Jurnal Jambi Wahyono

8/11/2019 Jurnal Jambi Wahyono

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The Efficiency and Characteristics of the Asianand US Stock Markets

--- Seoul, Tokyo, Jakarta, Shanghai, and New York ---

Kilman Shin*

In 1968, " the prevailing view among academic economists, even at the University ofChicago, was that the stock market was not a proper subject of serious study." Ray Ball,

"The Theory of Stock Market Efficiency: Accomplishments and Limitations", in The Revolution in Corporate Finance , 4th ed., 2003, p.12

Abstract

The January effect refers to the theory that the monthly average stock return is the highestin January than in any other month. Some argue that the January effect holds true only forsmall-firm stocks and it takes place only over the first week of a new year. Others arguethat the January returns are higher because the risk is higher in January. The Januaryeffect has received much attention since it directly contradicts the random walk theory,which argues that future stock prices are unpredictable using the present and past priceinformation. Defendants of the random walk theory argue that the January effect can lastonly in the short run and it cannot persist and will disappear in the long run. In this study,the following stock markets are examined: Korea, Tokyo, Jakarta, and Shanghai, and USstock markets (SP500, Dow-Jones, NASDAQ, and SP500 Total return index). To find ifthe January effect or any other periodic patterns exist in these markets, monthly stockreturns are compared with and without risk-adjustments. Also, various statistical methods,such as correlation, regression, autocorrelation, runs test, variance ratio test, unit root test,Johansen cointegration test, ARIMA, VAR, ARCH, ARCH-M, GARCH, spectralanalysis, and factor analysis are applied to the monthly stock prices and returns. For risk-adjustment, the Shin index is proposed with regard to the Sharpe index, Treynor index,Jensen index, and the Modigliani index.

I. Introduction

A large number of empirical studies have been published on the January effectwhich is a theory that monthly stock returns tend to be higher in January than in any other

month. The so-called January effect has received much attention since it contradicts therandom walk hypothesis which argues that stock returns should be independent _______________________________________________________________________* Ferris State University, Big Rapids, Michigan, 49307 USA: [email protected] paper was presented at the joint conference of the Korean Financial ManagementAssociation, Korean Securities Association, and Korea/America Finance Association,May 30, 2003, Chonan, Korea


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of the past returns. The random walk hypothesis implies the following propositions whenapplied to monthly returns: First, a given month's stock returns should have no significantcorrelations with other months' stock returns so that one month's stock return is useless in

predicting the stock returns of other future months. Second, monthly stock returns should

have no seasonality, periodic or cyclical patterns so that future stock returns cannot be predicted based on periodical patterns. Third, if international stock markets are globallyefficient, their stock returns of the same month may be correlated if they have closeeconomic relationships. But a country's stock returns of a given month should be uselessto predict stock returns of future months of other countries (see appendix notes ).

To support or refute the random walk hypothesis, there are much on-goingresearch in the periodical patterns in the stock returns in the following areas: (1) theJanuary effect monthly or daily stock returns are higher in January than in other months,(2) Early month effect stock prices rise during the first 2 weeks of each month, (3)Week-end effect stock prices fall on Monday relative to Friday (pure week-end effect,Friday close to Monday open), (4) Day-end effect stock prices rise near the closing time,

(5) Holiday effect stock prices rise on the day before the national holiday weekends,and (6) Daylight savings time effect stock prices fall after the change in the daylightsavings time (Kamstra, Kramer, and Levi, 2000, 2002; Pinegar, 2002; for a review, seeKhaksari and Bubnys, 1992; Malkiel, 2003).

The efficient market hypothesis is based on two assumptions: (1) all relevantinformation is free and available to all investors simultaneously, and (2) there are manycompetitive investors (Fama, 1965, 1970). Since information may not be freely availableand there may be less competitive investors in the emerging stock markets, it is oftenargued that stock markets in emerging countries may not be efficient. The majorobjective of this paper is to examine some selected Asian stock markets to find if thereare any monthly or seasonal patterns, such as the January effect, and if the stock pricesfollow the random walk. The following Asian stock markets are selected for our study:the Korea (Seoul) Stock Exchange, the Tokyo Stock Exchange, the Jakarta StockExchange, and the Shanghai Stock Exchange. The US stock market (SP 500 stocks, Dow-Jones 30 industrial stocks, NASDAQ stocks, and SP500 total return index) is alsoexamined in this study for the purpose of comparison (see appendix notes ). In section II,some of the previous empirical studies are reviewed. In section III, the random walktheory and the methods of measuring risk-adjusted returns (CAPM) are reviewed. Insection IV, empirical results are presented for the Asian and US stock markets. Asummary and conclusions are provided in section V.

II. Review of Previous Studies There are many studies on the seasonality and cyclical patterns in the monthly,

weekly, and daily stock returns. Some early studies are reviewed in Wachtel (1942),Granger and Morgenstern (1970). Since Wachtel (1942) is widely quoted as an early

proponent of tax-selling hypothesis, we will briefly review his study. His study is basedon the following assumptions: (1) The high-yielding stocks are usually the stocks whose

prices have decreased, and they are the best stocks to sell in December to obtain the


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largest realizable capital losses for tax saving, (2) individuals and corporations sell stocksfor tax-saving toward the middle of December to establish tax losses, and such pressuresdrives security prices below what they should be in the light of potential earnings, (3) therise at the year's end is nothing more than a normal reaction from depressed levels.

To prove the above theory, he selects 20 highest-yielding industrial stocks listedon the NYSE each year for the period 1927-42. Then he adds the values of the 20 stocksat every 2 weeks from the bases in December, and divides by 13 years (1927-42) toobtain the annual mean value. This procedure was followed to obtain the mean values forthe 30 Dow-Jones Industrial stocks. He then plots the series of the two mean values at 2-week time interval. He finds that the mean value of the high-yielding stocks rise morethan the low-yielding Dow-Jones stocks in the late December to the third Saturday inJanuary. Similar results were obtained for the median values. However, the followingcriticism may be made. First, there is no reason why the tax selling pressure should end atthe middle of December. In theory, the tax-selling pressure should continue until the endof December. As another possible reason, Wachtel mentions unusual demand for cash,

beginning a week or two before Christmas, causes many stock sales. But his data showthat stock prices rise 2 weeks before the year end. That is, unusual demand for cashshould not stop until the holiday season is over. Second, there is no statistical significancetest. So we can not tell whether thee difference is statistically significant.

Granger and Morgenstern (1963,1970) reviewed some early studies on the periodical patterns in the stock market. To examine the validity of such studies, theyapplied spectral analysis to various data, such as the Standard and Poor's Stock Index(Monthly, 1871-1956, 1918-64), SEC Stock Price Index (weekly, 1939-64), Dow-JonesIndustrial Average (1915-1961), and individual company stocks (daily, weekly, andmonthly). They plotted and examined several spectral diagrams, and concluded that thespectra of log price differences are flat for all series considered over a range of 0.5 cycles

per year up to 0.5 cycles per day, strongly supporting the random walk hypothesis. Theresults did not show a 12 month peak, though it showed some small peaks correspondingto a three month cycle. Weekly price series indicated the presence of a small monthlycycle. But none of the cycles was significant in any spectral diagram (pp. 130-131).

Bonin and Moses (1974) used the analysis of variance for the monthly data ofthe 30 DowJones industrial stocks for the period 1962-71, and found that 7 of the stocksdisplayed significant seasonal patterns. Officer (1975) used the Box-Jenkins time seriesanalysis for the Australian stock returns for the period 1958-70, and found 6-month, 9-month, and lesser 12-month seasonality in the autocorrelation function.

Rozeff and Kinney (1976) used the NYSE data for the period 1904-74. Theydivided the sample into 4 periods: 1904-28, 1929-40, 1941-74, and 1904-28 plus 1941-74.When they computed the autocorrelation functions, the results did not reveal seasonality.However, when average monthly returns were tested, except for the period 1929-40, theyfound statistically significant differences in the monthly returns due to the large Januaryreturns. They used the Kruskal-Wallis test, the Siegel-Tukey test, Bartletts test forhomogeneity of variances, and the analysis of variance. They found that the January


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return is significantly higher than other month's returns. They also found relatively higherreturns in July, November, and December, and low returns in February and June. Also,January had a relatively higher risk premium than other months. They also tested theCAPM adjusted returns, and found significant monthly differences.

Dyl (1977) selected 100 stocks for the period 1959-70 and divided into 3 portfolio groups based on the percentage change in stock prices: portfolio 1, priceincreased more than 20%; portfolio 2, price changed between 20% and -20%, and

portfolio 3, price decreased more than 20%. He found that the stocks whose pricesdecreased more than 20% during the year had abnormally higher trading volumes inDecember. He argued that it was evidence that investors sell to realize the capital lossesfor the purpose of tax deduction. He measured abnormal volume as the actual volume asa percentage of average monthly volume. Branch (1977) examined year-end lows of

NYSE stocks and found the average excess returns of 3.5% to 6.2% for the periods of oneto four weeks following the last Friday of the year over the period 1965-75. Branch andRyan (1980) examined tax-loss selling candidates of NYSE and AMEX stocks for the

period 1965-78. They found that such stock prices rose on the first 4 weeks of the year.The selected NYSE stocks increased from 3.4% to 6.7%, and the selected AMEX stocksrose from 5.2% to 14.4%.

