The Day of the Week Effect: Evidence from the Athens Stock
Exchange Using Parametric and Non-Parametric Tests
Dimitra Vatkali1, Ioannis A. Michopoulos2, Dimitrios S. Tinos3
1
Department of Accounting and Finance, University of Macedonia, Thessaloniki, Greece
Mfin, MIT Sloan School of Management, Boston, USA
Msc FinEng, National Technical University of Athens (NTUA), Athens, Greece
Abstract: This study is dealing with the day-of-the-week effect. We examined the presence of this effect in the Athens Stock Exchange and the general index of the market FTSE ASE/20 for a time period of five years, using the daily prices of the index from January 21st 2010 to January 21st 2015. In order to test the-day-of the week effect we used the OLS regression method and the Kruskall-Wallis equality test. Our findings, of a weak day-of-the-week effect in the Greek stock market, confirm the findings of other researches that had been conducted in the period which preceded the financial crisis in Greece.
Keywords: NHIBE 2015, day effect, financial markets, market efficiency, stock prices
1. INTRODUCTION
The day-of-the-week effect, usually named as the Monday effect or the weekend effect, because the lowest and simultaneously negative returns met on Mondays according to the most researches, is an anomaly of the Efficient Market Hypothesis, whereby the mean daily return is the same in value and direction for all trading days of the week, as the EMH indicates that. At an early stage, researchers and academics believed that the average return is distributed in the same way among the days of the week. However, this theory was rejected by many empirical results. The first among those who examined the day-of-the-week-effect was Fama (1965) whose findings claim that the variance of the returns on Monday was 20% higher than the returns of the other days of the week. Generally speaking, most studies about the day-of-the-week effect were concerning the stock market of the US, but in a short period of time the related research was expanded and in other geographical regions and markets, covering the stock markets of the major economies of Europe and the emerging markets of Asia and Eastern Asia. This phenomenon happened, mainly, for two reasons. On the one hand, researchers wanted to make clear if the day-of-the-week effect is a characteristic of the US market and whether this phenomenon is present in other markets due to correlation between the US stock market with that of the other countries markets, and on the other hand, if this was a permanent phenomenon that characterizes all markets regardless the correlation that exists between them.
In general, there are different returns for the different trading days of the week. Many explanations exist, in the financial literature that tries to explain this phenomenon. Below we express some of these explanations. One possible explanation has to do with the investors’ sentiment. People happen to be more concerned / anxious on Monday, the first day of the week, and thus usually think of Monday as the worst day of the week whereas they think of
Friday, the last day of the week, as the best day. As a result of this situation, because of the pessimistic outlook the investors have on Mondays and the more optimistic outlook they have on Fridays, they proceed in selling and buying respectively, forming the prices accordingly.
Another reason for different returns among the days of the week may be attributed to the attempt to balance the decision between investors and brokers for the placement of buy and sell orders. Usually, during the week investors do not have much time to think and analyze their investments, and, therefore, leave the decision to brokers who are likely to buy. However, during the weekend, when the investors take their time to evaluate the market in more depth, they decide to sell and, consequently, they will force relevant movements on the prices when the stock market opens on Monday. Another idea in support of the day of the week effect is “information release”. It has been observed that companies, in order to make positive impact on peoples’ sentiment, usually, announce good news in the beginning of the week, meaning on Mondays, and bad news at the end of the week, meaning at the closing of the Stock Exchange on Friday. This technique, certainly, affects the price adjustment in the market. Besides that, the-day-of-the-week effect may exist because of settlement delays. In most stock markets, the payment of a transaction happens three days after the real time of the deal. Payments for transactions operated on Monday or Tuesday happen the following days in the same week, but deals that operated from Wednesday to Friday are payable the next week, since the stock market is closed on weekends. Consequently, the stock prices on Mondays should be lower than prices on Fridays in order to hedge the strategy of the investors to delay their purchases until Monday. Moreover, another rational explanation to the discussed phenomenon is the dividend exclusion. Finance theory claims that when a stock pays dividends, then the price of the stock follows a downward, and because the day that stocks usually pay dividends is Monday, the prices tend to be lower on this day.
However, the above mentioned explanations are only implications of the day of the week effect, and there is no certain explanation for this phenomenon. It is an anomaly of the market that we are trying to test empirically depending on the conditions of each market. In our study we are trying to examine the-day-of-the-week effect in the Athens Stock Exchange and for the most representative index FTSE ASE/20, using parametric and non-parametric tests as it is common practice in the literature. This study consists of 4 parts. Firstly, in the literature review we are referring in a brief way, to studies that examined the-day-of-the-week effect, concentrated our analysis to findings for the Greek stock market. Then we expose the data and the methodology we used to examine the-day-of-the-week effect, following by the empirical results in which we conclude from our analysis, and the conclusions where we add some more comments about the discussed issue. The last part of our paper is referring to the bibliography which used in order to conduct this research.
