In recent years the testing of market anomalies in stock returns has become an active field of research in empirical finance and has been receiving attention not only from academic journals but also from the financial press as well. Among the more well-known anomalies are the size effect, the January effect and the day-of-the week effect. According to this phenomenon, the average daily return of the market is not the same for all days of the week, as we would expect on the basis of the efficient market theory. The objective of this paper is to examine the existence of day of week effect in Indian stock market.
Daily closing prices of S&P CNX Nifty index have been analyzed over fifteen years period commencing from January 1994 to December 2008. A set of parametric and non parametric tests has been used to test the equality of mean returns and standard deviations of the returns. The mean returns on Monday and Tuesday are negative while on Wednesday these are highly positive. Also, the impact of introduction of rolling settlement on the stock returns is observed. The results show that before rolling settlement came in 2001, Tuesday was showing highly negative returns and Wednesday highly positive.
But after the introduction of rolling settlement, the seasonality in the distribution of the mean returns across different days of the week ceased to appear. Thus the markets have become more efficient over a period of time. KEY WORDS: Market Efficiency, Calendar Anomalies and Day-of-the-Week Effect INTRODUCTION A Stock Exchange is a common platform where buyers and sellers come together to transact in securities. It may be a physical entity where brokers trade on a physical trading floor via an “open outcry” system or a virtual environment.
The Stock Exchange, Mumbai (BSE) and the National Stock Exchange (NSE) are the India’s two leading stock exchanges. Indian security market is one of the oldest markets in Asia. It has come a long way from earlier days of floor trading to the present day screen and net based trading. This study is an attempt to have a deeper insight in to the behaviour and patterns of stock price distribution in the Indian stock market. The price of a security should vibrate around its intrinsic worth in any efficient market.
In finance, the efficient-market hypothesis (EMH) asserts that financial markets are “informationally efficient”, or that prices on traded assets, e. g. , stocks, bonds, or property, already reflect all known information. The efficient-market hypothesis states that it is impossible to consistently outperform the market by using any information that the market already knows, except through luck. Therefore, the past price movements can in no way help in speculating the prices in future. The price of each day is independent. It may be unchanged, higher or lower from he previous price, but depends upon new pieces of information being received each day. So seasonalities cannot be used to formulate trading strategies to earn abnormal returns according to efficient market hypothesis theory. Calendar anomalies are cyclical anomalies in returns, where the cycle is based on the calendar. It describes the tendency of stocks to perform differently at different times. For example, a number of researchers have documented that historically, returns tend to be higher in January compared to other months (especially February).
There are three types of efficiencies as explained in efficient market hypothesis. So calendar anomalies mainly explain weak form of efficiency which says that previous price changes or changes in return are useless in predicting future price or return changes. Some of the calendar anomalies are Month-of-the year effect, Month-of-the quarter effect, Week-of-the month effect, Day-of-the-week effect or Weekend effect, Monday effect, Hour-of-the-day effect or the End of the-day effect, holiday effect and turn of the month effect etc. Among them the day-of-the-week effect is most widely documented across the countries and markets.
In context to stock market the majority of research findings, indicates that the stock returns remain low or negative on Monday. This paper examines the day-of-the-week effect in Indian stock market, using S;P CNX Nifty data of last fifteen years from January 1994 to December 2008. REVIEW OF LITERATURE There is an extensive literature on the day-of-the-week effect in the stock returns. This section examines a few research works on the day of the week effect in Indian and international stock markets. Ziemba (1993) investigated the weekend hypothesis for the Japanese market using daily data from 1949 to 1988.
Tuesday recorded negative returns following a one day weekend and Mondays declined after two days weekends. Balaban (1994) found day of the week effect in an emerging stock market ISECI of a developing country Turkey for the period 1988 to 1994. Highest returns on Friday and lowest returns on Tuesday were observed. Mishra (1999) studied day of the week effect in Indian stock market using Sensex and Natex for the period 1986 to 1998 indicating the presence of day of the week effect in Indian stock market. Friday returns were found highest and significantly different from the mean returns of other days. Hence there exists a Friday effect.
