Day-ofthe-week Effect on Stock Markets in the Region

47 Abstract: This research examines calendar anomalies (day-of-the-week effect) on stock exchanges in the region. The main objective of the study is to examine the effect of days of the week on stock exchanges in the region in the period from 2008 to 2014, and whether there are differences in relation to the effects that occur during the crisis period from 2008 to 2011 and postcrisis period from 2012 to 2014. The subsample of the analysis shows different results due to an increase in the maturity of the capital market, the financial crisis, accession to the European Union and other important events for the financial markets in the region. The purpose of this paper is to determine whether the relationships between the average stock returns in emerging markets are the same or different across different days of the week. The study includes a quantitative analysis of the yield of stock exchange indices on a certain day that uses daily data from 01.01.2008 to 31.12.2014 for capital markets in Bosnia and Herzegovina, Bulgaria, Montenegro, Croatia, Macedonia, Romania and Serbia. The results of the study indicate the effect of the days of the week on all observed stock markets in the region, except for the stock market in Bulgaria. Obtained panel results support earlier studies conducted on emerging markets and provide evidence of stock market inefficiency.


Introduction
The idea of capital market efficiency originally emerged in the nineteenth century, but it reached its academic maturity in the 80s.With the development of the capital market, the significance and empirical validity of the theory of capital market efficiency is changing.The efficient market hypothesis stems from the view that it is impossible to predict the future price of shares on the basis of the previous price information and that the prices represent a reflection of all relevant information.The efficient market hypothesis claims that securities prices reflect all available information and fair value, while excessive instability of the capital market is in direct contradiction to the efficient market hypothesis.This hypothesis is the subject of debate in numerous literature due to its important implications.Academics, investors and regulators are ready to investigate the behaviour of stock prices and react whenever they notice underestimated or overestimated securities in the financial market.In the world of the efficient market hypothesis, there is no possibility to take advantage of the underestimation or overestimation of assets, as the invisible hand of the market moves faster than any individual agent.The purpose of this paper is to determine whether the relationships between the average stock returns in emerging markets are the same or different across different days of the week.Milošević-Avdalović and Milenković (2017) investigated the effects of the months on the observed stock exchanges in the region.The results of the survey indicated that most of the observed stock exchanges in the region (Serbia, Montenegro, Croatia and Macedonia) recorded negative returns on stocks in November.On the stock exchanges in Bosnia and Herzegovina and Romania the effects of the month were not recorded.The stock market in Bulgaria recorded a positive effect in August, while the negative effects were present on this stock exchange during the month of October.
After the World War II, the number of EMH studies increased, but not all studies confirmed the hypothesis.During this period, the theory of market efficiency remained in the shadow of the theory of rational expectation and the capital valuation model.To some extent, the theoretical logic of EMH, articulated by Regnault (1863), Cowles (1937), Fama (1965), Samuelson (1965) and Mandelbort (1963) provides convincing and useful means to develop price models of assets so it has become intellectual paradigm for generations of scientists (Ang et al., 2011).

