IS THERE SEASONALITY IN THE SENSEX MONTHLY RETURNS? I M Pandey Indian Institute of Management Ahmedabad Vastrapur, Ahmedabad 380015 India E-mail: impandey@iimahd.ernet.in Web page: http://www.iimahd.ernet.in/~impandey/ii IS THERE SEASONALITY IN THE SENSEX MONTHLY RETURNS? ABSTRACT The presence of the seasonal or monthly effect in stock returns has been reported in several developed and emerging stock markets. This study investigates the existence of seasonality in India’s stock market. It covers the post-reform period. The study uses the monthly return data of the Bombay Stock Exchange’s Sensitivity Index for the period from April 1991 to March 2002 for analysis. After examining the stationarity of the return series, we specify an augmented autoregreessiv moving average model to find the monthly effect in stock returns in India. The results confirm the existence of seasonality in stock returns in India and the January effect. The findings are also consistent with the ‘tax-loss selling’ hypothesis. The results of the study imply that the stock market in India is inefficient, and hence, investors can time their share investments to improve returns. Key words: Market efficiency; efficient market hypothesis; tax-loss selling hypothesis; information hypothesis; stationarity; seasonality.IS THERE SEASONALITY IN THE SENSEX MONTHLY RETURNS? Introduction The topic of capital market efficiency is amongst the most researched areas in finance. Capital markets are considered efficient informationally. The weak form of market efficiency states that it is not possible to predict stock price and return movements using past price information. Following Fama (1965; 1970), a large number of studies were conducted to test the efficient market hypothesis (EMH). These studies generally have shown that stock prices behave randomly. More recently, however, researchers have collected evidence contrary to the EMH. They have identified systematic variations in the stock prices and returns. The 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 would be able to earn abnormal returns, that is, returns that are not commensurate with risk. More recently, one could witness the increasing attention being accorded by the capital market analysts, portfolio managers and researchers to the emerging capital markets (ECMs) due to the growing internationalisation of the world economy and globalisation of the capital markets. There are a few studies that have examined the issue of seasonality of stock returns in the ECMs. The objective of this study is to investigate the existence of seasonality in stock returns in India. We use monthly closing share price data of the Bombay Stock Exchange’s Sensitivity Index (Sensex) from April 1992 to March 2002 for this purpose. The Indian tax system differs from the USA and many other developed and developing countries. The tax year ends in March in India and not in December like in the USA. The taxpayers have to pay capital2 gain tax on the sale of shares. The capital losses can be set off against the capital gains. Both the resident and non-resident investors are liable to pay taxes. The ‘tax-loss-selling’ hypothesis may provide an explanation for the seasonality in stock returns in India. Yet an alternative explanation may be provided by the information hypothesis (Kiem, 1983). This study specified an autoregressive moving average model with dummy variables for months to test the existence of seasonality in stock returns. The results of the study confirmed the monthly effect in stock returns in India and also supported the ‘tax-loss selling’ hypothesis. These findings have important implications for financial managers, financial analysts and investors. The understanding of seasonality should help them to develop appropriate investment strategies. Review of Prior Research There would exit seasonality in stock returns if the average returns were not same in all periods. The month-of-the-year effect would be present when returns in some months are higher than other months. In the USA and some other countries, the year-end month (December) is the tax month. Based on this fact, a number of empirical studies have found the ‘year-end’ effect and the ‘January effect’ in stock returns consistent with the ‘tax-loss selling’ hypothesis. It is argued