According to the well known efficient market hypothesis, the stock prices in the future cannot be predicted from the historical trends in the stock prices. The market price of a particular day depends upon the demand and supply on that particular day and has no dependency on the historical data. It states that the market is efficient and no one can take abnormal profits because there are no trends in the stock prices and they cannot be forecasted. But in the recent researches that have been made in the stock indexes all around the world have given evidences of anomalies seen in the stock indexes and returns that clearly negate the efficient market hypothesis. These anomalies or the trends are called as the Calendar effects. There are many calendar effects that have been detected in the various stock exchanges; the most widely known and searched are January effect, December effect, September effect, Monday effect. And there are others also that depend upon the country that is under study for example the Halloween effect in US stock market and Xmas effect in the English stock markets and Ramadan effect in the Islamic countries are well known. It is interesting fact that even though a lot of research has been conducted on these calendar effects and they have shown a lot of evidence in the stock markets all around the world, even now this has not been honored as a part of the literature. Mainly because if these calendar effects are studied over a larger scale of data, they fall weak in their significance. And gave an impression that these are not a reality but a mere illusion of the data or data mining. We in our paper have tried to study if there are any anomalies in the Karachi Stock Exchange. A larger data sample is taken so that the effect of the data mining would be decreased. And other tests would also be run to check the validity of the data and minimize the corruption of data mining. This study would be helpful for the investors in the country and abroad in making the right decisions for gaining profits. The study would also be helpful for the researchers all around the world in understanding more clearly this illusion of calendar effects, better, because Karachi Stock Exchange is the one that has been least studied in this context. Finally it would be helpful for the Karachi Stock Exchange itself, we believe, in drawing the attention of the researchers towards it and giving a positive image in the research world.
To see the calendar affects and their historical existence, we will have to go back till Fama (1960) introduced the term called as the efficient market hypothesis, according to which the stock markets shows a random walk behavior and that the stock prices are not affected by the historical patterns in the stock market or in other words, the stock prices cannot be predicted. Also the theory stated that there is a uniformity of information in the market. And everyone trading in the market has the same information available to him and because of this uniformity in the stock information; no investor can take the abnormal profits. Various studies and researches were then performed to study the existence of this efficient market hypothesis. But some results were found that were totally contradictory to the efficient market hypothesis and its random walk behavior. Angel Berges, John J. McConnell, and Gary G. Schlarbaum (1984) found out that January effect was visible in the Canadian stock exchange and that the January stock returns were higher than every other month of the year ranging on a data period of 29 years from 1951-1980. These researches gave rise to other researches being conducted on January effect and finding out if there were any other anomalies in the stock exchanges as well. Lakonishok, J., Smidt, S. (1988) studied the Dow Jones over a period of 90 years data and found out significant abnormalities in the stock prices, the most obvious the Monday effect, at the end of the month, at the end of the year and the holiday effect. Having searched on this large scale data of 90 years considering these anomalies due to mere luck is not likely. The research then spreading to the other countries showed the presence of these anomalies in them as well. Anup and Kishore Tandon (1994) conducted a research on five seasonal patterns in the stock markets of eighteen countries. End of the month anomaly was seen in many countries. The large January returns are also seen in most countries. Apart from that Boudreaux (1995) also conducted research on stock markets of seven countries to find out significant positive monthly effects in Australia and Canada, while negative monthly effect in Japan’s market. P HansenA (2003) conducted research on 27 stock indices from 10 countries, Denmark, France, Germany, Hong Kong, Italy, Japan, Norway, Sweden, UK, and USA and found 17 possible calendar effects containing 12 month-of-the-year and the 5 day-of-the-week effects. Grimbacher, Swinkels and van Vliet (2010) used a sample from 1963-08 find the Halloween and the turn of the month effects as the most significant of all anomalies and the January effect to be the weakest. These anomalies in the stock exchanges have shown varying results in different countries. For example Bin Li, Benjamin Liu (2010) performed the research in New Zealand Stock Exchange found out significant positive results in June and negative results in August, an anomaly that is not to be seen in UK stock exchanges. Also there was a very less significant January and April effects, present in just two industries indices in the sector. Also there has been a lot of controversy regarding the acceptance of these calendar anomalies as realistic or just because of a mere chance or because of the data mining. Jacobsen, Zhang (2010) used a wide scale data of 317 years of UK stock exchange to verify if these calendar effects were real or just by mere chance. The results also proved the existence of the calendar anomalies. And also shows a change in these anomalies along the time. Pre 1850 there was a December present in the market that changed into the famous January effect afterwards. Underperformance of the stock in the months of July and October is also evident in the data. So there has been a research in the stock exchanges all around the globe and they have found anomalies in the stock exchange returns, despite of the fact that they might have been seen because of the data mining factor. A recent attention has also been given to the Karachi Stock Exchange as well to study if there exists any anomaly in KSE. F Husain (1998) took 36 individual stocks, 8 sector indices, and the general market index, covering the period from January 1, 1989 to December 30, 1993 to study if there was any Ramadan effect in the stock market and found out that although stock returns decline in the month of Ramadan, the reduction, in general, is not significant. There is strong evidence of a significant decline in the volatility of stock returns in this month. S Ali (2009) went to research with a bigger scale data of the KSE comprising closing daily, weekly and monthly data of the KSE 100 index for period starting November 1991 to October 2006. The results again showed neither monthly calendar effects nor days of the week effects. Positive average returns were witnessed in the first and second week while the third and fourth week showed average negative returns. There are no monthly calendar effects in the market either.