Keim (1983) used the NYSE and AMEX data for the period 1963-79. He dividedthe stocks (1,500 to 2,400 in total) into 10 portfolio groups. He regressed the daily excessreturns on the 11 dummy variables, where each dummy variable represents each monthfrom February to December. The excess return for January is measured by the interceptconstant. He found that the January effect is significant for small-firm portfolios (1 to 4deciles) and the excess returns are negatively related to larger firms (5 to 10 deciles). Healso found that the January effect occurred during the first 5 trading days of the year. Heused 3 types of beta, namely, the OLS estimated beta, Scholes-Williams beta, andDimson beta to calculate the risk adjusted excess returns for the portfolios of small firms(see appendix note).

Roll (1981) argues that the stocks of small-size firms are infrequently traded, andas a result the systematic risk is underestimated. As a result, the beta-risk adjusted returnsare overestimated. Using the SP500 data for the period 1963-77, he shows that theDimson beta is higher than the ordinary beta about 1.25 to 2.37 times. Roll (1983)compares the daily stock returns for the last trading day of December and the first 4trading days of January (turn-of- the year). He found that the very first day of Januaryshowed the largest mean return differences. He found that the January effect is significantfor both small and large firms. The mean and the frequency of positive returns on the 5trading days were larger on the AMEX stocks. Roll infers that the January effect may

persist because the relative trading cost is larger for the smaller firms than for the largerfirms.

In Australia, all tax-paying financial institutions pay normal taxes on capital gains,and capital losses are deductible without limit from ordinary income. Individual investorsdo not pay taxes on capital gains. Also, the Australian tax year is July 1 to June 30. Thus,


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to support the tax-selling hypothesis, there should be a June-July effect. Brown, Keim,Kleidon, and Marsh (1983) investigated the Australian stocks for the period 1958-81. Toallow for the size effect, the stocks were divided into 10 groups of portfolios. They foundthat the smallest decile of firms had average returns of 6.754%, while the largest decile offirms had 1.028 %. Also, they found higher returns over December-January and July-

August. Thus, they concluded that the January effect is not due to tax-selling activities.

Gultekin and Gultekin (1983) examined monthly stock returns for 17 countries:Australia, Austria, Belgium, Canada, Denmark, France, Germany, Italy, Japan,

Netherlands, Norway, Singapore, Spain, Sweden, Switzerland, UK, and the US. Theyused the Capital International Perspective data, published by Capital International, S.A.,located in Geneva, for the period 1959-79. The return data are based on the value-weighted indexes of month-end closing prices without dividend yields. They computedfirst 12 monthly autocorrelations, and found that they were mostly not significant exceptfor Australia, Denmark, and Norway. They used the Kruskal-Wallis test for the 17countries, and found that the monthly returns are not equal for 12 countries from a total

of 17 only at the 10% level. The monthly returns were equal for Australia, France, Italy,Singapore, and the US. Except for Australia, they the monthly returns were higher at the beginning of the tax year. In Australia, the tax year starts in July, and in the UK, it startsin April.

Berges, McConnell, and Schlarbaum (1984) used Canadian stocks for the period1951-80. In Canada, the capital gains tax was installed in January 1973. They divided391 stocks into 5 portfolio groups, and compared the January monthly returns with meansof February-December returns for the period 1951-72 and for the period 1973-80. Theyfound that the January returns are higher for each portfolio group than for the February-December returns. Also the January returns were higher for the period 1973-80 than forthe period 1951-72. The capital losses in excess of capital gains may be used to offsetordinary income up to a maximum of $2,000 in one tax year. Thus, there was noincentive for Canadian investors to sell stocks at the end of the tax year prior to 1973. Butthey found the January effect which was more pronounced for small-size firms. Thus,they conclude that tax-selling hypothesis is not a complete explanation for the Januaryeffect.

Tinic, Barone-Adesi, and West (1987) also used Canadian stocks for the period1950-81. They divided 317 stocks into 5 size-portfolios. They used regression analysiswith 5 dummy variables: 3 dummy variables representing for January, December, andthe period 1973-80 with capital gains tax respectively. Two other dummy variables arethe product of January dummy and the capital gains tax period dummy variable, and the

product of the December dummy and the capital gains tax period dummy variable. Theresults showed that stock returns are higher in January and December and the smallerfirms have higher returns than the large firms. The dummy variable representing thecapital-gains tax period had positive signs, but it was not statistically significant exceptfor one portfolio. They conclude that the results do not support tax-loss selling as the solefactor of seasonality, but they provide limited support for tax loss-selling hypothesis.


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Kato and Shallheim (1985) examined data (about 529 to 844 stocks) for the period 1964-81. They divided the stocks into 10 portfolios based on market capitalization.They calculated regression equations with monthly dummy variables. They foundJanuary and June returns are significantly higher than other monthly returns. In Japan,there is no capital gains tax for individual investors, but corporations are taxed on capital

gains, and each firm can choose its tax year arbitrarily. About 50% of Japanese firmschoose tax years ending Mach 31. Thus, the Japanese results do not necessarily supportthe tax-selling hypothesis. They present two possible reasons for the January and Juneeffects. First, most Japanese firms pay so-called bonuses equivalent to about two monthlysalaries to employees generally in June and December. Second, corporate earningsforecasts are made by financial analysts in March, June, September, and December. Theystate that these factors may partly explain the January and June effects.

Jaffe and Westerfield (1985) calculated daily returns for Tokyo stocks for the period 1970-83. They found that the January mean daily return 0.0013 was significantlyhigher than the overall daily average return 0.00035. However, there was no significant

difference between the average returns over the last 5 days of December and the first 5days of January. They also calculated the correlations coefficients between the Tokyostock daily returns and the SP500 daily stock returns. The correlation coefficient was thehighest for the contemporaneous calendar time at 0.154, with was highly significant(t=8.76). As for the day of the week effect, the lowest daily mean return occurred onTuesday in Tokyo, and the lowest mean return occurred on Monday in New York,

Keim (1985) used the NYSE stocks for the period 1931-78. He regressed theJanuary stock returns on the systematic risk beta, dividend yield, dummy variable that isequal to 1 if the firm pays zero dividend and is equal to zero otherwise, and the naturallog of the market value of the security. He found that the intercept, dividend yield, and

presence of dividend payment were positively correlated, but the firm size was negativelycorrelated. The systematic risk was not significant. When the Feb.Dec. returns wereregressed on the same independent variables, the firm size was significant and negativelycorrelated. Dividend variables and the systematic risk were not significant.

Arbel (1985) collected 1,000 companies: SP500 stocks and non-SP 500companies for the period 1971-80. The SP 500 companies are divided into highlyresearched, moderately researched, and research-neglected companies. The non-SP 500companies are all research-neglected companies. He found that the January returns werehigher for neglected companies. For the SP 500 stocks, the January returns were 2.48%for the highly researched companies, 4.95% for the moderately researched companies,and 7.62% for the neglected. The January returns were 11.32% for the non-SP 500neglected companies. Branch and Chang (1985) found that stocks whose prices werefalling throughout the year tended to rise in price in the first 4 weeks of the followingyear. The January effect was found in many other studies.

Lakonishok and Smidt (1986) used the daily stock data of the Chicago tape for the period 1970-81. They divided the stocks into 10 deciles and calculated daily returns overthe last 5 days and the first 4 days around the turn of the year using three methods of


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calculating the daily return: CRSP return, close-to-close, and open-to-open. They foundthat the returns of small companies are high around the turn of the year and are higherthan the returns of large firms, no matter how returns are measured.

Chang and Pinegar (1986) examined the holding period returns of the bonds

traded on the NYSE for the period 1963-82. They stratified the bonds into 6 groupsaccording to Moody's bond rating system: Aaa, Aa, A, Baa, Ba, and B. They found thatthe January returns are pronounced for the Baa and B-rated bonds. They also examinedstock returns of the firms whose bond returns were evaluated. The differences in thestock returns were not significant when the analysis of variance was applied. But whenthey compared the January returns with the average of the previous 11 monthly returns,the t-values were significant for 3 of the 6 stock portfolios.

Lo and MacKinlay (1988, 1989) applied the variance ratio test to weekly data forthe period Sept. 2, 1962 to Dec. 26, 1985 and 2 subperiods. For the equal-weighted indexfor the NYSE and AMEX stocks, the variance ratio test did reject the null hypothesis of

the random walk. But, the results were mixed for the value-weighted indexes. They alsoexamined 625 stocks and 3 size-sorted portfolios, each of which contained 100 stocks:small stocks, medium stocks, and large stocks. The results showed that the returns ofindividual returns and the 3 portfolio returns were not statistically significant, meaningthat they follow the random walk. However, for the equal-weighted portfolios of 625stocks, the random walk hypothesis was rejected, and the value-weighted portfolios weresupported for the random walk. However, Lo and Mackinlay (1999, p. 16) state that " themost current data (1986-1996) conform more closely to the random walk than ouroriginal 1962-1985 sample period."

