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Characteristics of the Asian and US

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

Kilman Shin*

Abstract The January effect refers to the theory that the monthly average stock return is the highest in January than in any other month. Some argue that the January effect holds true only for small-firm stocks and it takes place only over the first week of a new year. Others argue that the January returns are higher because the risk is higher in January. The January effect 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 price information. Defendants of the random walk theory argue that the January effect can occur only in the short run and it cannot persist and will disappear in the long run. In this study, some selected Asian stock markets and the US stock markets are examined to find if the January effect or other periodic patterns exist in the Asian and US stock markets. In addition to the simple comparison of monthly stock returns with and without risk-adjustments, various statistical methods, such as variance ratio test, unit root test, Johansen cointegration test, ARCH, ARCH-M, GARCH, VAR, ARIMA models, 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 effect which 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 the random walk hypothesis which argues that stock returns should be randomly distributed. The random walk hypothesis implies the following propositions when applied to the monthly returns: First, a given month's stock returns should have no significant correlations with other months' stock returns so that one month's stock return is useless in predicting the stock returns of other 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, the monthly returns of stocks in a stock exchange should be useless in predicting the monthly returns of stocks in other countries if the time zones are different. _______________________________________________ * Ferris State University, Big Rapids, Michigan, 49307 USA: kilman_shin@ferris.edu

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To support or refute the random walk hypothesis, there are much on-going research in the periodical patterns in the stock returns in the following areas: (1) the January 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 daylight savings time (Kamstra, Kramer, and Levi, 2000, 2002; Pinegar, 2002; for a review, see Khaksari and Bubnys, 1992; Malkiel, 2003). The major objective of this paper is to examine some selected Asian stock markets to find if there are any monthly or seasonal patterns, such as the January effect, and if the stock prices follow the random walk. The following stock markets were selected for our study: the Korea (Seoul) Stock Exchange, the Tokyo Stock Exchange, the Jakarta Stock Exchange, and the Shanghai Stock Exchange. The US stock market (SP 500 stocks) is also examined in this study for the purpose of comparison. In section II, some of the previous empirical studies are reviewed. In section III, the random walk theory and the methods of measuring the risk-adjusted returns (CAPM) are reviewed. In section IV, empirical results are presented for the Asian stock markets and the SP 500 stocks. A summary 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 based on 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 largest realizable capital losses for tax saving, (2) individuals and corporations sell stocks for tax-saving toward the middle of December to establish tax losses, and such pressures drives security prices below what they should be in the light of potential earnings, (3) the rise 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 listed

on the NYSE each year for the period 1927-42. Then he adds the values of the 20 stocks at every 2 weeks from the bases in December, and divides by 13 years (1927-42) to obtain the annual mean value. This procedure was followed to obtain the mean values for the 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 more than the low-yielding Dow-Jones stocks in the late December to the third Saturday in January. Similar results were obtained for the median values. However, the following criticism may be made. First, there is no reason why the tax selling pressure should end at the middle of December. In theory, the tax-selling pressure should continue until the end of December. As another possible reason, Wachtel mentions unusual demand for cash,

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beginning a week or two before Christmas, causes many stock sales. But his data show that stock prices rise 2 weeks before the year end. That is, unusual demand for cash should not stop until the holiday season is over. Second, there is no statistical significance test. So we can not tell whether thee difference was 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, they applied 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-Jones Industrial Average (1915-1961), and individual company stocks (daily, weekly, and monthly). They plotted and examined several spectral diagrams, and concluded that the spectra 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. The results did not show a 12 month peak, though it showed some small peaks corresponding to a three month cycle. Weekly price series indicated the presence of a small monthly cycle. 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 of

the 30 Dow–Jones industrial stocks for the period 1962-71, and found that 7 of the stocks displayed significant seasonal patterns. Officer (1975) used the Box-Jenkins time series analysis 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. They

divided 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, they found statistically significant differences in the monthly returns due to the large January returns. They used the Kruskal-Wallis test, the Siegel-Tukey test, Bartlett’s test for homogeneity of variances, and the analysis of variance. They found that the January return is significantly higher than other month's returns. They also found relatively higher returns 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 the CAPM 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, price increased 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 prices decreased more than 20% during the year had abnormally higher trading volumes in December. He argued that it was evidence that investors sell to realize the capital losses for the purpose of tax deduction. He measured abnormal volume as the actual volume as a 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 one to four weeks following the last Friday of the year over the period 1965-75. Branch and Ryan (1980) examined tax-loss selling candidates of NYSE and AMEX stocks for the

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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 stocks rose from 5.2% to 14.4%.

Keim (1983) used the NYSE and AMEX data for the period 1963-79. He divided

the stocks (1,500 to 2,400 in total) into 10 portfolio groups. He regressed the daily excess returns on the 11 dummy variables, where each dummy variable represents each month from February to December. The excess return for January is measured by the intercept constant. He found that the January effect is significant for small-firm portfolios (1 to 4 deciles) and the excess returns are negatively related to larger firms (5 to 10 deciles). He also found that the January effect occurred during the first 5 trading days of the year. He used 3 types of beta, namely, the OLS estimated beta, Scholes-Williams beta, and Dimson 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, and

as a result the systematic risk is underestimated. As a result, the beta-risk adjusted returns are overestimated. Using the SP500 data for the period 1963-77, he shows that the Dimson 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 4 trading days of January (turn-of- the year). He found that the very first day of January showed the largest mean return differences. He found that the January effect is significant for both small and large firms. The mean and the frequency of positive returns on the 5 trading 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 larger firms.

In Australia, all tax-paying financial institutions pay normal taxes on capital gains,

and capital losses are deductible without limit from ordinary income. Individual investors do not pay taxes on capital gains. Also, the Australian tax year is July 1 to June 30. Thus, 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. To allow for the size effect, the stocks were divided into 10 groups of portfolios. They found that the smallest decile of firms had average returns of 6.754%, while the largest decile of firms 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. They used 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 computed first 12 monthly autocorrelations, and found that they were mostly not significant except for Australia, Denmark, and Norway. They used the Kruskal-Wallis test for the 17 countries, and found that the monthly returns are not equal for 12 countries from a total

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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 starts in April. Berges, McConnell, and Schlarbaum (1984) used Canadian stocks for the period 1951-80. In Canada, the capital gains tax was installed in January 1973. They divided 391 stocks into 5 portfolio groups, and compared the January monthly returns with means of February-December returns for the period 1951-72 and for the period 1973-80. They found 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 for the period 1951-72. The capital losses in excess of capital gains may be used to offset ordinary income up to a maximum of $2,000 in one tax year. Thus, there was no incentive for Canadian investors to sell stocks at the end of the tax year prior to 1973. But they 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 January effect. Tinic, Barone-Adesi, and West (1987) also used Canadian stocks for the period 1950-81. They divided 317 stocks into 5 size-portfolios. They used regression analysis with 5 dummy variables: 3 dummy variables representing for January, December, and the period 1973-80 with capital gains tax respectively. Two other dummy variables are the 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. The results showed that stock returns are higher in January and December and the smaller firms have higher returns than the large firms. The dummy variable representing the capital-gains tax period had positive signs, but it was not statistically significant except for one portfolio. They conclude that the results do not support tax-loss selling as the sole factor of seasonality, but they provide limited support for tax loss-selling hypothesis. 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 found January 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 firms choose tax years ending Mach 31. Thus, the Japanese results do not necessarily support the tax-selling hypothesis. They present two possible reasons for the January and June effects. First, most Japanese firms pay so-called bonuses equivalent to about two monthly salaries to employees generally in June and December. Second, corporate earnings forecasts are made by financial analysts in March, June, September, and December. They state 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 significantly higher than the overall daily average return 0.00035. However, there was no significant

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difference between the average returns over the last 5 days of December and the first 5 days of January. They also calculated the correlations coefficients between the Tokyo stock daily returns and the SP500 daily stock returns. The correlation coefficient was the highest 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 on Tuesday 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 the January stock returns on the systematic risk beta, dividend yield, dummy variable that is equal to 1 if the firm pays zero dividend and is equal to zero otherwise, and the natural log 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 negatively correlated. The systematic risk was not significant. When the Feb.–Dec. returns were regressed on the same independent variables, the firm size was significant and negatively correlated. Dividend variables and the systematic risk were not significant.

Arbel (1985) collected 1,000 companies: SP500 stocks and non-SP 500

companies for the period 1971-80. The SP 500 companies are divided into highly researched, moderately researched, and research-neglected companies. The non-SP 500 companies are all research-neglected companies. He found that the January returns were higher 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 500 neglected companies. Branch and Chang (1985) found that stocks whose prices were falling throughout the year tended to rise in price in the first 4 weeks of the following year. 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 over the last 5 days and the first 4 days around the turn of the year using three methods of calculating the daily return: CRSP return, close-to-close, and open-to-open. They found that the returns of small companies are high around the turn of the year and are higher than 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 groups according to Moody's bond rating system: Aaa, Aa, A, Baa, Ba, and B. They found that the January returns are pronounced for the Baa and B-rated bonds. They also examined stock returns of the firms whose bond returns were evaluated. The differences in the stock returns were not significant when the analysis of variance was applied. But when they 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 for

the period Sept. 2, 1962 to Dec. 26, 1985 and 2 subperiods. For the equal-weighted index for the NYSE and AMEX stocks, the variance ratio test did reject the null hypothesis of

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the random walk. But, the results were mixed for the value-weighted indexes. They also examined 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 of individual returns and the 3 portfolio returns were not statistically significant, meaning that they follow the random walk. However, for the equal-weighted portfolios of 625 stocks, the random walk hypothesis was rejected, and the value-weighted portfolios were supported for the random walk. However, Lo and Mackinlay (1999, p. 16) state that " the most current data (1986-1996) conform more closely to the random walk than our original 1962-1985 sample period."

Branch and Chang (1990) used the Compustat data for the period 1971-83. Using

regression analysis, they found that low-price stocks that exhibited poor December performance are likely to rebound in January. They argue that an efficient market will not necessarily eliminate such predictable price patterns due to the following factors: transaction costs (commission and bid-ask spreads), search costs (costs of identifying such 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 use the Sharpe index to obtain risk adjusted returns. They find that the day-of-the-week and the day-of-the-month effects are more pronounced in the futures indexes than in the spot indexes. However, the January effect was more evident in the spot indexes than in the futures 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.

Yilmaz (2001) use weekly data for the period 1988-2000 and applied the variance ratio tests to 14 emerging stock markets. The random walk hypothesis was accepted for Indonesia, Korea, Malaysia, Taiwan, Argentina, Brazil, Mexico, Japan, and USA, but it was 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 period 1995-2000. They used a time varying parameter model with changing intercept and slope coefficients (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 daily data ( 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 variables for 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.

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Interpretation or Rationale for the January Effect There are 2 major questions on the January effect. The first question is the reasons for 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. The most popular hypothesis is the tax-selling hypothesis, which argues that investors sell stocks whose prices have been falling during the year, and the capital loss can be deducted 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 are some objections to this explanation. (1) Such investment strategy is subject to the tax laws against wash sales (see appendix note). (2) If the tax-selling hypothesis should hold true, the January effect should be larger after World War II, when income tax rates are higher. 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 capital gains tax, or the tax year does not start in January. But, Brown, Keim, Kleidon, and Marsh (1983) found higher returns over December – January and July – August in Australia 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 period 1951-80, where the capital gains tax was absent until1973.

A second alternative hypothesis for the January effect is the portfolio rebalancing

or window dressing hypothesis, which states that around the year-end institutional investors, rather than individual investors, sell losing stocks and buy winning stocks to represent respectable portfolio holdings. However, Griffiths and White (1993) and Sias and Starks (1997) found little support for the institutional portfolio rebalancing hypothesis.

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 is implemented 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 gains taxes and the tax year does not start in January.

A fourth hypothesis is, as stated in Wachtel (1942, p.186), that the unusual

demand for cash for the holiday season (Santa Claus effect) affects investors to sell the stocks in December. To purchase gifts and to finance travel, investors may sell some stocks and bonds. This hypothesis is consistent with the increasing sales during December. The cash balances are supposed to be reinvested in the stock market after the holiday 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 explain

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the persistence of both the January effect and the firm-size effect. One is the transaction cost theory and the other is the risk premium theory. First, Roll (1983), Stoll and Whaley (1983) argue that the January effect for smaller firms may persist to exist because the transaction cost is high for the small firms relative to their prices so that arbitrage cannot remove the return differential. However, this theory would not apply to the January 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 traded infrequently 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 weighted market portfolio returns. They found that variance and beta are much larger in January than in any other month, and variance and beta are much larger for the smaller firms than for the larger firms. But why should the risk levels be higher in January than in any other month? Why should January have higher risk? They argue that January is the beginning of 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. (5) The January effect will not necessarily disappear even if the market may be efficient due to trading costs, information costs, uncertainty, and differential marginal tax rates 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 institutional investment companies. So, neither the tax-selling hypothesis nor the institutional portfolio rebalancing hypothesis will matter. However, the new-year resolution hypothesis is not necessarily applicable since January in the contemporary Gregorian calendar is not the same as January in the Chinese lunar calendar, and thus the new year resolution can take place in February. That is, the new year's day in the Chinese lunar calendar is widely celebrated in Indonesia and Korea as well as China. January in the Chinese lunar calendar generally falls in February in the Gregorian calendar. Also, in Asia the holiday season usually begins with the new year's day and lasts for a couple of days.

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III. Risk-Adjusted Return Measures Before we discuss our empirical results, it may be useful to briefly review the random walk 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 two equations: 0)()|()( ,1,, ==− − tittiti ERERE εη (3-1) )|,.......,(),.......,( 1,,1,,1 −= ttnttnt RRfRRf η (3-2)

Where = stock return at time t for stock i, (tiR , 11 /) −− +− tttt PDPP , and 1−tη = 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 on all assets should be equal to the conditional distribution of expected returns for a given set 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 model requires that the serial correlation between returns for any lag be zero, but the fair game model 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 market efficiency and the CAPM) is stated as follows: tittiti RER ,,, )|( εβ =− (3-3) ])|([)|( ,,,,, tFtmtmtiFtii RRERRE −+= βββ (3-4)

0)( , =tiE ε (3-5) where E )|( ,tiiR β = the expected return on stock i for period t, given its systematic risk, ti ,β , .0>β )|( ,tmmRE β = the expected return on market portfolio for period t, given its predicted systematic risk ti ,β and tm,β are estimated systematic risk of stock i and the market portfolio respectively for time t, estimated at time t-1 based on the set of information, 1−tη (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 adjusted returns: Treynor (1965), Sharpe (1966), and Jensen (1968): Treynor beta index = pFp RR β/)( − (3-6)

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Sharpe total index = pFp RR σ/)( − (3-7) Jensen excess return: α = )( FMPFP RRRR −−− β (3-8) It should be noted that the ratio pFp RR β/)( − is the realized risk premium per unit of systematic risk beta using the security market line theory, and the ratio pFp RR σ/)−( is the 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 total return: pFpF RRRR β/)( −+=

), if the Treynor index is used, and pRR = FpF RR σ/)( −+

),

if the Sharpe index is used. Modigliani and Modigliani (1997) show the following risk-adjusted return: )](/) MpFR σσ[( PF RRR += −

) for the Sharpe index (see appendix note).

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

Shin beta index = MFM

PFP

RRRR

ββ

/)(/)(

−− (3-9)

Shin total index = MFM

PFP

RRRR

σσ

/)(/)(

−− (3-10)

where = return on portfolio i,PR Pσ = total risk of the portfolio, = return on the market portfolio,

MR

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

F

Mβ = 1, systematic risk of the market portfolio, =pβ systematic risk of the portfolio: if Pβ < 0, the absolute value should be used. Otherwise, a negative portfolio return with a negative beta would generate a positive performance index, which is clearly wrong. The two Shin indexes are essentially the same as the Sharpe index and the Treynor index respectively. Since the denominators MFM RR β/)( − and MFM RR σ/)−( are constants, dividing the Sharpe and Treynor indexes by the constants will not change the portfolio ranking by the Sharpe and Treynor indexes. But the advantage of the Shin indexes 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 ( >− )/ PFP RR β MFM RR β/)( − (3-11) and ( >− )/ PFP RR σ MFM RR σ/)( − (3-12)

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The common weakness of the beta based risk measures is that if the beta value is not significant, unstable, extremely low, or high, the indexes can be unreliable, and the portfolio performance can be greatly overestimated or underestimated. The systematic risk can be unstable and unreliable, if the sample period is short or if the stock returns are volatile independent of the market movement. Also, as stated before, if the beta value is negative, 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, a negative return divided by a negative beta value will give a positive value, and this will clearly distort the performance of the portfolio. An advantage of the beta-based measures is 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 measure appears to have a relatively small number of theoretical objections, but has no accompanying significance test. If the risk free rate is omitted, the above 5 indexes (Equations 3-6 to 3-10) can be reduced to ,/ PPR σ PPR β/ , MPP RR β− , ),/()/( Mpp RR β and )//()/( MMPP RR σσ 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 of a portfolio, called January portfolio, and taking the 12-month average returns as the returns 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 by applying the above 5 measures of risk-adjusted returns. IV. Empirical Results If the efficient market hypothesis holds true, the risk-adjusted monthly returns should be randomly distributed and they should not show any periodic patterns. To test the hypothesis, we have selected monthly data for the following stock markets: the Standard and Poor's 500 Stocks (1971-2002), the Korea Stock Exchange (KOSPI, 1980-2002), the Tokyo Stock Exchange (Daiwa Index, 1984-2002), the Shanghai Stock Exchange (1991-2002), and the Jakarta Stock Exchange (1989-2002). The monthly stock 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)

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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 Analysis 15. 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 be randomly distributed, and thus monthly returns should not show any seasonal patterns. First, we use the ANOVA to test the following null hypothesis: 1221 ...... µµµ === (4-1) where iµ = mean returns of month i. The results of ANOVA are presented in Table 1 for the 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 the Korean stocks, 0.903 for the Tokyo stocks, 0.804 for the Shanghai stocks, and 1.20 for the Jakarta stocks. However, ANOVA is based on the following two assumptions: (1) the population monthly stock returns are normally distributed, and (2) the population variances of monthly returns are all equal. If these two assumptions are not valid, ANOVA results are not valid, and nonparametric tests, such as the Kruskal-Wallis. Three tests of normality and the Bartlett's test for homogeneity are used. The results are summarized in Table 13. First, the chi-square test for the goodness of fit rejects the normality assumption for the SP500 stocks (chi-square 13), Korean stocks (22.23), Jakarta (13) and Shanghai stocks (82.5) at the 5% level. But the normality assumption is accepted for the Tokyo stocks (4.31) at the 5% level. Second, the Lilliefors test for normality show that the Tokyo and Jakarta stocks are accepted for normality at the 5% level, but the SP500 stocks, Korean stocks, and Shanghai stocks are not. Next, Bartlett's test shows that homogeneity of variances is accepted for the Tokyo stocks, but not for the 4 other stock exchanges. Third, the Jarque-Bera test test rejects the normality hypothesis for the 5 stock exchanges at the 5% level. The Tokyo stocks can be accepted for normality at 7.3% level. The Kruskal-Wallis test, which is a nonparametric test, is equivalent to ANOVA in terms of rank numbers. The results of the Kruskal-Wallis H statistic are listed in Table 1. The results are very similar to the ANOVA results. The H statistics are lower than the critical values, and thus we cannot reject the null hypothesis that the population medians of 12 monthly returns are all equal for the 5 stock exchanges.

14

2. Chi-Square Test for the Negative Returns: In this section, we apply the chi-square test of goodness of fit for the frequency distribution of negative monthly returns. to see if the negative population monthly returns are evenly distributed among the 12 months. The results of the chi-square tests are summarized in Table 1 for the 5 stock exchanges. The chi-square test was carried out as follows. For instance, for the SP 500 stocks, for January, there were 11 times when the January returns were negative over the 32 years. This is equivalent to 34.38%. For the month of February, there were 15 times when the monthly returns were negative (46.88%). For the month of September, there were 20 times when the monthly returns were negative, and so on. The average frequency of negative monthly returns was 13.58. Based on these data, we applied the chi-square test of goodness of fit for the observed frequencies of negative returns versus the expected frequencies, 13.58%. The null hypothesis is that the observed and expected frequencies are equal. The calculated chi-square value is 13.31 and the critical chi-square value is 4.57 at the 5% level. In effect, the chi-square test cannot reject the null hypothesis that the observed and expected frequencies of monthly negative returns are equal for the 5 stock exchanges. 3. t-Test for the Monthly Returns In Table 1, the monthly mean returns are calculated for each month. For the SP 500 stocks, the highest monthly mean return is 2.14% in January, and it is higher than any other monthly return. This result is consistent with the January effect. But, the question is whether it is statistically significant. Since the ANOVA and Kruskal-Wallis tests were unable to reject the null hypothesis that the 12 monthly population mean returns are equal, this time we tested the null hypothesis that the January population mean return or any other monthly return is equal to the population mean of 12 monthly returns:

µµ =i (4-2) where =iµ population mean return of month i, and µ = population mean of monthly returns. The results for the t-test for the paired samples are summarized also in Table 1. 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 negative September return was significantly different from the mean of the 12 monthly returns. In effect, 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 at 4.37%. 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%) and September (-2.01%). But when the 1998 data (financial crisis) are excluded, the March return is the highest at 3.57% and significant. The negative returns are significant in August (-2%) and September (-2.1%). These results do not support the January effect in Korea, but the positive March effect, and the negative August and September effects.

15

For the Tokyo stocks, the highest return is 2.91% in March, and it is significantly different 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 is 4.04% in December, and it is significant. The negative return is the largest at -5.52% in September, and it is significant. Excluding 1989 (high outlier) and 1998 data (the aftermath year of financial crisis), the May return is the highest at 4.83%, and it is significant. The next highest return is in December at 4.51%, and it is significant. The negative return is the highest in September at -4.36%, and it is significant. The positive December 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 entire sample period, 1991-2002, but it is not significant. None of the positive monthly returns is significant. But there are 3 months of negative returns, namely July, September, and December, and they are all significant. Excluding 1992 and 1994 (extremely high outliers), 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%), and December (-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 = ( PPR σ/ ), ( PPR β/ ), Treynor index = ( MPP RR β− ), Jensen's excess return = R-bRm, and Shin-beta index= ),/()/( Mpp RR β and Shin-total index = ( )//()/ MMMp RR σσ The results are presented in Table 1 for the 5 stock markets for the selected sample periods excluding outlier years. On the excess return basis (R-bRm), the highest return is 0.975% in December for 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 for Shanghai. 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 for Korea, 2.486 in March for Tokyo, 5.486 in December for Jakarta, and 0.754 in February for Shanghai.

16

Which month has the highest risk? The results are also mixed. The largest beta is 2.18 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 is 5.64 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 worst months for the positive and negative returns on the simple return and risk-adjusted bases are summarized in Table 15. 5. Regression Analysis with Dummy Variables A regression method of testing the January effect is to use dummy variables as used by Keim (1983), and others (Kato and Schallheim,1985). It takes the following form: (4-3) eDbaR tt tt ++= ∑ =

12

2

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

3D

2bD+ . Thus, if the coefficients of the dummy variables are all negative, it indicates that the January return is the largest, and it is consistent with the January effect. If the coefficient of a dummy variable is positive, it indicates that the given month's return is greater than the January return. The regression results with the dummy independent variables are summarized in Table 2. For the SP500 stocks, the dummy variables have negative coefficients, and the results are consistent with the January effect. The intercept is 2.1293 and it is highly significant. 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 R2

=0.0150 is not significant. 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 with the January effect. However, when the 1998 data are excluded, the dummy variables for March and November have positive signs, indicating the March and November expected returns 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 the coefficients are not significant. For the Jakarta stocks, all the dummy have negative variables, but the coefficients are not significant except for the negative signs for august and 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 at the 5 % level. In effect, the regression results with dummy variables are consistent with

17

the January effect only for the SP 500 stocks, but the regression model is not significant in terms of the F-value. 6. Correlation Analysis Thus far we have examined whether there are significant differences in the monthly returns or periodic patterns in the monthly returns. According to the random walk hypothesis, all monthly returns should be randomly distributed and the expected values of the monthly returns should be equal. The conventional statistical methods, such as ANOVA and Kruskal-Wallis tests cannot reject the null hypothesis that all monthly returns are equal. However, the t-tests of paired samples indicate that some monthly returns are significantly higher or lower than the mean of the 12 monthly returns. But the results tend to be inconclusive because the statistical significance is sensitive to the sample. Exclusion of certain observations can significantly alter that mean return and statistical significance. Another proposition of the random walk hypothesis is that the monthly returns should be independent of other monthly returns. To test this hypothesis, correlation coefficients 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% or 5% 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 significantly correlated to the April, June, and July returns. The July return is highly correlated to the October 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 returns are 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 13 significant correlations, if 1992 and 1994 are excluded. The January return is correlated to March, April, May, and November. For the Jakarta stocks, there are only 2 significant correlations for the period 1989-2002, and 3 significant correlations, if 1998 data is excluded. The above correlation results do not support the random walk hypothesis, strictly speaking. However, the conclusion is tentative for two reasons: First, the correlation coefficients are highly unstable, particularly in the Asian stock markets. Second, the correlation can be spurious. Fama and Blume (1966) selected the Dow-Jones 30 Industrial stocks, and they regressed today's return on each of the 5 lagged return variables and found significant correlation coefficients for the 30 stocks, but the coefficients of determination were very low, less than 0.123. There are many correlation studies on the other stock markets, such

18

as Norway, Sweden, Australia, UK, and Greece. The largest correlation coefficient was 0.134 for these countries (Granger, 1968; Elton et al., 2003). We will also test regression analysis 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: tttttttttt uRaRaRaRaaR ++++++= −−−−−−−− 12123322110 ...... (4-4) where = the monthly returns for the preceding 12 months. 121 ,...., −− tt RR In the above function (4-3), the January monthly return, for instance, is a function of 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 period was 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 one significant variable (t-value at the 5% level): January, March, April, and August. For example, 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's July and August returns. The August return is significantly correlated to last year's October return. Next, for the Korean stocks, the April return is significantly correlated to last year's returns of January, February, March, April, May, June, July, and September. The adjusted R2 is 0.7348. The July return is significantly correlated to last year's February return. 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's February return. The May return is significantly correlated to last year's July return. 8. ARIMA, ARCH, ARCH-M, and GARCH Models A time series model with a single dependent variable can be expressed by the following ARIMA (autoregressive integrated moving average) model: qtqtttptpttt eeeeyyyy −−−−−−− −−−−++++= βββαααα ..... 2211022110 (4-5) where are the autoregressive terms, and are the white noise error series. It states that dependent variable is a function of lagged dependent variables and error series.

ity − ite −

ty A random walk series can be expressed by an ARIMA model, ARIMA (1,0,0): (4-6) ttt eyy += −1

19

or, ttt eyy ++= −1δ (4-7) where δ = a constant or drift term. Equations (4-6) and (4-7) are estimated in arithmetic values and natural logarithms. The ARIMA models were tested for the 5 stock exchanges. The results are summarized in Table 5. For the SP 500 stocks, the adjusted R2 values are high and the coefficients of the MA term are close to 1.0 for all equations, with and without the drift term, in logarithms and arithmetic values. But the highest adjusted R

1−ty2 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 that the ARIMA models are appropriate and the residual series have no significant periodic patterns. For the Korean stocks, the highest adjusted R2 (0.9881) is obtained for the log model with a drift term. The Q statistics indicate that the residual series are white noise for the two log models, but not for the two non-log models. Similarly, the log model with a 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-log models are white noise, but the residual series are not white noise for the log models. For the Jakarta stocks, the adjusted R2 is the highest at 0.8705 for the model in arithmetic values with a drift term. The Q statistics indicate that the residual series are white noise for all 4 models. These results strongly support the random walk hypothesis for all 5 stock exchanges. For the monthly return series, various ARIMA models were tested, such as ARIMA(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 R2 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 and Shanghai stocks, there are one and two significant variables respectively. The Q statistics indicate that the residuals are not white noise for the SP500, Korea, Jakarta, and Shanghai stocks. But the residuals are white noise for the Tokyo stocks. In effect, the ARIMA models tend to support the random walk hypothesis for the 5 stock exchanges (see 10. autocorrelation analysis and appendix note). In Table 6, heteroscedasticity is tested in AR(1) with ARCH, ARCH-M and GARCH models. The ARCH model can stated as r ttt ur ++= −110 ββ (4-8) h (4-9) 2

1102

−+== tt uαασ

20

Estimation equations for the ARCH-M and GARCH models are listed in appendix note. The monthly return is calculated as the first difference in log monthly stock price indexes, rt = ln ; = the error term, and = error variance. In Table 6, we note the following results. For SP500, SP500 total return index, and NASDAQ stocks, there are some significant alpha coefficients in the variance equations for the ARCH model or GARCH model. For the Dow-Jones stocks, the variance equation is not significant. There are also significant alpha coefficients for the Korean and Shanghai stocks in the GARCH models, but there are no significant alpha coefficients in the variance equation for Tokyo and Jakarta markets. However, when the Lagrange multiplier method was used, heteroscedasticity was not significant for all 8 stock markets in spite of extreme outliers

1ln −− tt pp tu 2tσ

In the Asian stock markets. 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: (4-10) ttt eyy += −1

ttt eyy ++= − 01 α (4-11) ttt etyy +++= − 101 αα (4-12) Two tests are most widely used to test the unit root process: the augmented Dickey-Fuller test and the Phillips-Perron test. For the Dickey-Fuller test, the following two test regression equations are used: one with a constant and no trend, and the other with a constant and trend. ∆ (4-13) tjt

p

j jtt YYY εγαα +∆++= −=− ∑ 1110

∆ tjt

p

j jtt YtYY εγααα +∆+++= −=− ∑ 12110 (4-14)

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

1α = 0 for the unit root process. If ,0<α we would accept the alternative hypothesis that the series is stationary series. The lag- terms jtY −∆ are added to correct the problem of serial correlation in the regression equations. In the Phillips-Perron test, a non-parametric correction method , i.e., the Newey-West method, is used to estimate the error variance to correct the problem of serial correlation in the error terms..

21

The statistical results of the above two tests are summarized in Table 5 for the 5 stock exchanges. The test statistic is -1.0914 for the SP 500 stocks for the constant and no trend model and the critical value is -2.57. The test statistic is -1.3207 for the constant and trend model and the critical t value is -3.13 at the 10% level. Since the test statistic exceeds the critical value, we accept the null hypothesis of unit root. For the Korean stocks, the test statistic is -2.6395 for the model with constant and no trend, and the critical value is -2.57. Thus we reject the null hypothesis of unit root for the model. However, we note that for the model with a constant and trend, the test statistic is -2.2821 and the critical value is -3.13. Thus we accept the null hypothesis of unit root. Similarly, the test statistics indicate that the stock prices are of the unit root for all 5 stock price indexes. If two non-stationary variables are used to calculate regression and correlation, the correlation can be spurious. There are two remedies. First, differenced values can be used if the variables are difference-stationary. Second, if the two non-stationary time series are cointegrated series, the level-variables can be used for regression without causing a spurious correlation. If two times series are cointegrated, it implies that the two times series have a long-run equilibrium relationship. To examine if the 5 stock exchange prices have long-run equilibrium relationships, we have also applied two types of cointegration tests: the Dickey-Fuller test and the Phillips-Perron test, though the Johansen method which uses the maximum-likelihood procedure for estimation is widely used. In the Dickey-Fuller test of cointegration, two types of cointegration regression equations are first calculated, as shown by equations (4-13) and (4-14). For two variables X and Y, any variable can be selected as the dependent variable (regressand): (4-15) tjt

M

j jt uXY ++= ∑ = ,10 ββ

(4-16) tjt

M

j jt uXtY +++= ∑ = ,110 βββ

. 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: ∆ (4-17) tit

p

t ittt vuuu +∆+= −=− ∑ 11 αα where α = 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 method is concerned with the correction method of serial correction, as mentioned before. If the residual 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 two

22

variables are not cointegrated, differenced variables should be used for regression analysis to avoid spurious correlation. However, if the two variables are cointegrated, the level variables can be used for regression analysis without the problem of spurious correlation. The results for the variance ratio test are summarized in Table 7. The z-scores indicate that we cannot reject the null hypothesis of the random walk. For q=30, the high z-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 8). The results support randomness for the 5 stock exchanges for the median values. But the runs tests for the mean values support for the 4 stock exchanges except for the Korean stocks. When the runs test was applied to monthly returns for each month, the random walk hypothesis is supported for the 5 stock exchanges (Table 9). The cointegration test results for the pairs of the 5 stock exchange monthly stock prices are summarized also in Table 10. The test statistics indicate that we cannot reject the null hypothesis of non-stationarity (random walk) between the pairs of the monthly stock price indexes. In effect, the tests do not indicate any long-run equilibrium relationships between the stock exchanges over the sample period. 10. VAR Models To examine if there are independent relationships among the stock markets, the following VAR models are applied to the monthly returns and monthly stock prices in the 5 stock exchanges:

Y 112110 ... uZY ttt ++++= −− ααα (4-18) Z 212110 ... uZY ttt ++++= −− βββ (4-19) where Y , …. , = monthly stock price indexes or monthly returns of the 5 stock exchanges. The results are presented in Table 11. For the monthly returns, there are no significant variables in each equation at the 5% level. Only for the SP500, the lagged Jakarta is significant at the 5.49%. For the monthly prices, in all equations, its own lagged stock price is significant. But for the SP500 stock prices, the lagged Jakarta and lagged Shanghai are significant. When tested without the Shanghai stocks, the results were very similar as to the significance of the variables in each equation.

t tZ

11. Autocorrelation Analysis

23

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

2

1

1

)(

))(()(

yy

yyyyky n

t t

ktn

kt t

−

−−=

∑∑

=

−+= (4-20)

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-square distribution with k-c degrees of freedom, where c = the number of autocorrelation coefficients, k = selected lag length in the autocorrelation function. It is used to test the null 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 autocorrelation functions (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 series is a random walk series, the autocorrelation coefficients are expected to be high over the shorter time lags and gradually decline. We note that the autocorrelation functions exactly follow the patterns of random walks for the 5 stock price indexes. On the other hand, the autocorrelation functions of the monthly returns are not significant in all 5 series. The Q statistics indicate that the monthly return series are white noise These results 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 into sine 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 sine curves of different frequencies. The Fourier analysis is to find optimal coefficients in the following finite Fourier function:

tfk

f ft eNft

Nfty +++= ∑ =

]2)sin(2)cos([2 1

0 πβπαα

(4-21).

