An evidence of calendar effects on the stock market of Pakistan: a case study of (KSE-100 index)

Transcription

1 An evidence of calendar effects on the stock market of Pakistan: a case study of (KSE-100 index) Khurram Shehzad 1 *, Nadeem Sohail 1 1 University Community College, Government College University, Faisalabad ARTICLE INFO *Corresponding Author: jamezband007@gmail.com DOI: /nijesr Keywords: Calendar effect, Karachi stock exchange, January effect. Jell Classification: G14, G15 ABSTRACT This is the study that investigates the Daily impact, weekly impact, and Monthly impact by excluding the holidays for most updated time period through February 1991 to MAY Study used the dummy variables to explore the independent variables and used stock return as dependent variable. Ordinary least square and descriptive statistics technique is used to examine the data. Middle day effect was proven in the equity market of Pakistan, study also showed first week of the month has more return as compare to any other week in a month. Whereas month wise results showed that month of May had negative return. I. INTRODUCTION These days, calendar impacts are capturing a great interest of researchers and investors, because of confirmation of excess return connected with a specific day, month or week in the most famous worldwide stock markets [1]. Calendar effects are the specific stock values that are connected with calendar. There is significance importance of the day wise, week wise and month wise effects in the stock return anomaly. According to the efficient market theory, it is difficult to predict the accurate stock prices in an open market [1].It is considered that financial investors are rational and prices of stocks are measured by the rule of supply and demand of a specific stock [2]. If an investor is going to predict the future stock price for a specific security, it will be considered that stock price prevailing today is managed with float term. In other words, we can say that there is no existence of patterns in stock price. On the other hand, if there is a regular or calendar impact prevailing in the market, it will permit the financial investors to get a strange benefits [3]. This nullifies the appearance of financial sector effectiveness that describes prices of stocks are independent from the previous prices. There are some authors who investigate the Day wise, Week wise and Month wise effect of the stock anomalies. But no one includes all these effects at the same time. Some authors also investigate the Ramadan impact. There are many studies on the seasonal impacts of the stock return but there is huge confliction between their results. As the Pakistan is an under develop nation so examination of stock return in this region can establish knowledgeable conclusion. In this study author wants to discover true results about daily, weekly and monthly effects prevailed in the stock market of Pakistan. For this purpose author has utilized the day to day, week by week and month to month stock return gathered from the figures given in Karachi stock exchange 100 index. Accepting Pakistan a developing market, the formal wish would be that the business sector is uneconomical. 46 Karachi stock trade was been welcomed as one of the best performing developing markets in the middle of 1990 [1]. Before 1990, the KSE couldn't assume its urgent part in monetary improvement. The stock exchange was limited and not be able to provide the capital needs of the economy for a long time [1]. Financial institutions and business banks fulfil the capital needs for the long term period Stocks was no more a 'side illustrate' a pursuing ground for the rich where fortunes were made or lost [1]. Due to these reasons the gainful working of stock trade was a noteworthy question mark because The KSE had been portrayed as a speculative business. By the Government side there was no implementation of rules and regulations and the investors were not ready to invest their resources in KSE without having any support by government [1]. Besides, limitation on outpouring and inflow of remote exchange liquidity imperatives, restricted exchanging base and constrained utilization of technology were obliged to build up the business. In the same way as other developing markets KSE is viewed as a narrow market, assumes a restricted part for increasing funds and is a decently unpredictable marketplace [3]. The business sector has encountered the blasts and busts of nearly brief time term, which may be because of poor data, powerless institutional backings and absence of consistence with managing power prerequisites. Accordingly data played a restricted part in stock exchange. These measures have killed the possibilities of imitation cheats and defer in exchange, and subsequently have brought on decay in the instability of stock costs. Notwithstanding that, the trade gives data on continuous premise to financial specialists through the Internet. The Security and Exchange Commission of Pakistan (SECP) gives rules to fortify great corporate administration, with the point of upgrading speculator certainty by expanding straightforwardness in the business practices of recorded organizations [3]. With a specific end goal to minimize the hierarchical shortcoming and to progress the money related soundness the legislature has privatized the monetary what's more, non-budgetary

