Declaration of originality
The capital market efficiency is one of the most explored areas of interest in finance. Capital markets are believed to be informationally efficient. Market efficiency is a term, which is used to define the relation between share price and available information in the capital market. The market efficiency concept had been expected hopefully by Bachelier in 1990 in his dissertation. But this concept was brought in the literature of financial economics by Fama. Fama(1970 and 1991) defines market efficiency and on the basis of efficiency categorized it into three forms:
Ø The Weak Form: in this form current prices completely speculate all information held in historical prices, which means that no investor can prepare a trading pattern based on past price figures to earn trading profit.
Ø The Semi-Strong Form: a market is said to be semi strong efficient if that market is efficient enough to for prices to reflect all publically available information.
Ø The Strong Form: a market is having a strong form if current prices reflect all public as well as non-public information.
There are strong empirical evidences have been found by researchers which defend Efficient Market Hypothesis (EMH) and proof that while reacting on a revealing of a new information , no investor can gain abnormal returns. This is grounded on the assumption that disclosure of any new information is accessible to all investors equally and comprised into stock prices without any delay.
Three main assumptions of Efficient Market Hypothesis are:
All investors have cost-less access to currently available information about the future.
They are good analysts; and
They pay close attention to the market process and adjust their holdings appropriately.
Complying with Fama (1970), there were a so many studies took to test Efficient Market Hypothesis and these tests shown the random behaviour of stock prices and also shown that information of past stock prices can’t predict the future prices.
On the other hand, despite of strong proofs defending the efficient market mechanism, there are some cases seen, in past, when these price information helps the investors to gain abnormal returns by showing some patterns in stock price market. Numbers of studies have been persuaded to testify that inefficiency in markets does exist. Some researches prove that stock prices shows kind of anomalous behaviour, which appears to be incompatible to Efficient Market Hypothesis. These empirical studies and researches highlighting various anomalies, related to capital market efficiency, and keyed out some parameters as
the low P/E effect
the small firm and neglected firm effects
market over-reaction and under-reaction
the monthly effect
day of the week effect
the continuity of technical analysis.
These parameters have some prognostic power to site patterns in stock price trends and helps investors to earn extra returns. As indicated above, previous researches have been pointed out various anomalies but study under consideration moves around two basic anomalies monthly effect and day of the week effect. Turn of the week, month, year and holidays are accounted to have systematically returned extra equity returns in developed capital markets and are known as calendar or seasonal anomalies.
Ø The January Effect: This is one of the most researched effects in stock market and it was explored by many researchers. They investigate that, as compared to other months, January has a highest return. This was first observed on US stock market by Rozeff and Kinney (1976). After that January effect detected for other countries capital markets by researchers like Chang and Pinegar (1986) and Gultekin (1983).
Ø The Day-of-The-Week Effect: This effect mentions that stock returns are dependent on the day of week. An anomaly, named Monday effect, in daily stock prices intimates that as compared to other days stocks returns are mostly either negative or lower on Monday. This effect has been widely studied in international markets by French (1980), Kamara (1997), Lakonishok and Smidt (1988), Gibbons and Hess (1981) and Lakonishok and Levi (1982).
The analysing for stock market anomalies has turn to dynamic field of research in empirical finance. The day of the week effect is a form of anomaly and according to this the normal daily return is not equal for all days of week. This anomaly shows a detectable trend or pattern of stock returns on some particular day(s) of week, which means stock returns adopt a cyclic pattern and contradicts to a weak form of efficiency.
It was Field (1931) who introduced the day of the week effect in stock market, and found that this effect particularly depends on two days the last trading day (Friday) and the first trading day (Monday), positive returns can be seen on Friday and zero or negative returns on Monday. Many researchers did this study on various countries stock markets like USA, Malaysia, Hong Kong, Turkey and Canada. For western countries (USA, UK and Canada) researchers found that on Mondays the market shows negative returns whereas, on Fridays it gives positive returns. Studies on capital markets of countries France, Japan, Australia, and Turkey shows the highest negative returns on Tuesdays instead of Monday. The most acceptable reason for occurrence of negative returns on Mondays is that the most of unfavourable news comes out on weekends which influence bulk of investors negatively and making them to sell on Monday. The explanation for Tuesday’s negative returns is that the unfavourable news affecting the USA market also act negatively on other countries markets behind by one day.
PURPOSE OF STUDY
Calendar or seasonal anomalies are not only well analysed area of capital markets but also are the best examples of financial market’s inefficiencies. It can be a seasonal effect over a particular month, day or even over specific years. In recent years, there are many empirical evidences of calendar anomalies in USA markets and many more developed countries but there are a few studies on under developed or developing countries specially emerging Asian markets. This study is tried to fill this gap of analysing anomalous behaviour in Indian stock market.
The sole motive of this study is to investigate the presence of the day-of-the-week effect or weekend effect and January effect in Indian stock exchange (on the basis of analysing two main indices BSE SENSEX and NSE NIFTY) over the time span January 1995 to March 2009. Further in this study time span divided into two parts, first January 1995 to December 2001, time period before Rolling Settlement, and second January 2002 to March 2009, time-period after Rolling Settlement. So this study will also analyse the consequences of Rolling Settlement on anomalous behaviour of Indian stock exchange.