If the α or β coefficient is large and significant, it indicates a strong periodicity at the given frequency. The coefficients α and β are converted to amplitude and phase angles for each frequency. The periodogram is defined by (4-22) 2/)( 22

fff NP βα += where = periodogram (periodogram value) at frequency f, and N = total number of observations.

fP

24

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 line spectrum indicates periodicity. If a series is a linear trend series, the periodogram would show a flat line. If a series is a random walk series, the periodogram would show spikes of 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 their analysis, they used logarithmic first differences for the following reasons: First, the transformed data have more symmetric and more nearly normal histograms. Second, if the 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. That is, when cycles are present in a time series, spikes are expected to show up in the periodograms. In effect, the periodograms do not reveal any significant spikes to indicate seasonal 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 market should be available in another stock market instantaneously, and thus stock market returns 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's stock 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 are correlated, it would contradict the random walk hypothesis. Reilly and Wright (represented in Reilly and Brown, 2003, p.94) calculated correlation 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 high correlation with the Toronto stocks (0.769), the London Stock Exchange (0.641), and the Frankfurt 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 period 1989-2002. The correlation coefficients are significant between monthly returns for the 4

25

stock exchanges, namely, SP500, Korea, Tokyo, and Jakarta, but the Shanghai stocks are not correlated to the other stock market returns (See Table 12). Next, correlation coefficients were calculated for the 5 stock exchanges by month for the period 1991-2002. The Shanghai stocks did not also show any significant correlation with other stock exchanges. So, omitting the Shanghai stocks, the correlation coefficients were recalculated for the 4 countries for the period 1989-2002. The results are presented in Table 7. It is interesting to note that the 4 stock returns are not always correlated. For instance, the Korean stocks are correlated to the Jakarta stocks only in January and April. The US stocks are correlated to Jakarta stocks only in March. The US stocks are correlated to the Tokyo stocks only in May, June, and August. It is interesting to note that the Korean stocks are not correlated to the SP500 stocks in any month, though the correlation coefficient is significant for the overall period (0.278). The Korean stocks are correlated 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. The Tokyo stocks are, as stated before, significantly correlated to the Korean stocks in February, April, May, June, July, and August. The Jakarta stocks are correlated to the Korean stocks in January and April. The Jakarta stocks are also correlated to the SP 500 stocks only in March. But the Jakarta stocks are not correlated to the Tokyo stocks in any month. Simple and multiple regression equations are calculated for monthly stock prices in 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 index is significantly correlated with other 4 stock prices indexes. (2) The Korean stock price index is also significantly correlated with other 4 stock price indexes. (3) The Tokyo stock 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 index is correlated with the Korea, SP500, and Shanghai stock prices indexes, except for the Tokyo stock price index. (5) The Shanghai stock price index is significantly correlated with other 4 stock exchange price indexes. As for the multiple regression results, we note the following. (1) For the SP500 stock price index, the Tokyo and Korean stock price indexes are significant. (2) For the Korean stock price index, 3 stock exchange indexes are 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 the Shanghai stock price index, the Tokyo and Jakarta stock price indexes are significant, but the Korean index and SP500 indexes are not significant. However, these statistical results are subject to estimation problems since the data contain extreme outliers and the low DW statistics indicate significant serial correlations. 14. Characteristics of the 5 Stock Exchanges Some descriptive statistics and other characteristics of the Asian stock markets are

26

Summarized in Table 14. The sample period varies with the stock market due to availability of data. Over the available sample period, the Shanghai stocks have the highest average monthly return at 3.2841 % during the 12 years (1991-2002). The next highest average monthly return is for the Korean stocks, with the average monthly return of 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 average return (0.3554%) for the period 1984-2002. The total risk is the largest at 22.3845% for the Shanghai stocks, corresponding to 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 the Tokyo 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 the 5 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 highest median 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-risk relationship does not hold true. Next, we have applied the chi-square test and Lilliefors test for the null hypothesis that monthly returns are normally distributed. The chi-square test supports normality for the Tokyo stock returns, and the Lilliefors test supports both Tokyo and Jakarta stock returns 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 analysis was applied. The results are summarized in Table 15. When 5 factors are specified, the results show that 2 factors are significant. When 4 factors are specified, the Tokyo and Korean stocks are grouped to the common factor. The Jakarta stocks, SP500, and the Shanghai 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 are independent. Finally, when two factors are specified, Korea, SP500, Tokyo, and Jakarta belong to the common factor and Shanghai is independent. In Table 16, the correlation coefficient 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 significantly correlated 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 stock returns. The results are summarized in Table 17. As we have reviewed before, the simple average monthly return is the highest at 2.038% in Shanghai, and the next highest returns are 0.853% in Korea, 0.623% in Jakarta, and 0.695% for the SP 500, and 0.31% in Tokyo.

27

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 monthly mean return series of individual stock exchanges. The results show that only the mean of the Tokyo return series is significantly lower than the mean of the average series of the 5 stock exchanges. The total risk (standard deviation) is calculated from the 12 monthly returns over the sample period for each exchange. The total risk is the highest in the order of Shanghai, Jakarta, Korea, Tokyo, and SP500. The systematic risk beta is obtained by regressing the monthly return series of each stock exchange on the average monthly return series of the 5 stock exchanges. The systematic risk is the highest at 1.7496 for Shanghai, 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 - β Rm), Shanghai has the highest excess return at 0.333%, and the next highest excess returns are 0.2427% for SP500, 0.0323% for Korea, -0.3280 for Tokyo, and -0.40185 for Jakarta. On the Return/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 (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 performance during 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. Another reason 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 positive January effect and the negative September effect are significant. For the Korean stocks for the period 1980-2002, excluding 1998, the positive March effect and negative August and 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 November effect is significant. For the Jakarta stocks, the positive May and December effect, and negative August and September effect are significant. As for the risk-adjusted returns, the results vary with the risk-adjustment measures, as shown in Table 18. For the SP 500 stocks, January concedes to March and December. It is interesting to note that December can be good for the SP 500 stocks, but bad for the Shanghai stocks. For the negative returns, all 5 measures point to December as a bad month for the stocks.

28

These results do not support any of the three hypotheses to explain the January effect since there is no January effect in the Asian stock markets. However, it is interesting to note that the monthly returns tend to be higher in the springtime in the Asian 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, and Tokyo. The bad month is August for Jakarta and it is December for Shanghai. Why the springtime effect in Asia? As briefly mentioned before, the new school year starts in March in Korea, and in April in Japan. The new year in Chinese lunar calendar begins in February in the Gregorian calendar. 17. The January Barometer Theory The January effect discussed in this paper should not be confused with the January effect of version 2, which is often called the January predictive hypothesis or the January barometer theory. The January barometer theory states that the January return is a predictor of the stock market conditions of the rest of the year. That is, if the January return is high, the stock returns for the rest of the year should be also good. Bloch and Pupp (1983) used the SP500 stock indexes for the period 1950-82. They calculated 12 regression 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 the January return is not significant in predicting the next 12 month stock returns. To test the January barometer theory, we test the following simple regression equations for the Asian and US stock market monthly returns: iiii xy βα += , where x = the January return. For the dependent variable, we have tested two types of average returns: = the average of monthly returns, January to December, and y = the average of monthly returns, February to December, excluding the January return of the year. The regression results are summarized in Table 19. When the dependent variable is y , the January return is significant for the 4 US stock markets, Korea and Tokyo stock markets. But, it is not significant for Jakarta and Shanghai stock markets. The significance is largely due to the fact that the dependent variable, i.e., the average of the 12 monthly returns, includes the independent variable, i.e., the January return (built-in effect)

1y

2

1

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

excluding the January return, the independent variable, i.e., the January return, is significant at the 5% level only for the SP500 total index returns. It is not significant for all other stock markets, namely, the SP500, Dow-Jones, NASDAQ, and the 4 Asian stock markets. These results generally support the Bloch-Pupp conclusion that the January return is statistically not significant in predicting the average return for the next 11 months. IV. Summary and Conclusions We have applied various statistical analyses to the monthly returns of the 5 stock exchanges to find if there exist monthly or periodic patterns, such as the January effect that contradict the random walk theory. We have applied ANOVA, the Kruskal-Wallis

29

test, the chi-square test, the runs test, etc. These tests showed that we cannot reject the null hypothesis that the population monthly returns are all equal. Also, we have applied regression analysis, autocorrelation analysis, and the VAR models. These results tended to support the random walk theory in the sense the coefficients were mostly not significant or the R2 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 models and autoregression analysis were consistent with the random walk theory. The spectral analysis did not show significant periodical patterns. These results are also consistent with the random walk theory. Correlation analysis was applied to the monthly returns of the 5 stock exchanges for the period 1991-2002. The results show that the SP500 stocks, Tokyo stocks, Korean stocks, and the Jakarta stocks are significantly correlated. The Shanghai stocks were not correlated to any other stock markets. When the correlation coefficients were calculated by month, the correlation coefficients were significant only for some months and not for all months. For instance, the Korean stocks were correlated to the Tokyo stocks only for the months of February, April, May, June, July, and August. The Korean stocks were not correlated to the SP 500 stocks in any month. The Tokyo stocks were correlated to the SP 500 stocks only in May, June, and August. The Jakarta stocks were correlated to the Korean stocks in January and April. The Shanghai stocks were not correlated to any other stock markets. Since we have examined the stock market behavior in the selected Asian countries, two interesting questions may be briefly discussed. First, do the March and September effects, for instance, imply that if investors buy SP500 stocks, the Korean stocks, the Tokyo stocks, and the 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 largest risk-adjusted excess returns? Should the investors in Shanghai buy stock indexes in December (or the last trading day of the month), and sell in April or June? The second question is, do these March and September effects or the June, April and December effects contradict the random walk theory? For the first question, the answer depends upon many factors. First, if the market is efficient, the information on the March and September effects should travel fast and arbitrage activities is supposed to wipe out the opportunities for the excess risk-adjusted returns. If the market is inefficient, excess returns can be made. Second, the March and September effects are concerned with the expected returns. That is, 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 the long period. Thus, following the above trading rule will not guarantee that the investors will make the highest excess returns every year. Third, the excess risk-adjusted return does not mean a return net of trading costs. Fourth, we have used systematic risk beta and standard deviation as total risk in measuring the risk-adjusted returns. However, there may be other risk types that are more important. That is, if systematic risk or total risk underestimates the true relevant risk, the true risk-adjusted return should be lower than the wrong risk-adjusted return, and the apparent March or

30

September effect can persist. For the second question, unless these questions are answered, it is difficult to conclude that the stock prices do not follow the random walk on a risk-adjusted basis. Finally, the following points may be noted. First, our study is a macro analysis in that we dealt with the aggregate stock market indexes instead of individual firm's stock prices or portfolio returns. Thus, this study does not directly contradict the January effect found over the first weeks of new years for individual small firm-stocks or portfolios. Second, the stock returns in this study are calculated based on the closing prices of the last trading day for each month. It is possible that the results could be different, if the prices at the beginning of the month or at the middle of the month, or daily prices are used. Third, the systematic risk beta values are highly unreliable since the beta values are mostly not significant. A better or reliable method of risk measurement is needed. Fourth, except for the Tokyo stocks, the stock returns do not include dividend payments. Stock returns with dividend payments can bring different results, as we have seen that the Tokyo stock returns were normally distributed. Fifth, it may be useful to examine also other stock markets in Asia, such as Thailand, Hong Kong, Taiwan, and the Philippines. Appendix Notes: Note 1: Stock market indexes The SP500 Stocks: In New York, 24 brokers formed the first organized stock market in 1792. In 1863 during the Civil War, the organization was named New York Stock Exchange. As of December 2002, there were 2,783 listed companies and 2,959 issues on the NYSE. Instead of NYSE index, the Standard and Poor's 500 Index is used in this paper. It is a value weighted index of 400 industrial stocks and 100 financial corporate stocks that are traded on the NYSE, AMEX, and the National Market System (NASDAQ). The companies are leading companies in the leading industries in the United Stated. The base period index is set at 1941-43=100. The monthly closing closing prices are used to calculate the percentage change in the price index. The index does not include dividend payments. The AMEX started as Outdoor Curve Market in 1840's, and it moved inside in 1921 as New York Curb Exchange. The name was changed to American Stock Exchange in 1953. The NASDAQ (National Association of Security Dealers Automated Quotation) Stock Market system started in 1971 as the world's first electronic stock market. The number of companies listed on the Nasdaq stock market system was 3,765 as of September 30, 2002, and the number of stock issues was 4,001. The stocks are divided into two categories. The larger companies (about 3000), are traded on the Nasdaq National Market, and the smaller companies are traded on the Nasdaq SmallCap Market. There are more than 13 Nasdaq indices. The two major indices are: (1) NASDAQ Composite Index measures all Nasdaq domestic and international based companies (about 4001 companies). It began in 1971 with a base of 100. (2) NASDAQ National Market Composite Index is a subset of the NASDAQ Composite Index listed in the NASDAQ National Market (about 3000). It began in 1984 with a base of 100. All Nasdaq indices are value weighted indices.

31

The number of companies listed on the AMEX was 678 as of September 30, 2002, and the number of issues was 777. In 1998, the AMEX and the NASD (National Association of Security Dealers Association) merged to form the NASDAQ-Amex Market Group. The Amex now trades NASDAQ stocks on an unlisted trading privileges (UTP) basis. The Korea Stock Price Index (KOSPI) is a value weighted index. There were 837 listed stocks in the Korea Stock Exchange as of Nov. 22, 2002. The KOSPI index was installed in 1983, and the base index was set at 100 for the average price level of August 1983. The monthly closing price was used to calculate the percentage change in the KOSPI. No dividend payments are included. The Shanghai Stock Price Index is a value weighted average index. There were 1,185 listed stocks in the Shanghai Stock Exchange as of November 1, 2002. There are 2 stock exchanges in China. The Shanghai Stock Exchange started trading on Dec. 17, 1990 and the Shenzhen Stock Exchange commenced trading on April 3, 1991. There are two classes of shares traded in both exchanges. The A shares are for domestic investors and the B shares are for the foreign investors. Other classes include C, H, and N shares for over seas investors in Hong Kong and New York. The Jakarta Stock Price Index is a value weighted average index. There were 276 listed stocks in the Jakarta Stock Exchange (Harga Saham Gabungan) as of Nov. 1, 2002. The Tokyo Stock Exchange opened in 1878. After World War II, it reopened in 1949, and closed down during World War II. It reopened in 1949 after World War II. There were 1,496 listed stocks in Section 1 and 581 listed stocks in Section 2 as of January 2, 2003. Of the listed stocks, 2,119 were domestic stocks and 34 were foreign stocks. In this study, instead of Tokyo Stock Price Index (TOPIX), we have used the Daiwa Tokyo Stock Price Index, which was developed by Daiwa Institute of Research. It includes only stocks listed in Section 1 of Tokyo Stock Exchange. The Daiwa index is calculated as follows: (1) Calculate the total rate of return on each stock including the dividends (2) Then calculate the index return by weighting each stock's return with its market capitalization of the previous day. (3) Then calculate: the index for current day = (index for previous day)(1+ index return(1+index return). In this study, the stock return is calculated as the percentage change in the Daiwa Tokyo Index. Daiwa Institute of Research also publishes the Daiwa All Stock Index, which is a value weighted average index, including dividends. It consists of all stocks listed on the Tokyo, Osaka, and Nagoya stock exchanges, and those registered on the JASDAQ. It consists of 3,424 stocks, 500 large stocks, 90.32% of market share, and 2,924 small stocks, 9.68%. In effect, the stock price indexes for the above stock exchanges are all value weighted indexes. Rozeff and Kinney (1976) and Lo and MacKinlay (1988) tested both value-weighted indexes and equally weighted indexes. Equally weighted indexes tended to support the non-random walks. In this paper, equally weighted indexes were not tested since the data are not available. We tested the Dow-Jones stock price index which is a price-weighted index. The results were very similarly to the SP500. Note 2: Capital gains tax countries In 1995, the following countries had the capital gains tax: the US, 28%, Canada, 23.8%, France, 18.1%, Italy, 25%, Japan, 20%, and Sweden, 16.8% (Moor and Silvia, 1995).

32

According to ACCF (1998), the capital gains tax rates are as follows: (1) USA For individuals: 39.6% for the short-term gains, 20% for the long- term gains. For corporations, 35% for both short and long-term gains. (2) Korea For individuals and corporations: 20% for both short-term and long-term gains, but they are exempt for the shares traded on the major exchanges. (3) Japan For individuals, 20% of net gain, or 1.25% of sales price for both short and long-term gains. For corporations, 34.5% for both short and long-term gains. (4) Indonesia. For individuals and corporations, 0.1% for both short and long-terms gains. (5) China For individuals, 20% for both short and long-term gains, but they are exempt on the shares traded on major exchanges. For corporations, 33% for both short and long-term gains, but they are exempt on the shares traded on the major exchanges. Note 3: Tax loss selling and wash sale in the US. In the US tax law, capital loss is subtracted from capital gain, and the net capital loss is deductible from ordinary income up to $3,000 for the year. The excess loss is carried forward. However, "You cannot deduct losses from sales or trade of stocks or securities in a wash sale. However, "You cannot deduct losses from sales or trades of stock or securities in a wash sale. A wash sale occurs when you sell or trade stock or securities at a loss and within 30 days before or after the sale you 1) buy substantially identical stocks or securities, 2) acquire substantially identical stocks or securities in a fully taxable trade, or 3) acquire a contract or option to buy substantially identical stock or securities. If you sell stocks and your spouse or a corporation you control buys substantially identical stocks, you also have a wash sale. If your loss was disallowed because of the wash sale rules, add the disallowed loss to the cost of the new stock or securities. The result is your basis in the new stock or securities. This adjustment postpones the loss deduction until the disposition of the new stock or securities. Your holding period for the new stock or securities begins on the same day as the holding period of the stock or securities sold." (Investment Income and Expenses: Including Capital Gains and Losses, for Use in Preparing 2002 Returns, IRS Publication 550, 2002, p.52). Note 4: Stock market behavior and the random walk There are 4 types of possible stock price behavior or stock return behavior: (1) the fair game model: ,0)|(( 11 =− ++ ttt rErE η (2) the submartingale: E ,0)|( 1 >+ ttr η (3) the martingale: ,0)|( 1 =+ ttrE η and the random walk: )|....,(....,(

1,,1,1)1,,1,1 ttnttnt rrfrrf η++++ = . These

forms can be stated in terms of price levels. The random walk equation implies that all the parameters of a distribution (such as mean variance, skewness, and kurtosis) should be the same with or without information set tη for all stocks 1 to n. (Copeland and Weston, 1992, pp. 346-347) Note 5: Statistical and economic efficient market hypotheses: There is a controversy on the difference between the random walk theory and the efficient market hypothesis (Malkiel, 2003). For the purpose of clarification, I would divide the efficient market hypothesis into two categories: statistical forms and economic

33

forms. The statistical forms of the efficient market hypothesis can be expressed by the following 3 equations (weak form, semi-strong form, and the strong form): (1) ),...,( ,2,1 tntttt eRRRfR −−−=

(2) ).....,...,...,...,( ,2,1,2,1,2,1,2,1 tttttttttt eZZYYXXRRfR −−−−−−−−=

(3) ),...,,.....,...,...,,...,( 21,2,1,2,1,2,12,1 tttttttttttt eHHZZYYXXRRfR −−−−−−−−−−= where Rt = stock return (daily, weekly, monthly, annual), X , Y , and Z = a series of publicly available information variables, and H = a series of inside information variables. In Equation 1, to support the random walk theory (i.e., the weak form of the statistical efficient market hypothesis), none of the independent variables, i.e., lagged variables, should be significant. To support the semi-strong form of the statistical efficient market hypothesis), none of the publicly available variables should be significant. To support the strong form of the statistical efficient market hypothesis, none of the inside information variables, as well as other independent variables, should be significant. Suppose that some independent variables are found to be significant in the above equations. It would reject the statistical efficient market hypothesis. However, to reject the economic efficient market hypothesis, one must develop trading rules based on the information given by equations (1) to (3) and must show that extra returns above the buy- and-hold policy and above the market portfolio return, on a risk-and-cost adjusted basis, can be obtained consistently. Mauboussin (2002) lists the following points against the standard, classical capital market theory: (1) stock market returns are not random, (2) investors are not rational, (3) stock returns are not normal, and (4) risk and return relationship (CAPM) is ambiguous. He argues that the stock market should be regarded as a complex adaptive system. Under the new paradigm, determinate and unique equilibrium solutions should be replaced with multiple equilibria; risk and return or the cause and effect should be replaced with nonlinear relationships, and traditional discounted cash flow analysis should remain the key value. Note 6: Risk-adjusted measures : Given the CAPM model R ),( FmpFp RRR −+= β ).( FmpFp RRRR −=− β For Jensen's α and pβ values are obtained as an intercept and slope of the regression line by regressing on such that RFP RR − )Fm R− Fp R(R ).( Fmp RR −+=− βα However, when

pβ are given and the mean values R Fp R− and FRmR − are known, α can be obtained by: α = ).Fm R−(RpFp R −−R β And when is dropped, FR mp RR βα −= . Another measure of portfolio performance is Sharpe's information ratio (Sharpe, 1994; Goodwin, 1994), which is also known as the appraisal ratio: Information Ratio =

ERBp RR σ/)( − , where any benchmark return an analyst wants to use as a criterion for the purpose of comparison, such SP500 average return, historic average return of the 1-month or 3-month Treasury bill, or any other benchmark rate,

=BR

ERσ = standard

34

deviation of the excess return ( Bp RR − ), which is called the tracking error. The excess

return is equal to , tFBBp RRRRR εα +=−=− )(( FP R −− ) tε = residual risk (Goodwin, 1998, p.35).

pFRpR σ/)

Fp RR−

pβ/)−

p

)

pFp RR β/)( −+Fp RR =)

)](/) MpFR σσ pFP RR σ/)−

pFRPR σ/)−(

m

Aσp

FP RRσ

=−

mp

FP RRA σσ−

=

Fp R− pσ

)[( MFPF RRR −+ ](/) p σσ

mβ

mpFR ββ ]/) pFP RR β/)( −+FRR =)

In the above measures, ( is the realized excess return (risk premium) per unit of the total risk, and ( is the realized excess return per unit of

systematic risk. Thus, the "risk adjusted return" is equal to R pFpF RRR σ/)( −+= if

the Sharpe index is used, and to if the Treynor index is used. Modigliani and Modigliani (1998) present another measure of risk-adjusted performance. It is a modified Sharpe index, and it is given by )

[( PF RRR −+= , where ( is the Sharpe index. It is multiplied by the total risk of the market portfolio and the risk free rate is added. It is derived as follows. Since

FRis the slope of a straight line CML for pσ , we

have the following property of proportion:

. Thus,

where A is the "extended excess return" of R when is extended to the market total risk mσ . Then, the risk-adjusted return can be written as R =

)

Since the Modigliani index is obtained by multiplying the Sharpe index by a constant mσ , both indexes lead to the same ranking of portfolio performance. The advantage of Modigliani measure is that the it can be directly compared to the market portfolio return. The Modigliani index is not applicable to the Treynor index, since such adjustment does not affect the Treynor index, because =1:

PF RRR [( −+=)

= There is Fama's (1972) performance measure: Over-all performance index = Selectivity + Risk, and Selectivity = Net selectivity + Diversification, and Risk = Manager's risk + Investor's risk. The risk-adjusted measures are explained in Reilly and Brown (2003) and Reilly and Norton (2003). Note 7 ANOVA and Kruskal-Wallis Tests To compare the sensitivity of the tests, the following experiments were conducted: In place of the January returns for the SP500 stocks, we have replaced with constants, such as 2.0, 2.5, and 3.0. The results show that the Kruskal-Wallis test is more sensitive. January returns ANOVA Kruskal-Wallis 2.0 1.3671 p=0.1862 18.710 p=0.0665 2.5 1.6149 p=0.0923 22.769 p=0.0190

35

3.0 1.9362 p=0.0337 26.817 p=0.0049 Note 7 Three betas: Keim (1983, p. 18) used three estimates of beta values to measure the risk-adjusted excess returns: (1) The OLS beta was obtained regressing daily portfolio returns against the daily returns of the CRSP value-weighted index for the period 1963-79. (2) The Scholes-Williams beta are defined as bi=∑+

−=+

1

1)21/(

k ik rB , where i = 1, 10, r = the autocorrelation of the daily market return, and the Bik = the slope coefficients from three OLS regressions. (3) The Dimson beta is obtained by summing up the slope coefficients on the ten lagged, five leading and the contemporaneous value-weighted daily market returns in the following regression: Rit = a i + ∑+

−= + +5

10 ,k ktmik Rb itu , i = 1, 10 Note 8 Autocorrelation analysis, ARIMA models, and Q statistic A stationary time series is a time series which has a constant mean and a constant variance over time. A non-stationary time series (random walk, unit root process) is a time series with time-varying mean and time-varying variance. However, if a time series has a zero mean and a constant variance, the series is called white noise. Thus a white noise series is a stationary series in that the mean and variance are constant. However, a stationary series is not necessarily a white noise series since its mean is not necessarily equal to zero. In testing the autocorrelation function and ARIMA models, two test statistics are used: Box-Pierce statistic ∑ =

=k

t tynQ1

2 (1)

Ljung-Box statistic ∑ = −+=

k

tt

tny

nn1

2

)2(Q (2)

For ARIMA models, the Q statistic (Box-Pierce and Ljung-Box) is used to test the null hypothesis that the autocorrelation function of the residual series is white noise and the series does not show any patterns. The Q statistic is compared with the critical value of the chi-square distribution with the degrees of freedom, k-p-q, where k = a selected lag length for the autocorrelation coefficients, p = AR terms, and q = MA terms. If the Q statistic is less than the critical chi-square value, the null hypothesis is accepted. For autocorrelation analysis, the Q statistic is used to test the null hypothesis that the autocorrelation functions are white noise and do not show any patterns, where the degrees of freedom is given by k-c, c= the number of autocorrelation coefficients, and k = a selected lag length in the autocorrelation function. It should be noted that conventional t-test for correlation coefficient is used to test the single correlation coefficient is equal to zero, while the Q statistic is used to test if a series of autocorrelation coefficients as a group is equal to zero.. Note 9: ARCH, ARCH-M, and GARCH models The ARCH (m) model can be stated by the following:

36

tjtjtp

jt uxy ++= −−=∑ ββ10

h 2

102

jtm

j jtt u −=∑+== αασ

where is the variance conditional on the past. th The ARCH-in-Mean or ARCH-M (m) given by ttjtj

p

jt uhgxy +++= −=∑ )(10 γββ

ttt vh ⋅=u , or u tt hlog= h 2

0 jtm

jt jtt u −− −∑+= αα

The GARCH (p, q) model is given by ∑∑ = −−−

+

=+++=

r

j jtjtjtjtm

jt uuxy110 θββ

where u defines the GARCH process by t

ttt vh ⋅=u , or u tt hlog= h + 2

10 jtq

j jt u −=∑+= αα jtp

j j h −=∑ 1φ

∑ ∑ 1

1 1<+

= =

q

j

p

j jj δα

In addition to the above models, there are other specifications, such as integrated GARCH, Exponential GARCH (EGARCH), and nonlinear ARCH, and multivariate GARCH (Whistler, et. al., Shazam User's Reference Manual Version 9, pp. 223-238; Hamilton, 1994, pp. 657-676) Note 10: Time-Varying Parameter Model: A time varying parameter model-in-mean (GARCH-M) or AR(1) with time changing intercept and slope coefficients is given by (1) r ttttt ehr +++= − 21101 βββ ,

(2) (3)),0(~ tt hNe 12

2110 −− ++= ttt ehh ααα tititi ,1,, ηββ += − ,

;where );,0(~ 21,1 νη Nt 1,0=i t0β = time varying intercept; t,1β and t,2β are time varying

slope coefficients, which are estimated by a maximum likelihood estimation (Hall and Urga, 2002).