2. LITERATURE REVIEW
There is a lot of academic and scientific research in the field of the Efficient Market Hypothesis, and consequently the day of the week effect has been examined numerous times in the past due to its importance in the market and investment strategies for decision making. Cross (1973), French (1980), Gibbons and Hess (1981), Lakonishok and Levi (1982), Keim and Stambaugh (1984), Lakonishok and Smidt (1988), Connolly (1989) and Lakonishok and Maberly (1990) are the researchers who first introduced the day of the week effect. They focused their studies on the US stock market and found that Mondays are bad days for the US stocks, in comparison to other days of the week. More specifically, they found that average returns are negative on Mondays and lower that the average returns of the other days, while the returns on Friday tend to be higher. Similar results were proven in the paper of Hakan Berument and Halil Kiymaz (2001) who examined the S&P 500 market index for the US market for the period 1973-1997. Their analysis confirmed the above results of other papers showing that the day of the week effect is present in both volatility and return equations with the highest and lowest returns being observed on Wednesday and Monday and the highest and the lowest volatility on Friday and Wednesday, respectively.
Among the first who examined the day effect for the Greek stock market were Alexakis and Xanthakis (1995) who examined the period 1984-1994 separating, though, the sample in two sub-periods. They found that there were negative returns for the whole period only on Tuesdays whereas all the other days' average returns were strongly positive. Also, Nikou (1997) in his study confirmed the day effect for the Greek market by examining the banking and insurance sectors. Lyroudi, Noulas and Komisopoulos (2002) examined the day of the week effect in the Athens Stock Exchange using the prices of the general index along with five other sector indices for the period 1994 to 1999. They conclude that the day of the week effect is present in the Greek stock market, especially in the sub period 1997-1999. Kenourgios, Samitas and Papathanasiou (2005), investigated the day of the week effect in the Athens Stock Exchange (ASE) General Index for a ten year period,1995-2004 using two sub periods: 1995-2000 and 2001-2004. Using a conditional variance framework, they tried to test for possible existence of day of the week variation in both return and volatility equations. The findings indicated that the day of the week effect is present for the period 1995-2000, but much weaker for the period 2001-2004 there were negative returns for the whole period only on Tuesdays whereas all the other days' average returns were strongly positive. Another research taking notice of the recent financial crisis, was conducted by Hourvouliades and Kourkoumelis (2010), who examined the day effect for Greece, Turkey, Bulgaria, Romania and Cyprus for tow sub periods 2003- early 2007 and late 2007-2009 , before and after the crisis. They found strong evidence of the day effect in the first, pre-crisis, period but the results showed an absence of the seasonality of the average return in the second period both after and during the crisis.
3. DATA AND METHODOLOGY
The data set used in this paper consists of the closing daily prices of the general index FTSE ASE of the Athens Stock Exchange for a time period of five years from 21/01/2010 to 20/01/2015. From the Data sample, we created five more time series each of which consists of the closing prices of the days Monday to Friday respectively. In other words, each time series represents a different trading day of the week for the ASE. At first stage, we calculated the daily returns for all days and then the returns for each day from Monday to Friday for the whole period of our examination and in order to examine the day-of-the-week effect we used the standard OLS (Ordinary Least Squares) regression with dummy variables and the equality tests of mean which include the F-test and the Kruskall-Wallis test.
The model we used is widely accepted in the financial literature as a means for testing the day-of-the-week effect and includes five dummy variables each one for each trading day of the week, Monday to Friday. In our model we added a sixth variable which takes notice of the return of the previous day (t-1) in order to remove autocorrelation. The model has the following form:
Rt= β1Mont + β2Tuet + β3Wedt + β4Thut + β5Frit + β6Rt-1 + et (1)
Where Rt is the average return of the index on day t, Mont is the dummy variable for Mondays and takes the value 1 if the corresponding day is Monday and 0 otherwise. In the same way Tuet is the dummy variable for Tuesday and takes the value 1 if the corresponding day is indeed Tuesday and 0 otherwise etc. The factor et is the error term for which we assume that et ~ N (0, σ2). The factor βi, i=1…5 represents the average return of the days Monday to Friday.
