Literature Review on Day of the Week Effect
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Literature Review on Day of the Week Effects
Efficient Market Hypothesis (EMH) claims that financial markets are “informationally efficient” Fama (1970). In other words, financial markets reflect all known information and according to stock prices rapidly adjust to any new information (Reilly and Brown, 1997), so the current price already reflects all known information about the stock. Therefore, according to this theory, it would be impossible to earn excess returns and beat the market on a regular basis unless it is through luck.
The EMH was initially expressed by Bachelier (1900) in the form of random walks (Bachelier, 1900 cited in Fama, 1965). The random walk theory is explained by prices that are unpredictable and that future stock prices cannot be forecasted using prior information (Lo & Mackinlay, 1988). Bachelier (1900) concluded that commodity speculation was a “fair game”. This meant that investors could not make abnormal profits as the existing price of a share was a fair estimate of its future price. However this theory was ignored until Samuelson (1965) developed the theoretical framework for the random walk. This theory created by Samuelson (1965), combined with empirical findings from other researchers including Fama (1965) formed the foundation to the development of the EMH. The theory of EMH was finally proposed by Fama (1970).
Fama (1970) states that three different levels of market efficiency exist when based on what is meant as available information. These include the weak-form, which asserts that security prices reflect all historical information, meaning that abnormal profits cannot be gained by using trading strategies based on past information. In other words if the market is set to be weak-form efficient, then it follows a random walk. The second level of efficiency is called semi-strong-form, which asserts that security prices reflect all publicly available information. Therefore prices will immediately adjust for all public announcements. And finally the third level is known as strong-form and states that all information including private and public is reflected in the stock prices. All three forms of efficiency are transparent, meaning that if a stock market is strong-form efficient, it would also mean it is efficient in the weak-form.
However in recent years the EMH has come under scrutiny and many market analysts have argued for market inefficiency, at least in its weak-form (Malkiel, 2003). Since the EMH is based on the assumption that investors are rational, researchers have found that some investors sometimes take irrational approaches to decision making opposed to the conventional rational or logical thinking. In recent years, Behavioural Finance has emerged as one of the key explanations into why and how markets may be inefficient.
Some of the explanations that behavioural finance proposes include feedback mechanisms which describe why short-run serial correlation was not zero found by Lo & Mackinlay (1999). Long-run return reversals has also been established as an explanation as to why markets may not be efficient as DeBondt & Thaler (1985) found that investors were subject to waves of optimism and pessimism which causes stock prices to deviate from their fundamental true value and later to experience a concept known as mean reversion. The concept of mean reversion is a contradiction to the EMH as it follows a trend. This is also consistent with the behavioural decision theory proposed by Kahneman & Tversky (1979) in which they claimed that investors may be overconfident in their ability to forecast future stock prices. The day of the week effect as proposed earlier has been identified as one of the key violations to the EMH and is discussed further in section 2.2.
2.2 - Review of Literature on Day of the Week Effects
The phenomenon of day of the week effects has been extensively researched over the last few decades. Although the literature on this irregularity has been widely documented, only a few have been able to explain these cyclic patterns in stock returns. Also, the explanations that have been proposed by researchers have not been concrete reasons. They have been more like suggestions and some of the more popular ones are as follows. Calendar time hypothesis is a process which operates continuously, so that the return on Monday would represent a three-calendar-day investment, therefore the expected return for Mondays would be three times the expected return for any of the other days of the week (French, 1980). The settlement period hypothesis has been found to explain some calendar effects across different markets in which returns have been higher on pay-in days compared to pay-out days (Kumari & Raj, 2006). Other explanations include Measurement errors in stock prices (Gibbons & Hess, 1981) and spill-over effect which implies that negative Tuesdays returns found in other international markets have been caused by negative Monday returns found in the U.S. & U.K (Jaffe & Westerfield, 1985).
2.3 - Evidence from Developed Markets
Fama (1965) examined the behaviour of stock prices and discovered that there was evidence of abnormality in stock returns. This brought forward the theory of stock prices being influenced by non-trading days. Therefore, Fama (1965) established that anticipation of economical events that occur during non-trading days have a continuous effect on stock prices. He tested the hypothesis that Monday's variance is three times greater than the other trading days in the week because of the accumulation of variances over the non-trading days. He found that the variance was approximately 20% higher than the other trading days which fell short of his hypothesis. As this was an opening study into this field, there was bound to be limitations and short-comings which may have compromised the accuracy of his results. As the day of the week effect was a secondary focus in his paper only a small sample of stocks were used. In addition, he considered only variances to determine the effect which only describes the spread of the returns, however had he used mean returns in addition, it would have explained the day of the week better as one can confirm by how much the return differs between each day of the week. Nevertheless, this was an introductory study and if it wasn't for this paper, the issue of day of the week effects may not have been picked up as early as it was.