that investors, towards the end of the year, sell shares whose values have declined to book losses in order to reduce their taxes. This lowers stock returns by putting a downward pressure on the stock prices. As soon as the tax year ends, investors start buying shares and stock prices bounce back. This causes higher returns in the beginning of the year, that is, in the month of January.3 In the US market, a number of studies have found the seasonal or the year-end effect in stock. Wachtel (1942) was the first to point out the seasonal effect in the US markets. Rozeff and Kinney (1976) found that stock returns in January were statistically larger than in other months. Keim (1983) investigated the seasonal and size effects in stock returns. He showed that small firm returns were significantly higher than large firm returns during the month of January. He attributed this effect to the ‘tax-loss-selling’ hypothesis and the ‘information’ hypothesis. Reinganum (1983) arrived at similar conclusions, but he found that the tax-loss-selling hypothesis could not explain the entire seasonality effect. There is also evidence of the day-ofthheweek effect in the US (Smirlock and Starks, 1986) and other markets (Jaffe and Westerfield, 1985; 1989) and intra-month effects in the US stock returns (Ariel, 1987). The issue of the seasonality of stock returns has been investigated in many other developed countries. The existence of seasonal effect has been found in Australia (Officer, 1975; Brown, Keim, Kleidon and Marsh, 1983), the UK (Lewis, 1989), Canada (Berges, McConnell, and Schlarbaum, 1984; Tinic, Barone-Adesi and West, 1990) and Japan (Aggarwal, Rao and Hiraki, 1990). Boudreaux (1995) reported the presence of the month-end effect in markets in Denmark, Germany and Norway. In a study of 17 industrial countries with different tax laws, Gultekin and Gultekin (1983) confirmed the January effect. Jaffe and Westerfield (1989) found a weak monthly effect in stock returns of many countries. The research on the seasonal effect in the ECMs has started surfacing recently. A few studies have revealed the presence of seasonal effect of stock returns for the ECMs (Aggarwal and Rivoli, 1989; Ho, 1990; Lee Pettit and Swankoski, 1990; Lee, 1992; Ho and Cheung, 1994; Kamath, Chakornpipat, and Chatrath, 1998; and Islam, Duangploy and Sitchawat, 2002). Ramcharran (1997), however, rejected the seasonal effect for the stock market in Jamaica. In this4 study, we extend the investigation of the monthly effect in stock returns for the Indian stock market. Methodology and Data In examining seasonality in the ECMs, most studies adopted the methodology similar to 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 normality, autocorrelation, heteroskedasticity etc. In this study, we follow a more robust approach as discussed below. The seasonal effect is easily detectable in the market indices or large portfolios of shares rather than in individual shares (Officer, 1975; Boudreaux, 1995). This study analyses returns of the BSE’s Sensitivity Index. We measure stock return as the continuously compounded monthly percentage change in the share price index as shown below: ( ) 100 P ln P ln r 1 t t t × − = − (1) where rt is the return in the period t, Pt is the monthly closing share price of the Sensex for the period t and ln natural logarithm. The results of the OLS regressions will be spurious if the dependent variable is nonstatiionary We first determine whether the Sensex return series is stationary. One simple way of determining whether a series is stationary 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. The ADF test is a common method for determining unit roots. It consists of regressing the first difference of the series against a5 constant, the series lagged one period, the differenced series at n lag lengths and a time trend (Pindyck and Rubinfeld, 1998, p. 509): t 1 t n1 i i t i t r t r r ε + ρ + λ + ∆ β + α = ∆ − = − ∑ (2) If the coefficient of ρ is significantly different from zero, then the hypothesis that r is nonstatiionar 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. We will next 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 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 the monthly seasonality is as follows: t Dec 12 Nov 11 Oct 10 Sep 9 Aug 