37

Note 11. Spectral analysis: Spectral analysis is similar to multiple regression analysis where the dependent variable is the observed time series, and the independent variables are since functions of possible discrete frequencies. Since any periodical series can be estimated in terms of sine curves, the estimation method is based on the following Fourier series:

tfk

f ft eNft

Nfty +++= ∑ =

]2)sin(2)cos([2 1

0 πβπαα

.(1)

where N = total number of observations, k = (N-1)/2 if N is odd, and k = N/2 if N is even, k = number of sine or cosine functions. The regression coefficients are iα and iβ : β ,20 tY=α

=fα cosine coefficients, =fβ sine coefficients; f = ,Nπ frequency in periods. The objective of

the Fourier analysis is to determine optimal values of fα and fβ coefficients that best fit to the data. If the α or β coefficient is significantly large, it indicates a strong periodicity at the given frequency. The coefficients α and β are converted to amplitude and phase angles for each frequency. The periodogram is defined by (2) 2/)( 22

fff NP βα += where Pf = periodogram (periodogram value) at frequency f , and N = total number of observations. The sums of squares are equal to the variances of the data at the given frequencies. There are sometimes large periodogram values for two or more adjacent frequencies and they can cause chaotic spikes when, in fact, there is only one sine or cosine function at a frequency. For such cases, the periodogram values are smoothed by a weighted moving average method (such as Daniel's equal weight window, Tukey window, Hamming window, Prazen window, and Bartlett window) to identify the frequency region or spectral densities. The spectral density values are plotted against the frequencies or periods to obtain the spectral diagram. If there is no periodicity in the data series the time series is referred to as a white noise series (Makridakis, Wheelwright, and McGee, 1983, pp. 369-372, 392-405; DeLurgio, 1998, pp. 67-76; Statsoft, Time Series Analysis, 1984, 2003, pp. 1-38). Granger and Morgenstern (1970, pp. 45-70, 91-110) provide the following explanations. The finite Fourier series is given by b t

tin xe∑ −= ωω)( , πωπ ≤≤− ,

ω = frequency which is defined at any point on the range -π and π , 1−−=∆ ttt xxx , and tie ω−

t= complex valued periodic function which may be written as = cos tie ω−

ti ωω sin− . Let ,cos txP t ωα+= where P = random walk model with a periodic term,

ttxtx εα +∆ −1=∆ . Or, = for |tx∆0

∞

=∑ssα 1−tε α | < 1, the spectrum of tx∆ is given by

|)2/1() =(∆ ωxf 220

| εϖ σα si

sse−∞

=∑ . The relative heights of the spectrum of at the two extremes of the frequency range 0 and

tx∆π is given by

. The 2)]α1/()1[()( απ −+=∆/)0 f(= ∆f x)(αλ α and )(αλ values are: α αλ( )

38

0.1 and 1.49 0.05 and 1.21 0.01 and 1.02. For =α 0.05, the spectrum at ω =0 would be about 20% higher than at .πω = Let )cos( αω +⋅= tAy , where A is the amplitude that ranges between +A and -A, α is the phase which determines where the value of y at t=0, and f is the frequency. The period and the frequency are related concepts in that both concepts measure the speed of a cycle. The period is the length of time for a full cycle, such as the time length from a peak to the next peak. The frequency measures the number of cycles completed during π2 periods. The two measures are related by the period = 2π /Frequency, or frequency =

= period/2π (Hamilton, 1994, p.708). A simple seasonal model is explained as an introduction to Fourier analysis in Cryer (1986, pp. 33-34) in terms of a cosine function:

),2cos( απβ += fty where f is the frequency, or f = 1/12 for the monthly data, the objective is to estimate the parametersβ and α . But we cannot apply the linear OLS method since β and α are not expressed in a non-linear equation. But using the trigonometric relation, )2cos( απβ += fty )2sin()2cos( 2 ftft1 πβπβ += ,which can be restated as y = )12/2 t⋅cos(10 + πββ )12/t2(2 ⋅+ πβ , where t=1,2 … 144 for 12 years. Now applying the multiple regression analysis, we can estimate the three β parameters. Note12. Random walk hypothesis and the variance ratio test. In addition to the unit root test, the variance ratio test is often used to test the random walk hypothesis (Lo and MacKinlay, 1988, 1989; Tse, Ng, and Zhang, 2002). The mean and variances of the 1-period differenced and q-period differenced series are given by )()/1()()/1( 01 XXnXXn ntt −=−= ∑ −µ) (1)

211

21 )()1/(1( µσ )) −−−= −=∑ t

n

t t XXn (2)

22 )()1)(1(

µσ )) qXXkqn

kqt

n

qt tq −−++−

= −=∑ (3)

where n = the number of total observations for time series variable X: ; q = difference interval, and k = n/q. The ratio of the two variances is given by

kqXXX ,...,, 10

1)/()( 2

12 −= σσ )) qq qrM (4)

The variance ratio test statistic is defined as 1+ M . The significance of the variance ratio is evaluated by the critical z-score of the standardized normal distribution. If the computed variance ratio is less than or equal to the z-value, the null hypothesis of random walk is accepted. If it is significantly different from 1.0, the alternative hypothesis is accepted. Lo and Mackinlay show that the variable M (q) is approximately equal to the weighted average of the first-order autocorrelation coefficients for q period

)(qr

r

39

differenced series can be shown as the first-order autocorrelation coefficient estimator of the differenced series for q=2. Note 13.Back to the random walk Lo and MacKinlay (1999, p.16) state: "In a recent update of our original variance ratio test for weekly US stock market indexes, we discovered that the most current data (1986-1996) conform more closely to the random walk than our original 1986-1996 sample period." They offer an explanation: "Over the past decade several investment firms --most notably Morgan Stanley and D.E. Shaw -- have been engaged in high-frequency trading strategies specifically designed to take the advantage of the kind of patterns we uncovered in 1988. Previously known as 'pairs trading' and now called 'statistical arbitrage,' these strategies have fared reasonably well until recently, and are now regarded as a very competitive and thin-margin business because of the proliferation of hedge funds engaged in these activities. This provides a plausible explanation for the trend towards randomness in the recent data, one harkens back to Samuelson's 'Proof that Properly Anticipated Prices Fluctuate Randomly.'" Note 14. NASDAQ, Dow-Jones, and SP500 Total Indexes When the NASDAQ composite index was examined, the January return was also the highest at 4.91% than any other monthly returns over the sample period 1985.1 to 2002.12. Systematic risk beta was the highest at 2.3361 in December. Total risk was the largest at 9.22% in February. But, ANOVA and Kruskal-Wallis tests were unable to reject the null hypothesis of equal monthly returns. On a risk-adjusted basis, the excess return (R-bRm) was the largest 3.330 in January. The R/beta ratio and the Shin beta ratio were the largest in February at 18.05 and 17.909 respectively. The R/std. ratio and the Shin total index were the largest in January at 0.8164 and 2.566 respectively. That is, the best month is either January or February depending upon the risk measures. Note that for the SP500 stocks, the best month was either January or March. The largest negative return was -1.53 in September. On the 5 measures of risk-adjusted returns, September was the worst month. September was also the worst month for the negative returns for the SP500 stocks. For the Dow-Jones industrial 30 stocks, the monthly return is also the highest at 2.41% in January for period 1971-2002. When the 5 risk-adjusted indexes are calculated, the December returns were the highest. The monthly returns were negative only in September. The systematic risk beta was the highest at 2.2253 in January, and the lowest in October at -0.0707. The total risk was the largest at 6.640 in October. The Return/beta ratio is -10.73 or 10.73 (if absolute value is used), and the Return/std. ratio is 0.117 in October. This example indicates that the Return/beta measure is unreliable. The SP500 total index includes dividend payments. The total return is calculated in this paper as the percentage rate of change in the SP500 total index. Table 1 (8) shows that the January return is the largest than in any other month for the period 1971-2002. Both the R/beta ratio and the excess return (R-bRm) are the largest in March, and the R/std ratio is the largest December. REFERENCES

40

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Figure 1(1) Monthly Stock Price Indexes and Monthly Returns (%)

1-A: SP500 Stocks, Monthly Price Index, 1971-2002

1-B: SP500 Stocks, Monthly Return (%), 1971-2002

DATE

2002.09

2001.01

1999.05

1997.09

1996.01

1994.05

1992.09

1991.01

1989.05

1987.09

1986.01

1984.05

1982.09

1981.01

1979.05

1977.09

1976.01

1974.05

1972.09

1971.01

SP50

0 St

ock

Pric

e In

dex

2000

1000

0

DATE

2002.09

2001.01

1999.05

1997.09

1996.01

1994.05

1992.09

1991.01

1989.05

1987.09

1986.01

1984.05

1982.09

1981.01

1979.05

1977.09

1976.01

1974.05

1972.09

1971.01

SP50

0 M

onth

ly R

etur

ns (%

)

20

10

0

-10

-20

-30

2-A: Korean Stocks, Monthly Price Index, 1980-2002

2-B: Korean Stocks, Monthly Return (%), 1980-2002

DATE

2002.03

2001.01

1999.11

1998.09

1997.07

1996.05

1995.03

1994.01

1992.11

1991.09

1990.07

1989.05

1988.03

1987.01

1985.11

1984.09

1983.07

1982.05

1981.03

1980.01

Kore

an S

tock

Pric

es

1200

1000

800

600

400

200

0

DATE

2002.03

2001.01

1999.11

1998.09

1997.07

1996.05

1995.03

1994.01

1992.11

1991.09

1990.07

1989.05

1988.03

1987.01

1985.11

1984.09

1983.07

1982.05

1981.03

1980.01

Kore

an S

tock

Mon

thly

Ret

urns

(%)

60

40

20

0

-20

-40

3-A: Tokyo Stocks, Monthly Price Index, 1984-2002

3-B: Tokyo Stocks, Monthly Return (%), 1984-2002

DATE

2002.01

2001.01

2000.01

1999.01

1998.01

1997.01

1996.01

1995.01

1994.01

1993.01

1992.01

1991.01

1990.01

1989.01

1988.01

1987.01

1986.01

1985.01

1984.01

Toky

o St

ock

Pric

es

500

400

300

200

100

0

DATE

2002.01

2001.01

2000.01

1999.01

1998.01

1997.01

1996.01

1995.01

1994.01

1993.01

1992.01

1991.01

1990.01

1989.01

1988.01

1987.01

1986.01

1985.01

1984.01

Toky

o St

ock

Mon

thly

Ret

urns

(%)

20

10

0

-10

-20

-30

4-A: Jakarta Stocks, Monthly Price Index, 1989-2002

4-B: Jakarta Stocks, Monthly Return (%), 1989-2002

DATE

2002.07

2001.10

2001.01

2000.04

1999.07

1998.10

1998.01

1997.04

1996.07

1995.10

1995.01

1994.04

1993.07

1992.10

1992.01

1991.04

1990.07

1989.10

1989.01

Jaka

rta S

tock

Pric

es

800

700

600

500

400

300

200

100

DATE

2002.07

2001.10

2001.01

2000.04

1999.07

1998.10

1998.01

1997.04

1996.07

1995.10

1995.01

1994.04

1993.07

1992.10

1992.01

1991.04

1990.07

1989.10

1989.01

Jaka

rta S

tock

Mon

thly

Ret

urns

(%)

60

40

20

0

-20

-40

5-A: Shanghai Stocks, Monthly Price Index, 1991-2002

5-B: Shanghai Stocks, Monthly Return (%), 1991-2002

DATE

2002.05

2001.09

2001.01

2000.05

1999.09

1999.01

1998.05

1997.09

1997.01

1996.05

1995.09

1995.01

1994.05

1993.09

1993.01

1992.05

1991.09

1991.01

Shan

ghai

Sto

ck P

rices

3000

2000

1000

0

DATE

2002.05

2001.09

2001.01

2000.05

1999.09

1999.01

1998.05

1997.09

1997.01

1996.05

1995.09

1995.01

1994.05

1993.09

1993.01

1992.05

1991.09

1991.01

Shan

ghai

Sto

ck M

onth

ly R

etur

ns (%

)

200

100

0

-100

6-A: Dow-Jones Industrial Stocks, Monthly Price Index, 1971-2002

F-2: Dow-Jones 30 Stocks, Monthly Return (%)

6-B: Dow-Jones Industrial Stocks, Monthly Return (%), 1971-2002

DATE

2002.09

2001.01

1999.05

1997.09

1996.01

1994.05

1992.09

1991.01

1989.05

1987.09

1986.01

1984.05

1982.09

1981.01

1979.05

1977.09

1976.01

1974.05

1972.09

1971.01

Mon

thly

Ret

urn

(%)

20

10

0

-10

-20

-30

DATE

2002.09

2001.01

1999.05

1997.09

1996.01

1994.05

1992.09

1991.01

1989.05

1987.09

1986.01

1984.05

1982.09

1981.01

1979.05

1977.09

1976.01

1974.05

1972.09

1971.01

Mon

thly

Pric

es

14000

12000

10000

8000

6000

4000

2000

0

7-A: NASDAQ Composite Stocks, Monthly Price Index, 1985-2002

7-B: NASDAQ Composite Stocks, Monthly Returns (%)

DATE

2002.06

2001.07

2000.08

1999.09

1998.10

1997.11

1996.12

1996.01

1995.02

1994.03

1993.04

1992.05

1991.06

1990.07

1989.08

1988.09

1987.10

1986.11

1985.12

1985.01

NAS

DAQ

Mon

thly

Pric

es

5000

4000

3000

2000

1000

0

DATE

2002.06

2001.07

2000.08

1999.09

1998.10

1997.11

1996.12

1996.01

1995.02

1994.03

1993.04

1992.05

1991.06

1990.07

1989.08

1988.09

1987.10

1986.11

1985.12

1985.01

Mon

thly

Ret

urn

(%)

30

20

10

0

-10

-20

-30

8-A: SP500 Total Return Index, Monthly Prices, 1971-2002

8-B: SP500 Total Return Index, Monthly Returns (%)

DATE

2002.09

2001.01

1999.05

1997.09

1996.01

1994.05

1992.09

1991.01

1989.05

1987.09

1986.01

1984.05

1982.09

1981.01

1979.05

1977.09

1976.01

1974.05

1972.09

1971.01

SP50

0 To

tal R

etur

n In

dex

5000

4000

3000

2000

1000

0

DATE

2002.09

2001.01

1999.05

1997.09

1996.01

1994.05

1992.09

1991.01

1989.05

1987.09

1986.01

1984.05

1982.09

1981.01

1979.05

1977.09

1976.01

1974.05

1972.09

1971.01

SP50

0 To

tal R

etur

ns (%

)

20

10

0

-10

-20

-30

Figure 2(1) Monthly Returns by Year, 1971-2002

1. SP 500 Stocks, 1971-2002]

2. Korean Stocks, 1980-2002

3. Tokyo Stocks, 1984-2002

SP 500

-30

-20

-10

0

10

20

1 2 3 4 5 6 7 8 9 10 11 12

January to December

Ret

urn

(%)

Korean Stocks

-40

-20

0

20

40

60

1 2 3 4 5 6 7 8 9 10 11 12

January to December

Ret

urn

(%)

Tokyo Stocks

-30

-20

-10

0

10

20

1 2 3 4 5 6 7 8 9 10 11 12

January to December

Ret

urn

(%)

Figure 2(2) Monthly Returns by Year, 1971-2002

4. Jakarta Stocks, 1989-2002

5. Shanghai Stocks

6. Dow-Jones Industrial Stocks, 1971-2002

Jakarta Stocks

-40

-20

0

20

40

60

1 2 3 4 5 6 7 8 9 10 11 12

January to December

Ret

urns

(%)

Shanghai Stocks

-50

0

50

100

150

200

1 2 3 4 5 6 7 8 9 10 11 12

January to December

Ret

urn

(%)

Dow-Jones

-30.00

-20.00

-10.00

0.00

10.00

20.00

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31

January to December

Ret

urn

(%)

Figure 2(3) Monthly Returns by Year, 1971-2002

7. NASDAQ Composite Stocks, 1985-2002

8. SP500 Total Return Index, 1971-2002

SP500 Total Return Index

-25.00-20.00-15.00-10.00-5.000.005.00

10.0015.0020.00

1 2 3 4 5 6 7 8 9 10 11 12

January to December

Ret

urn

(%)

NASDAQ

-30.00

-20.00

-10.00

0.00

10.00

20.00

30.00

1 2 3 4 5 6 7 8 9 10 11 12

January to December

Ret

urn

(%)

Figure 3 (1) Autocorrelation Analysis

1-A. SP500 Stocks, Monthly Stock Prices, 1971-2002D. Jakarta Stocks, Monthly 1989-2002

1-B. SP500 Monthly Returns, 1971-2002D-2. Jakarta Stocks, Monthly Returns, 1989-2002

6555453525155

1.00.80.60.40.20.0

-0.2-0.4-0.6-0.8-1.0Au

toco

rrel

atio

n

LBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLag

1.6E+041.6E+041.6E+041.6E+041.6E+04

1.6E+041.6E+041.6E+041.5E+041.5E+041.5E+041.5E+041.5E+041.5E+041.4E+041.4E+041.4E+041.4E+041.4E+041.4E+04

1.3E+041.3E+041.3E+041.3E+041.3E+041.2E+041.2E+041.2E+041.2E+041.1E+041.1E+041.1E+041.1E+041.0E+041.0E+04

9934.189662.829386.639105.568819.788529.508235.027936.497633.907327.387017.036702.566383.976061.215734.29

5403.575069.264731.294389.354043.373693.473339.532981.662620.142255.051886.541514.871140.24 763.06 383.08

1.08 1.10 1.12 1.15 1.17

1.19 1.21 1.24 1.27 1.29 1.32 1.35 1.37 1.40 1.43 1.46 1.49 1.52 1.55 1.59

1.62 1.66 1.69 1.73 1.77 1.80 1.84 1.88 1.92 1.97 2.01 2.05 2.10 2.15 2.20

2.25 2.30 2.36 2.42 2.48 2.54 2.61 2.68 2.75 2.83 2.92 3.01 3.11 3.22 3.33

3.46 3.59 3.75 3.93 4.13 4.36 4.62 4.94 5.32 5.81 6.44 7.32 8.6811.2319.50

0.490.500.510.520.52

0.530.540.550.560.570.580.590.600.610.610.620.630.640.650.66

0.670.680.690.700.710.720.730.740.750.750.760.770.780.790.80

0.810.810.820.830.840.840.850.860.870.870.880.890.890.900.91

0.910.920.930.930.940.950.950.960.960.970.970.980.980.990.99

6564636261

605958575655545352515049484746

454443424140393837363534333231

302928272625242322212019181716

151413121110 9 8 7 6 5 4 3 2 1

SP500

6555453525155

1.00.80.60.40.20.0

-0.2-0.4-0.6-0.8-1.0Au

toco

rrel

atio

n

LBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLag

51.4449.2647.2946.3942.98

42.8840.6940.6539.7939.7339.3639.3139.2039.0939.0938.9238.8037.5536.8435.78

35.7735.7733.5233.5233.5133.4333.4131.1928.9928.9228.3626.0325.0723.4521.68

21.6521.4220.6520.6519.8018.6918.1618.1416.6116.6116.0515.8715.6615.4113.53

13.5213.4211.5311.5110.5610.52 5.77 5.72 5.72 5.68 4.77 1.40 1.03 0.70 0.01

-1.21 1.15-0.78-1.53-0.27

-1.24 0.18-0.78-0.21-0.51-0.19-0.28 0.28-0.02 0.35 0.30 0.96-0.72 0.89 0.03

-0.00-1.30-0.07 0.05 0.24-0.15-1.31 1.31 0.24-0.66 1.37 0.88-1.15-1.21-0.15

0.43 0.80 0.02 0.85 0.97 0.67 0.13-1.15-0.03-0.70-0.39-0.43-0.47 1.29-0.09

-0.30-1.31 0.11 0.93-0.18 2.11-0.22-0.05 0.20-0.93 1.81-0.60 0.58-0.83-0.08

-0.07 0.07-0.04-0.09-0.02

-0.07 0.01-0.04-0.01-0.03-0.01-0.02 0.02-0.00 0.02 0.02 0.05-0.04 0.05 0.00

-0.00-0.07-0.00 0.00 0.01-0.01-0.07 0.07 0.01-0.04 0.07 0.05-0.06-0.07-0.01

0.02 0.04 0.00 0.05 0.05 0.04 0.01-0.06-0.00-0.04-0.02-0.02-0.02 0.07-0.00

-0.02-0.07 0.01 0.05-0.01 0.11-0.01-0.00 0.01-0.05 0.09-0.03 0.03-0.04-0.00

6564636261

605958575655545352515049484746

454443424140393837363534333231

302928272625242322212019181716

151413121110 9 8 7 6 5 4 3 2 1

SP500

Figure 3(2) Autocorrelation Analysis

2-A. Korean Stocks, Monthly Prices, 1980-2002E. Shanghai Stocks, 1991-2002

2-B. Korean Stocks, Monthly Returns, 1980-2002E-2. Shanghai Stocks, Monthly Returns, 1991-2002

6252423222122

1.00.80.60.40.20.0

-0.2-0.4-0.6-0.8-1.0Au

toco

rrel

atio

n

LBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLag

7019.297007.11

6993.596978.796962.546944.626925.076904.116881.926858.586833.896807.686779.846750.246718.566684.566648.10

6609.086567.236522.206473.816421.746365.316304.236238.896169.086094.626014.935930.475841.155746.945647.76

5543.435433.995319.525200.245076.534948.384815.804678.194535.584388.134236.434080.363919.993755.153585.93

3411.753232.123046.142853.742653.932446.572231.572009.021779.471543.241300.641052.14 798.04 538.36 272.39

0.44 0.47

0.49 0.52 0.54 0.57 0.59 0.61 0.63 0.65 0.67 0.70 0.72 0.75 0.78 0.81 0.84

0.88 0.91 0.95 0.99 1.04 1.09 1.13 1.18 1.23 1.28 1.33 1.38 1.43 1.48 1.54

1.59 1.65 1.70 1.76 1.81 1.87 1.93 2.00 2.07 2.14 2.21 2.29 2.37 2.46 2.56

2.67 2.80 2.94 3.10 3.29 3.50 3.75 4.03 4.37 4.79 5.34 6.09 7.25 9.4216.41

0.180.19

0.200.210.230.240.250.250.260.270.280.290.300.310.320.330.34

0.350.370.380.400.420.430.450.470.480.500.520.530.550.560.58

0.590.610.620.630.650.660.670.690.700.710.720.730.740.760.77

0.780.800.810.830.850.860.880.900.910.920.940.950.960.970.99

6261

605958575655545352515049484746

454443424140393837363534333231

302928272625242322212019181716

151413121110 9 8 7 6 5 4 3 2 1

Korean Stocks

6252423222122

1.00.80.60.40.20.0

-0.2-0.4-0.6-0.8-1.0Au

toco

rrel

atio

n

LBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLag

73.5173.21

72.7772.7171.3170.0066.2965.9865.7565.4362.8761.3361.0859.1059.1059.0958.90

57.8757.2756.8454.5847.5545.9442.6542.3642.3439.9638.3238.3237.9437.7737.39

36.9636.9433.0632.8231.7631.7628.6728.4428.3221.0820.3620.3218.6818.6718.64

16.6015.8314.78 6.92 6.92 6.85 6.16 5.03 4.72 4.29 2.69 2.46 2.38 1.95 1.93

0.40 0.48

-0.18-0.87 0.84 1.43 0.42 0.36-0.43-1.21-0.94 0.38-1.08-0.07-0.07-0.33-0.79

-0.60-0.51-1.18-2.12-1.02 1.47 0.44-0.12-1.27 1.06 0.03 0.51-0.34-0.51 0.55

0.11 1.68 0.42-0.88-0.03-1.53 0.41 0.31 2.40-0.76-0.17-1.16-0.08 0.16-1.31

-0.81 0.95-2.66-0.03 0.26 0.79 1.03 0.54 0.63 1.24 0.47-0.27-0.65 0.15 1.38

0.03 0.04

-0.01-0.06 0.06 0.10 0.03 0.03-0.03-0.09-0.07 0.03-0.08-0.00-0.01-0.02-0.06

-0.04-0.04-0.08-0.15-0.07 0.10 0.03-0.01-0.09 0.07 0.00 0.03-0.02-0.03 0.04

0.01 0.11 0.03-0.06-0.00-0.10 0.03 0.02 0.16-0.05-0.01-0.07-0.01 0.01-0.08

-0.05 0.06-0.16-0.00 0.02 0.05 0.06 0.03 0.04 0.08 0.03-0.02-0.04 0.01 0.08

6261

605958575655545352515049484746

454443424140393837363534333231

302928272625242322212019181716

151413121110 9 8 7 6 5 4 3 2 1

Korean Stocks

Figure 3 (3) Autocorrelation Analysis

3-A. Tokyo Stocks, Monthly Prices in Log, 1984-2002

3-B. Tokyo Stocks, Monthly Return, 1985-2002

55453525155

1.00.80.60.40.20.0

-0.2-0.4-0.6-0.8-1.0Au

toco

rrel

atio

n

LBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLag

2331.702306.672282.092258.312235.052212.182190.422170.042151.23

2133.772118.072104.772093.082082.332072.012062.362053.612045.682038.572032.412027.25

2023.042019.672017.282015.662014.682014.122013.852013.812013.752013.272012.002009.77

2005.821999.441990.281977.631961.391941.271916.531887.061852.501812.821766.051711.98

1650.381579.241497.591404.531300.361185.041058.77 918.87 763.87 594.09 410.86 213.45

-0.97 -0.96 -0.95 -0.95 -0.95 -0.93 -0.91 -0.88 -0.85

-0.81 -0.75 -0.71 -0.68 -0.67 -0.65 -0.62 -0.60 -0.57 -0.53 -0.49 -0.44

-0.40 -0.33 -0.28 -0.21 -0.16 -0.11 -0.04 0.06 0.15 0.25 0.33 0.44

0.56 0.68 0.80 0.91 1.02 1.14 1.26 1.38 1.50 1.65 1.80 1.96

2.15 2.37 2.61 2.86 3.15 3.47 3.90 4.45 5.20 6.28 8.25 14.51

-0.29-0.28-0.28-0.28-0.28-0.27-0.26-0.25-0.24

-0.23-0.21-0.20-0.19-0.19-0.18-0.18-0.17-0.16-0.15-0.14-0.12

-0.11-0.09-0.08-0.06-0.05-0.03-0.01 0.02 0.04 0.07 0.09 0.12

0.16 0.19 0.22 0.25 0.28 0.31 0.34 0.37 0.40 0.44 0.47 0.50

0.54 0.58 0.62 0.66 0.70 0.73 0.77 0.81 0.85 0.89 0.92 0.96

575655545352515049

484746454443424140393837

363534333231302928272625

242322212019181716151413

121110 9 8 7 6 5 4 3 2 1

Tokyo Stocks

55453525155

1.00.80.60.40.20.0

-0.2-0.4-0.6-0.8-1.0Au

toco

rrel

atio

n

LBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLag

40.2539.8139.7339.3139.3038.7238.5738.56

38.4837.0935.7835.7135.6235.0734.1533.9932.9432.3731.8431.74

31.7031.6730.3230.1930.0829.9727.4025.8625.4625.1020.7419.96

19.9619.5419.5118.9418.8618.7517.2717.1013.6310.2810.24 9.36

7.29 7.16 7.16 6.02 4.73 4.39 3.87 3.11 0.65 0.48 0.41 0.30

-0.51-0.22 0.49-0.08-0.58-0.30-0.03 0.22

-0.92 0.90 0.21-0.23-0.59-0.76-0.31-0.83-0.61 0.59 0.26-0.16

0.15 0.95 0.29 0.28 0.28-1.34-1.05 0.54 0.51 1.80-0.77 0.01

0.57 0.14 0.66-0.25-0.29 1.09 0.36 1.69-1.68-0.19 0.87-1.35

0.34-0.03 1.01 1.09 0.57-0.69-0.84 1.54 0.41 0.26 0.32 0.55

-0.04-0.02 0.04-0.01-0.04-0.02-0.00 0.02

-0.07 0.07 0.02-0.02-0.04-0.06-0.02-0.06-0.05 0.04 0.02-0.01

0.01 0.07 0.02 0.02 0.02-0.10-0.08 0.04 0.04 0.13-0.05 0.00

0.04 0.01 0.05-0.02-0.02 0.08 0.03 0.12-0.12-0.01 0.06-0.09

0.02-0.00 0.07 0.07 0.04-0.05-0.06 0.10 0.03 0.02 0.02 0.04

5655545352515049

484746454443424140393837

363534333231302928272625

242322212019181716151413

121110 9 8 7 6 5 4 3 2 1

Tokyo Stocks

Figure 3 (4) Autocorrelation Analysis

4-A. Jakarta Stocks, Monthly Prices in Log, 1989-2002

4-B. Jakarta Stocks, Monthly Return, 1990-2002

423222122

1.00.80.60.40.20.0

-0.2-0.4-0.6-0.8-1.0Au

toco

rrel

atio

n

LBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLag

874.23856.36841.47830.31820.91812.24

804.38798.00792.13786.48780.84775.72771.51767.92764.45760.17754.78748.52

741.54734.86728.89723.15716.62709.14701.43694.92689.81685.88683.70683.09

683.08682.19677.67667.09647.67618.29576.53521.06452.44370.15269.64147.35

-1.12 -1.03 -0.90 -0.84 -0.81 -0.78

-0.70 -0.68 -0.67 -0.67 -0.65 -0.59 -0.55 -0.54 -0.60 -0.68 -0.74 -0.79

-0.78 -0.74 -0.73 -0.78 -0.84 -0.86 -0.80 -0.71 -0.63 -0.47 -0.25 -0.03

0.30 0.69 1.06 1.46 1.84 2.27 2.74 3.24 3.87 4.85 6.62

12.03

-0.28-0.26-0.22-0.21-0.20-0.19

-0.17-0.17-0.16-0.16-0.16-0.14-0.13-0.13-0.14-0.16-0.18-0.19

-0.18-0.17-0.17-0.18-0.20-0.20-0.18-0.16-0.14-0.11-0.06-0.01

0.07 0.16 0.24 0.33 0.41 0.49 0.56 0.63 0.69 0.76 0.84 0.93

424140393837

363534333231302928272625

242322212019181716151413

121110 9 8 7 6 5 4 3 2 1

Jakarta Stocks

40302010

1.00.80.60.40.20.0

-0.2-0.4-0.6-0.8-1.0Au

toco

rrel

atio

n

LBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLag

43.1742.2438.1137.0136.90

36.2534.9434.4634.3033.9733.3233.1832.6629.5929.2129.1229.07

26.6526.2325.7223.1023.0521.9119.1119.0218.9415.7114.3514.34

7.77 6.39 6.33 6.20 4.93 4.91 4.83 3.86 3.66 2.47 2.19 1.77

-0.69 1.49 0.78-0.24-0.60

0.86 0.52 0.31-0.44-0.62 0.28 0.56 1.38 0.49-0.23-0.18-1.26

-0.52 0.59 1.34-0.19-0.89-1.42-0.26 0.24-1.57-1.02-0.11-2.34

-1.09 0.23-0.34 1.06-0.13 0.26 0.94 0.43-1.06-0.51-0.64 1.32

-0.06 0.14 0.07-0.02-0.05

0.08 0.05 0.03-0.04-0.06 0.03 0.05 0.12 0.04-0.02-0.02-0.11

-0.05 0.05 0.12-0.02-0.08-0.12-0.02 0.02-0.13-0.09-0.01-0.19

-0.09 0.02-0.03 0.08-0.01 0.02 0.07 0.03-0.08-0.04-0.05 0.10

4140393837

363534333231302928272625

242322212019181716151413

121110 9 8 7 6 5 4 3 2 1

Jakarta Stocks

Figure 3 (5) Autocorrelation Analysis

5-A. Shanghai Stocks, Monthly Prices in Log, 1991-2002

5-B. Shanghai Stocks, Monthly Return, 1992-2002

3525155

1.00.80.60.40.20.0

-0.2-0.4-0.6-0.8-1.0Au

toco

rrel

atio

n

LBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLag

1003.79 995.76 988.49 981.81 975.41 969.27 963.25 957.28 951.64

945.97 940.88 936.45 932.75 929.44 925.52 920.57 913.65 905.27

895.86 886.22 877.06 868.01 857.02 842.86 824.78 801.73 772.51

737.32 693.75 642.48 582.75 514.48 437.49 349.29 247.14 130.41

0.65 0.63 0.61 0.60 0.59 0.59 0.59 0.58 0.58

0.55 0.52 0.48 0.45 0.50 0.56 0.67 0.74 0.79

0.81 0.80 0.80 0.89 1.02 1.17 1.34 1.54 1.73

1.98 2.23 2.52 2.86 3.26 3.84 4.76 6.4011.30

0.200.190.190.180.180.180.180.180.18

0.170.160.140.140.150.170.200.220.24

0.240.240.230.260.300.340.380.430.47

0.530.580.620.670.710.770.830.890.94

363534333231302928

272625242322212019

181716151413121110

9 8 7 6 5 4 3 2 1

Shanghai Stocks

3525155

1.00.80.60.40.20.0

-0.2-0.4-0.6-0.8-1.0Au

toco

rrel

atio

n

LBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLag

54.2652.0751.9451.4451.0951.0751.0650.32

50.1641.0137.6337.1233.9332.6132.4132.3932.13

31.5930.7828.9728.3625.6525.3225.2324.5620.83

18.59 9.92 9.76 6.03 5.89 5.08 1.28 1.20 0.92

-1.00 0.25-0.48-0.41-0.10 0.09-0.60-0.27

2.20-1.36-0.53-1.35-0.87-0.34 0.11 0.39 0.58

0.71-1.07 0.63-1.34-0.47-0.24-0.68 1.63-1.29

2.66-0.36 1.80 0.36-0.85-1.89-0.28 0.52-0.95

-0.11 0.03-0.05-0.04-0.01 0.01-0.06-0.03

0.23-0.14-0.05-0.14-0.09-0.03 0.01 0.04 0.06

0.07-0.10 0.06-0.13-0.05-0.02-0.06 0.15-0.12

0.24-0.03 0.16 0.03-0.07-0.16-0.02 0.04-0.08

3534333231302928

272625242322212019

181716151413121110

9 8 7 6 5 4 3 2 1

Shanghai Stocks

Figure 3 (6) Autocorrelation Analysis

6-A. Dow-Jones Industrial Stocks, Monthly Prices in Log, 1971-2002

6-B. Dow-Jones Industrial Stocks, Monthly Return, 1971-2002

6555453525155

1.00.80.60.40.20.0

-0.2-0.4-0.6-0.8-1.0Au

toco

rrel

atio

n

LBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLag

1.6E+041.6E+041.6E+041.6E+041.6E+04

1.6E+041.6E+041.6E+041.5E+041.5E+041.5E+041.5E+041.5E+041.5E+041.4E+041.4E+041.4E+041.4E+041.4E+041.4E+04

1.3E+041.3E+041.3E+041.3E+041.3E+041.2E+041.2E+041.2E+041.2E+041.1E+041.1E+041.1E+041.1E+041.0E+041.0E+04

9859.609589.739315.429036.568753.348465.878174.377878.937579.627276.466969.506658.416343.116023.555699.77

5372.075040.884706.084367.214024.183677.103325.802970.382611.152248.121881.501511.461138.16 762.04 382.75

1.10 1.12 1.14 1.16 1.18

1.20 1.23 1.25 1.28 1.31 1.33 1.36 1.39 1.41 1.44 1.47 1.50 1.53 1.56 1.60

1.63 1.67 1.70 1.74 1.78 1.81 1.85 1.89 1.93 1.97 2.02 2.06 2.11 2.15 2.20

2.25 2.30 2.36 2.42 2.48 2.54 2.61 2.67 2.75 2.83 2.91 3.00 3.10 3.21 3.32

3.45 3.59 3.74 3.92 4.12 4.35 4.62 4.93 5.32 5.80 6.43 7.32 8.6811.2319.49

0.500.510.510.520.53

0.540.550.560.560.570.580.590.600.610.620.630.640.650.650.66

0.670.680.690.700.710.720.730.740.750.760.760.770.780.790.80

0.800.810.820.830.830.840.850.850.860.870.870.880.890.900.90

0.910.910.920.930.930.940.950.950.960.970.970.980.980.990.99

6564636261

605958575655545352515049484746

454443424140393837363534333231

302928272625242322212019181716

151413121110 9 8 7 6 5 4 3 2 1

Dow-Jones Industrials

6555453525155

1.00.80.60.40.20.0

-0.2-0.4-0.6-0.8-1.0Au

toco

rrel

atio

n

LBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLag

44.7643.0041.2940.8637.62

37.5537.3336.8536.5236.4935.5035.2235.1235.1135.0734.7834.7631.7631.7530.89

30.8930.6529.2429.1529.1229.0729.0427.8226.6426.6026.4923.3522.5621.8520.94

20.9320.5920.4720.4718.7518.3717.4617.4016.3316.3114.9014.4913.3913.3413.23

12.7612.55 8.62 8.60 7.78 7.78 4.73 4.72 4.51 4.13 2.23 1.52 0.36 0.23 0.00

-1.10 1.09-0.54-1.51-0.21

-0.39 0.59-0.49 0.14-0.85-0.45-0.27 0.06-0.18 0.46 0.11 1.50-0.11 0.81 0.04

0.43-1.04 0.26 0.16 0.19-0.15-0.98 0.96 0.18 0.30 1.59 0.80-0.76-0.87 0.06

0.53 0.32-0.05 1.21 0.57 0.88 0.23-0.96-0.12-1.11-0.61-0.99 0.20 0.32 0.65

-0.43-1.90 0.14 0.87 0.05 1.70 0.07-0.45 0.60-1.36 0.83-1.07 0.36-0.47-0.07

-0.06 0.06-0.03-0.08-0.01

-0.02 0.03-0.03 0.01-0.05-0.02-0.02 0.00-0.01 0.03 0.01 0.08-0.01 0.04 0.00

0.02-0.06 0.01 0.01 0.01-0.01-0.05 0.05 0.01 0.02 0.09 0.04-0.04-0.05 0.00

0.03 0.02-0.00 0.06 0.03 0.05 0.01-0.05-0.01-0.06-0.03-0.05 0.01 0.02 0.03

-0.02-0.10 0.01 0.05 0.00 0.09 0.00-0.02 0.03-0.07 0.04-0.05 0.02-0.02-0.00

6564636261

605958575655545352515049484746

454443424140393837363534333231

302928272625242322212019181716

151413121110 9 8 7 6 5 4 3 2 1

Dow-Jones Industrials

Figure 3 (7) Autocorrelation Analysis

7-A. NASDAQ Composite Stocks, Monthly Prices in Log, 1985-2002

7-B. NASDAQ Composite Stocks, Monthly Return, 1985-2002

52423222122

1.00.80.60.40.20.0

-0.2-0.4-0.6-0.8-1.0Au

toco

rrel

atio

n

LBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLag

5830.345812.975793.685772.615749.715724.70

5697.365667.585635.065599.855561.905521.275477.865431.535382.245329.645273.645213.91