OBJECTIVE OF STUDY
This study concentrates on seasonal anomalies in stock market especially, monthly effect and day of the week effect. By analysing non-random pattern of stock returns, the presence of anomalous behaviour can be found out. Particularly, the present study means to achieve the following objectives:
To key out anomalous pattern in the returns of stock indices over the different trading days in a week.
To identify the non-random pattern of stock returns for all months of the year.
Has there any effect of compulsory the rolling settlement on anomalous pattern of stock returns, if yes, what are those effects?
There is large amount of literature accessible to make investors questioning and unbelieving to efficient market theory and many analyses have been accomplished to determine the anomalies in stock market. Some of the most discussed anomalies by researchers are seasonal anomalies and calendar effects. These anomalies have different market returns depends upon distinct time periods like specific day(s) of week, turn of the year or a month and a specific month of year. The most common calendar anomaly is January effect. It is one of the most debated topics that in a specific month the stock market returns are different to a considerable degree as compared to returns on other months of year. This breaches the EMH theory, developed by Eugene Fama (1960). The days of week is also one of the most researched and interesting area in financial literature. The day of week effect was first noticed in 1931 by Fields. Field detected this effect on US stock market and found that Friday and Monday are two days which systematically showing positive and negative returns respectively.
After Field, in 1965 Fama analysed that variance of returns on Monday is 20% more than the returns on other days of week. Afterward in 1980’s this effect once again researched by French (1980), which pursued by Gibbons and Hess (1981), Lakonishok and Levi (1982), Gultekin and Gultekin (1983), Keim and Stambagh (1984), Theobald and Price (1984), Jaffe and Westerfield (1985), Santesmases (1986), Board and Sutcliffe (1988) and Lakonishok and Smidt (1988). This anomaly got more attention when Jaffe and Westerfield, 1985;Peiro, 1994; Agarwal and Tandon, 1994 found out the similar seasonality effects on stock markets of many other countries.
As stated by Haugen and Jorion (1996), "The January effect is, perhaps the best-known example of anomalous behaviour in security markets throughout the world”. Panday (2000) analysed EMAS index of KualaLumpur stock market and found that for December and February average returns are significantly different from another months. Which depicts presence of seasonality in market, thus the Malaysian stock market is informational effective. The presence of seasonality in Istanbul stock market is also probed by Oguzsoy and Guven (2003) and they noticed that returns on Tuesday were making low peak whereas returns on Friday were high. Many researchers found that the day of week effect was commonly effected the US and UK stock markets, but no one knew that whether European market also affected by this anomaly or not? To found this, in 2004, Ajayi, Mehdian, and Perry studied Eastern European Emerging stock Markets (EEEMs) and proved that six of the EEEMs showed returns on Monday were negative (out of which only two markets were statistically significant) and left five markets showed positive returns on Monday (out of which one was statistically significant). This study supplies no proof which shows any specific daily pattern in returns of EEEM stock markets.
Most of the studies, Cross (1973), Gibbons & Hess (1981), Keim & Stambaugh (1984), Theobald and Price (1984), Jaffe & Westerfield (1985), Harris (1986), Simrlock & Starts (1986), Board and Sutcliffe (1988), and Kohers and Kohers (1995), Tang and Kwok (1997) for six indices [Dow Jones Industrial Average Index( US), Financial Times Index (UK), Nikkei Average Index (Japan), Hang Seng Index (Hong Kong) were based on analyses in already developed countries like USA, UK and Canada, concluded that these stock markets have remarkable negative Monday returns and positive Friday returns. Otherwise stated, stock market begins from lower peak and ends to upper peak.
Whereas, many other researchers studied on other countries’ stock markets such as O’Hanlon & Ward (1987), Solnik & Bousqet (1990) studied the stock exchange of France, Athanassakos & Robinson (1994) in the Canadian stock exchange, Jaffe & Westerfield (1985) investigate the stock exchanges of Australia and Japan, Kim (1988) analyse Japanese and Korean stock markets, Aggarwal & Rivoli (1989) studies stock markets of four countries Hong Kong, Singapore, Malaysia and Philippines, Ho (1990) in the stock markets of Australia, Hong Kong, Japan, Korea, Malaysia, New Zealand, Philippines, Singapore, Taiwan and Thailand, Wong, Hui and Chan (1992) analyse the market returns of Singapore, Malaysia, Hong Kong and Thailand, Dubois & Louvet (1996) investigate the stock exchanges of Japan, Australia, Agrawal and Tandon (1994) for eighteen countries and many others, all of them detected the Tuesday’s average returns negative. According to Aydooan (1994), Balaban (1995) and Bildik (1997), there is a presence of seasonality anomaly in Istanbul stock market as they found Tuesday’s average returns were negative. Contrastive to these studies Santemases (1986), Pena (1995) and Gardeazabal and Regulez (2002) found that there is no week day effect present in Spanish stock exchange. Solnik and Bousquet (1990) found retained negative Tuesday returns, while their study, on period 1978-1987, related to CAC index of Paris stock market. The week day effect on French stock market (along with US, UK, Australia, and Swiss markets) was re- examined by Dubois and Louvet (1996), they used statistical approaches and noticed that, except Australian market, Wednesday showed the highest return whereas Monday showed negative or lowest returns. Since last three decades, seasonal anomalies are well analysed for different countries’ stock exchanges. Lindley et al. (2004) studied that for many years, in between 1962-2000, did not have calendar anomaly and they also noticed that many years had negative returns on January month.