8 Jul 7 Jun 6 May 5 Apr 4 Mar 3 Feb 2 1 t D D D D D D D D D D D y ε + α + α + α + α + α + α + α + α + α + α + α + α = (3) The intercept term α1 indicates mean return for the month of January and coefficients α2…α12 represent the average differences in return 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. εt is the white noise error term. The problem with this approach is that the residuals may have serial correlation.6 We improve upon Equation (3) by constructing an ARIMA model for the residual series µt. We then substitute the ARIMA model for the implicit error term in Equation (3). The augmented model is as follows: ( ) ( ) t 1 Dec 12 Nov 11 Oct 10 Sep 9 Aug 8 Jul 7 Jun 6 May 5 Apr 4 Mar 3 Feb 2 1 t B B D D D D D D D D D D D y η θ φ + α + α + α + α + α + α + α + α + α + α + α + α = − (4) where ηt is a normally distributed error term and it may have different variance from εt (Pindyck and Rubinfeld, 1998, p.590). We also check for the ARCH effect in residuals. As we show later, since we not find any ARCH effect, we do not make any adjustment in the model. Our data include the closing share price index of the Sensex. The Sensex includes thirty most actively traded shares, and it is a value (market capitalization) weighted share price index. The equal-weighted index places greater weight on small firms and potentially would magnify anomalies related to small firms. Therefore, it is more appropriate to use a value-weighted index to detect the seasonal effect in stock returns. In our analysis, we use monthly returns, calculated by Equation (1), for the period from April 1991 to March 2002. This constitutes a sample size of 132 monthly observations. The Indian economy and capital market witnessed significant economic reforms and deregulation after 1991. Therefore, our study covers post-reform period. Results 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. Returns in the months of March, April, May, September, October and7 November are negative. Stock returns show negative skewness for six months and positive for other six months. They also show leptokurtic (kurtosis >3) distribution for four months. That means flatter tails than the normal distribution. The Jarque-Bera test indicates that returns are normally distributed in all months. Given positive skewness and excess kurtosis for many months, this result is suspicious. It may possibly be due to 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 show high dispersion, and it is leptokurtic and skewness is positive. The Jarque-Bera test shows that returns are not normally distributed. Table 1: Descriptive Statistics, the Sensex Returns: April 1991-March 2002 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 1991-02 Mean 1.718 2.915 -0.686 -0.332 -0.212 0.514 0.459 1.170 -0.581-1.728-0.150 1.208 0.358 Median 1.700 3.060 -2.090 -1.040 0.950 1.010 0.500 1.960 0.290 -1.030-0.030 1.490 0.300 Maximum 8.140 11.75015.230 5.800 7.620 5.440 10.910 5.360 3.610 2.660 8.250 3.630 15.23 Minimum -5.490 -2.430 -7.130 -5.100-11.170-5.460 -5.290 -4.570-6.230-6.550-5.820-2.130 -11.17 Std. Dev. 4.350 3.906 6.404 3.718 4.709 2.960 4.509 3.462 3.193 2.563 4.293 1.758 3.999 Skewness -0.123 0.862 1.424 0.504 -0.827 -0.382 0.935 -0.429-0.377-0.303 0.444 -0.295 0.440 Kurtosis 2.103 3.496 4.482 2.046 4.136 2.871 3.729 1.837 1.846 2.586 2.385 2.337 4.203 Jarque-Bera 0.397 1.474 4.723 0.882 1.846 0.275 1.847 0.957 0.871 0.247 0.535 0.361 12.22 Probability 0.820 0.479 0.094 0.643 0.397 0.871 0.397 0.620 0.647 0.884 0.765 0.835 0.002 Obs. 11 11 11 11 11 11 11 11 11 11 11 11 1328 Figure 1: Monthly Sensex Returns, April 1991-March 2002 Figure 1 gives the plot of the return series, which shows variations in monthly returns. In Figures 2 and 3 we show the ACF and the PACF of the series. Figure 2 shows that the autocorrelation function falls off quickly as the number of lags increase. This is a typical behaviour in the case of a stationary series. The PACF in Figure 3 also does not indicate any large spikes. In Table 2 we present result of the ADF tests. Each of the test scores is well below the critical value at 5 percent level. The results show consistency with different lag structures and to the presence of the intercept or intercept and trend. Thus, the ADF tests also prove that the Sensex return series is