Branch and Chang (1990) used the Compustat data for the period 1971-83. Usingregression analysis, they found that low-price stocks that exhibited poor December

performance are likely to rebound in January. They argue that an efficient market willnot necessarily eliminate such predictable price patterns due to the following factors:transaction costs (commission and bid-ask spreads), search costs (costs of identifyingsuch stocks), and differential capital gains tax rates (high marginal tax rates).

Khaksari and Bubnys (1992) use daily data for the SP500, NYSE stock indexes,and stock index futures for the period 1982-1988 to test the day-of-the-week, day-of-the-month, and month-of-the-year effects on stock indexes and stock index futures. They usethe Sharpe index to obtain risk adjusted returns. They find that the day-of-the-week andthe day-of-the-month effects are more pronounced in the futures indexes than in the spotindexes. However, the January effect was more evident in the spot indexes than in thefutures indexes. They conclude that the use of the Sharpe ratio sharply reduces the day-of-the-week effect in spot and futures index returns, but it does not reduce the month-of-the-year effect. They state that these results tend to disagree with efficient market

proponents.

Ojah and Karemera (1999) apply the variance ratio test of Lo and MacKinlay(1988), multiple variance ratio test of Show and Denning (1993), and auto-regressive


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fractionally integrated moving average test of Geweke and Porter-Hudak (1983) to themonthly data of Latin American countries for the period 1987-1997. The resultssupported the random walk hypothesis for Argentina, Brazil, and Mexico, but not forChile. Yilmaz (2001) use weekly data for the period 1988-2000 and applied the varianceratio tests to 14 emerging stock markets. The random walk hypothesis was accepted for

Indonesia, Korea, Malaysia, Taiwan, Argentina, Brazil, Mexico, Japan, and USA, but itwas rejected for the Philippines, Thailand, Chile, Greece, and Turkey at the 5 % level.Hall and Urga (2002) test the Russian stock market with monthly data for the period1995-2000. They used a time varying parameter model with changing intercept and slopecoefficients (AR(1) with generalized autoregressive conditional heteroscedasticity-in-mean-GARCH-M). They find that the stock market indexes are initially inefficient and

predictable, but two and a half years later it becomes efficient (see appendix note).Mookerjee and Yu (1999) test the Shanghai and Shenzhen stock exchanges with dailydata ( Dec. 19, 1990-May 20, 1992 for the Shanghai stocks, and April 3, 1991 - Dec. 17,1993 for the Shenzhen stocks). They applied the ARIMA models with dummy variablesfor Monday, Holiday, and January (for the first 5 days). The results showed that the

week-end and holiday effects are significant, but the January effect is not significant.Interpretation or Rationale for the January Effect

There are 2 major questions on the January effect. The first question is the reasonsfor the January effect. The second question is the persistence of the January effect.

As for the rationale for the January effect, there are several explanations. Themost popular hypothesis is the tax-selling hypothesis, which argues that investors sellstocks whose prices have been falling during the year, and the capital loss can bededucted from capital gains tax, and then in the following year, the investors can buy

back the identical or similar stocks or other entirely new stocks. However, there aresome objections to this explanation. (1) Such investment strategy is subject to the taxlaws against wash sales (see appendix note). (2) If the tax-selling hypothesis should holdtrue, the January effect should be larger after World War II, when income tax rates arehigher. However, Keim (1983) found that the January effect was larger during the pre-war period. (3) The January effect should not exist in countries where there is no capitalgains tax, or the tax year does not start in January. But, Brown, Keim, Kleidon, andMarsh (1983) found higher returns over December January and July August inAustralia where the tax year is July 1 June 30. Also, as reviewed before, Berges,McConnell, and Schlarbaum (1983) found the January effect in Canada for the period1951-80, where the capital gains tax was absent until1973.

A second alternative hypothesis for the January effect is the portfolio rebalancingor window dressing hypothesis, which states that around the year-end institutionalinvestors, rather than individual investors, sell losing stocks and buy winning stocks torepresent respectable portfolio holdings. However, Griffiths and White (1993) and Siasand Starks (1997) found little support for the institutional portfolio rebalancinghypothesis.


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A third hypothesis for the January effect is the new-year resolution hypothesis,which states that people make new resolutions in December or January about on habits,future plans, consumption, savings, and investments, and the plan or decision isimplemented in January, the beginning of a new year. So, people start investing in

bonds and stocks in January, and the January prices go up. If this hypothesis is true, the

January effect should be found in other countries, too, even if there are no capital gainstaxes and the tax year does not start in January.

A fourth hypothesis is, as stated in Wachtel (1942, p.186), that the unusualdemand for cash for the holiday season (Santa Claus effect) affects investors to sell thestocks in December. To purchase gifts and to finance travel, investors may sell somestocks and bonds. This hypothesis is consistent with the increasing sales duringDecember. The cash balances are supposed to be reinvested in the stock market after theholiday season is over, and it causes the stock prices to rise.

The second question on the January effect is the persistence of the January effect.

Why do the January effect and the firm-size effect persist to exist? If market is efficient,arbitrage activities will remove the return differentials. There are two theories to explainthe persistence of both the January effect and the firm-size effect. One is the transactioncost theory and the other is the risk premium theory. First, Roll (1983), Stoll andWhaley (1983) argue that the January effect for smaller firms may persist to exist becausethe transaction cost is high for the small firms relative to their prices so that arbitragecannot remove the return differential. However, this theory would not apply to theJanuary effect for larger firms.

An alternative explanation is the risk premium theory. Rogalski and Tinic (1986)estimated variance, beta, and Dimson (1979) beta for small firms whose shares are tradedinfrequently for the period 1963-82 for 20 firm-sized portfolios using the market model.They regressed the daily returns of each portfolio on the daily returns of equally weightedmarket portfolio returns. They found that variance and beta are much larger in Januarythan in any other month, and variance and beta are much larger for the smaller firms thanfor the larger firms. But why should the risk levels be higher in January than in any othermonth? Why should January have higher risk? They argue that January is the beginningof a new uncertain year, so the risk should be higher

In effect, the findings of the previous empirical studies for the January effect may be summarized as follows:

(1) The January abnormal average return is higher than that for any other month.(2) The January abnormal average return is larger for small firm stocks or low price

stocks than for large firms or high-price stocks.(3) The January effect takes place over the first week of the trading days of a new year,

particularly on the first trading day.(4) There are several hypotheses to explain the January effect, such as tax-selling,

portfolio rebalancing, new year resolution, unusual demand for cash, year-end bonuses, investment decision making, etc.


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(5) The January effect will not necessarily disappear even if the market may be efficientdue to trading costs, information costs, uncertainty, and differential marginal taxrates on capital gains.

In this study, our objective is to examine the monthly patterns of the stock returns,

such as the January effect, for some Asian stock markets, such as China, Indonesia,Korea, and Japan in comparison with the US stock market Except for Japan and the US,the selected countries have neither the capital gains taxes nor large institutionalinvestment companies. So, neither the tax-selling hypothesis nor the institutional

portfolio rebalancing hypothesis will matter. However, the new-year resolutionhypothesis is not necessarily applicable since January in the contemporary Gregoriancalendar is not the same as January in the Chinese lunar calendar, and thus the new yearresolution can take place in February. That is, the new year's day in the Chinese lunarcalendar is widely celebrated in Indonesia and Korea as well as China. January in theChinese lunar calendar generally falls in February in the Gregorian calendar. Also, inAsia the holiday season usually begins with the new year's day and lasts for a couple of

days.

III. Risk-Adjusted Return Measures

Before we discuss our empirical results, it may be useful to briefly review the randomwalk theory and the methods of measuring risk-adjusted returns in the framework of capital asset

pricing model (CAPM). The efficient market theory can be explained using the following twoequations:

0)()|()( ,1,, == t it t it i E R E R E (3-1)

)|,.......,(),.......,( 1,,1,,1 = t t nt t nt R R f R R f (3-2)

Where = stock return at time t for stock i, (t i R , 11 /) + t t t t P D P P , and 1t = a set of information available at time t -1.

Equation (3-1) states that actual return on asset i is equal to its expected return predicted at time t -1 with the given set of information. This model is often called a fair-game model. Equation (3-2) states that the unconditional distribution of actual returns onall assets should be equal to the conditional distribution of expected returns for a givenset of information. Equation (3-2) is called the random walk model. The difference

between the fair game model and the random walk model is that the random walk modelrequires that the serial correlation between returns for any lag be zero, but the fair gamemodel does not require it (Fama, 1965, 1970; Copeland and Weston, 1992, pp. 346-350).

The risk-adjusted efficient market hypothesis (or the joint hypothesis of marketefficiency and the CAPM) is stated as follows:

t it t it i R E R ,,, )|( = (3-3)

])|([)|( ,,,,, t F t mt mt i F t ii R R E R R E += (3-4)


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0)( , =t i E (3-5)

where E )|( ,t ii R = the expected return on stock i for period t , given its systematic

risk, t i , , .0> )|( ,t mm R E = the expected return on market portfolio for period t ,

given its predicted systematic risk t i , and t m, are estimated systematic risk of stock i and the market portfolio respectively for time t, estimated at time t -1 based on the set ofinformation, 1t (Copeland and Weston, 1992, pp. 350-352).

