Calendar effects in the Dutch stock market

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Calendar effects in the Dutch stock market

Name: Rick Pasman Student number: s2207702

Date: January 14, 2016 Study program: MSc Finance

Supervisor: dr. Y.R. Kruse

Field key words: efficient market hypothesis, market efficiency, market anomalies, small-firm effect, size effect, January effect, Monday effect, day of the week effect, monthly effect, calendar effect

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1 Introduction

According to the Efficient Market Hypothesis one should not be able to consistently earn excess returns, because all information is already incorporated in the price of securities. However, several market anomalies have been found that run counter market efficiency such as the size effect, January effect and Monday effect . The Monday effect is a day of the week effect, whereas the January effect is a monthly effect. These effects are also known as calendar effects and can be found in several stock markets. A day of the week effect may also be found in the volatility. Some

researchers found that the effects are disappearing. Therefore the goal of this paper is to see whether there still is a day of the week effect or monthly effect in the mean excess return or in the volatility in the Dutch stock market.

The first goal of this paper is to test whether the mean excess returns of all days of the week are equal or whether there is a day of the week effect. The second goal is to test whether there is a day of the week effect in the volatility. The third goal is to test whether the expected excess returns of all months are equal or whether there is a monthly effect. The fourth goal is to test whether there is a monthly effect in the volatility. When a significant day of the week effect or monthly effect is found this will be translated into an investment strategy, which will be back tested and be compared to a hold strategy. A GARCH(1,1) model will be used to test for these effects.

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found in the full period, but is found on an individual stock level for DSM, Shell and Unilever. When comparing with the sub periods, the perceived effects do not seem to be stable. Effects in the volatilities have been found, especially daily effects. Again, these effects do not seem to be stable when comparing with the sub periods.

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2 Literature review

According to Fama (1970) and his Efficient Markets Hypothesis (EMH) investors cannot consistently earn excess returns, because prices already reflect all information. This is based on three conditions: 1) there are no transaction costs, 2) all information is costlessly available to all market participants and 3) all investors agree on the implications of current information for the current price and distributions of future prices. If all these conditions are met one can say that the prices of security reflect all available information. There are three forms of efficiency: the weak form, the semi-strong form and the strong form. In the weak form prices are based on historical information only. In the semi-strong form prices are reflected by all publicly available information. In the strong form prices also reflect information that is not publicly available.

However, some anomalies that run counter market efficiency have been found. For instance several types of calendar effects have been found such as season effects, monthly effects and weekly effects. Yuan, Zheng and Zhu (2006) even found an effect of lunar phases. They found that stock returns were lower when there was a full moon than when there was a new moon. Their sample consisted of 48 countries and they found statistically and economically significant evidence. An explanation they give for this effect is investor mood. Shu (2010) found that mood has an impact on the risk attitude and time preference of investors. In his research he found a positive correlation between investor mood and asset prices.

The January effect can be placed under the category of calendar effects. The January effect is the effect that stock returns are higher in January than in the other months of the year. Rozeff and Kinney (1976) were one of the first to discover the January effect. They found higher mean returns in January compared to most other months on the New York Stock Exchange. They also state that January has a relatively high risk premium compared to other months. A possible explanation for the January effect that is given by the authors is the tax-selling hypothesis, which means that investors realize their losses for tax purposes at the end of the year.

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Banz (1981) found that, on average, smaller firms had higher risk adjusted return than larger firms. He called this the size effect. Keim (1983) found that nearly fifty percent of this size effect is caused by abnormal returns in January. The main part of this January effect takes place in the first week and especially on the first trading day of the year. An explanation for this effect may be that investors realize their losses for tax purposes at the end of the year, which will lead to lower stock prices. In January the stocks prices will return to equilibrium. This should lead to abnormal returns (Jones, Pearce & Wilson, 1987). However, in their research they found that the January effect also existed before the introduction of taxes and that there was no significant change after the introduction of taxes.

Mehdian and Perry (2002) research whether the January effect is stable over a long period of time. The have tested this on the Dow Jones Composite, the New York Stock Exchange and the S&P 500. They have found significant evidence of a positive January effect in all three of the indices. However, they found a change around 1987. In that year there was a stock market crash. When testing the period before the crash they found the January effect in all three indices. However, in the period after the crash the return in January was positive, but statistically insignificant. This indicates that there is no January effect in the US stock market after 1987. Because the January effect has disappeared the results also question the tax-selling hypothesis.

Sun and Tong (2010) research the higher risk premium that was found by Rozeff and Kinney (1976). Their results show that the risk premium in January is higher than other months but the risk itself is not. This suggest that the January effect is caused by a higher risk compensation. It is not clear why this is the case.

Another, maybe less famous, effect in the category of calendar effects is the Monday effect. Also called the weekend effect. French (1980) stated, since stocks are only traded from Monday till Friday, that if returns are generated continuously in calendar time, the returns off Monday will represent a three day investment and therefore should, on average, be three times higher than the return of the other days of the week. If however returns are generated in trading time, the return will be the same for each day. However he found an interesting result, namely that the mean return for Mondays was significantly negative, while the return for the other four days was positive. This runs counter with both calendar time and trading time.