stationary. Autocorrelation Function -1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 Lags AC Figure 2: Autocorrelation Function of the Sensex Returns -15 -10 -505 10 15 20 92 93 94 95 96 97 98 99 00 01 02 Monthly Return Month/Year9 Partial Autocorrelation Function -1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 Lags PAC Figure 3: Partial Autocorrelation Function of the Sensex Returns Table2: Augmented Dickey-Fuller Stationarity (ADF) Test ADF: with constant ADF: with constant & trend 5 lags -3.6953 5 lags -3.6804 (-2.8844) (-3.4458) 10 lags -3.9906 10 lags -3.8463 (-2.8853) (-3.4472) Parentheses have critical t-statistics 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 on the right-hand side of the equation. . The results are presented in Table 3. None of the coefficients is significant. R2 of 0.09 is low, and the insignificant F-statistic suggests poor model fit. Durbin-Watson statistic of less than 2 indicates serial correlation in the residuals. Further, the Ljung-Box Q-statistic for the hypothesis that there is no serial correlation up to order of 24 is 37.11 with a significant ρ-value of 0.043 is rejected. The Ljung-Box Q-statistic to order of 36 is 47.90 and it is also significant at 0.089. Thus, the residuals of the model are not white noise.10 Table 3:The Regression Model to Test Seasonality Variable Coefficient Std. Error t-Statistic Prob. Constant 1.718 1.202 1.430 0.16 D2 (Feb) 1.196 1.699 0.704 0.48 D3 (Mar) -2.405 1.699 -1.415 0.16 D4 (Apr) -2.050 1.699 -1.206 0.23 D5 (May) -1.930 1.699 -1.136 0.26 D6 (Jun) -1.205 1.699 -0.709 0.48 D7 (Jul) -1.259 1.699 -0.741 0.46 D8 (Aug) -0.548 1.699 -0.323 0.75 D9 (Sep) -2.299 1.699 -1.353 0.18 D10 (Oct) -3.446 1.699 -2.028 0.04 D11 (Nov) -1.868 1.699 -1.099 0.27 D12 (Dec) -0.510 1.699 -0.300 0.76 R2 0.090 F-stat 1.082 D-W stat. 1.79 Prob. 0.381 We next examine the residuals obtained from the estimation of Equation (3). Figures 4 and 5 show the sample autocorrelation and partial autocorrelation functions for the residuals. The steadily declining autocorrelation function implies that the residuals series is stationary. After experimenting, we fit the ARIMA (6,0,2) model to the residual series. The results of the model are given in Table 5. The Ljung-Box Q-statistic to order of 36 is 34.42 is insignificant with ρ-value of 0.188. Thus, we can conclude that the residuals of the ARIMA model are white noise. Autocorelation Function -1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 Lags AC Figure 4: Autocorrelation Function of the Residual Series11 Partial Autocorrelation -1.00 -0.75 -0.50 -0.25 0.00 0.25 0.50 0.75 1.00 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 Lags PAC Figure 5: Partial Autocorrelation Function Table 4: ARIMA Model for the Residuals of Equation (3) Variable Coefficient Std. Error t-Statistic Prob. Constant -0.195 0.351 -0.556 0.58 AR (1) -0.066 0.091 -0.728 0.47 AR (2) -0.698 0.090 -7.748 0.00 AR (3) -0.019 0.108 -0.172 0.86 AR (4) -0.094 0.108 -0.866 0.39 AR (5) -0.047 0.085 -0.556 0.58 AR (6) 0.073 0.084 0.871 0.39 MA (1) 0.166 0.003 50.48 0.00 MA (2) 0.980 0.000 2113.8 0.00 R2 0.228 F-stat 4.325 D-W stat 1.99 Prob 0.00 We combine the ARIMA 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 given in Table 5. The R2 is 0.32 and the D-W statistic is very close to 2. The sample autocorrelations for the residuals of the model [Equation (5)] are almost zero. Further, the Ljung-Box Q-statistic is mostly insignificant. Thus, the residuals of the model are white noise. Hence, our estimations do not suffer from the problem of serial correlation. The residuals do not exhibit conditional autoregressive heteroskedasticity. A Lagrange Multiplier (LM) test for the presence12 of the ARCH effects in the residuals (F-statistic of 0.279 and ρ-value of 0.60) reveals no such effects.We note from Table 5 that the estimated coefficients of the monthly dummy variables change significantly once we account for the serial correlation in the residuals. We find the coefficients of intercept, and dummy variables for the months of March, July and October to be statistically significant. The average return in the benchmark month of January is 1.85 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. The returns for the months of March, July and October are amongst