In 1931, Fields was the first who studied US stock exchange and discovered Monday effect. Cross (1973) studied S&P 500 index over 17 years period and found the week day effect and conclude that Friday has higher average returns as compared to Monday. The similar conclusions were found by French (1980) in his studies.
Weekday effect was also studied by Haris (1986) on different international stock exchanges and his study supported the existence of negative average returns on Monday as compared to other days of week. Board and Sutcliffe (1988) found no anomalous behaviour in UK stock market for a specific period of time. Wickremasinghe (2007) reported that there is no significant difference in average returns for weekdays on analysing Colombo Stock Exchange (CSE).
There is number of studies in finance literature available, which gives evidence in defend of presence of anomalous patterns in stock exchange and this makes investors disbelieving in efficient market hypothesis.The first contradiction to EMH noticed by Fields (1931) when he was discovered Monday effect in the US stock exchange. Later in 1985, Jaffe and Westerfield (1985) looked into the day of week effect in stock exchanges of four different countries i.e., Australian, Canadian, Japanese, and UK and observed the weekday effect in Japanese and Australian markets and reports same evidences. Dyl and Maberly (1986), Gay and Kim (1987) and Flannery and Protopapadakis (1988) documented that these anomalies not only found out on stock markets but also in US Treasury bills and future markets too. Rozeff and Kinney (1976) studied New York Stock Exchange and give documented proofs that in January mean returns were 3.5% in comparison of other months for time-period 1904-1974. Furthermore, Keim (1983) evidenced that for the small firms half of the abnormal returns took place in January and rest half arrived on first five trading days. Balaban (1995) studied the calendar anomalies on Turkish stock market and analysed that the three months which had abnormal returns were January, June and September, where January showed combined return of 22 %, almost four times more than global return while considering a full year. Balaban also documented that presence of seasonal anomalies is international issue.
Many empirical studies supply evidence of calendar and seasonal anomalies in capital exchanges but every study shows different type and pattern of anomalies. Rozeff and Kinney (1976) investigate the New York Stock Exchange over the period 1904-1974 and detected existence of January effect in market. French (1980) examined US market’s everyday returns over the time-period 1953-1977. French also documented that market showed negative Monday returns and returns on other days were positive. Lakonishok and Smidt (1988) and Cadsby (1989) found out turn of the month anomaly for US stock market and Canada stock exchange respectively. Ogden (1990) examined US stock exchange for period 1969-1986 and documented the turn of the month effects. Aggarwal and Tandon (1994) studied 18 countries’ stock market and noticed that nine countries were affected negative returns on Monday and eight countries by negative mean returns on Tuesday whereas, 17 countries showed abnormal or positive returns happened on Friday. Duobis & Louvel (1996) probed the weekday effect in US, UK, German, Japanese, Australian and French stock exchange and also analysed that highly positive returns occurred on Wednesday whereas, lowest or negative returns always happened on Monday. Balaban and Bulu (1996) investigate the Turkish stock exchange and found non existence of semi-monthly effects. According to studies of Steeley (2001), the day of the week effect totally vanished in 1990s from the UK stock market. Tang and Kwok (1997) looked into six indicies and found that Monday had negative average returns and Friday had positive returns. Lian (2002) considered Asia Pacific capital markets and detect monthly effect. Hellstorm (2002) analysed the calendar anomaly on the Swedish stock securities for the time period 1987-96. According to Pandey (2002), Malaysian stock exchange had seasonal trend in two indices EMAS index and Composite index and found that returns of December was highly positive as compared to other months of the year. Al-Saad (2004) studied Kuwati Stock Exchange detected the seasonality anomaly in month of July and explained it by the effect of summer holidays.
Wachtel (1942) and Rozeff and Kinney (1976) investigate seasonal anomaly in the US markets and documented that January returns were statistically higher in comparison of other months. Keim (1983) also studied US stock market and found size and seasonal effects on returns. Keim pointed that, in the month of January, returns of small firm stock prices were statistically more than the returns of large firm stock prices. Keim explained this effect by ‘tax-loss-selling’ hypothesis. Reinganum (1983) got same conclusions, but he obtained that all seasonality effect could not be define by the tax-loss-selling hypothesis. Smirlock and Starks (1986) tested the day of the week effect in US stock exchange. The anomalous behaviour of stock returns has been studied on many developed countries such as seasonal anomaly detected on Australia (Officer, 1975; Keim, Kleidon and Marsh, 1983), Canada (Berges, McConnell, and Schlarbaum, 1984; Tinic, Barone-Adesi and West, 1990), UK (Lewis, 1989) and Japan (Aggarwal, Rao and Hiraki, 1990). Boudreaux (1995) described the existence of end of month effect in Denmark, Germany and Norway exchanges.