Chang, Pinegar, and Ravichandran (1993) found evidence of the day-of-the week effect in Canada, Hong Kong, France, Italy, the Netherlands, Spain and Sweden. However, the effects were not

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Wang, Li and Erickson (1997) researched the Monday effect during the period 1962-1993. They found that the Monday effect was mainly caused by the last two weeks of the month. In the first three weeks they didn’t find a significantly negative Monday return. When testing for different sub periods the results were still the same. This is also the case for different types of indices. The authors give the correlation between the Friday return and the Monday return as a possible explanation for their findings. However, after testing this they cannot find evidence that can fully explain the differences between the Monday return of the first three weeks and Monday return of the fourth week. According to Wang, Li and Erickson their findings may help investors who already decided to buy or sell a stock in timing their trade. Investors should sell their stocks before the end of the third week and buy after the fourth Monday of the month.

Dubois and Louvet (1996) tested for the day-of-the-week effect on eleven indexes from nine

countries, among them the U.S., the U.K. and Japan, over the period 1969-1992. They found negative returns on Mondays, but abnormal positive returns on Wednesday, except in Japan and Australia. There they found negative effects on Tuesday.

Jaffe and Westerfield (1985) tested for the weekend effect on daily returns of stock market indices in five countries: Japan, Canada, Australia, the U.K. and the U.S. A weekend effect has been found for each of the indices. However, in contrast to Canada, the U.K. and the U.S., in Australia and Japan the lowest mean return was on Tuesday instead of Monday. This was also found by Dubois and Louvet (1996). A possible explanation that is given, is that this could be because of the time zone

differences. After testing this they state that the time zone differences cannot explain this for Japan but may explain it for Australia.

According to Sullivan, Timmermann and White (2001) the research of calendar effects in stock returns often suffers from data-mining biases, which may cause the statistical significance of these effects to be invalid. In their research, the authors try to deal with these data-mining biases. They find that the evidence of calendar anomalies is then much weaker. The authors state that especially the statistical significance of the Monday effect is weak. According to them the effect on Mondays has to do with a lot of other causes than only the Monday rule.

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effect took place in the last two weeks of the month. However, in the 1987-1999 period they found different results. Monday returns became significantly positive for the large cap indices. For the small cap indices the Monday returns were negative but insignificant. The results of this research show that a reversal of the Monday effect took place in U.S. large cap stocks. This is not the case for U.S. small cap stocks, were there still is a Monday effect. Possible explanations that are given are an increase in institutional trading volume and a transaction cost advantage in large-cap stock for institutional investors.

Kohers et al. (2006) found evidence of a day-of-the-week effect in the period 1980-1990 in, under among others, the Netherlands. Monday returns were significantly lower and negative compared to most days of the week. However, they also found a reversal of the Monday effect. It started to fade away starting in the 1990s. According to them this may be caused by an increased in market efficiency.

Dicle and Levendis (2014) test for day-of-the-week effects in 51 markets from 33 countries between January 2000 and December 2007. They also test for a day-of-the-week effects on an individual stock level. They found an effect on Mondays for 24 of the 51 markets and an effect on Fridays for 32 of the of the 51 markets. At the individual stock level they found a day-of-the-week effect for around 8% of the stocks on markets that have a day-of-the-week effect and for around 7% of the stocks on markets that do not show this effect. The stocks that show a day-of-the-week effect often are smaller stocks. The authors give several possible explanations for the day-of-the-week effect, but after testing the hypotheses they cannot find one that can explain all the day-of-the-week effects that they have found.

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3 Data

The data that I will use is the excess returns of the Amsterdam Exchange Index (AEX) and the excess return of individual stocks on the AEX index. The AEX is the big cap index of the Netherlands. It contains the 25 companies with the biggest market capitalization. The index is calculated based on the weighted average of the stocks in the AEX. Besides the AEX the Dutch stock market consists of the AMX (MidCap) and the AScX (SmallCap).

The data consist of the Return Index of the AEX and the individual stocks. The return index assumes that all dividends are reinvested and therefore it better reflects the real return . The time period from which the data is collected is from January 1, 2000 till December 31, 2014. Only the firms that were in the AEX index during the whole sample period will be used for the individual stock analysis, which are the following stocks: Ahold, Akzo Nobel, DSM, Heineken, ING, Philips, Shell and Unilever. The data is collected on both daily basis and monthly basis using DataStream. This is a database containing information on equities, indices, macro-economic data and financial data on companies. It can be accessed at the Rijksuniversiteit Groningen.

Returns of the index and the individual stocks are calculated using the following formula: 𝑅𝑡 = 100 ∗ ln

𝐼𝑡

𝐼𝑡−1

In which It is the value of the index or stock at time t, It-1 is the value of the index or stock on the

previous day or in the previous month and Rt is the daily or monthly return of the index or stock.

The Eonia rate is being used as the risk free rate for the daily data. Eonia stands for Euro OverNight Index Average. This is the rate at which banks loan to each other with a duration of one day. Because it is an annualized rate, it has to be transformed into a daily rate. We do this by using the day count method. Therefore we have to divide the annualized rate by 360 to get the daily risk free rate (Hull, 2012).

The one month Euribor rate is being used as the risk free rate for the monthly data. Euribor stands for Euro Interbank Offered Rate. This rate is based on the average rate at which European banks want to lend money to each other. Because the Euribor rate is an annualized rate, it has to be transformed into a monthly rate. Again, we use the day count method. Therefore we have to divide the annualized rate by 12 to get the monthly risk-free rate (Hull, 2012).

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Figure 1: Mean excess returns of the AEX index for each day of the week for the full period, period before the crisis and period after the crisis.

Figure 2: Mean excess returns of the AEX index for each month for the full period, period before the crisis and period after the crisis.