The CAPM models are often used to measure the performance of individual portfolio returns on the risk-adjusted basis. There are 3 popular measures of risk adjustedreturns: Treynor (1965), Sharpe (1966), and Jensen (1968):

Treynor beta index = p F p R R /)( (3-6)

Sharpe total index = p F p R R /)( (3-7)

Jensen excess return: = )( F M P F P R R R R (3-8)

It should be noted that the ratio p F p R R /)( is the realized risk premium per unit of

systematic risk beta using the security market line theory, and the ratio p F p R R /)( isthe realized risk premium per unit of total risk using the capital market line theory. Thus,

by adding the risk free rate to the risk premium, we obtain the risk-adjusted totalreturn: p F p F R R R R /)( +=

), if the Treynor index is used, and p R R = F p F R R /)( +

),

if the Sharpe index is used. Modigliani and Modigliani (1997) show the following risk-adjusted return: )](/) M p F R [( P F R R R +=

) for the Sharpe index (see appendix note).

The first two measures can be modified to measure the relative performance of agiven portfolio with respect to the market portfolio (Shin, 1996):

Shin beta index = M F M

P F P

R R R R

/)(/)(

(3-9)

Shin total index = M F M

P F P

R R R R

/)(/)(

(3-10)

where = return on portfolio i, P R P = total risk of the portfolio, = return on themarket portfolio,

M R

M = total risk of the market portfolio, R = return on the risk free portfolio,

F

M = 1, systematic risk of the market portfolio, = p systematic risk of the

portfolio: if P < 0, the absolute value should be used. Otherwise, a negative portfolioreturn with a negative beta would generate a positive performance index, which is clearlywrong.


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The two Shin indexes are essentially the same as the Sharpe index and theTreynor index respectively. Since the denominators M F M R R /)( and M F M R R /)(are constants, dividing the Sharpe and Treynor indexes by the constants will not changethe portfolio ranking by the Sharpe and Treynor indexes. But the advantage of the Shinindexes is that if the Shin index is greater than 1, it indicates that the given portfolio's

performance is better than the performance of the market portfolio over the sample period.That is, if the indexes are greater than 1, it implies that

( > )/ P F P R R M F M R R /)( (3-11)and ( > )/ P F P R R M F M R R /)( (3-12)

The common weakness of the beta based risk measures is that if the beta value isnot significant, unstable, extremely low, or high, the indexes can be unreliable, and the

portfolio performance can be greatly overestimated or underestimated. The systematicrisk can be unstable and unreliable, if the sample period is short or if the stock returns arevolatile independent of the market movement. Also, as stated before, if the beta value isnegative, the absolute value should be used for the above 3 beta risk-related measures:R/beta, R-bRm, and the Shin beta index. Otherwise, when the return is negative, anegative return divided by a negative beta value will give a positive value, and this willclearly distort the performance of the portfolio. An advantage of the beta-based measuresis that statistical significance of beta and alpha can be tested. Jobson and Korkie (1981)conclude that all the performance measures have shortcomings, but the Sharpe measureappears to have a relatively small number of theoretical objections, but has noaccompanying significance test.

If the risk free rate is omitted, the above 5 indexes (Equations 3-6 to 3-10) can bereduced to ,/ P P R P P R / , M P P R R , ),/()/( M p p R R and )//()/( M M P P R R respectively. The above indexes can be applied to individual securities as well as to

portfolios.

In effect, we are taking the January return, for instance, as the return ofa portfolio, called January portfolio, and taking the 12-month average returns as thereturns of the market portfolio. That is, we have 12 portfolios for each stock exchange,and we will evaluate the performance of the 12 portfolios for each stock exchange byapplying the above 5 measures of risk-adjusted returns.

IV. Empirical ResultsIf the efficient market hypothesis holds true, the risk-adjusted monthly returns

should be randomly distributed and they should not show any periodic patterns. To testthe hypothesis, we have selected monthly data for the following stock markets: theStandard and Poor's 500 Stocks (1971-2002), the Korea Stock Exchange (KOSPI, 1980-2002), the Tokyo Stock Exchange (Daiwa Index, 1984-2002), the Shanghai StockExchange (1991-2002), and the Jakarta Stock Exchange (1989-2002). The monthly stock


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prices, monthly return series, and the monthly returns by year are plotted in Figures 1 ~2 for the stocks of the 5 stock exchanges. There are some outliers in the monthly returns,

but we are unable to detect any clear monthly periodic patterns in the graphs.

The following analyses are applied to the monthly returns:

1. ANOVA and the Kruskal-Wallis test (Table 1)2. Chi-square Test for the negative returns (Table 1)3. t-Test for two means (Table 1)4. Risk-adjusted returns (Table 1)5. Regression analysis with dummy variables (Table 2)6. Correlation analysis (Table 3)7. Regression analysis with monthly returns (Table 4)8. ARIMA, ARCH, ARCH-M, and GARCH models (Tables 5, 6)9. Unit root, variance ratio, runs, and cointegration tests (Tables 7, 8, 9, 10)

10. VAR models (Table 11)11. Autocorrelation analysis (Figure 3)

12. Spectral analysis (Figure 4)13. International correlation and regression analyses (Tables 12 and 13)14. Characteristics of the Asian and US stock market returns (Tables 14, 15, 16)

- Descriptive statistics, Normality, Homogeneity, and Factor Analysis15. Evaluation of the Asian and US stock markets (Table 17)16. The best and worst months in the 5 stock exchanges (Table 18)17. January Barometer Effect (Table 19)

1. ANOVA and Kruskal-Wallis Test :

If stock returns are randomly distributed, the 12 monthly returns should also berandomly distributed, and thus monthly returns should not show any seasonal patterns.First, we use the ANOVA to test the following null hypothesis:

1221 ...... === (4-1)

where i = mean returns of month i. The results of ANOVA are presented in Table 1 forthe 5 stock exchanges. The F-values are extremely low, and the null hypothesis cannot

be rejected at the 5% level. The F-values are 1.27 for the SP500 stocks, 1.28 for theKorean stocks, 0.903 for the Tokyo stocks, 0.804 for the Shanghai stocks, and 1.20 forthe Jakarta stocks.

However, ANOVA is based on the following two assumptions: (1) the populationmonthly stock returns are normally distributed, and (2) the population variances ofmonthly returns are all equal. If these two assumptions are not valid, ANOVA results arenot valid, and nonparametric tests, such as the Kruskal-Wallis could be used. Three testsof normality and the Bartlett's test for homogeneity are used. The results are mixed assummarized in Table 14 (3) . First, the Jarque-Bera test rejects the normality hypothesisfor all 8 stock markets at the 5% level. The Tokyo stocks are accepted for normality at7.3% level (the 4 groups of US stocks are regarded as 4 stock markets). Second, the


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Lilliefors test for normality indicates that the Tokyo and Jakarta stocks are accepted fornormality at the 5% level, but the 4 groups of US stocks, Korean stocks, and Shanghaistocks are not accepted for normality at the 5 % level. Third, the chi-square test for thegoodness of fit accepts normality for SP500, Dow-Jones, and Jakarta stocks, and rejectsnormality for SP500 total return index, NASDAQ, Korea, Tokyo, and Shanghai.

The Kruskal-Wallis test, which is a nonparametric test, is equivalent to ANOVAin terms of rank numbers. The Kruskal-Wallis H statistics are listed in Table 1. Theresults are very similar to the ANOVA results. The computed H statistics are lower thanthe critical values, and thus we cannot reject the null hypothesis that the populationmedians of 12 monthly returns are all equal for the 8 stock exchanges.

2. Chi-Square Test for the Negative Returns:

In this section, we apply the chi-square test of goodness of fit for the frequencydistribution of negative monthly returns to see if the negative monthly returns are evenly

distributed among the 12 months. The results of the chi-square test are summarized inTable 1 for the 8 stock exchanges. The chi-square test is carried out as follows. For theSP 500 stocks for January, for instance, the January returns are negative 11 times over the

period of 32 years (34.38%). For the month of February, the monthly returns arenegative for 15 times (46.88%). For the month of September, the monthly returns arenegative for 20 times (62.5%), and so on. The average frequency of negative monthlyreturns was 13.58 (42.44%). Based on these data, we apply the chi-square test ofgoodness of fit for the observed frequencies of negative returns versus the expectedfrequencies, 13.58. The null hypothesis is that the observed and expected frequencies areequal. The calculated chi-square value is 13.31 and the critical chi-square value is 19.675at the 5% level for DF=11. In effect, the chi-square test cannot reject the null hypothesisthat the observed and expected frequencies of monthly negative returns are equal for the8 stock markets.

3. t-Test for the Monthly Returns

In Table 1 , the monthly mean returns are calculated for each month. For the SP500 stocks, the highest monthly mean return is 2.14% in January, and it is higher thanany other monthly return. This result is consistent with the January effect. But, thequestion is whether it is statistically significant. Since the ANOVA and Kruskal-Wallistests were unable to reject the null hypothesis that the 12 monthly population meanreturns are equal, this time we tested the null hypothesis that the January population meanreturn or any other monthly return is equal to the population mean of 12 monthly returns:

=i (4-2)

where =i population mean return of month i , and = population mean of monthlyreturns.