The end month of the year i.e. December is consider as the tax month in US and many other countries. Some researchers debated that in order to cut down there tax investors sell their shares at low values and this makes a high downward force on stock prices and results to negative or low returns. In January, as the tax year ends investors starts purchasing stocks and prices shows upward trend which makes high returns in starting of the year. Many studies also proved that the ‘January effect’ and the ‘year-end effect’ in stock exchanges are governed with ‘tax-loss selling’ hypothesis. However Reinganum (1983) documented that the entire seasonal anomalies could not be explicate by tax-loss-selling hypothesis. Smirlock and Starks (1986) and Ariel (1987) studied US stock exchange and documented the week day effect and intra-month effects respectively. Gultekin and Gultekin (1983) studied 17 industrial countries stock markets having distinct tax laws and found the presence of January effect. Raj and Thurston (1994) looked into the NZ stock returns and found that this exchange is not affected by anomalous behaviour of January and April months. Brown and Luo (2004) investigated the data from New York Stock Exchange over the period 1941-2002 and evidenced that returns of January month can predict the returns of next 12 months.
There are many empirical evidences available on seasonal anomalies in developed countries, but these studies are very rare on emerging markets or under developed countries. Maghyereh (2003) investigated Amman Stock Exchange (ASE) of country Jordan by using the method of standard GARCH, exponential GARCH (EGARCH) and the GJR and proved the non-existence of seasonal anomaly. Alagidede and Panagiotidis (2006) studied Ghana stock returns and found both monthly effect and weekend effect but instead of January effect they found April as month giving high returns. Doran et al.(2008.) investigated data from Chinese stock returns and evidenced that instead of January, Chinese stock returns are highly positive at turn of the Chinese new year.
The existence of the day of the week and January effect has been studied mainly on USA stock market. Whereas these anomalous behaviour have not been researched in a widespread way onemerging capital markets.The studies of seasonality anomalies on Asian stock exchanges are amazingly low. Chan, Gup, and Pan (1992), investigated some major Asian markets and US market and evidenced that these markets not weak form efficient markets. Dickinson and Muragu (1994) analysed the small stock exchange, Nairobi Stock Exchange, and found the empirical evidence which shows weak- form efficiency in market. Ho, Richard and Cheung (1994) studied Asian Stock Exchanges and they evidenced the presence of day of the week effect in most of the Asian exchanges. Barnes (1986) found out the weak form of efficiency in the Kuala Lumpur Stock Market.
Indian stock market is one of the most rapidly growing among the emerging capital markets. There are number of studies associating to stock market anomalies, especially seasonal and calendar anomaly, have been held. Many researchers analysed the day of week effect in Indian stock exchange such as, Chaudhury (1991), Poshakwala (1996), Goswami and Anshuman (2000), Choudhry (2000), Bhattacharya, Sarkar and Mukhopadhyay (2003).
Chaudhury (1991), Poshakwale (1996), and Goswami and Anshuman (2000) applied Ordinary Least Squares (OLS) fitting and serial autocorrelation tests to found out the day of week effect on Indian stock returns. On studying of BSE Sensex index of Indian market Chaudhary (1991) observed that negative or low returns occurred on Mondays and high returns on Fridays. Similar results found out by Agarwal and Tandon (1994). Except Choudhry (2000) and Bhattacharya et al (2003), all analyses were based on time period of 1980s and mid 1990s and all of them used established methods such as Ordinary Least Square fitting and autocorrelation tests Choudhry (2000) probed presence of seasonality of stock price returns by using a merged framework but his analyses has a unclear issue with conditional mean used in his study. To study the week day effect Bhattacharya et al. (2003) used both reporting weeks and non-reporting weeks and applied the GARCH model by comprising the lagged returns (BSE 1001) as informative variables in conditional mean.
Choudhury (1991) and Obiadulla (1994) were discovered the Calendar anomalies in Indian stock exchange and they examined the daily return and monthly returns respectively, but the defined null hypothesis by them was not rejected. Broaca’s (1992) found that in Indian stock market, instead of Monday, Wednesday gives negative or lowest average returns on stock prices. The results given by previous researchers were re-analysed by Sarma (2004) and he concluded that Indian stock exchange has weak form efficiency, with calendar anomalies and weekend effect. Sarma studied three indices of Indian stock exchange (NATEX, SENSEX, and BSE200) and reasoned out that Indian stock markets have seasonality anomalies in their stock returns pattern. His study shows that the pair of two days Monday and Friday expresses the highest positive deviation than any other pair of days. Kaur (2004) analyses the Indian stock market by using two main indices Sensex and Nifty and documented that none of the weekend effect, January effect and day of the week effect exist in this stock market but stock returns shows the intra-week and intra-year seasonality. The non-randomness in the returns was also detected by Agarwal and Tandon (1994) and Poshakwale (1996) and both evidenced the interdependence of stock returns on different trading days.