In figure 1 above the mean excess return of the AEX index for each day of the week is shown. In the full period the Thursday has the highest (0,028 %) and the Wednesday has the lowest mean excess return (-0,057%). In the period before the crisis again the Thursday has the highest mean excess return (0,107 %) and the Wednesday again has the lowest mean excess return (-0,126 %). However in the period after the crisis the Wednesday has the highest mean excess return (0,090 %) and the Friday has the lowest mean excess return (0,020 %).

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3.1 Daily data

Descriptive statistics of the daily data are shown table 1, 2 and 3 below. All data is observed from January 1, 2000 till December 31, 2014. In this period the financial crisis of 2007-2008 took place. Therefore, the data will also be observed for sub periods before and after this crisis: January 1, 2000 till December 31, 2006 and January 1, 2009 till December 31, 2014. The sharp ratio can be used to calculate a risk adjusted return. It can be calculated by dividing the excess return with the standard deviation. A higher sharp ratio means a higher risk adjusted return.

3.1.1 Full period

In table 1 the descriptive statistics of the full period are shown. The highest mean excess return is of DSM (0.000383). The lowest is of the Ahold (-0.000064). The highest standard deviation of the excess returns is of ING (0.030676), while the lowest is of Unilever (0.014658). DSM has the highest sharp ratio (0.022387). The lowest sharp ratio in the is the AEX index (-0.003376).

Table 1: Descriptive statistics of full period daily data Index/Stock Number of observations (trading days) Minimum daily excess return Maximum daily excess return Mean daily excess return Standard deviation of daily excess return Sharp ratio AEX Index 3913 -0.096027 0.100157 -0.000050 0.014708 -0.003376 Ahold 3913 -0.995009 0.237668 -0.000064 0.026082 -0.002437 Akzo Nobel 3913 -0.114962 0.183582 0.000165 0.019326 0.008519 DSM 3913 -0.167023 0.097253 0.000383 0.017111 0.022387 Heineken 3913 -0.130600 0.095865 0.000224 0.015006 0.014898 ING 3913 -0.321349 0.256528 -0.000092 0.030676 -0.002988 Philips 3913 -0.141565 0.136272 0.000009 0.024639 0.000381 Shell 3913 -0.103166 0.131038 0.000144 0.015497 0.009300 Unilever 3913 -0.107245 0.104204 0.000281 0.014658 0.019176

3.1.2 Before crisis period

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Table 2: Descriptive statistics of before crisis period daily data Index/Stock Number of observations (trading days) Minimum daily excess return Maximum daily excess return Mean daily excess return Standard deviation of daily excess return Sharp ratio AEX Index 1825 -0.075433 0.095103 -0.000134 0.014907 -0.008989 Ahold 1825 -0.995009 0.237668 -0.000578 0.034893 -0.016564 Akzo Nobel 1825 -0.096389 0.125136 0.000087 0.018745 0.004625 DSM 1825 -0.071033 0.097253 0.000497 0.015551 0.031959 Heineken 1825 -0.130600 0.074328 0.000124 0.014928 0.008306 ING 1825 -0.161112 0.157022 0.000219 0.023898 0.009163 Philips 1825 -0.141565 0.136272 -0.000052 0.029210 -0.001783 Shell 1825 -0.103166 0.085772 0.000068 0.015776 0.004323 Unilever 1825 -0.107245 0.104204 0.000192 0.015358 0.012501

3.1.3 After crisis period

In table 3 the descriptive statistics of the period after the crisis are shown. The highest mean excess return is of DSM (0.000791). The lowest is of ING (0.000418). The highest standard deviation of the excess returns is of ING (0.033294), while the lowest is of Unilever (0.014907). Heineken has the highest sharp ratio (0.053073). The lowest sharp ratio is of ING (0.012554).

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3.2 Monthly data

Descriptive statistics of the daily data are shown in table 4, 5 and 6 below. All data is observed from January 1, 2000 till December 31, 2014. In this period the financial crisis of 2007-2008 took place. Therefore, the data will also be observed for sub periods before and after this crisis: January 1, 2000 till December 31, 2006 and January 1, 2009 till December 31, 2014. The sharp ratio can be used to calculate a risk adjusted return. It can be calculated by dividing the excess return with the standard deviation. A higher sharp ratio means a higher risk adjusted return.

In table 4 the descriptive statistics of the full period are shown. The highest mean excess return is of DSM (0.008327). The lowest is of the ING index (-0.001993). The highest standard deviation of the excess returns is of ING (0.129273), while the lowest is of Unilever (0.054887). DSM has the highest sharp ratio (0.111628). The lowest sharp ratio in the is the AEX index (-0.027719).

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In table 5 the descriptive statistics of the before crisis period are shown. The highest mean excess return is of DSM (0.010803). The lowest is of Ahold (-0.012569). The highest standard deviation of the excess returns is of Ahold (0.169197), while the lowest is of Heineken (0.053027). DSM has the highest sharp ratio (0.147569). The lowest sharp ratio is of Ahold (-0.074286).