The results for the t-test for the paired samples are summarized also in Table 1.


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For the SP stocks, the t-value is significant for the positive January return. Similarly,when the t-test for the paired samples was applied to each monthly return, the negativeSeptember return was significantly different from the mean of the 12 monthly returns. Ineffect, the results support the positive January effect and the negative September effect.

For the Korean stocks, the simple monthly return is the highest in January at4.37%. However, the t-static is not significant. But, the t-statistic is significant for the positive November return (3.61%), and the negative returns in August (-2.33%) andSeptember (-2.01%). But when the 1998 data (financial crisis) are excluded, the Marchreturn is the highest at 3.57% and significant. The negative returns are significant inAugust (-2%) and September (-2.1%). These results do not support the January effect inKorea, but the positive March effect, and the negative August and September effects.

For the Tokyo stocks, the highest return is 2.91% in March, and it is significantlydifferent from the mean of the 12 monthly returns. The largest negative return is -1.64%in September, and it is significantly different from the 12 month average return.

For the Jakarta stocks, the January return is the highest at 4.54 % for the overall period, 1989-2002, but it is not significant at the 5% level. The next highest return is4.04% in December, and it is significant. The negative return is the largest at -5.52% inSeptember, and it is significant. Excluding 1989 (high outlier) and 1998 data (theaftermath year of financial crisis), the May return is the highest at 4.83%, and it issignificant. The next highest return is in December at 4.51%, and it is significant. Thenegative return is the highest in September at -4.36%, and it is significant. The positiveDecember effect and the negative September effect are significant in both sample periods.

For the Shanghai stocks, the May return is the highest at 13.83% for the entiresample period, 1991-2002, but it is not significant. None of the positive monthly returnsis significant. But there are 3 months of negative returns, namely July, September, andDecember, and they are all significant. Excluding 1992 and 1994 (extremely highoutliers), the June return is the highest at 8.29%, but it is not significant at the 5 % level.There are 3 months of negative returns, namely, May (-0.51%), September (-1.12%), andDecember (-4.63%), but none of negative returns is significant.

4. Risk-Adjusted Returns

Thus far, we have examined simple average returns without adjusting for risk. Now we examine the risk-adjusted returns. We have calculated 5 measures of risk-adjusted returns: Sharpe index = (

P P R / ), (

P P R / ), Treynor index = (

M P P R R ),

Jensen's excess return = R-bRm, and Shin-beta index= ),/()/( M p p R R and Shin-total

index = ( )//()/ M M M p R R The results are presented in Table 1 for the 5 stockmarkets for the selected sample periods excluding outlier years.


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On the excess return basis (R-bRm), the highest return is 0.975% in Decemberfor the SP 500 stocks, 2.561% in March for Korea, 2.037% in March in Tokyo, 3.879%in December for Jakarta, and 5.013% in April for Shanghai.

On the Shin beta index basis (beta-risk adjusted index relative to the market

portfolio), the highest index is 16.611 in March for the SP500, 3.540 in March for Korea.14.879 in April for Tokyo, 10.885 in January for Jakarta, and 2.818 in April forShanghai.

On the Shin total index basis (total risk-adjusted index relative to the market portfolio), the highest index is 0.897 in December for the SP500, 1.672 in March forKorea, 2.486 in March for Tokyo, 5.486 in December for Jakarta, and 0.754 in Februaryfor Shanghai.

Which month has the highest risk? The results are also mixed. The largest beta is2.18 in January for the SP500, 1.797 in November for Korea, 2.812 in March for Tokyo,

1.754 in August for Jakarta, and 2.318 in January for Shanghai. The largest total risk is5.64 in August for the SP500, 9.840 in October for Korea, 7.650 in March for Tokyo,12.29 in August for Jakarta, and 19.129 in January for Shanghai. The best and worstmonths for the positive and negative returns on the simple return and risk-adjusted basesare summarized in Table 18 .

5. Regression Analysis with Dummy Variables

A regression method of testing the January effect is to use dummy variables asused by Keim (1983), and others (Kato and Schallheim,1985). It takes the followingform:

(4-3)e Dba R t t t t ++= =12

2

where = monthly dummy variables;t D =2 D 1 for February and 0 for other months, =dummy variable 1 for March and 0 for other months, etc., and e = the error term. Theintercept constant a is expected to represent the average January return since January isrepresented by the situation when each of the 11 dummy variables is equal to 0. Theexpected return for February is equal to a

3 D

2bD+ . Thus, if the coefficients of the dummyvariables are all negative, it indicates that the January return is the largest, and it isconsistent with the January effect. If the coefficient of a dummy variable is positive, itindicates that the given month's return is greater than the January return.

The regression results with the dummy independent variables are summarized inTable 2 . For the SP500 stocks, the dummy variables have negative coefficients, and theresults are consistent with the January effect. The intercept is 2.1293 and it is highlysignificant. The September dummy variable has the largest negative coefficient -3.3766,so the September expected return is -1.2473(2.12993-3.3766). However, the adjusted R 2

=0.0150 is not significant.


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For the Korean stocks, the coefficients of the dummy variables are all negative,and the intercept constant is highly significant. The results, therefore, are consistent withthe January effect. However, when the 1998 data are excluded, the dummy variables forMarch and November have positive signs, indicating the March and November expectedreturns are higher than the January return. But none of the coefficients is significant. In

effect, the January effect is not supported for Korean stocks.

For the Tokyo stocks, the March dummy variable has a positive sign. But thecoefficients are not significant. For the Jakarta stocks, all the dummy have negativevariables, but the coefficients are not significant except for the negative signs for augustand September. For the Shanghai stocks, The dummy variables for April, May, June,August, and November have positive signs, but none of the coefficients is significant atthe 5 % level. In effect, the regression results with dummy variables are consistent withthe January effect only for the SP 500 stocks, but the regression model is not significantin terms of the F-value.

6. Correlation AnalysisThus far we have examined whether there are significant differences in the

monthly returns or periodic patterns in the monthly returns. According to the randomwalk hypothesis, all monthly returns should be randomly distributed and the expectedvalues of the monthly returns should be equal. The conventional statistical methods, suchas ANOVA and Kruskal-Wallis tests cannot reject the null hypothesis that all monthlyreturns are equal. However, the t-tests of paired samples indicate that some monthlyreturns are significantly higher or lower than the mean of the 12 monthly returns. But theresults tend to be inconclusive because the statistical significance is sensitive to thesample. Exclusion of certain observations can significantly alter that mean return andstatistical significance.

Another proposition of the random walk hypothesis is that the monthly returnsshould be independent of other monthly returns. To test this hypothesis, correlationcoefficients are calculated between monthly returns. The results are presented in Table 3 .

First, for the SP 500 stocks, 9 correlation coefficients are significant at the 1% or5% level. For instance, the January return is significantly correlated to the June return,which is in turn correlated to the September return. The September return is significantlycorrelated to the April, June, and July returns. The July return is highly correlated to theOctober return, etc.

As for the Korean stocks, there are 8 significant correlations for the period 1980-2002. Excluding 1998, the aftermath year of the 1997 financial crisis, 5 monthly returnsare significant. February and October returns are significant for both sample periods.

For the Tokyo stocks, there are 8 significant correlations for the period 1984-2002.For China, there are 7 significant correlations for the period 1991-2002, and 13significant correlations, if 1992 and 1994 are excluded. The January return is correlated


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to March, April, May, and November. For the Jakarta stocks, there are only 2 significantcorrelations for the period 1989-2002, and 3 significant correlations, if 1998 data isexcluded.

The above correlation results do not support the random walk hypothesis, strictly

speaking. However, the conclusion is tentative for two reasons: First, the correlationcoefficients are highly unstable, particularly in the Asian stock markets. Second, thecorrelation can be spurious.

Fama and Blume (1966) selected the Dow-Jones 30 Industrial stocks, and theyregressed today's return on each of the 5 lagged return variables and found significantcorrelation coefficients for the 30 stocks, but the coefficients of determination were verylow, less than 0.123. There are many correlation studies on the other stock markets, suchas Norway, Sweden, Australia, UK, and Greece. The largest correlation coefficient was0.134 for these countries (Granger, 1968; Elton et al., 2003). We will also test regressionanalysis and ARIMA models using the lagged variables in the next sections.

7. Regression Analysis with the Monthly Returns

To examine if the monthly returns are correlated to the past 12 monthly returns,we test the following regression model:

t t t t t t t t t t u Ra Ra Ra Raa R ++++++= 12123322110 ...... (4-4)

where = the monthly returns for the preceding 12 months.121 ,...., t t R R

In the above function (4-3), the January monthly return, for instance, is a functionof the preceding 12 monthly returns. The regression results are summarized in Table 4 for the SP500 stocks, the Korean stocks, and the Tokyo stocks. Since the sample periodwas too short, the regression model was not tested for the Shanghai and Jakarta stocks.

