International Trade and Finance Association SEASONALITY IN ASIA S EMERGING MARKETS: INDIA AND MALAYSIA

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1 International Trade and Finance Association International Trade and Finance Association 15th International Conference Year 2005 Paper 53 SEASONALITY IN ASIA S EMERGING MARKETS: INDIA AND MALAYSIA T. Chotigeat I. M. Pandey Department of Economics & Finance, Nicholls State University Indian Institute of Management, Ahmedabad, India This working paper site is hosted by The Berkeley Electronic Press (bepress) and may not be commercially reproduced without the publisher s permission. Copyright c 2005 by the authors.

2 SEASONALITY IN ASIA S EMERGING MARKETS: INDIA AND MALAYSIA Abstract Presented at 15th International Conference, Istanbul, Turkey, May 2005.

3 INTRODUCTION The topic of capital market efficiency is amongst the most researched areas in finance. The weak form of market efficiency states that predicting stock prices and return movements is impossible using past price information. Following Fama (1965; 1970), a large number of studies were conducted to test the efficient market hypothesis (EMH). These studies have generally shown that stock prices behave randomly. More recently, however, researchers have collected evidence contrary to the EMH, identifying systematic variations in stock prices and returns. Significant anomalies include the small firm effect and the seasonal effect. The existence of the seasonal effect negates the weak form of the EMH and implies market inefficiency. In an inefficient market, investors are able to earn abnormal returns, i.e., returns that are not commensurate with risk. Capital market analysts have been given increasing attention to the study of emerging capital markets (ECMs) due to the growing internationalization of the world economy and globalization of capital markets. A few studies have examined the issue of seasonality of stock returns in the ECMs, but so far the evidence of the seasonal effect has been inconclusive. The objective of this study is to investigate seasonality in stock returns in India and Malaysia, using a modified time-series model (a combined regression and autoregressive moving average model with dummy variables, called ARMA or ARIMA) (Enders, 1995, pp.63-99). The data selected for analysis are the monthly returns for the India s Bombay Stock Exchange (Sensitivity Index) from April 1991 to March 2002 and Malaysia s Kuala Lumpur Stock Exchange (EMAS index) from January 1992 to June 2002). The findings of this study on market efficiency and the seasonal effect have important implications for financial managers, financial analysts and investors. The understanding of seasonality should help develop appropriate investment strategies. OVERVIEW OF PRIOR RESEARCH Seasonality would be a factor in stock returns if the average returns were not the same in all periods. The month-of-the-year effect would be present when returns of some months are higher than those of other months. In the U.S. and some other countries, the year-end month (December) is the tax month. Based on this fact, a number of empirical studies have found a year-end effect and a January effect on stock returns consistent with the tax-loss selling hypothesis which posits that towards the end of the year, investors sell shares whose values have declined to book losses and offset taxes on their gains from other sales. This lowers stock returns by putting downward pressure on stock prices, i.e., a year- Hosted by The Berkeley Electronic Press