Literature review
In modern finance, the theory of the efficient market hypothesis remains the subject of further discussion.On the one hand, the efficient market hypothesis perfectly describes the conditions of trading on modern stock exchanges, as the flow of information and the execution of trade is faster than ever.On the other hand, there are certain patterns in stock prices, which the efficient market hypothesis did not explain.In the last decades of the twentieth century, many EMH studies have concluded the existence of inefficiency, so called the efficient market paradox.Regarding the day-of-the-week literature, it claims that investors behave differently in various days of the week (Berument and Dogan, 2012).Bildik (1999) investigated the stock exchange yields and trading activities in emerging markets, such as the Istanbul Stock Exchange.By using the daily stock exchange index values at the closing on ISE-100 from 1988 to 1999, he found that Monday showed the lowest return and recorded the greatest instability during the week.On the other hand, Marquering, Nisser and Valla (2006) recorded the decrease in Monday effect on DJIA from 1960 to 2003.Doyle and Chen (2009) documented a wandering weekday effect for eleven major stock markets over the period from 1993 to 2007.Al-Khazali et al. (2008) using stochastic dominance analysis recorded that there exists a strong day effect with the highest observed on Fridays and the lowest on Tuesdays in the Athens Stock Exchange.Muhammad and Rahman (2010) investigated the elements of financial market efficiency and market anomalies.The study examined whether the day of the week effect really exists in Malaysia and whether there are differences in relation to the effect that occurs in the period between the beginning of financial crisis (1999)(2000)(2001)(2002) and four years after the financial crisis (2003)(2004)(2005)(2006), using daily data in the period from 04.01.1999 until 29.12.2006, which is a total of 2,085 observations.The researchers concluded that the effect of the day in a week was present in the capital market in Malaysia.Ivanov, Lomeov and Bogdanova (2012) examined the market efficiency of seven Eastern European stock exchanges based on the main stock exchange indices (BELEX15, BET, CROBEX, ISE100, PFTS, RTSI, SOFIX).Findings indicate that there is strong evidence of a deviation from market efficiency in Eastern European financial markets.Diaconasu and associates (2012) investigated the stock exchange in Bucharest, and the study results for the entire period from 2000 to 2011 point to the absence of any calendar effects -Monday's effect and the effect of January (2012).Caporale and Zakirova (2017) document in the Russian stock market, analysing the behaviour of the MICEX index over the period Sept.1997-Apr. 2016, that once transaction costs (proxied by the bid-ask spreads) are taken into account calendar anomalies disappear.
Based on all of the above, it can be noticed that the financial market efficiency has stirred up the interest of many researchers and has been the subject of debate for decades.The efficient market hypothesis has its advocates as well as opponents.It is clear that some markets are characterized by a higher, and some by lower efficiency together with the existence of anomalies.

Research methodology
While the calendar anomalies in developed capital markets have been explored intensively, stock exchanges in emerging economies have received less attention.This study includes analysis of the anomalies of the seven stock exchange indices that are indicators of changes in the capital market in the countries of the region (Serbia-BELEXline, Bosnia and Herzegovina-BIRS, Bulgaria-SOFIX, Montenegro-MONEX, Croatia-CROBEX, Macedonia-MBI10 and Romania-BET).It is important to emphasize that during this study data of daily changes of stock exchange indices were used, in the period from 01.01.2008 to 31.12.2014.For the analysis Day-of-the-week effect, daily data on stock market indices were used, taken from the archives of daily reports(indices) available on the official websites of the observed stock exchanges in the region.The number of observations in the observed period amounts to 1,767 trading days on the Belgrade Stock Exchange; 1,741 trading days on the Banja Luka Stock Exchange; 1,734 trading days on the Sofia Stock Exchange; 1,728 trading days on the Montenegro Stock Exchange; 1,747 trading days on the Zagreb Stock Exchange; 1,718 trading days on the Macedonian Stock Exchange and 1,760 trading days at the Bucharest Stock Exchange.
The T-test was used to indicate significant differences in average yields on the stock market.The obtained results are dependent on the characteristics of the capital market (maturity, size, degree of integration, models, data frequencies, etc.).The daily return to stock exchange indices is used through the following mathematical formula: Where is: P ntreturn in period t P nt-1return in period t-1 The next step, after conducting the analysis of average stock market yields on the stock markets in the region, is to test the value of average daily yields for all days of the week, in order to examine whether they are statistically different from zero.In order to test this hypothesis, it is necessary to use the T-test, which is calculated using the following formula: Where is:  ̅ -average daily return µ -hypothetical value that is equal to zero (0) σ/√n -standard error Hypothesis in the case day-of-the-week effect is: H0= µ1 = µ2 H1= µ1 ≠ µ2 µ1average yield of the stock exchange index on a certain day in% µ2 -yield of the stock exchange index on the remaining days of the week in%

