Characteristics of the Asian and US Stock Markets --- Seoul, Tokyo, Jakarta, Shanghai, and New York ---

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1 1 Characerisics of he Asian and US Sock Markes --- Seoul, okyo, Jakara, Shanghai, and New York --- Kilman Shin* Absrac he January effec refers o he heory ha he monhly average sock reurn is he highes in January han in any oher monh. Some argue ha he January effec holds rue only for small-firm socks and i akes place only over he firs week of a new year. Ohers argue ha he January reurns are higher because he risk is higher in January. he January effec has received much aenion since i direcly conradics he random walk heory, which argues ha fuure sock prices are unpredicable using he presen and pas price informaion. Defendans of he random walk heory argue ha he January effec can occur only in he shor run and i canno persis and will disappear in he long run. In his sudy, some seleced Asian sock markes and he US sock markes are examined o find if he January effec or oher periodic paerns exis in he Asian and US sock markes. In addiion o he simple comparison of monhly sock reurns wih and wihou riskadjusmens, various saisical mehods, such as variance raio es, uni roo es, Johansen coinegraion es, ARCH, ARCH-M, GARCH, VAR, ARIMA models, and facor analysis are applied o he monhly sock prices and reurns. For risk-adjusmen, he Shin index is proposed wih regard o he Sharpe index, reynor index, Jensen index, and he Modigliani index. I. Inroducion A large number of empirical sudies have been published on he January effec which is a heory ha monhly sock reurns end o be higher in January han in any oher monh. he so-called January effec has received much aenion since i conradics he random walk hypohesis which argues ha sock reurns should be randomly disribued. he random walk hypohesis implies he following proposiions when applied o he monhly reurns: Firs, a given monh's sock reurns should have no significan correlaions wih oher monhs' sock reurns so ha one monh's sock reurn is useless in predicing he sock reurns of oher monhs. Second, monhly sock reurns should have no seasonaliy, periodic or cyclical paerns so ha fuure sock reurns canno be prediced based on periodical paerns. hird, he monhly reurns of socks in a sock exchange should be useless in predicing he monhly reurns of socks in oher counries if he ime zones are differen. * Ferris Sae Universiy, Big Rapids, Michigan, USA: kilman_shin@ferris.edu

2 2 o suppor or refue he random walk hypohesis, here are much on-going research in he periodical paerns in he sock reurns in he following areas: (1) he January effec monhly or daily sock reurns are higher in January han in oher monhs, (2) Early monh effec sock prices rise during he firs 2 weeks of each monh, (3) Week-end effec sock prices fall on Monday relaive o Friday (pure week-end effec, Friday close o Monday open), (4) Day-end effec sock prices rise near he closing ime, (5) Holiday effec sock prices rise on he day before he naional holiday weekends, and (6) Dayligh savings ime effec sock prices fall afer he change in he dayligh savings ime (Kamsra, Kramer, and Levi, 2000, 2002; Pinegar, 2002; for a review, see Khaksari and Bubnys, 1992; Malkiel, 2003). he major objecive of his paper is o examine some seleced Asian sock markes o find if here are any monhly or seasonal paerns, such as he January effec, and if he sock prices follow he random walk. he following sock markes were seleced for our sudy: he Korea (Seoul) Sock Exchange, he okyo Sock Exchange, he Jakara Sock Exchange, and he Shanghai Sock Exchange. he US sock marke (SP 500 socks) is also examined in his sudy for he purpose of comparison. In secion II, some of he previous empirical sudies are reviewed. In secion III, he random walk heory and he mehods of measuring he risk-adjused reurns (CAPM) are reviewed. In secion IV, empirical resuls are presened for he Asian sock markes and he SP 500 socks. A summary and conclusions are provided in secion V. II. Review of Previous Sudies here are many sudies on he seasonaliy and cyclical paerns in he monhly, weekly, and daily sock reurns. Some early sudies are reviewed in Wachel (1942), Granger and Morgensern (1970). Since Wachel (1942) is widely quoed as an early proponen of ax-selling hypohesis, we will briefly review his sudy. His sudy is based on he following assumpions: (1) he high-yielding socks are usually he socks whose prices have decreased, and hey are he bes socks o sell in December o obain he larges realizable capial losses for ax saving, (2) individuals and corporaions sell socks for ax-saving oward he middle of December o esablish ax losses, and such pressures drives securiy prices below wha hey should be in he ligh of poenial earnings, (3) he rise a he year's end is nohing more han a normal reacion from depressed levels. o prove he above heory, he selecs 20 highes-yielding indusrial socks lised on he NYSE each year for he period hen he adds he values of he 20 socks a every 2 weeks from he bases in December, and divides by 13 years ( ) o obain he annual mean value. his procedure was followed o obain he mean values for he 30 Dow-Jones Indusrial socks. He hen plos he series of he wo mean values a 2- week ime inerval. He finds ha he mean value of he high-yielding socks rise more han he low-yielding Dow-Jones socks in he lae December o he hird Saurday in January. Similar resuls were obained for he median values. However, he following criicism may be made. Firs, here is no reason why he ax selling pressure should end a he middle of December. In heory, he ax-selling pressure should coninue unil he end of December. As anoher possible reason, Wachel menions unusual demand for cash,