Berument and Halil Kiymaz (2001) tested the presence of the day of the week effect on stock market volatility by using the S;P 500 market index during the period of January 1973 and October 1997. The findings showed that the day of the week effect is present in both volatility and return equations. While the highest and lowest returns were observed on Wednesday and Monday, the highest and the lowest volatility were observed on Friday and Wednesday, respectively. Further investigation of sub-periods reinforced findings that the volatility pattern across the days of the week was statistically different.
Sarma (2004) examined seasonality across the days of week in Indian stock market using BSE indices- SENSEX, NATEX and BSE 200. Highest variance on Monday was found and weekend effect was confirmed by this study. Nath and Dalvi (2004) examined the day of the week anomaly in Indian stock market for the period from 1999 to 2003 using index S;P CNX NIFTY data. The study found that before introduction of rolling settlement in January 2002, Monday and Friday were significant days. However after the introduction of the rolling settlement, Friday became significant. Mondays were found to have higher standard deviations followed by Fridays.
Davidsson (2006) found evidence of day of week effect in S;P 500 index. Davidsson found Wednesday was the weekday with highest rate of return and Monday was weekday with lowest rate of return. Also Monday was the only day with negative rate of return. Wednesday’s returns were found approximately four times of Monday’s returns. Badhani (2008) examined the presence of day-of-the-week effect on stock returns, trading volume and price volatility at the NSE during the period of 10 years from 1995-2005. Wednesday effect was found during earlier weekly settlement regime which now disappeared.
Monday and Tuesday returns were consistently low but during recent sub period these were not significantly different from other days of week. Also on Monday the average trading volume was significantly low and price volatility was high consistently across the entire sample period. Mangala (2008) examined day-of-the-week effect in sub periods in Indian stock market using S;P CNX Nifty data. Highest returns on Wednesday and lowest on Tuesday were observed. Also findings showed that seasonality in return distribution across weekdays was confined to pre rolling settlement time period; thereafter seasonality vanished.
DATA AND METHODOLOGY This study covers a sample period of fifteen years from January 1, 1994 to December 31, 2008 comprising a total of 3695 observations(days). The stock prices are represented by S;P CNX Nifty index. The closing values of this index have been obtained from the official website of National Stock Exchange (www. nseindia. com). There was trading on certain weekly closing days (i. e. 18 Saturdays and 3 Sundays); these days have been excluded from the sample. During the above sample period of fifteen years many structural changes also took place in the market.
For example rolling settlement was introduced in place of weekly settlement system. Therefore, the behaviour of stock prices has been studied on an yearly basis so as to gauge the impact of these changes on the stock prices. Measuring the Daily Returns Daily percent return on the index for a given day of the week has been calculated by subtracting the closing price of the previous trading day from closing price of that day, then dividing the resulting no. by closing price as on the previous trading day and multiplying by 100. Rt = Pt-Pt-1 * 100 Pt-1 Rt is daily return on the share price index for day t
Pt is the closing value of index for the day‘t’ and Pt-1 is the closing value of the index for the preceding day. Hypothesis and Testing Procedure The null hypothesis is that there are no differences in the mean daily returns across the weekdays. The non parametric Kruskall- Wallis (H) test has been applied to test seasonality in returns across weekdays to test the hypothesis. Null hypothesis is: – Ho: µ1= µ2= µ3= µ4= µ5 Here, µ1, µ2…µ5 represent mean returns of different trading days of week. It means that mean returns across all the five days of week are equal. Alternative hypothesis is: – H1: µ1? µ2? µ3? µ4? µ5
It implies that there is significant difference in mean returns across the trading days in a week. Different statistical tools have been used to find the results like mean, standard deviation, range, skewness ; kurtosis etc. Then the most scientific and logical non-parametric Kruskall-Wallis (H) test has been applied to check the hypothesis. The Kruskall Wallis test requires the entire set of observations being ranked – higher the value, higher is the rank and vice-versa- then arranged into nj ? 5 matrix where nj represents the rank of the return and columns represent the day of the week (Monday through Friday).
