The Taiwan stock market does follow a random walk. Abstract

Transcription

1 The Tiwn soc mre does follow rndom wl D Bue Loc Feng Chi Universiy Absrc Applying he Lo nd McKinly vrince rio es on he weely reurns from he Tiwn soc mre from 990 o mid 006, I obined resuls srongly indicive of he fc h no only does he Tiwn composie soc index move in rndom wl fshion, reurns for he individul socs do so s we. Previous uhors employing he sme mehodology obined opposie resuls, nmely, h he movemens of he Tiwn soc composie index do no follow rndom wl. Ciion: Loc, D Bue, (007) "The Tiwn soc mre does follow rndom wl." Economics Bullein, Vol. 7, No. 3 pp. -8 Submied: Jnury 5, 007. Acceped: Mrch 5, 007. URL: hp://economicsbullein.vnderbil.edu/007/volume7/eb-07g0000a.pdf

2 . Inroducion The erly wor of Fm nd French (965) suggesed h soc price movemens re no correled o such degree h one cn ruly profi from he insignificn uo-corrlelions. This ide ws subsnied in heir ler survey of he exn lierure (Fm nd French, 970). Since hen, number of uhors hve neverheless discovered significn uocorrelion in boh he U.S. nd non-u.s. soc reurns. These findings pu o quesion he percepion h soc reurns follow rndom wl, or h socs offer posiive long-run reurn bu h wheher soc will move up or down on ny given dy is fify-fify. Amongs hese ppers, he one by Lo nd McKinly (988) no only refued he rndom wl hypohesis for he U.S. weely reurns, bu i lso presened ler reserchers wih powerful vrince rio es for he invesigion of he pplicbiliy of he rndom wl hypohesis s descripion of soc price movemens for non-u.s. mres. This es is prediced upon he fc h for price movemens h follow rndom wls, he vrince of he log-price relives, log P - log P -, smpled regulr inervls of lengh ime, is n imes he vrince of he log-price relives smpled inervls of lengh ime /n. Hence he vrince of he monhly smpled log-price relives wih smpling inervl of lengh four wees is four imes h of he weely smpled. The es sisic derived by Lo nd McKinly o es if series of price movemens follows rndom wl is robus o mny forms of heeroscedsiciy nd nonnormliy. Ler on, Chng nd Ting (000) pplied he Lo nd McKinly mehodology on he weely movemens of he Tiwn composie vlue-weighed soc mre index (Tiex). These uhors concluded h hese movemens do no fi rndom wl. The d hey used rn from 97 o 996. Ting ino ccoun h he Tiwn invesmen environmen hs chnged much in he wo decdes since he incepion of he Tiex in 97, i is quie possible h he sme Lo nd McKinly mehodology pplied on more curren d my produce differen resuls. The presen sudy exended he Chng nd Ting (000) sudy by incorporing Tiex vlues beyond 996. In conrs o Chng nd Ting, he resuls obined here re in srong suppor of he fc h he weely movemens of he Tiex do indeed follow rndom wl. The d used re from 97 o 006. This pper is orgnized s follows: Secion summrizes he Lo nd McKinly Fm nd French (988), Poerb nd Summers (988), s well s Lo nd McKinly (988). Urrui (995) repored significnly uocorreled Lin Americn monhly reurns. Chng nd Ting (000) suggesed h he Tiwn Composie Soc Index does no follow rndom wl.

3 mehodology. Secion 3 presens he empiricl resuls, nd secion 4 concludes.. Mehodology Le denoe he log of he price of some soc ime, nd h = μ + + ε, hen he price vrible is sid o incremen in rndom wl fshion. Here μ snds for n rbirry drif prmeer, nd ε is he rndom disurbnce llowed o vry wih ime 3 nd devie from normliy. This specificion of is fr more lenien hn he rdiionl rndom wl specificion which resrics ε o being ideniclly nd independenly disribued (i.i.d.). If he movemen of does follow rndom wl, hen he vrince of is /n imes he vrince of n number of price movemens represened by + consecuive. Furhermore, given finie s, wrien s,,..., 0, nd en o be segmen from n infinie series, he quesion of wheher = μ + + ε holds rue for he enire series cn be ddressed by esiming he rio of he vrince of o /n he vrince of s n follows (Lo nd McKinly, 988), under he rndom wl hypohesis, his vrince rio hs vlue close o one. nd Le ˆ μ = ( ) = ( 0 ), = ( ˆ) μ, = = c ( = ( q q ˆ) μ q = q q( q + )( ), hen nd ( ) re unbised esimors for he vrinces of nd q respecively (Lo c ( nd McKinly, 988). Now, le VR( =, q =, 4, 8, nd 6, hen under he rndom wl hypohesis, he four vrince rios VR (), VR (4), VR(8), nd VR(6) will ll hve vlues close o one since he vrince of he incremens of rndom wl is liner in he smpling inervl. To es wheher he vrince rios of he smpled price movemens devie enough from uniy o rejec he rndom wl hypohesis, Lo nd McKinly (988) derived he sympoiclly sndrd norml c q 3 One exmple is when he vrince vries in deerminisic fshion; noher is when condiionl vrince vries wih ps informion.