3 3 beginning a week or wo before Chrismas, causes many sock sales. Bu his daa show ha sock prices rise 2 weeks before he year end. ha is, unusual demand for cash should no sop unil he holiday season is over. Second, here is no saisical significance es. So we can no ell wheher hee difference was saisically significan. Granger and Morgensern (1963,1970) reviewed some early sudies on he periodical paerns in he sock marke. o examine he validiy of such sudies, hey applied specral analysis o various daa, such as he Sandard and Poor's Sock Index (Monhly, , ), SEC Sock Price Index (weekly, ), Dow-Jones Indusrial Average ( ), and individual company socks (daily, weekly, and monhly). hey ploed and examined several specral diagrams, and concluded ha he specra of log price differences are fla for all series considered over a range of 0.5 cycles per year up o 0.5 cycles per day, srongly supporing he random walk hypohesis. he resuls did no show a 12 monh peak, hough i showed some small peaks corresponding o a hree monh cycle. Weekly price series indicaed he presence of a small monhly cycle. Bu none of he cycles was significan in any specral diagram (pp ). Bonin and Moses (1974) used he analysis of variance for he monhly daa of he 30 Dow Jones indusrial socks for he period , and found ha 7 of he socks displayed significan seasonal paerns. Officer (1975) used he Box-Jenkins ime series analysis for he Ausralian sock reurns for he period , and found 6-monh, 9- monh, and lesser 12-monh seasonaliy in he auocorrelaion funcion. Rozeff and Kinney (1976) used he NYSE daa for he period hey divided he sample ino 4 periods: , , , and plus When hey compued he auocorrelaion funcions, he resuls did no reveal seasonaliy. However, when average monhly reurns were esed, excep for he period , hey found saisically significan differences in he monhly reurns due o he large January reurns. hey used he Kruskal-Wallis es, he Siegel-ukey es, Barle s es for homogeneiy of variances, and he analysis of variance. hey found ha he January reurn is significanly higher han oher monh's reurns. hey also found relaively higher reurns in July, November, and December, and low reurns in February and June. Also, January had a relaively higher risk premium han oher monhs. hey also esed he CAPM adjused reurns, and found significan monhly differences. Dyl (1977) seleced 100 socks for he period and divided ino 3 porfolio groups based on he percenage change in sock prices: porfolio 1, price increased more han 20%; porfolio 2, price changed beween 20% and -20%, and porfolio 3, price decreased more han 20%. He found ha he socks whose prices decreased more han 20% during he year had abnormally higher rading volumes in December. He argued ha i was evidence ha invesors sell o realize he capial losses for he purpose of ax deducion. He measured abnormal volume as he acual volume as a percenage of average monhly volume. Branch (1977) examined year-end lows of NYSE socks and found he average excess reurns of 3.5% o 6.2% for he periods of one o four weeks following he las Friday of he year over he period Branch and Ryan (1980) examined ax-loss selling candidaes of NYSE and AMEX socks for he

4 4 period hey found ha such sock prices rose on he firs 4 weeks of he year. he seleced NYSE socks increased from 3.4% o 6.7%, and he seleced AMEX socks rose from 5.2% o 14.4%. Keim (1983) used he NYSE and AMEX daa for he period He divided he socks (1,500 o 2,400 in oal) ino 10 porfolio groups. He regressed he daily excess reurns on he 11 dummy variables, where each dummy variable represens each monh from February o December. he excess reurn for January is measured by he inercep consan. He found ha he January effec is significan for small-firm porfolios (1 o 4 deciles) and he excess reurns are negaively relaed o larger firms (5 o 10 deciles). He also found ha he January effec occurred during he firs 5 rading days of he year. He used 3 ypes of bea, namely, he OLS esimaed bea, Scholes-Williams bea, and Dimson bea o calculae he risk adjused excess reurns for he porfolios of small firms (see appendix noe). Roll (1981) argues ha he socks of small-size firms are infrequenly raded, and as a resul he sysemaic risk is underesimaed. As a resul, he bea-risk adjused reurns are overesimaed. Using he SP500 daa for he period , he shows ha he Dimson bea is higher han he ordinary bea abou 1.25 o 2.37 imes. Roll (1983) compares he daily sock reurns for he las rading day of December and he firs 4 rading days of January (urn-of- he year). He found ha he very firs day of January showed he larges mean reurn differences. He found ha he January effec is significan for boh small and large firms. he mean and he frequency of posiive reurns on he 5 rading days were larger on he AMEX socks. Roll infers ha he January effec may persis because he relaive rading cos is larger for he smaller firms han for he larger firms. In Ausralia, all ax-paying financial insiuions pay normal axes on capial gains, and capial losses are deducible wihou limi from ordinary income. Individual invesors do no pay axes on capial gains. Also, he Ausralian ax year is July 1 o June 30. hus, o suppor he ax-selling hypohesis, here should be a June-July effec. Brown, Keim, Kleidon, and Marsh (1983) invesigaed he Ausralian socks for he period o allow for he size effec, he socks were divided ino 10 groups of porfolios. hey found ha he smalles decile of firms had average reurns of 6.754%, while he larges decile of firms had %. Also, hey found higher reurns over December-January and July- Augus. hus, hey concluded ha he January effec is no due o ax-selling aciviies. Gulekin and Gulekin (1983) examined monhly sock reurns for 17 counries: Ausralia, Ausria, Belgium, Canada, Denmark, France, Germany, Ialy, Japan, Neherlands, Norway, Singapore, Spain, Sweden, Swizerland, UK, and he US. hey used he Capial Inernaional Perspecive daa, published by Capial Inernaional, S.A., locaed in Geneva, for he period he reurn daa are based on he valueweighed indexes of monh-end closing prices wihou dividend yields. hey compued firs 12 monhly auocorrelaions, and found ha hey were mosly no significan excep for Ausralia, Denmark, and Norway. hey used he Kruskal-Wallis es for he 17 counries, and found ha he monhly reurns are no equal for 12 counries from a oal