The value of H is calculated by formula: |H |= |12 |( |[pic] |(Rj)2 |) | — |3(N+1) | | | |[pic] | | |[pic] | | | | | | |N(N+1) | | |nj | | | | | | | | | | | | | | Where: Rj= sum of ranks in the jth column nj = number of cases in the jth column N = sum of observations in all the columns The calculated H value has been compared with the table value of the chi-square(? 2) distribution with (k-1) degree of freedom, where k stands for the number of trading days in a week.
Hence H0 is rejected if H;gt; ? 2 H0 is accepted if H;lt; ? 2 The value of H in our study is taken as the critical value at 1% as well as 5% level of significance. Further Dunn’s multiple pair comparison test based on rank matrix built in K-W test has been used to find seasonality by a pair wise multiple comparison procedure. It identifies whether particular day of the week differs from other days of the week. The test procedure relies on Kruskall-Wallis rank sum Rj. The data in the rank-day matrix prepared for ‘H’ test is used for this purpose. For a given level of ? decide ? µ ? ? if |Ru-Rv| ? Z [? /k(k-1)] [N(N+1)/12]1/2 [1/nµ + 1/nv]1/2 Where, µ = 1, 2……k-1 v= +1,……. k k = 5 N = total number of observations nµ = corresponding number of observations in the uth column nv = corresponding number of observations in the vth column Ru = Average K-W rank sums in the uth columns of the rank matrix Rv = Average K-W rank sums in vth columns of the rank matrix Z[? /k(k-1)] = the upper percentage point of the unit normal distribution for a given significance level for 99 percent confidence level is 2. 575 Further the returns have been analyzed for two sub-periods i. e.
Sub period-1 before rolling settlement (weekly settlement period) ; sub period-2 after the rolling settlement was introduced. In weekly settlement time period, Tuesday used to be as the settlement day on NSE. In 2001, rolling settlement was introduced which shifted settlement cycle from a fixed day of the week to fixed settlement lag. Tuesday settlement might be the possible reason for the observed seasonality in stock returns. DATA ANALYSIS Here the day of the week pattern of the S;P CNX Nifty data from January 1994 to December 2008 has been tested, results of which have been depicted in Table 1.
It is observed from the table that the mean returns on Monday i. e. -0. 08563 percent are minimum followed by Tuesday. Mean returns on Wednesday, Thursday and Friday are positive out of which Wednesday’s return with 0. 303 percent is maximum across all the days of the week. The mean return on Wednesday is about 8 times the overall mean return. The variation in mean returns measured in terms of standard deviation is found maximum on Monday (1. 870303 percent) followed by Friday (1. 740897 percent). It shows that trading on week start and week end is more volatile than other days of week.
Skewness is positive only on Wednesday while other days of week have negatively skewed distributions. Kurtosis tells us the extent to which a distribution is peaked or flat topped when compared with a normal curve. The return distribution on Monday, Tuesday and Friday is leptokurtic while on Wednesday and Thursday are platykurtic. Through table it is also observed that range on Monday is highest which is also a measure of Dispersion. There is a significant difference in mean returns across different the different days of the week as evident by K-W (H) statistics (21. 78) which is highly significant at 1 percent level of significance. Therefore the null hypothesis of equality of mean returns across various days of the week stands rejected. |Table 1. Summary Statistics of Daily Stock Returns of S;P CNX Nifty(Jan 1994-Dec. 2008) | | |Monday |Tuesday |Wednesday |Thursday |Friday |All Days | |Mean |-0. 08563 |-0. 07615 |0. 30300 |0. 1895 |0. 03221 |0. 03838 | |Standard Deviation |1. 87030 |1. 50858 |1. 62655 |1. 55153 |1. 74090 |1. 66944 | |Skewness |-0. 71612 |-0. 15909 |0. 40400 |-0. 05609 |-0. 35999 |-0. 24662 | |Kurtosis |4. 29741 |4. 47636 |1. 79652 |1. 53957 |5. 66062 |3. 98682 | |Range |7. 54838 |8. 29523 |7. 9590 |6. 30507 |7. 83089 |20. 53297 | |No. of Observations |741 |742 |740 |744 |728 |3695 | |K – W(H) Statistics 21. 278* | * Significant at 1 percent level for 5-1 degrees of freedom Table 2 represents actual and expected multiple comparison values as per Dunn’s multiple pair comparison test to study pair wise comparison among different days of the week. This test is based on rank matrix built in Kruskall Wallis Test.