the lowest as compared to the month of January. Table 5: The Time Series and Regression Model [Equation (5)] Variable Coefficient Std. Error t-Statistic Prob. Constant 1.835 0.966 1.900 0.06 D2 (Feb) 0.949 1.511 0.628 0.53 D3 (Mar) -2.569 1.447 -1.776 0.08 D4 (Apr) -1.994 1.618 -1.233 0.22 D5 (May) -2.225 1.591 -1.398 0.16 D6 (Jun) -1.419 1.490 -0.953 0.34 D7 (Jul) -2.496 1.321 -1.890 0.06 D8 (Aug) -0.877 1.498 -0.586 0.56 D9 (Sep) -2.629 1.635 -1.608 0.11 D10 (Oct) -4.144 1.546 -2.680 0.01 D11 (Nov) -2.209 1.461 -1.512 0.13 D12 (Dec) -0.218 1.476 -0.148 0.88 AR (1) 0.000 0.099 0.003 1.00 AR (2) -0.682 0.095 -7.211 0.00 AR (3) -0.046 0.113 -0.406 0.69 AR (4) -0.079 0.114 -0.696 0.49 AR (5) -0.002 0.091 -0.021 0.98 AR (6) 0.100 0.089 1.123 0.26 MA (1) 0.085 0.042 2.026 0.05 MA (2) 0.980 0.000 2845.6 0.00 R2 0.324 F-stat 2.676 D-W stat 1.98 Prob. 0.00 13 The statistically significant coefficients for the intercept term, which represents the benchmark month of January, and three other months, viz., March, July and October clearly indicate the presence of seasonality in the Sensex returns. Our results do confirm the January effect for stock returns in India. It is interesting to note that the Indian tax year ends in March in contrast with the US tax system where the tax year ends in December. The average return for March is negative as compared to the January average return. As stated earlier, the coefficient of the dummy variable for the month of March is statistically significant. This evidence is consistent with the ‘tax-loss-selling’ hypothesis. It appears that investors in India sell shares that have declined in values, and book losses to save taxes. This causes share prices to decline that results in lower returns. As regards the year-end effect, we notice that the coefficients of dummy variables for the months of November and December are not statistically significant. However, we do find the coefficients of dummy variable for the month of October and the intercept, representing January to be statistically significant. This could result from several social, economic and political factors. These results of the study could be attributed to the ‘information’ hypothesis. Summary and Conclusions The focus of this study was on investigating the existence of seasonality in stock returns in India. We used the monthly returns data of the BSE’s Sensex for the period from April 1991 to March 2002. The analysis of descriptive statistics showed that the maximum average return (positive) occurred in the month of February and lowest (negative) in the month of March. The positive average returns arose for six months and negative for the remaining six months. The regression14 results confirmed the seasonal effect in stock returns in India. We found that returns were statistically significant in March, July and October. The Indian tax year ends in March. The statistically significant coefficient for March is consistent with the ‘tax-loss selling’ hypothesis. Our results also supported the January effect. The results of the study indicate that stock returns in India are not entirely random. This implies that the Indian stock market may not informationally efficient. As a consequence, perhaps investors can improve their returns by timing their investments. We would, however, like to caution that more research is needed before making any firm conclusion in this regard. In the future, one could study other stock indices (like the BSE’s National Index, the NSE’s Nifty etc.) in India and also investigate the weekly and the intra-month effects. References 1. Aggarwal, Raj, Ramesh P. Rao and Takto Hiraki, “Regularities in Tokyo Stock Exchange Security Returns: P/E, Size and Seasonal Influences,” Journal of Financial Research, Vol. 13, (Fall 1990), 249-263. 2. Aggarwal. R. and P. Rivoli, “Seasonal and Day-of-the Week effects In Four Emerging Stock Markets. “The Financial Review, 24, (1989), 541-550. 3. Ariel, Robert A., “A Monthly Effect in Stock Returns,” Journal of Financial Economics, Vol. 18, (March 1987), 161-174. 4. Berges, A., J. McConnell, and G. Schlarbaum, “An Investigation of the Turn-of-the-Year Effect, the Small Firm Effect and the Tax-Loss Selling Pressure Hypothesis in Canadian Stock Returns,” Journal of Finance, 39, (March1984), 185-192. 