5 5 of 17 only a he 10% level. he monhly reurns were equal for Ausralia, France, Ialy, Singapore, and he US. Excep for Ausralia, hey he monhly reurns were higher a he beginning of he ax year. In Ausralia, he ax year sars in July, and in he UK, i sars in April. Berges, McConnell, and Schlarbaum (1984) used Canadian socks for he period In Canada, he capial gains ax was insalled in January hey divided 391 socks ino 5 porfolio groups, and compared he January monhly reurns wih means of February-December reurns for he period and for he period hey found ha he January reurns are higher for each porfolio group han for he February- December reurns. Also he January reurns were higher for he period han for he period he capial losses in excess of capial gains may be used o offse ordinary income up o a maximum of $2,000 in one ax year. hus, here was no incenive for Canadian invesors o sell socks a he end of he ax year prior o Bu hey found he January effec which was more pronounced for small-size firms. hus, hey conclude ha ax-selling hypohesis is no a complee explanaion for he January effec. inic, Barone-Adesi, and Wes (1987) also used Canadian socks for he period hey divided 317 socks ino 5 size-porfolios. hey used regression analysis wih 5 dummy variables: 3 dummy variables represening for January, December, and he period wih capial gains ax respecively. wo oher dummy variables are he produc of January dummy and he capial gains ax period dummy variable, and he produc of he December dummy and he capial gains ax period dummy variable. he resuls showed ha sock reurns are higher in January and December and he smaller firms have higher reurns han he large firms. he dummy variable represening he capial-gains ax period had posiive signs, bu i was no saisically significan excep for one porfolio. hey conclude ha he resuls do no suppor ax-loss selling as he sole facor of seasonaliy, bu hey provide limied suppor for ax loss-selling hypohesis. Kao and Shallheim (1985) examined daa (abou 529 o 844 socks) for he period hey divided he socks ino 10 porfolios based on marke capializaion. hey calculaed regression equaions wih monhly dummy variables. hey found January and June reurns are significanly higher han oher monhly reurns. In Japan, here is no capial gains ax for individual invesors, bu corporaions are axed on capial gains, and each firm can choose is ax year arbirarily. Abou 50% of Japanese firms choose ax years ending Mach 31. hus, he Japanese resuls do no necessarily suppor he ax-selling hypohesis. hey presen wo possible reasons for he January and June effecs. Firs, mos Japanese firms pay so-called bonuses equivalen o abou wo monhly salaries o employees generally in June and December. Second, corporae earnings forecass are made by financial analyss in March, June, Sepember, and December. hey sae ha hese facors may parly explain he January and June effecs. Jaffe and Weserfield (1985) calculaed daily reurns for okyo socks for he period hey found ha he January mean daily reurn was significanly higher han he overall daily average reurn However, here was no significan

6 6 difference beween he average reurns over he las 5 days of December and he firs 5 days of January. hey also calculaed he correlaions coefficiens beween he okyo sock daily reurns and he SP500 daily sock reurns. he correlaion coefficien was he highes for he conemporaneous calendar ime a 0.154, wih was highly significan (=8.76). As for he day of he week effec, he lowes daily mean reurn occurred on uesday in okyo, and he lowes mean reurn occurred on Monday in New York, Keim (1985) used he NYSE socks for he period He regressed he January sock reurns on he sysemaic risk bea, dividend yield, dummy variable ha is equal o 1 if he firm pays zero dividend and is equal o zero oherwise, and he naural log of he marke value of he securiy. He found ha he inercep, dividend yield, and presence of dividend paymen were posiively correlaed, bu he firm size was negaively correlaed. he sysemaic risk was no significan. When he Feb. Dec. reurns were regressed on he same independen variables, he firm size was significan and negaively correlaed. Dividend variables and he sysemaic risk were no significan. Arbel (1985) colleced 1,000 companies: SP500 socks and non-sp 500 companies for he period he SP 500 companies are divided ino highly researched, moderaely researched, and research-negleced companies. he non-sp 500 companies are all research-negleced companies. He found ha he January reurns were higher for negleced companies. For he SP 500 socks, he January reurns were 2.48% for he highly researched companies, 4.95% for he moderaely researched companies, and 7.62% for he negleced. he January reurns were 11.32% for he non-sp 500 negleced companies. Branch and Chang (1985) found ha socks whose prices were falling hroughou he year ended o rise in price in he firs 4 weeks of he following year. he January effec was found in many oher sudies. Lakonishok and Smid (1986) used he daily sock daa of he Chicago ape for he period hey divided he socks ino 10 deciles and calculaed daily reurns over he las 5 days and he firs 4 days around he urn of he year using hree mehods of calculaing he daily reurn: CRSP reurn, close-o-close, and open-o-open. hey found ha he reurns of small companies are high around he urn of he year and are higher han he reurns of large firms, no maer how reurns are measured. Chang and Pinegar (1986) examined he holding period reurns of he bonds raded on he NYSE for he period hey sraified he bonds ino 6 groups according o Moody's bond raing sysem: Aaa, Aa, A, Baa, Ba, and B. hey found ha he January reurns are pronounced for he Baa and B-raed bonds. hey also examined sock reurns of he firms whose bond reurns were evaluaed. he differences in he sock reurns were no significan when he analysis of variance was applied. Bu when hey compared he January reurns wih he average of he previous 11 monhly reurns, he -values were significan for 3 of he 6 sock porfolios. Lo and MacKinlay (1988, 1989) applied he variance raio es o weekly daa for he period Sep. 2, 1962 o Dec. 26, 1985 and 2 subperiods. For he equal-weighed index for he NYSE and AMEX socks, he variance raio es did rejec he null hypohesis of

7 7 he random walk. Bu, he resuls were mixed for he value-weighed indexes. hey also examined 625 socks and 3 size-sored porfolios, each of which conained 100 socks: small socks, medium socks, and large socks. he resuls showed ha he reurns of individual reurns and he 3 porfolio reurns were no saisically significan, meaning ha hey follow he random walk. However, for he equal-weighed porfolios of 625 socks, he random walk hypohesis was rejeced, and he value-weighed porfolios were suppored for he random walk. However, Lo and Mackinlay (1999, p. 16) sae ha " he mos curren daa ( ) conform more closely o he random walk han our original sample period." Branch and Chang (1990) used he Compusa daa for he period Using regression analysis, hey found ha low-price socks ha exhibied poor December performance are likely o rebound in January. hey argue ha an efficien marke will no necessarily eliminae such predicable price paerns due o he following facors: ransacion coss (commission and bid-ask spreads), search coss (coss of idenifying such socks), and differenial capial gains ax raes (high marginal ax raes). Khaksari and Bubnys (1992) use daily daa for he SP500, NYSE sock indexes, and sock index fuures for he period o es he day-of-he-week, day-of-hemonh, and monh-of-he-year effecs on sock indexes and sock index fuures. hey use he Sharpe index o obain risk adjused reurns. hey find ha he day-of-he-week and he day-of-he-monh effecs are more pronounced in he fuures indexes han in he spo indexes. However, he January effec was more eviden in he spo indexes han in he fuures indexes. hey conclude ha he use of he Sharpe raio sharply reduces he dayof-he-week effec in spo and fuures index reurns, bu i does no reduce he monh-ofhe-year effec. hey sae ha hese resuls end o disagree wih efficien marke proponens. Yilmaz (2001) use weekly daa for he period and applied he variance raio ess o 14 emerging sock markes. he random walk hypohesis was acceped for Indonesia, Korea, Malaysia, aiwan, Argenina, Brazil, Mexico, Japan, and USA, bu i was rejeced for he Philippines, hailand, Chile, Greece, and urkey a he 5 % level. Hall and Urga (2002) es he Russian sock marke wih monhly daa for he period hey used a ime varying parameer model wih changing inercep and slope coefficiens (AR(1) wih generalized auoregressive condiional heeroscedasiciy-inmean-garch-m). hey find ha he sock marke indexes are iniially inefficien and predicable, bu wo and a half years laer i becomes efficien (see appendix noe). Mookerjee and Yu (1999) es he Shanghai and Shenzhen sock exchanges wih daily daa ( Dec. 19, 1990-May 20, 1992 for he Shanghai socks, and April 3, Dec. 17, 1993 for he Shenzhen socks). hey applied he ARIMA models wih dummy variables for Monday, Holiday, and January (for he firs 5 days). he resuls showed ha he week-end and holiday effecs are significan, bu he January effec is no significan.