French (1980) extended Fama's (1965) contribution in which he examined whether the process of generating stock returns operates continuously or during active trading days only. This was done on S&P 500 stock returns with the following two methods. The Calendar-time hypothesis  and the Trading- time hypothesis  , in which the returns are only generated during the active trading days of the week. Therefore if the alternative hypothesis was rejected, the returns for each day of the week should be identical since any of the returns represent only one trading day.
French (1980) found that during 1953-1977, the daily returns from the S&P 500 portfolio were inconsistent with both the Trading day model and the Calendar time model. The average returns on the Mondays were negative compared to the other four positive trading day returns. This was an unusual finding which led others to examine this anomaly further.
Gibbons & Hess (1981) investigated further into French's (1980) research as they examined the S&P 500 index and the equal weighted index from 1962-1978 for the day of the week affect on asset returns. They considered the delay between trading and settlements in stocks and measurement errors as possible explanations for the day of the week effect. They found a similar result to French (1980) however Mondays were not the only day found to give significantly low mean returns. Tuesday appeared to also have low returns, and Wednesday and Friday had higher mean returns than Tuesday and Thursday. In the overall analysis, the annual mean return on a Monday ranged from -33.5% (S&P 500) to 26.8% (equally-weighted index). The hypothesis of the equality of means was rejected in each of the sub-periods run. The inclusion of the sub-periods was very valuable as it gave a different perspective of the market at different time periods.
Following on from Gibbons & Hess (1981), Rogalski (1984) developed his understanding of Monday returns further as he set out to examine the Dow Jones Industrial Average index (DJIA) in terms of trading day and non-trading day returns. This study was different from the previous papers as it distinguished between trading and non-trading day returns, in which the examination from Friday close to Monday close was decomposed into two parts. First one being from Friday close to Monday open; second one was from Monday open to Monday close. He found that all of the average negative returns from Friday close to Monday close occur during non-trading hours and that the actual returns during Monday trading hours are positive.
Smirlock & Starks (1986) proposed a further analysis into the nature and timing of the day of the week effect on the Dow Jones Industrial Average. The use of hourly returns for a 21 year period was justified as a more efficient and thorough manner as the likes of Rogalski (1984) and others had used disparate time periods. For the empirical analysis, the total sample period was divided into three sub-periods. The first sub-period was from 1963-1968, second was from 1968-1974, and the most recent sub-period was from 1974-1983. In the pre 1974 periods, results showed that the hourly returns on Monday were significantly lower than the other trading days in the week. However, in the post 1974 period, there was nothing odd about Monday returns compared to the other trading days. To break this down further, the first sub-period showed that returns from Friday close to Monday open were positive. These returns were eliminated by the negative returns that occurred all day during Monday, resulting in a negative return for the entire day. In the second sub-period, the non-trading weekend returns were vaguely negative. This affected the opening hours of Monday in a negative manner and although the Monday returns did recover with the rest of the day showing positive returns, the returns for the entire day were significant and negative. For the most recent sub-period, the non-trading weekend returns were significantly negative, however, after noon the Monday hourly returns were positive, yielding no weekend effect in trading time, thus, concluding that the weekend effect was ‘moving up in time'. The results from this latter period are consistent with that of Rogalski (1984).
As many researchers had focused primarily on the U.S. stock market for these anomalies, Jaffe & Westerfield (1985) decided to expand this research area and found evidence of this phenomenon in four other developed economies. They demonstrated that this irregularity wasn't just an element of the U.S. stock market.
Jaffe & Westerfield (1985) found that along with the US, Canada, UK, Japan and Australia had shown evidence of day of the week effects. US, Canada and UK exhibited the lowest mean returns on a Monday which is consistent with the literature so far. Contrary to the negative Monday returns, the lowest returns for Japan and Australia were found on Tuesday. This was an unexpected twist in their study which led them to investigate further into this matter. They also confirmed that measurement errors and settlement periods were not the cause of the day of the week effect. They tested whether the anomalies found in the other four economies was a result of the seasonality found in the US stock market. Results showed that there may have been some evidence of a one day time lag between the US and Australia. The time zone theory or the spill-over effect may have explained some of the seasonality in the Australian stock market.