4 sisic z( = q j= ( VR( ) ( q q j) ˆ( δ j), where ˆ( δ j) = = j+ ( = ( ˆ) μ ( j ˆ) μ j ˆ) μ. I hs lso been shown in Lo nd McKinly (988) h when q =, VR( - esimes he firs-order uocorrelion coefficien of he ( )s. Thus, if he s re weely prices, hen VR() pproximes he firs-order uocorrelion of weely reurns. 3. D nd resuls The d re from he Tiwn Economic Journl d bn. These re he Fridy vlues of he Tiex he mre s close. Under invesigion is wheher weely movemens of he Tiex follow rndom wl. Resuls re presened in ble. Tble Vrince rios for he weely vlues of he Tiex nd he corresponding z sisics for he null hypohesis h rio hs vlue of Smpling period: o For q = = 864 VR( = 0.97 z( = -0.5 NOT rejeced 5% q = 4 = 864 VR( =.09 z( = 0.80 NOT rejeced 5% q = 8 = 864 VR( =.5 z( =.5 NOT rejeced 5% q = 6 = 864 VR( =.4 z( =.78 NOT rejeced 5% Smpling period: o For q = = 560 VR( = 0.97 z( = NOT rejeced 5% q = 4 = 560 VR( =. z( = 0.84 NOT rejeced 5% q = 8 = 560 VR( =.30 z( =.4 NOT rejeced 5% q = 6 = 560 VR( =.46 z( =.56 NOT rejeced 5% Smpling period: o For q = = 88 VR( =.0 z( = 0.3 NOT rejeced 5% q = 4 = 88 VR( =.0 z( = 0.0 NOT rejeced 5% q = 8 = 88 VR( =.09 z( = 0.43 NOT rejeced 5% 3

5 q = 6 = 88 VR( =.7 z( = 0.9 NOT rejeced 5% ( VR( c, where is he esimed vrince of he weely differences, nd ( ) is men o provide n unbised esimion of /q imes he vrince of. Under he c q rndom wl null hypohesis, he vrince rio VR( is, nd he es sisic z( follows sndrd norml disribuion sympoiclly. The ls column ells wheher he rndom wl hypohesis is rejeced he 5 percen level of significnce. denoes he number of weely observion in he series. q Tble presens he vrince rios bsed on he weely vlues of he Tiex. Also shown re he corresponding z sisics for he null hypohesis h rio hs vlue of. D from hree smpling periods re used. The full smple period runs from Jn 6, 990 hrough Nov 3, 006 wih ol of 864 weely Tiex vlues. However, relizing h es resuls cn be highly ime-dependen, he full smple period is subdivided ino wo shorer sub-periods. For ech period smpled in ble, if he d suppor he rndom wl hypohesis, he VR(s hve vlues close o for he vlues of q ssigned. This is in fc he cse wih he resul presened in ble. The rndom wl hypohesis, i.e. he hypohesis h he vrince rio is equl o, is no rejeced by he d from he full smple period, nor by he d from he sub-periods. None of he es sisic z( is lrge or smll enough o rejec he hypohesis h he corresponding vrince rio is in fc. As menioned before, he vrince rio VR( when q = is pproximely equl o plus he firs-order uocorrelion coefficien esimor of weely reurns. Thus, he firs-order uocorrelion for he weely reurns in he full smple period is mere -.03; nd for he wo sub-periods, -.03 nd.0 respecively. Overll, he resuls obined provide srong suppor h he incremens of he Tiex follow rndom wl. As menioned before, Chng nd Ting (000) pplied he sme mehodology on he weely movemen of he Tiwn soc index nd obined drsiclly differen resuls from hose presened in his pper. These uhors employed d from he 970s nd he 980s in heir sudy nd obined consisenly srong rejecion of he rndom wl hypohesis he 5 percen level. However, he 970s nd he 980s were he Tiwn mre s formive yers nd i is highly plusible h fledgling mre is less efficien h mured one. Th being sid, i is highly suspeced h Chng nd Ting s resuls re minly cused by d from hese wo decdes. Therefore, he Tiex vlues from he wo decdes re pu hrough he es. The resuls re in ble. 4