8 8 Inerpreaion or Raionale for he January Effec here are 2 major quesions on he January effec. he firs quesion is he reasons for he January effec. he second quesion is he persisence of he January effec. As for he raionale for he January effec, here are several explanaions. he mos popular hypohesis is he ax-selling hypohesis, which argues ha invesors sell socks whose prices have been falling during he year, and he capial loss can be deduced from capial gains ax, and hen in he following year, he invesors can buy back he idenical or similar socks or oher enirely new socks. However, here are some objecions o his explanaion. (1) Such invesmen sraegy is subjec o he ax laws agains wash sales (see appendix noe). (2) If he ax-selling hypohesis should hold rue, he January effec should be larger afer World War II, when income ax raes are higher. However, Keim (1983) found ha he January effec was larger during he prewar period. (3) he January effec should no exis in counries where here is no capial gains ax, or he ax year does no sar in January. Bu, Brown, Keim, Kleidon, and Marsh (1983) found higher reurns over December January and July Augus in Ausralia where he ax year is July 1 June 30. Also, as reviewed before, Berges, McConnell, and Schlarbaum (1983) found he January effec in Canada for he period , where he capial gains ax was absen unil1973. A second alernaive hypohesis for he January effec is he porfolio rebalancing or window dressing hypohesis, which saes ha around he year-end insiuional invesors, raher han individual invesors, sell losing socks and buy winning socks o represen respecable porfolio holdings. However, Griffihs and Whie (1993) and Sias and Sarks (1997) found lile suppor for he insiuional porfolio rebalancing hypohesis. A hird hypohesis for he January effec is he new-year resoluion hypohesis, which saes ha people make new resoluions in December or January abou on habis, fuure plans, consumpion, savings, and invesmens, and he plan or decision is implemened in January, he beginning of a new year. So, people sar invesing in bonds and socks in January, and he January prices go up. If his hypohesis is rue, he January effec should be found in oher counries, oo, even if here are no capial gains axes and he ax year does no sar in January. A fourh hypohesis is, as saed in Wachel (1942, p.186), ha he unusual demand for cash for he holiday season (Sana Claus effec) affecs invesors o sell he socks in December. o purchase gifs and o finance ravel, invesors may sell some socks and bonds. his hypohesis is consisen wih he increasing sales during December. he cash balances are supposed o be reinvesed in he sock marke afer he holiday season is over, and i causes he sock prices o rise. he second quesion on he January effec is he persisence of he January effec. Why do he January effec and he firm-size effec persis o exis? If marke is efficien, arbirage aciviies will remove he reurn differenials. here are wo heories o explain

9 9 he persisence of boh he January effec and he firm-size effec. One is he ransacion cos heory and he oher is he risk premium heory. Firs, Roll (1983), Soll and Whaley (1983) argue ha he January effec for smaller firms may persis o exis because he ransacion cos is high for he small firms relaive o heir prices so ha arbirage canno remove he reurn differenial. However, his heory would no apply o he January effec for larger firms. An alernaive explanaion is he risk premium heory. Rogalski and inic (1986) esimaed variance, bea, and Dimson (1979) bea for small firms whose shares are raded infrequenly for he period for 20 firm-sized porfolios using he marke model. hey regressed he daily reurns of each porfolio on he daily reurns of equally weighed marke porfolio reurns. hey found ha variance and bea are much larger in January han in any oher monh, and variance and bea are much larger for he smaller firms han for he larger firms. Bu why should he risk levels be higher in January han in any oher monh? Why should January have higher risk? hey argue ha January is he beginning of a new uncerain year, so he risk should be higher In effec, he findings of he previous empirical sudies for he January effec may be summarized as follows: (1) he January abnormal average reurn is higher han ha for any oher monh. (2) he January abnormal average reurn is larger for small firm socks or low price socks han for large firms or high-price socks. (3) he January effec akes place over he firs week of he rading days of a new year, paricularly on he firs rading day. (4) here are several hypoheses o explain he January effec, such as ax-selling, porfolio rebalancing, new year resoluion, unusual demand for cash, year-end bonuses, invesmen decision making, ec. (5) he January effec will no necessarily disappear even if he marke may be efficien due o rading coss, informaion coss, uncerainy, and differenial marginal ax raes on capial gains. In his sudy, our objecive is o examine he monhly paerns of he sock reurns, such as he January effec, for some Asian sock markes, such as China, Indonesia, Korea, and Japan in comparison wih he US sock marke Excep for Japan and he US, he seleced counries have neiher he capial gains axes nor large insiuional invesmen companies. So, neiher he ax-selling hypohesis nor he insiuional porfolio rebalancing hypohesis will maer. However, he new-year resoluion hypohesis is no necessarily applicable since January in he conemporary Gregorian calendar is no he same as January in he Chinese lunar calendar, and hus he new year resoluion can ake place in February. ha is, he new year's day in he Chinese lunar calendar is widely celebraed in Indonesia and Korea as well as China. January in he Chinese lunar calendar generally falls in February in he Gregorian calendar. Also, in Asia he holiday season usually begins wih he new year's day and lass for a couple of days.