Anshuman and Goswami (1997) studied the Bombay Stock Exchange and found out that abnormal positive returns occurred on Fridays. The day of the week effect was also evidenced by Karmakar and Chakarborty (2003) and Gupta (2006). Lakonishok and Levi (1982) analysed a unique kind of study which was based on effect on the day of the week effect by trading settlement system. Later, Amanulla and Thiripalraju (2001) studied the affect of trade settlement on specific pattern of returns in Indian market and evidenced the day of the week effect which occurred in time period of ban on carry-forward transactions. The uniformly occurrence of highly positive returns on Wednesday has been never noticed on any other emerging capital market. Lazar et al. (2005) analysed monthly returns of Bombay Stock Exchange, an index of Indian stock market, for the period 1991-2005 and documented that May, October and November months shows anomalous behaviour of highly positive returns as compared to rest of months and November gives the maximum mean return among these three months. They also found that, as known in India the tax year ends in month March, the monthly mean returns in April also represent significantly high values which explained by tax-loss selling hypothesis.
Indian stock market is one of the most rapidly increasing capital market and number of studies related to seasonal anomalies conducted on this market. Pandey (2002) documented that it is possible for an investor to earn extra return in Indian stock market as there is an existence of monthly effect. Rotkar, Patel and Patil (2002) analysed Indian stock market for period January 1995 to December 1999 and evidenced that due to the T+5 rolling settlement Monday and Wednesday gives high positive returns whereas negative or lowest returns happened on Friday. In the most recent study based on affects of insertion of rolling settlement in Indian stock market is conducted by Nath and Dalvi (2005). Nath and Dalvi (2005) considered the time period 1999 to 2003 for their study on Indian exchange market and determined that before January 2002, i.e. before introduction of rolling settlement, the average returns were significantly positive on Monday and Friday.
Incontrovertibility of the above studies held on different countries’ stock exchanges, there is some consider that some of these anomalous patterns are artefacts and induced by institutional factors like tax, liquidity effect etc. The researches of existence or non-existence of the seasonal anomalies in the ECMs has begun coming out recently. There are a few documents which uncovered the existence of seasonal anomalies in Emerging Capital Markets.Moreover, the some above explained researches have serious limitations. Some of them are time-period studied by them is not large enough, lack of agreement in the results and most of studies analysed on developed countries, there are very rare studies on under developed countries and Emerging capital markets. Hence there necessitate to carry a new fresh study and the existence of market anomalies would be reinforced if it analysed on Emerging Capital Markets or developing countries such as India. In this study, we extend the investigation of the monthly effect and the day of the week effect in stock returns for the Indian stock market.This study is a step in this direction as it an emerging economy (India). Accordingly, the study has been divided into four sections. The next section discusses the data and methodology used to analyze seasonal anomalies, the third section covers the results and evidence of the study and the final section concludes the study.
Stock Exchange of India- An overview
Period of Study
This study empirically investigates the period from January1st 1995 to March 31st 2009 to verify the seasonal anomalies like ‘day of the week’ and ‘calendar month anomaly’ in Indian stock market. Onwards 2002, there are major changes occurred in functioning and structure of Indian Stock Exchange. The most important change happened in terms of settlement and trading rules, according to that trading has shifted to a one day rolling settlement and settlement cycle also moved to T+2 from T+5 and due to this governance became more effective. Therefore, it is very important to study the capital market anomalies in these years. So to study the impacts of these changes, this study is further divided into two different time-spans one is before Rolling Settlement (i.e. January 1995 to December 2001) and another is after Rolling Settlement (i.e. January 2002 to March 2009).
Stock market indices Sensex and Nifty are representative of trading activeness and whole industry sector of India. Therefore, the sample population taken from these two indices fully represents the Indian stock exchange and its behaviour. The historical daily stock price data on Sensex and Nifty have been brought from their official sites www.bseindia.com and www.nseindia.com respectively. The official websites of these two indices provides daily data including opening, high, low, and close values.
To analyse the day of the week effect data used in this study is belongs to two different time-periods:
1) January 1995 to December 2001 (Before Rolling Settlement)
This time-period spanning over 365 weeks and total of 1712 trading days for each of the indices, out of which 9 Saturdays and 2 Sundays are included. So, after excluding weekend days no of observation of this study is 1701 for this time span.
2) January 2002 to March 2009 (After Rolling Settlement)
This time-period spanning over 378 weeks and making up a total of 1,814 (days) observations for each of the indices, out of which 9saturdays and 1 Sunday are included. So, after excluding weekend days no of observation of this study is 1804 for this time span. It is noticed that from this high frequency data, provide from BSE and NSE, there is no missing value.
DATA AND METHODOLOGY
Measuring the Daily Returns
For this study, only daily closing values of indices are enough to calculate the daily returns with the assumption that trading of a stocks done at closing values. The combined annual rate of return is approved approach of assessing the daily returns. Thus the return of a market index is calculated by formula:
RI = Daily return on the Index (I),
ln = Natural log of underlying market index (I),
It = Closing value of a given index (I) on a specific trading day (t), and
It-1 = Closing value of the given index (I) on preceding trading day (t-1)
It is cleared up that mean return on Wednesday is based on closing value of a given market indices (I) on Wednesday and closing value on Tuesday. As we know, Friday representing the last trading day of the week in stock markets so return on Monday is based on closing value of market index under condition on Monday and its comparable value on Friday. In the case of public holiday(s), the return on market indices were calculated on the basis of its closing value on the day before public holiday(s) and its closing value on the day after public holiday(s).