4 end effect. As soon as the tax year ends, investors start buying and prices bounce back. This causes higher returns in the beginning of the year, i.e., in January. In the U.S. market, a number of studies has found a seasonal or year-end effect (Rozeff and Kinney 1976; Keim 1983; Reinganum 1983). The existence of a seasonal effect has also been found in Australia (Officer, 1975; Brown et al., 1983), the UK (Lewis, 1989), Canada (Berges et al., 1984; Tinic et al.,1987) and Japan (Aggarwal et al., 1990). There is also evidence of a day-of-the-week effect in the U.S. (Smirlock and Starks, 1986) and other markets (Jaffe and Westerfield, 1985; 1989) and an intra-month effect on U.S. stock returns (Ariel, 1987). In a study of 17 industrial countries with different tax laws, Gultekin and Gultekin (1983) confirmed the January effect.boudreaux (1995) reported the presence of a month-end effect on markets in Denmark, Germany, and Norway. Jaffe and Westerfield (1989) found a weak monthly effect on stock returns of many countries. Research on the seasonal effect in ECMs has started surfacing only recently. A few studies have revealed the presence of a seasonal effect on stock returns for ECMs (Aggarwal and Rivoli, 1989; Ho, 1990; Lee et al., 1990; Lee, 1992; Ho and Cheung, 1994; Kamath et al.,1998; and Islam et al., 2001). Ramcharran (1997), however, rejected the seasonal effect for the stock market in Jamaica. In this study, we extend the investigation of the monthly effect on stock returns for the stock markets in India and Malaysia, and compare their results. METHODOLOGY AND DATA In examining seasonality in the ECMs, most studies adopted a methodology similar to that used in the study of the developed stock markets (Keim, 1983; Kato and Schallheim, 1985; Jaffe and Westerfield, 1989). The methodologies of a number of studies have been criticised as they fail to handle the issues of autocorrelation and heteroskedasticity. In this study, we follow a more robust approach as discussed below. The seasonal effect is easily detectable in market indices or large portfolios of shares rather than in individual shares (Officer, 1975; Boudreaux, 1995). This study analyses returns of two stock indices of India and Malaysia. Each index is expected to be informationally efficient. Hence, they are appropriate indices to study to unravel capital market anomalies such as the seasonality of stock returns. We measure stock return as the continuously compounded monthly percentage change in the share price index in order to avoid the influences of extreme index values: r t = (lnp t lnp t-1 )x 100 (1)

5 where r t is the return in the period t, P t is the monthly closing share price of the stock index for the period t, and ln is a natural logarithm. The results of the OLS regressions will be spurious if the dependent variable is non-stationary. We first determine whether each index return series is stationary. One simple way of determining this is to examine the sample autocorrelation function (ACF) and the partial autocorrelation function (PACF). We also use a formal test of stationarity, that is, the Augmented Dickey-Fuller (ADF) test, a common method for determining unit roots consisting of regressing (1) the first difference of the series R t against a constant, (2) the series lagged one period, (3) the differenced series at n lag lengths, and (4) a time trend (Pindyck and Rubinfeld, 1998, p. 509): R t = + n ir t i + t + R t 1 + t (2) i= 1 If the coefficient of is significantly different from zero, then the hypothesis that R is non-stationary is rejected. The ADF test can be carried out with and without the constant and/or trend. One has also to choose the appropriate lag length. If a series is found to be non-stationary in level, one should difference the series until the stationarity is established. Next we will conduct a test for seasonality in stock returns. We use a month-of-the-year dummy variable for testing monthly seasonality. The dummy variable takes a value of unity for a given month and a value of zero for all other months. We specify an intercept term along with dummy variables for all months except one. The omitted month, that is January, is our benchmark month. Thus, the coefficient of each dummy variable measures the incremental effect of that month relative to the benchmark month of January. The existence of a seasonal effect will be confirmed when the coefficient of at least one dummy variable is statistically significant. Thus, similar to earlier studies, our initial model to test for monthly seasonality is as follows. r t = D 9 2 Sep D Feb + + D 10 3 Oct D Mar + + D 11 D Apr + 5D May + + D + 4 Nov 12 Dec The intercept term 1 indicates the mean return for the month of January and coefficients 2 12 represent the average differences in returns between January and each month. These coefficients should be equal to zero if the return for each month is the same and if there is no seasonal effect. t is the white noise error term. If the residuals have serial correlation, the results of Equation (3) will be biased. t 6 D Jun + 7 D Jul + 8 D Aug (3) Hosted by The Berkeley Electronic Press