5. Boudreaux, Denis O., “The Monthly Effect in International Stock Markets: Evidence and Implications”, Journal of Financial and Strategic Decisions, Vol. 8, No. 1, (1995), 15-20.15 6. Brown, P., D.B. Keim, A.W. Keleidon, and T.A. Marsh “Stock Return Seasonalities and the Tax-Loss-Selling-Hypothesis: Analysis of the Arguments and Australian Evidence,” Journal of Financial Economics, 12, (June1983), 105-127. 7. Fama, Eugene F., “Efficient Capital Markets: A Review of Theory & Empirical Work,” Journal of Finance, (1970), 383-417. 8. Fama, Eugene F., “The Behavior of Stock Market Prices,” Journal of Business, Vol. 38, (January 1965), 34-105. 9. Gultekin, M.N., and N.B. Gultekin, “Stock Market Seasonality: International Evidence,” Journal of Financial Economics, 12, (December 1983), 469-481. 10. Ho, R. and Y. Cheung, “Seasonal Patterns in Volatility in Asian Stock Markets,” Applied Financial Economics, 4, (1994), 61-67. 11. Ho, Y., “Stock Return Seasonalities in Asia Pacific Markets,” Journal of International Financial Management and Accounting, 2, (1990), 47-77. 12. Islam, Anisul M., Orpin Duangploy, and Saowanww Sitchwart, “Seasonality in Stock Returns: An Empirical Study of Thailand,” Global Business and Finance Review, Vol. 6, No. 2, (2001), 65-75. 13. Jaffe, Jeffery, and Randolph Westerfield, “The Week-End Effect in common Stock Returns: The International Evidence,” Journal of Finance, Vol. 40, (June 1985), 433-454. 14. Jaffe, Jeffrey F., and Randolph Westerfield and M. Christopher, “A Twist on The Monday Effect in Stock Prices: Evidence from the U.S. and Foreign Stock Markets,” Journal of Banking and Finance, Vol. 13, (1989), 641-650.16 15. Jaffe, Jeffrey F., and Randolph Westerfield, “Is There a Monthly Effect in Stock Market Returns? Evidence from Foreign Countries,” Journal of Banking and Finance, Vol. 13, (1989), 237-244. 16. Kamath, R., R. Chakornpipat, and R. Chatrath, “Return Distribution and the Day-of-the-Week Effects in the Stock Exchange of Thailand,” Journal of Economics and Finance, 22, 2-3, (1988), 97-107. 17. Kato, K. and J.S. Schallheim, “Seasonal and Size Anomalies in the Japanese Stock Market,” Journal of Financial and Quantitative Analysis, 20, (1985), 243-272. 18. Keim, D.B., “Size-Related Anomalies and Stock Return Seasonality: Further Empirical Evidence,” Journal of Financial Economics, 12, (June 1983), 13-32. 19. Lee, I., “Stock Market Seasonality: Some Evidence From the Pacific-Basin Countries,” Journal of Business Finance and Accounting, 19, (1992), 192-209. 20. Lee, I., R. Pettit, and M.V. Swankoski, “Daily Return Relationship Among Asian Stock Markets,” Journal of Business Finance and Accounting, 17, (1990), 265-283. 21. Lewis, Mario, “Stock Market Anomalies: A Re-Assessment Based on The U.K. Evidence,” Journal of Banking and Finance, Vol. 13, (1989), 675-696. 22. Officer, R.R., “Seasonality in Australian Capital Markets: Market Efficiency and Empirical Issues,” Journal of Financial Economics, Vol. 2, (March 1975), 29-52. 23. Pindyck, Robert S. and Daniel L. Rubinfeld, Econometric Models and Economic Forecasts, New York: McGraw-Hill, International Edition, (1998). 24. Ramacharran, H., “Seasonality in the Jamaican Stock Market: An Examination of Stock Returns and the Volume Traded,” Journal of Emerging Markets, 2, 1, (1997), 23-35,17 25. Reinganum, M.R. “The Anomalous Stock Market Behavior of Small Firms in January Empirical Test for Year-End Tax Effect,” Journal of Financial Economics, 12, (June 1983), 89-104. 26. Rozeff, Michael S., and William R. Kinney, “Capital Market Seasonality: The Case of Stock Market Returns, “ Journal of Financial Economics, Vol. 3, (October 1976), 376-402. 27. Smirlock, Michael, and Laura Starks, “Day of the Week and Intraday Effects in Stock Returns,” Journal of Financial Economics, Vol. 17, (1986), 197-210. 28. Tinic, Seha M., and Richard R. Wesst, “Risk and Return: January and the Rest of the Year,” Journal of Financial Economics, Vol. 13, (December 1984), 561-574. 29. Tinic, Seha M., Giovanni Barone-Adesi and Richard R. West, “Seasonality in Canadian Stock Prices: A Test of the ‘Tax-Loss Selling’ Hypothesis,” Journal of Financial and Quantitative Analysis, Vol. 22, (1987), 51-64. 30. Wachtel, S.B., “Certain Observation on Seasonal Movement in Stock Prices,” Journal of Business, 15, (1942), 184-193.