More International evidence was documented by Condoyanni et al. (1987) as they found results which concur with Jaffe & Westerfield's (1985). Condoyanni et al. (1987) tested for day of the week effects in six National stock exchanges which include Australia, Canada, France, Japan, Singapore & U.K during the periods 1969-1984. Canada and U.K was found to exhibit the conventional negative Monday returns, whereas, negative Tuesdays were found for Australia, France, Japan & Singapore. They discovered that not all markets in the same continent behave identically as France and U.K had contrasting day of the week effects.
A study by Mehdian & Perry (2001) claimed that day of the week effects in the U.S. have been reducing over time. They studied three major stock indices during the period 1964-1998 and although they found negative Monday returns for the the entire period; when analysing sub periods, they found that the negative sign for Monday had switched to a positive one from 1987 onwards. This is consistent with findings by Smirlock & Starks (1986) as they too found that the sign for the Monday coefficient had changed as time went on.
This theory of disappearing day of the week effects was also agreed by Kohers et al. (2004) who studied whether the increase in market efficiency over the previous 22 years had caused the day of the week seasonality to decline over time. They inspected the world's largest economies and found clear evidence of the presence of this anomaly during the 1980's. However from 1990 onwards, they concluded that the day of the week effects were fading away as the markets had become more efficient.
Most of the literature reviewed so far has used the OLS regression to investigate the day of the week effect. However there is a major drawback to this method. The error variance are assumed to be constant through time and does not take into account the time varying volatility that stock returns have.
Berument and Kiymaz (2001) introduced a new method for testing the day of the week effect by incorporating stock market volatility. As previously stated, the OLS regression has a major limitation as it assumes a constant variance. They employed Bollerslev (1986)'s generalised version of Engle (1982)'s ARCH model, called the GARCH(1,1)  . They used three models to examine the S&P 500 for the day of the week effect in return and volatility equation. The three models were the OLS Regression, which assumes a constant variance through time; GARCH(1,1), which incorporates heteroscedasticity and the Modified GARCH, which permits the constant term of the conditional variance to alter for each trading day.
Results from the OLS and the GARCH(1,1) were quite similar as both found Mondays to produce the lowest return and Wednesdays to perform the highest. The result from the Modified GARCH showed that Fridays were the most volatile and Wednesdays were the least volatile.
Clearly, there has been extensive literature expressing the day of the week anomaly in the more developed economies of the world. However, the same cannot be said for the emerging economies. There has been inadequate and inconclusive evidence of the day of the week effect in different emerging markets around the globe.
Brooks & Persand (2001) found that during 1989-1996 both Thailand and Malaysia exhibited significant positive Monday returns and Negative Tuesday returns. They also found Taiwan to display negative Wednesday returns.
Yalcin and Yucel (2006) examined 20 emerging economies for the day of the week effect and found that only 3 of the countries hold for the anomaly in returns. India's lowest return was found on Tuesdays and highest on Wednesdays between 1996-2005.
2.5 - Evidence from Indian Stock Markets
Published papers on the day of the week effect in the Indian stock market seem to be limited. The papers that have been published have to some extent been unable to explain why seasonality may exist in the Indian stock market. One of the early papers on the Indian stock market involved Poshakwale (1996) to test for weak-form efficiency and the day of the week effect on the Bombay stock exchange (BSENI) using daily prices during the pre-reform period 1987-1994.
The Indian stock market was an attractive case study for Poshakwale (1996) as the time period considered was during the pre-reform era in which the markets were starting to gain momentum and regulatory reforms like removals of barriers were being considered which would drive international equity investments.
Various auto-regression tests were employed to test the efficiency of the Indian stock market and the results found positive mean returns for all days of the week apart from Monday and Wednesday. Fridays had the highest mean return and Mondays had the lowest. The day of the week effect on the BSE seems to concur with results from developed markets in terms of the week starting off on a low and finishing on a high. The irregularity found in this paper supports the first order autocorrelation and is a violation of the random walk theory, thus Poshakwale (1996) rejected the null hypothesis.
The study by Poshakwale (1996) drove Ignatius (1998) to further examine the relationship between the stock price patterns of the BSE with the New York Stock Exchange (NYSE). He used daily closing figures from the BSE during the period 1979-1990. Results using the OLS method found to be significant, thus rejecting the null hypothesis. Resembling Poshakwale's (1996) findings, the lowest mean return occurred on a Monday except it was found to be insignificant. Friday's had the highest mean return was significant at the 1% level. Oddly, Tuesday had the second highest return and was significant at the 5% level.