6 We improve upon Equation (3) by constructing an ARIMA model for the residual series µ t of this equation. We then substitute the ARIMA model for the implicit error term in the equation. The augmented model is as follows: r t = D Feb D Dec + 1 R t p R t-p + 1 µ t q µ t-q (4) The residuals of the augmented ARIMA model in Equation (4) may exhibit conditional autoregressive heteroskedasticity. This can be corrected by including an ARCH or GARCH specification for the errors. DATA FOR THE STOCK RETURNS OF INDIA We use monthly closing share price data of the Bombay Stock Exchange s Sensitivity Index from April 1991 to March 2002 for this purpose; it is the postreform period because the Indian economy and capital markets witnessed significant economic reforms and deregulations after The Indian tax system differs from that of the U.S. and many other developed and developing countries. The tax year ends in March in India. Both resident Indian taxpayers and nonresident investors must pay capital gains taxes on the sale of shares, but capital losses can be offset against the capital gains. We investigate whether the taxloss-selling hypothesis can provide an explanation for the seasonality in stock returns in India. There are many alternative hypotheses, including the information hypothesis (Kiem, 1983), as an explanation for the seasonal effects in stock returns. DATA FOR THE STOCK RETURNS OF MALAYSIA We use monthly closing share price data of the Kuala Lumpur Stock Exchange s EMAS index from January 1992 to June Resident and nonresident shareholders in Malaysia are not taxed on capital gains. Hence, the taxloss-selling hypothesis is irrelevant. Nevertheless, if seasonality is found in the Malaysian stock market, it would be due to the information hypothesis. EMPIRICAL RESULTS THE INDIAN CASE We first present descriptive statistics for the entire period and each month in Table 1. There are wide variations of returns across months. Returns for the months of January, February, August and December are higher than returns of other months. The maximum average return occurs in the month of February.

7 Returns in the months of March, April, May, September, October and November are negative. Stock returns are negatively skewed for six months. They also show leptokurtic (kurtosis>3) distribution for four months, i.e., flatter tails than the normal distribution. The Jarque-Bera test indicates that returns are normally distributed in all months. Given positive skewed and excess kurtosis for many months, this result is suspicious. It may possibly be due to the small sample size for each month. The average monthly return (0.356 percent) for the entire period from April 1991 to March 2002 is positive. The return series for the entire period shows high dispersion; it is leptokurtic and the skewness is positive. The Jarque- Bera test shows that returns are not normally distributed. The violation of the normality assumption could bias the regression results in the case of small samples. In Figures 1 and 2 we show the ACF and the PACF of the series. Figure 1 shows that the autocorrelation function falls off quickly as the number of lags increases. This is a typical behavior in the case of a stationary series. The PACF in Figure 2 also does not indicate any large spikes. In Table 2 we present the results of the ADF tests. Each of the test scores is well below the critical value at the 5 % level. The results show consistency with different lag structures and with the presence of the intercept or intercept and trend. Thus, the ADF tests also confirm that the Sensex return series is stationary. Table 1: Descriptive Statistics, the Sensex Returns: April 1991-March 2002 Mean Max. Min. Std. Skewness Kurtosis Jarque- Prob. Obs. Dev. Bera Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Hosted by The Berkeley Electronic Press

8 Figure 1: Autocorrelation Function of the Sensex Monthly Returns Autocorrelation Function AC Lags Figure 2: Partial Autocorrelation Function of the Sensex Monthly Returns PAC Partial Autocorrelation Function Lags Table2: Augmented Dickey-Fuller Stationarity (ADF) Test ADF: with constant ADF: with constant & trend 5 lags lags ( ) ( ) 10 lags lags ( ) ( ) Parentheses have critical t-stat for ADF stationarity testing. A value greater than the critical t-value indicates non-stationarity. We estimate Equation (3), which includes the month-of-the-year dummy variables. The results are given in Table 3. The coefficient for the month of October is significant at the 5 percent level of significance. However, the

9 coefficients for all other months are not statistically different from zero. The low R 2 of 0.09 and the insignificant F-statistic suggest poor model fit. The Durbin- Watson statistic of less than 2 indicates serial correlation in the residuals. One simple test to check the adequacy of the model is to see whether the residuals from the model are white noise. We can check the autocorrelation and the partial autocorrelation functions for the residuals of the model. The residuals from a correctly specified model should be white noise. This means that the autocorrelations and partial autocorrelations should all be zero. We can also examine the Ljung-Box Q-statistics. If the -value for the computed Ljung-Box Q-statistic is insignificant, it means there is no serial correlation. The Ljung-Box Q-statistic up to a lag of 24 is with a significant -value of Hence, the hypothesis of no serial correlation is rejected, and thus, the residuals of the model are not white noise. Table 3: Results of the Regression Model with Dummy Seasonal Variables C D Feb D Mar D A pr D May D Jun D Jul D Aug D Sep D Oct D Nov D Dec Coeff t-stat * Prob R SE LL F-stat Adj. R SSR DW Prob SE = sd. error of regression; SSR = sum squared error; LL = log likelihood; DW = Darwin- Watson stat However, the ACF and PACF of the residuals do not have a nice pattern to easily identify the ARMA model. The autocorrelation declines up to lag 4. Except at lags 6 and 12, the autocorrelations are not statistically significant. The partial autocorrelations with spikes at lags 6, 12 and 16 seem statistically significant, but the rest are not. After substantial experimentation, we fit the ARMA (12, 4) model to the residual series. The results of the model are in given Table 4. Hosted by The Berkeley Electronic Press