Hypothesis and Testing Procedure
In order to achieve the said objectives, the study under consideration intends to examine the validity of the following null hypothesis:
= That returns of each weekday are uniformly distributed and coming from same population; that is to say that average return on each weekday is same.
= That, in absence of H01, anomalous pattern gradually subsides in the long run of reinforce randomness in market series that trading strategies based on
anomalous behaviour fails to yield consistent abnormal returns in the long run.
=: That, arbitrage across the markets and the indices does not yield abnormal
returns, especially after the introduction of compulsory rolling settlement, in
the Indian markets
The hypothesis to be tested is associates with equality of mean returns during all the five weekdays. In other words, the null hypothesis is that mean returns during all the five weekdays do not show statistically significant differences and our alternative hypothesis is that the mean returns during the weekdays are not same or it shows some statistically significant difference. The accepted model for return is:
j = 1, 2 …5
Where, is the overall daily mean,
quantify the day effect and its expected value is ‘0′, and is mutually
independent random variable.
The null hypothesis for this given model would be that the population means shows are equal.
Mathematically we can write:
: = 0 for j = 1, 2 …5
: 0 for at least one value of j.
= is mean return on Monday
= is the mean return on Tuesday
= is the mean return on Wednesday
= is the mean return on Thursday
= is the mean return on Friday
For both of indices.
The statistical software SPSS (Software Packages for Social Sciences) is used to analyze the descriptive statistics such as arithmetic mean, variance, kurtosis, standard deviation and skewness for all trading days of the week. Descriptive statistics is used to test the normality of the distribution. After that results were validated by parametric and non-parametric tests. According to the normality test, the distributions of daily returns are not normal. So here we can use the non-parametric test. Kruskal-Wallis is the non parametric test used to check the equality of means, especially when sample sizes are more than two and here we have five samples as we considering five trading days of the week.
In the past, it has been seen that researchers usually use the parametric tests (a dummy variable regression) on any data set without analysing data’s distributional properties. It is true that parametric tests are more powerful than non-parametric tests. But when conditions not met with parametric tests then it is important to make a choice between valid test having less power (a non-parametric) and invalid test having high power (a parametric). A non-parametric test is always in order, especially when in question. One of the biggest advantage of non-parametric test is it is independent of distributional assumptions. And it has disadvantage of loss of information. But in case of this seasonality study, this limitation doesn’t effect because the concentration is not on estimation of daily returns. Hence, a non-parametric Kruskall-Wallis test is used instead of parametric one- way analysis of variance.
The Kruskal Wallis test is used to check out the equality of the mean across the day of the week. In Kruskal-Wallis test the whole set of observations is being ranked and these ranks are represents each observation depends upon their values. i.e. higher the value higher the rank and vice-versa, then arranged into matrix where represents the rank of the return and columns represent the day-of -the-week (Monday to Friday).
The formula for calculating the test statistic ‘H’ is as under:
Where = sum of the ranks in the jth column.
= number of cases in the jth column.
N = sum of observations in all the columns
Since the sampling distribution of ‘H’ is asymptotically , based on four degree of freedom, the critical value at 1% level of significance is 13.28, 5% level of significance is 9.48, and for 10% it is 7.77 and for 25% it is 5.38.
The null hypothesis tested is that there are no differences in the mean daily returns across the weekdays. If the computed H is greater than the critical value, the null hypothesis cannot be accepted. Conversely, if the computed H value is less than the critical value, the alternate hypothesis cannot be accepted.
Data analysis and result
As pointed out earlier, this study is based on two major stock market indices of Indian capital market to analysis the impact of Rolling Settlement and existence of seasonal anomalies. The volatility in these indices is discussed below:
day of the week effect
Day-of-the-Week Effect on the Bombay Stock Exchange
Day-of-the-week effect stands for identify non-random pattern in returns of all trading days of week. Available studies points to occurrence of positive mean returns on Fridays and negative on Mondays (Chaudary, 1991). To achieve the objective of finding day-of-the-week effect in Indian market, this study examine the main index of Bombay Stock Exchange i.e. SENSEX. This index is the best representative of BSE.
A) Rolling Settlement and BSE SENSEX Returns
The SENSEX based mean returns of all trading days in a week are described in Table 1. This table also shows the descriptive summary statistics, viz. Median, standard deviation, skewness and kurtosis, of these return values. Shown descriptive statistics helps to interpret pattern of mean returns for each trading day along with the Kruskal-Wallis H test statistics.
A). BEFORE ROLLING SETTLEMENT, JANUARY 1995- DECEMBER 2001
B). AFTER ROLLING SETTLEMENT, JANUARY 2001- MARCH 2009
Table 1: Rolling Settlement and BSE SENSEX Returns, January 1995-March 2009
In the period of before Rolling Settlement, result reveals that Monday and Thursday are only two days which produce positive mean returns and rest of trading days give negative values and Wednesday gives the highest negative value. The distribution of mean return in this time-span was considered statistically significant at 0.01 level to invalidate but not at 0.05 level of significance. In this period, a kind of contradiction can be seen regarding mean returns on Mondays and Fridays as compared to previous literature. The series of mean returns was also found out negatively skewed on first three trading days and positively skewed on Thursdays and Fridays. Therefore, a specific differentiation was pointed out for distribution of daily average returns on BSE SENSEX index before the introduction of Rolling Settlement.