10 10 III. Risk-Adjused Reurn Measures Before we discuss our empirical resuls, i may be useful o briefly review he random walk heory and he mehods of measuring risk-adjused reurns in he framework of capial asse pricing model (CAPM). he efficien marke heory can be explained using he following wo equaions: E( Ri, ) E( Ri, η 1 ) = E( ε i, ) = 0 (3-1) f R,..., R ) f ( R,..., R η ) (3-2) ( 1, n, = 1, n, 1 Where R i, = sock reurn a ime for sock i, ( P + P 1 D ) / P 1, and η 1 = a se of informaion available a ime -1. Equaion (3-1) saes ha acual reurn on asse i is equal o is expeced reurn prediced a ime -1 wih he given se of informaion. his model is ofen called a fairgame model. Equaion (3-2) saes ha he uncondiional disribuion of acual reurns on all asses should be equal o he condiional disribuion of expeced reurns for a given se of informaion. Equaion (3-2) is called he random walk model. he difference beween he fair game model and he random walk model is ha he random walk model requires ha he serial correlaion beween reurns for any lag be zero, bu he fair game model does no require i (Fama, 1965, 1970; Copeland and Weson, 1992, pp ). he risk-adjused efficien marke hypohesis (or he join hypohesis of marke efficiency and he CAPM) is saed as follows: E R i, E( R i, β ) = ε i, (3-3) ( Ri i, F i, m, m, F, β ) = R + β [ E( R β ) R ] (3-4) E( ε, ) = 0 (3-5) i where E R β ) = he expeced reurn on sock i for period, given is sysemaic ( i i, risk, β, β > 0. E β ) = he expeced reurn on marke porfolio for period, i, ( R m m, given is prediced sysemaic risk β i, and β m, are esimaed sysemaic risk of sock i and he marke porfolio respecively for ime, esimaed a ime -1 based on he se of informaion, η 1 (Copeland and Weson, 1992, pp ). he CAPM models are ofen used o measure he performance of individual porfolio reurns on he risk-adjused basis. here are 3 popular measures of risk adjused reurns: reynor (1965), Sharpe (1966), and Jensen (1968): reynor bea index = ( R ) / β (3-6) p R F p

11 11 Sharpe oal index = ( R ) / σ (3-7) p R F p Jensen excess reurn: α = R R β R R ) (3-8) P F P ( M F I should be noed ha he raio ( R ) / β is he realized risk premium per uni of p R F sysemaic risk bea using he securiy marke line heory, and he raio p ( R ) / σ is p R F he realized risk premium per uni of oal risk using he capial marke line heory. hus, by adding he risk free rae o he risk premium, we obain he risk-adjused oal ) ) reurn: R = RF + ( R p RF ) / β p, if he reynor index is used, and R = RF + ( R p RF ) / σ p, if he Sharpe index is used. Modigliani and Modigliani (1997) show he following riskadjused reurn: R = R F ) + [( RP RF ) / σ p ]( σ M ) for he Sharpe index (see appendix noe). he firs wo measures can be modified o measure he relaive performance of a given porfolio wih respec o he marke porfolio (Shin, 1996): p Shin bea index = Shin oal index = ( R ( R P M ( R ( R R R P M F F R R ) / β P ) / β F F M ) / σ P ) / σ M (3-9) (3-10) where RP = reurn on porfolio i, σ P = oal risk of he porfolio, R M = reurn on he marke porfolio, σ M = oal risk of he marke porfolio, R F = reurn on he risk free porfolio, β = 1, sysemaic risk of he marke porfolio, β = sysemaic risk of he M porfolio: if β P < 0, he absolue value should be used. Oherwise, a negaive porfolio reurn wih a negaive bea would generae a posiive performance index, which is clearly wrong. he wo Shin indexes are essenially he same as he Sharpe index and he reynor index respecively. Since he denominaors( RM R F ) / β M and ( RM R F ) / σ M are consans, dividing he Sharpe and reynor indexes by he consans will no change he porfolio ranking by he Sharpe and reynor indexes. Bu he advanage of he Shin indexes is ha if he Shin index is greaer han 1, i indicaes ha he given porfolio's performance is beer han he performance of he marke porfolio over he sample period. ha is, if he indexes are greaer han 1, i implies ha p and ( RP R F / β P ) > ( RM R F ) / β M (3-11) ( RP R F / σ P ) > ( RM R F ) / σ M (3-12)

12 12 he common weakness of he bea based risk measures is ha if he bea value is no significan, unsable, exremely low, or high, he indexes can be unreliable, and he porfolio performance can be grealy overesimaed or underesimaed. he sysemaic risk can be unsable and unreliable, if he sample period is shor or if he sock reurns are volaile independen of he marke movemen. Also, as saed before, if he bea value is negaive, he absolue value should be used for he above 3 bea risk-relaed measures: R/bea, R-bRm, and he Shin bea index. Oherwise, when he reurn is negaive, a negaive reurn divided by a negaive bea value will give a posiive value, and his will clearly disor he performance of he porfolio. An advanage of he bea-based measures is ha saisical significance of bea and alpha can be esed. Jobson and Korkie (1981) conclude ha all he performance measures have shorcomings, bu he Sharpe measure appears o have a relaively small number of heoreical objecions, bu has no accompanying significance es. If he risk free rae is omied, he above 5 indexes (Equaions 3-6 o 3-10) can be reduced o RP / σ P, RP / β P, RP β P RM, ( R p / β p ) /( RM ), and ( RP / σ P ) /( RM / σ M ) respecively. he above indexes can be applied o individual securiies as well as o porfolios. In effec, we are aking he January reurn, for insance, as he reurn of a porfolio, called January porfolio, and aking he 12-monh average reurns as he reurns of he marke porfolio. ha is, we have 12 porfolios for each sock exchange, and we will evaluae he performance of he 12 porfolios for each sock exchange by applying he above 5 measures of risk-adjused reurns. IV. Empirical Resuls If he efficien marke hypohesis holds rue, he risk-adjused monhly reurns should be randomly disribued and hey should no show any periodic paerns. o es he hypohesis, we have seleced monhly daa for he following sock markes: he Sandard and Poor's 500 Socks ( ), he Korea Sock Exchange (KOSPI, ), he okyo Sock Exchange (Daiwa Index, ), he Shanghai Sock Exchange ( ), and he Jakara Sock Exchange ( ). he monhly sock prices, monhly reurn series, and he monhly reurns by year are ploed in Figures 1 ~ 2 for he socks of he 5 sock exchanges. here are some ouliers in he monhly reurns, bu we are unable o deec any clear monhly periodic paerns in he graphs. he following analyses are applied o he monhly reurns: 1. ANOVA and he Kruskal-Wallis es (able 1) 2. Chi-square es for he negaive reurns (able 1) 3. -es for wo means (able 1) 4. Risk-adjused reurns (able 1) 5. Regression analysis wih dummy variables (able 2) 6. elaion analysis (able 3) 7. Regression analysis wih monhly reurns (able 4)