2 organization. They created the stores from stock exchanges that at last enhanced the execution of stock exchange. Further, they moreover aided in connecting data about the regularly changing political and financial environment, and helped speculators to relate all such data to the exchanging action of the business in a productive way; this has minimized the chances for speculators winning above ordinary benefit [3]. As talked about in the writing, value and exchanging volume are the two most essential variables in examination of productive business speculation on the grounds that the chartists watch both value and exchanging volume. Since stock value design gives the signs, numerous professionals accepted that the exchanging volume should ascend to fortify the pattern. Such support demonstrates purchasers' or merchants' advantage, and this investment may be identified with a change in basics. Various studies have been directed with respect to the connection between trading volume and stock return. A large portion of these studies discovered the observational relationship between exchanging volume and comes back to be direct and nonlinear [4]. In Karachi stock exchange data is accessible on an ongoing premise with exchanging volume and it controls the arrival. That is the reason it is exciting to examine the relationship in the middle of danger and come back with data in Karachi stock exchange. It is normal that, in the KSE, return is emphatically identified with both hazard and exchanging volume [4]. The presence of calendar seasonality impacts disproves the EMH (efficient market hypothesis), which expresses that business sectors are educationally effective, and in this way unusual returns are unachievable [2], [3], [4]. The presence of calendar impacts has taken everyone's attention because of businessmen looking for gainful exchanging systems trying to exploit any unique anomaly. Numerous studies have researched the January impact in the US Rozeff and Kinney [3] [4], Mehdian and Perry [4], Keim [5], Rogalski and Tinic [6], and outside the US Berges, et al. [7], Robins, et al. [8],Auret and Cline [9]. The day-of-the-week impact has gotten investigation in numerous US and UK studies Doyle and Chen [10], Steeley [11], Gibbons and Hess [12], and also other created and developing markets Basher and Sadorsky [13], Jaffe and Westerfield [14]. Preholiday impact incorporates various studies in created and creating markets Bhana [15], Lakonishok and Smidt [16], Vergin and McGinnis [17], Marrett and Worthington [18], Kim and Park [19], Brockman and Michayluk [20]. A number of the literature cited focus on these seasonality in each study Holden, et al. [21]. Now a days, studies are including various calendar impacts like daily impact, weekly impact and monthly impact, in one study to examine whether over various years, stock exchange returns experience different sorts of anomalies in their stock returns (see for instance Chatterjee and Maniam [22], Ziemba [23], Holden, et al. [21], Coutts and Sheikh [24], Studies done on various schedule impacts in South Africa are to a great degree restricted. Coutts and Sheik (2002) is the main known distributed paper that tests for each of the three picked calendar impacts at one time for South African stock exchange. Ali and Akbar [25] investigate calendar impacts with the use of daily, weekly and monthly data in one study without including the holidays from November 1991 to October 2006, for the Karachi stock exchange in Pakistan. But it does not consider late changes in innovation, principles and regulations and additionally monetary changes. Along these lines, there is a need to re-examine these schedule impacts utilizing a later example period. This study evaluates the presence of the day-of-the-week impacts on the KSE by taking data from 1991 to These sorts of calendar abnormalities have had a large number of articles committed to them, to such an extent, that impressive inspiration is needed for the initiation of this study. This study endeavours to fill a hole in writing in the accompanying ways. Firstly, past writing has a tendency to concentrate on every individual seasonality concerning different markets over the world (see for instance Cadsby and Ratner [26], Rozeff and Kinney [3]. Furthermore, most work performed on calendar abnormalities has focused solely on well developed markets. The couple of existing studies concentrating on developing economies give minor consideration to the initial markets of Pakistan see also Alagidede [27]. Experimental examination of various calendar inconsistencies in one study in Pakistan is constrained. This study will take an amplified approach to deal KSE 100 index with the aim of uncovering the presence of different calendar seasonality for the one time period. This method is utilized by Chien, et al. [28]. The methodology taken will take after the recommendation by Chien, et al. [28], by researching the dayof-the-week impacts, for the whole Karachi stock exchange 100 index. (Additionally see Ziemba [23], Chan, et al. [29]. Anomaly will be specifically investigated on mean returns of stocks recorded for the KSE 100 index utilizing descriptive statistics. Furthermore, this study will likewise utilize an OLS variable relapse model. Utilizing two methods of analyzing data will permit the straightforward correlation of results got in this study with past writing. If we find calendar seasonality under one methodology but no anomaly under second methodology, one can reason that the presence of the inconsistency is the immediate after effect of the methodological approach used. Likewise, the benefit of utilizing these techniques additionally describe that one method do test seasonality as lower statistical moments (standard deviation and mean) whereas other one measure higher moments (skewness and kurtosis) that is very rare in anomaly studies. Rowjee [30]. Main purpose of this research is to investigate the day wise, week wise and month wise effect on stock return. Market efficiency of Karachi stock exchange return could be tested indirectly with these actions. For this purpose author has decided to use the time series financial data registered on the Karachi stock exchange 100 index, for the period of February 2, 1991 to May 24, This research has focused on the 47