Source: Author
Table 1 shows descriptive statistics of the stock exchange index returns in the local currency for each country.The average daily returns range between -0.0835% for Macedonia and -0.0177% for Romania.The skewness ranges between −0.995 for Bulgaria and 0.856 for Montenegro.
The following figures show the average daily return of stock exchange indexes for observed stock exchanges in the region.
The    In the period from 2008 to 2011, there was a negative effect on Tuesdays on the Belgrade Stock Exchange and the hypothesis that the average daily yield in the observed period is equal to the yield on other days of the week can be rejected.After the crisis period, the research indicates that the stock index BELEXline records positive effects on Thursdays and Fridays, as the p value is significantly lower than 0.05 and the direction is positive.The effect of the day of week for the entire observed period observed (2008)(2009)(2010)(2011)(2012)(2013)(2014) indicates that the negative average yield recorded on Tuesdays on the Belgrade Stock Exchange is statistically significant in relation to the average yields of the index, as well as the positive average yield on Thursdays and Fridays in relation to other days in a week.The observed day of the week anomaly is in line with the studies conducted by numerous researchers in the world and confirms the notion that the negative average yield is present on Tuesdays, while the positive average yield is present on Thursdays and Fridays, which is in line with Western theoretical frameworks.The obtained results thus indicate that Tuesday has recorded a negative effect during the crisis period and entire observation period, while Thursday and Friday recorded a positive effect during the postcrisis period and entire observation period.From all of the above, it can be concluded that the negative and positive effects, measured by the BELEXline stock market index, are stable for the whole period of observation.One possible explanation for the effect of the days of the week is that most negative economic news comes early in the week and investors are trying to sell their investments, which results in a negative statistically significant yield at the beginning of the week.Comparing the crisis and post-crisis period on the Belgrade Stock Exchange, it was noticed that the standard deviation was significantly higher during the crisis period, which is in line with the higher risk.
The lowest average yield was recorded on Tuesday (-1697), while the highest average yield was recorded on the last days of the week, i.e.Thursday and Friday (0.0242).The highest instability measured by standard deviation was recorded on Monday (1.15717).
In the observed crisis period, the BIRS Stock Exchange index recorded positive effects on Fridays and the null hypothesis is rejected, as the average yield of the stock exchange index is significantly higher than on other days of the week, which suggests to investors what the ideal timing for gaining return on the stock market is.Post-crisis period did not record significant effects of the days of the week, as evidenced by the obtained p-values of the T-test, which are significantly higher than the critical value of 0.05.The research results for the period from 2008 to 2014 indicate that a positive effect exists on Friday, but it is not stable for the entire research period.Positive returns on Friday, after the crisis period, indicate that they are slightly different from other days of the week.During the crisis period, there was a significantly higher standard deviation compared to the post-crisis period.Interestingly, during the crisis period, positive average yield on the observed stock market was recorded on Friday, while other days recorded negative average yields.The highest average yield was recorded on Friday and was 0.0162.The greatest instability, measured by the standard deviation, was present at the Banja Luka Stock Exchange on Tuesdays and Mondays, 0.77454 and 0.69219, respectively.Based on the conducted empirical research, it can be concluded that the effects of the day are present (lower average return on Mondays and Tuesdays compared to Friday).
The observed crisis period did not record the effect of the days of the week.In the period from 2008 to 2011, on the Sofia Stock Exchange negative average yield of the SOFIX Stock Exchange index for all trading days, as well as high standard deviation, was recorded.The null hypothesis is accepted, because not one day in a week has recorded a significantly higher or lower yield compared to the average yield on other days of the week.In the period from 2012 to 2014, there was also no day of the week effect.The highest average yield was recorded in the middle, but it is not statistically significant, that is, pvalue is greater than 0.05 and is 0.175.The T-test points to statistically significant differences in yields on the observed stock market on a certain day, compared to the average yields of other days.Thus, the highest negative and statistically significant yield for the observed period was recorded in Wednesday, while the highest positive yield was recorded on Friday.The null hypothesis for these days in the period from 2008 to 2011 is rejected.In the aftermath of the crisis period, the effect of the days of the week on the observed stock exchange was not recorded.It is believed that the high market instability that followed the period of the financial crisis led to the disappearance of calendar anomalies -days of the week effect.Analysing the day of the week effect on the Montenegro Stock Exchange, during the entire research period, results indicate that a positive effect exists on Friday.Testing effects of the day of the week indicates that the lowest average yield was recorded in Wednesday, and the highest average yield was recorded on Friday at 0.1114.The greatest instability, measured by the standard deviation, was present at the Montenegro Stock Exchange on Monday at 1.69856.During the crisis period, the T-test confirms the presence of anomalies on the Zagreb Stock Exchange, i.e. confirms that the average yields realized on Monday compared to other days in the observed period are negative and statistically significant, and hence the null hypothesis due to the existence of anomalies is rejected.In the period after the crisis on the Zagreb Stock Exchange, a negative effect was observed on Mondays and a positive effect was recorded on Thursday and Friday.Based on the analysis of the entire research period, the obtained results indicate that there is a negative effect on Mondays and such an effect was stable for the whole observation period while the positive effects were observed on Thursdays and Fridays but only in the period from 2011 to 2014, that is, in the post-crisis period.Testing the effects of the day of the week indicates that the lowest average yield was recorded on Mondays and Tuesdays, respectively at the beginning of the week compared to the last days of the week.The highest average yield was recorded on Thursday and is 0.0307.The highest instability, measured by the standard deviation, is present at the Zagreb Stock Exchange on Monday and equals 1.63721.Based on the conducted empirical research, it can be concluded that the effects of the day are present (lower average yield on Monday compared to Friday).It is considered that the negative average return on Tuesday was caused by a negative return that is present on the stock exchanges on Monday.
The observed crisis period did not record the presence of calendar anomalies on the Macedonian Stock Exchange.All days recorded a negative return on the stock market index MBI10, as well as a high standard deviation.The postcrisis period recorded the effects of days on Tuesdays and Fridays.Tuesday was marked by negative yields, while Friday recorded positive yields and indicates the presence of anomalies after the crisis period.
The conducted study for the period from January 2008 to December 2014 indicates that the lowest average yield was recorded at the beginning of the week compared to the last days of the week.The lowest average yield was recorded on Tuesdays and Mondays, amounting to -0.1897 and -0.1710, respectively.The highest average yield was recorded on Friday and amounted to -0.0112, (if we exclude the business data on Saturday, since only 3 days of trading were recorded).The greatest instability, measured by standard deviation, was present on the Macedonian Stock Exchange on Thursdays and Mondays, amounting to 1.38820 and 1.33580, respectively.Based on the conducted empirical research, it can be concluded that the effects of the day were present (lower average return on Mondays compared to Friday).The obtained results of the research on the Macedonian Stock Exchange indicate the presence of a positive effect on Friday and a negative effect on Tuesdays after the crisis period, but it is not stable for the duration of the research, neither for the crisis period nor the entire research period.
The observed crisis period, from 2008 to 2011, recorded the presence of a negative effect on Tuesdays and a positive effect on Thursday, indicating that the beginning of the week is characterised by lower return rates compared to the end of the week which recorded higher statistically significant return rates.
The observed period from 2012 to 2014 has no traditional effect on Mondays or any other days.It is possible that the financial crisis has led to the disappearance of calendar anomalies on the observed stock exchanges.deviation, is present at the Bucharest Stock Exchange on Monday, amounting to 1.94136.Based on the conducted empirical research, it can be concluded that the effects of the day are present.It is considered that the negative average yield on Tuesday was caused by the negative yield that is present on the stock exchange on Monday.The analysis of the entire period rejects the null hypothesis of equal average yields on all days of the week, since a higher yield rate was recorded on Thursday (as well as a lower dispersion around the mean value), while a statistically significantly lower yield rate was present on Tuesday (with greater dispersion over the mean values).The obtained results indicate that the effects of the days of the week were not stable for the observed periods, i.e. they were not recorded only in the post-crisis period.From the presented graph, one can generalize the result for countries in the region (emerging economies) that average standard deviations are higher at the beginning of the week (Monday, Tuesday, Wednesday) compared to the end of the week (Thursday, Friday) in the period from 2008 to 2014.The following table also presents statistical calculations of standard deviation values per day compared to the average value of standard deviation.
Standard deviation values for a particular day that are higher than the average standard deviation of up to 5% represent a mean standard deviation, while values greater than the average standard deviation of 5-10% represent a high standard deviation for a particular day.
The presented table shows that the statistically significant negative and positive rates of stock market yields in the region were recorded on certain days of the week.In the beginning of the week, the negative return on the stock exchanges in selected emerging economies gives clear signals to investors when they need to buy, when to sell certain securities, in order to achieve higher yields.