13 13 8. ARIMA, ARCH, ARCH-M, and GARCH models (ables 5, 6) 9. Uni roo, variance raio, runs, and coinegraion ess (ables 7, 8, 9, 10) 10. VAR models (able 11) 11. Auocorrelaion analysis (Figure 3) 12. Specral analysis (Figure 4) 13. Inernaional correlaion and regression analyses (ables 12 and 13) 14. Characerisics of he Asian and US sock marke reurns (ables 14, 15, 16) - Descripive saisics, Normaliy, Homogeneiy, and Facor Analysis 15. Evaluaion of he Asian and US sock markes (able 17) 16. he bes and wors monhs in he 5 sock exchanges (able 18) 17. January Baromeer Effec (able 19) 1. ANOVA and Kruskal-Wallis es: If sock reurns are randomly disribued, he 12 monhly reurns should also be randomly disribued, and hus monhly reurns should no show any seasonal paerns. Firs, we use he ANOVA o es he following null hypohesis: µ = = (4-1) 1 µ 2 =... µ 12 where µ i = mean reurns of monh i. he resuls of ANOVA are presened in able 1 for he 5 sock exchanges. he F-values are exremely low, and he null hypohesis canno be rejeced a he 5% level. he F-values are 1.27 for he SP500 socks, 1.28 for he Korean socks, for he okyo socks, for he Shanghai socks, and 1.20 for he Jakara socks. However, ANOVA is based on he following wo assumpions: (1) he populaion monhly sock reurns are normally disribued, and (2) he populaion variances of monhly reurns are all equal. If hese wo assumpions are no valid, ANOVA resuls are no valid, and nonparameric ess, such as he Kruskal-Wallis. hree ess of normaliy and he Barle's es for homogeneiy are used. he resuls are summarized in able 13. Firs, he chi-square es for he goodness of fi rejecs he normaliy assumpion for he SP500 socks (chi-square 13), Korean socks (22.23), Jakara (13) and Shanghai socks (82.5) a he 5% level. Bu he normaliy assumpion is acceped for he okyo socks (4.31) a he 5% level. Second, he Lilliefors es for normaliy show ha he okyo and Jakara socks are acceped for normaliy a he 5% level, bu he SP500 socks, Korean socks, and Shanghai socks are no. Nex, Barle's es shows ha homogeneiy of variances is acceped for he okyo socks, bu no for he 4 oher sock exchanges. hird, he Jarque-Bera es es rejecs he normaliy hypohesis for he 5 sock exchanges a he 5% level. he okyo socks can be acceped for normaliy a 7.3% level. he Kruskal-Wallis es, which is a nonparameric es, is equivalen o ANOVA in erms of rank numbers. he resuls of he Kruskal-Wallis H saisic are lised in able 1. he resuls are very similar o he ANOVA resuls. he H saisics are lower han he criical values, and hus we canno rejec he null hypohesis ha he populaion medians of 12 monhly reurns are all equal for he 5 sock exchanges.

14 14 2. Chi-Square es for he Negaive Reurns: In his secion, we apply he chi-square es of goodness of fi for he frequency disribuion of negaive monhly reurns. o see if he negaive populaion monhly reurns are evenly disribued among he 12 monhs. he resuls of he chi-square ess are summarized in able 1 for he 5 sock exchanges. he chi-square es was carried ou as follows. For insance, for he SP 500 socks, for January, here were 11 imes when he January reurns were negaive over he 32 years. his is equivalen o 34.38%. For he monh of February, here were 15 imes when he monhly reurns were negaive (46.88%). For he monh of Sepember, here were 20 imes when he monhly reurns were negaive, and so on. he average frequency of negaive monhly reurns was Based on hese daa, we applied he chi-square es of goodness of fi for he observed frequencies of negaive reurns versus he expeced frequencies, 13.58%. he null hypohesis is ha he observed and expeced frequencies are equal. he calculaed chisquare value is and he criical chi-square value is 4.57 a he 5% level. In effec, he chi-square es canno rejec he null hypohesis ha he observed and expeced frequencies of monhly negaive reurns are equal for he 5 sock exchanges. 3. -es for he Monhly Reurns In able 1, he monhly mean reurns are calculaed for each monh. For he SP 500 socks, he highes monhly mean reurn is 2.14% in January, and i is higher han any oher monhly reurn. his resul is consisen wih he January effec. Bu, he quesion is wheher i is saisically significan. Since he ANOVA and Kruskal-Wallis ess were unable o rejec he null hypohesis ha he 12 monhly populaion mean reurns are equal, his ime we esed he null hypohesis ha he January populaion mean reurn or any oher monhly reurn is equal o he populaion mean of 12 monhly reurns: µ i = µ (4-2) where µ i = populaion mean reurn of monh i, and µ = populaion mean of monhly reurns. he resuls for he -es for he paired samples are summarized also in able 1. For he SP socks, he -value is significan for he posiive January reurn. Similarly, when he -es for he paired samples was applied o each monhly reurn, he negaive Sepember reurn was significanly differen from he mean of he 12 monhly reurns. In effec, he resuls suppor he posiive January effec and he negaive Sepember effec. For he Korean socks, he simple monhly reurn is he highes in January a 4.37%. However, he -saic is no significan. Bu, he -saisic is significan for he posiive November reurn (3.61%), and he negaive reurns in Augus (-2.33%) and Sepember (-2.01%). Bu when he 1998 daa (financial crisis) are excluded, he March reurn is he highes a 3.57% and significan. he negaive reurns are significan in Augus (-2%) and Sepember (-2.1%). hese resuls do no suppor he January effec in Korea, bu he posiive March effec, and he negaive Augus and Sepember effecs.

