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Literature Review Investigating The Calendar Effect

Famas’ (1965) general work, which called “calendar effect”, is between the most investigated subjects in finance. The distribution of the stock returns is a puzzling empirical finding, which has been accomplished by many researchers in the world stock markets. The most unusual empirical result is that the distributions of stock returns are not the same for all days of the week. This is the “Day-of the-week”. Monday, the first trading day of the week, is characterized by an abnormally negative mean of return while on Friday, the last trading day of the week returns producing the highest returns of the week. According to French (1980), Gibbson and Hess (1981) and Keim and Stambaugh (1984), the return on Monday in US’s stock market is significantly negative and on Friday is significantly positive. They all used the Standard and Poor’s 500 Stock index, which is the portfolio of 500 of the largest firms on the New York Stock Exchange.

To start with, French (1980) examined two different models about the process of stock returns for the period 1953 through 1977. The first model was under the calendar time hypothesis, in which the process of generating stock returns operated consecutively and the expected return for Monday was three times more than the expected return of the other days of the week. According to French, the reason was that the time between Friday and Monday is three days. The second was under the trading time hypothesis in which the returns were generated only in trading time and the expected return was the same for all the days of the week. In those frameworks he used the daily returns of the Standard and Poor’s composite portfolio, to examine if the returns are generated in trading or calendar time. He concluded that the expected return on Mondays during the period examined was significantly lower than the other days.

At the same vein, Gibbons and Hess, (1981) also investigated that only the Monday’s mean return is constant significant low or negative and the other days of the week the mean returns are variable. They examined the asset returns for day of the week effects, for the period 1962 to 1978. To test the day of the week effects, they used a dummy variable for Monday, the means and the variances of the returns for every trading day, f-statistics and p-value in three different stock indexes. S & P 500, CRSP Value-weighted and CRSP Equal-weighted. They conclude that the mean returns on Monday are significant low.

On the other hand Keim, and Stambaugh, (1984), examined the period from 1928 through 1982. From 1928 to 1952, the New York stock exchange was open on Saturdays for two hours. They reported the continuously negative mean return on Monday, for the Standard and Poor’s 500 Stock index (henceforth S&P 500), for all firm’s size, and for returns of stocks which traded over-the-counter market (OTC). They find evidence that the return on Friday is significantly larger than the other days if Friday is the last day of trading. In order to presence the measurement error, they applied a test which based on autocorrelation. They examined the correlations between returns and computed the correlation coefficient among the return of one day and of the following. They found that results between the test and the measurement error, for the correlation between Monday’s and Friday’s result were opposite. Finally, they used a test for special-related bias which allowed examining if day of the week effects occur from factors attributable only to the actions or attend from the specialist of the Exchanges.

For the UK stock exchange Theobald & Price (1984), and Board and Sutcliffe (1988) also found negative returns on Monday. Steeley (2001) noticed that during the 1990s the weekend effect disappeared. To begin with, Theobald & Price (1984), used two index the FTO (Financial Times Ordinary) and FTAS (Financial Time All Share) and found that the negative return on Monday was a pervasive phenomenon as long as negative returns documented in the Second Monday of the Stock Exchange Account. Account Date system was employed in London Stock Exchange. That system divided the trading year into a set of Accounts, which are commence on a Mondays and were duration of two weeks. The period they were examined for both indexes and Accounts was from 1975 through 1981. In order to get seasonality results they used the mean and the variance of the return distributions for those two indexes and a variety of tests. To test the whole data they used kurtosis, skewness, t-tests, Median tests, Mann-Whitney. To examine the differential impact of seasonality they used Kruskal-Wallis test and f-test to test the variance equality across the days. End long, they used Box and Pierce Q-statistic in order to detect the different impacts on seasonal and thin trading.