3 query whether the starting days of the week has more return of the ending days of the week. Study has generated the following hypothesis to ascertain the true results. HO: The stock return is positive on Monday. H1: The stock return is negative on Monday. HO: The stock return is positive on Tuesday. H1: The stock return is negative on Tuesday. HO: The stock return is positive on Wednesday. H1: The stock return is negative on Wednesday. HO: The stock return is positive on Thursday. H1: The stock return is negative on Thursday. H0: The stock return is positive on Friday. H1: The stock return is negative on Friday. II. LITERATURE REVIEW Malkiel [31], in evidence of Fama [32], a market that represent the fully and true evidence related to individual and whole stock return in market is said to be an efficient market. Fama [32] describe the three types of market efficiency prevailing in all over the world. The type which comes at first is called the weak form of market efficiency, it does not have the ability to present all the information to predict upcoming price. This behavior of EMH advance the situation to Random walk theory that describe today s prices are independent from previous day prices. Basically RWT describe that today s price of a security does not depend on the yesterday s price. According to sense of investor, he cannot predict that tomorrow what would be the price of a security? Hence prices of securities are secretive at some extent. The second form of market efficiency is called semi strong form of market efficiency in which historical prices convey the full information. In other words we can say that an investor can predict future prices of at some extent [59]. As there is no need to analyze the financial statement of a company to predict future prices as they already reveal such information. The strong form of efficiency reveal security price including historical, public insider or private information [59]. If there is existence of EMH then an investor can t beat the market neither with the selection of a specific security nor with selection of specific time [58]. Though both studies was unable to explain the calendar seasonality. There is dispute between RWT and EMH due to these anomalies because of demonstrating the calendar seasonality. Coutts, et al. [33]. The existence of these anomaly patterns according to time challenge the market efficiency, because any anomaly should dispel once it appear in efficient market. Chen, et al. [34]. An abnormal positive return on Friday and negative return of Monday is normally called the day of the week impact. Negative returns on Monday is because of bad news and negative information during the weekend Lakonishok and Maberly [35]. Monday s return shows the return of investment of three days that begins with the end of Friday to the end of Monday. Mean and variance for these three days may be higher as compared to other days. Though a reasonable and 48 generally accepted description of these days is not yet cleared. If this pattern is reliable then an investor can avail these type of information available to select not only the best amount of investment but also the timing and portfolio of securities, i.e. an investor can buy the securities on Monday because of less price and sell it on Friday due to higher price on that day. French [36] found that Monday had the negative return. Fama [37] analyzed the different day s variances and found the variance on Monday was 20% greater as compared to other day variance. Gibbons and Hess [12] analyzed the S&P 500 index and found great day of week impact based on similarly biased portfolios taken from the CRSP. During the study from 1962 to 1978 the researcher found that mean return for Monday was -33.5% for the index of S&P and negative 26.8% for similar weighted portfolio. Even that while the study on other assets like the T. Bills market study also discover the lessen return for the Monday. With the elimination of the market efficiency (using adjusted mean returns), stocks returns shows the significant day impact. Dubois and Louvet [38] analyzed the daily impact at various phases of development for the various markets of nine states during the period of 1969 to 1992 by using the ARIMA model. Study concluded that anomalies exist for some of the European states but was not significant for the United States. Study of Dubois and Louvet [38] and Gibbons and Hess [12] is backward so these results should be retested for the recent times as there might be possibility of changes in results while testing by most recent stock returns. Berument and Kiymaz [39] test the S&P index with the help of OLS during the period of Jan to 1997 October. Study concluded that there was Monday and Wednesday impact for the period of 1973 to While there was continuous first three days seasonality pattern of the week during the period of 1987 to These results were similar to the results of Ajayi, et al. [40]. This study will strengthen the study done by Berument and Kiymaz [39] with the use of recent data and new methodology that would focus the higher statistical moments. Chinzara and Slyper [41] observe the South Africa by taking entirely share index to test the days of week impact. Study used the data form 1995 January to December Results of the study found that there was significant and positive return on Monday while significant negative impact for the day of Friday was also found. Study also reveal that the results was not altered when study used the risk factor. Basher and Sadorsky [13] evaluated by employing the unrestricted and restricted risk, twenty one markets with the use of five changed models by taking closing prices of each day. Every model present altered results for each state. Although these impacts are widespread for the state of Pakistan, Taiwan and Philippine. Study also reveal that out of five models four models provide evidence for positive seasonality pattern for the state of Turkey, Thailand and Malaysia but there was no seasonality pattern for most of the emerging markets. Study reveals that there was Monday impact found in South Africa.