5150.125081.925009.104931.414848.924762.514672.084577.424478.394374.674266.434153.95

4037.403916.773791.593662.013528.333390.413248.543102.562952.602799.082642.102481.26

2316.302146.681972.091792.811609.171421.161228.921032.94 833.71 630.99 424.65 214.40

0.51 0.54 0.57 0.59 0.62 0.65

0.69 0.72 0.75 0.79 0.82 0.85 0.89 0.92 0.96 1.00 1.04 1.08

1.13 1.17 1.23 1.28 1.32 1.37 1.41 1.46 1.52 1.57 1.63 1.68

1.74 1.80 1.87 1.94 2.01 2.08 2.16 2.25 2.34 2.43 2.54 2.66

2.81 2.97 3.15 3.36 3.61 3.90 4.27 4.75 5.41 6.43 8.3514.54

0.240.260.270.280.300.31

0.330.340.360.370.390.400.410.430.440.460.480.49

0.510.530.550.570.580.600.610.630.640.660.670.69

0.700.720.730.740.760.770.780.800.810.820.830.84

0.860.870.890.900.910.920.930.940.960.970.980.99

545352515049

484746454443424140393837

363534333231302928272625

242322212019181716151413

121110 9 8 7 6 5 4 3 2 1

NASDAQ Stocks

52423222122

1.00.80.60.40.20.0

-0.2-0.4-0.6-0.8-1.0Au

toco

rrel

atio

n

LBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLag

43.0143.0142.5640.7239.6138.93

38.8038.6337.8637.8237.0437.0236.6236.4535.5635.1733.7733.36

33.1433.0831.1231.0030.0327.2226.5526.1225.9325.9225.6725.32

24.2424.0922.2822.0921.5621.4921.4919.8218.2318.2117.8117.63

16.3115.7814.91 7.33 7.32 6.70 5.66 3.73 3.19 2.72 2.59 2.32

0.03 0.50 1.02-0.80-0.62 0.28

-0.31 0.68 0.15 0.68-0.10-0.50-0.32-0.74-0.49-0.94-0.51 0.38

-0.19 1.13-0.28-0.80-1.39 0.68-0.54-0.37 0.09 0.42-0.50 0.89

0.32-1.16 0.37 0.63-0.23 0.01-1.14 1.12-0.11-0.57 0.37-1.04

-0.66 0.85 2.59 0.06-0.75 0.97 1.34-0.72-0.66-0.36-0.51 1.51

0.00 0.04 0.08-0.06-0.05 0.02

-0.02 0.05 0.01 0.05-0.01-0.04-0.02-0.06-0.04-0.07-0.04 0.03

-0.01 0.09-0.02-0.06-0.10 0.05-0.04-0.03 0.01 0.03-0.04 0.07

0.02-0.09 0.03 0.05-0.02 0.00-0.08 0.08-0.01-0.04 0.03-0.08

-0.05 0.06 0.18 0.00-0.05 0.07 0.09-0.05-0.05-0.02-0.04 0.10

545352515049

484746454443424140393837

363534333231302928272625

242322212019181716151413

121110 9 8 7 6 5 4 3 2 1

NASDAQ Stocks

Figure 3 (8) Autocorrelation Analysis

8-A. SP500 Total Return Index, Monthly Prices in Log, 1971-2002

8-A. SP500 Total Return Index, Monthly Return, 1971-2002

6555453525155

1.00.80.60.40.20.0

-0.2-0.4-0.6-0.8-1.0Au

toco

rrel

atio

n

LBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLag

1.7E+041.7E+041.6E+041.6E+041.6E+04

1.6E+041.6E+041.6E+041.6E+041.5E+041.5E+041.5E+041.5E+041.5E+041.5E+041.4E+041.4E+041.4E+041.4E+041.4E+04

1.3E+041.3E+041.3E+041.3E+041.3E+041.2E+041.2E+041.2E+041.2E+041.1E+041.1E+041.1E+041.1E+041.0E+041.0E+04

9937.509664.009385.989103.378816.338525.018229.627930.277626.977319.827008.896693.996375.136052.275725.42

5394.865060.734722.994381.434036.023686.803333.672976.692616.082251.901884.261513.401139.43 762.67 382.94

1.12 1.14 1.16 1.18 1.20

1.22 1.25 1.27 1.30 1.32 1.35 1.38 1.40 1.43 1.46 1.48 1.51 1.54 1.58 1.61

1.64 1.68 1.71 1.75 1.79 1.82 1.86 1.90 1.94 1.98 2.02 2.07 2.11 2.16 2.21

2.26 2.31 2.37 2.42 2.49 2.55 2.61 2.68 2.76 2.84 2.92 3.01 3.11 3.22 3.33

3.46 3.60 3.75 3.93 4.12 4.35 4.62 4.94 5.32 5.80 6.44 7.32 8.6811.2319.49

0.510.520.530.530.54

0.550.560.570.580.590.590.600.610.620.630.640.650.650.660.67

0.680.690.700.710.720.730.740.740.750.760.770.780.780.790.80

0.810.820.820.830.840.850.850.860.870.870.880.890.890.900.91

0.910.920.920.930.940.940.950.960.960.970.970.980.980.990.99

6564636261

605958575655545352515049484746

454443424140393837363534333231

302928272625242322212019181716

151413121110 9 8 7 6 5 4 3 2 1

SP500 Total Return Index

6555453525155

1.00.80.60.40.20.0

-0.2-0.4-0.6-0.8-1.0Au

toco

rrel

atio

n

LBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLagLBQTCorrLag

51.7349.5647.6246.5743.24

43.1541.1641.1340.3040.2639.7939.7839.5239.4039.4039.2139.0737.8937.4436.46

36.4636.4233.5733.5633.5433.4733.4530.8328.6328.5727.9725.5224.8223.2121.46

21.4321.1620.5420.5419.7618.6318.2018.1816.6216.6216.0915.8815.7515.4813.56

13.5513.4711.7011.6910.6910.68 5.87 5.79 5.79 5.74 4.83 1.38 0.94 0.53 0.01

-1.21 1.15-0.84-1.52-0.25

-1.18 0.15-0.76-0.17-0.57-0.10-0.44 0.29 0.01 0.37 0.31 0.93-0.57 0.85-0.05

0.16-1.47-0.10-0.12 0.23-0.13-1.43 1.32 0.21-0.69 1.40 0.75-1.14-1.20-0.14

0.48 0.72 0.03 0.81 0.98 0.61 0.12-1.16 0.02-0.68-0.42-0.34-0.49 1.31-0.08

-0.28-1.26 0.09 0.96-0.10 2.13-0.28-0.02 0.22-0.93 1.83-0.66 0.63-0.72-0.09

-0.07 0.06-0.05-0.08-0.01

-0.07 0.01-0.04-0.01-0.03-0.01-0.02 0.02 0.00 0.02 0.02 0.05-0.03 0.05-0.00

0.01-0.08-0.01-0.01 0.01-0.01-0.08 0.07 0.01-0.04 0.08 0.04-0.06-0.06-0.01

0.03 0.04 0.00 0.04 0.05 0.03 0.01-0.06 0.00-0.04-0.02-0.02-0.03 0.07-0.00

-0.01-0.07 0.00 0.05-0.01 0.11-0.01-0.00 0.01-0.05 0.09-0.03 0.03-0.04-0.00

6564636261

605958575655545352515049484746

454443424140393837363534333231

302928272625242322212019181716

151413121110 9 8 7 6 5 4 3 2 1

SP500 Total Return Index

Figure 4 (1) Spectral Analysis

1. SP 500 Stocks, Log Price Differences, 1971-2002

2. Korean Stocks, Log Price Differences, 1980-2002

Periodogram of Korean Stocks

Period

300200

10050

4030

2010

54

32

1

Perio

dogr

am

.05

.04

.03

.02

.01

.005

.004

.003

.002

.001

.0005

.0004

.0003

.0002

Figure 4 (2) Spectral Analysis

3. Tokyo Stocks, Log Price Differences, 1984-2002

4. Jakarta Stocks, Log Price Differences, 1989-2002

Periodogram of Tokyo Stocks

Period

300200

10050

4030

2010

54

32

1

Perio

dogr

am

.04

.03

.02

.01

.005

.004

.003

.002

.001

.0005

.0004

.0003

.0002

.0001

Periodogram of Jakarta Stocks

Period

200100

5040

3020

105

43

21

Perio

dogr

am

.05

.04

.03

.02

.01

.005

.004

.003

.002

.001

.0005

.0004

.0003

.0002

.0001

Figure 4 (3) Spectral Analysis

5. Shanghai Stocks, Log Price Differences, 1991-2002

6. Dow-Jones Industrial Stock Price Index, Log Price Differences, 1971-2002

Periodogram of Shanghai Stocks

Period

200100

5040

3020

105

43

21

Perio

dogr

am

.4

.3

.2

.1

.05

.04

.03

.02

.01

.005

.004

.003

.002

.001

Periodogram of Dow-Jones Stocks

Period

400300

200100

5040

3020

105

43

21

Perio

dogr

am

.03

.02

.01

.005.004

.003

.002

.001

.0005.0004

.0003

.0002

.0001

.00005.00004

.00003

.00002

.00001

Figure 4 (4) Spectral Analysis

7. NASDAQ Stock Price Index, Log Price Differences, 1985-2002

8. SP500 Total Return Index, Log Price Differences, 1971-2002

Periodogram of NASDAQ Stocks

Period

300200

10050

4030

2010

54

32

1

Perio

dogr

am

.05.04

.03

.02

.01

.005.004

.003

.002

.001

.0005.0004

.0003

.0002

.0001

.00005.00004

.00003

.00002

.00001

Figure 4 (5) Spectral Analysis

9. Hypothetical Cyclical Data In Log

10. Hypothetical Cyclical Data In Log

* The data is a series of repeated numbers from 1 to 12 in log for the 32 cycles (years)

Periodogram of LOGC

Period

400300

200100

5040

3020

105

43

21

Perio

dogr

am

100101.1

.01.001

.0001.00001

.000001.0000001

.00000001.000000000

.0000000000.00000000000

.000000000000.0000000000000

.00000000000000.000000000000000

.0000000000000000.00000000000000000

Spectral Density of LOGC

Window : Tukey-Hamming (5)

Frequency

.6.5.4.3.2.10.0

Den

sity

100101.1

.01.001

.0001.00001

.000001.0000001

.00000001.000000000

.0000000000.00000000000

.000000000000.0000000000000

.00000000000000.000000000000000

Table 1(1) SP 500 Stocks, Monthly Returns (%), 1971-2002

1 2 3 4 5 6 7 8 9 10 11 12 Av. Std.1971 4.05 0.91 3.67 3.64 -4.16 -0.93 -3.16 3.61 -0.74 -4.14 -0.25 8.62 0.93 3.91972 1.81 2.53 0.59 0.44 1.73 -2.18 0.23 3.45 -0.49 0.93 4.56 1.18 1.23 1.781973 -1.48 -3.97 -0.14 -4.08 -1.89 -0.66 3.8 -3.67 4.01 -0.13 -11.39 1.66 -1.5 4.141974 -1.00 -0.36 -2.33 -3.91 -3.36 -1.47 -7.78 -9.03 -11.93 16.3 -5.32 -2.02 -2.68 6.951975 12.28 5.99 2.17 4.73 4.41 4.43 -6.77 -2.11 -3.46 6.16 2.47 -1.15 2.43 5.131976 11.83 -1.14 3.07 -1.1 -1.44 4.09 -0.81 -0.51 2.26 -2.22 -0.78 5.25 1.54 4.061977 -5.05 -2.17 -1.4 0.02 -2.36 4.54 -1.62 -2.1 -0.25 -4.34 2.7 0.28 -0.98 2.71978 -6.15 -2.48 2.49 8.54 0.42 -1.76 5.39 2.59 -0.73 -9.16 1.66 1.49 0.19 4.781979 3.97 -3.65 5.52 0.17 -2.63 3.87 0.87 5.31 0 -6.86 4.26 1.68 1.04 3.881980 5.76 -0.44 -10.18 4.11 4.66 2.7 6.5 0.58 2.52 1.6 10.24 -3.39 2.06 5.221981 -4.57 1.33 3.6 -2.35 -0.17 -1.04 -0.22 -6.21 -5.38 4.91 3.66 -3.01 -0.79 3.681982 -1.75 -6.05 -1.02 4 -3.92 -2.03 -2.3 11.6 0.76 11.04 3.6 1.52 1.29 5.511983 3.31 1.9 3.31 7.5 -1.24 3.23 -3.03 1.13 1.02 -1.52 1.74 -0.88 1.37 2.841984 -0.92 -3.89 1.35 0.55 -5.94 1.75 -1.65 10.63 -0.35 -0.01 -1.51 2.24 0.19 4.041985 7.41 0.86 -0.29 -0.46 5.41 1.21 -0.48 -1.2 -3.47 4.25 6.51 4.51 2.02 3.471986 0.24 7.15 5.28 -1.41 5.02 1.41 -5.87 7.12 -8.54 5.47 2.15 -2.83 1.27 5.131987 13.18 3.69 2.64 -1.15 0.6 4.79 4.82 3.5 -2.42 -21.76 -8.53 7.29 0.55 8.821988 4.04 4.18 -3.33 0.94 0.32 4.33 -0.54 -3.86 3.97 2.6 -1.89 1.47 1.02 2.951989 7.11 -2.89 2.08 5.01 3.51 -0.79 8.84 1.55 -0.65 -2.52 1.65 2.14 2.09 3.611990 -6.88 0.85 2.43 -2.69 9.2 -0.89 -0.52 -9.43 -4.96 -0.84 5.99 2.48 -0.44 5.231991 4.15 6.73 2.22 0.03 3.86 -4.79 4.49 1.96 -1.91 1.18 -4.39 11.16 2.06 4.551992 -1.99 0.96 -2.18 2.79 0.1 -1.74 3.94 -2.4 0.91 0.21 3.11 0.93 0.39 2.161993 0.7 1.05 1.87 -2.54 2.27 0.08 -0.53 3.44 -1 1.94 -1.29 1.01 0.58 1.711994 4.54 -4.2 -4.57 1.15 1.24 -2.68 3.15 3.76 -2.69 2.08 -3.95 1.23 -0.08 3.331995 2.43 3.61 2.73 2.8 3.63 2.13 3.18 -0.03 4.01 -0.5 4.1 1.74 2.49 1.481996 3.26 0.69 0.79 1.34 2.29 0.23 -4.57 1.88 5.42 2.61 7.34 -2.15 1.59 3.131997 6.13 0.59 -4.26 5.84 5.86 4.35 7.81 -5.75 5.32 -3.45 4.46 1.57 2.37 4.61998 1.02 7.04 4.99 0.91 -1.88 3.94 -1.16 -14.58 6.24 8.03 5.91 5.64 2.18 6.21999 4.1 -3.23 3.88 3.79 -2.5 5.44 -3.2 -0.63 -2.86 6.25 1.91 5.78 1.56 3.792000 -5.09 -2.01 9.67 -3.08 -2.19 2.39 -1.63 6.07 -5.35 -0.49 -8.01 0.41 -0.78 4.942001 3.46 -9.23 -6.42 7.68 0.51 -2.5 -1.07 -6.41 -8.17 1.81 7.52 0.76 -1.01 5.732002 -1.57 -2.06 3.67 -6.14 -0.91 -7.25 -7.9 0.49 -11 8.64 5.71 -4.98 -1.94 5.89

1971-2002 0.70 1.3727Aver R 2.14 0.07 1.00 1.16 0.64 0.76 -0.06 0.02 -1.25 0.88 1.37 1.61 0.70 0.90t-test 1.826 -1.014 0.415 0.825 -0.1 0.122 -1.039 -0.68 -2.811 0.149 0.814 1.574 p 0.039 0.159 0.34 0.208 0.461 0.452 0.154 0.251 0.004 0.441 0.211 0.063 Tests (1) ANOVA F=1.27(p=0.238), (2) Kruskal-Wallis H = 13.93 (p=0.237), (3) Chi-square = 13.31 (p=0.273)Std 5.12 3.88 3.92 3.64 3.46 3.13 4.31 5.64 4.56 6.59 5.02 3.52 4.40 1.03CV 2.40 54.17 3.93 3.14 5.42 4.14 -77.03 240.58 -3.66 7.52 3.65 2.18 20.54 74.99Beta 2.18 1.277 0.086 1.344 0.992 0.976 0.988 0.646 1.975 -0.71 1.296 0.907 1.00 0.77R/beta 0.979 0.055 11.628 0.863 0.645 0.779 -0.061 0.031 -0.633 1.239 1.057 1.775 1.53 3.25R/std 0.417 0.018 0.255 0.319 0.185 0.243 -0.014 0.004 -0.274 0.134 0.273 0.457 0.17 0.21R-bRm 0.609 -0.824 0.940 0.219 -0.054 0.077 -0.752 -0.432 -2.633 0.383 0.463 0.975 -0.09 1.00Shin B 1.399 0.078 16.611 1.233 0.922 1.112 -0.087 0.044 -0.904 1.771 1.510 2.536 2.19 4.64Shin T 0.818 0.035 0.500 0.625 0.363 0.476 -0.027 0.007 -0.538 0.262 0.535 0.897 0.33 0.41NM 11 15 11 11 14 14 20 14 20 14 11 8 13.58 3.60NM(%) 34.38 46.88 34.38 34.38 43.75 43.75 62.50 43.75 62.50 43.75 34.38 25.00 42.45 11.26

Table 1 (2) Korea Stock Exchange Monthly Returns (%), 1980-2002

1 2 3 4 5 6 7 8 9 10 11 12 Aver Std.1980 5.89 -2.03 1.21 10.56 0.29 -3.27 0.08 -0.05 -2.04 -4.20 1.15 -0.06 0.63 4.061981 -1.09 -1.51 3.17 13.97 3.19 19.40 -1.79 -5.40 -5.57 -7.03 7.64 -0.83 2.01 8.081982 -4.30 2.49 -0.74 -5.03 -5.63 7.92 1.16 -2.51 -1.83 1.84 1.44 4.31 -0.07 4.041983 -8.31 4.42 -3.00 9.72 -4.30 -2.66 2.12 -4.97 -0.93 3.15 -3.12 3.04 -0.40 5.001984 2.37 4.50 2.85 1.69 -3.78 -0.15 3.27 -0.04 -3.23 -0.25 4.41 5.11 1.40 2.931985 -2.50 -2.86 1.13 -1.69 -0.04 1.86 0.59 -0.65 1.77 1.43 6.58 8.80 1.20 3.461986 -1.81 9.66 13.56 1.58 13.87 5.32 12.49 -3.33 -4.23 -5.00 11.71 1.35 4.60 7.381987 13.80 7.98 20.94 -11.48 8.19 6.13 17.90 -2.36 2.39 4.88 -6.57 10.41 6.02 9.541988 20.66 -3.35 7.21 -1.42 20.11 -9.59 2.60 -7.86 1.97 7.71 13.88 9.15 5.09 9.941989 -2.85 4.15 9.30 -6.26 -0.82 -8.38 4.80 8.89 -3.37 -5.13 1.38 0.37 0.17 5.751990 -1.49 -3.86 -2.40 -18.10 15.87 -11.42 -4.02 -10.54 -0.66 14.48 1.00 -0.13 -1.77 9.691991 -8.72 6.32 -2.33 -2.16 -5.31 -0.99 18.46 -4.73 3.22 -1.30 -6.30 -6.32 -0.85 7.391992 11.39 -9.99 -1.01 1.59 -6.78 -3.86 -7.62 10.36 -8.70 19.80 7.76 2.27 1.27 9.411993 -1.16 -4.12 3.70 8.22 4.26 -0.46 -2.53 -8.91 8.12 4.43 8.04 6.80 2.20 5.581994 9.18 -2.84 -5.62 4.79 3.39 -0.65 -0.58 1.75 11.26 5.25 -2.82 -4.38 1.56 5.351995 -9.91 -4.31 5.20 -3.73 -1.62 1.35 4.38 -2.09 7.50 0.77 -5.99 -5.15 -1.13 5.131996 -0.47 -2.96 2.50 12.21 -7.93 -9.49 0.52 -4.89 1.05 -4.06 -4.11 -10.36 -2.33 6.161997 5.32 -1.36 0.12 3.82 7.61 -1.50 -2.59 -4.23 -6.94 -27.25 -13.37 -7.74 -4.01 9.371998 50.77 -1.48 -13.94 -12.44 -21.17 -10.29 15.26 -9.66 0.05 30.01 12.01 24.47 5.30 21.571999 1.59 -8.99 19.02 21.59 -2.20 19.97 9.82 -3.28 -10.84 -0.32 19.57 3.15 5.76 11.812000 -8.19 -12.24 3.93 -15.74 0.89 12.21 -14.03 -2.42 -10.99 -16.10 -1.02 -0.91 -5.38 8.882001 22.45 -6.44 -9.49 10.35 6.03 -2.78 -9.00 0.66 -12.00 12.12 19.72 7.74 3.28 11.592002 7.84 9.61 9.22 -5.94 -5.45 -6.74 -3.33 2.56 -12.22 1.93 10.00 -13.42 -0.50 8.51

1980-2002 1.04 3.037Ave R 4.37 -0.84 2.81 0.70 0.81 0.08 2.09 -2.33 -2.01 1.62 3.61 1.64 1.040 3.037t-test 1.3292 -1.428 1.0730 -0.168 -0.124 -0.527 0.7037 -2.627 -2.136 0.2699 1.7396 0.4410p 0.0987 0.0837 0.1475 0.4339 0.4514 0.3018 0.2445 0.0077 0.0220 0.3949 0.0479 0.3318Tests (1) ANOVA F=1.178(p=0.303), (2) Kruskal-Wallis H=14.78(p=0.193), (3) Chi-square = 9.10(p=0.613)Std 13.41 6.05 8.11 10.02 8.85 8.62 8.24 5.13 6.45 11.44 8.61 8.03 8.58 2.28CV 3.07 -7.24 2.89 14.32 10.90 102.77 3.95 -2.20 -3.21 7.08 2.39 4.90 11.64 29.30Beta 2.4598 0.3240 0.7089 0.7218 0.3167 0.3857 1.4513 -0.137 0.2057 2.0109 1.8133 1.7392 1.00 0.85R/beta 1.78 -2.58 3.96 0.97 2.56 0.22 1.44 -16.99 -9.77 0.80 1.99 0.94 -1.22 6.08R/Std 0.33 -0.14 0.35 0.07 0.09 0.01 0.25 -0.46 -0.31 0.14 0.42 0.20 0.08 0.27R-bRm -1.757 -1.642 1.040 -1.097 0.023 -0.876 -1.529 -2.677 -2.522 -3.391 -0.907 -2.693 -1.50 1.25Shin B 0.713 -1.035 1.589 0.389 1.029 0.087 0.577 -6.824 -3.923 0.323 0.799 0.378 -0.49 2.44Shin T 0.435 -0.185 0.463 0.093 0.123 0.013 0.339 -0.609 -0.417 0.189 0.560 0.273 0.11 0.36NM 12 15 8 11 12 15 9 18 14 10 8 10 11.83 3.00NM(%) 52.17 65.22 34.78 47.83 52.17 65.22 39.13 78.26 60.87 43.48 34.78 43.48 51.45 13.021980-97,1999-2002, Excluding 1998Ave R 2.26 -0.81 3.57 1.30 1.81 0.56 1.49 -2.00 -2.10 0.33 3.23 0.60 0.85 2.960t-test 0.8372 -1.221 1.9436 0.2257 0.6282 -0.167 0.4267 -2.322 -1.979 -0.278 1.5528 -0.229p 0.2060 0.1179 0.0327 0.4118 0.2683 0.4347 0.3370 0.0152 0.0305 0.3918 0.0677 0.4104Tests (1) ANOVA F=1.1046 (p=0.358), (2) Kruskal-Wallis H=13.41(p=0.2675)Std 9.02 6.19 7.41 9.83 7.62 8.52 7.90 4.99 6.59 9.84 8.61 6.45 7.75 1.50CV 3.99 -7.68 2.08 7.58 4.21 15.34 5.32 -2.49 -3.13 30.29 2.67 10.75 5.74 9.90Beta 1.5912 0.3729 1.1866 1.1137 0.8806 0.6761 1.2821 0.0256 0.1771 1.5314 1.7967 1.3661 1.00 0.58R/beta 1.42 -2.16 3.01 1.16 2.06 0.82 1.16 -78.20 -11.88 0.21 1.80 0.44 -6.68 22.86R/std 0.25 -0.13 0.48 0.13 0.24 0.07 0.19 -0.40 -0.32 0.03 0.37 0.09 0.08 0.26

R-bRm 0.673 -1.177 2.384 0.188 0.933 -0.118 0.209 -2.027 -2.280 -1.201 1.436 -0.761 -0.15 1.40Shin B 1.597 0.374 1.191 1.118 0.884 0.679 1.287 0.026 0.178 1.537 1.803 1.371 1.00 0.58Shin T 0.194 -0.1 0.372 0.102 0.184 0.05 0.145 -0.31 -0.247 0.026 0.289 0.072 0.06 0.20

Table 1 (3) Tokyo Stock Exchange Monthly Returns (%), 1984-2002

1 2 3 4 5 6 7 8 9 10 11 12 Aver Std1984 6.62 0.08 13.88 -1.05 -10.12 2.67 -4.05 6.62 1.08 4.96 2.08 4.97 2.31 6.021985 1.88 5.51 3.19 -3.55 3.52 3.60 -3.00 2.24 1.38 -0.57 -2.14 4.33 1.37 3.001986 -1.13 4.97 17.70 -2.16 4.18 4.50 6.13 9.03 -1.13 -7.83 7.01 3.69 3.75 6.451987 14.93 1.24 5.16 12.07 2.54 -5.70 -1.55 7.20 -0.83 -9.92 -3.90 -7.11 1.18 7.621988 12.16 7.86 3.66 1.87 -3.37 2.68 3.29 -5.54 1.44 0.51 6.12 3.42 2.84 4.681989 4.43 -0.72 0.81 0.51 1.83 -3.63 7.55 -1.16 3.60 -0.44 5.43 1.69 1.66 3.141990 -5.30 -6.59 -13.01 -0.97 10.42 -4.32 -4.33 -11.93 -20.01 17.71 -10.55 5.70 -3.60 10.591991 -0.86 13.85 0.81 -0.38 0.30 -7.61 2.46 -6.44 5.77 3.13 -8.01 -1.08 0.16 6.081992 -5.15 -4.95 -8.36 -7.46 4.30 -10.35 -0.62 14.27 -5.11 -2.46 3.56 -1.15 -1.96 6.791993 -0.67 -1.09 12.01 13.22 0.93 -3.16 5.16 2.01 -4.10 0.81 -15.99 4.92 1.17 7.651994 13.30 -0.02 -4.11 2.62 5.19 -0.82 -2.26 0.22 -3.54 0.54 -4.05 2.65 0.81 4.881995 -6.05 -7.80 -2.45 1.96 -5.68 -4.72 11.75 6.51 1.17 -2.15 5.18 6.63 0.36 6.161996 1.94 -3.44 5.51 4.24 -1.87 1.89 -7.58 -2.48 5.85 -4.76 0.79 -5.96 -0.49 4.521997 -7.22 1.40 -0.83 4.74 3.11 5.08 -0.88 -7.26 -2.50 -8.85 -1.97 -6.02 -1.77 4.801998 8.05 0.61 -1.49 -2.28 -0.34 0.98 2.16 -12.90 -5.74 0.07 10.48 -5.35 -0.48 6.131999 3.78 -0.55 13.63 5.11 -3.25 8.45 4.29 -2.05 3.28 3.00 1.90 4.09 3.47 4.542000 -0.15 -0.75 1.72 -2.68 -5.60 4.71 -8.44 3.96 -2.82 -5.38 -1.72 -4.16 -1.78 3.942001 0.61 -3.56 2.93 6.69 -4.35 -0.54 -8.10 -6.33 -7.85 2.94 -0.82 -1.62 -1.67 4.592002 -5.78 4.534 4.544 2.21 3.85 -8.37 -5.73 -2.27 -1.02 -6.87 2.84 -5.31 -1.45 4.88

0.31 2.03Ave R 1.86 0.56 2.91 1.83 0.29 -0.77 -0.20 -0.33 -1.64 -0.82 -0.20 0.23 0.31 2.03t-test 1.1434 0.2261 1.8039 1.2659 -0.012 -0.991 -0.454 -0.409 -1.738 -0.714 -0.356 -0.085p value 0.1339 0.4118 0.044 0.1109 0.4952 0.1675 0.3276 0.3437 0.0497 0.2422 0.3631 0.4666Tests (1) ANOVA F=0.903 (p=0.5386), (2) Kruskal-Wallis H=7.441 (p=0.7624), (3) Chi-square = 2.41 (p=0.9965)Std 6.71 5.18 7.65 5.14 4.88 5.23 5.67 7.21 5.84 6.25 6.48 4.69 5.91 0.95CV 3.60 9.30 2.63 2.81 16.57 -6.78 -28.72 -21.75 -3.57 -7.63 -32.75 20.60 -3.81 16.86Beta 1.7185 1.0080 2.8124 0.3954 -0.740 1.0706 1.5119 1.1273 1.7483 -0.534 0.8844 0.9964 1.00 0.97R/beta 1.084 0.553 1.035 4.620 0.398 -0.721 -0.131 -0.294 -0.936 -1.534 -0.224 0.229 0.34 1.56R/std 0.277 0.108 0.380 0.356 0.060 -0.147 -0.035 -0.046 -0.280 -0.131 -0.031 0.049 0.05 0.20R-bRm -1.677 -1.519 -2.883 1.0123 -1.23 -2.977 -3.312 -2.654 -5.237 -1.919 -2.02 -1.825 -2.19 1.48Shin B 0.526 0.268 0.502 2.243 0.193 -0.350 -0.063 -0.143 -0.454 -0.744 -0.109 0.111 0.17 0.76Shin T 0.6128 0.2375 0.8402 0.7853 0.1333 -0.326 -0.077 -0.102 -0.618 -0.29 -0.067 0.1072 0.10 0.45NM 9 10 6 8 8 10 11 10 11 10 9 9 9.25 1.42NM(%) 47.37 52.63 31.58 42.11 42.11 52.63 57.89 52.63 57.89 52.63 47.37 47.37 48.68 7.49

Table 1 (4) Jakarta Stock Exchange Monthly Returns (%), 1989-2002

1 2 3 4 5 6 7 8 9 10 11 12 Ave Std.1989 -2.31 3.11 8.52 -11.27 -0.32 9.15 -0.40 48.31 -5.63 -1.62 -8.99 -0.56 3.17 9.431990 10.54 14.14 20.77 4.89 -0.38 -1.90 -1.72 -6.94 -17.95 -11.10 -8.23 9.31 0.95 9.611991 -8.32 2.17 4.29 1.38 -3.90 -12.91 -1.82 -11.47 -17.21 -9.03 6.46 2.52 -3.99 9.561992 11.45 1.91 -0.82 -0.51 7.92 4.79 1.40 -5.24 -0.96 3.08 -7.14 -3.95 0.99 9.541993 2.12 7.22 3.46 1.08 8.84 5.41 -1.01 16.98 0.64 11.00 11.29 13.49 6.71 9.641994 0.55 -7.73 -9.88 -6.07 8.52 -8.87 -1.36 13.12 -2.41 5.13 -7.81 -2.69 -1.63 9.621995 -7.62 4.55 -5.50 -2.84 14.13 3.58 4.02 -2.21 -1.50 -0.97 -1.37 6.46 0.89 9.881996 12.81 1.15 0.08 6.52 -1.03 -3.76 7.03 -13.90 4.81 -1.03 7.92 3.98 2.05 10.341997 8.42 2.06 -6.12 -1.54 6.74 0.00 3.73 -31.58 10.67 -8.46 -19.73 0.00 -2.98 10.071998 20.97 -0.73 12.24 -15.01 -8.62 6.05 8.03 -28.91 -19.36 8.92 28.43 3.05 1.26 8.431999 3.49 -3.85 -0.53 25.69 18.18 1.54 0.61 -5.16 -3.37 8.38 -1.70 15.95 4.94 8.892000 -5.99 -9.40 1.17 -9.69 -13.75 13.38 -4.45 -5.24 -9.66 -3.79 5.89 -3.00 -3.71 8.182001 2.23 0.63 -11.03 -5.99 13.30 7.82 1.48 -1.92 -9.89 -2.23 -0.89 3.08 -0.28 7.782002 15.20 0.36 6.29 10.85 -0.61 -4.86 -8.19 -4.31 -5.49 -11.99 5.68 8.96 0.99 7.46

