00, No. 5. Bkchada, Sushl, Hschlefe, Davd & Welch Ivo (998): Leag fom he Behavo of Ohes: Cofomy, Fads ad Ifomaoal Cascades, Joual of Ecoomc Pespecves, Vol., No. 3, pp Bkchada, Sushl & Shama, Sul (00): Hed Behavo Facal Makes, IMF Saff Papes, Vol. 47, No 3, pp Blume, Mashall E. (975): Beas ad The Regesso Tedeces, The Joual of Face, Vol. 30, No. 3, pp Cajueo, Dael O. & Tabak, Bejam M. (007): Mulfacaly ad Hedg Behavo he Japaese Sock Make, Chaos, Solos & Facals, do:0.06/j.chaos Chamley, Csophe P. (004): Raoal Heds: Ecoomc Models of Socal Leag, Cambdge Uvesy Pess. Chag, Ec C, Cheg, Joseph W. & Khoa, Ajay (000): A Examao of Hed Behavo Equy Makes: A Ieaoal Pespecve, Joual of Bakg ad Face, Vol. 4, pp Chag, Thomas C. & Zheg DaZh (008): A Empcal Aalyss of Hedg Behavo Global Makes: Evdece fom Idusy Sock Reus, Cofeece Pape, hp:// Chse, Wllam G. & Huag, Roge (995): Followg he Ped Ppe: Do Idvdual Reus Hed aoud he Make?, Facal Aalyss Joual, Vol. 5, No. 4, pp Deme, Rza & Kua, Al M. (006): Does Hed Behavo Exs Chese Sock Makes?, Ieaoal Facal Makes, Isuos ad Moey, Vol. 6, pp Deveow, Adea & Welch Ivo (996): Raoal Hedg ad Facal Ecoomcs, Euopea Ecoomc Revew, Vol. 40, pp Fabozz, Fak J. & Facs, Jack C. (978): Bea as a Radom Coeffce, The Joual of Facal ad Quaave Aalyss, Vol. 3, No., pp

18 Foo, Keeh A., Schafse, Davd S. & Se, Jeemy C. (99): Hed o he See: Ifomaoal Ieffceces a Make wh Sho-Tem Speculao, The Joual of Face, Vol. 47, No. 4, pp Gleaso, Kmbely C., Mahu, Ike & Peeso, Mak A. (004): Aalyss of Iaday Hedg amog he Seco ETFs, Joual of Empcal Face, Vol., pp Goueoux, Chsa & Jasak, Joa (00): Facal Ecoomecs: Poblems, Models ad Mehods, Pceo Uvesy Pess, Pceo ad Oxfod. Heke, Jula, Heke Thomas & Mssos, Aa (006): Do Ivesos Hed Iaday Ausala Eques, Ieaoal Joual of Maageal Face, Vol., No. 3, pp Hshlefe, Davd & Teoh, Sew Hog (003): Hed Behavou ad Cascadg Capal Makes: a Revew ad Syhess, Euopea Facal Maageme, Vol. 9, No., pp Hwag, Soosug & Salmo, Mak (004): Make Sess ad Hedg, Joual of Empcal Face, Vol., pp Hwag, Soosug & Salmo, Mak (006): Seme ad Bea Hedg, Cofeece Pape. hp:// Koeke, Roge (005): Quale Regesso, Cambdge Uvesy Pess. Koeke, Roge & Hallock, Kev F. (00): Quale Regesso: A Ioduco, hp:// Rome, Davd (993): Raoal Asse-Pce Movemes whou News, The Ameca Ecoomc Revew, Vol. 83, No. 5, pp Schafse, Davd S. & Se, Jeemy C. (990): Hed Behavo ad Ivesme, The Ameca Ecoomc Revew, Vol. 80, No. 3. Shlle, Robe J. (984): Sock Pces ad Socal Dyamcs, Bookgs Papes o Ecoomc Acvy, No., pp Ta, L (005): Empcal Aalyss of Chese Sock Make Behavo: Evdece fom Dyamc Coelaos, Hedg Behavo, ad Speed of Adjusme, Ph.D. Thess, Dexel Uvesy, hp://dea.lbay.dexel.edu/hadle/860/54. Ta, L, Chag, Thomas C., Maso, Joseph R. & Nellg, Edwad (008): Hedg Behavo Chese Sock Makes: A Examao of A ad B Shaes, Pacfc-Bas Facal Joual, 6, pp Tuema, Be (994): Aalys Foecass ad Hedg Behavo, The Revew of Facal Sudes, Vol. 7, No., pp Welch, Ivo (99): Sequeal Sales, Leag ad Cascades, The Joual of Face, Vol. 47, No., pp