DATA & METHADOLOGY
We have used the daily Karachi Stock Index ranging across a period of five years from January 2006 to December 2010.The close of day Rt is computed from KSE 100 index as follows: Rt =ln (It/I t-1) Rt is the daily return on KSE100 index on day t. It and I t-1 are closing values of the month respectively. To investigate the calendar effect we estimate the following regression equation: Rt =Î²1Jt+ Î²2Ft+ Î²3MRt+ Î²4APt+ Î²5MYt+ Î²6JNt+ Î²7JLt+ Î²8AUt+ Î²9St+ Î²10Ot+ Î²11Nt +Î²12Dt+á½²t Where Rt is the daily returns and Jt, Ft, MRt, APt, MYt, JNt, JLt, AUt, St, Ot, Nt & Dt are dummy variables for January, February, March, April, May, June, July, August, September, October, November, December respectively. If it is January than J=1 and “0”? for all other days of the year, if it is February then F=1 and F= 0 for all other days of the year and so forth, á½² is a random term. B1 – B12 are co-efficient to be estimated using OLS.
We conducted study to investigate the Calendar effect in Karachi stock exchange. We calculate monthly market returns for each month of the year, by using KSE-100 index daily data.
Table- 1 Descriptive Statistics
months Minimum Maximum Sum Mean Std. Deviation Variance Skewness Kurtosis Statistic Statistic Statistic Statistic Statistic Statistic Statistic Std. Error Statistic January -5.2785 4.7051 13.2874 .119706 1.4792473 2.188 -.789 .229 3.671 February -5.1349 4.1101 20.7684 .205628 1.3439130 1.806 -.354 .240 2.518 March -4.5007 5.3012 25.6476 .231059 1.5719945 2.471 .052 .229 1.590 April -3.9478 4.3185 15.3018 .143008 1.3536062 1.832 -.080 .234 2.408 May -4.6204 3.5514 -42.1196 -.382905 1.5753882 2.482 -.582 .230 .389 June -6.0418 8.2547 11.8456 .109681 2.1339432 4.554 .218 .233 2.150 July -4.5345 3.8806 5.1754 .046625 1.5524969 2.410 -.554 .229 1.439 August -3.9848 4.3948 -25.1996 -.229087 1.7060419 2.911 -.140 .230 .129 September -2.6705 2.9424 22.4747 .210044 .9636335 .929 .453 .234 .955 October -4.4355 2.8350 18.1200 .163244 1.0256923 1.052 -.889 .229 4.644 November -4.6738 2.7165 -2.3470 -.021934 1.1849094 1.404 -.775 .234 2.411 December -4.8184 2.6518 -41.2052 -.371218 1.5305945 2.343 -1.303 .229 1.285 By descriptive statistics we noted that mean return of the March is higher than the rest of the months. The mean return on March is 0.231059 whereas the mean returns of the rest of the months is an average of -0.018596. The higher mean return shows that there is March effect in Karachi stock exchange.
Table- 2 Regression Analysis
Model Unstandardized Coefficients Standardized Coefficients T B Std.Error Beta B (Constant) .047 .141 .331 Jan .073 .199 .014 .367 Feb .159 .204 .028 .779 Mar .184 .199 .034 .926 Apr .096 .201 .018 .479 May -.430 .200 -.080 -2.151 Jun .063 .201 .012 .314 July .033 .148 .006 .221 Aug -.276 .200 -.051 -1.381 Sep .163 .201 .030 .813 Oct .117 .199 .022 .585 Nov -.069 .201 -.013 -.341 Dec -.418 .199 -.078 -2.097 Regression results and related statistics are presented in table 2 and ANOVA test results are presented in table 3
Table- 3 ANOVA
Sum of Squares
1 Regression 60.081 11 5.462 2.480 .004(a) Residual 2848.185 1293 2.203 Total 2908.265 1304 The results show that there is March effect in Pakistani stock market. The t value for the month of March is 0.926 which indicates a greater impact on the Rt. ANOVA suggest that the model is significant with F significance 0.004. Which indicate the fitness of the model.
In this study we have examined daily returns of KSE-100 Index, from the period starting 2006 till end of 2010, with a purpose to find out if there exist any monthly anomalies in the returns. In Karachi Stock Exchange, trading occurs five days a week (Monday, Tuesday, Wednesday, Thursday and Friday) throughout the year. The Efficient Market Hypothesis explains that there are constant market returns for the whole year. Empirical results of this study indicate that there is a significant March effect in Karachi Stock market. And this is proven by both the regression results and the descriptive statistics that are highest for the month of March than any other month of the year. March Returns are more volatile compared to other months of the year. So the results have concluded that in the recent five years, there has existed a month effect in Karachi stock market which is the March Effect. And thus the Efficient Market Hypothesis is violated in KSE.