Conclusions
Since its inception in the 1980s, the efficient market hypothesis has gained much attention and has been seen as an absolute truth.However, since then, it has provoked numerous controversies.Many studies concluded the inefficiency of the market, and the EMH is currently seen as a relative truth.
Obtained panel results obtained support earlier studies conducted on emerging markets and provide evidence of stock market inefficiency.The obtained results indicate that the P value is lower than 0.05 indicating that the mean value on observed days is different from other days, and the null hypothesis can be rejected.Such findings are in line with the numerous studies in the world that prove the presence of the effect of days of the week, or the presence of anomalies on stock exchanges.The results show that all stock exchanges, except the Sofia Stock Exchange, recorded statistically significant negative returns at the beginning of the week, while average yields are higher at the end of the week, i.e.Thursday and Friday.These findings are in general agreement with those of Al-Khazali et al. (2008), Bildik (1999), Muhammad and Rahman (2010), they are somewhat different from Brusa, Pu and Schulman (2000), Brusa and Liu (2004).Interestingly, the only stock market in Croatia recorded the traditional effect on Monday, which reflects statistically significant negative directions of the average return of the stock index CROBEX for all periods of observation.Other stock exchanges in the region record positive or negative effects on a particular day, but not on Monday.Different statistical approaches have been developed to address the issue of market efficiency.Alternative methodologies and alternative theoretical frameworks are examined to obtain a valuable insight that would help resolve the debate in the future.
The obtained research results on the effects of the day on the week, can have significant implications for different players in the capital market, such as investors, managers and regulatory bodies.Investors can formulate their strategies based on this result and can earn more yields by predicting future prices.The only weakness of this part of the study is that it does not consider the individual stock price but stock exchange indices.Thus, the investment strategy based on the findings of these studies can not provide the expected results when investing in individual securities.But, if the size of a portfolio closely represents market, then such an investment strategy, based on the findings of stock market studies in the region, can provide extra profit for investors.As the presence of the day of week-anomalies indicates the inefficiency of the financial market, it informs regulators and economic policy makers to take the appropriate steps to remove such anomalies in order to make the market efficient.
Fig.1 represents the daily yields of stock exchange indices for countries in the region in the period from 2008 to 2014.The greatest instability of daily yields in the countries in the region is visible in the period of 2008, when all observed stock exchanges recorded an average negative yield rate.All stock exchanges show a clear tendency to renew the standard model of behaviour during 2009 and 2010.In contrast, 2011 brings a new wave of instability for all stock exchanges, because the sovereign debt crisis in the Eurozone deepened during the second half of 2011.The next figure represents the standard deviations of the stock exchange index yield.