Table 5: Descriptive statistics of before crisis period monthly data Index/Stock Number of observations (trading days) Minimum monthly excess return Maximum monthly excess return Mean monthly excess return Standard deviation of monthly excess return Sharp ratio AEX Index 84 -0.228813 0.144502 -0.003653 0.061494 -0.059404 Ahold 84 -1.199110 0.442179 -0.012569 0.169197 -0.074286 Akzo Nobel 84 -0.212206 0.137045 0.001883 0.077445 0.024314 DSM 84 -0.282659 0.134327 0.010803 0.073206 0.147569 Heineken 84 -0.104978 0.146727 0.002698 0.053027 0.050879 ING 84 -0.463016 0.351859 0.004753 0.099319 0.047855 Philips 84 -0.331769 0.244833 -0.001132 0.108428 -0.010440 Shell 84 -0.190869 0.132474 0.001482 0.057367 0.025833 Unilever 84 -0.166906 0.189600 0.004173 0.062079 0.067220

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4 Methodology

4.1 Day of the week effect

To test for calendar effects in mean stock returns the Ordinary Least Squares (OLS) method can be used to estimate unknown variables. Dummy variables will be created for the days of the week and the months. So, to test for the day of the week effect the following OLS regression can be used:

𝑅𝑡 = 𝛼1+ ∑5𝑖=2𝛼𝑖𝐷𝑖𝑡+ 𝜀𝑡 (1)

In which Rt is the daily excess return of the index or stock. Dit = 1 for day i and will be 0 for all other

days of the week (i = 2 till i = 5 stands for Tuesday till Friday). The α1 stands for the expected excess

return on a Monday. The α2, α3, α4, and α5 stand for the difference in expected excess return

between Monday and the expected excess return of the other days of the week. This means that if there are no differences in expected excess returns between a Monday and another day the αi will

be zero. The εt is an error term.

The two previous equations assume the covariance matrix is the same for all days of the week. However, this may not be the case because returns on Mondays may have a higher variance relative to other days (Fama, 1965). He found that the variance of returns on Mondays is approximately 22% higher than the variance on other days of the week. If this is the case we have to deal with

heteroscedasticity. Therefore we have to make use of the GARCH (1,1) test instead of OLS. The GARCH model allows the conditional variance to depend on its own previous lags.Equation 1, for the day of the week effect, will therefore transform in:

𝑅𝑡 = 𝛼1+ ∑5𝑖=2𝛼𝑖𝐷𝑖𝑡+ 𝜀𝑡

𝜎𝑡2= 𝜔1+ 𝛾𝜀𝑡−1+ 𝛽𝜎𝑡−12 + ∑5𝑖=2𝜔𝑖𝐷𝑖𝑡 (2)

In which σt2 is the conditional variance. The ω1 is the expected variance on a Monday. The ω2, ω3, ω4

and ω5 stand for the difference in expected variance between a Monday and the expected variance

of the other days of the week. When the estimates of α2, α 3, α 4, and α 5 are close to zero and the

F-statistic, measuring the joint significance, is insignificant we can say that the expected excess return is the same for each day of the week (French, 1980). This can be tested using a Wald test.

Hypothesis 1, for the day of the week effect in excess returns, therefore becomes: 𝐻0: 𝛼2= 𝛼3 = 𝛼4= 𝛼5= 0

𝐻1: 𝛼2≠ 0 𝑜𝑟 𝛼3≠ 0 𝑜𝑟 𝛼4≠ 0 𝑜𝑟 𝛼5 ≠ 0

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𝐻1: 𝜔2≠ 0 𝑜𝑟 𝜔3 ≠ 0 𝑜𝑟 𝜔4 ≠ 0 𝑜𝑟 𝜔5 ≠ 0

These two hypotheses will be tested over the full period (January 1, 2000 – December 31, 2014). I will also test the hypotheses in two sub periods. One period before the financial crisis of 2007-2008 (January 1, 2000 – December 31, 2006) and one period after the crisis (January 1, 2009 – December 31, 2014). When one of the null hypothesis is rejected there is a day of the week effect in the excess returns or variance of the excess returns.

4.2 Monthly effect

To test for the monthly effect the following OLS regression can be used:

𝑅𝑡 = 𝛼1+ ∑12𝑖=2𝛼𝑖𝐷𝑖𝑡+ 𝜀𝑡 (3)

In which Rt is the monthly excess return of the index or stock. Dit = 1 for month i and will be 0 for all

other months (i = 2 till i = 12 stands for February till December). The α1 stands for the expected

excess return in January. The α2 till α12 stand for the difference in expected excess returns between

January and the expected excess return of the other months. This means that if there are no differences in expected excess returns between January and another month the αi will be zero. The

εt is an error term.

Again, we will transform this into a GARCH(1,1) model. Therefore equation 3, for the monthly effect, will be transformed in the following equation:

𝑅𝑡 = 𝛼1+ ∑5𝑖=2𝛼𝑖𝐷𝑖𝑡+ 𝜀𝑡

𝜎𝑡2= 𝜔1+ 𝛾𝜀𝑡−1+ 𝛽𝜎𝑡−12 + ∑12𝑖=2𝜔𝑖𝐷𝑖𝑡 (4)

In which σt2 is the conditional variance. The ω1 is the expected variance in January. The ω2 till ω12

stand for the difference in expected variance between January and the expected variance of the other months.

Hypothesis 3, for the monthly effect in excess returns, therefore becomes: 𝐻0: 𝛼2= 𝛼3 = 𝛼4= 𝛼5= 𝛼6= 𝛼7= 𝛼8= 𝛼9= 𝛼10= 𝛼11= 𝛼12 = 0

𝐻1: 𝛼2≠ 0 𝑜𝑟 𝛼3≠ 0 𝑜𝑟 𝛼4≠ 0 𝑜𝑟 𝛼5 ≠ 0 𝑜𝑟 𝛼6 ≠ 0 𝑜𝑟 𝛼7 ≠ 0 𝑜𝑟 𝛼8 ≠ 0 𝑜𝑟 𝛼9 ≠

0 𝑜𝑟 𝛼10 ≠ 0 𝑜𝑟 𝛼11 ≠ 0 𝑜𝑟 𝛼12 ≠ 0

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𝐻1: 𝜔2≠ 0 𝑜𝑟 𝜔3 ≠ 0 𝑜𝑟 𝜔4 ≠ 0 𝑜𝑟 𝜔5 ≠ 0 𝑜𝑟 𝜔6 ≠ 0 𝑜𝑟 𝜔7 ≠ 0 𝑜𝑟 𝜔8 ≠ 0 𝑜𝑟 𝜔9 ≠