15 15 For he okyo socks, he highes reurn is 2.91% in March, and i is significanly differen from he mean of he 12 monhly reurns. he larges negaive reurn is -1.64% in Sepember, and i is significanly differen from he 12 monh average reurn. For he Jakara socks, he January reurn is he highes a 4.54 % for he overall period, , bu i is no significan a he 5% level. he nex highes reurn is 4.04% in December, and i is significan. he negaive reurn is he larges a -5.52% in Sepember, and i is significan. Excluding 1989 (high oulier) and 1998 daa (he afermah year of financial crisis), he May reurn is he highes a 4.83%, and i is significan. he nex highes reurn is in December a 4.51%, and i is significan. he negaive reurn is he highes in Sepember a -4.36%, and i is significan. he posiive December effec and he negaive Sepember effec are significan in boh sample periods. For he Shanghai socks, he May reurn is he highes a 13.83% for he enire sample period, , bu i is no significan. None of he posiive monhly reurns is significan. Bu here are 3 monhs of negaive reurns, namely July, Sepember, and December, and hey are all significan. Excluding 1992 and 1994 (exremely high ouliers), he June reurn is he highes a 8.29%, bu i is no significan a he 5 % level. here are 3 monhs of negaive reurns, namely, May (-0.51%), Sepember (-1.12%), and December (-4.63%), bu none of negaive reurns is significan. 4. Risk-Adjused Reurns hus far, we have examined simple average reurns wihou adjusing for risk. Now we examine he risk-adjused reurns. We have calculaed 5 measures of riskadjused reurns: Sharpe index = ( RP / σp ), ( RP / β P ), reynor index = ( RP β P RM ), Jensen's excess reurn = R-bRm, and Shin-bea index= R / β ) /( R ), and Shin-oal ( p p M index = ( R σ ) /( R / σ ) he resuls are presened in able 1 for he 5 sock p / M M M markes for he seleced sample periods excluding oulier years. On he excess reurn basis (R-bRm), he highes reurn is 0.975% in December for he SP 500 socks, 2.561% in March for Korea, 2.037% in March in okyo, 3.879% in December for Jakara, and 5.013% in April for Shanghai. On he Shin bea index basis (bea-risk adjused index relaive o he marke porfolio), he highes index is in March for he SP500, in March for Korea in April for okyo, in January for Jakara, and in April for Shanghai. On he Shin oal index basis (oal risk-adjused index relaive o he marke porfolio), he highes index is in December for he SP500, in March for Korea, in March for okyo, in December for Jakara, and in February for Shanghai.

16 16 Which monh has he highes risk? he resuls are also mixed. he larges bea is 2.18 in January for he SP500, in November for Korea, in March for okyo, in Augus for Jakara, and in January for Shanghai. he larges oal risk is 5.64 in Augus for he SP500, in Ocober for Korea, in March for okyo, in Augus for Jakara, and in January for Shanghai. he bes and wors monhs for he posiive and negaive reurns on he simple reurn and risk-adjused bases are summarized in able Regression Analysis wih Dummy Variables A regression mehod of esing he January effec is o use dummy variables as used by Keim (1983), and ohers (Kao and Schallheim,1985). I akes he following form: 12 R = a + = b D + e 2 (4-3) where D = monhly dummy variables; D2 = 1 for February and 0 for oher monhs, D 3 = dummy variable 1 for March and 0 for oher monhs, ec., and e = he error erm. he inercep consan a is expeced o represen he average January reurn since January is represened by he siuaion when each of he 11 dummy variables is equal o 0. he expeced reurn for February is equal o a + bd 2. hus, if he coefficiens of he dummy variables are all negaive, i indicaes ha he January reurn is he larges, and i is consisen wih he January effec. If he coefficien of a dummy variable is posiive, i indicaes ha he given monh's reurn is greaer han he January reurn. he regression resuls wih he dummy independen variables are summarized in able 2. For he SP500 socks, he dummy variables have negaive coefficiens, and he resuls are consisen wih he January effec. he inercep is and i is highly significan. he Sepember dummy variable has he larges negaive coefficien , so he Sepember expeced reurn is ( ). However, he adjused R 2 = is no significan. For he Korean socks, he coefficiens of he dummy variables are all negaive, and he inercep consan is highly significan. he resuls, herefore, are consisen wih he January effec. However, when he 1998 daa are excluded, he dummy variables for March and November have posiive signs, indicaing he March and November expeced reurns are higher han he January reurn. Bu none of he coefficiens is significan. In effec, he January effec is no suppored for Korean socks. For he okyo socks, he March dummy variable has a posiive sign. Bu he coefficiens are no significan. For he Jakara socks, all he dummy have negaive variables, bu he coefficiens are no significan excep for he negaive signs for augus and Sepember. For he Shanghai socks, he dummy variables for April, May, June, Augus, and November have posiive signs, bu none of he coefficiens is significan a he 5 % level. In effec, he regression resuls wih dummy variables are consisen wih