1989-2002 0.67 3.087Ave R 4.54 1.11 1.64 -0.18 3.50 1.39 0.53 -2.75 -5.52 -0.98 0.70 4.04 0.670 3.087t-test 1.6606 0.2997 0.429 -0.331 1.2762 0.3771 -0.109 -0.688 -2.671 -0.984 0.0107 2.713p 0.0604 0.3846 0.3375 0.373 0.1121 0.3561 0.4576 0.2516 0.0096 0.1714 0.4958 0.0089Tests (1) ANOVA F=1.1998 (p=0.2914), (2) Kruskal-Wallis H=13.659 (p=0.1891), (3) Chi-square = 10.00 (p=0.5304)Std. 8.99 5.84 8.66 10.29 9.09 7.27 4.30 19.62 8.67 7.53 11.62 6.14 9.00 19.29CV 1.98 5.24 5.29 -57.39 2.60 5.24 8.20 -7.14 -1.57 -7.69 16.58 1.52 -2.26 19.32Beta 0.7478 0.6664 0.6785 1.2393 1.2166 0.6064 0.1953 2.6065 0.4969 1.4177 0.7904 1.3383 1.00 19.34R/beta 6.07 1.67 2.41 -0.14 2.88 2.29 2.69 -1.05 -11.11 -0.69 0.89 3.02 0.74 19.36R/std 0.50 0.19 0.19 -0.02 0.39 0.19 0.12 -0.14 -0.64 -0.13 0.06 0.66 0.11 19.36R-bRm 3.5889 0.2672 0.7769 -1.753 1.9563 0.617 0.277 -6.058 -6.153 -2.78 -0.303 2.3432 -0.60 19.36Shin B 4.779 1.3158 1.9016 -0.114 2.2662 1.8012 2.1167 -0.83 -8.751 -0.544 0.6981 2.3787 0.58 19.65Shin T 2.04 0.7706 0.7641 -0.07 1.5557 0.7704 0.4927 -0.566 -2.573 -0.525 0.2436 2.6617 0.46 19.96NM 4 4 6 8 7 5 7 11 11 9 8 4 7 2.52NM(%) 28.57 28.57 42.86 57.14 50.00 35.71 50.00 78.57 78.57 64.29 57.14 28.57 50 18.02

1989-2002, Excluding 1989 and 1998 0.41 3.25Ave R 3.74 1.1 0.18 1.98 4.83 0.35 -0.02 -4.82 -4.36 -1.75 -0.8 4.51 0.41 3.25t-test 1.5039 0.3987 -0.094 0.6812 1.967 -0.028 -0.312 -1.626 -2.017 -1.227 -0.499 3.157 p 0.0804 0.3489 0.4636 0.2549 0.037 -0.028 0.3804 0.0661 0.034 0.1228 0.3137 0.005 F-test (1) ANOVA F=1.7131(p=0.0770), Kruskal-Wallis H=18.3355 (p=0.0741)Std. 8.12 6.29 8.48 9.43 9 7.34 4.05 12.29 8.36 7.58 8.87 6.5 8.03 20.4CV 2.17 5.72 46.66 4.76 1.86 20.88 -173.4 -2.55 -1.92 -4.33 -11.05 1.44 -9.15 21.76Beta 0.838 0.675 0.482 1.687 1.472 0.428 0.175 1.754 0.631 1.451 0.8687 1.539 1.00 3.70R/beta 4.46 1.63 0.38 1.17 3.28 0.82 -0.13 -2.75 -6.91 -1.21 -0.92 2.93 0.23 4.12R/std 0.46 0.17 0.02 0.21 0.54 0.05 -0.01 -0.39 -0.52 -0.23 -0.09 0.69 0.08 4.47Shin B 10.89 3.979 0.919 2.863 8.005 2.006 -0.32 -6.71 -16.9 -2.94 -2.253 7.146 0.56 5.49Shin T 3.650 1.387 0.170 1.666 4.252 0.380 -0.05 -3.11 -4.13 -1.83 -0.717 5.5 0.6 2.91

Table 1(5) Shanghai Stock Exchange Monthly Returns (%), 1991 - 2002

1 2 3 4 5 6 7 8 9 10 11 12 Ave Std.1991 1.85 2.34 -9.64 -5.20 0.78 19.79 4.54 24.08 1.40 20.83 18.76 12.77 7.69 11.1291992 7.00 16.42 4.55 16.82 177.2 -3.52 -11.68 -21.75 -14.69 -27.78 42.85 7.70 16.10 54.291993 53.57 11.80 -30.90 46.75 -31.15 7.65 -12.51 1.66 -0.60 -8.48 20.89 -15.34 3.61 26.841994 -7.62 0.09 -8.63 -15.88 -6.13 -15.63 -28.85 135.2 0.74 -17.21 4.37 -5.23 2.93 42.651995 -13.16 -2.37 17.78 -10.36 20.79 -9.98 10.30 4.07 -0.20 -0.71 -10.62 -13.39 -0.65 11.851996 -3.23 2.90 0.62 22.42 -5.51 24.95 2.27 -1.52 8.10 11.56 5.76 -11.22 4.76 10.741997 5.20 7.83 18.68 12.89 -7.79 -2.72 -4.84 2.63 -10.13 7.56 -3.45 4.78 2.55 8.621998 2.41 -1.34 3.02 8.08 5.04 -5.10 -1.66 -12.66 8.06 -2.06 2.47 -8.07 -0.15 6.301999 -1.05 -3.93 6.23 -3.21 14.13 32.06 -5.21 1.60 -3.47 -4.21 -4.63 -4.77 1.96 11.082000 12.32 11.70 5.00 2.00 3.17 1.77 4.95 -0.12 -5.49 2.68 5.57 0.14 3.64 4.912001 -0.38 -5.15 7.84 0.30 4.49 0.17 -13.42 -4.49 -3.78 -4.29 3.48 -5.84 -1.76 5.652002 -15.15 9.17 5.19 3.98 -9.10 14.31 -4.68 0.90 -5.10 -4.69 -4.86 -5.33 -1.28 8.24

1991-2002 3.28 4.88Ave R 3.48 4.12 1.65 6.55 13.83 5.31 -5.07 10.80 -2.10 -2.23 6.72 -3.65 3.28 5.84t-test 0.0397 0.5131 -0.376 0.6975 0.7385 0.4617 -2.400 0.6304 -1.923 -1.290 1.125 -3.490 p value 0.4845 0.3090 0.3571 0.2500 0.2378 0.3266 0.0176 0.2707 0.0404 0.1118 0.1423 0.0025 3 tests (1) ANOVA F=0.804 (p=0.6360), (2) Kruskal-Wallis H=12.97 (p=0.2952), (3) Ch-square = 6.82 (p=0.8135)Std 17.67 7.07 13.27 16.80 53.07 14.65 10.57 40.61 6.62 12.70 14.63 8.55 18.02 14.17CV 5.08 1.72 8.06 2.56 3.84 2.76 -2.09 3.76 -3.15 -5.69 2.18 -2.34 1.39 3.94Beta 0.8776 0.8798 -0.588 0.8988 8.2697 0.1442 -0.206 -0.686 -0.554 -0.725 2.650 1.040 1.00 2.50R/beta 3.966 4.684 2.798 7.289 1.672 36.837 -24.58 15.745 -3.784 -3.080 2.534 -3.511 3.38 14.19R/std 0.197 0.583 0.124 0.390 0.261 0.363 -0.479 0.266 -0.317 -0.176 0.459 -0.427 0.10 0.36R-bRm 3.3141 3.9542 1.5344 6.3801 12.258 5.2845 -5.105 10.669 -2.203 -2.371 6.2123 -3.848 3.01 5.59Shin B 2.8951 3.4193 2.0425 5.3201 1.2207 26.888 -17.94 11.493 -2.762 -2.248 1.8499 -2.563 2.47 10.36Shin T 0.4084 1.2078 0.2572 0.8083 0.5402 0.7518 -0.994 0.5513 -0.657 -0.365 0.9516 -0.885 0.21 0.75NM 6 4 3 4 5 5 8 5 8 8 4 8 5.67 1.87NM(%) 50.00 33.33 25.00 33.33 41.67 41.67 66.67 41.67 66.67 66.67 33.33 66.67 47.22 15.621991,1993,1995-2002, excluding 1992, 1994 2.04 3.0203Ave R 4.24 3.29 2.38 7.77 -0.51 8.29 -2.03 1.62 -1.12 1.82 3.34 -4.63 2.04 3.0203t-test 0.382 0.65 0.069 1.123 -0.524 1.545 -1.745 -0.176 -1.655 -0.098 0.489 -2.782p value 0.356 0.266 0.477 0.145 0.307 0.078 0.058 0.432 0.066 0.462 0.318 0.011Tests (1) ANOVA F = 1.00 (p=0.4503), (2) Kruskal-Wallis H =12.445 (p=0.3311)Std 19.129 6.4652 14.211 16.604 14.259 13.961 7.6532 9.2266 5.8246 9.0276 10.16 8.5821 11.259 4.2482CV 4.512 1.962 5.962 2.138 -27.72 1.684 -3.776 5.710 -5.192 4.964 3.044 -1.855 -0.714 9.248Beta 2.318 0.745 -2.266 1.353 -1.381 2.202 0.735 2.027 0.357 2.224 2.291 1.390 1.000 1.494p value 0.298 0.324 0.160 0.493 0.412 0.164 0.416 0.036 0.608 0.014 0.030 0.151 0.259 0.196R/beta 1.829 4.414 1.050 5.743 -0.369 3.765 -2.762 0.799 -3.135 0.818 1.458 -3.331 0.857 2.930R/Std 0.222 0.509 0.167 0.468 -0.036 0.594 -0.265 0.176 -0.192 0.202 0.329 -0.539 0.136 0.339R-bRm -0.813 1.665 -2.560 4.821 -3.520 3.490 -3.632 -2.799 -1.899 -3.028 -1.654 -7.660 -1.466 3.401Shin B 0.898 2.166 0.515 2.818 -0.181 1.848 -1.355 0.392 -1.538 0.402 0.715 -1.635 0.420 1.438Shin T 0.630 1.447 0.476 1.331 -0.102 1.689 -0.754 0.499 -0.547 0.573 0.935 -1.534 0.387 0.964The standard deviations are calculated from the average series of the 12 monthly returns for the sample period.If beta < 0, the absolute value is used for the performance indexes: R/beta, R-bRm, and Shin beta index.

Table 1( 6) NASDAQ Stocks, Monthyly Returns (%), 1985-2002

1 2 3 4 5 6 7 8 9 10 11 12 Av R Std1985 12.79 1.97 -1.76 0.50 3.64 1.86 1.72 -1.20 -5.85 4.35 7.35 3.47 2.40 4.691986 3.35 7.06 4.23 2.27 4.44 1.32 -8.41 3.10 -8.41 2.88 -0.33 -3.00 0.71 4.941987 12.41 8.39 1.20 -2.86 -0.31 1.97 2.40 4.62 -2.35 -27.23 -5.60 8.29 0.08 10.061988 4.30 6.47 2.07 1.23 -2.35 6.59 -1.88 -2.76 2.95 -1.34 -2.88 2.67 1.26 3.481989 5.22 -0.40 1.75 5.14 4.35 -2.44 4.25 3.42 0.77 -3.66 0.11 -0.29 1.52 2.981990 -8.58 2.41 2.28 -3.54 9.26 0.72 -5.21 -13.01 -9.63 -4.27 8.88 4.09 -1.38 7.161991 10.81 9.39 6.44 0.50 4.41 -5.97 5.49 4.71 0.23 3.06 -3.51 11.92 3.96 5.481992 5.78 2.14 -4.69 -4.16 1.15 -3.71 3.06 -3.05 3.58 3.76 7.86 3.71 1.28 4.191993 2.86 -3.67 2.89 -4.16 5.91 0.49 0.11 5.41 2.68 2.16 -3.19 2.97 1.21 3.381994 3.05 -1.00 -6.19 -1.29 0.18 -3.98 2.30 6.02 -0.17 1.73 -3.50 0.22 -0.22 3.331995 3.09 2.39 2.96 3.28 2.44 7.97 7.26 1.89 2.30 -0.72 2.23 -0.67 2.87 2.581996 0.73 3.80 0.12 8.09 4.44 -4.70 -8.81 5.64 7.48 -0.44 5.82 -0.12 1.84 5.061997 6.88 -5.14 -6.67 3.20 11.07 2.98 10.52 -0.41 6.20 -5.46 0.44 -1.89 1.81 6.061998 3.12 9.33 3.68 1.78 -4.79 6.51 -1.18 -19.93 12.98 4.58 10.06 12.47 3.22 9.041999 14.28 -8.69 7.58 3.31 -2.85 8.73 -1.77 3.82 0.25 8.02 12.46 21.98 5.59 8.412000 -3.17 19.20 -2.64 -15.57 -11.91 16.62 -5.02 11.66 -12.68 -8.26 -22.90 -4.90 -3.30 12.982001 12.23 -22.39 -14.48 15.00 -0.27 2.37 -6.18 -10.94 -16.98 12.77 14.22 1.03 -1.14 13.102002 -0.84 -10.47 6.58 -8.51 -4.29 -9.44 -9.22 -1.01 -10.86 13.45 11.21 -9.69 -2.76 8.77

1.05 3.30Av R 4.91 1.15 0.30 0.23 1.36 1.55 -0.59 -0.11 -1.53 0.30 2.15 2.90 1.05 1.72Std. 6.01 9.22 5.57 6.55 5.45 6.25 5.74 7.75 7.77 8.94 8.86 7.23 7.11 1.38Beta 1.4986 0.0614 0.8882 1.3347 0.6674 0.1236 1.2041 -0.110 2.3098 0.5157 1.1700 2.3361 1.00 0.81p 0.0146 0.9526 0.1408 0.0539 0.2652 0.8500 0.0464 0.8995 0.0022 0.6054 0.2277 0.0006 t-test 3.2151 0.0459 -0.616 -0.593 0.2485 0.3218 -1.371 -0.604 -1.695 -0.358 0.5513 1.3587 p 0.0025 0.4820 0.2730 0.2806 0.4034 0.3758 0.0941 0.2761 0.0542 1.7396 0.2943 0.0960 Tests (1) ANOVA F = 1.0119 (p=0.4370), (2) Kruskal-Wallis H = 11.3199 (p=0.4169), (3) Chi-square GOF=3.60 (p=0.9802)R/beta 3.2741 18.805 0.3348 0.1747 2.0413 12.538 -0.488 1.02 -0.662 0.5795 1.8391 1.2428 3.39 5.99R/std. 0.8164 0.1253 0.0534 0.0356 0.2499 0.2478 -0.102 -0.014 -0.197 0.0334 0.2429 0.4017 0.16 0.27R-bRm 1.775 1.026 -1.559 -2.556 -0.033 1.291 -3.104 0.117 -6.357 -0.779 -0.294 -1.979 -1.04 2.27Shin B 3.118 17.909 0.319 0.166 1.944 11.941 -0.465 0.971 -0.631 0.552 1.752 1.184 3.23 5.71Shin T 2.566 0.394 0.168 0.112 0.785 0.779 -0.322 -0.045 -0.619 0.105 0.763 1.262 0.50 0.84NM 3 7 6 7 7 6 9 8 8 8 7 7 6.92 1.51NM(%) 0.167 0.389 0.333 0.389 0.389 0.333 0.500 0.444 0.444 0.444 0.389 0.389 0.38 0.08

Table 1 (7) Dow-Jones Industrial Average, Monthly Returns (%), 1971-2002

1 2 3 4 5 6 7 8 9 10 11 12 Av R Std1971 3.53 1.19 2.91 4.14 -3.61 -1.84 -3.67 4.62 -1.21 -5.43 -0.92 7.09 0.57 3.921972 1.35 2.87 1.36 1.44 0.68 -3.30 -0.46 4.22 -1.08 0.23 6.56 0.18 1.17 2.541973 -2.06 -4.39 -0.43 -3.11 -2.17 -1.08 3.89 -4.19 6.70 1.00 -14.04 3.48 -1.37 5.261974 0.55 0.57 -1.60 -1.17 -4.13 0.02 -5.61 -10.40 -10.42 9.48 -7.03 -0.40 -2.51 5.511975 14.20 5.03 3.94 6.91 1.34 5.61 -5.40 0.46 -4.96 5.30 2.95 -0.96 2.87 5.361976 14.42 -0.28 2.77 -0.26 -2.18 2.83 -1.81 -1.11 1.69 -2.56 -1.83 6.07 1.48 4.831977 -5.01 -1.89 -1.85 0.85 -3.04 1.96 -2.86 -3.21 -1.67 -3.39 1.38 0.18 -1.55 2.171978 -7.37 -3.61 2.06 10.55 0.39 -2.57 5.29 1.68 -1.25 -8.47 0.82 0.75 -0.14 5.181979 4.25 -3.62 6.60 -0.85 -3.81 2.40 0.52 4.87 -1.01 -7.16 0.82 1.98 0.42 3.981980 4.44 -1.46 -8.96 3.98 4.14 2.00 7.77 -0.29 -0.02 -0.85 7.44 -2.95 1.27 4.721981 -1.73 2.88 3.01 -0.61 -0.60 -1.50 -2.52 -7.43 -3.57 0.31 4.27 -1.57 -0.76 3.181982 -0.45 -5.36 -0.19 3.11 -3.41 -0.93 -0.41 11.46 -0.55 10.64 4.80 0.69 1.62 5.121983 2.79 3.39 1.60 8.51 -2.14 1.83 -1.87 1.42 1.39 -0.64 4.15 -1.36 1.59 3.001984 -3.02 -5.41 0.89 0.51 -5.63 2.49 -1.51 9.78 -1.45 0.06 -1.53 1.91 -0.24 4.071985 6.21 -0.22 -1.34 -0.69 4.55 1.53 0.90 -1.00 -0.40 3.44 7.12 5.07 2.10 3.041986 1.57 8.79 6.41 -1.90 5.20 0.85 -6.20 6.93 -6.89 6.23 1.94 -0.95 1.83 5.131987 13.82 3.06 3.63 -0.79 0.23 5.54 6.35 3.53 -2.50 -23.22 -8.02 5.74 0.61 9.221988 1.00 5.79 -4.03 2.22 -0.06 5.45 -0.61 -4.56 4.00 1.69 -1.59 2.56 0.99 3.341989 8.01 -3.58 1.56 5.46 2.54 -1.62 9.04 2.88 -1.63 -1.77 2.31 1.73 2.08 3.941990 -5.91 1.42 3.04 -1.86 8.28 0.14 0.85 -10.01 -6.19 -0.42 4.81 4.06 -0.15 5.201991 2.73 5.33 1.10 -0.89 4.83 -3.99 4.06 0.62 -0.88 1.73 -5.68 9.47 1.54 4.171992 1.72 1.37 -0.99 3.82 1.13 -2.31 2.27 -4.02 0.44 -1.39 2.45 -0.12 0.36 2.231993 0.27 1.84 1.91 -0.22 2.91 -0.32 0.67 3.16 -2.63 3.53 0.09 1.90 1.09 1.781994 5.97 -3.68 -5.11 1.26 2.08 -3.55 3.85 3.96 -1.79 1.69 -4.32 2.55 0.24 3.751995 0.25 4.35 3.65 3.93 3.33 2.04 3.34 -2.08 3.87 -0.70 6.71 0.84 2.46 2.471996 5.44 1.67 1.85 -0.32 1.33 0.20 -2.22 1.58 4.74 2.50 8.16 -1.13 1.98 2.931997 5.66 0.95 -4.28 6.46 4.59 4.66 7.17 -7.30 4.24 -6.33 5.12 1.09 1.84 5.091998 -0.02 8.08 2.97 3.00 -1.80 0.58 -0.77 -15.13 4.03 9.56 6.10 0.71 1.44 6.301999 1.93 -0.56 5.15 10.25 -2.13 3.89 -2.88 1.63 -4.55 3.80 1.38 5.69 1.97 4.152000 -4.84 -7.42 7.84 -1.72 -1.97 -0.71 0.71 6.59 -5.03 3.01 -5.07 3.59 -0.42 4.882001 0.92 -3.60 -5.87 8.67 1.65 -3.75 0.19 -5.45 -11.08 2.57 8.56 1.73 -0.46 5.822002 -1.01 1.88 2.95 -4.40 -0.21 -6.87 -5.48 -0.84 -12.37 10.60 5.94 -6.23 -1.34 6.24

0.71 1.31Av R 2.140 0.527 1.077 2.130 0.525 0.475 0.594 0.011 -1.304 0.759 1.662 1.982 0.88 1.00Std. 5.338 4.012 3.759 3.938 3.287 3.048 4.029 5.914 4.532 6.460 5.327 3.157 4.40 1.12Beta 2.2253 1.1636 0.3916 1.1545 0.9962 0.9138 0.5632 1.1579 1.4345 -0.071 1.6808 0.3889 1.00 0.63p 0.001 0.0323 0.4574 0.0304 0.0248 0.0265 0.3167 0.1574 0.0186 0.9384 0.019 0.3787 t-value 1.7489 -0.343 0.4626 2.1201 -0.602 -0.813 -0.442 -0.934 -3.167 -0.202 0.7619 1.6927p 0.045 0.3671 0.3234 0.0211 0.2758 0.2113 0.3309 0.1788 0.0017 0.4207 0.2259 0.0503Tests (1) ANOVA F=1.7426 (p=0.0626) (2) Kruskal-Wallis H = 17.9758 (p=0.0821) (3) Chi-square GOF =11.17 (p=0.4291)R/beta 0.962 0.453 2.751 1.845 0.527 0.520 1.054 0.010 -0.909 10.73 0.989 5.095 2.002 3.142R/std. 0.401 0.131 0.287 0.541 0.160 0.156 0.147 0.002 -0.288 0.117 0.312 0.628 0.216 0.243R-bRm 0.560 -0.299 0.799 1.310 -0.183 -0.174 0.194 -0.811 -2.322 0.809 0.469 1.705 0.171 1.059Shin T 0.740 0.242 0.529 0.998 0.294 0.288 0.272 0.003 -0.531 0.217 0.576 1.158 0.399 0.449Shin B 1.354 0.637 3.875 2.598 0.742 0.732 1.485 0.014 -1.280 15.12 1.393 7.176 2.820 4.425NM 10 14 11 14 15 14 16 15 23 13 10 9 13.667 3.725NM(%) 0.3125 0.4375 0.3438 0.4375 0.4688 0.4375 0.500 0.4688 0.7188 0.4063 0.3125 0.2813 0.4271 0.116The October beta is negative and close to zero. Thus, the October results are misleading.

Table 1 (8) SP500 Total Return Index, Monthly Returns (%), 1971-2002

1 2 3 4 5 6 7 8 9 10 11 12 Av R Std1971 4.32 1.17 3.94 3.89 -3.91 0.33 -3.87 3.88 -0.44 -3.91 0.02 8.88 1.19 3.97121972 2.06 2.77 0.83 0.68 1.97 -1.94 0.48 3.69 -0.25 1.19 4.81 1.42 1.47 1.791973 -1.49 -3.53 0.08 -3.83 -1.63 -0.40 4.07 -3.41 4.27 0.17 -11.1 1.98 -1.23 4.131974 -0.72 -0.07 -2.05 -3.59 -3.02 -1.14 -7.42 -8.64 -11.5 16.81 -4.89 -1.56 -2.32 6.971975 12.72 6.38 2.54 5.10 4.76 4.77 -6.44 -1.76 -3.12 6.53 2.82 -0.81 2.79 5.161976 12.17 -0.84 3.37 -0.78 -1.11 4.43 -0.48 -0.18 2.58 -1.86 -0.41 5.61 1.88 4.061977 -4.73 -1.82 -1.05 0.42 -1.96 4.94 -1.54 -1.42 0.16 -3.90 3.16 0.75 -0.58 2.721978 -5.74 -2.03 2.94 9.02 0.92 -1.38 5.83 3.01 -0.32 -8.72 2.15 1.96 0.64 4.791979 4.43 -3.21 5.96 0.63 -2.17 4.35 1.34 5.77 0.43 -6.40 4.75 2.14 1.50 3.881980 6.22 -0.01 -9.72 4.62 5.15 3.16 6.96 1.01 2.94 2.02 10.65 -3.02 2.50 5.231981 -4.18 1.74 4.00 -1.93 0.26 -0.63 0.21 -5.77 -4.93 5.40 4.13 -2.56 -0.36 3.691982 -1.31 -5.59 -0.52 4.52 -3.41 -1.50 -1.78 12.14 1.25 11.51 4.04 1.93 1.77 5.511983 3.72 2.29 3.69 7.88 -0.87 3.89 -2.95 1.50 1.38 -1.16 2.11 -0.52 1.75 2.911984 -0.56 -3.52 1.73 0.95 -5.54 2.17 -1.24 11.04 0.02 0.39 -1.12 2.63 0.58 4.041985 7.79 1.22 0.07 -0.09 5.78 1.57 -0.15 -0.85 -3.13 4.62 6.86 4.84 2.38 3.471986 0.56 7.47 5.58 -1.13 5.32 1.69 -5.59 7.42 -8.27 5.77 2.43 -2.55 1.56 5.141987 13.47 3.95 2.89 -0.89 0.87 5.05 5.07 3.73 -2.19 -21.5 -8.24 7.61 0.81 8.831988 4.21 4.66 -3.09 1.11 0.87 4.59 -0.38 -3.40 4.26 2.78 -1.43 1.74 1.33 2.921989 7.32 -2.49 2.33 5.19 4.05 -0.57 9.03 1.95 -0.41 -2.32 2.04 2.40 2.38 3.591990 -6.71 1.29 2.65 -2.49 9.75 -0.67 -0.32 -9.04 -4.87 -0.43 6.46 2.79 -0.13 5.311991 4.36 7.15 2.42 0.24 4.31 -4.58 4.66 2.37 -1.67 1.34 -4.03 11.44 2.33 4.571992 -1.86 1.30 -1.94 2.94 0.49 -1.49 4.09 -2.05 1.18 0.35 3.41 1.23 0.64 2.151993 0.83 1.36 2.11 -2.42 2.68 0.29 -0.40 3.79 -0.77 2.07 -0.95 1.21 0.82 1.751994 3.40 -2.71 -4.36 1.28 1.64 -2.45 3.28 4.10 -2.45 2.25 -3.64 1.48 0.15 3.051995 2.59 3.90 2.95 2.94 4.00 2.32 3.32 0.25 4.22 -0.36 4.39 1.93 2.70 1.501996 3.40 0.93 0.96 1.47 2.58 0.38 -4.42 2.11 5.63 2.76 7.56 -1.98 1.78 3.141997 6.25 0.78 -4.11 5.97 6.09 4.48 7.96 -5.60 5.48 -3.34 4.63 1.72 2.52 4.601998 1.11 7.21 5.12 1.01 -1.72 4.06 -1.06 -14.5 6.41 8.13 6.06 5.76 2.30 6.211999 4.18 -3.11 4.00 3.87 -2.36 5.55 -3.12 -0.49 -2.74 6.33 2.03 5.89 1.67 3.782000 -5.02 -1.89 9.78 -3.01 -2.05 2.47 -1.56 6.21 -5.28 -0.42 -7.88 0.49 -0.68 4.952001 3.55 -9.12 -6.34 7.77 0.67 -2.43 -0.98 -6.26 -8.08 1.91 7.67 0.88 -0.90 5.732002 -1.46 -1.93 3.76 -6.06 -0.74 -7.12 -7.79 0.66 -10.9 8.80 5.89 -5.87 -1.90 5.96

0.98 1.39Av R 2.34 0.43 1.27 1.42 0.99 1.07 0.15 0.35 -0.97 1.15 1.70 1.87 0.98 0.89Std 5.1333 3.8524 3.9057 3.6698 3.4978 3.1448 4.3434 5.6667 4.5754 6.6039 5.0181 3.581 4.42 1.02Beta 2.1697 1.2425 0.0663 1.3645 0.9747 1.00 1.0012 0.7172 1.9689 -0.70 1.2867 0.9093 1.00 0.76p 0.000 0.010 0.898 0.003 0.029 0.012 0.075 0.337 0.000 0.422 0.046 0.048t-test 1.7226 -0.901 0.3943 0.7734 0.0167 0.1786 -1.142 -0.634 -2.822 0.1378 0.8652 1.5007p 0.0475 0.1873 0.348 0.2226 0.4934 0.4297 0.1312 0.2655 0.0041 0.4457 0.1968 0.0718Tests (1) ANOVA F=1.23 (p=0.2641), (2) Kruskal-Wallis H=14.575 (p=0.2655), (3) Chi-Square GOF=9.75(p=0.5535)R/beta 1.0782 0.3446 19.1 1.0371 1.0148 1.0689 0.1488 0.4927 -0.493 1.6387 1.321 2.056 2.40 5.30R/std 0.4557 0.1111 0.3242 0.3856 0.2828 0.3399 0.0343 0.0624 -0.212 0.174 0.3387 0.5221 0.23 0.21R-bRm 0.2131 -0.789 1.2014 0.078 0.034 0.0889 -0.832 -0.349 -2.901 1.8357 0.4387 0.9784 0.00 1.20Shin B 1.1002 0.3517 19.49 1.0583 1.0356 1.0907 0.1518 0.5027 -0.504 1.6722 1.3479 2.0979 2.45 5.41Shin T 0.6464 0.1577 0.4599 0.547 0.4011 0.482 0.0486 0.0884 -0.301 0.2467 0.4804 0.7405 0.33 0.29NM 11 15 9 11 13 13 19 14 18 12 10 8 12.75 3.3609NM(%) 0.3438 0.4688 0.2813 0.3438 0.4063 0.4063 0.5938 0.4375 0.5625 0.375 0.3125 0.25 0.3984 0.105

Table 2 (1) Regression Results with Dummy Variables

A. SP 500, 1971-2002 B. Korean Stocks, 1980-2002B t-ratio Sig p B t-ratio Sig p

Jan(const) 2.1293 2.6689 0.0079 Jan(const) 4.3678 2.3659 0.0187Feb -2.0580 -1.8240 0.0690 Feb -5.2030 -1.9928 0.0473March -1.1325 -1.0037 0.3162 March -1.5622 -0.5983 0.5501April -0.9706 -0.8602 0.3902 April -3.6678 -1.4048 0.1612May -1.4897 -1.3203 0.1875 May -3.5561 -1.3620 0.1744June -1.3731 -1.2170 0.2244 June -4.2839 -1.6408 0.1020July -2.1856 -1.9371 0.0535 July -2.2826 -0.8743 0.3828Aug. -2.1055 -1.8661 0.0628 Aug. -6.7026 -2.5672 0.0108Sept. -3.3766 -2.9927 0.0029 Sept. -6.3774 -2.4426 0.0152Oct. -1.2507 -1.1085 0.2684 Oct. -2.7522 -1.0541 0.2928Nov. -0.7561 -0.6701 0.5032 Nov. -0.7596 -0.2909 0.7713Dec. -0.5428 -0.4811 0.6307 Dec. -2.7300 -1.0456 0.2967Adj R Sq 0.0070 Adj R Sq 0.0110F 1.2620 p=0.245 F 1.2760 p=0.238DW 2.0440 DW 1.8490

C. Tokyo Stocks, 1984-2002 D. Jakarta Stocks, 1989-2002B t-ratio Sig p B t-ratio Sig p

Jan(const) 1.8532 1.3506 0.1782 Jan(const) 4.5383 1.7428 0.0833Feb -1.2958 -0.6678 0.5050 Feb -3.4243 -0.9299 0.3539March 1.0574 0.5449 0.5864 March -2.8987 -0.7871 0.4324April -0.0263 -0.0136 0.9892 April -4.7179 -1.2811 0.2021May -1.5589 -0.8034 0.4226 May -1.0373 -0.2817 0.7786June -2.6247 -1.3526 0.1776 June -3.1499 -0.8553 0.3937July -2.0505 -1.0567 0.2918 July -4.0135 -1.0898 0.2775Aug. -2.1847 -1.1259 0.2615 Aug. -7.2870 -1.9787 0.0496Sept. -3.4889 -1.7980 0.0736 Sept. -10.0594 -2.7315 0.0070Oct. -2.6721 -1.3770 0.1699 Oct. -5.5188 -1.4986 0.1360Nov. -2.0511 -1.0570 0.2917 Nov. -3.8386 -1.0423 0.2989Dec. -1.6253 -0.8376 0.4032 Dec. -0.4950 -0.1344 0.8933Adj R Sq -0.0050 Adj R Sq 0.0130F 0.9020 p=0.540 F 1.2000 p=0.291DW 1.9770 DW 1.8240

Table 2 (2) Regression Results with Dummy Variables

E. Shanghai Stocks, 1991-2002 F. Korean Stocks, 1980-2002, Exc. 1989B t-ratio Sig p B t-ratio Sig p

(Constant) 3.9608 0.6093 0.5434 (Constant) 2.2586 1.3444 0.1800Feb -0.4192 -0.0456 0.9637 Feb -3.0645 -1.2898 0.1983March -2.3158 -0.2519 0.8015 March 1.3082 0.5506 0.5824April 2.5883 0.2815 0.7787 April -0.9614 -0.4046 0.6861May 9.8675 1.0733 0.2851 May -0.4477 -0.1884 0.8507June 1.3525 0.1471 0.8833 June -1.7032 -0.7168 0.4741July -9.0267 -0.9818 0.3280 July -0.7723 -0.3250 0.7454Aug. 6.8392 0.7439 0.4583 Aug. -4.2605 -1.7931 0.0742Sept. -6.0575 -0.6589 0.5111 Sept. -4.3618 -1.8358 0.0676Oct. -6.1942 -0.6737 0.5017 Oct. -1.9336 -0.8138 0.4165Nov. 2.7550 0.2997 0.7649 Nov. 0.9677 0.4073 0.6841Dec. -7.6117 -0.8279 0.4092 Dec. -1.6586 -0.6981 0.4858Adj R Sq -0.0150 Adj R Sq 0.0070F 0.8060 p=0.634 F 1.1780 p=0.303DW 2.0860 DW 1.8650

G. NASDAQ Composite, 1985-2002 H. Dow Jones Industrial, 1971-2002B t-ratio Sig p B t-ratio Sig p

Jan(cons) 4.9061 2.8775 0.0044 Jan(cons) 2.1749 2.7164 0.0069Feb -3.7511 -1.5557 0.1213 Feb -1.6941 -1.4962 0.1354March -4.6089 -1.9114 0.0574 March -1.1580 -1.0227 0.3071April -4.6722 -1.9377 0.0540 April -0.1041 -0.0919 0.9268May -3.5433 -1.4695 0.1432 May -1.7902 -1.5811 0.1147June -3.3567 -1.3921 0.1654 June -1.8719 -1.6532 0.0991July -5.4928 -2.2780 0.0238 July -1.7816 -1.5735 0.1165Aug. -5.0178 -2.0810 0.0387 Aug. -2.4132 -2.1313 0.0337Sept. -6.4339 -2.6683 0.0082 Sept. -3.8016 -3.3575 0.0009Oct. -4.6072 -1.9107 0.0574 Oct. -1.7042 -1.5052 0.1331Nov. -2.7539 -1.1421 0.2548 Nov. -0.8048 -0.7108 0.4777Dec. -2.0033 -0.8308 0.4070 Dec. -0.5074 -0.4482 0.6543Adj R Sq 0.0010 Adj R Sq 0.0210F 6.0110 p=0.437 F 1.7420 p=0.063DW 1.8430 DW 2.0590

Table 3(1): Correlation Coefficients of Monthy Returns

A. SP 500 StocksJan. Feb. March April May June July Aug. Sept. Oct. Nov. Dec.

Jan. 1.000Feb. 0.225 1.000March -0.156 0.282 1.000April 0.248 -0.150 -0.311 1.000May 0.200 0.411 -0.204 0.079 1.000June 0.389 0.229 0.103 0.195 -0.038 1.000July 0.152 -0.085 -0.312 0.328 0.316 0.043 1.000Aug. 0.060 -0.215 0.202 0.067 -0.238 -0.095 0.005 1.000Sept. 0.211 0.149 -0.146 0.349 0.002 0.435 0.487 -0.017 1.000Oct. -0.242 0.008 -0.122 -0.201 -0.075 -0.297 -0.570 -0.229 -0.295 1.000Nov. -0.023 -0.006 -0.249 0.377 0.353 -0.019 -0.079 -0.190 0.090 0.231 1.000Dec. 0.331 0.164 0.208 0.108 -0.084 0.132 0.316 0.022 0.275 -0.379 -0.322 1.000The critical r values are about 0.449 and 0.349 for 1% and 5%levels, respectively, N= 32, d.f.=29.