Ignatius (1998) proposed that the release of bad news over the weekend may have caused this weekend effect, however there was no explanation for the unusually high mean return on Tuesday. When looking for a spill-over, it appeared that the BSE and NYSE are more segmented rather than integrated. A reason for this may be because in that particular time period, India's markets were relatively closed in nature and International investment may not have been encouraged.
Choudhry (2000) on the other hand found evidence against the day of the week effect during the pre-reform period. He investigated the day of the week effect on returns and volatility for seven Asian stock markets. One of which was India and daily prices from the BSE100 during the pre-reform period 1990-1995 were examined.
This was the first paper to investigate the Asian stock market for day of the week effect on returns and volatility using the GARCH(1,1) model. He found that the mean returns for India were not significant enough and concluded that India's stock market did not contain the day of the week effect during the pre-reform era. The rest of the paper went on to conclude that the day of the week effect is present in some of the other Asian markets in terms of returns and volatility and is not just an anomaly found in the developed markets of the world. The day of the week effect results found in this paper for the other markets were not explained by the settlement procedure but did show some evidence of a possible spill-over from the Japanese market.
As Choudhry (2000) tested a specific time period of 5 years, it maybe that for those 5 years, the Indian market may not have had this anomaly in their stock market, however, a 5 year time period is not a sufficient quantity to draw possible conclusions on. Also, in those 5 years, the Indian stock markets were seen quite closed in nature as it had not really taken off on the International stage. Choudhry (2000) tested for the day of the week under a unified framework, however the study had a misspecification problem regarding the conditional mean in the GARCH(1,1) specification. Therefore due to this error the results may not have emerged as intended and may well be inaccurate or invalid.
Contrary to Choudhry (2000), a more recent study, Sarma (2004) found that the Indian stock markets do manifest a seasonality pattern in terms of returns in the days of the week, but for a different time period. Daily returns were examined for the post-reform period of 1996-2002. Sarma (2004) looked at three indices in the Indian stock market, including the SENEX, NATEX and BSE200.
Using the non-parametric Kruskal-Wallis test, results found that both SANEX and NATEX had negative mean returns on Tuesdays and Fridays, with Tuesday being the lowest. Wednesday's for both indices had the highest mean return. BSE200 had the lowest mean return on Monday. All mean returns were significant at the 1% level, thus rejecting the null hypothesis.
A recent study by Kumari & Raj (2006) examined the Indian stock market in terms of the BSE and NSE during 1987-1998. They found no indication of seasonality in both indices; however they did find evidence of a positive Monday return which is in contrast to findings in developed markets. They concluded that the high Monday return may be explained by the settlement period. During the time period they chose to examine, the settlement period was two weeks which then reduced to a week and in both cases it would start on a Monday and end on a Friday. This would mean that low closing Friday returns combined with high Monday opening returns would produce high closing Monday returns.
According to the studies discussed in this paper, evidence of seasonal patterns from the Indian stock market seems to be dissimilar for different periods. Most researchers have studied different periods therefore none of them can really agree or disagree with any other study on the Indian capital market. The methods used to test for day of the week effects seem to be consistent with the conventional OLS model (apart from Choudhry, 2000), which does not take into account time varying volatility which is persistent in stock returns. Therefore this paper will attempt to analyse the Indian stock market using a more robust model in the GARCH(1,1) during most of the periods discussed in the review of the Indian stock market literature, with the inclusion of the recent financial crisis which has never been analysed in this context before.
As discussed earlier and with evidence provided by existing literature it has not been easy to give an exact explanation as to why patterns of this nature are found in security returns. Although the literature so far has provided a few explanations, there have been other studies that have also been able to give their version of an explanation for the phenomena.
Rystrom and Benson (1989) argue that investor psychology is one explanation for the market inefficiency. They suggest that investors, although assumed rational, may sometimes act irrationally which in turn would lead their economic decision making to be influenced by emotions and moods. If these emotions are to vary across the days of the week it can very well generate high or low degree of optimism or pessimism across the days of the week. This would produce different returns across the days of the week. So if investors felt a high degree of pessimism on a Monday in comparison to any other day of the week then they would sell their securities and depress prices. Conversely, investors would buy on Fridays if they felt more optimistic creating an upward pressure in security prices.
Another explanation also arises from the behaviour of investor. Pettengill (2003) gives a similar explanation as Rustrom and Benson (1989) as he believes that investors keep away from buying securities on Mondays because they are fearful of possible losses from trading with well informed traders who may be selling their securities on Monday based on critical information they may have received over the weekend.
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