6 Tble Resuls for he weely movemens of he Tiex Smpling period: o q = = 976 VR( =. z( = 4.5 rejeced 5% q = 4 = 976 VR( =.49 z( = 5.35 rejeced 5% q = 8 = 976 VR( =.64 z( = 4.40 rejeced 5% q = 6 = 976 VR( =.78 z( = 3.66 rejeced 5% ( VR( c, where is he esimed vrince of he weely differences, nd ( ) is men o provide n unbised esimion of /q imes he vrince of. Under he c q rndom wl null hypohesis, he vrince rio VR( is, nd he es sisic z( follows sndrd norml disribuion sympoiclly. The ls column ells wheher he rndom wl hypohesis is rejeced he 5 percen level of significnce. denoes he number of weely observion in he series. q When he ess re performed solely on d from he formive yers of he Tiwn soc mre, he rndom wl hypohesis is soundly rejeced s descripion of how he Tiwn soc index behves. The lrge VR() vlue of. sys h he series from 97 o 989 is much highly uocorreled hn he one whose resuls re presened in ble. To give n ide of how he Tiwn soc index hs progressed since is incepion in 97 he following ble is provided: Tble 3 Hisoricl nnul d of he Tiwn soc mre Tiex Volume Amoun Mre Cp. (close) (Mil.Shres) (NTD$M) (NTD$000,000) 97/ ,79 9,006 97/ 8.03,5 33,6 7,39 973/ ,6 77,90 76, / 93.06,907 4,64 47, / ,998 5,0 70, / ,540 0,9 9, / ,85 53,409 7, / ,93 33,507 50, / ,030 0,76 76, / ,50 47,59 0,749 98/ ,065 09,040 4,998 5

7 98/ ,09 33,78 9,94 983/ , ,473 94, / ,998 34,68 359, / ,384 9,850 40, / , ,58 538, / ,763,658,300,35, / ,36 7,95,03,87, / ,553 5,678,970 5,783, / ,6,36,54,90,835 99/ ,53 0,33,905 3,50,70 99/ ,359 6,7,636,546,08 993/ ,67 9,85,984 4,960, / ,565 9,436,364 6,444,69 995/ ,39 0,9,37 5,, / ,676 3,38,0 7,3,98 997/ ,680 37,70,886 9,79,09 998/ ,975 9,760,77 8,46,75 999/ ,497 9,490,93,734, / ,96 30,86,356 8,6,575 00/ ,63 8,40,47 0,03,38 00/ ,3,937,59 8,99, / ,036,666 0,48,74,40,99 004/ ,099,55 4,77,88 3,880, / ,7 9,050,955 5,566,3 Looing ble 3, i is esy o see h in erms of he vlue of he Tiwn composie index (Tiex), volume rded, moun rded, nd mre cpilizion, he Tiwn mre prior o he le 80 s ws bu miniure of wh i hs become ody. The close scruiny h lrge mre is subjeced o my help explin why he Tiwn mre is more rndom in he recen yers. 4. Conclusions Applying he Lo nd McKinly vrince rio mehodology ono he Tiex vlues from 990 o 006, i hs been shown h he weely movemens of he Tiwn Composie Soc Index do seem o follow rndom wl. However, he sme es performed on he index vlues en beween 97 nd 989 resuled in he srong rejecion of he rndom wl. Looing he hisoricl d of he Tiwn mre, i 6

8 is plusible h he discrepncy in resuls cn be due o he fledgling nure of he mre he erlier ime period. In he 970s nd he 980s, he Tiwn mre ws sill is infncy, rde vlues nd volumes s well s ol mre cpilizion were sill very smll; since hen, he mre hs experienced remendous growh. I is herefore resonble o conjecure h he subsequen increse in he degree of scruiny he mre is subjeced o s i mured hs mde he mre more rndom in erms of price movemens. 5. References Chng, K. nd K. Ting (000) A Vrince Rio Tes of he Rndom Wl Hypohesis for Tiwn s Soc Mre Applied Finncil Economics 0, Fm, E. F. (960) The Behvior of Soc Mre Prices Journl of Business 38, Fm, E. nd K. French (988) Permnen nd Temporry Componens of Soc Prices Journl of Poliicl Economy 96, Frennberg, P. nd B. Hnsson (993) Tesing he Rndom Wl Hypohesis on Swedish Soc Prices: Journl of Bning nd Finnce 7, Hung, B. (995) Do Asin Soc Mre Prices Follow Rndom Wls? Evidence from he Vrince Rio Tes Applied Finncil Economics 5, 5-6. Lee, S. nd K. P. Chng (955) Men-Vrince-Insbiliy Porfolio Anlysis: A Cse of Tiwn s Soc Mre Mngemen Science 4, Lo, A. W. nd C. McKinly (988) Soc Mre Prices Do No Follow Rndom Wls: Evidence from Simple Specificion Tes Review of Finncil Sudies, Lo, A. W. nd C. McKinly (988) The Size nd Power of he Vrince Rio Tess in Finie Smples: A Mone Crlo Invesigion Journl of Economerics 40, Mlliropulos, D. nd R. Priesley (999) Men Reversion in Souhes Asin Soc 7

9 Mres Journl of Empiricl Finnce 6, Pn, M. S., J. R. Chiou., R. Hocing nd H. K. Rim (99) An Exminion of Men-Revering Behvior of Soc Prices in Pcific-Bsin Soc Mres Pcific-Bsin Cpil Mre Reserch, Poerb, J. nd L. Summer (988) Men Reversion in Soc Prices: Evidence nd Implicions Journl of Finncil Economics, Urrui, J. (995) Tess of Rndom Wl nd Mre Efficiency for Lin Americn Emerging Equiy Mres Journl of Finncil Reserch 8, Wrigh, J. H. (000) Alernive Vrince Rio Tess Using Rns nd Signs Journl of Business nd Economic Sisics 8, -9. 8