4 Plimsoll, et al. [2] investigated the top index price (TOPI) and all share index (ALSI) and used the same methodology as Basher and Sadorsky [13]. Study was basically done to confirm or reject the result concluded. Sutheebanjard and Premchaiswadi [42] said that Monday has more return as compared to other days by analyzing the daily returns of Thailand stock exchange during the period of 2005 January to march The results of this study should be infer with high observance because of exclusive features of Thailand stock market (see Aggarwal, et al. [43]. Jaffe and Westerfield [14] investigated the stocks of UK, US, Canada, Australia and Japan because of these countries generate 87% stock market listed returns of the world. Study analyzed the weekly and daily returns and found every selected countries have daily and weekly effect. Study also reveals in contradiction that there was low return on Tuesday for Australian and Japanese stock markets. That study had particular importance because of its comparison between formed and emerging markets. See Barone [44]. Results of their research strongly recommend the sighting the seasonality effects in emerging markets. Chen, et al. [34] studied the 13 US price indices over period of 1993 to 2007 and concluded that there was no any Monday effect but significant weekend effect was found. Steeley [11] test the significance of UK stock market using the daily returns over the period of 1991 to 1998 and found day of week effect in FTSE index. BothChen, et al. [34] and Steeley [11] highlight the convenience of recognizing anomaly or deficiency in that department. On the off chance that one can distinguish seasonality with sureness; a methodology can be made to concentrate any benefits accessible. On the off chance that no seasonality is distinguished, markets may "avail" in being productive, and speculators can accept their choices are construct exclusively with respect to behavioral predilections and not any kind of market disparities. Thus, a study uncovering distinctive sorts of abnormalities on one specific market over a solitary time period is required and justified. Numerous studies uncover a noteworthy day-of-the-week impact that is not simply limited to a Monday and a Friday. Bayar and Kan [45] considered the subsequent 19 states for day s effect, Austria, Australia, Belgium, Canada, Denmark, France, Finland, Germany, Italy, Japan, Hong Kong, New Zealand, Norway, Netherlands, Sweden, Spain, Switzerland, US and UK. The sample period was consist of July 1993 to July 1998 based on dummy variables by applying the ordinary least square method. Results were according to two aspects. One define the pattern in terms of local currency and the other one define in dollar term. In terms of local currency Tuesday and Wednesday have higher return but there was less return on last days of week Friday and Thursday. For dollar twelve states shows high return on Tuesday and Wednesday and less return was found on Thursday and Friday. This study is very beneficial because there was existence of seasonality pattern on almost all the days of the week but return on different day for the different country. Abraham and Ikenberry [46] investigate the stock indices of Belgium, Brazil, Australia, Canada, France, Denmark, Hong Kong, Germany, Italy, Mexico, Japan, Luxembourg, Netherlands, New Zealand, Sweden, Singapore, Switzerland, US and UK. This study used the ordinary least square methodology for all the above explained countries and concluded that there was Monday, Tuesday, Wednesday, Thursday and Friday impact for various countries but Friday and Wednesday effect was strongly found. South Africa was not include in both studies of Abraham and Ikenberry [46] and Bayar and Kan [45]. Balaban [47] concluded that there was high stock return and low standard deviation on Friday tracked by Wednesday, based on Turkish index over 1988 to He also concluded that day of the week effect changes according to magnitude and direction during a year. Dubois and Louvet [38] used the indices of nine countries and determined the positive Wednesday and negative Tuesday and Monday effect during the period of 1969 to Aggarwal and Rivoli [48] evaluated the Singapore, Malaysia, Hong Kong and Philippines for the period of September June Study also found the strong Tuesday impact (also see Barone [44]. Holiday or the before holiday impact has also much importance. Preholiday impact has high abnormal return on the days before holidays. This seasonality bring much curiosity for investors. The days before holidays are said to be lower liquid days that means less cash. Therefore investors sell their securities to have more cash before holidays. Investors do lessen their stockholding before a holiday because of their supposed bad beliefs about an info. Most of the investors sell their securities on the day before holiday therefore share prices goes down earlier a holiday. Now a day there is a new trend of buying securities on the day before a holiday when the prices of shares are low and sell the shares after the holidays when other investors are busy to buy the shares. When the other investors are busy to buy the securities the prices of share will increase, which is the best time for selling. Marrett and Worthington [18] describe that holiday impact is because of the psychology of investors, indicating that investors have a tendency to purchase shares before holidays due to great spirit and holiday excitement. Lakonishok and Smidt [16] investigated the DJIA index and concluded preholiday return was twenty three time higher than the return on any regular day, this increase represent round about fifty percent of total increase in price of DJIA. Cadsby and Ratner [26] studied the eleven stock indices gathered from the ten different countries and applied the A.M on each indices and also compared them with each other. Results described that five out of ten countries have significant holiday impact e.g. US, Canada, Hong Kong, Japan. This study lightens the necessity of anomalies outside the United States. Study also explains the merits of finding a pre-holiday impact in various countries as each country has its specific characteristics. 49