10 Table 4: Results of ARMA (12, 4) Model for the Residuals of Equation (3) C R t-1 R t-2 R t-3 R t-4 R t-5 R t-6 R t-7 R t-8 R t-9 R t-10 R t-11 R t-12 Coeff t-stat Prob µ t-1 µ t-2 µ t-3 µ t-4 Coeff t-stat Prob R SE LL F-stat Adj. R SSR DW Prob SE = std error of regression; SSR =sum squared error; LL = log likelihood; DW = Darwin-Watson stat The estimated ACF and PACF derived from the dependent variable of ARMA (12,4) model (not shown here) indicate that the autocorrelations and partial autocorrelations are not statistically different from zero. The Ljung-Box Q- statistic up to a lag of 36 is 34.42, and it is insignificant with a -value of Thus, we can conclude that the residuals of the ARMA (12, 4) model are nearly white noise and that they are purely random. We combine the ARMA model with the regression model (Equation (3)) and estimate all parameters simultaneously as given in Equation (4). The results of the estimation of Equation (4) are shown in Table 5. Table 5: Results of the Time Series and Regression Model C D Feb D Mar D Apr D May D Jun D Jul D Aug D Sep D Oct D Nov D Dec R t-1 R t-2 Coeff t-stat * * Prob R t-3 R t-4 R t-5 R t-6 R t-7 R t-8 R t-9 R t-10 R t-11 R t-12 µ t-1 µ t-2 µ t-3 µ t-4 Coeff t-stat Prob R SE LL F-stat Adj. R SSR DW Prob SE = std. error of regression; SSR =sum squared error; LL = log likelihood; DW = Darwin-Watson stat

11 The R 2 of is higher and the D-W statistic is about 2. The sample autocorrelations for the residuals of the model are not statistically different from zero. Furthermore, the Ljung-Box Q-statistic is mostly insignificant at various lags. Thus, the residuals of the model are nearly white noise, and our estimations do not suffer from the problem of serial correlation. We note that the estimated coefficients of the monthly dummy variables change once we account for the serial correlation in the residuals. The average return in the benchmark month of January is percent. Except for the month of February, returns are lower for all months as compared to the benchmark month of January. The relatively lowest return occurs in the month of October. We find that only the coefficients of the dummy variables for the months of March and October are statistically significant, indicating the presence of seasonality in the Sensex monthly returns. It is notable that the study finds seasonality in stock returns after controlling for the riskiness of returns. Further, it is noteworthy that the Indian tax year ends in March when the average return is negative, and the coefficient of the dummy variable for the month of March is statistically significant (at the 5 % level). However, the coefficient of the month of April is not significant. It appears that investors in India sell shares in March that have declined in value and book losses to save taxes. This causes share prices to decline resulting in lower returns. However, these investors do not rush to buy shares immediately after the tax month and do not cause a rise in prices in the month of April. This evidence thus only partially supports the tax-loss-selling hypothesis; and the phenomenon of seasonality in the Indian stock market is not absolutely consistent with, and is not entirely explicable by, the tax-loss-selling hypothesis. This is contrary to the January effect in a number of markets where January returns have been found to be positive. With regard to the year-end effect, we notice that the coefficients of dummy variables for the months of November and December are not statistically significant. We do find the coefficient of the dummy variable for the month of October (which corresponds to a number of social events in India) statistically significant (at the 5 % level). Thus, the results of the study confirm the existence of seasonality in monthly returns. But these results cannot be explained by the tax-loss selling hypothesis alone. The phenomenon of seasonality in stock returns in India could be attributed partially to the tax-loss selling hypothesis (as revealed by significant negative returns in March), but much more to the inefficiency of the Indian capital market, which might be caused by (1) non-disclosure, (2) low quality of disclosure, and/or (3) the slow processing of disclosed information. Hence, as argued by many researchers (Roll, 1983; Kiem, 1983; Reinganum,1983; Constantinides, 1984) of developed markets, the information inefficiency hypothesis seems to be the most plausible explanation for the phenomenon of seasonal effects in the returns of the emerging stock market of India. Hosted by The Berkeley Electronic Press