17 17 he January effec only for he SP 500 socks, bu he regression model is no significan in erms of he F-value. 6. elaion Analysis hus far we have examined wheher here are significan differences in he monhly reurns or periodic paerns in he monhly reurns. According o he random walk hypohesis, all monhly reurns should be randomly disribued and he expeced values of he monhly reurns should be equal. he convenional saisical mehods, such as ANOVA and Kruskal-Wallis ess canno rejec he null hypohesis ha all monhly reurns are equal. However, he -ess of paired samples indicae ha some monhly reurns are significanly higher or lower han he mean of he 12 monhly reurns. Bu he resuls end o be inconclusive because he saisical significance is sensiive o he sample. Exclusion of cerain observaions can significanly aler ha mean reurn and saisical significance. Anoher proposiion of he random walk hypohesis is ha he monhly reurns should be independen of oher monhly reurns. o es his hypohesis, correlaion coefficiens are calculaed beween monhly reurns. he resuls are presened in able 3. Firs, for he SP 500 socks, 9 correlaion coefficiens are significan a he 1% or 5% level. For insance, he January reurn is significanly correlaed o he June reurn, which is in urn correlaed o he Sepember reurn. he Sepember reurn is significanly correlaed o he April, June, and July reurns. he July reurn is highly correlaed o he Ocober reurn, ec. As for he Korean socks, here are 8 significan correlaions for he period Excluding 1998, he afermah year of he 1997 financial crisis, 5 monhly reurns are significan. February and Ocober reurns are significan for boh sample periods. For he okyo socks, here are 8 significan correlaions for he period For China, here are 7 significan correlaions for he period , and 13 significan correlaions, if 1992 and 1994 are excluded. he January reurn is correlaed o March, April, May, and November. For he Jakara socks, here are only 2 significan correlaions for he period , and 3 significan correlaions, if 1998 daa is excluded. he above correlaion resuls do no suppor he random walk hypohesis, sricly speaking. However, he conclusion is enaive for wo reasons: Firs, he correlaion coefficiens are highly unsable, paricularly in he Asian sock markes. Second, he correlaion can be spurious. Fama and Blume (1966) seleced he Dow-Jones 30 Indusrial socks, and hey regressed oday's reurn on each of he 5 lagged reurn variables and found significan correlaion coefficiens for he 30 socks, bu he coefficiens of deerminaion were very low, less han here are many correlaion sudies on he oher sock markes, such

18 18 as Norway, Sweden, Ausralia, UK, and Greece. he larges correlaion coefficien was for hese counries (Granger, 1968; Elon e al., 2003). We will also es regression analysis and ARIMA models using he lagged variables in he nex secions. 7. Regression Analysis wih he Monhly Reurns o examine if he monhly reurns are correlaed o he pas 12 monhly reurns, we es he following regression model: R a0 a R a R a R... a R + u (4-4) = where R 1,..., R 12 = he monhly reurns for he preceding 12 monhs. In he above funcion (4-3), he January monhly reurn, for insance, is a funcion of he preceding 12 monhly reurns. he regression resuls are summarized in able 4 for he SP500 socks, he Korean socks, and he okyo socks. Since he sample period was oo shor, he regression model was no esed for he Shanghai and Jakara socks. Firs, for he US socks, he following monhly reurns have a leas one significan variable (-value a he 5% level): January, March, April, and Augus. For example, his year's January reurn is significanly correlaed o las year's April reurn. he March reurn is significanly correlaed o las year's March reurn, and las year's July and Augus reurns. he Augus reurn is significanly correlaed o las year's Ocober reurn. Nex, for he Korean socks, he April reurn is significanly correlaed o las year's reurns of January, February, March, April, May, June, July, and Sepember. he adjused R 2 is he July reurn is significanly correlaed o las year's February reurn. he Augus reurn is significanly correlaed o las year's July and Augus reurns. For he okyo socks, he February reurn is significanly correlaed o las year's February reurn. he May reurn is significanly correlaed o las year's July reurn. 8. ARIMA, ARCH, ARCH-M, and GARCH Models A ime series model wih a single dependen variable can be expressed by he following ARIMA (auoregressive inegraed moving average) model: y = α 0 + α1 y + α 2 y +.. α y + e0 β1e β 2e 2... β e (4-5) 1 2 p p 1 q q y i where are he auoregressive erms, and are he whie noise error series. I saes y ha dependen variable is a funcion of lagged dependen variables and error series. A random walk series can be expressed by an ARIMA model, ARIMA (1,0,0): e i y y + e = 1 (4-6)

19 19 or, y δ y + e (4-7) = + 1 where δ = a consan or drif erm. Equaions (4-6) and (4-7) are esimaed in arihmeic values and naural logarihms. he ARIMA models were esed for he 5 sock exchanges. he resuls are summarized in able 5. For he SP 500 socks, he adjused R 2 values are high and he coefficiens of he MA erm y 1 are close o 1.0 for all equaions, wih and wihou he 2 drif erm, in logarihms and arihmeic values. Bu he highes adjused R values are obained for he log models: for he log models wih and wihou he drif erm. he Q saisics indicae ha residual series are whie noise for all models. I implies ha he ARIMA models are appropriae and he residual series have no significan periodic paerns. For he Korean socks, he highes adjused R 2 (0.9881) is obained for he log model wih a drif erm. he Q saisics indicae ha he residual series are whie noise for he wo log models, bu no for he wo non-log models. Similarly, he log model wih a drif erm is he bes for he okyo socks (0.9603) and he Shanghai socks (0.9420). For he Shanghai socks, he Q saisics indicae ha he residual series for he non-log models are whie noise, bu he residual series are no whie noise for he log models. For he Jakara socks, he adjused R 2 is he highes a for he model in arihmeic values wih a drif erm. he Q saisics indicae ha he residual series are whie noise for all 4 models. hese resuls srongly suppor he random walk hypohesis for all 5 sock exchanges. For he monhly reurn series, various ARIMA models were esed, such as ARIMA(12, 0, 0 ), ARIMA (12,0,12), and ARIMA (12, 1, 12). he resuls for ARIMA (12, 0, 0) are presened in able 4. he adjused R 2 values are negaive for he SP500, Korea, okyo, and Jakara socks, excep for he Shanghai socks. For he SP500, Korea, and okyo socks, none of lagged variables is significan. Bu for he Jakara and Shanghai socks, here are one and wo significan variables respecively. he Q saisics indicae ha he residuals are no whie noise for he SP500, Korea, Jakara, and Shanghai socks. Bu he residuals are whie noise for he okyo socks. In effec, he ARIMA models end o suppor he random walk hypohesis for he 5 sock exchanges (see 10. auocorrelaion analysis and appendix noe). In able 6, heeroscedasiciy is esed in AR(1) wih ARCH, ARCH-M and GARCH models. he ARCH model can saed as r β r + u (4-8) = 0 + β h σ = α + α u (4-9) = 0 1 1