0 𝑜𝑟 𝜔10 ≠ 0 𝑜𝑟 𝜔11 ≠ 0 𝑜𝑟 𝜔12 ≠ 0

These two hypotheses will be tested over the full period (January 1, 2000 – December 31, 2014). I will also test the hypotheses in two sub periods. One period before the financial crisis of 2007-2008 (January 1, 2000 – December 31, 2006) and one period after the crisis (January 1, 2009 – December 31, 2014). When one of the null hypothesis is rejected there is a monthly effect in the excess returns or variance of the excess returns.

4.3 Investment Strategy

When a hypothesis is rejected we can say that there is a day of the week effect or a monthly effect. When this is the case I will look at the mean returns. Is the excess return on a certain day higher or lower than on another day? Is the excess return in a certain month higher or lower than in another month? With the perceived effects in the mean excess returns I hope to create one or more investment strategies. For instance by finding the best day or month to sell a stock or buy a stock. The strategy will be evaluated by back testing and by an out-of-sample test for 2015. The

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5 Results

5.1 Day of the week effect

Table 9, in the Appendix, shows the day of the week effect in the mean excess returns after running the regression of equation 2 for the full period. A positive Monday coefficient is found for the AEX index and for all of the individual stocks. This shows a positive mean excess returns on Monday, which runs counter with the Monday effect found by French (1980). When we look at the Wald test of hypothesis 1 in table 9 we cannot see a day of the week effect in the mean excess returns of the AEX index. When looking at an individual stock level we see a Wald test F-statistic which is significant at the 10% level for Heineken (p-value of 0.0620), which implies a day of the week effect.

 For Heineken, looking at the coefficients of the dummies we can see statistical significant results for the Thursday (p-value of 0.0396) and Friday (p-value of 0.0064). This means that the mean excess return on Thursdays is 0.000004 (0.001286 0.001282) and on Fridays is -0.000386 (0.001286 - 0.001672). So, the mean excess return for Heineken is positive on all days except for Fridays.

 All other individual stocks do not show a day of the week effect in the mean excess returns. Table 10, in the Appendix, shows the day of the week effect in the volatility of the excess returns after running the regression of equation 2 for the full period. When looking at the Wald test of hypothesis 2 we see a highly significant day of the week effect in volatility for the AEX index and for all of the individual stocks.

 The AEX index shows a higher volatility on Thursdays.

 Ahold shows higher volatility on Tuesdays and Thursdays, but lower volatility on Fridays.  Akzo shows higher volatility on Thursdays, but lower volatility on Fridays.

 DSM shows higher volatility on Tuesdays, Wednesdays and Fridays, but lower volatility on Thursdays.

 Heineken shows higher volatility on Wednesdays, but lower volatility on Tuesdays, Thursdays and Fridays.

 ING shows higher volatility on Wednesdays and Thursdays

 Philips shows lower volatility on Tuesdays, Wednesdays, Thursdays and Fridays.  Shell shows higher volatility on Tuesdays, Wednesdays and Thursdays.

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Table 13, in the Appendix, shows the day of the week effect in the mean excess returns after running the regression of equation 2 for the period before the crisis. A positive Monday coefficient is found for the AEX index and for all of the stocks, except Ahold and Unilever. When we look at the Wald test of hypothesis 1 in table 13 we cannot see a day of the week effect for the AEX index. When looking at an individual stock level we cannot see a day of the week for any of the stocks.

Table 14, in the Appendix, shows the day of the week effect in the volatility of the excess returns after running the regression of equation 2 for the period before the crisis. When looking at the Wald test of hypothesis 2 we cannot see a day of the week effect in volatility for the AEX index, but there is a day of the week effect in volatility for all of the individual stocks.

 Ahold shows lower volatility on Tuesdays, Wednesday, Thursday and Fridays.  Akzo shows higher volatility on Tuesdays, Thursdays, but lower volatility on Fridays  DSM shows higher volatility on Tuesdays, Wednesdays, Thursdays and Fridays.  Heineken shows lower volatility on Tuesdays, Wednesdays, Thursdays and Fridays.  ING shows higher volatility on Wednesdays

 For Philips looking at the coefficients of the dummies we cannot see any statistical significant results. Therefore we cannot tell what the cause of the day of the week effect in volatility is.  Shell shows higher volatility on Tuesdays, Wednesdays and Thursdays and Fridays.

 Unilever shows higher volatility on Thursdays.

Table 17, in the Appendix, shows the day of the week effect in the mean excess returns after running the regression of equation 2 for the period after the crisis. A positive Monday coefficient is found for the AEX index and for all of the individual stocks, except ING. When looking at the Wald test of hypothesis 1 in table 17 we cannot see a day of the week effect for the AEX. When looking at an individual stock level we see a statistical significant day of the week effect for Heineken (p-value of 0.0268) and Shell (p-value of 0.0325).

 For Heineken we see a statistical significant result for the Friday (p-value of 0.0012). This means that the mean excess return on Fridays is -0.001062 (0.001903 - 0.002965).  For Shell we see a statistical significant result for the Tuesday (p-value of 0.001634). This

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hypothesis 2 we see a day of the week effect in volatility of the AEX index. There is also a day of the week effect in volatility for all of the individual stocks, except for ING.