B-1. Korean Stocks, 1980-2002Jan. Feb. March April May June July Aug. Sept. Oct. Nov. Dec.

Jan. 1.000Feb. -0.084 1.000March -0.336 0.260 1April -0.128 -0.167 0.074 1.000May -0.187 0.003 0.355 -0.042 1.000June -0.358 -0.155 0.431 0.325 0.046 1.000July 0.171 0.577 0.297 -0.061 -0.157 0.035 1.000Aug. -0.105 0.016 0.131 0.060 -0.204 -0.016 -0.234 1.000Sept. -0.075 0.132 -0.136 -0.094 0.069 -0.247 0.361 -0.311 1.000Oct. 0.617 -0.096 -0.372 -0.210 -0.256 -0.400 0.171 -0.056 0.183 1.000Nov. 0.428 -0.206 0.044 0.264 0.036 0.118 -0.074 0.013 -0.404 0.471 1.000Dec. 0.626 -0.117 -0.184 -0.177 -0.094 -0.018 0.289 -0.254 0.108 0.599 0.451 1.000The critical r values are 0.4160 and 0.3525 for 5% and 10% levesls respectively, d.f.= 21.

B-2. Korean Stocks, 1980-2002, Exluding 1998Jan. Feb. March April May June July Aug. Sept. Oct. Nov. Dec.

Jan. 1.000Feb. -0.102 1.000March 0.005 0.279 1.000April 0.138 -0.181 -0.063 1.000May 0.401 -0.011 0.149 -0.244 1.000June -0.253 -0.167 0.363 0.270 -0.118 1.000July -0.149 0.625 0.542 0.043 0.041 0.140 1.000Aug. 0.207 0.010 -0.010 -0.032 -0.466 -0.107 -0.140 1.000Sept. -0.195 0.134 -0.117 -0.078 0.128 -0.238 0.360 -0.305 1.000Oct. 0.378 -0.099 -0.171 -0.068 0.052 -0.318 -0.023 0.141 0.173 1.000Nov. 0.417 -0.206 0.160 0.346 0.184 0.184 -0.161 0.085 -0.429 0.433 1.000Dec. 0.307 -0.130 0.136 0.000 0.367 0.192 0.100 -0.082 0.083 0.399 0.416 1.000The critical r values are 0.3598 and 0.4227 at 10% and 5% levels respectively, d.f.=20

Table 3(2): Correlation Coefficients of Monthy Returns

C. Tokyo Stocks, 1984-2002Jan Feb March April May June July Aug Sep Oct Nov Dec

Jan 1.000Feb 0.240 1.000March 0.211 0.330 1.000April 0.248 -0.075 0.339 1.000May -0.188 0.041 -0.444 -0.084 1.000June 0.213 0.079 0.486 0.011 -0.360 1.000July -0.012 0.067 0.153 0.056 -0.015 -0.071 1.000Aug -0.015 -0.157 0.295 -0.125 -0.148 -0.155 0.156 1.000Sep 0.231 0.470 0.521 0.069 -0.470 0.182 0.283 0.278 1.000Oct -0.039 -0.209 -0.326 -0.168 0.082 -0.072 -0.043 -0.434 -0.507 1.000Nov 0.140 0.000 0.113 -0.460 -0.306 0.214 0.227 0.115 0.313 -0.338 1.000Dec -0.044 -0.127 0.122 -0.135 -0.053 0.118 0.483 0.175 -0.103 0.583 -0.133 1.000The critical r values are 0.575 and 0.456 at 1% and 5% levels respectively. N=19, d.f. = 17.

D-1. Jakarta Stocks, 1989-2002Jan. Feb. March April May June July Aug. Sept. Oct. Nov. Dec.

Jan. 1.000Feb. 0.150 1.000March 0.338 0.535 1.000April 0.100 0.146 0.054 1.000May -0.170 0.181 -0.491 0.476 1.000June -0.048 -0.092 0.008 -0.387 -0.062 1.000July 0.274 0.121 -0.127 -0.199 0.169 0.136 1.000Aug. -0.455 0.092 0.056 -0.094 0.206 0.214 -0.342 1.000Sept. -0.008 -0.081 -0.556 0.251 0.481 0.009 0.195 0.067 1.000Oct. 0.051 -0.228 -0.172 -0.027 0.352 0.317 0.425 0.217 0.146 1.000Nov. 0.232 -0.084 0.340 -0.100 -0.351 0.100 0.203 -0.155 -0.427 0.401 1.000Dec. -0.071 0.275 0.203 0.352 0.351 -0.020 0.078 0.212 0.110 0.195 0.283 1.000The critical r values are 0.661 and 0.532 at the 1% and 5% levels respectively. N= 14, d.f.= 13.

D-2. 1989-2002, Excluding 1998Jan. Feb. March April May June July Aug. Sept. Oct. Nov. Dec.

Jan. 1.000Feb. 0.260 1.000March 0.217 0.595 1.000April 0.440 0.083 0.203 1.000May 0.068 0.111 -0.486 0.344 1.000June -0.173 -0.080 -0.063 -0.357 0.006 1.000July 0.032 0.173 -0.396 -0.021 0.426 0.052 1.000Aug. -0.310 0.019 0.186 -0.361 0.010 0.318 -0.229 1.000Sept. 0.326 -0.169 -0.507 0.053 0.356 0.106 0.541 -0.164 1.000Oct. -0.166 -0.252 -0.384 0.114 0.550 0.275 0.283 0.390 0.368 1.000Nov. -0.157 -0.100 0.112 0.198 -0.269 -0.035 -0.255 0.067 -0.245 0.176 1.000Dec. 0.170 0.399 0.321 0.753 0.401 -0.104 -0.084 -0.033 -0.073 0.200 0.370 1.000The critical r values are 0.684 and 0.553 at the 1% and 5% levels respectively. N=13, d.f..=12

Table 3(3): Correlation Coefficients of Monthy Returns

E-1. Shanghai Stocks, 1991-2002Jan. Feb. March April May June July Aug. Sept. Oct. Nov. Dec.

Jan. 1.000Feb. 0.472 1.000March -0.699 -0.244 1.000April 0.790 0.567 -0.490 1.000May -0.105 0.388 0.241 0.006 1.000June 0.040 -0.069 -0.167 0.211 -0.193 1.000July -0.166 -0.036 0.383 -0.039 -0.082 0.327 1.000Aug. -0.200 -0.239 -0.287 -0.474 -0.274 -0.335 -0.594 1.000Sept. -0.072 -0.554 -0.305 -0.027 -0.571 0.181 0.200 0.200 1.000Oct. -0.109 -0.278 0.101 -0.075 -0.585 0.461 0.668 -0.161 0.448 1.000Nov. 0.491 0.610 -0.488 0.453 0.658 -0.033 -0.265 -0.129 -0.322 -0.385 1.000Dec. -0.147 0.307 0.177 -0.259 0.431 0.054 0.045 -0.007 -0.512 0.149 0.429 1.000The critical r values are 0.4973 and 0.5760 at 10% and 5% levels respectively, d.f.=10

E-2. Shanghai Stocks, 1991-2002, Excluding 1992 and 1994Jan. Feb. March April May June July Aug. Sept. Oct. Nov. Dec.

Jan. 1.000Feb. 0.453 1.000March -0.786 -0.301 1.000April 0.794 0.550 -0.674 1.000May -0.132 0.375 0.220 -0.049 1.000June -0.056 -0.171 -0.320 0.026 -0.278 1.000July -0.443 -0.235 0.307 -0.526 -0.236 0.013 1.000Aug. -0.036 -0.255 -0.202 -0.286 -0.611 0.421 0.478 1.000Sept. -0.047 -0.544 -0.284 0.033 -0.564 0.273 0.423 0.265 1.000Oct. -0.201 -0.377 0.011 -0.275 -0.683 0.355 0.618 0.806 0.541 1.000Nov. 0.491 0.612 -0.517 0.477 0.657 -0.062 -0.427 -0.306 -0.319 -0.435 1.000Dec. -0.162 0.302 0.168 -0.312 0.428 0.031 0.005 0.185 -0.510 0.137 0.427 1.000The critical r values are 0.5214 and 0.6021 at 10% and 5% levels respectively, d.f.= 9

Table 4 (1) Regression Equations with Monthly Returns

A. SP 500 Stocks, 1971-2002January February

Coeff SE t Stat P-value Coeff SE t Stat P-valueIntercept 3.469 1.334 2.600 0.018 -0.053 1.071 -0.049 0.961Jan. -0.154 0.227 -0.678 0.506 0.118 0.182 0.651 0.523Feb. 0.157 0.332 0.473 0.642 -0.003 0.267 -0.010 0.992Mar. -0.153 0.318 -0.481 0.636 -0.108 0.255 -0.423 0.677Apr. -0.714 0.323 -2.210 0.040 -0.032 0.259 -0.122 0.904May 0.021 0.413 0.051 0.960 -0.085 0.331 -0.258 0.800June 0.701 0.406 1.727 0.101 0.129 0.326 0.397 0.696July 0.098 0.405 0.242 0.812 0.028 0.325 0.086 0.933Aug. -0.113 0.185 -0.609 0.550 0.060 0.149 0.404 0.691Sept. 0.219 0.292 0.750 0.463 0.190 0.235 0.809 0.429Oct. -0.024 0.209 -0.116 0.909 0.018 0.167 0.110 0.914Nov. 0.128 0.249 0.515 0.613 -0.155 0.200 -0.774 0.449Dec. -0.341 0.356 -0.958 0.351 0.352 0.286 1.232 0.234Adj R sq. = 0.092 F=1.252 p=0.3235 Adj.R sq. =-0.013 F = 0.967 p=0.510March April

Coeff SE t Stat P-value Coeff SE t Stat P-valueIntercept 0.593 0.760 0.781 0.445 1.627 0.620 2.624 0.017Jan. -0.169 0.129 -1.306 0.208 0.050 0.105 0.477 0.639Feb. -0.338 0.189 -1.787 0.091 -0.179 0.154 -1.161 0.261Mar. -0.739 0.181 -4.076 0.001 0.553 0.148 3.740 0.001Apr. 0.032 0.184 0.175 0.863 -0.514 0.150 -3.422 0.003May 0.263 0.235 1.118 0.278 -0.274 0.192 -1.427 0.171June 0.376 0.231 1.627 0.121 -0.065 0.189 -0.343 0.735July -0.555 0.231 -2.410 0.027 0.149 0.188 0.793 0.438Aug. 0.232 0.105 2.204 0.041 -0.036 0.086 -0.417 0.682Sept. -0.053 0.167 -0.320 0.753 0.236 0.136 1.735 0.100Oct. -0.192 0.119 -1.615 0.124 -0.100 0.097 -1.029 0.317Nov. -0.039 0.142 -0.276 0.785 0.442 0.116 3.822 0.001Dec. 0.750 0.203 3.695 0.002 -0.179 0.166 -1.082 0.293Adj.R sq. = 0.497 F = 3.469 p = 0.0087 Adj.R sq. = 0.560 F = 4.185 p = 0.0032May June

Coeff SE t Stat P-value Coeff. SE t Stat P-valueIntercept 1.190 0.923 1.290 0.213 0.251 0.844 0.298 0.769Jan. 0.027 0.157 0.170 0.867 -0.070 0.143 -0.488 0.631Feb. 0.321 0.230 1.397 0.180 -0.091 0.210 -0.435 0.669Mar. 0.076 0.220 0.347 0.733 0.027 0.201 0.134 0.895Apr. -0.288 0.223 -1.289 0.214 0.002 0.204 0.012 0.990May -0.098 0.285 -0.344 0.734 -0.126 0.261 -0.484 0.634June -0.392 0.281 -1.396 0.180 0.523 0.257 2.037 0.057July 0.125 0.280 0.446 0.661 0.206 0.256 0.806 0.431Aug. -0.088 0.128 -0.689 0.500 -0.005 0.117 -0.043 0.966Sept. 0.152 0.202 0.753 0.461 -0.171 0.185 -0.928 0.366Oct. -0.062 0.144 -0.430 0.673 0.056 0.132 0.425 0.676Nov. 0.024 0.172 0.139 0.891 0.084 0.158 0.535 0.600Dec. 0.198 0.246 0.804 0.432 0.113 0.225 0.503 0.621Adj.R sq. = 0.061 F= 1.1625 p = 0.3753 Adj.R sq. = -0.2211 F = 0.5173 p = 0.8554

Table 4 (2) Regression Equations for Monthly Returns

A-2. SP 500 Stocks, 1971-2002July August

Coeff. SE t Stat P-value Coeff. SE t Stat P-valueIntercept 1.002 0.938 1.068 0.299 2.069 1.544 1.340 0.197Jan. -0.378 0.159 -2.372 0.029 -0.020 0.262 -0.078 0.939Feb. 0.141 0.234 0.605 0.553 0.006 0.384 0.016 0.987Mar. 0.004 0.224 0.016 0.987 -0.556 0.368 -1.511 0.148Apr. -0.380 0.227 -1.675 0.111 -0.211 0.374 -0.564 0.580May -0.100 0.290 -0.346 0.733 0.120 0.478 0.250 0.805June 0.024 0.285 0.084 0.934 -0.001 0.469 -0.002 0.999July 0.256 0.284 0.899 0.381 -0.168 0.468 -0.360 0.723Aug. -0.187 0.130 -1.436 0.168 -0.035 0.214 -0.166 0.870Sept. 0.132 0.206 0.641 0.530 0.141 0.338 0.418 0.681Oct. 0.121 0.147 0.827 0.419 -0.545 0.241 -2.260 0.036Nov. 0.265 0.175 1.513 0.148 0.018 0.288 0.062 0.951Dec. 0.053 0.250 0.212 0.835 -0.472 0.412 -1.145 0.267Adj.R sq. = 0.2997 F= 2.0699 p = 0.0791 Adj.R sq. = 0.0145 F = 1.0367 p = 0.4571September October

Coeff. SE t Stat P-value Ccoeff. SE t Stat P-valueIntercept -1.180 1.079 -1.093 0.289 -1.642 1.700 -0.966 0.347Jan. -0.271 0.183 -1.476 0.157 0.481 0.289 1.665 0.113Feb. -0.196 0.269 -0.730 0.475 -0.423 0.424 -0.999 0.331Mar. 0.148 0.257 0.575 0.573 0.923 0.406 2.276 0.035Apr. -0.100 0.261 -0.383 0.706 0.775 0.412 1.882 0.076May -0.123 0.334 -0.368 0.717 0.546 0.526 1.039 0.313June 0.597 0.328 1.817 0.086 -0.067 0.517 -0.130 0.898July 0.543 0.327 1.659 0.114 -0.269 0.516 -0.522 0.608Aug. -0.155 0.150 -1.034 0.315 -0.030 0.236 -0.126 0.901Sept. 0.106 0.237 0.448 0.660 -0.157 0.373 -0.422 0.678Oct. 0.307 0.169 1.818 0.086 0.191 0.266 0.717 0.483Nov. 0.125 0.202 0.619 0.544 -0.481 0.317 -1.515 0.147Dec. 0.002 0.288 0.008 0.993 -0.336 0.454 -0.739 0.469Adj.R sq. = 0.1325 F = 1.3818 p = 0.0598 Adj.R sq. = 0.0835 F = 1.2277 p = 0.3371November December

Coeff. SE t Stat P-value Coeff. SE t Stat P-valueIntercept 1.176 1.426 0.825 0.420 2.218 1.076 2.062 0.054Jan. -0.056 0.242 -0.230 0.821 -0.293 0.183 -1.606 0.126Feb. 0.014 0.355 0.039 0.970 0.267 0.268 0.996 0.332Mar. 0.561 0.340 1.649 0.116 -0.211 0.257 -0.824 0.421Apr. -0.414 0.345 -1.200 0.246 -0.037 0.260 -0.143 0.888May -0.022 0.441 -0.049 0.962 -0.044 0.333 -0.133 0.895June -0.061 0.434 -0.140 0.890 0.146 0.327 0.446 0.661July 0.409 0.432 0.945 0.357 -0.003 0.326 -0.008 0.994Aug. 0.188 0.198 0.951 0.354 0.077 0.149 0.514 0.613Sept. 0.192 0.312 0.614 0.547 -0.034 0.236 -0.145 0.887Oct. 0.042 0.223 0.188 0.853 0.024 0.168 0.145 0.886Nov. 0.336 0.266 1.263 0.223 0.038 0.201 0.187 0.854Dec. -0.077 0.381 -0.202 0.842 0.173 0.287 0.601 0.555Adj.R sq. = 0.0886 F = 0.7965 p = 0.6501 Adj.R sq. = -0.3859 F = 0.3039 p = 0.9799

Table 4 (3) Regression Equations for Monthly Returns

B-1. Korean Stocks, 1980-2002January February

Coeff. SE t Stat P-value Coeff. SE t Stat P-valueIntercept -2.344 3.835 -0.611 0.556 -1.877 1.771 -1.060 0.317Jan. 0.080 0.339 0.236 0.819 -0.065 0.157 -0.414 0.689Feb. -0.840 0.667 -1.260 0.240 0.010 0.308 0.032 0.976March 0.888 0.545 1.630 0.137 0.295 0.252 1.172 0.271April -0.233 0.373 -0.625 0.547 0.120 0.172 0.695 0.505May -0.523 0.415 -1.262 0.239 0.211 0.191 1.101 0.299June -0.133 0.488 -0.272 0.792 -0.070 0.225 -0.313 0.762July 0.467 0.634 0.736 0.481 0.066 0.293 0.224 0.828Aug. -0.261 0.653 -0.400 0.698 0.087 0.302 0.290 0.779Sept. 0.416 0.672 0.620 0.551 -0.295 0.310 -0.951 0.366Oct. -0.446 0.475 -0.939 0.372 0.366 0.219 1.669 0.129Nov. 1.202 0.615 1.954 0.082 -0.543 0.284 -1.911 0.088Dec. -0.541 0.584 -0.926 0.378 0.364 0.270 1.350 0.210Adj.R sq = 0.1213 F = 1.241 p = 0.3795 Adj.R sq.=-0.0697 F = 0.8860 p=0.5870March April

Coeff. SE t Stat P-value Coeff. SE t Stat P-valueIntercept 2.758 2.130 1.295 0.228 4.508 1.560 2.890 0.018Jan. 0.112 0.188 0.593 0.568 0.441 0.138 3.194 0.011Feb. -0.169 0.371 -0.455 0.660 0.832 0.271 3.064 0.013March 0.065 0.303 0.213 0.836 0.328 0.222 1.478 0.173April -0.275 0.207 -1.326 0.218 -0.480 0.152 -3.158 0.012May 0.395 0.230 1.714 0.121 -0.618 0.169 -3.667 0.005June -0.129 0.271 -0.475 0.646 0.710 0.198 3.579 0.006July -0.228 0.352 -0.646 0.534 -1.322 0.258 -5.125 0.001Aug. 0.021 0.363 0.058 0.955 -0.123 0.266 -0.461 0.655Sept. 0.102 0.373 0.273 0.791 0.808 0.273 2.958 0.016Oct. -0.230 0.264 -0.872 0.406 -0.424 0.193 -2.195 0.056Nov. -0.227 0.342 -0.664 0.523 -0.083 0.250 -0.330 0.749Dec. 0.440 0.324 1.358 0.208 0.048 0.237 0.201 0.845Adj.R sq = 0.2382 F = 1.5473 p = 0.2598 Adj.R sq.=-0.7348 F = 5.8500 p=0.0062May June

Coeff SE t Stat P-value Coeff SE t Stat P-valueIntercept 3.190 2.302 1.386 0.199 1.852 3.060 0.605 0.560Jan. 0.154 0.204 0.758 0.468 0.030 0.271 0.112 0.914Feb. 0.376 0.400 0.938 0.373 0.513 0.532 0.964 0.360March -0.283 0.327 -0.867 0.409 0.046 0.435 0.105 0.918April -0.491 0.224 -2.191 0.056 -0.132 0.298 -0.444 0.667May 0.135 0.249 0.541 0.601 -0.070 0.331 -0.212 0.837June -0.007 0.293 -0.024 0.981 0.390 0.389 1.001 0.343July 0.352 0.381 0.925 0.379 -0.829 0.506 -1.637 0.136Aug. 0.651 0.392 1.660 0.131 -0.103 0.521 -0.197 0.848Sept. 0.447 0.403 1.108 0.296 0.065 0.536 0.121 0.906Oct. -0.157 0.285 -0.553 0.594 0.073 0.379 0.191 0.852Nov. 0.211 0.369 0.571 0.582 -0.159 0.491 -0.325 0.753Dec. -0.237 0.350 -0.676 0.516 0.478 0.466 1.027 0.331Adj.R sq = 0.2574 F = 1.6065 p = 0.2417 Adj.R sq.=-0.3910 F = 0.5081 p=0.8638

Table 4 (4) Regression Equations for Monthly Returns

B-2. Korean Stocks, 1980-2002 July August

Coeff SE t Stat P-value Coeff SE t Stat P-valueIntercept -0.427 2.223 -0.192 0.852 -3.312 1.205 -2.748 0.023Jan. -0.064 0.197 -0.325 0.752 -0.093 0.107 -0.876 0.404Feb. -0.944 0.387 -2.440 0.037 0.284 0.210 1.354 0.209March 0.686 0.316 2.171 0.058 0.301 0.171 1.759 0.113April 0.061 0.216 0.282 0.784 -0.028 0.117 -0.241 0.815May 0.171 0.240 0.710 0.495 -0.028 0.130 -0.213 0.836June -0.185 0.283 -0.653 0.530 -0.102 0.153 -0.663 0.524July 0.292 0.368 0.795 0.447 -0.590 0.199 -2.959 0.016Aug. 0.157 0.379 0.415 0.688 -0.640 0.205 -3.120 0.012Sept. -0.472 0.389 -1.212 0.256 0.164 0.211 0.775 0.458Oct. 0.253 0.275 0.918 0.383 0.186 0.149 1.244 0.245Nov. -0.538 0.357 -1.509 0.165 0.036 0.193 0.187 0.855Dec. 0.312 0.338 0.921 0.381 0.077 0.183 0.420 0.684Adj.R sq = 0.2026 F = 1.4446 p = 0.2948 Adj.R sq.= 0.3816 F = 2.0800 p=0.1387September October

Coeff SE t Stat P-value Coeff SE t Stat P-valueIntercept -0.372 1.526 -0.244 0.813 0.100 2.586 0.039 0.970Jan. -0.013 0.135 -0.095 0.927 -0.380 0.229 -1.662 0.131Feb. -0.562 0.265 -2.116 0.063 -0.511 0.450 -1.137 0.285March -0.025 0.217 -0.117 0.909 0.692 0.367 1.882 0.092April 0.191 0.149 1.283 0.232 0.142 0.252 0.565 0.586May 0.168 0.165 1.020 0.334 -0.238 0.280 -0.853 0.416June -0.157 0.194 -0.808 0.440 -0.303 0.329 -0.922 0.381July 0.503 0.252 1.995 0.077 0.299 0.428 0.700 0.501Aug. 0.462 0.260 1.778 0.109 0.000 0.440 0.001 0.999Sept. 0.301 0.267 1.127 0.289 0.553 0.453 1.222 0.253Oct. 0.002 0.189 0.008 0.994 -0.146 0.320 -0.455 0.660Nov. -0.154 0.245 -0.628 0.546 0.697 0.415 1.680 0.127Dec. -0.251 0.232 -1.079 0.309 -0.511 0.394 -1.299 0.226Adj.R sq = 0.3189 F = 1.8192 p = 0.1874 Adj.R sq.= 0.4521 F = 2.4438 p=0.0934November December

Coeff SE t Stat P-value Coeff SE t Stat P-valueIntercept 3.980 2.265 1.757 0.113 0.212 1.964 0.108 0.917Jan. -0.049 0.200 -0.247 0.811 -0.165 0.174 -0.948 0.368Feb. 0.445 0.394 1.128 0.288 -0.086 0.342 -0.252 0.806March 0.431 0.322 1.339 0.213 0.287 0.279 1.029 0.330April -0.405 0.221 -1.837 0.099 -0.046 0.191 -0.243 0.814May -0.175 0.245 -0.715 0.493 0.047 0.212 0.220 0.831June 0.392 0.288 1.361 0.207 -0.013 0.250 -0.053 0.959July -0.449 0.375 -1.200 0.261 0.212 0.325 0.652 0.531Aug. 0.189 0.386 0.489 0.637 0.151 0.334 0.451 0.663Sept. 0.326 0.397 0.821 0.433 0.230 0.344 0.667 0.521Oct. -0.115 0.280 -0.410 0.691 -0.123 0.243 -0.507 0.625Nov. 0.398 0.363 1.094 0.302 0.706 0.315 2.239 0.052Dec. -0.209 0.345 -0.607 0.559 -0.073 0.299 -0.246 0.812Adj.R sq = 0.2386 F = 1.5484 p = 0.2595 Adj.R sq.= 0.2301 F = 1.5229 p=0.2677

Table 4 (5) Regression Equations for Monthly Returns

C-1. Tokyo Stocks, 1984-2002January February

Coeff SE t Stat P-value Coeff SE t Stat P-valueIntercept 4.276 2.530 1.690 0.152 1.412 1.374 1.027 0.352Jan. -0.439 0.394 -1.112 0.317 -0.018 0.214 -0.082 0.938Feb. 0.874 0.716 1.220 0.277 0.417 0.389 1.073 0.332March -0.989 0.523 -1.891 0.117 -0.259 0.284 -0.910 0.404April 1.464 0.976 1.500 0.194 0.458 0.530 0.865 0.427May -0.015 0.515 -0.030 0.977 0.312 0.280 1.114 0.316June 0.741 0.629 1.177 0.292 0.392 0.342 1.148 0.303July -0.274 0.465 -0.590 0.581 0.381 0.252 1.512 0.191Aug. 0.672 0.725 0.926 0.397 1.055 0.394 2.677 0.044Sept. 0.161 0.453 0.355 0.737 -0.316 0.246 -1.284 0.255Oct. 0.471 0.993 0.474 0.656 0.986 0.539 1.827 0.127Nov. 1.099 0.615 1.786 0.134 0.687 0.334 2.054 0.095Dec. 0.986 0.931 1.059 0.338 -0.902 0.506 -1.782 0.135Adj.R sq = 0.0521 F=1.0778 p = 0.5036 Adj.R sq=0.55050 F=2.7349 p = 0.1375March April

Coeff SE t Stat P-value Coeff SE t Stat P-valueIntercept 1.887 2.323 0.812 0.454 1.111 1.889 0.588 0.582Jan. 0.417 0.362 1.152 0.301 0.335 0.294 1.139 0.306Feb. 0.402 0.657 0.611 0.568 -0.004 0.535 -0.007 0.995March -0.696 0.480 -1.450 0.207 -0.498 0.390 -1.277 0.258April 0.536 0.896 0.598 0.576 -0.184 0.729 -0.252 0.811May 0.385 0.473 0.813 0.453 -0.130 0.385 -0.337 0.750June 0.710 0.578 1.228 0.274 -0.193 0.470 -0.411 0.698July -0.730 0.427 -1.711 0.148 -0.476 0.347 -1.371 0.229Aug. 0.471 0.666 0.707 0.511 -0.655 0.542 -1.209 0.281Sept. -0.348 0.416 -0.837 0.441 0.051 0.338 0.149 0.887Oct. -0.687 0.912 -0.754 0.485 -1.152 0.742 -1.553 0.181Nov. 0.354 0.565 0.627 0.558 0.126 0.459 0.275 0.794Dec. 0.675 0.855 0.789 0.466 1.263 0.696 1.815 0.129Adj.R sq = 0.4302 F = 2.0695 p = 0.2175 Adj.R sq = 0.1660 F = 1.2820 p = 0.4172May June

Ccoeff SE t Stat P-value Coeff SE t Stat P-valueIntercept -0.179 1.763 -0.101 0.923 -0.572 2.658 -0.215 0.838Jan. 0.065 0.275 0.235 0.823 0.068 0.414 0.165 0.876Feb. 0.463 0.499 0.928 0.396 0.063 0.752 0.083 0.937March -0.046 0.364 -0.127 0.904 0.048 0.549 0.087 0.934April 0.030 0.680 0.045 0.966 -0.158 1.025 -0.154 0.883May -0.329 0.359 -0.916 0.402 -0.235 0.541 -0.434 0.682June -0.034 0.439 -0.077 0.942 0.332 0.661 0.502 0.637July 0.954 0.324 2.948 0.032 0.037 0.488 0.076 0.942Aug. 0.296 0.505 0.585 0.584 0.011 0.762 0.014 0.989Sept. -0.445 0.316 -1.411 0.217 -0.370 0.476 -0.776 0.473Oct. 0.439 0.692 0.635 0.553 -0.162 1.043 -0.155 0.883Nov. -0.228 0.429 -0.532 0.617 0.131 0.646 0.202 0.848Dec. -0.850 0.649 -1.310 0.247 -0.334 0.978 -0.341 0.747Adj.R sq = 0.1677 F = 1.2854 p = 0.4159 Adj.R sq = -0.8149 F = 0.3639 p = 0.9297

Table 4 (6) Regression Equations for Monthly Returns

C-2. Tokyo Stocks, 1984-2002July August

Coeff SE t Stat P-value Coeff SE t Stat P-valueIntercept 1.788 1.931 0.926 0.397 -4.701 3.073 -1.530 0.187Jan. 0.590 0.301 1.963 0.107 0.587 0.479 1.225 0.275Feb. -1.103 0.546 -2.019 0.099 -0.572 0.869 -0.658 0.540March 0.254 0.399 0.638 0.552 0.249 0.635 0.393 0.711April -0.742 0.745 -0.996 0.365 -0.204 1.185 -0.172 0.870May 0.422 0.393 1.072 0.333 -0.261 0.626 -0.416 0.694June 0.095 0.480 0.197 0.852 -0.582 0.764 -0.761 0.481July 0.191 0.354 0.539 0.613 -0.662 0.564 -1.173 0.294Aug. 0.072 0.553 0.131 0.901 -0.702 0.881 -0.797 0.462Sept. 0.571 0.346 1.650 0.160 -0.386 0.550 -0.701 0.514Oct. 0.442 0.758 0.583 0.585 -1.815 1.206 -1.505 0.193Nov. -0.554 0.469 -1.179 0.291 -0.590 0.747 -0.789 0.466Dec. -0.735 0.711 -1.035 0.348 1.972 1.131 1.743 0.142Adj.R sq = 0.2427 F = 1.4539 p = 0.3580 Adj.R sq = -0.1236 F = 0.8441 p = 0.6276September October