5 III. DATA AND METHODOLOGY In this study stock return of KSE-100 Index is used. KSE- 100 index is an index that This study includes the daily stock returns of Karachi stock exchange 100 index. Karachi stock exchange 100 index is a business quality biased index and records for pretty nearly 85% of the aggregate business underwriting. Study used the data for the period of 1991 to 2015 for the day wise returns, for the week wise and month wise returns. To lessen the impact of high values of Day wise prices of stock, we ascertain log returns utilizing the accompanying equation. R = ln KSE100t ln KSE100t-1*100Ali and Akbar [25], Mustafa and Nishat [49], Abdalla [50]. Where R denoted for the stock returns of KSE 100 index and KSE 100t is the value of stock price at time T(current day) and KSE100t-1 is the worth of stock price on time T- 1(previous day). We have the last day return of month as monthly return and last day of week return as weekly return. There was three time changes in the Pakistani business market and holidays was rescheduled for three times in Pakistan according to Ali and Akbar [25]. Following lines interpret around the official days and the public holidays in prevailing in the Pakistan. To test the daily impacts we separate our examination into three sections, 1st section deals when marketplace stayed shut on Thursdays & Fridays Ali and Akbar [25], For Period II when business stayed shut on Fridays & Saturdays Ali and Akbar [25]. For period iii when the business stayed shut on Saturday and Sunday [25]. A general examination is likewise completed for all the working days in a week. Here dummies represent all the days in a week, this would help taking a glimpse at any unusual stock return for any successive working days for the whole period. To test the week of the month effect, author has included each week having complete seven days in a calendar. All the weeks that have five days or less than seven days in a calendar are excluded from the study. Hence this study include each week consist of five working days on which stocks are traded. In this study author has denominated the weeks as W1, W2, W3, and W4 in a month and value of the last day of the week is used as the stock return value of the week. Since weekly impact could be checked independent of the actuality what was the end day in a week for every month subsequently the examination is stretched out sensibly to the whole period from 1991 to Analysis of month wise data present controlled information for the period used in this research subsequently this investigation covers the twenty four years, this information purposed that twenty four observations of monthly closing stocks are available to test the month wise anomaly. Though significance of the investigation for all the days in a week, weeks in a month and months in a year would be tested with the help of T-test. This study has use the log return because subsequent arrangement of log return does not show any pattern. Hence this arrangement of data is stationary and it has zero mean and also has consistent change. In this manner, ordinary least square technique would be utilized to investigate the data and generate true results. R + βij D + εit Where R shows the return calculated by using the formula (ln KSE100t ln KSE100t-1) and D shows a dummy variable indicating days in a week. Least square technique is the key technique that was utilized by the other researchers to investigate the day wise impact in KSE. Anyway their Inadequacy lies in using only one regression to discover impact on all exchanging days of the week. This methodology is possible just on the off chance that we hold an earlier opinion that an impact exists on one particular day, for example, Monday. Though, this condition is not suitable if there is no hopes on which of the Day-of-the- Week Effect may exist. This study would not depend on only one technique to discover the day wise anomaly. Descriptive statistics technique would also be utilized to ascertain the true results Borges [51]. Study has used the following regression line to ascertain the results. Rt =αt + β(mon)t+ β(tue)t+ β(wed)t+ β(thu)t+ β(fri)t+ β(sat)t+ β(sun)t+ μt Where, Rt = Return of KSE 100 Index on the day t, αt = intercept MONt = 1 would be assign to dummy variable if t was Monday TUEt = 1 would be assign to dummy variable if t was Tuesday WEDt = 1 would be assign to dummy variable if t was Wednesday THUt = 1 would be assign to dummy variable if t was Thursday FRIt= 1 would be assign to dummy variable if t was Friday SATt= 1 would be assign to dummy variable if t was Saturday SUNt = 1 would be assign to dummy variable if t was Sunday Rt =αt + β(1st week)t+ β(2nd week)t+ β(3rd week)t+ β(4th week)t+μt\ Where, 1st week = 1 would be assign to dummy variable if t was week 1 2nd week = 1 would be assign to dummy variable if t was week 2 3rd week = 1 would be assign to dummy variable if t was week 3 4th week = 1 would be assign to dummy variable if t was week 4 50