The calculation of actual and expected values is shown in table 3 while the deviation of actual from expected ranks is shown in table 3. So it is observed from the table 3 that there is inequality in Monday – Wednesday, Tuesday – Wednesday, Wednesday – Thursday and Wednesday – Friday pairs as these are showing positive deviation of absolute rank sum values from the corresponding Z value or expected value. It means these pairs are showing more inequality in returns than expected and Tuesday – Wednesday is showing highest positive deviation. Also it is observed from the table that Wednesday appears in all above pairs.
It means Wednesday returns are significantly different from the other days of week. Wednesday is showing highly different mean returns from rest of the days. So a trading strategy of buying on Tuesday and selling on Wednesday may help an investor to earn abnormal returns. |Table 2. Actual and Expected Multiple Comparison Values | | | | |Actual |Expected | | ||RU ?
Rv| |Z |[N(N+1)/12]1/2 |(1/nu+1/nv)1/2 |Z[N(N+1)/12]1/2 (1/nu+1/nv)1/2 | |Monday-Tuesday |40. 64 |2. 575 |1066. 799 |0. 0519 |142. 6521 | |Monday-Wednesday |197. 07 |2. 575 |1066. 799 |0. 0520 |142. 7620 | |Monday-Thursday |30. 38 |2. 575 |1066. 799 |0. 0519 |142. 5697 | |Monday-Friday |50. 24 |2. 75 |1066. 799 |0. 0522 |143. 3388 | |Tuesday-Wednesday |237. 71 |2. 575 |1066. 799 |0. 0520 |142. 7070 | |Tuesday-Thursday |71. 02 |2. 575 |1066. 799 |0. 0519 |142. 5147 | |Tuesday-Friday |90. 88 |2. 575 |1066. 799 |0. 0522 |143. 3114 | |Wednesday-Thursday |166. 69 |2. 575 |1066. 99 |0. 0519 |142. 6246 | |Wednesday-Friday |146. 83 |2. 575 |1066. 799 |0. 0522 |143. 3938 | |Thursday-Friday |19. 86 |2. 575 |1066. 799 |0. 0521 |143. 2015 | |Table 3. Deviation of Actual from Expected Rank Differences | |Monday-Tuesday |-102. 12 | | | |Monday-Wednesday |54. 308 | | | |Monday-Thursday |-112. 190 | | | |Monday-Friday |-93. 099 | | | |Tuesday-Wednesday |95. 03 | | | |Tuesday-Thursday |-71. 495 | | | |Tuesday-Friday |-52. 431 | | | |Wednesday-Thursday |24. 065 | | | |Wednesday-Friday |3. 436 | | | |Thursday-Friday |-123. 41 | | | Table 4 represents the yearly distribution of mean returns on S;P CNX Nifty for different days of the week from 1994 to 2008. Also to test whether these differences in the mean returns on different days are statistically significant or not, the non parametric ‘H’ statistics has been used. The table value of the chi-square (? 2) distribution at 1 percent level of significance is 13. 277 and at 5 percent level of significance is 9. 488. If we look at year wise KW statistics, up to year 1999 ‘H’ statistics is highly significant and after 1999 it is insignificant. |Table 4.