 The AEX index shows lower volatility on Wednesdays and Fridays.

 Ahold shows higher volatility on Tuesdays and Thursday, but lower volatility on Fridays.  Akzo shows higher volatility on Thursdays, but lower volatility on Fridays.

 DSM shows higher volatility on Tuesdays, but lower volatility on Wednesdays.  Heineken shows higher volatility on Wednesdays, but lower volatility on Thursdays.  Philips shows lower volatility on Tuesdays, Wednesdays, Thursdays and Fridays.  Shell shows higher volatility on Tuesdays and Thursday, but lower volatility on Fridays  Unilever shows higher volatility on Tuesdays, Thursdays, but lower volatility on Fridays.

5.2 Monthly effect

Table 11, in the Appendix, shows the monthly effect in mean excess returns after running the regression of equation 4 for the full period. A negative January coefficient is found for the AEX index and for all of the individual stocks, except Philips. The negative mean January excess returns runs counter to the January effect, which implies higher returns in January. When we look at the Wald test of hypothesis 3 we can see a statistical significant monthly effect in the mean excess returns of the AEX index (p-value of 0.0807). When looking at an individual stock level we see a statistical significant monthly effect for DSM (p-value of 0.0006), Philips (p-value of 0.0277), Shell (p-value of 0.0001) and Unilever (p-value of 0.0148).

 For the AEX Index, looking at the coefficients of the dummies we cannot see any statistical significant results. Therefore we cannot tell what the cause of the monthly effect is.

 For DSM we see statistical significant results for March (p-value of 0.0296), April (p-value of 0.0049) and December (p-value of 0.0838). This means that the mean excess return in March is 0.039650 (-0.015470 + 0.055120), in April is 0.059128 (-0.015470 + 0.074598) and in December is 0.029414 (-0.015470 + 0.044884).

 For Philips looking at the coefficients of the dummies we cannot see any statistical significant results. Therefore we cannot tell what the cause of the monthly effect is.

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 For Unilever we see statistical significant results for February value of 0.0147), March (p-value of 0.0001), April (p-(p-value of 0.0009), May (p-(p-value of 0.0036), July (p-(p-value of 0.0182), August (p-value of 0.0071), September (p-value of 0.0072), October (p-value of 0.0004), November (p-value of 0.0001) and December (p-value of 0.0000). This means that the mean excess return in February is 0.000186 0.044097 + 0.044283), in March is 0.028777 0.044097 + 0.072874), in April is 0.015067 0.044097 + 0.059164), in May is 0.012677 0.044097 + 0.056774), in July is 0.006964 0.044097 + 0.051061), in August is 0.003681 (-0.044097 + 0.047778), in September is 0.004232 (-(-0.044097 + 0.048329), in October is 0.013263 (-0.044097 + 0.057360), in November is 0.028724 (-0.044097 + 0.072821), in December is 0.025988 (-0.044097 + 0.070085)

Table 12, in the Appendix, shows the monthly effect in the volatility of the excess returns after running the regression of equation 4 for the full period. When looking at the Wald test of hypothesis 4 we see a significant monthly effect in volatility for Ahold, Akzo, ING and Philips.

 Ahold shows lower volatility in March.

 Akzo shows statistical significant differences in volatility.  ING shows lower volatility in May and December.  Philips shows lower volatility in November.

Table 15, in the Appendix, shows the monthly effect in mean excess returns after running the regression of equation 4 for the period before the crisis. A negative January coefficient is found for the AEX index and for Ahold, Akzo, ING, Shell and Unilever. A positive January coefficient is found for DSM, Heineken and Philips. When we look at the Wald test of hypothesis 3 we cannot see any statistical significant results for the AEX or at an individual stock level.

Table 16, in the Appendix, shows the monthly effect in the volatility of the excess returns after running the regression of equation 4 for the period before the crisis. When looking at the Wald test of hypothesis 4 we see a statistical significant monthly effect in volatility for the AEX index and Unilever.

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 For Unilever looking at the coefficients of the dummies we cannot see any statistical

significant results. Therefore we cannot tell what the cause of the monthly effect in volatility is.

Table 19, in the Appendix, shows the monthly effect in mean excess returns after running the regression of equation 4 for the period after the crisis. A positive January coefficient is found for the AEX index, Ahold, Heineken, ING and Philips. A negative January coefficient is found for Akzo, DSM, Shell and Unilever. When we look at the Wald test of hypothesis 3 we cannot see a statistical significant result for the AEX index. On an individual stock level we can see statistical significant results for Akzo value 0.0297), DSM value of 0.0407), Heineken value of 0.0609) and Shell (p-value of 0.0152).

 For Akzo we see statistical significant results for July value of 0.0779) and December (p-value of 0.0635). This means that the mean excess return in July is 0.083247 (-0.017656 + 0.100903) and December 0.068781 (-0.017656 + 0.086437).

 For DSM looking at the coefficients of the dummies we cannot see any statistical significant results. Therefore we cannot tell what the cause of the monthly in volatility is.

 For Heineken looking at the coefficients of the dummies we cannot see any statistical significant results. Therefore we cannot tell what the cause of the monthly effect in volatility is.

 For Shell we see statistical significant results for April value of 0.0569) and December (p-value of 0.0162). This means that the mean excess return in April is 0.047345 (-0.005285 + 0.052630) and December 0.050983 (-0.005285 + 0.056268).

Table 20, in the Appendix, shows the monthly effect in the volatility of the mean excess returns after running the regression of equation 4 for the period after the crisis. When looking at the Wald test of hypothesis 4 we cannot see any statistical significant result for the AEX index or at an individual stock level.