Coeff SE t Stat P-value Coeff SE t Stat P-valueIntercept -0.824 2.043 -0.403 0.703 2.202 1.654 1.331 0.241Jan. -0.060 0.318 -0.189 0.857 -0.231 0.258 -0.895 0.412Feb. -0.342 0.578 -0.591 0.580 0.111 0.468 0.237 0.822March -0.346 0.422 -0.820 0.449 0.126 0.342 0.370 0.727April 0.155 0.788 0.197 0.852 -0.804 0.638 -1.260 0.263May 0.472 0.416 1.135 0.308 -0.019 0.337 -0.055 0.958June 0.770 0.508 1.515 0.190 -0.301 0.412 -0.731 0.498July -0.054 0.375 -0.145 0.891 -0.031 0.304 -0.104 0.922Aug. 0.338 0.586 0.577 0.589 0.065 0.474 0.136 0.897Sept. -0.228 0.366 -0.622 0.561 0.655 0.296 2.212 0.078Oct. -0.158 0.802 -0.197 0.851 0.287 0.649 0.442 0.677Nov. 0.244 0.497 0.492 0.644 -0.596 0.402 -1.482 0.198Dec. -0.094 0.752 -0.125 0.906 -0.102 0.609 -0.167 0.874Adj.R sq = 0.2460 F = 1.4621 p = 0.3555 Adj.R sq = 0.5424 F = 2.6790 p = 0.1426November December

Cccoeff SE t Stat P-value Coeff SE t Stat P-valueIntercept 0.712 3.249 0.219 0.835 0.703 1.998 0.352 0.739Jan. -0.299 0.506 -0.590 0.581 0.392 0.311 1.260 0.263Feb. -0.338 0.919 -0.367 0.728 -0.791 0.565 -1.399 0.221March 0.300 0.671 0.447 0.674 0.381 0.413 0.922 0.399April 0.680 1.253 0.543 0.611 -1.144 0.771 -1.484 0.198May 0.542 0.662 0.819 0.450 0.174 0.407 0.427 0.687June 0.680 0.808 0.841 0.439 -0.527 0.497 -1.060 0.338July 0.194 0.597 0.326 0.758 -0.185 0.367 -0.504 0.636Aug. 0.435 0.931 0.467 0.660 -0.418 0.573 -0.730 0.498Sept. 0.318 0.582 0.546 0.608 0.513 0.358 1.433 0.211Oct. 1.177 1.275 0.923 0.398 -0.687 0.784 -0.876 0.421Nov. 0.273 0.790 0.345 0.744 -0.796 0.486 -1.639 0.162Dec. -1.205 1.196 -1.007 0.360 0.514 0.736 0.699 0.516Adj.R sq = -0.5696 F = 0.4859 p = 0.8581 Adj.R sq = -0.2165 F = 0.7479 p = 0.6864

Table 5 (1): ARIMA Models

I. ARIMA (1,0,0) for Monthly Stock PricesA. SP500, 1971-2002

Variable Coeff Std Error T-Stat Signif Ad.R^2 DW Q K-p-q1. Y(t) = Constant + Y(t-1)

1 Constant 1850.107 3807.476 0.486 0.627 0.995 2.097 67.651 36-12 AR{1} 0.999 0.004 276.976 0.000 (p=0.0008)

2. log Y = log a + log Y(t)1 Constant 15.198 40.942 0.371 0.711 0.998 2.002 28.964 36-12 AR{1} 0.999 0.003 392.187 0.000 (p=0.7539)

3. Y = Y(t-1)1 AR{1} 1.002 0.003 398.334 0.000 0.995 2.095 66.755 36-1

4. log Y = log Y(t-1) (p=0.001)1 AR{1} 1.001 0.000 2427.887 0.000 0.998 2.003 0.757 36-1

(p=0.7574)

B. Korean Stocks, 1980-2002Variable Coeff Std Error T-Stat Signif Ad.R^2 DW Q K-p-q

1. Y(t) = Constant + Y(t-1)1 Constant 641.524 181.193 3.541 0.000 0.971 1.832 52.572 36-12 AR{1} 0.982 0.010 95.304 0.000 (p=0.0286)

2. log Y = log a + log Y(t) 1 CONSTANT 6.627 0.588 11.278 0.000 0.988 1.821 39.886 36-12 AR{1} 0.989 0.007 150.939 0.000 (p=0.2618)

3. Y = Y(t-1)1 AR{1} 0.998 0.005 196.568 0.000 0.970 1.839 53.240 36-1

4. log Y = log Y(t-1) (p=0.0248)1 AR{1} 1.001 0.001 1171.889 0.000 0.988 1.820 40.007 36-1

(p=0.2575)

C. Tokyo Stocks, 1984-2002Variable Coeff Std Error T-Stat Signif Ad.R^2 DW Q K-p-q

1. Y(t) = Constant + Y(t-1)1 Constant 237.869 37.820 6.290 0.000 0.956 1.857 42.719 36-12 AR{1} 0.975 0.014 70.079 0.000 (p=0.1734)

2. log Y = log a + log Y(t)1 Constant 5.446 0.146 37.375 0.000 0.960 1.908 30.975 36-12 AR{1} 0.973 0.013 73.966 0.000 (p=0.6628)

3. Y = Y(t-1)1 AR{1} 0.999 0.004 254.085 0.000 0.956 1.875 43.222 36-1

4. log Y = log Y(t-1) (p=0.1603)1 AR{1} 1.000 0.001 1369.149 0.000 0.956 1.923 31.705 36-1

(p=0.6280)

Table 5 (2): ARIMA Models

D. Jakarta Stocks, 1989-2002Variable Coeff Std Error T-Stat Signif Ad.R^2 DW Q K-p-q

1. Y(t) = Constant + Y(t-1)Constant 709.240 71.217 9.959 0.000 0.871 1.754 33.535 36-1

AR{1} 0.932 0.028 33.420 0.000 (p=0.5389)2. log Y = log a + log Y(t)

AR{1} 0.929 0.028 32.713 0.000 0.866 1.724 35.456 36-13. Y = Y(t-1) (p=0.4467)

AR{1} 0.995 0.006 154.349 0.000 0.867 1.807 34.710 36-14. log Y = log Y(t-1) (p=0.4820)

AR{1} 1.000 0.001 874.669 0.000 0.862 1.782 36.248 36-1(p=0.4102)

E. Shanghai Stocks, 1991-2002Variable Coeff Std Error T-Stat Signif Ad.R^2 DW Q K-p-q

1. Y(t) = Constant + Y(t-1)1 Constant 1290.599 283.236 4.557 0.000 0.933 2.199 33.379 35-12 AR{1} 0.956 0.022 44.434 0.000 (p=0.4979)

2. log Y = log a + log Y(t-1)1 Constant 7.112 0.263 27.055 0.000 0.942 2.157 54.480 35-12 AR{1} 0.944 0.020 48.043 0.000 (p=0.0144)

3. Y = Y(t-1)1 AR{1} 0.998 0.010 102.895 0.000 0.931 2.220 35.701 35-1

4. log Y = log Y(t-1) (p=0.3884)1 AR{1} 1.002 0.002 493.893 0.000 0.939 2.220 54.027 35-1

(p=0.0159)

Table 5 (3): ARIMA Models II. ARIMA (12, 0,0) for Monthly Stock Returns

SP500, 1984-2002 Korea, 1984-2002 Tokyo, 1984-2002 Coeff T-Stat Signif Coeff t-Stat Signif Coeff t-Stat SignifCONST 0.797 2.113 0.036 0.796 2.432 0.016 0.975 1.081 0.281AR{1} -0.018 -0.263 0.793 -0.037 -0.529 0.598 0.043 0.616 0.538AR{2} -0.056 -0.818 0.414 -0.008 -0.107 0.915 -0.017 -0.236 0.814AR{3} 0.002 0.025 0.980 0.029 0.408 0.684 -0.060 -0.865 0.388AR{4} -0.105 -1.511 0.132 -0.097 -1.384 0.168 -0.028 -0.406 0.685AR{5} 0.096 1.371 0.172 0.037 0.528 0.598 0.021 0.308 0.758AR{6} -0.013 -0.183 0.855 -0.058 -0.835 0.405 0.072 1.035 0.302AR{7} 0.083 1.169 0.244 0.008 0.109 0.914 0.025 0.362 0.718AR{8} -0.036 -0.513 0.609 0.027 0.394 0.694 0.018 0.258 0.797AR{9} 0.036 0.514 0.608 0.011 0.168 0.867 0.097 1.396 0.164AR{10} 0.130 1.833 0.068 0.052 0.765 0.445 0.057 0.828 0.408AR{11} 0.056 0.790 0.430 -0.015 -0.212 0.833 0.034 0.489 0.626AR{12} 0.014 0.203 0.839 0.107 1.557 0.121 0.000 0.006 0.995

Adj. R^2 = -0.0057 Adj. R^2 = -0.0211 Adj R^2 = -0.02945DW = 1.9946 DW = 1.9863 DW = 1.9906Q = (36-12) = 16.1969 Q (36-12) = 31.4824 Q = (36-12) 38.3646Sig p = 0.8808 Sig p = 0.1404 Sig p = 0.0382

Jakarta, 1989-2002 Shanghai, 1991-2002VariableCoeff T-Stat Signif Coeff T-Stat SignifCONST 0.385 0.434 0.665 2.538 1.023 0.308AR{1} 0.179 2.038 0.044 -0.059 -0.648 0.518AR{2} -0.079 -0.889 0.376 -0.080 -0.898 0.371AR{3} -0.039 -0.440 0.661 -0.026 -0.293 0.770AR{4} -0.021 -0.236 0.814 -0.134 -1.531 0.128AR{5} 0.017 0.208 0.836 -0.080 -0.913 0.363AR{6} 0.064 0.797 0.427 0.073 0.829 0.409AR{7} -0.098 -1.220 0.225 0.136 1.550 0.124AR{8} 0.007 0.087 0.931 0.040 0.452 0.652AR{9} 0.005 0.068 0.946 0.189 2.164 0.032AR{10} 0.062 0.768 0.444 -0.055 -0.616 0.539AR{11} -0.033 -0.404 0.687 0.216 2.433 0.016AR{12} 0.033 0.417 0.677 -0.024 -0.265 0.791

Adj. R^2 = -0 -0.0296 Adj. R^2 = 0.0438DW = 1.9899 DW = 2.0017Q = (35-12) = 19.999 Q (33-12) = 29.0185Sig p = 0.6419 Sig p = 0.1136

Table 6(1) ARCH, ARCH-M, and GARCH Models

1. SP500, 1971-2002, Monthly Returns1-A: Arch(1)

Var. Coeff. t-Value Sig p Log of LF R^2Mean Equation 16.7475 0.00001

SP3 0.0059 6.552 0Constant 0.0092 328.7 0

Variance EquationAlpha0 0.0550 12630 0Alpha1 -0.0026 inf 0

Delta -0.0294 -14.72 0

1-B. ARCHM(0.5)Var. Coeff. t-Value Sig p Log of LF R^2

Mean Equation 640.15 0.0003SP3 0.0058 0 1

Constant -0.0052 0 1Gamma 0.2601 0.0131 0.99

Variance EquationAlpha0 0.0019 0 1Alpha1 0.0746 0 0.998

Delta 0 0 1

1-C. GARCH(1,1)Var. Coeff. t-Value Sig p Log of LF R^2

Mean Equation 643.058 0.0011SP3 0.0059 0.6195 0.536

Constant 0.0057 2.554 0.011Variance Equation

Alpha0 0.00013 1.442 0.149Alpha1 0.0649 2.188 0.029

Phi 0.08793 14.73 0Delta 0.00051 0.00001 1

(1) SP3 indicates the SP500 index lagged variable.Similarly, Dow3, Spt3, Tokyo3, Jak3, and Sha3 are all lagged variables.(2) Constant, Alpha, and Alpha0 are coefficients for the constant term.Significant alpha1 coefficients are indicated in boldface.(3) Delta: estimate of the standard deviation of the pre-sample innovations.(4) Phi: parameter estimate on the lagged variances. See Shazam User's Manual Version 9 .(5) Monthly returns are calculated by the first difference of the log monthly price index.(6) The sample period is for the initial data period for the price index levels without regard to differences and lags.

Table 6(2) ARCH, ARCH-M, and GARCH Models

2. Dow-Jones, 1971-2002, Monthly Returns2-A: Arch(1)

Var. Coeff. t-Value Sig p Log of LF R^2Mean Equation 635..439 0.00004

Dow3 0.00058 0.087 0.931Constant 0.0062 2.638 0.008

Variance EquationAlpha0 0.0021 12.06 0Alpha1 0.0273 0.6199 0.535

Delta 0.00057 0 1

2-B. ARCHM(0.5)Var. Coeff. t-Value Sig p Log of LF R^2

Mean Equation 633.38 0.0005Dow3 0.0031 0 1 Alpha 0.0033 0 1

Gamma 0.0609 0.0031 0.998Variance Equation

Alpha0 0.0021 0 1Alpha1 0.0259 0.0009 0.999

Delta -0.0008 0.0001 1

2-C. GARCH(1,1)Var. Coeff. t-Value Sig p Log of LF R^2

Mean Equation 634.957 0.0001Dow3 -0.0129 -0.236 0.814 Alpha 0.0057 2.438 0.015

Variance EquationAlpha0 0.0001 1.089 0.276Alpha1 0.0386 1.56 0.119

Phi 0.9008 12.3 0Delta 0.0001 0 1

Table 6(3) ARCH, ARCH-M, and GARCH Models

3. SP500 Total Return Index, 1971-2002, Monthly Returns3-A: Arch(1)

Var. Coeff. t-Value Sig p Log of LF R^2Mean Equation 640.339 0.00002

SPT3 -0.0236 -0.4221 0.673Constant 0.0097 4.0083 0

Variance EquationAlpha0 0.0019 11.37 0Alpha1 0.0722 1.27 0.204

Delta 0.0000 0.0000 1.0000

3-B. ARCHM(0.5)Var. Coeff. t-Value Sig p Log of LF R^2Mean Equation 640.473 0.0002

SPT3 0.0057 0.00005 1 Alpha -0.0045 0.00001 1

Gamma 0.3079 0.1551 0.988Variance Equation

Alpha0 0.0019 0 1Alpha1 0.0741 0.0032 0.997

Delta 0.0000 0 1

3-C. GARCH(1,1)Var. Coeff. t-Value Sig p Log of LF R^2

Mean Equation 641.71 0SPT3 -0.0024 -0.4368 0.6620 Alpha 0.0088 3.8800 0.0000

Variance EquationAlpha0 0.0001 1.4920 0.1360Alpha1 0.0681 2.3000 0.0210

Phi 0.8804 15.8100 0.0000Delta 0.0002 0.0000 1.0000

Table 6(4) ARCH, ARCH-M, and GARCH Models

4. NASDAQ, 1985-2002, Monthly Returns4-A: Arch(1)

Var. Coeff. t-Value Sig p Log of LF R^2Mean Equation 268.236 0.0107

NAS3 0.1323 1.915 0.055Constant 0.0157 4.088 0

Variance Equation Alpha0 0.0026 6.567 0Alpha1 0.7889 4.342 0

Delta 0 0 1

4-B. ARCHM(0.5)Var. Coeff. t-Value Sig p Log of LF R^2

Mean Equation 271.852 0.0021NAS3 0.2161 0.0124 0.99 Alpha -0.0102 0.0000 1

Gamma 0.3702 0.0158 0.987Variance Equation

Alpha0 0.0023 0 1Alpha1 0.8316 0.1129 0.91

Delta 0.0000 0 1

4-C. GARCH(1,1)Var. Coeff. t-Value Sig p Log of LF R^2

Mean Equation 275.14 0.0107NAS3 0.1658 2.117 0.034 Alpha 0.0074 1.716 0.086

Variance EquationAlpha0 0.0002 1.41 0.159Alpha1 0.1008 2.36 0.018

Phi 0.8708 15.11 0Delta 0.0001 0 1

Table 6(5) ARCH, ARCH-M, and GARCH Models

5. Korean Stocks, 1980-2002, Monthly Returns5-A: Arch(1)

Var. Coeff. t-Value Sig p Log of LF R^2Mean Equation 284.93 0.007

Kor3 0.0564 0.8232 0.41Constant 0.0082 1.604 0.109

Variance EquationAlpha 0.0065 9.188 0

Alpha1 0.1384 1.696 0.09Delta 0 0 1

5-B. ARCHM(0.5)Var. Coeff. t-Value Sig p Log of LF R^2

Mean Equation 285.129 0.0118Kor3 0.0751 0.0055 0.996

Alpha 0.0663 0.0003 1Gamma -0.6929 -0.0369 0.971

Variance Equation Alpha0 0.0066 0 1Alpha1 0.1044 0.0074 0.994

Delta 0 0 1

5-C. GARCH(1,1)Var. Coeff. t-Value Sig p Log of LF R^2

Mean Equation 295.139 0.007Kor3 0.0787 1.249 0.212

Alpha 0.006 1.294 0.196Variance Equation

Alpha0 0.0005 1.923 0.055Alpha1 0.0563 2.09 0.037

Phi 0.8598 14.68 0Delta -0.7905 -1.141 0.254

Table 6(6) ARCH, ARCH-M, and GARCH Models

6. Tokyo Stocks, 1984-2002, Monthly Returns6-A: Arch(1)

Var. Coeff. t-Value Sig p Log of LF R^2Mean Equation 320.114 0.0013

Tok3 0.06484 0.9074 0.364Constant 0.00087 0.3264 0.821

Variance EquationAlpha0 0.0031 8.367 0Alpha1 0.0961 1.209 0.227

Delta 0.3751 1.041 0.298

6-B. ARCHM(0.5)Var. Coeff. t-Value Sig p Log of LF R^2

Mean Equation 320.711 0.0276Tok3 0.0571 0.004 0.997

Constant -0.1115 -0.0005 1Gamma 1.924 0.1473 0.883

Variance EquationAlpha0 0.0032 0 1Alpha1 0.0600 0.002 0.998

Delta 0.3663 0.0647 0.948

6-C. GARCH(1,1)Var. Coeff. t-Value Sig p Log of LF R^2

Mean Equation 321.376 0.0013Tok3 0.0801 1.108 0.268

Alpha 0.0019 0.4884 0.625Variance Equation

Alpha0 0.0012 1.31 0.19Alpha1 0.1068 1.41 0.159

Phi 0.5564 1.889 0.059Delta 0.2738 0.9608 0.337

Table 6(7) ARCH, ARCH-M, and GARCH Models A23

7. Jakarta Stocks, 1989-2002, Monthly Returns7-A: Arch(1)

Var. Coeff. t-Value Sig p Log of LF R^2Mean Equation 152.378 0.0165

Jak3 0.1391 1.72 0.085Constant 0.002 0.2626 0.793

Variance EquationAlpha0 0.0091 8.02 0Alpha1 0.0252 0.4 0.689

Delta 0.0005 0 1

7-B. ARCHM(0.5)Var. Coeff. t-Value Sig p Log of LF R^2

Mean Equation 152.826 0.0223Jak3 0.1414 0.0018 0.999 Alpha 0.321 0.0018 0.848

Gamma -3.3113 -0.1922 0.0848Variance Equation

Alpha0 0.0091 0 1Alpha1 0.0257 0.0006 1

Delta -0.0001 0 1

7-C. GARCH(1,1)Var. Coeff. t-Value Sig p Log of LF R^2

Mean Equation 154.692 0.0165Jak3 0.1573 1.945 0.052

Alpha 0.0017 0.245 0.806Variance Equation

Alpha0 0.0007 0.7814 0.435Alpha1 0.0384 1.054 0.292

Phi 0.8803 6.93 0Delta 0 0 1

Table 6(8) ARCH, ARCH-M, and GARCH Models

8. Shanghai Stocks, 1991-2002, Monthly Returns8-A: Arch(1)

Var. Coeff. t-Value Sig p Log of LF R^2Mean Equation 87.4608 0.0063

Sha3 -0.2254 -3.371 0.001Constant -0.0032 -0.464 0.643

Variance EquationAlpha0 0.0059 4.612 0Alpha1 1.3475 4.612 0

Delta 0.0453 0.451 0.652

8-B. ARCHM(0.5)Var. Coeff. t-Value Sig p Log of LF R^2

Mean Equation 87.9175 0.0207Sha3 -0.2716 -0.0148 0.988 Alpha -0.0183 -0.0001 1

Gamma 0.1252 0.006 0.99Variance Equation

Alpha0 0.0058 0 1Alpha1 1.3721 0.3283 0.743

Delta -0.0194 -0.003 0.998

8-C. GARCH(1)Var. Coeff. t-Value Sig p Log of LF R^2

Mean Equation 85.494 0.0063Sha3 -0.9205 -0.977 0.329 Alpha 0.0092 1.109 0.267

Variance EquationAlpha0 0.0002 1.016 0.309Alpha1 0.0719 2.337 0.019

Phi 0.9016 29.88 0Delta -0.031 -1.042 0.297

Table 6(8) Heteroscedasticity Test for the Dependent Variable

The Lagrange Multiplier TestPeriod N Initial N Effec. N R^2 NR^2

SP500 1971-2002 384 382 0.01815 6.93200Dow-Jones 1971-2002 384 382 0.00650 2.48410SP500total 1971-2002 384 382 0.01755 6.70357NASDAQ 1985-2002 216 214 0.00179 0.38210Korea 1980-2002 276 274 0.00091 0.24857Tokyo 1984-2002 228 226 0.02326 5.25750Jakarta 1989-2002 168 166 0.00109 0.18160Shanghai 1991-2002 144 142 0.00041 0.05865* The dependent variable is the monthly return. The critical chi-square value is 149.45 at 0.001 level for DF = 100. Since NR^2 is less than the critical value, the null hypothesis of homoscedasticity cannot be rejected.

Table 7 Unit Root Test

A. Dickey-Fuller Testsa(1)=0 Constant, a(1)=0 Constant,t-Stat. No trend t-Stat Trend

Critical(0.1) Critical(0.1)1. SP500 1984-2002 -1.091 -2.57 -1.321 -3.132. Korea 1984-2002 -2.640 -2.57 -2.282 -3.133. Tokyo 1984-2002 -1.867 -2.57 -2.460 -3.134. Jakarta 1989-2002 -2.855 -2.57 -2.611 -3.135. Shanghai 1991-2002 -1.896 -2.57 -2.723 -3.13 6. Dow-Jones 1971-2002 -1.969 -2.57 -2.683 -3.137. SP500 1971-2002 -1.892 -2.57 -2.795 -3.138. NASDAQ 1985-2002 -1.123 -2.57 -1.864 -3.139.SP500Total 1971-2002 -2.312 -2.57 -3.131 -3.13

B. Phillips-Perron Tests1. SP500 1984-2002 -1.934 -2.57 -4.580 -3.132. Korea 1984-2002 -2.292 -2.57 -2.075 -3.133. Tokyo 1984-2002 -1.855 -2.57 -2.151 -3.134. Jakarta 1989-2002 -2.907 -2.57 -2.700 -3.135. Shanghai 1991-2002 -1.990 -2.57 -2.723 -3.136. Dow-Jones 1971-2002 -0.029 -2.57 -1.723 -3.137. SP500 1971-2002 -0.366 -2.57 -1.613 -3.138. NASDAQ 1985-2002 -1.123 -2.57 -1.871 -3.139.SP500Total 1971-2002 -0.147 -2.57 -1.564 -3.13If the computed t- value is less than the critical value, the null hypothesis of a unit root is rejected. The critical values are at the 10% level.

Table 8 Variance Ratio Test, Monthly Log Prices

SP500 Seoul Tokyo Jakarta Shanghai Dow-Jones NASDAQ SP500Tot 1971-2002 1980-2002 1984-2002 1989-2002 1991-2002 1971-2002 1985-2002 1971-2002q N=384 N=276 N=228 N=168 N=144 N=384 N=216 N=3842 1.0208 0.9300 0.9627 0.8834 1.0899 1.0200 0.9157 1.04173 1.0490 0.8973 0.9405 0.8695 1.0817 1.0360 0.8999 1.06754 1.0482 0.8960 0.9219 0.8815 1.0908 1.0362 0.9021 1.06405 1.0591 0.9017 0.8979 0.9057 1.1795 1.0570 0.9164 1.07436 1.0317 0.8958 0.8556 0.9183 1.2827 1.0545 0.9399 1.04587 1.0303 0.8746 0.8410 0.9230 1.3525 1.0770 0.9341 1.04348 1.0308 0.8528 0.8427 0.9652 1.3303 1.0898 0.9170 1.04369 1.0324 0.8321 0.8351 1.0018 1.3223 1.1062 0.9142 1.0445

10 1.0416 0.8089 0.8178 1.0280 1.2445 1.1226 0.9156 1.053711 1.0249 0.7827 0.7940 1.0282 1.2192 1.1140 0.8861 1.036812 1.0136 0.7587 0.7748 1.0235 1.1626 1.1045 0.8596 1.025313 0.9976 0.7386 0.7579 1.0115 1.1343 1.0885 0.8444 1.009130 1.0585 0.7386 0.6773 2.0976 2.3631 1.1874 0.9471 1.0827

The numbers are z-scores for the variance ratio test.

Table 9 Runs Test for Monthly Returns

A. Runs Test for the Entire Sample PeriodSP500Korea Tokyo Jakarta Shanghai

z for the median -0.511 -1.809 -0.664 0.155 0.836 p value 0.609 0.070 0.507 0.877 0.403 z for mean -0.298 -2.070 -0.128 -0.037 0.902 p value 0.766 0.038 0.898 0.970 0.367

B. Runs Test for Each Month1. SP 500 Stocks, 1971-2002

Jan Feb. March April May June July Aug. Sept. Oct. Nov. Dec.Test Value 0 0 0 0 0 0 0 0 0 0 0 0Total Cases 23 23 23 23 23 23 23 23 23 23 23 23Number of Runs 13 10 11 14 12 9 10 8 11 14 11 9Z 0.01 -0.44 0.00 0.44 0.00 -0.91 -0.65 -0.21 -0.21 0.52 0.00 -1.22Sig. (2-tailed) 0.99 0.66 1.00 0.66 1.00 0.36 0.51 0.83 0.84 0.60 1.00 0.22

2. Korean Stocks, 1980-2002Jan Feb. March April May June July Aug. Sept. Oct. Nov. Dec.

Test Value 0 0 0 0 0 0 0 0 0 0 0 0Total Cases 23 23 23 23 23 23 23 23 23 23 23 23No. of of Runs 13 10 11 14 12 9 10 8 11 14 11 9Z 0.01 -0.44 0.00 0.44 0.00 -0.91 -0.65 -0.21 -0.21 0.52 0.00 -1.22Sig. (2-tailed) 0.99 0.66 1.00 0.66 1.00 0.36 0.51 0.83 0.84 0.60 1.00 0.22

3. Tokyo Stocks, 1984-2002Jan Feb. March April May June July Aug. Sept. Oct. Nov. Dec.

Test Value 0 0 0 0 0 0 0 0 0 0 0 0Total Cases 19 19 19 19 19 19 19 19 19 19 19 19No. of of Runs 12 7 9 8 8 6 13 6 10 12 13 8Z 0.49 -1.41 0.00 -0.86 -0.86 -1.88 1.08 -1.88 0.00 0.49 0.96 -0.93Sig. (2-tailed) 0.63 0.16 1.00 0.39 0.39 0.06 0.28 0.06 1.00 0.63 0.34 0.35

4. Jakarta Stocks, 1989-2002Jan Feb. March April May June July Aug. Sept. Oct. Nov. Dec.

Test Value 0 0 0 0 0 0 0 0 0 0 0 0Total Cases 14 14 14 14 14 14 14 14 14 14 14 14No. of of Runs 8 5 11 10 9 8 7 4 5 5 12 8Z 0.55 -0.84 1.50 0.93 0.28 0.04 -0.28 -1.05 -0.18 -1.18 2.07 0.55Sig. (2-tailed) 0.59 0.40 0.13 0.35 0.78 0.97 0.78 0.30 0.85 0.24 0.04 0.59

5. Shanghai StocksJan Feb. March April May June July Aug. Sept. Oct. Nov. Dec.

Test Value 0 0 0 0 0 0 0 0 0 0 0 0Total Cases 12 12 12 12 12 12 12 12 12 12 12 12No. of of Runs 6 7 4 6 6 7 6 9 8 6 8 6Z -0.30 0.11 -0.84 0.00 -0.21 0.00 0.00 1.04 0.80 0.00 0.80 0.00Sig. (2-tailed) 0.76 0.91 0.40 1.00 0.84 1.00 1.00 0.30 0.42 1.00 0.42 1.00

Table 10 (1) Cointegration Test for the Monthly Stock Price Indexes

A. Dickey-Fuller Test (1) Korea and SP500 (1984-2002)Cointegration equation Constant, No trend Constant, Trend

R^2 0.0800 0.8164DW 0.1039 0.5776

t-Test Stat Asy. Critical at 0.1 t-Test Stat Asy. Critical at 0.1No constant, No trend -1.0714 -3.04 -1.9353 -3.5

(2) Korea and Tokyo (1984-2002)Conintegration equation: Constant, No trend Constant, Trend

R^2 0.3194 0.5715DW 0.0614 0.1224

t-Test Stat Asy. Crtical at 0.1 t-Test Stat Asy. Critcal at 0.1No constant, No trend -1.5944 -3.04 -2.9546 -3.5

(3) Tokyo and SP500 (1984-2002)Cointegration equation Constant, No trend Constant, Trend

R^2 0.0414 0.79DW 0.1086 0.4768

t-Test Stat Asy. Critical at 0.1 t-Test Stat Asy. Critical at 0.1No constant, No trend -1.6148 -3.04 -1.4186 -3.5

(4) Jakarta and SP500 (1989-2002)Conintegration equation: Constant, No trend Constant, Trend

R^2 0.1864 0.7435DW 0.2174 0.5689

t-Test Stat Asy. Crtical at 0.1 t-Test Stat Asy. Critcal at 0.1No constant, No trend -1.5668 -3.04 -1.8936 -3.5

(5) Jakarta and Korea (1989-2002)Conintegration equation: Constant, No trend Constant, Trend

R^2 0.1836 0.1858DW 0.1841 0.182

t-Test Stat Asy. Crtical at 0.1 t-Test Stat Asy. Critcal at 0.1No constant, No trend -2.7773 -3.04 -2.7751 -3.5

(6) Jakarta and Tokyo (1989-2002)Conintegration equation: Constant, No trend Constant, Trend

R^2 0.2398 0.5732DW 0.1116 0.1425

t-Test Stat Asy. Crtical at 0.1 t-Test Stat Asy. Critcal at 0.1No constant, No trend -1.5668 -3.04 -2.4914 -3.5

Table 10 (2) Cointegration Tests for the Monthly Stock Price Indexes

(7) Dow and SP500 (1971-2002)Cointegration equation: Constant, No trend Constant, Trend

R^2 0.9898 0.99DW -0.0869 -0.0872

t-Test Stat Asy. Crtical at 0.1 t-Test Stat Asy. Critcal at 0.1No constant, No trend -2.8309 -3.04 -2.5044 -3.5

(8) Dow and NASDAQ (1985-2002)Cointegration equation: Constant, No trend Constant, Trend

R^2 0.4411 0.7724DW 0.0168 0.0275

t-Test Stat Asy. Crtical at 0.1 t-Test Stat Asy. Critcal at 0.1No constant, No trend -1.525 -3.04 -2.5476 -3.5

(9) SP500 and NASDAQ (1985-2002)Cointegration equation: Constant, No trend Constant, Trend

R^2 0.4475 0.7627DW 0.0168 0.0252

t-Test Stat Asy. Crtical at 0.1 t-Test Stat Asy. Critcal at 0.1No constant, No trend -1.138 -3.04 -2.2615 -3.5* If the computed t value is greater than the critical t value, we cannot reject the null hypothesis that the two variables are not cointegrated (non-stationarity).

B. Phillips-Perron Test (1) Korea and SP500 (1984-2002)Cointegration equation Constant, No trend Constant, Trend

R^2 0.0799 0.8164DW 0.1039 0.5776

t-Test Stat Asy. Critical at 0.1 t-Test Stat Asy. Critical at 0.1No constant, No trend -1.8813 -3.04 -5.3144 -3.55

(2) Korea and Tokyo (1984-2002)Conintegration equation: Constant, No trend Constant, Trend

R^2 0.3194 0.5715DW 0.0614 0.1224

t-Test Stat Asy. Crtical at 0.1 t-Test Stat Asy. Critcal at 0.1No constant, No trend -1.6386 -3.04 -3.0108 -3.5

(3) Tokyo and SP500 (1984-2002)Cointegration equation Constant, No trend Constant, Trend

R^2 0.0414 0.79DW 0.1086 0.4768

t-Test Stat Asy. Critical at 0.1 t-Test Stat Asy. Critical at 0.1No constant, No trend -2.2433 -3.04 -4.6517 -3.5

Table 10 (3) Cointegration Tests for the Monthly Stock Price Indexes

(4) Jakarta and SP500 (1989-2002)Conintegration equation: Constant, No trend Constant, Trend

R^2 0.1864 0.7435DW 0.2174 0.5689

t-Test Stat Asy. Crtical at 0.1 t-Test Stat Asy. Critcal at 0.1No constant, No trend -2.5586 -3.04 -4.4574 -3.5

(5) Jakarta and Korea (1989-2002)Conintegration equation: Constant, No trend Constant, Trend

R^2 0.1837 0.1858DW 0.1841 0.182

t-Test Stat Asy. Crtical at 0.1 t-Test Stat Asy. Critcal at 0.1No constant, No trend -2.9134 -3.04 -2.9104 -3.05

(6) Jakarta and Tokyo (1989-2002)Conintegration equation: Constant, No trend Constant, Trend

R^2 0.2398 0.5732DW 0.1116 0.1425

t-Test Stat Asy. Crtical at 0.1 t-Test Stat Asy. Critcal at 0.1No constant, No trend -2.9104 -3.5 -1.8246 -3.04

(7) Dow and SP500 (1971-2002)Cointegration equation: Constant, No trend Constant, Trend

R^2 0.9898 0.99DW 0.0869 0.0872

t-Test Stat Asy. Crtical at 0.1 t-Test Stat Asy. Critcal at 0.1No constant, No trend -1.8475 -3.04 -1.9674 -3.5

(8) Dow and NASDAQ (1985-2002)Cointegration equation: Constant, No trend Constant, Trend

R^2 0.4411 0.7724DW 0.0168 0.0275

t-Test Stat Asy. Crtical at 0.1 t-Test Stat Asy. Critcal at 0.1No constant, No trend -0.9108 -3.04 -2.0729 -3.5

(9) SP500 and NASDAQ (1985-2002)Cointegration equation: Constant, No trend Constant, Trend

R^2 0.4475 0.7627DW 0.0167 0.0252

t-Test Stat Asy. Crtical at 0.1 t-Test Stat Asy. Critcal at 0.1No constant, No trend -1.1194 -3.04 -1.8267 -3.05* If the computed t value is less than the critical t value, we can reject the null hypothesis ofno cointegration.