Yearly Distribution of Mean Returns on S;P CNX Nifty by Day-of-the-Week | |(January 1994 – December 2008) | | | | | |Year/Day |Monday |Tuesday |Wednesday |Thursday |Friday |KW Statistics | |1994 |0. 47012 |-0. 16573 |-0. 36687 |0. 01075 |0. 32745 |9. 945** | |1995 |-0. 51580 |-0. 33583 |0. 25709 |-0. 6627 |0. 11756 |11. 145** | |1996 |-0. 35599 |-0. 35342 |0. 53600 |0. 18662 |0. 07796 |10. 114** | |1997 |-0. 46253 |-0. 14396 |1. 04706 |-0. 16222 |-0. 06761 |19. 917* | |1998 |-0. 12914 |-0. 52606 |0. 78280 |-0. 15417 |-0. 22507 |13. 245** | |1999 |-0. 00553 |0. 07532 |0. 98097 |0. 10327 |-0. 00305 |14. 48* | |2000 |-0. 16997 |-0. 28629 |0. 49777 |-0. 10239 |-0. 16992 |4. 989 | |2001 |-0. 21325 |0. 11775 |0. 30553 |0. 08010 |-0. 60214 |4. 987 | |2002 |0. 00508 |-0. 15830 |-0. 05939 |0. 07054 |0. 22584 |4. 226 | |2003 |0. 15214 |0. 13598 |0. 26208 |0. 13987 |0. 38014 |2. 323 | |2004 |-0. 4126 |0. 26824 |0. 04482 |0. 02138 |0. 07889 |1. 236 | |2005 |0. 29696 |0. 04875 |0. 02291 |0. 08195 |0. 18711 |1. 806 | |2006 |-0. 09098 |0. 01140 |0. 22203 |0. 22753 |0. 33653 |1. 198 | |2007 |0. 24310 |0. 32425 |0. 02874 |0. 30801 |0. 02442 |2. 139 | |2008 |-0. 36369 |-0. 13064 |-0. 04547 |-0. 5441 |-0. 24632 |1. 46 | | All Years |-0. 08563 |-0. 07615 |0. 30300 |0. 01895 |0. 03221 |21. 278* | | | | | | | | | |*Significant at 1% level | | | |**Significant at 5% level | | |
Further entire study period has been divided into two sub periods: Period 1 (January 1994 to Decemeber 2001) and period 2 (January 2002 to December 2008). Period 1 represents the time when weekly settlement was operational and during this time frame NSE had fixed settlement day – Tuesday. Period 2 represents the time period when rolling settlement was introduced in place of weekly settlement cycle. | | | | | | | | |Table 5.
Mean Daily returns on S;P CNX Nifty by Day of the Week for Sub-Periods | | |Monday |Tuesday |Wednesday |Thursday |Friday |KW Statistics | |Subperiod-1 |-0. 17276 |-0. 20228 |0. 50504 |-0. 01304 |-0. 06810 |42. 752* | |Subperiod-2 |0. 00197 |0. 05294 |0. 09734 |0. 03923 |0. 12735 |2. 84 | | | | | | | | | | | |*Significant at 1% level | | | It is analyzed from the above table that in sub period 1 (1994 to 2001) all days except Wednesday gives negative rate of return. This is clearly the impact of Tuesday settlement that returns on Tuesday are lowest and on Wednesday it is highest positive. It means beginning of settlement cycle ives maximum returns while last day of settlement cycle called settlement day gives lowest returns. Also a very high value of KW statistics i. e. 42. 752 represents a high degree of seasonality in sub period 1 (before rolling settlement time period). To bring more frequency in the transactions and to bring Indian markets at par with the international markets rolling settlement on T+5 basis was introduced in December 2001. So in sub period 2 when rolling settlement was introduced, returns on all the days have become positive and Friday is giving maximum returns and Monday is giving lowest returns.
This hints towards the presence of some sort of weekend seasonality. But the value of ‘H’ statistics is very low i. e. 2. 684. From this it can be inferred that the return distributions are not significantly different across the week days and the null hypothesis stands rejected in the sub period 2. Thus it may be concluded that with the introduction of rolling settlement on NSE the stock markets have become more efficient. CONCLUSION During the period 1994 to 2008, S;P CNX Nifty index recorded highest positive returns on Wednesday and most negative returns on Monday with highest volatility on Monday and Friday.
It means week start and week end tend to be more volatile in Indian stock market. Also it has been analyzed that Wednesday is giving significantly higher returns than other days of the week which points towards the existence of Wednesday effect in Indian stock market. There was presence of day of the week effect in pre-rolling settlement period which gradually phased away with the introduction of the rolling settlement. Markets have become efficient after rolling settlement has been introduced.
So in present scenario we can’t rely on a trading strategy formulated on the basis of historical return movements on different days to earn abnormal returns as seasonality has disappeared in the recent years of the study period.
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