12 THE MALAYSIAN CASE The descriptive statistics for the EMAS returns are presented in Table 6. The average monthly return for the entire period from April 1992 to March 2002 is positive but very small (0.08 percent). Average returns for the months of February and December are much higher than returns of other months. The maximum average return occurs in the month of February. Average returns in the months of January, March, May, June, July, August, and November are negative. March has the maximum negative average return. Stock returns show negative skewness for seven months and positive for five. They also show leptokurtic (kurtosis >3) distribution for five months. Further, the Jarque-Bera test indicates that returns are normally distributed in all months. Looking at the ACF and the PACF of the EMAS series, the ACF graph falls off quickly as the number of lags increases, thus implying that the series is stationary. When the ADF and PP tests are also used, the EMAS return series is found to be stationary. Thus, the original data of the EMAS return index is appropriate in a regression model to test for seasonality in stock returns in Malaysia. Table 6: Descriptive Statistics, KLSE-EMAS Returns: Jan 1992-Jun 2002 Mean Max. Min. Std. Dev. Skewness Kurtosis J-B Test Prob. Obs. JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Overall We estimate Equation (2), which includes the month-of-the-year dummy variables on the right-hand side of the equation. The results for the EMAS Index are

13 presented as follows (t-statistics are given in the parentheses): r t = D Feb 1.400D Mar D Apr D May 0.899D Jun D Jul -0.16) (1.41) (-0.74) (0.39) (0.02) (-0.48) (0.03) D Aug D Sep D Oct D Nov D Dec (-0.69) (0.40) (0.33) (0.06) (1.12) R 2 = 0.07 D-W stat. = 1.85 F-stat. = (prob. = 0.61) None of the coefficients is significant. R 2 of 0.07 is low, and the insignificant F-statistic suggests a poor model fit. The Durbin-Watson statistic of <2 indicates serial correlation in the residuals. Further, the Ljung-Box Q-statistic for the hypothesis of no serial correlation up to the order of 36 is with a significant -value at the 1% level is rejected. Thus, the residuals of the model are not white noise. The steadily declining autocorrelation function for the residuals (not shown here) implies that the residuals series is stationary. After experimenting, we fit the ARIMA (8,0,6) model to the residual series. The results of the model are as follows: ( B B B B B B B B 8 ) µ t = ( B 0.133B B B B B 6 ) t R 2 = D-W stat F-stat. = (prob. = 0.008) Q-stat. (36) = (-value = 0.614) The residuals of the ARIMA (8,0,6) model are white noise since the Ljung-Box Q-statistic to the order of 36 is 19.50, and it is insignificant with a -value of The results of the estimation of Equation (3) combined with the ARIMA (8,0,6) model are given below (t-statistics are given within parentheses): r t = D Feb 0.759D Mar D Apr D May 0.176D Jun D Jul (-0.65) (1.64)* (-0.46) (0.56) 0.21) (-0.11) (0.26) 0.745D Aug D Sep D Oct D Nov D Dec +[( B 0.329B 2 + (-0.45) (0.89) (0.67) (0.36) (1.65)* 0.533B B B 6 )/( B-0.495B B B B B B B 8 )] t R 2 = D-W stat. = 2.00 F-stat. = (prob. = 0.041) Hosted by The Berkeley Electronic Press