To counter point pre-rolling settlement period, day of the week effect in the post-settlement period was documented by Gupta (2006) and evidenced that the mean returns were highest on Fridays and lowest on Mondays. In this study, the post-settlement period shows same result and it also shows that only Tuesdays are positively skewed as compared to other trading days of week. Moreover, in the post-settlement period the distribution of average stock returns is not found statistically significant at both levels 0.01 and 0.05.
It can be understood that an effect of rolling settlement on Indian stock exchanges acted rationally and non-random pattern pointed out earlier has vanished. It means that market trends cannot be consistently trusted for strategies of earning abnormal returns in the long run.
Thus, the results described above support the earlier conclusions as consider to the withdrawal of day-of-the-week effect in the long run. In this study it is noted that the distribution and spread of mean returns noticed earlier the introduction of Rolling Settlement has vanished. It can be deduced that market trends has polished and smooth after the launching of Rolling Settlement. The graphical presentation (Figure 1) of mean returns and all trading days of week in both periods shows the interesting effect of introduction Rolling Statement i.e., in pre- rolling settlement period Friday returns were negative and in post-rolling settlement it become the highest positive.
It may be deduced that various trade settlement cycle on the stock exchanges (BSE and NSE) in pre-rolling settlement might have added to the lowest Friday returns. After introduction of the rolling settlement, day of the week effect noticed before has vanished to indicate smoothed market trends for all trading days in a week. As a consequence, market variability and volatility has reduced substantially.
Day-of-the-Week Effect on the National Stock Exchange
As the change of trading settlement, its effect can be seen on both indices BSE and NSE. The significantly high return value on Wednesdays evidenced the presence of day of the week effect on NSE. NSE was also initiatives to adopt new technologies for reformation and smoothened market microstructure. Due to which, equally distributed mean returns are expected on the NSE in comparison to BSE. In the period of before Rolling Settlement, one can easily detect the trend in trading positions due to the different starting and ending settlement days on both exchanges. For vivacious securities industry mechanism of NSE, it has found a substantial boost in the trading volume. Considering all these aspects, an investigation of NSE indices is the best to get the picture of day of the week effect.
B) Rolling Settlement and S and P CNX Nifty Returns
As discussed earlier NIFTY is broad-based index and it has higher trading volume as compared to SENSEX. The distribution of mean return series of this index is also distributed with less variance. For a deep analysis of the consequences of introduction of Rolling Settlement the result were found for both time-spans.
A). BEFORE ROLLING SETTLEMENT, JANUARY 1995- DECEMBER 2001
B). AFTER ROLLING SETTLEMENT, JANUARY 2001- MARCH 2009
Table 2: Rolling Settlement and CNX Nifty Returns, January 1995-March 2009
In Table 2, the time period before Rolling Settlement (i.e. Panel A) suggests the highest and only positive value of mean return on Wednesday and rest of trading days shows negative returns with lowest value on Thursday. The mean returns on Wednesdays, Thursdays and Fridays are positively skewed. Mondays shows the highest variability among all trading weekdays and Tuesday returns were showing a leptokurtic curve. This analysis of NSE NIFTY before Rolling Settlement was considered statistically significant at both levels 0.01 and 0.05. In addition, the pre-rolling settlement period indicates the Wednesday effect or mid of the week effect.
During the period after the introduction of compulsory rolling settlement, mean return values were positive for all trading days except Mondays. Mondays indicates the lowest value whereas Fridays shows the highest mean return. Table 2 also explains that mean returns were negatively skewed for all trading days except for Tuesdays. Returns on Monday were also viewed more varying in the comparison of other trading days’ return. Even so, the post-rolling settlement period was not considered statistically significant in terms of Kruskal-Wallis test statistics on both level of significance 0.01 and 0.05.
Figure 2 indicates that during time-span after Rolling Settlement, the returns on Fridays noticed highest (positive) values as compared to other trading days of week while Monday shows the lowest (negative) mean returns. Mondays mean returns were also showed highest variability in comparison of other trading days. Summing up all, the distinction noticed in a return series of CNX NIFTY tells that it was studied a statistically significant to evidence which confirm the day-of-the-week effect in CNX NIFTY index.
From Figure 2 it can be seen undoubtedly that in a pre-rolling settlement period Wednesdays were giving tremendous positive returns as compared to other trading days of week, which is believed due to strategic investment decision to gain extra returns. it may be deducted that market players may have webbed their places on Friday on BSE exchange and on Tuesday on the NSE exchange and then regenerated their trading places on Wednesday on both the stock exchanges.
Monthly effect is evidenced by so many researchers and most of them studied it in the developed countries’ stock markets. There is a trend of stock prices getting up in January comparative to December due to tax-induced selling. Yet, this January effect is detected in many nations, some nations have months other than December as the tax year-end such as the United Kingdom, Hong Kong and New Zealand (Agrawal and Tandon, 1994) and Australia (Brown et al., 1983). Therefore, it has been debated that the tax-loss selling account cannot be the only determining factor of the January effect. In India, the financial year ending is March.