The null hypothesis claims that the average returns of all trading days of the week are equal. So, we set as: Ho: β1=β2=β3=β4=β5. In order the day-of-the-week effect be present in the FTSE ASE we must reject the null hypothesis H0 and under this assumption the coefficients βi with i=1...5 are statistically significant at a 5% level, which is the level we set for our study.
The other test we used in our study includes the equality test of an F-test and the Kruskall-Wallis test. The Kruskall-Kruskall-Wallis test is a non-parametric test which examines the possible differences between the daily returns in a week that relax the assumption of normally distributed data. Again the null hypothesis is that there is no difference in the returns among the days of the week. The statistic test equation is shown below:
)
1
(
3
)
1
(
12
1 2+
−
+
−
∑
=n
n
R
n
n
=
W
K
k i i i (2) Where,n: is the total number of sample observations, ni: is the sample sizes in i trading day,
k: is the number of trading days’ return (k = 5), Ri: is the rank sum of the i trading day.
For large sample size, the test statistic of Kruskall-Wallis will follow the, x2 distribution with (k − 1) degrees of freedom. In order to reject the null hypothesis of no existence of the day of the week effect the chi-square statistic must exceed the critical value with (k-1) 4 degrees of freedom.
4. EMPIRICAL RESULTS
The results of our analysis seem to be in accordance to studies which examine almost the same period of time. The implementation of the OLS regression in the model (1) as we mentioned above, gave as the results that are presented in the table 1 below. According to the OLS coefficients we see that the return on Monday is negative and close to the price of the return of Tuesday. In the same way the returns of the rest days are again negative and have similar values. These findings are confirmed by the p-values leading us not to reject the null hypothesis of the equal returns of the trading days. The day-of-the-week effect would be present for the examined index if the coefficient of the dummy variable Mon was significant at a 5% level, something that is not confirmed by the t-statistic and the p-values for Mon. Consequently, if there was a day that has extremely different return than the other days, this would have been confirmed from the regression test, but in table 1 we cannot claim this theory. In other words, it seems that the day-of-the-week effect is not confirmed for the FTSE ASE since the OLS regression method we used does not give any evidence of the contrary.
Table 1: The OLS regression results
Variable OLS Coefficient t-stat prob
Mon -0,001756 -0,6670 0,386 Tue -0,001269 -0,1870 0,693 Wed -0,000207 -0,3176 0,237 Thu -0,008950 -0,0890 0,486 Fri -0,003220 -0,2300 0,585 Rt-1 0,054220 1,3540 0,352 Adjusted R-Squared 0,0036
The other test that we adopted in our study in order to examine the day of the week effect is the equality tests of an F-test and the Kruskall-Wallis test. The results of the equality test are presented below in table 2. The F-test, using the F-statistic is trying to test if the mean return of each day is equal, with each other, among the days of the week and not different from zero.
With the F-statistic has a value of 0.3291 and a probability around 0.8956, we can claim that the day-of-the-week effect cannot be confirmed.
Table 2: The equality tests of the F-test and Kruskall-Wallis test results Value Probability
F-statistic 0,3291 0,8956
K-W 2,1063 0,8342
We reach the same results by implementing the Kruskall-Wallis test. The calculation of the K-W statistic gave 2,1063 as a result. The critical value which we used to compare the above mentioned statistic is given by the chi-squared distribution with 4 degrees of freedom and is 9,48773 at the 5% level, and 13, 27670 at the 1% level. The K-W statistic is not significant at the 5% and 1% level, and therefore, the day-of-the-week, according to Kruskall-Wallis test, is not confirmed. Besides, the results of no day-of-the-week effect in the Athens stock market indicate that this market is efficient in past price and volume information and thus stock movements cannot be predicted using this historical information.
5. CONCLUSIONS
With the implementation of the above methodology, we have strong evidence that the day-of-the-week effect is weak for the Athens stock exchange and more specifically for the FTSE ASE/20. This picture is contradicted, compared to the studies for the same index the previous years. This may be attributed to the fact that we examined the period after the crisis in Greece, where many measures for the economy and the market have been applied. Consequently, investors have adjusted their investment behavior and seem not to concentrate in the returns of a specific trading day, as the return of each day tends to be the same in value and direction.
Of course, the sample we have examined for the period after the start of the financial crisis is small and thus, we have to evaluate a bigger sample which will evince a more complete picture of the crisis in the stock market. Some further suggestions for research over the same topic could be the examination of more indices of the Athens Stock Exchange, for instance the banking sector, construction sector and the insurance sector which may present the financial issues that rose to the surface in the Greek economy and Stock Market after the crisis in more depth and detail.
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