Moreover Board & Sutcliffe 1988 also examined the Financial Time All Share Index but for a longer period covering the years 1962-1986. They computed the mean and the variance of every day separately. They used t-test to test if the mean is significantly different from zero, skewness, kurtosis and the Kolmogorov D statistics to test the normality and the Mann-Whitney U statistic to exam the difference of distribution of all days of the week. They used data from returns over bank holidays to examine if the weekend effect due to the fact that the market is close but there were no result for this case. Finally, they concluded that the Mondays’ returns were positive only every first trading day of an account and the possible explanation they gave for the weekend effect, was the stock exchange account effects and the measurement errors.

Finally , Steeley (2001) considered a most recent period between 1991-1998 for the weekend effect in UK stock market and he observed that the weekend effect has disappeared. The possible explanations he gave was the market-new arrivals which occurred that period in the UK’s stock exchange. His analysis is based on data from the FTSE100 index. He used f-statistic to test whether the daily returns are different every day, Kruskal-Wallis statistic which is an alternative test of f-statistic, Tukey statistic to test by pair the differences in means. Moreover, he compared and contrasted the positive and the negative returns of all days of the week, and he found that the negative returns between Monday and Friday are significantly different from the negative returns of the other trading days.

Investigations for the day of the week effect occurred not only in UK’s and USA’s stock markets but also in more developing exchange. Singapore by Tan and Tat (1998), Indonesia, Malaysia, Thailand by Choudhry (2000) are some of them which examined and negative returns on Monday have been reported.

Tan & Tat 1998 considered the day of the week effect in Singapore stock market for the years 1975 to 1994. They tested the calendar anomalies and analysed the relationships between them. They got the data from the SES All-Singapore Index. They examined the daily return with a skewness statistic and with a kurtosis statistic. They tested the equality of mean returns for every day of the week using an f-test. They used t-test to document that the differences of means between the days before holidays, the days after holidays and the ordinary days were important. The standard deviation of returns on days before holidays is lower than the ordinary days but after holidays is higher.

In the same vein, Choudhry 2000 considered seven emerging Asian markets: Indonesia, South Korea, Taiwan, Malaysia, India, Thailand and Philippines, for the period 1990 through 1995. He used for the empirical results the Generalized Autoregressive Conditional Heteroscedasticity (GARCH) model to model the daily returns from these markets. The GARCH models were able to capture the most empirical features which commonly found in stock return data. These are the leptokurtosis, the skewness and the volatility clustering. Choudhry, documented that Indonesia, Malaysia, and Philippines inflict significant negative return on Monday, South Korea, Taiwan and India have significant return on Tuesday and Thailand’s returns are affected by all trading days. In his results showed that these markets could be affected from a possible spill-over effect from the Japanese stock market.

The day of the week effect, in some markets presented negative returns on Tuesday and not on Monday. Barone (1990) found that Italy has low negative return on Thusday. That was also observed by Sahtmases (1986) for Spain and by Choudhry (2000), for South Korea.

Additionally, Sahtmases (1986) analysed the seasonal phenomena in the Madrid Stock Exchange market for the period 1979 to 1983 and used the Madrid Stock Exchange Index and the daily returns for a sample of 40 stocks. He used the different means of returns across all days of the week. The returns on Tuesday were negative.

Moving on, Barone (1989) examined the period from 1975 to 1989 for the Milan Stock Exchange in Italy. He used for the empirical test the MIB index series. He observed that the means of return were negative for Monday and especially Tuesday and positive for Friday. He used the means and the standard deviations of the rates of change across all days of the week.

A most recent investigation about the day of the week effect on the volatility and volume is Kiymaz’s & Berument’s (2003). They examined the main indexes of Canada, Germany, United Kingdom, Japan and United States, which are five of the largest stock markets in the world. They used a framework of conditional variance, and they found that in both volatility and return equation day of the week effect is presented. For Japan and Germany the highest volatility took place on Monday, for United Kingdom on Thursday, and for Canada and United States on Friday. They presented the drawbacks of the OLS methodology and they considered two various models of GARCH to examine the day of the week effect in volatility and return equations. Thereinafter, they used the quasi-maximum likelihood estimation method, to estimate parameters. Finally, they argued that that high volatility and low trading might accompany each other because of the disinclination of traders to trade high stock market’s volatility periods.