19 Welch, Ivo (000): Hedg amog Secuy Aalyss, Joual of Facal Ecoomcs, Vol. 58, pp Wemes, Russ (999): Muual Fud Hedg ad he Impac o Sock Pces, The Joual of Face, Vol. 54, No., pp APPENDIX Measue fo Sock Reu Dspeso The ae of eu s calculaed fom sock pces (o sock dces) wh whee = p p, (A) p p dcaes he value (pce) of a secuy peod. The basc fomula o calculae β s ˆ cov(,, m, ) β =. 0 (A) va( ) m, The mehod o measue hedg s esseally he same as Chag (000) ad Ta (005). Fs, we calculae he absolue value of devao of excess eu (AVD) fo each sock peod. Ths s AVD = ˆ β β E [( )]. (A3),, m, m, f, Sce we kow ha β always, equao (A3) ca be expessed as, m = AVD = ˆ β E [( )]. (A4),, m, f, 0 See devao Goueoux & Jasak (00, p. 9). 7

20 Nex, we eed a measue fo he expeced coss-secoal aveage devao (CSAD) fo socks. We oba hs fom E[ CSAD ] ˆ = AVD, = β, E [( m, f, )]. (A5) = = Quale Regesso A smple way o udesad QR s o daw a aalogue fom leas squaes egesso (Koeke 005). OLS solves he mmzao poblem mp β R = ( y x β ). (A6) T I a smla mae, T Q ( τ x) = x β specfes he τh codoal fuco, ad ˆ β ( τ ) solves he y mmzao poblem T m ρ ( β ) τ y β x p R =. (A7) A esmao ˆ β ( τ ) ca be foud by solvg ˆ T T β = + τ ag m τ y x β ( τ ) y x β β. (A8) T T : y > x β : y < x β Thus, QR mmzes a weghed sum of he absolue eos. Choosg a value τ (0,) gves he appopae weghs fo he mmzao poblem. Seg τ = 0. 5 yelds meda egesso as a specal case of QR. By asympoc omaly, coeffces ca be compaed o he ccal values of -sascs. Table A: Advaced Dckey-Fulle Tes fo U Roo. Tes CSAD m m ADF -4.86* -5.* -.7* The Advaced Dckey-Fulle es fo each me sees. * dcaes a % sgfcace level fo ejecg a u oo. 8

21 Table A: Quale Pocess Coeffces. QUANTILE α η η (-4.90***) (-9.07***) (-9.***) (-5.86***) (-8.5***) (-5.03***) (-5.84***) (-5.***) E-05 (-3.57***) E-05 (-.79*) E-06 (-0.30) E-05 (.8*) E-05 (3.30***) (5.36***) (5.***) (5.9***) (8.8***) (8.0***) (5.75***) (74.6***) (50.00***) (7.3***) (5.80***) (45.08***) (58.***) (83.40***) (.36***) (0.70***) (58.53***) (9.86***) (40.5***) (5.58***) (53.63***) (6.35***) (37.6***) (7.6***) (5.97***) (7.34***) (-3.53***) (-7.08***) (-3.97***) (-.39**) (-.***) (-.8) (-.) (-0.76) (-0.60) (0.3) (.34) (0.89) (.7) (.07**) (.66*).4366 (.7) (4.80***) (4.6***) (3.6***) The esuls fo quale egesso o CSAD ( τ x) = α + η m, ( τ ) + η[ m, ( τ )] + ε wh vayg values fo τ. T-sascs ae epoed paeheses. * dcaes a 0% sgfcace level; ** dcaes a 5% sgfcace level; *** dcaes a % sgfcace level. 9