First, for the US stocks, the following monthly returns have at least onesignificant variable (t-value at the 5% level): January, March, April, and August. Forexample, this year's January return is significantly correlated to last year's April return.The March return is significantly correlated to last year's March return, and last year'sJuly and August returns. The August return is significantly correlated to last year'sOctober return.

Next, for the Korean stocks, the April return is significantly correlated to lastyear's returns of January, February, March, April, May, June, July, and September. Theadjusted R 2 is 0.7348. The July return is significantly correlated to last year's Februaryreturn. The August return is significantly correlated to last year's July and August returns.For the Tokyo stocks, the February return is significantly correlated to last year'sFebruary return. The May return is significantly correlated to last year's July return.

8. ARIMA, ARCH, ARCH-M, and GARCH Models


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A time series model with a single dependent variable can be expressed by the

following ARIMA (autoregressive integrated moving average) model:

qt qt t t pt pt t t eeee y y y y ++++= ..... 2211022110 (4-5)

where are the autoregressive terms, and are the white noise error series. It statesthat dependent variable is a function of lagged dependent variables and error series.

it y it e

t y

A random walk series can be expressed by an ARIMA model, ARIMA (1,0,0):

(4-6)t t t e y y += 1or t t t e y y ++= 1 (4-7)

where = a constant or drift term. Equations (4-6) and (4-7) are estimated in arithmeticvalues and natural logarithms.

The ARIMA models were tested for the 5 stock exchanges. The results aresummarized in Table 5 . For the SP 500 stocks, the adjusted R 2 values are high and thecoefficients of the MA term are close to 1.0 for all equations, with and without thedrift term, in logarithms and arithmetic values. But the highest adjusted R

1t y2 values are

obtained for the log models: 0.9975 for the log models with and without the drift term.The Q statistics indicate that residual series are white noise for all models. It implies thatthe ARIMA models are appropriate and the residual series have no significant periodic

patterns.

For the Korean stocks, the highest adjusted R 2 (0.9881) is obtained for the logmodel with a drift term. The Q statistics indicate that the residual series are white noisefor the two log models, but not for the two non-log models. Similarly, the log model witha drift term is the best for the Tokyo stocks (0.9603) and the Shanghai stocks (0.9420).For the Shanghai stocks, the Q statistics indicate that the residual series for the non-logmodels are white noise, but the residual series are not white noise for the log models.For the Jakarta stocks, the adjusted R 2 is the highest at 0.8705 for the model in arithmeticvalues with a drift term. The Q statistics indicate that the residual series are white noisefor all 4 models. These results strongly support the random walk hypothesis for all 5stock exchanges.

For the monthly return series, various ARIMA models were tested, such asARIMA(12, 0, 0 ), ARIMA (12,0,12), and ARIMA (12, 1, 12). The results for ARIMA(12, 0, 0) are presented in Table 4. The adjusted R 2 values are negative for the SP500,Korea, Tokyo, and Jakarta stocks, except for the Shanghai stocks. For the SP500, Korea,and Tokyo stocks, none of lagged variables is significant. But for the Jakarta andShanghai stocks, there are one and two significant variables respectively. The Q statisticsindicate that the residuals are not white noise for the SP500, Korea, Jakarta, andShanghai stocks. But the residuals are white noise for the Tokyo stocks. In effect, the


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ARIMA models tend to support the random walk hypothesis for the 5 stock exchanges(see appendix note ).

In Table 6 , heteroscedasticity is tested in AR(1) with ARCH, ARCH-M andGARCH models. For the ARCH(m) model, the mean and variance equations are given

below:

(4-8)t jt jt p

jt u x y ++= = 10

h (4-9)210

2 jt

m

j jt t u =+==

where is the variance conditional on the past.t h

The mean and variance equations for the ARCH-in-Mean or ARCH-M (m) aregiven by

(4-10)t t jt j p

jt uh g x y +++= = )(10

t t t vh =u , or u t t hlog= (4-11)

h (4-12)20 jt m

jt jt t u +=

The mean and variance equations for the GARCH (p, q) model are given by

= +

= +++=

r

j jt jt jt jt

m

jt uu x y

110 (4-13)

t t t vh =u , or u (4-14)t t hlog=

h +210 jt

q

j jt u =+= jt

p

j jh = 1 (4-15)

(4-16)11 1


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9. Unit Root, Variance Ratio, Runs, and Cointegration Tests

For the monthly stock prices , unit root and cointegration tests were applied.Before we present the test results, it may be useful to briefly review the meaning and

methodology of such tests in interpreting the test results. Economic time series data can be divided into two types: stationary time series and non-stationary time series (unit root,random walk). Non-stationary time series can be divided into the following three types:(1) simple random walk with no constant and no trend, (2) random walk with a constant(drift), and (3) random walk with a constant and around a stochastic trend:

(4-17)t t t e y y += 1 t t t e y y ++= 01 (4-18)

t t t et y y +++= 101 (4-19)

Two tests are most widely used to test the unit root process: the augmentedDickey-Fuller test and the Phillips-Perron test. For the Dickey-Fuller test, the followingtwo test regression equations are used: one with a constant and no trend, and the otherwith a constant and trend.

(4-20)t jt p

j jt t Y Y Y +++= = 1110

t jt p

j jt t Y t Y Y ++++= = 12110 (4-21)

where Y = stock price index, 0 = constant, and t = trend. The null hypothesis is that

1 = 0 for the unit root process. If ,0


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If two non-stationary variables are used to calculate regression and correlationcoefficients, the correlation can be spurious. There are two remedies. First, differencedvalues can be used if the variables are difference-stationary. Second, if the two non-stationary time series are cointegrated, the level-variables can be used for regression. Iftwo times series are cointegrated, it implies that the two times series have a long-run

equilibrium relationship.

To see if the 8 stock market prices have long-run equilibrium relationships, wehave also applied the Dickey-Fuller test, Phillips-Perron test, and the Johansen test. Inthe Dickey-Fuller test of cointegration, two types of cointegration regression equationsare first calculated, as shown by equations (4-22) and (4-23).

(4-22)t jt M

j jt u X Y ++= = ,10

(4-23)t jt M

j jt u X t Y +++= = ,110

. where X is taken as the independent variable, M = the number of independent variables.

Then the residuals are tested by the unit root test procedure:

(4-24)t it p

t it t t vuuu ++= = 11

where = 1 is the null hypothesis that the error series is unit root (non-stationarity)

The difference between the Dickey-Fuller method and the Phillips-Perron methodis concerned with the correction method of serial correction, as mentioned before. If theresidual series is not unit root, we accept that the residual series is stationary, and we

accept the alternative hypothesis that the two variables are cointegrated. If the twovariables are not cointegrated, differenced variables should be used for regressionanalysis to avoid spurious correlation. However, if the two variables are cointegrated, thelevel variables can be used for regression analysis without the problem of spuriouscorrelation.

The results for the variance ratio test are summarized in Table 8. The z-scoresindicate that we cannot reject the null hypothesis of the random walk. For q=30, the highz-scores indicate that there are some outliers (see appendix note).

The runs tests for randomness were applied for the mean and median values for

the overall sample periods ( Table 9 ). The results support randomness for the 5 stockmarkets for the median values. But the runs tests for the mean values support for the 4stock exchanges except for the Korean stocks. When the runs test is applied to monthlyreturns for each month, the random walk hypothesis is supported for the 5 stock markets

The cointegration test results for the pairs of the 8 stock market monthly stock prices are summarized in Table 10 . The Dickey-Fuller test indicates no cointegration, butthe Phillips-Perron test indicates that SP500 stocks are cointegrated with Korean and


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Tokyo stocks. When the Johansen test (Johansen, 1988, Johansen and Juselius, 1990),which uses the maximum likelihood estimation method for cointegrating vectors, isapplied, the results indicate that only SP500 and NASDAQ are cointegrated, and all otherstock markets are not cointegrated.

10. VAR Models

To examine if there are independent relationships among the stock markets, thefollowing VAR models are applied to the monthly returns and monthly stock prices in the5 stock exchanges:

Y 112110 ... u Z Y t t t ++++= (4-25) Z 212110 ... u Z Y t t t ++++= (4-25)

where Y , . , = monthly stock price indexes or monthly returns of the 5 stockexchanges. The results are presented in Table 11 . For the monthly returns, there are nosignificant variables in each equation at the 5% level. Only for the SP500, the laggedJakarta is significant at the 5.49%. For the monthly prices, in all equations, its ownlagged stock price is significant. But for the SP500 stock prices, the lagged Jakarta andlagged Shanghai are significant. When tested without the Shanghai stocks, the resultswere very similar as to the significance of the variables in each equation.

t t Z

11. Autocorrelation Analysis

Autocorrelation coefficients are calculated for the 5 stock price indexes to test ifthe stock market price indexes are random walks. The autocorrelation function is given

by

21

1

)(

))(()(

y y

y y y yk y n

t t

k t

n

k t t

=

=

+= (4-27)

where y(k) = autocorrelation coefficient at time lag k for the time series data, i.e.,monthly stock prices or monthly returns. The test statistic Q is distributed as a chi-squaredistribution with k-c degrees of freedom, where c = the number of autocorrelationcoefficients, k = selected lag length in the autocorrelation function. It is used to test thenull hypothesis that the time series is white noise (mean is zero and variance is constant) ,using the critical values of a chi-square distribution. If the Q statistic is less than the

critical chi-square statistic, we would accept the null hypothesis that the autocorrelationfunctions (ACFs) are white noise and do not show any patterns..