Figure 1 .
Figure 1.Average daily returns stock indexes in the region for the period from 2008 to 2014

Figure 2 .
Figure 2. Standard deviation of the stock exchange indices in the region for the period from 2008 to 2014

Figure 3 .
Figure 3.Average standard deviation by days on observed stock exchanges in the region from 2008 to 2014

Table 1 .
Descriptive statistics of the stock exchange index returns for the period from 2008 to 2014

Table 2 .
The effect of the day on the week for the stock exchange index BELEXline -Serbia

Table 3 .
The effect of the day on the week for the stock exchange index BIRS -Bosnia and Herzegovina

Table 4 .
The effect of the day on the week for the stock exchange index SOFIX -Bulgaria

Table 5 .
The effect of the day on the week for the stock exchange index MONEX -Montenegro

Table 6 .
The effect of the day on the week for the stock exchange index CROBEX -Croatia

Table 7 .
The effect of the day on the week for the stock exchange index MBI10 -Macedonia

Table 8 .
The effect of the day on the week for the stock exchange index BET -RomaniaThe analysis of the T-test for the entire research period confirms the presence of anomalies on the Bucharest Stock Exchange, that is, statistically significant negative yields on Tuesdays and positive yields on Thursdays, as effects of the day in the week.Testing the effects of the day on the week indicates that the lowest average yield was recorded at the beginning of the week compared to the last days of the week.The lowest average yield was recorded on It is noticeable that in the observed period only the Sofia Stock Exchange did not register statistically (the tests values are not significant) significant anomalies (effects of the day).Numerous research in Europe indicate that membership in the European Union leads to a reduction in calendar anomalies.Bulgaria joined the EU in 2007.Likewise, this result can be a consequence of the global financial crisis, after which investors got more cautious on the stock market.From the foregoing findings, it follows that the capital market in Bulgaria is reasonably efficient, where prices reflect all publicly available information.