5.3 Investment Strategy

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26 Table 7: Back testing investment strategies

Hold strategy Return hold strategy Investment Strategy Return investment strategy With transactions costs (1%) Return with transaction costs (1%) Strategy A € 2.398,16 139,82 % € 4.826,66 382,67 % € 0,00 -100,00 % Strategy B € 4.476,26 347,63 % € 9.348,89 834,89 % € 5.115,31 411,53 % Strategy C € 1.757,50 75,75 % € 2.101,39 110,14 % € 1.149,79 14,98 % Strategy D € 3.003,50 200,35% € 7.699,13 669,91 % € 4.212,63 321,26 %

Table 8: Out-of-sample testing investment strategies for 2015 Hold strategy Return hold

strategy Investment Strategy Return investment strategy With transactions costs (1%) Return with transaction costs (1%) Strategy A € 1.357,46 35,75 % € 1.545,45 54,55 % € 543,40 -45,66 % Strategy B € 943,64 -5,64 % € 980,72 -1,93 % € 942,08 - 5,79 % Strategy C € 813,95 -18,60 % € 981,45 -1,85 % € 942,78 -5,72 % Strategy D € 1.265,25 26,52 % € 1.112,36 11,23 % € 1.068,53 6,85 % 5.3.1 Strategy A

Strategy A is a daily strategy for Heineken. The strategy will be followed from the period January 1, 2000 till December 31, 2014 and will be started with an investment of € 1000. Since the mean excess return in positive for the Monday, Tuesday, Wednesday and Thursday, the money will be invested in the stock during these days. The mean excess return on Friday is negative, therefore the money will be invested in the risk-free rate on Fridays.

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strategy outperformed the hold strategy in 2015. When taking transaction costs into account the return is -45,66 %, which is a much lower return than the return of the hold strategy.

5.3.2 Strategy B

Strategy B is a monthly strategy for DSM. The strategy will be followed from the period January 1, 2000 till December 31, 2014 and will be started with an investment of € 1000. The mean excess return is negative in January and the results only show significant positive mean excess results in March, April and December. Therefore the money will only be invested in the stock in March, April and December and will be invested in the risk-free rate during all other months.

For back testing, the results of the hold and investment strategy can be found in table 7 above. Following the hold strategy would have resulted in a return of 347,60 %, while the investment strategy would have resulted in a return of 834,89 %. So again, the investment strategy doubles the hold strategy. When taking transaction costs into account the return is 411,53 %, which is still higher than the return of the hold strategy.

For the out-of-sample test the results can be found in table 8 above. Following the hold strategy has a return of -5,64 %, while the investment strategy has a return of -1,93 %. So, the investment strategy outperformed the hold strategy in 2015. When taking transaction costs into account the return is -5,79 %, which slightly lower than the return of the hold strategy.

5.3.3 Strategy C

Strategy C is a monthly strategy for Shell. The strategy will be followed from the period January 1, 2000 till December 31, 2014 and will be started with an investment of € 1000. The mean excess return is negative in January and the results only show significant positive mean excess results in April, June and July. Therefore the money will only be invested in the stock in April, June and July and will be invested in the risk-free rate during all other months.

For back testing, the results of the hold and investment strategy can be found in table 7 above. Following the hold strategy would have resulted in a return of 75,75 %, while the investment strategy would have resulted in a return of 110,14 %. When taking transaction costs into account the return is 14,98 %, which is lower than the return of the hold strategy.

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5.3.4 Strategy D

Strategy D is a monthly strategy for Unilever. The strategy will be followed from the period January 1, 2000 till December 31, 2014 and will be started with an investment of € 1000. The mean excess return is negative in January and the results only show significant positive mean excess results in all other months, except for June. Therefore the money will be invested in the stock in all months, except for January and June. During these months the money will be invested in the risk-free rate. For back testing, the results of the hold and investment strategy can be found in table 7 above. Following the hold strategy would have resulted in a return of 200,35 %, while the investment strategy would have resulted in a return of 669,91 %. So, the return of the investment strategy is three times the return of the hold strategy. When taking transaction costs into account the return is 321,26 %, which is still higher than the return of the hold strategy.

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6 Conclusion

The goal of this study is to test for calendar effects in the Dutch stock market and to test whether excess returns can be realized by taking advantage of these effects. The study focuses on the day of the week effect and on monthly effects. The day of the week effects exists when the mean excess return on a certain day is higher or lower than on other days of the week. A monthly effect exists when the mean excess return in a certain month is higher or lower than in the other months. This study also examines day of the week and monthly effects in the volatility.

Calendar effects have been researched extensively in the past. Several effects have been found, like the January effect and the weekend effect. Where the January effects is a monthly effect and the weekend effect is a day of the week effect. These perceived effect run counter to the Efficient Markets Hypothesis. However, some studies show the disappearance of the calendar effects. This study focuses on the period from January 1, 2000 till December 31, 2014. The periods before and after the financial crisis of 2007-2008 have also been studies separately. The study analyses the effects in the AEX index, which is the large cap index of the Dutch stock market. Eight stocks have also been analysed on an individual level. This study makes use of an GARCH (1,1) model. Dummy variables are being used for the different trading days and months.

For the full period a day of the week effect in mean excess returns is not found for the AEX index. On an individual stock level the day of the week effect is found only for Heineken. The mean excess return on Fridays was significantly lower than on other days. In the period before the crisis no day of the week effect in the mean excess returns has been found. In the period after the crisis a day of the week effects in mean excess returns is found for Heineken and Shell. For Heineken again the Friday has lower mean excess returns. For Shell the Tuesdays have higher mean excess returns.