Athens’ stock is characterised by a different order of other countries. That increases its risk and it’s uncertainly for the investors. Only a few researches have been and the results for the day of the week effect in Athens Stock Exchange are mixed for different periods. According to Alexakis and Petrakis (1991), the variability of the stock price index was influenced by alternative investment opportunities and socio-political factors and not by company’s profits and economic situation. Alexakis and Xanthakis (1995), found significant negative returns on Tuesday. Coutts et al. (2000), documented significant positive returns on Friday, and on the other days the returns where insignificant. Mills et al (2000), reported low returns on Wednesday. Tsangarakis (2007), reported that the weekend effect was not constant for the duration of 21 years he examined. Al-Khazali et al (2008) also reports the highest returns were on Friday and the lowest on Tuesday. Kenourgios & Samitas (2008) noticed that the day of the week effect increased after the Greek eccession to Euro-Zone.

To begin with, Tsangarakis, (2007), examined the day of the week effect in the Athens Stock Exchange for the period 1981 through 2002.The focus of the study is on the ASE general composite index. The methodology he followed is the ordinary least squares model. He investigated separately each year and he used F-statistic to measure the joint significance of returns. His findings suggested that there is no persistent effect in ASE and he assumed that the investors may had no investment strategy and that effected the daily returns. and he found that was significant in only 6 years. He also found that there is no systematic pattern of significant returns across the days of the week, and the effect appeared and disappeared in different periods.

Continuing with, Alexakis, P. & Petrakis (1991), examined the period between 1985 and 1994. To test the day of the week effect they used an ARCH-type model because these types of models were Martingale Difference, their unconditional mean is zero and serially uncorrelated, White Noise, and yielded observation with heavier tails than those of a normal distribution. They followed the GARCH-M model for their research. They found significant negative return on Tuesday and positive return across the other days of the week.

Al-Khazali, Koumanakos, & Pyun 2008 examined then years from 1985 to 2004 which was a transition period for the Athens Stock Exchange. The number of companies listed in the “Main” section of the exchange almost doubled, the “Parallel” section increased from 0 to 123, the market capitalization increased from US$13.5 billion to US$ 92.1 billion and the daily volume of shares traded jumped from 5 million shares to 24.9 million shares. They documented the closing price and tested the normality of return distributions for all series with a Jarque-Bera normality test. They used a stochastic dominance analysis in order to investigate if they would get different results. The results they got were almost the same with Alexakis and Xanthakis, Coutts et al, and Mills et al. that the highest returns are on Friday and the lowest on Tuesday.

Continuing in the same vein, Coutts, Kaplanidis & Roberts 2000 investigated the security price anomalies in the Athens Stock Exchange General Index, during the period 1986 – 1996 in three major industries: Banking, insurance and leasing. The methodology they followed was a least squares model. They found the day of the week effect in the Banking indices but not in the Leasing and Insurance indices. They also documented high positive returns in pre-holiday trading days. The mean returns on Monday were positive and the mean returns on Tuesday and Wednesday were negative.

Moreover, Mills et al (2000) examined over an approximate ten year period from 1986 to 1997. They tried to explain the factors for the day of the week effect, such us the measurement errors, the differences which reported in settlement time of transactions, different attitudes of certain investor groups, and the tendency the investors had to delay the announcement of bad news until the weekend. They used a framework in which evaluated two hypothesis: the trading time hypothesis in which returns are created only in trading days of the week, and calendar time hypothesis in which returns were also created in non-trading days. They used regressions with dummy variables to test these hypotheses. They found significantly high returns on Friday and lower returns on Tuesday and Wednesday.

Finally, Kenourgios & Samitas 2008 observed the day of the week effect on volatility and return in ASE. They examined the period 1995-2000 which was a very important period for the ASE. They tested the time series stock price behaviour toward volatility by using GARCH model and the conditional variability of stock returns by using M-GARCH model. They got the set of data from the ASE General index, and from three major industry indexes: Insurance, Banking and Miscellaneous. They investigated that the day of the week effect over the period 2001-2005 lost its significance and strength after the entry to the Euro-Zone.

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