6 Rt =αt + β(january)t+ β(february)t+ β(march)t+ β(april)t+ β(may)t+ β(june)t+ β(july)t+ β(august)t+ β(september)t + β(october)t+ β(november)t+ β(december)t +μt Where, January = 1 would be assign to dummy variable if t was January February = 1 would be assign to dummy variable if t was February March = 1 would be assign to dummy variable if t was March April = 1 would be assign to dummy variable if t was April May = 1 would be assign to dummy variable if t was MAY June = 1 would be assign to dummy variable if t was June and 0 for any other day. July = 1 would be assign to dummy variable if t was July and 0 for any other day. August = 1 would be assign to dummy variable if t was August September = 1 would be assign to dummy variable if t was September October = 1 would be assign to dummy variable if t was October November = 1 would be assign to dummy variable if t was November December = 1 would be assign to dummy variable if t was December Table 1: Ordinary least square period 1 SAT SUN MON Mean Jarque-Bera Probability Sum Sum Sq. Dev Observations TUE WED Mean Jarque-Bera Probability 0 0 Sum Sum Sq. Dev Observations IV. RESULTS AND DISCUSSION As we have divided the daily data into three periods. Period 1 shows the returns from November 1991 to February containing the holiday of Thursday and Friday. Table 4.1 shows the results of period one. Here results derived with the help of OLS shows that all the days shows the insignificancy except the Monday that shows significance and prove there is Monday affect. Ali and Akbar [25] had analyzed the Pakistani stock market from the period of 1992 to 2006, and found that there was positive return for Monday. As here Monday is a third day of week so can say that research shows third day effect. Positive and significant Monday return was also found in other countries. Berument and Kiymaz [39] test the S&P index with the help of OLS during the period of Jan to 1997 October. Study concluded that there was Monday and Wednesday impact for the period of 1973 to Results of the study found that there was significant and positive return on Monday while significant negative impact for the day of Friday was also found. See also Ajayi, et al. [40]. Table 2: Descriptive statistics period 1 Sequence of Days Day # 1 Day # 2 Days Sat Sun Coeff. t- Statistic Prob Day # 3 Mon Day # 4 Tue Day # 5 Wed This investigation shows Saturday, Sunday and Wednesday have negative return. Ali and Akbar [25] also conclude that Saturday have negative return in Pakistani equity market. Evidence for the negative Sunday and Wednesday was also found during analyzing the Pakistani equity market by Ali and Akbar [25]. The above investigation reveals that market begins with negative returns and then goes for recovery with middle day of the week and again goes down at the end of the week. As the period one consist of November 1991 to February 1992 so there are less observations so results can t endorsed full information to make final conclusion. We have also calculated the numerous descriptive statistics for the Karachi stock exchange 100 index for first period. Results of descriptive statistics (Table 4.2) showed that Saturday, Sunday and Wednesday has negative mean return while the Monday and Tuesday have positive return. Ali and Akbar [25] also found positive mean return while testing the descriptive statistics for Pakistani stock market. Here Monday have highest return as compared to any other days. Results of descriptive statistics proved the validity of OLS results. Standard deviation of the Monday (middle day of the week) is greater than all the other days that show return on Monday is more volatile as compared to other days. Jarque-Bera test is significant for all the days that shows return variable is not

7 normally distributed at 1% level of alpha. Second period consist of 1085 observation from March 1992 to February 1997 with the holiday of Friday and Saturday. Results of the second periods are shown in table 4.3.Second period shows that Sunday and Monday have negative significant return. Ali and Akbar [25] investigated the Pakistani stock market and found that Monday s return was negative for second period and also found negative Sunday return in period one. Table : 3 Ordinary least square period 2 Sequence of Days Days Coefficient t- Statistic Prob. - SUN DAY # MON DAY # DAY # 3 TUE DAY # 4 WED DAY # 5 THU Table 4 : Descriptive statistics period 2. DAY 1 DAY 2 DAY 3 SUN MON TUE Mean Std. Dev Jarque-Bera Probability Sum SumSq. Dev Observations DAY 4 DAY 5 WED THU Mean Std. Dev Jarque-Bera Probability 0 0 Sum SumSq. Dev Observations Haroon and Shah [52] analyzed the daily stock return from KSE-100 index and found that there is no impact of days on return in sub period 1 ( ). Sub period 2 found that there was negative impact on Monday [60] but Friday was positive. Tuesday has positive but insignificant result while the last days of the week Wednesday and Thursday has the positive and significant results according to the ordinary least square. Ali and Akbar [25] found positive return for Wednesday. Berument and Kiymaz [39] analyzed the S&P index and found that Wednesday has altered significant result as compared to other days. This situation rejects the null hypothesis that there is same stock return for all the days. In this study Sunday, Monday and Thursday shows significance at 1% level while Wednesday shows significance at 5% level and Tuesday remains insignificant. Results of the second period (table 4.4) represented by the descriptive statistics follow the same pattern shown by the results of OLS technique. Results shows that first two days of the week (Sunday, Monday) have negative return while the middle day (Tuesday) and last two days (Wednesday, Thursday) of the week shows positive return. These results confirm the results of Ali and Akbar [25] for Tuesday, Wednesday and Thursday while testing the descriptive statistics of second period. Jarque- Bera test is significant for all the days at 1% level, which displays return is not normally distributed. Table 5: Ordinary least square period 3 Sequence of Days Name of Days Coef. t-statistic Prob. DAY # 1 MON DAY # 2 TUE DAY # 3 WED DAY # 4 THU DAY # 5 FRI Table 6: Descriptive statistics period 3 DAY 1 DAY 2 DAY 3 MON TUE WED Mean td. Dev Jarque-Bera Probability Sum SumSq. Dev Observations DAY 4 DAY5 THU FRI Mean td. Dev Jarque-Bera Probability 0 0 Sum SumSq. Dev Observations Third period include the more than 4000 observations from the period of March 1997 to May 2014 consist of holidays of Saturday and Sunday. Table 4.5 shows the results of 3rd period. 52