14 The model s F-statistic is significant at the 5% level. The R 2 is The D-W statistic of 2 is insignificant and implies an absence of autocorrelation. The sample autocorrelations for the residuals (not shown here) are almost zero. Further, the Ljung-Box Q-statistic of to the order of 36 is insignificant with a -value of This indicates that the residuals of the model are white noise. A Lagrange Multiplier (LM) test for the presence of the ARCH effects in the residuals (F-statistic of with a -value of 0.129) testifies to the absence of such effects. The estimated coefficients of the monthly dummy variables change once we account for the serial correlation in the residuals. We find the coefficients of the dummy variables for the months of February and December to be statistically significant at the 10% level. The average return in the benchmark month of January is negative ( percent), and it is the lowest. The months of February and December have higher returns with December being the highest. Seasonality is evidenced in the EMAS returns. The statistically significant coefficients for the months of February and December indicate the presence of seasonality in the EMAS returns. The coefficient of the intercept term, representing the benchmark month of January, is not statistically significant. Thus, we can rule out the January effect for the EMAS returns. The Malaysian tax year ends in December, but capital gains are not taxed. The average return for December is positive for the EMAS. It appears that investors in Malaysia trade in shares towards the end of the year and make capital gains on which they are not required to pay any tax. Thus, there is a year-end effect (the coefficient for December is significant); but unlike in the U.S. and some other countries, this cannot be attributed to the tax-loss-selling hypothesis. The results of the study could rather be ascribed to the information hypothesis. SUMMARY AND CONCLUSIONS The focus of this study was an investigation of the existence of seasonality in monthly stock returns in the emerging Asian stock markets of India and Malaysia and then comparing their results. The time-series models--arma and ARIMA--were found to be appropriate respectively for analyzing the monthly effect for: (a) the Bombay Stock Exchange s Sensitivity Index (Sensex) from April 1991 to March 2002) and (b) the Kuala Lumpur Stock Exchange s EMAS index from January 1992 to June THE RESULTS OF THE INDIAN CASE The regression results confirmed the seasonal effect in monthly stock returns in India. We found that coefficients for the months of March and October

15 were statistically significant. The Indian tax year ends in March. The statistically significant (negative) coefficient for March is consistent with the tax-loss selling hypothesis. But since the coefficient of April (the month after the tax-year ends) was not found to be statistically significant, the tax-loss selling hypothesis can be considered only a partial explanation of the seasonality in stock returns in India. Curiously, the coefficient for January is found to be significant but negative. It is difficult to explain this in terms of the available hypothesis. The most probable hypothesis for this phenomenon and generally for the seasonal effect on stock returns in India could be the information (inefficiency) hypothesis. Perhaps the Indian stock market is not yet informationally efficient. As a consequence, perhaps investors could earn abnormal returns by timing their investments. As the extent and quality of information disclosure becomes more credible and investors are able to process the flow of information more quickly, the Indian stock market would move in the direction of a higher level of efficiency and investors would earn returns commensurate with risk. A number of recent regulatory reforms in India have been aimed at improving the disclosure of information. THE RESULTS OF THE MALAYSIAN CASE The study reveals evidence of seasonality. The coefficients for only two months (February and December) are statistically significant. The average return for December is positive, thus it rules out the tax-loss selling hypothesis, as expected, because resident and non-resident shareholders in Malaysia are not required to pay taxes on capital gains. The seasonality found in the Malaysian stock market is probably due to the information hypothesis (Kiem, 1983). A relatively inefficient Malaysian stock market thus can provide ample opportunity for investors to time their stock investments to earn abnormal returns. Table 7: A Comparison of the Statistically Significant Coefficients of the Two Markets Return Index C D Feb D Mar D Apr D May D Jun D Jul D Aug D Sep D Oct D Nov D Dec India s Sensex. * * Malaysia s EMAS * * * = statistically significant coefficient. THE OVERALL RESULTS FOR BOTH MARKETS This study empirically confirms the existence of seasonality in stock returns in both capital markets (see Table 7 for a comparison of estimated results). Hosted by The Berkeley Electronic Press

16 The tax-loss selling hypothesis provides only a partial explanation of the seasonality in monthly stock returns in India, but not at all in Malaysia (no capital gain taxes). A more plausible explanation for both markets seems to be the information hypothesis. These findings have important implications for financial managers, financial analysts and investors. In particular, with the lack of informationally efficient markets, investors may be able to time their stock investments to earn abnormal returns.

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