The graphs of autocorrelation coefficients against time lags (correlograms) are presented in Figure 3 for the monthly prices and monthly returns. If the stock price seriesis a random walk series, the autocorrelation coefficients are expected to be high over theshorter time lags and gradually decline. We note that the autocorrelation functionsexactly follow the patterns of random walks for the 5 stock price indexes. On the other


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hand, the autocorrelation functions of the monthly returns are not significant in all 5series. The Q statistics indicate that the monthly return series are white noise Theseresults are consistent with the random walk hypothesis (see appendix note).

12. Spectral Analysis

The objective of spectrum analysis is to decompose the original time series intosine and cosine function of different frequencies. It is based on Joseph Fourier's idea(1822) that any periodical time series can be expressed in terms of one or more sinecurves of different frequencies. The Fourier analysis is to find optimal coefficients in thefollowing finite Fourier function:

t f

k

f f t e

N ft

N ft

y +++= = ]2)sin(2)cos([2 10

(4-28).

If the or coefficient is large and significant, it indicates a strong periodicity at the given

frequency. The coefficients and are converted to amplitude and phase angles for eachfrequency. The periodogram is defined by

(4-29)2/)( 22 f f f N P +=

where = periodogram (periodogram value) at frequency f, and N = total number ofobservations.

f P

A periodogram plots line spectra (a set of amplitudes) corresponding to all

frequencies. By examining the periodogram, we can determine if a series is a random

walk series or if it contains periodicity, such as cycles and seasons. A spike in the linespectrum indicates periodicity. If a series is a linear trend series, the periodogram wouldshow a flat line. If a series is a random walk series, the periodogram would show spikesof roughly equal size spread throughout the spectrum.

As reviewed previously, spectral analysis was used by Granger and Morgenstern(1963, 1970, pp. 103-131), and they did not find any significant seasonal or periodical

patterns in the various stock prices for the periods 1871-1956 and 1918-64. In theiranalysis, they used logarithmic first differences for the following reasons: First, thetransformed data have more symmetric and more nearly normal histograms. Second, ifthe random walk hypothesis is correct, the logarithmic first differences are a well-

behaved variable whereas the levels are not.Using their methodology, we applied spectral analysis to the first differences in

the log prices for the 5 stock price indexes. The spectral diagrams (periodograms) are presented in Figure 4 . For the purpose of comparison, hypothetical data are used to show periodograms for cyclical data, and they are shown in the last 2 panels of Figure 4. Thatis, when cycles are present in a time series, spikes are expected to show up in the


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periodograms. In effect, the periodograms do not reveal any significant spikes to indicateseasonal or periodical patterns in the Asian and US stock markets (see appendix note).

13. International Correlation Analysis

Extending the random walk theory to the international stock markets, two propositions are possible: First, if the market is efficient, information in one stock marketshould be available in another stock market instantaneously, and thus stock marketreturns should be highly correlated. Second, according to the random walk hypothesis,yesterday's stock returns should not be correlated to today's stock returns, and today'sstock returns cannot be used tomorrow's stock returns. Since there are time differences

between the US stock markets and the Asian markets, if the two stock markets arecorrelated, it would contradict the random walk hypothesis.

Reilly and Wright (represented in Reilly and Brown, 2003, p.94) calculatedcorrelation coefficients between the SP 500 stocks and other capital market assets using

the monthly data for the period 1980-1999. They found that the SP 500 stocks have highcorrelation with the Toronto stocks (0.769), the London Stock Exchange (0.641), and theFrankfurt Stock Exchange (0.518), and low correlations with the Tokyo Stock Exchange(0.306).

In our study, the correlation coefficients are calculated for the 5 countries for the period 1991-2002, and for the 4 countries excluding the Shanghai stocks for the period1989-2002. The correlation coefficients are significant between monthly returns for the 4stock exchanges, namely, SP500, Korea, Tokyo, and Jakarta, but the Shanghai stocks arenot correlated to the other stock market returns (See Table 12 ).

Next, correlation coefficients were calculated for the 5 stock exchanges by monthfor the period 1991-2002. The Shanghai stocks did not also show any significantcorrelation with other stock exchanges. So, omitting the Shanghai stocks, the correlationcoefficients were recalculated for the 4 countries for the period 1989-2002. The resultsare presented in Table 7. It is interesting to note that the 4 stock returns are not alwayscorrelated. For instance, the Korean stocks are correlated to the Jakarta stocks only inJanuary and April.

The US stocks are correlated to Jakarta stocks only in March. The US stocks arecorrelated to the Tokyo stocks only in May, June, and August. It is interesting to note thatthe Korean stocks are not correlated to the SP500 stocks in any month, though thecorrelation coefficient is significant for the overall period (0.278). The Korean stocks arecorrelated to the Tokyo stocks in February, April, May, June, July, and August.

The Tokyo stocks are correlated to the US stocks in May, June, and August. TheTokyo stocks are, as stated before, significantly correlated to the Korean stocks inFebruary, April, May, June, July, and August. The Jakarta stocks are correlated to theKorean stocks in January and April. The Jakarta stocks are also correlated to the SP 500


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stocks only in March. But the Jakarta stocks are not correlated to the Tokyo stocks in anymonth.

Simple and multiple regression equations are calculated for monthly stock pricesin logarithms for the 5 stock exchanges. The results are presented in Table 13 . First, as

for the simple regression results, we note the following. (1) The SP500 stock price indexis significantly correlated with other 4 stock prices indexes. (2) The Korean stock priceindex is also significantly correlated with other 4 stock price indexes. (3) The Tokyostock price index is significantly correlated with the SP500, Korea, and Shanghai stock

price indexes, except for the Jakarta stock price indexes. (4) The Jakarta stock price indexis correlated with the Korea, SP500, and Shanghai stock prices indexes, except for theTokyo stock price index. (5) The Shanghai stock price index is significantly correlatedwith other 4 stock exchange price indexes. As for the multiple regression results, we notethe following. (1) For the SP500 stock price index, the Tokyo and Korean stock priceindexes are significant. (2) For the Korean stock price index, 3 stock exchange indexesare significant except for the Shanghai index. (3) For the Jakarta stock price index, 3

stock exchange price indexes are significant except for the SP500 index. (4) For theShanghai stock price index, the Tokyo and Jakarta stock price indexes are significant, butthe Korean index and SP500 indexes are not significant. However, these statistical resultsare subject to estimation problems since the data contain extreme outliers and the lowDW statistics indicate significant serial correlations.

14. Characteristics of the 5 Stock Markets

Some descriptive statistics and other characteristics of the Asian stock markets areSummarized in Table 14 . The sample period varies with the stock market due toavailability of data. Over the available sample period, the Shanghai stocks have thehighest average monthly return at 3.2841 % during the 12 years (1991-2002). The nexthighest average monthly return is for the Korean stocks, with the average monthly returnof 1.009% over the 23 years (1980-2002). The next follows the SP500 stocks (0.68%),and the Jakarta stocks (0.6683%). The Tokyo stocks have the lowest monthly averagereturn (0.3554%) for the period 1984-2002.

The total risk is the largest at 22.3845% for the Shanghai stocks, correspondingto the highest average return. But the next highest total risk values are the Jakarta stocks(9.81%) and the Korean stocks (8.91%). The total risk values are 8.91% and 22.38%respectively. Their total risk values are higher than the SP 500 stocks (4.52%), but theTokyo and Jakarta stocks have lower returns and higher risk values (5.92% and 9.80%)than the SP 500 stocks. The risk-return relationship does not necessarily hold true for the5 stock exchanges. Systematic risk will be discussed in the next section.

As for the median values of monthly returns, the SP 500 stocks have the highestmedian return 0.805%, and the next highest values are Shanghai (0.4634%), Tokyo(0.15%), Jakarta (-0.16 %), and Korea (-0.285%). Also, in this case, the return-riskrelationship does not hold true.


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Next, we have applied the chi-square test and Lilliefors test for the null hypothesisthat monthly returns are normally distributed. The chi-square test supports normality forthe Tokyo stock returns, and the Lilliefors test supports both Tokyo and Jakarta stockreturns for normality, but normality hypothesis is not supported for the SP 500, Korea,and Shanghai stocks.

To see if the 5 stock exchanges can be grouped into similar groups, factor analysiswas applied. The results are summarized in Table 15 . When 5 factors are specified, theresults show that 2 factors are significant. When 4 factors are specified, the Tokyo andKorean stocks are grouped to the common factor. The Jakarta stocks, SP500, and theShanghai stocks are grouped independently. When 3 factors are specified, Tokyo, SP500,and the Korean stocks are grouped to the common factor, and Jakarta and Shanghai areindependent. Finally, when two factors are specified, Korea, SP500, Tokyo, and Jakarta

belong to the common factor and Shanghai is independent. In Table 16 , the correlationcoefficient matrixes are presented. The correlation coefficients of the monthly stock

prices for the period 1989-2002 are all significantly correlated for the 8 stock markets.