8 In this periods a wide range of observations are included, this category show that all of the days are insignificant, but the Wednesday unveil surplus return that was proved at 1% level of significance. Ali and Akbar [25] analyzed the Pakistani stock market and found Wednesday, Thursday and Friday have positive return. Haroon and Shah [52] investigated days of the week effect by using the data of Karachi stock exchange 100 index and conclude no day wise impact in period one second period show positive Friday and negative Monday. While the Friday is also significant at 10% level of alpha but it does not have more returns as compared to Wednesday return. As the coefficient value of Wednesday is greater than Friday. If we compared the second period Wednesday has positive and significant result in that period also. Ali and Akbar [25] Found Wednesday had positive return in third period. Bayar and Kan [45] analyzed nineteen countries and found higher return on Wednesday (see also Agrawal and Tandon [53]. Balaban [47] that there was high stock return and low standard deviation on Friday tracked by Wednesday, based on Turkish index over 1988 to 1994.Dubois and Louvet [38] Used the indices of nine countries and determined the positive Wednesday and negative Tuesday and Monday effect during the period of 1969 to 1992.As here Wednesday is the third day of the week so research shows middle day effect. Here Monday have negative but insignificant return that was showed significant and negative return in period two Table 7: Ordinary least square whole period results. Days Coefficient t- Statistic Prob. DAY DAY DAY DAY DAY Table 8: Descriptive statistics whole period results. DAY1 DAY2 DAY3 Mean Std. Dev Jarque-Bera Probability Observations DAY4 DAY5 Mean Std. Dev Jarque-Bera Probability 0 0 Observations While Tuesday show positive and insignificant result in both periods. Overall results of both period shows that starting days of the week shows negative returns and days near to holidays shows positive returns, but the third day has highest and more significant return. Results of the third period (table 4.6) showed that Wednesday has inordinate mean return as compared to other days. Results of the descriptive statistics prove that Wednesday (Day 3) has more return as compared to other days [61]. While testing the descriptive statistics of the third period from 1997 to 2006 Ali and Akbar [25] found positive mean return for the Wednesday. Hence it proved that there was third day effect in KSE-100 index. P value of jarque- Bera test is zero for all the days which indicate return is not normally distributed at 1% level of significance. To know the comprehensive results study includes the whole daily data into one model (table 4.7) by assigning the numbers to the days of week. Study assigns the numbers to the working days from Day # 1 to Day 5. As in the first period Saturday is the first working day so author assign the Saturday as Day # 1 and it continued for all the working days of the first period. In the second period Sunday is the first working day so the author assign the Sunday as Day # 1 and continued for the last working day as Day # 5. In the third period first working day is Monday so author defines Monday as Day # 1 for the third period, and continued till the last working days as Day # 5. These results include the data from 11th February 1991 to 28 MAY Whole period results shows that day 1 has negative return and it is significant at 5% level of alpha. Day 2 has positive and significant return at 10% of alpha. Day 3 has highest return and most significant at 1% level as compared to other days, as also founded in the third period of daily return. Ali and Akbar [25] analyzed the days impact and found that day third has positive and significant return. While the Day 4 and Day 5 also has positive return. Ali and Akbar [25] also found that fourth and fifth day has positive return. Whole period results also proved the middle day of the week effect for the Karachi stock exchange 100 index in Pakistan. Table 9: Ordinary least square week wise Variables Coefficient t-stat. Prob. WEEK WEEK WEEK WEEK Table 10: Descriptive statistics week wise. WEEK1 WEEK2 WEEK3 WEEK4 Mean Std. Dev Jarque- Bera Prob Sum SumSq. Dev