Table 10(4) Cointegration Test

C. Johansen Maximum Likelihood Test Period Trace Test Maximum

eigenvalue test1. SP500 and Dow 1971-2002 6.868 5.9172. SP500 and SPTotal 1971-2002 15.597 11.0113. SP500 and NASDAQ 1985-2002 24.219 17.8414. SP500 and Korea 1980-2002 13.898 10.4925. SP500 and Tokyo 1984-2002 9,871 9.0446. Korea and Tokyo 1984-2002 11.744 11.298*For the trace test, the critical values are 15.6 for the 10% level and 17.8 for the 5% level. For the maximum eignevalue test, the critical values are 12.8 for the 10% level and 14.6 for the 5% level. The above results indicate that only SP500 and NASDAQ are cointegrated.

Table 11 (1) VAR Modles for Monthly Returns, 1991-2002

I. VAR Model for 4 Stock Exchanges A. SP500

Variable Coeff Std Error T-Stat Signif Ad. R^2 DW1 SP500{1} -0.0286 0.0920 -0.3113 0.7561 0.0432 1.97732 Korea{1} 0.0310 0.0399 0.7771 0.43843 Tokyo{1} -0.0427 0.0721 -0.5924 0.55454 Jakarta{1} -0.0856 0.0434 -1.9720 0.05055 Constant 0.7893 0.3638 2.1694 0.0317

B. KoreaVariable Coeff Std Error T-Stat Signif Ad. R^2 DW

1 SP500{1} 0.1332 0.2213 0.6018 0.5483 0.0277 1.93902 Korea{1} 0.1427 0.0958 1.4890 0.13873 Tokyo{1} -0.1561 0.1735 -0.8997 0.36984 Jakarta{1} -0.0349 0.1044 -0.3346 0.73845 Constant 0.2809 0.8750 0.3211 0.7486

C. TokyoVariable Coeff Std Error T-Stat Signif Ad. R^2 DW

1 SP500{1} 0.0300 0.1190 0.2523 0.8012 0.0209 1.91232 Korea{1} 0.0508 0.0515 0.9851 0.32623 Tokyo{1} 0.0259 0.0933 0.2782 0.78134 Jakarta{1} -0.0623 0.0561 -1.1091 0.2693

5 Constant -0.3175 0.4704 -0.6750 0.5008

D. JakartaVariable Coeff Std Error T-Stat Signif Ad. R^2 DW

1 SP500{1} 0.4570 0.1880 2.4311 0.0163 0.1016 1.98032 Korea{1} 0.1568 0.0814 1.9257 0.05613 Tokyo{1} -0.0257 0.1474 -0.1743 0.86194 Jakarta{1} -0.0102 0.0887 -0.1149 0.90875 Constant 0.0351 0.7433 0.0472 0.9624

Table 11 (2) VAR Modles for Monthly Returns, 1991-2002

II. VAR Model for 5 Stock ExchangesA. SP500 Stocks

Variable Coeff Std Error T-Stat Signif Ad. R^2 DW1 SP500{1} -0.0287 0.0920 -0.3118 0.7556 0.0439 1.97162 Korea{1} 0.0299 0.0400 0.7492 0.45503 Tokyo{1} -0.0419 0.0721 -0.5811 0.56214 Jakarta{1} -0.0843 0.0436 -1.9357 0.05495 Shanghai{1} -0.0053 0.0159 -0.3324 0.74006 Constant 0.8073 0.3677 2.1955 0.0297

B. Korean StocksVariable Coeff Std Error T-Stat Signif Ad. R^2 DW

1 SP500{1} 0.1333 0.2211 0.6029 0.5475 0.0293 1.93092 Korea{1} 0.1463 0.0961 1.5231 0.12993 Tokyo{1} -0.1589 0.1734 -0.9162 0.36114 Jakarta{1} -0.0394 0.1048 -0.3762 0.70735 Shanghai{1} 0.0185 0.0383 0.4822 0.63046 Constant 0.2180 0.8839 0.2467 0.8055

C. Tokyo StocksVariable Coeff Std Error T-Stat Signif Ad. R^2 DW

1 SP500{1} 0.0298 0.1182 0.2520 0.8014 0.0336 1.90512 Korea{1} 0.0453 0.0514 0.8822 0.37913 Tokyo{1} 0.0302 0.0927 0.3261 0.74494 Jakarta{1} -0.0555 0.0560 -0.9909 0.32345 Shanghai{1} -0.0280 0.0205 -1.3693 0.17316 Constant -0.2221 0.4725 -0.4700 0.6390

D. Jakarta StocksVariable Coeff Std Error T-Stat Signif Ad. R^2 DW

1 SP500{1} 0.4571 0.1879 2.4332 0.0162 0.1027 1.98352 Korea{1} 0.1595 0.0816 1.9537 0.05273 Tokyo{1} -0.0278 0.1474 -0.1885 0.85074 Jakarta{1} -0.0135 0.0890 -0.1517 0.87965 Shanghai{1} 0.0137 0.0326 0.4205 0.67486 Constant -0.0115 0.7511 -0.0153 0.9878

E. Shanghai StocksVariable Coeff Std Error T-Stat Signif Ad. R^2 DW

1 SP500{1} 0.6007 0.4797 1.2520 0.2126 0.0310 2.02832 Korea{1} 0.0655 0.2084 0.3141 0.75393 Tokyo{1} -0.5584 0.3763 -1.4838 0.14014 Jakarta{1} -0.0272 0.2273 -0.1196 0.90505 Shanghai{1} -0.0521 0.0831 -0.6270 0.53176 Constant 2.8002 1.9180 1.4600 0.1465

Table 12 Correlation Coefficients of Monthly Returns, 1989-2002

January FebruaryUS Korea Tokyo Jakarta US Korea Tokyo Jakarta

US 1 1Korea 0.034 1.000 0.245 1Tokyo 0.366 0.384 1.000 0.283 0.619 1Jakarta -0.238 0.682 -0.014 1 0.306 0.242 -0.251 1Crtical r: 0.532 at 0.05 and 0.661 at 0.01

March AprilUS Korea Tokyo Jakarta US Korea Tokyo Jakarta

US 1 1Korea 0.375 1 0.481 1Tokyo 0.199 0.523 1 0.092 0.591 1Jakarta 0.578 0.017 -0.249 1 -0.165 0.537 0.282 1

May JuneUS Korea Tokyo Jakarta US Korea Tokyo Jakarta

US 1 1Korea -0.476 1 0.429 1Tokyo 0.533 -0.538 1 0.766 0.542 1Jakarta 0.053 0.313 -0.086 1 0.477 0.192 0.270 1

July AugustUS Korea Tokyo Jakarta US Korea Tokyo Jakarta

US 1 1Korea 0.163 1 0.336 1Tokyo 0.496 0.584 1 0.604 0.623 1Jakarta 0.206 0.344 0.237 1.000 0.508 0.501 0.340 1

September OctoberUS Korea Tokyo Jakarta US Korea Tokyo Jakarta

US 1 1Korea 0.426 1 0.486 1Tokyo 0.273 0.062 1 -0.053 0.495 1Jakarta 0.334 0.020 0.370 1 0.294 0.385 -0.030 1

November DecmberUS Korea Tokyo Jakarta US Korea Tokyo Jakarta

US 1 1Korea 0.274 1 0.369 1Tokyo 0.089 0.240 1 0.242 0.077 1Jakarta -0.016 0.364 -0.035 1 0.044 0.065 0.4383 1

January-December, 1989-2002 January-December, 1991-2002USA Korea Tokyo Jakart US Korea Tokyo Jakart

US 1 Korea .3263 1Korea 0.3356 1 Tokyo .3507 .3839 1Tokyo 0.3694 0.3905 1 Jakarta .3135 .3718 .2372 1 Jakarta 0.2579 0.3223 0.1582 1 Shang .0185 .0393 .0296 .0700 Critical r: 0.151 at 0.5 and 0.195 at 0.01. Critical r: 0.164 at 0.05, and 0.214 at 0.01 N=168, d.f.=166 N=144, d.f.=142

Table 13 (1) Regression Results, Monthly Stock Prices (in Log)

A-1. SP500 - Simple RegressionIndepen Intercept Slope Ad.R^2 F Sig. p DW Period

Korea 0.00612 0.998 0.987 21713.1 0 1.834 1980-2002(0.148) (147.4)**

Tokyo -0.644 1.287 0.429 171.65 0 0.077 1984-2002(-1.21) (13.102)**

Jakarta 4.93 0.268 0.066 12.8111 0 0.172 1989-2002(10.79)** (3.58)**

Shanghai 7.011 -0.0687 0.024 4.591 0.034 0.155 1991-2002(31.87)** (-2.14)**

** Significant at the 1 % level, * Significant at the 5 % level.

A-2. SP500 - Multiple Regression, 1991-2002Indepen Coeff. t-value Sig. p Ad. R^2 F Sig. p DW

Const. 1.3230 3.341 0.001 0.86 219.745 0 1.75Korea 0.9660 24.991 0.000Tokyo -0.1590 -2.329 0.021Jakarta -0.0013 -0.321 0.749Shanghai -0.0239 -1.379 0.170

B-1. Korean Stocks - Simple Regression Indepen Intercept Slope Ad.R^2 F Sig. p DW Period

SP500 0.00612 0.998 0.987 21713.1 0 1.834 1980-2002(0.148) (147.4)**

Tokyo -0.84 1.322 0.442 180.487 0 0.047 1984-2002(-1.58) (1.32)**

Jakarta 3.757 0.457 0.191 34.834 0 0.150 1989-2002(7.96)** (5.90)**

Shanghai 7.003 -0.068 0.024 4.506 0.036 0.143 1989-2002(31.91)** (-2.12)*

B-2. Korean Stocks - Multiple Regression, 1991-2002Indepen Coeff. t-value Sig. p Ad. R^2 F Sig. p DW

Const. -0.745 -1.959 0.052 0.876 254.132 0 1.683SP500 0.847 24.99 0.000Tokyo 0.204 3.264 0.001Jakarta 0.0973 2.527 0.013Shanghai 0.0076 0.469 0.640

Table 13 (2) Correlation and Regression Results for 5 Stock Exchanges

C-1: Tokyo Stocks - Simple RegressionIndepen Intercept Slope Ad.R^2 F Sig. p DW Period

Korea 3.287 0.336 0.442 180.487 0 0.062 1984-2002(20.76)** (13.44)**

SP500 3.288 0.335 0.429 171.65 0 0.090 1984-2002(20.26)** (13.10)**

Jakarta 5.159 0.0471 -0.003 0.438 0.509 0.062 1989-2002(11.89)** (0.66)

Shanghai 6.338 -0.141 0.318 67.751 0 0.180 1991-2002(54.02)** (-8.23)**

C-2. Tokyo Stocks - Multiple Regression, 1991-2002Indepen Coeff. t-value Sig. p Ad. R^2 F Sig. p DW

Const. 4.661 14.998 0 0.485 34.638 0 0.269Korea 0.348 3.264 0.001SP500 -0.237 -2.329 0.021Jakarta 0.170 3.441 0.001Shanghai -0.153 -9.108 0.000

D-1. Jakarta Stocks-Simple RegressionIndepen Intercept Slope Ad.R^2 F Sig. p DW Period

Korea 3.89 0.335 0.107 21.096 0 0.142 1989-2002(8.12)** (4.59)**

Tokyo 5.785 0.0559 -0.003 0.438 0.509 0.139 1989-2002(12.57)** (0.66)

SP500 4.336 0.267 0.066 12.811 0 0.164 1989-2002(8.85)** (3.58)**

Shanghai 5.293 0.117 0.091 15.28 0 0.146 1991-2002(25.72)** (3.91)**

D-2. Jakarta Stocks - Multiple Regression, 1991-2002Indepen Coeff. t-value Sig. p Ad. R^2 F Sig. p DW

Const. -0.415 -0.5 0.618 0.392 24.021 0 0.222Korea 0.451 2.527 0.013Tokyo 0.462 3.441 0.001SP500 -0.055 -0.321 0.749Shanghai 0.209 6.909 0.000

Table 13 (3) Correlation and Regression Results for 5 Stock Exchanges

E-1. Shanghai Stocks - Simple RegressionIndepen Intercept Slope Ad.R^2 F Sig. p DW Period

Korea 9.781 -0.453 0.024 4.506 0.036 0.063 1991-2002(7.01)** (-2.12)*

Tokyo 19.151 -2.293 0.318 67.751 0.000 0.134 1991-2002(12.78)* (-8.23)*

Jakarta 1.776 0.828 0.091 15.28 0.000 0.075 1991-2002(1.38) (3.91)**

SP500 9.802 -0.458 0.024 4.591 0.034 0.065 1991-2002(7.04)** (-2.14)*

E-2. Shanghai Stocks - Multiple Regression, 1991-2002Indepen Coeff. t-value Sig. p Ad. R^2 F Sig. p DW

Const. 14.832 9.509 0 0.497 36.361 0 0.221Korea 0.207 0.469 0.640Tokyo -2.436 -9.108 0.000Jakarta 1.221 6.909 0.000SP500 -0.566 -1.379 0.170All stock prices are in natural log prices.

Table 14 (1) Characteristics of the Asian and US Stock Markets

A. Descriptive Statistics of Monthly Returns (%)SP500 Korea Tokyo Jakarta Shanghai

1 Period 1971-2002 1980-2002 1984-2002 1989-2002 1991-20022 Months 384 276 228 168 144 3 Mean 0.6809 1.0092 0.3554 0.6683 3.2841 4 Sample variance 20.3988 79.3996 35.0700 96.1879 501.0663 5 Sample standard deviation 4.5165 8.9106 5.9220 9.8075 22.3845 6 Minimum -21.76 -27.25 -20.01 -31.58 -31.152946 7 Maximum 16.3 50.77 17.71 48.31 177.2261889 8 Range 38.06 78.02 37.72 79.89 208.3791349 9 Population variance 20.3457 79.1119 34.9162 95.6153 497.5867

10 Population standard deviation 4.5106 8.8945 5.9090 9.7783 22.3067

11 Confid. interval 95.% lower 0.2277 -0.0467 -0.4175 -0.8256 -0.4032 12 Confid. interval 95.% upper 1.1341 2.0651 1.1282 2.1621 6.9714 13 half-width 0.4532 1.0559 0.7728 1.4939 3.6873

14 Skewness -0.3823 1.0054 0.2935 0.5279 4.8416 15 Kurtosis 1.9428 3.5302 0.8089 3.6059 32.9301 16 Coefficient of variation 663.33% 882.94% 1666.52% 1467.59% 681.60%

17 1st quartile -1.9300 -4.1400 -3.5775 -5.1800 -5.2018 18 Median 0.8050 -0.2850 0.1500 -0.1600 0.4634 19 3rd quartile 3.6625 5.2125 3.7975 6.3325 7.1404 20 Interquartile range 5.5925 9.3525 7.3750 11.5125 12.3423 21 Mode 3.3100 -3.8600 0.8100 -5.9900 na

22 Low extremes 1 0 0 0 0 23 Low outliers 4 1 1 2 4 24 High outliers 3 13 4 2 2 25 High extremes 0 1 0 1 4 26 Suggested interval width 2 5 5 5 10

Table 14 (2) Characteristics of the Asian and US Stock Markets

B. Descriptive Statistics of Monthly Returns (%) Dow-Jones NASDAQ SP500Total

1 Period 1971-2002 1985-2002 1971-20022 Months 384 216 384 3 Mean 0.7056 1.0524 0.9796 4 Sample variance 20.9500 52.3640 20.5997 5 Sample standard deviation 4.5771 7.2363 4.5387 6 Minimum -23.2177 -27.2339 -21.5362 7 Maximum 14.4181 21.9759 16.8091 8 Range 37.6358 49.2097 38.3454 9 Population variance 20.8954 52.1216 20.5461

10 Population standard deviation 4.5712 7.2195 4.5328

11 Confi. Interval 95% lower 0.2464 0.0819 0.5243 12 Confid. Interval 95% upper 1.1649 2.0229 1.4350 13 Half-width 0.4593 0.9705 0.4554

14 skewness -0.4371 -0.3499 -0.5888 15 kurtosis 2.3019 1.9110 1.7453 16 coefficient of variation (CV) 648.66% 463.30% 687.59%

17 1st quartile -1.7770 -1.6848 -2.8638 18 median 0.7856 1.1061 1.9283 19 3rd quartile 3.5311 3.9998 4.6435 20 interquartile range 5.3081 5.6846 7.5073 21 Mode na na na

22 low extremes 1 1 1 23 low outliers 7 4 6 24 high outliers 3 3 3 25 high extremes 0 0 0 26 suggested interval width 2 2 5

Table 14 (3) Characteristics of the Asian and US Stock Markets

C. Means and Location Tests ANOVA p Kruskal- p Friedman p Period

WallisSP500 1.270 0.238 13.930 0.237 15.770 0.150 1971-2002SP500TR 1.230 0.264 14.575 0.266 14.577 0.203 1971-2002Dow-Jones 1.743 0.063 17.976 0.082 19.988 0.046 1971-2002NASDAQ 1.012 0.437 11.320 0.417 16.043 0.140 1985-2002Korea 1 1.178 0.303 14.782 0.193 12.378 0.336 1980-2002Korea 2 1.105 0.358 13.410 0.268 12.776 0.308 Ex. 1998Tokyo 0.903 0.539 7.441 0.762 17.459 0.095 1984-2002Jakarta 1 1.200 0.291 13.659 0.189 9.597 0.567 1989-2002Jakarta 1 1.713 0.077 18.336 0.074 16.907 0.111 Ex.1989,98Shanghai 1 0.804 0.636 12.970 0.295 15.628 0.156 1991-2002Shanghai 2 1.000 0.450 12.445 0.331 16.785 0.114 Ex.1992,94* Equality of means or locations are rejected only for the Dow-Jones by the Friedman test atthe 5% level.

* SP500TR = SP500 Total return index.

D. Normality TestsJarque- p Lilliefors Critical Chi-square Sig.Berra at 0.05 p

SP500 63.891 0.000 0.0478 0.0451 5.918 0.116SP500TR 66.264 0.000 0.0464 0.0456 8.450 0.038Dow-Jones 97.009 0.000 0.0604 0.0456 4.132 0.248NASDAQ 39.894 0.000 0.0757 0.0607 9.984 0.007Korea 1 189.270 0.000 0.0866 0.0537 24.351 0.000Tokyo 5.236 0.073 0.0533 0.0591 9.128 0.028Jakarta 1 98.777 0.000 0.0557 0.0688 4.863 0.088Shanghai 1 7161.670 0.000 0.2271 0.0742 59.568 0.000* Jarque-Berra test rejects normality for all stock markets, except for Tokyo at the 5 % level.Lilliefors test rejects normality for all stock markets, except for Tokyo and JakartaChi-square test rejects normality for all stock markets, except for SP500, Dow-Jones, and Jakarta.

Table 14 (4) Characteristics of the Asian and US Stock Markets

E. Kurtosis, Skewness, and Bartlett's TestSkewness Signi. Kurtosis Signi. Bartlett's Signi.

(Sk=0) p (Ku=0) p D pSP500 -0.3538 0.0048 1.8688 0 35.2215 0SP500TR -0.3499 0.0053 1.9109 0 34.7317 0Dow-Jones -0.4371 0 2.3019 0 42.4394 0NASDAQ -0.9822 0 2.7518 0 13.5988 0.2560Korea 1 0.9383 0 3.5968 0 32.8888 0Tokyo 0.1259 0.4408 0.6984 0.0340 9.9302 0.5367Jakarta 1 0.5276 0.0057 3.6052 0 45.4339 0Shanghai 1 4.8669 0 33.1492 0 110.312 0* Bartlett's test rejects the null hypothesis of equality of variances for all stock markets,except for NASDAQ and Tokyo.

F. Chi-square Test of Goodness of Fit and Runs TestChi-sq Sig. Runs test Sig. Runs test Sig.

p Mean p Median pSP500 13.31 0.2734 -0.511 0.609 -0.298 0.766SP500TR 9.75 0.5535 -0.302 0.763 -0.102 0.919Dow-Jones 11.17 0.4291 0.516 0.606 0.920 0.358NASDAQ 3.60 0.9802 -0.01 0.992 -0.409 0.682Korea 1 9.10 0.6126 -1.809 0.07 -2.07 0.038Tokyo 2.41 0.9965 -0.664 0.507 -0.128 0.898Jakarta 1 10.00 0.5304 0.155 0.877 -0.037 0.970Shanghai 1 6.82 0.8135 0.836 0.403 0.902 0.367* Chi-square test for the goodness of fit (frequency of negative monthly returns)cannot reject the normality hypothesis for all stock markets.The runs test accepts randomness hypothesis for all stock markets except for Korea (median test).

Table 15 Factor Analysis of Monthly Returns, 1991-2002

A: 5-Factor Model1 2 3 4 5

Korea 0.7461 -0.1057 -0.0207 0.4577 0.4714SP500 0.7214 0.0443 0.0834 -0.6464 0.2301Tokyo 0.7014 -0.0695 0.5547 0.1407 -0.4192Jakarta 0.6707 0.1290 -0.6484 0.0377 -0.3342Shanghai 0.0092 0.9880 0.1177 0.0829 0.0543Extraction Method: Principal Component Analysis.

B. 4- Factor Model1 2 3 4

Tokyo 0.8507 -0.0444 0.3129 0.0253Korea 0.7218 0.5021 -0.0207 -0.0651Jakarta 0.0925 0.9116 0.2172 0.0397SP500 0.2083 0.2088 0.9274 0.0017Shanghai -0.0122 0.0234 0.0028 0.9982

C. 3-Factor Model1 2 3

Tokyo 0.8965 -0.0260 0.0063SP500 0.6229 0.3718 0.0551Korea 0.5930 0.4528 -0.1077Jakarta 0.1403 0.9304 0.0397Shanghai -0.0029 0.0196 0.9949

D. 2-Factor Model1 2

Korea 0.7467 -0.1013SP500 0.7211 0.0486Tokyo 0.7018 -0.0653Jakarta 0.6699 0.1331Shanghai 0.0033 0.9881

E. 4-Factor Model for the 8 Stock Markets1 2 3 4

SP500 0.9738 0.1377 0.1245 0.0033Dow 0.9066 0.1252 0.1900 0.0164Sptotal 0.9746 0.1330 0.1236 0.0086Korea 0.8080 0.2573 0.0811 -0.0017Tokyo 0.1846 0.6246 0.5031 -0.1236NASDAQ 0.2255 0.8912 0.0058 0.0641Jakarta 0.1899 0.0801 0.9256 0.0717Shanghai 0.0123 0.0046 0.0371 0.9924Extraction Method: Principal Component Analysis. Rotation converged in 5 iterations. Rotation Method: Varimax with Kaiser Normalization.

Table 16 Correlation Matrix of Monthly Returns

1. Corelation of Monthly Stock Prices, 1991-2002SP500 Dow Sptotal Korea Tokyo NASDAQ Jakarta Shanghai

SP500 1.000 Dow .985 1.000

Sptotal .999 .990 1.000 Korea -.221 -.210 -.216 1.000 Tokyo -.384 -.457 -.408 .417 1.000

NASDAQ .929 .872 .921 -.053 -.155 1.000 Jakarta .311 .339 .308 .478 .192 .345 1.000

Shanghai .844 .866 .856 -.261 -.532 .744 .182 1.000 * N=144, The critical r values are 0.164 for the 5% leve, and 0.214 for the 1% level.

2. Correlaion of Monthly Stock Returns, 1991-2002SP500 Dow Sptotal Korea Tokyo NASDAQ Jakarta Shanghai

SP500 1.000 Dow .924 1.000

Sptotal .999 .922 1.000 Korea .327 .335 .324 1.000 Tokyo .351 .347 .347 .384 1.000

NASDAQ .789 .636 .791 .385 .342 1.000 Jakarta .311 .349 .310 .372 .237 .247 1.000

Shanghai .020 .031 .025 -.035 .026 .025 .073 1.000 * N=144, The critical r values are 0.164 for the 5% leve, and 0.214 for the 1% level.

3. Correlation of Monthly Stock Returns, 1989-2002SP500 Dow Sptotal Korea Tokyo NASDAQ Jakarta

SP500 1.000 Dow .933 1.000

Sptotal .999 .931 1.000 Korea .336 .338 .334 1.000 Tokyo .370 .372 .367 .391 1.000

NASDAQ .795 .657 .797 .384 .339 1.000 Jakarta .256 .301 .256 .322 .158 .229 1.000

* N=168. The critical r values are 0.151 for the 5% level, and 0.198 for the 1% level.

Table 17 (1) Evaluation of the Asian and US Stock Markets

SP500 Korea Tokyo Jakarta Shanghai Ave R Std 1971-2002 1980-2002 1984-2002 1989-2002 1991-2002

1 Jan. 2.14 2.26 1.86 3.27 4.24 2.75 0.992 Feb. 0.07 -0.81 0.56 1.26 3.29 0.87 1.553 March 1.00 3.57 2.91 0.82 2.38 2.14 1.204 April 1.16 1.30 1.83 0.96 7.77 2.60 2.915 May 0.64 1.81 0.29 4.43 -0.51 1.33 1.926 June 0.76 0.56 -0.77 1.03 8.29 1.97 3.607 July -0.06 1.49 -0.20 -0.05 -2.03 -0.17 1.258 Aug. 0.02 -2.00 -0.33 -0.74 1.62 -0.29 1.319 Sept. -1.25 -2.10 -1.64 -4.46 -1.12 -2.11 1.37

10 Oct. 0.88 0.33 -0.82 -1.74 1.82 0.09 1.4011 Nov. 1.37 3.23 -0.20 -1.43 3.34 1.26 2.1012 Dec. 1.61 0.60 0.23 4.12 -4.63 0.39 3.19

0.90 1.4093 1 Ave R (%) 0.695 0.853 0.310 0.623 2.038 0.90 1.40932 Std 0.9 1.824 1.304 2.565 3.788 2.076 1.021 3 Beta 0.50 0.9085 0.7059 1.1335 1.7496 1.000 0.4804 p 0.0024 0.0108 0.0039 0.0304 0.0217 5 t-test -0.8095 -0.134 -2.1899 -0.4835 1.2833 6 p 0.2177 0.4479 0.0255 0.3191 0.1129 7 Tests (1) ANOVA F= 0.958(p=0.438), (2) Kruskal-Wallis H= 3.244 (p=0.518), (3) Chi-sq=2.50 (p=0.6446)8 R/beta 1.389 0.939 0.439 0.549 1.165 0.896 0.3609 R/std 0.771 0.468 0.238 0.243 0.538 0.452 0.200

10 R-bRm 0.243 0.032 -0.328 -0.402 0.457 0.000 0.32811 Shin Beta 1.544 1.043 0.488 0.611 1.294 0.996 0.40012 Shin Total 1.209 0.732 0.372 0.380 0.842 0.707 0.31313 NM 2 3 6 5 4 4.000 1.41414 NM(%) 0.167 0.250 0.500 0.417 0.333 0.333 0.118

NM = No. of negative average monthly returns for each stock exchange during the sample period.The chi-square test of goodness of fit is for the null hypothesis that the population frequencies of negative average monthly returns are all equal. The t-tests are for the two population means: thepopulation mean of monthly returns for each stock exchange and the population mean of the 5 stockexchange monthly returns. The bold italics indicate that the numbers are significant either at the 5%or 1 % level. The standard deviation 1.403 is calculated from the average monthly return column series.

Table 17 (2) Risk and Return in the US and Asian Stock Markets

Mean Std. R/Std. Jan R Jan std. Jan beta Jan R/. JanR/Return Jan std. Jan Beta

SP500 0.70 1.373 0.510 2.14 5.12 2.180 0.418 0.982Dow Jones 0.71 1.310 0.542 2.14 5.34 2.225 0.401 0.962Nasdaq 1.05 3.300 0.318 4.91 6.01 1.499 0.817 3.276SP500Total 0.98 1.390 0.705 2.34 5.13 2.170 0.456 1.078

Korea 0.85 2.960 0.287 2.26 9.02 1.591 0.251 1.420Tokyo 0.31 2.030 0.153 1.86 6.71 1.719 0.277 1.082Jakarta 0.41 3.250 0.126 3.74 8.12 0.838 0.461 4.463Shanghai 2.04 3.020 0.675 4.24 19.13 2.318 0.222 1.829Mean return= mean of 12 monthly returns over the sample period, Std. = standard deviation of the means of 12 monthly returns over the sample period.

Table 18 Best and Worst Months for Monthly Stock Returns

Positive Returns Negative ReturnsSimple R/beta Shin B R-bRm R/std. Shin T Simple R/Beta Shin B R-bRm R/std. Shin T

SP 500 Jan. March March Dec. Dec. Dec. Sept. Sept. Sept. Sept. Sept. Sept.Korea March March March March March March Sept. Aug. Aug. Sept. Aug. Aug.Tokyo March April April March March March Sept. Oct. Oct. Sept. Sept. Sept.Jakarta May Jan. Jan. May Dec Dec. Aug. Sept. Sept. Aug. Sept. Sept.Shanghai June April April April June June Dec. Dec. Dec. Dec Dec. Dec.Simple R = average of monthly returns for each month, unadjsuted, Shin B = Shin beta index: (R/beta)/Rm. Shin T= Shin total index: (R/std)/(Rm/stdm), R = average monthly return for each month, Rm = market protfolioreturn (the average series of 12 monthly returns over the sample period; Stdm = standard deviation of Rmover the sample period, SP 500 = 1971-2002; Korea = 1980-2002 (exc. 1998); Tokyo = 1984-2002; Jakarta = 1989-2002, exc. 1989 and 1998; Shanghai = 1991-2002, excl. 1992 and 1994.

Table 19 January Return and the Rest of the Year

A: Dependent Variable: Average of January-December Returns, Ind. Var.= January returnIntercept January Ad R^2 F p Period Sum

SP500 0.361 0.1564 0.3186 15.4968 0.0005 1971-2002 0.517(1.66) (3.94)**

SP500Total 0.6099 0.1581 0.3211 15.659 0.0004 1971-2002 0.768(2.74)* (3.96)**

Dow-Jones 0.4154 0.1335 0.2736 12.6746 0.0013 1971-2002 0.549(1.95) (0.00)**

NASDAQ 0.0076 0.2129 0.2777 7.4991 0.0146 1985-2002 0.221(0.013) (2.74)*

Korea 0.4939 0.1261 0.2774 9.4442 0.0058 1980-2002 0.620(0.87) (3.07)**

Tokyo 0.01746 0.1573 0.2275 6.2997 0.0225 1984-2002 0.175(0.04) (2.51)*

Jakarta 0.2678 0.0882 -0.0119 0.8476 0.3754 1989-2002 0.356(0.29) (0.92)

Shanghai 3.0512 0.0669 -0.0350 0.6238 0.4479 1991-2002 3.118(2.09)* (0.79)

The t-ratios are in parentheses. ** Significant at the 1 % level. * Significant at the 5% level.Sum = the sum of intercept and slope coefficients.

B: Dependent Variable: Average of February-December Returns, Ind. Var. : January returnIntercept January Ad R^2 F p Period Sum

SP500 0.3939 0.0797 0.1015 3.3903 0.0750 1971-2002 0.4736(1.66) (1.84)

SP500Total 0.7932 0.1467 0.1636 7.0655 0.0125 1971-2002 0.9399(3.77)** (2.66)*

Dow-Jones 0.4532 0.0547 0.0248 1.7885 0.1912 1971-2002 0.5079(1.95)# (1.34)

NASDAQ 0.0083 0.1414 0.1479 2.7779 0.1150 1985-2002 0.1497(0.01) (1.67)

Korea 0.5388 0.0467 0.0039 1.0867 0.3091 1980-2002 0.5855(0.87) (1.04)

Tokyo 0.019 0.0807 0.0214 1.3936 0.2540 1984-2002 0.0997(0.04) (1.18)

Jakarta 0.2922 0.0053 -0.0831 0.0026 0.9601 1989-2002 0.2975(0.29) (0.05)

Shanghai 0.2922 0.0053 -0.0831 0.0026 0.9600 1991-2002 0.2975(0.29) (0.05)