The correlation coefficients of the monthly returns, however, are also significantlycorrelated for the 7 stock markets except for the Shanghai stocks.

15. Evaluation of the Asian and US Stock Returns

In this section, we compare the performance of the Asian and US market stockreturns. The results are summarized in Table 17 . As we have reviewed before, the simpleaverage monthly return is the highest at 2.038% in Shanghai, and the next highest returnsare 0.853% in Korea, 0.623% in Jakarta, and 0.695% for the SP 500, and 0.31% in Tokyo.However, when the analysis of variance is applied, the F-test cannot reject the equality of

population means (F=0.958). Also, the Kruskal-Wallis H test cannot reject the equality of population medians (H=3.244). The t-test for paired samples is applied for the monthlymean return series of individual stock exchanges. The results show that only the mean ofthe Tokyo return series is significantly lower than the mean of the average series of the 5stock exchanges.

The total risk (standard deviation) is calculated from the 12 monthly returns overthe sample period for each exchange. The total risk is the highest in the order ofShanghai, Jakarta, Korea, Tokyo, and SP500. The systematic risk beta is obtained byregressing the monthly return series of each stock exchange on the average monthlyreturn series of the 5 stock exchanges. The systematic risk is the highest at 1.7496 forShanghai, and the next highest beta values are 1.1336 for Jakarta, 0.9085 for Korea,0.7095 for Tokyo, and 0.50 for SP 500. The total risk ranking and the systematic

ranking are consistent.

In terms of the CAPM- adjusted excess returns ( R - Rm ), Shanghai has thehighest excess return at 0.333%, and the next highest excess returns are 0.2427% forSP500, 0.0323% for Korea, -0.3280 for Tokyo, and -0.40185 for Jakarta. On theReturn/beta and the Shin beta index bases, the SP 500 stocks are the best (1.389, 1.544),the next best stock markets are Shanghai (1.165, 1.294), Korea (0.939, 1.043), Jakarta


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(0.549, 0.380) and Tokyo (0.439, 0.372). On the Return/std. and the Shin total index bases, the SP500 is again the best (0.771, 1.209). The next best markets are Shanghai(0.538, 0.842), Korea (0.468, 0.732), Jakarta (0.53, 0.380), and Tokyo (0.238, 0.372).In effect, on the risk-adjusted bases, the SP 500 stocks showed the best performanceduring the sample period, but it is not surprising because the SP 500 stocks are a selection

of the best leading corporations in the leading industries in the United Sates. Anotherreason is that the US stock market was booming during the 1990s until January 2000.

16. The Best and Worst Months

As we have examined before, the best and worst months varied with the risk-adjusted return measures. For the SP 500 stocks for the period 1971-2002, the positiveJanuary effect and the negative September effect are significant. For the Korean stocksfor the period 1980-2002, excluding 1998, the positive March effect and negative Augustand September effect are significant. For the Tokyo stocks for the period 1984-2002, the

positive March effect and negative September effect are significant. For the Shanghai

stocks for the period 1991-2002, excluding 1992 and 1994, only the negative Novembereffect is significant. For the Jakarta stocks, the positive May and December effect, andnegative August and September effect are significant. As for the risk-adjusted returns, theresults vary with the risk-adjustment measures, as shown in Table 18 . For the SP 500stocks, January concedes to March and December. It is interesting to note thatDecember can be good for the SP 500 stocks, but bad for the Shanghai stocks. For thenegative returns, all 5 measures point to December as a bad month for the stocks.

These results do not support any of the three hypotheses to explain the Januaryeffect since there is no January effect in the Asian stock markets. However, it isinteresting to note that the monthly returns tend to be higher in the springtime in theAsian stock markets: Korea (March), Tokyo (March), Jakarta (May), and Shanghai (June).As for the negative returns, September is a bad month for the SP 500 stocks, Korea, andTokyo. The bad month is August for Jakarta and it is December for Shanghai. Why thespringtime effect in Asia? As briefly mentioned before, the new school year starts inMarch in Korea, and in April in Japan. The new year in Chinese lunar calendar begins inFebruary in the Gregorian calendar.

17. The January Barometer Theory

The January effect discussed in this paper should not be confused with theJanuary effect of version 2, which is often called the January predictive hypothesis or theJanuary barometer theory. The January barometer theory states that the January return isa predictor of the stock market conditions of the rest of the year. That is, if the Januaryreturn is high, the stock returns for the rest of the year should be also good. Bloch andPupp (1983) used the SP500 stock indexes for the period 1950-82. They calculated 12regression equations for the months January to December, with 3 independent variables:the January return, the January return-squared, and the time trend. They conclude that theJanuary return is not significant in predicting the next 12 month stock returns. To test theJanuary barometer theory, we test the following simple regression equations for the


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Asian and US stock market monthly returns: iiii x y += , where = the January return.For the dependent variable, we have tested two types of average returns: = the averageof monthly returns, January to December, and y = the average of monthly returns,February to December, excluding the January return of the year. The regression resultsare summarized in Table 19. When the dependent variable is y , the January return issignificant for the 4 US stock markets, Korea and Tokyo stock markets. But, it is notsignificant for Jakarta and Shanghai stock markets. The significance is largely due to thefact that the dependent variable, i.e., the average of the 12 monthly returns, includes theindependent variable, i.e., the January return (built-in effect)

1 y

2

1

When the dependent variable is 2 y , the average of the 11 monthly returns,

excluding the January return, the independent variable, i.e., the January return, issignificant at the 5% level only for the SP500 total index returns. It is not significant forall other stock markets, namely, the SP500, Dow-Jones, NASDAQ, and the 4 Asian stockmarkets. These results generally support the Bloch-Pupp conclusion that the January

return is statistically not significant in predicting the average return for the next 11months.

IV. Summary and Conclusions

We have applied various statistical analyses to the monthly returns of the 5 stockexchanges to find if there exist monthly or periodic patterns, such as the January effectthat contradict the random walk theory. We have applied ANOVA, the Kruskal-Wallistest, the chi-square test, the runs test, etc. These tests showed that we cannot reject thenull hypothesis that the population monthly returns are all equal. Also, we have appliedregression analysis, autocorrelation analysis, and the VAR models. These results tended

to support the random walk theory in the sense the coefficients were mostly notsignificant or the R 2 values were extremely low. The unit root test and ARIMA (1,0,0)model strongly supported the random walk theory. The results of other ARIMA modelsand autoregression analysis were consistent with the random walk theory. The spectralanalysis did not show significant periodical patterns. These results are also consistentwith the random walk theory.

Correlation analysis is applied to the monthly returns of the 5 stock exchanges forthe period 1991-2002. The results show that the SP500 stocks, Tokyo stocks, Koreanstocks, and the Jakarta stocks are significantly correlated. The Shanghai stocks are not

correlated to any other stock markets. When the correlation coefficients are calculated bymonth, the correlation coefficients are significant only for some months and not for allmonths. For instance, the Korean stocks are correlated to the Tokyo stocks only for themonths of February, April, May, June, July, and August. The Korean stocks are notcorrelated to the SP 500 stocks in any month. The Tokyo stocks are correlated to the SP500 stocks only in May, June, and August. The Jakarta stocks are correlated to theKorean stocks only in January and April. The Shanghai stocks are not correlated to anyother stock markets.


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Thus far we have examined the stock market behavior in the Asian and US stock

markets. There are three interesting questions to be briefly discussed. First, do the Marchand September effects, for instance, imply that if investors buy SP500 stocks, Koreanstocks, Tokyo stocks, and Jakarta stocks in September 30 (or the last trading day of the

month) and sell in March (or the last trading day of the month), they will make the largestrisk-adjusted excess returns? Should the investors in Shanghai buy stock indexes inDecember (or the last trading day of the month), and sell in April or June? The secondquestion is, do these March and September effects or the June, April and Decembereffects contradict the random walk theory? The third question is, why do I make thissecret information publicly available instead of using it for private gain?

Since the above three questions are all related, they can be answered as follows.First, if the market is efficient, the information on the March and September effectsshould travel fast and arbitrage activities are supposed to wipe out the opportunities forthe excess risk-adjusted returns. However, if investors do not know the information, or if

they do not get the information simultaneously, or if they do not trust the information touse it, some investors who use the information may be able to make excess returns.Second, the March and September effects are concerned with the expected returns. Thatis, a March return can be lower or negative for a year, but it can be higher in another year.But the average return should be higher over a long period of time. Thus, using the abovetrading rule does not guarantee that investors will make the highest excess returns everyyear. Third, the excess risk-adjusted return is really a gross return in the sense that tradingcost, information cost (research cost and the price to pay for the information), and taxesare not yet subtracted. Thus, if these costs are subtracted, the excess return may disappear.Fourth, this study is concerned with aggregate market indexes. If investors wish to selecta number of specific stocks, they will incur selection cost. Fifth, in this paper, we haveconsidered only two types of

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