Monthly effect before rolling settlement
In this time-span of seven years, the month-of-the-year effect is found in April. It can be named as April effect. It also determined that month-of-the-year effect is discovered to be more predominant than the day-of-the-week effect in India. In 1995-2001, it is found that during the sampling period of time the mean return value is more negative and has very low values of mean return in the months of March and May and this fall begins from April (Table 4). SENSEX and NIFTY both indices’ mean return series confirms the April effect in the years 1996, 1997 and 2001 because these years had negative (low) mean return in the month March and positive mean return values in April. If we test the existence of the January effect in time period before Rolling Settlement, then it can be seen that only January 1996 and January 1998 mean return values are greater than their preceding December month’s values for both indices. Moreover, for BSE SENSEX January 1997 and January 1999 values are more positive than the December 1996 and December 1998 respectively. And for NSE NIFTY January 1999 and January 2001 values are more positive than the December 1997 and December 2000 respectively. And these January return values are significantly higher as compared to other months of the same year. This shows the existence of January effect in the time-period before the introduction of rolling settlement.
Monthly effect before rolling settlement
Monthly effect after rolling settlement
As pointed out earlier that April effect is detected in BSE and NSE stock exchanges in time period before rolling settlement, similar pattern is discovered in time period after the settlement even it gives more strong evidence of presence of April effect.
SENSEX and NIFTY both indices’ mean return series confirms the April effect in the years 2002, 2003, 2004, 2007, and 2008 because these years had negative (low) mean return in the month March and positive mean return values in April. In the time-span 2002-2009, this study found out a noticeable change in mean returns in month of December and that is for all these seven years December mean returns are highly positive for both indices. In Table 5, it can be also seen that for the years 2003, 2004, 2005, 2008 and 2009 mean returns value of month January for both indices are highly negative and all January return values are not significantly higher than return values of other months of the year. Hence it verifies that January effect is eliminated after introduction of Rolling Settlement in Indian stock exchange.
Monthly effect after rolling settlement
The result accounted in the study-reported proves on the day of week effect on two main stock exchanges, NSE and BSE for fourteen-year study period, January 1995 – March 2009. In pre-rolling settlement period, market players, especially the day dealers, were tended to square off their places on Wednesday on the BSE to renew similar places on the NSE. This study evidenced the mid-of-the-week effect on the BSE for lowest Wednesday returns in the time period before introduction of rolling settlement. These results were so strong to continue the long run. It examined hard to detect any believable systematic interpretation to the lowest Friday return on the NSE in the same time period exclude for trader thoughts and sentiments. Trader’s thoughts on Friday making up it as the last trading day on the BSE were wont to be depressing (equivalent to widely distributed stock selling) to have an experience similar price trend on the NSE too. Cognate to these trends, mean returns were highest on Thursday on the BSE and on Wednesday on the NSE, which were the first trading days in the settlement cycle, in the period before rolling settlement (Table 3).
Table 3: Day-of-Week-Effect on the Indian Stock Exchanges, April 1997- March 2007
S AND P CNX NIFTY
A). BEFORE ROLLING SETTLEMENT, JANUARY 1995- DECEMBER 2001
AT 0.01 LEVEL
AT 0.05 LEVEL
B). AFTER ROLLING SETTLEMENT, JANUARY 2001- MARCH 2009
AT 0.01 LEVEL
AT 0.05 LEVEL
It is the evocative of Indian investor sentiments and its trading behaviour. After introduction of Rolling Settlement, It can be deduced that investment chances existed all over the securities industry before rolling settlement have vanished resultant to compulsory of the Rolling Settlement. Moreover, in this study the main evidenced results regarding the consequences of introduction of Rolling Settlement on anomalous behaviour of Indian stock exchange are as follows:
Day of the week effect was observed as a presence of two critically significant trading days Mondays and Fridays before the introduction of the rolling settlement.
Before the introduction of Rolling Settlement it was discovered that stock returns were equally and uniformly distributed in the sense that the day of week effect noticed, which was vanished in the period after introducing the Rolling Settlement.
In a pre-rolling settlement period, April and January both effects were detected in both indices.
Post-rolling settlement period also evidenced the existence of April effect in the market but January effect was eliminated by the introduction of Rolling Settlement.
On the whole, this study reported that there was a day effect, January effect, April effect in the NSE and BSE indices. The study also resolves that there is the existence of seasonality all over the months of the year from 1995 to 2009. The seasonal pattern of weekday effect and January effect both were deleted by introduction of rolling settlement. March is a end month of tax year in India and March’s statistically significant coefficient is logical with the ‘tax-loss selling’ hypothesis. According to this study, stock returns in India exchanges are not totally random which further suggests that the Indian stock exchange may not informationally efficient and traders can earn abnormal returns by trading strategy based on monthly effects. This study is based on only two main indices of stock exchange of India, so it is recommend for doing more research in this field before making any final decision. For further future study one could investigates the other stock indices of Bombay Stock Exchange and National Stock Exchange and for the deep research one could also be investigates intra-month and turn-of-the-month effects.