9 To test the validity of these results descriptive statistics may be used. (Table 4.8 shows descriptive statistics of whole period. These results include 5469 observation that are enough to check the validity of research. Results of descriptive statistics showed that day 1 has negative return while the all other days have positive return. Mean values shows that day 3 have more mean return as compared to any other day. Probability value of jarque-bera for all the days rejects the null hypothesis at 1% level of significance. To analyze the week wise impact of stock anomalies in Pakistan this study run with specific assumptions. For easy handling of the data this study has divided a month into four week and each week consist of five working days in a week having the recent value of the return that would be used to investigate the week wise impact. Since our investigation for weekend is not influenced by the market correction of holidays and working days sequence consequently the whole information from November 1991 to October 2015 is designed in the same manner. As the stock market in Pakistan remains close on Thursday, Friday for the 1st period, and market remains close for the day of Friday, Saturday in 2nd period, while in third period market remains closed on the day of Saturday and Sunday. Ali and Akbar [25]. Simply we have taken the five days returns without including holidays return. Table 4.9 shows that first three weeks have positive returns. First two weeks shows significant positive return. While the fourth week has negative and insignificant return. Ali and Akbar [25] analyzed the weekly effect of Pakistani stock market and found that first three weeks have positive return while the last week of the month have negative return. Results of Ali and Akbar [25] confirm the results concluded in this study. The value of T-statistics of first week shows the significance at 1% level. Table 11: Ordinary least square month wise. Variable Coefficient Std. Error t- Statistic Prob. JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Weekly results of the descriptive study (table 4.10) shows that all the weeks have positive return except last week of the month.week1 has more return as compared to any other day. 54 While the jarque-bera test shows significant results for all the weeks which accept that return is not normally distributed. To ascertain the monthly effect we regress the data without taking any intercept or the bench mark category. Results (table 4.11) indicate that all the months have positive returns except the month of May and August that has negative returns. P values shows that all the months have no significant returns except the month of May that has significant but negative returns. Patel, Jayen B [57] analyzed the U.S stock market and concluded that there was no January effect in that market. Table 12: Descriptive statistics month wise. Month Mean Std. Dev. Jarque- Bera Prob. Obs. JAN FEB MAR APR MAY JUN JUL AUG SEP OCT NOV DEC Zafar, et al. [54] analyzed the Karachi stock form 1991 to 2007 and found that month of MAY had negative and significant return with the use of OLS technique. Rafique and Shah [55] investigated the share prices of Karachi stock exchange and found that month of MAY, June and August had negative return. According to Rafique and Shah [55]. We have found one significant coefficient ( ) for the dummy Variable of MAY (D5t) which enables us to believe that mean returns Of each month are not equal to each other and thus not equal to zero. This provides evidence for the negative anomaly in returns for the Month of May (May Effect) instead of a January Effect. Result of table 4.12 indicates that all the months have positive mean returns except the month of May and August. Jarque-Bera test shows that all the months is not normally distributed and reject the null hypothesis at 1% level of significance. V. CONCLUSION This study done a complete investigation of the calendar seasonality with the use of Karachi stock exchange hundred index for the period of 1991 to Hence this investigation has research the answer to these questions: (i) whether the starting days of the week have more return or ending days of the week? (ii) Whether the Friday has negative return? To find the answers of above explained questions study have use the descriptive statistics and regression technique. Rafique and Shah [55], Ali and Akbar [25] and Zafar, et al. [54] use the same techniques to analyze the stock anomaly in KSE-100 index. These tests had been used very rarely to analyze the seasonality that s why this study present a complete

10 investigation of the research questions being tested. Moreover, a large number of studies about the anomalies in Pakistan have focused on the daily seasonality in KSE (Zafar, et al. [54], Mustafa and Nishat [49], and Nishat and Mustafa [56]. This section represents the summary of findings of empirical analysis of this study. Generally this study suggests that equity market of Pakistan is not a weak form efficient market. The daily findings of this study suggest that an investor can buy the shares from stock market on first day of the week due to fewer prices on that day, and can sell on the third day of the week due high return on that day in Pakistan. Lakonishok and Maberly [35] said that there may be bad news or any bad roamer behind the negative Monday return. Investors can purchase first day of the week I.e. Monday as it have low price and can sell shares on the third day of week due to highest return on that day. A study established with the help thirty stocks by the Dow Jones Index, Gibbons and Hess [12] also derived the results that Monday had negative return. These results proved that seasonality exist in the stock market of Pakistan. This conclusion is consistent with the results of Ali and Akbar [25] and Zafar, et al. [54]. Weekly results showed that there was high and surplus return on starting week of the month while the last week of the month has negative return, which shows that an investor can buy the stocks at the end of the month and could sell during first week of the month to earn high profit. Monthly analysis shows that return on month of MAY and August was negative and all the other months are positive especially the month of January has highest positive mean return as compared to any other positive month of the year throughout the complete period examined in this research. These results proved that seasonality exist in stock exchange. 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