For the full period a day of the week effect in volatility is found for the AEX index and for all the individual stocks. In the period before the crisis a day of the week effect in volatility is not found for the AEX, but is found for the individual stocks. In the period after the crisis a day of the week effect in volatility is found for the AEX index and all individual stocks, except ING.

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For the full period a monthly effect in volatility is not found for the AEX index, but is found for Ahold, Akzo, ING and Philips. In both the period before and after the crisis a clear monthly effect in volatility is not found for the AEX index or for any of the individual stocks.

Most of the found effects in the full period are not found in the sub periods. However, for Heineken the negative Friday effect is found in the full period and in the period after the crisis and for Shell the positive April effect is found in both the full period and in the period after the crisis.

A clear and stable day of the week effect or monthly effect in mean excess returns does not seem to exist in the AEX index or in the eight individual stocks. For day of the week effects in volatility more results are being found, but these are also not stable when being compared to the sub periods. For the monthly effect in volatility strong results are not found.

Four investment strategies have been created and are back tested. The returns of three of the four strategies are more than twice as high as the return of an hold strategy. When taking transaction costs into account only two of the four strategies outperform the hold strategy. The daily strategy for Heineken loses its whole investment because of high and frequent transaction costs. The four

strategies have also been tested out-of-sample for the year 2015. Three of the four strategies still outperform the hold strategy. When taking transaction costs into account only one of the strategies outperforms the hold strategy. Again, the daily strategy for Heineken loses a large part of its

investment because of high and frequent transaction costs.

Without transaction costs the strategies also seem to work in the future. However, when taking transaction costs into account they do not seem to work. Transactions take place too often and transactions costs are too high to earn an excess return over an hold strategy, especially for a daily strategy.

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7 References

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8 Appendix

8.1 Full period

Table 9: Day of the week effect in mean excess return

Index/Stock AEX Index Ahold Akzo DSM Heineken ING Philips Shell Unilever

C 0.000644 (0.0623) * 0.000903 (0.0586) * 0.000975 (0.0725) * 0.000979 (0.0244) ** 0.001286 (0.0035) *** 0.000164 (0.7791) 0.001503 (0.0203) ** 0.000173 (0.6165) 0.000105 (0.7848) Tuesday -0.000323 (0.5261) 0.000338 (0.6178) -0.000667 (0.3850) -0.000061 (0.9342) -0.000904 (0.1380) 0.000829 (0.2978) -0.001802 (0.0417) ** 0.001052 (0.0396) ** 0.000371 (0.4955) Wednesday -0.000282 (0.5548) 0.000583 (0.3763) -0.000396 (0.6087) -0.000197 (0.7744) -0.000393 (0.5727) 0.000421 (0.6045) -0.001512 (0.1012) 0.000152 (0.7691) 0.000193 (0.7347) Thursday 0.000203 (0.6862) 0.000306 (0.6596) -0.000221 (0.7879) -0.000740 (0.2647) -0.001282 (0.0396) ** 0.001379 (0.1025) -0.000500 (0.5782) -0.000088 (0.8787) 0.000715 (0.2406) Friday -0.000157 (0.7432) 0.000153 (0.8079) -0.000111 (0.8807) -0.000062 (0.9230) -0.001672 (0.0064) *** 0.000348 (0.6687) -0.001388 (0.1125) 0.000021 (0.9707) 0.000441 (0.4270) Wald test 0.364831 (0.8338) 0.217127 (0.9290) 0.229022 (0.9222) 0.372928 (0.8281) 2.242831 (0.0620) * 0.794466 (0.5286) 1.419556 (0.2247) 1.461254 (0.2113) 0.393297 (0.8136)

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Table 10: Day of the week effect in volatility of excess returns

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35 Table 11: Monthly effect in mean excess return

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36 Table 12: Monthly effect in volatility of excess returns

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8.2 Before crisis period

C 0.000960 (0.0442) ** -0.001502 (0.7381) 0.001312 (0.0714) * 0.001283 (0.0293) ** 0.000595 (0.3850) 0.000993 (0.1740) 0.001592 (0.0893) * 0.000063 (0.9132) -0.000641 (0.2976) Tuesday -0.001058 (0.1225) 0.001969 (0.6649) 0.000017 (0.9870) -0.001484 (0.0828) * -0.000484 (0.5888) 0.000091 (0.9252) -0.002663 (0.0403) ** 0.000797 (0.3581) 0.000270 (0.7409) Wednesday -0.000963 (0.1602) 0.001618 (0.7222) -0.000499 (0.6569) 0.000001 (0.9995) 0.000194 (0.8452) -0.000458 (0.6587) -0.001844 (0.1683) -0.000522 (0.5387) 0.001471 (0.1120) Thursday -0.000278 (0.6878) 0.002429 (0.6036) -0.000973 (0.3684) -0.001086 (0.2461) -0.001003 (0.2729) 0.000618 (0.5655) 0.000241 (0.8658) 0.000245 (0.7832) 0.001647 (0.0541) ** Friday -0.000156 (0.8177) 0.001945 (0.6709) -0.000308 (0.7613) 0.000272 (0.7583) -0.000820 (0.3792) -0.000087 (0.9312) -0.001237 (0.3471) 0.000804 (0.4155) 0.001637 (0.0543) ** Wald test 0.987892 (0.4129) 0.117785 (0.9762) 0.281436 (0.8901) 1.420059 (0.2248) 0.605281 (0.6589) 0.257959 (0.9049) 1.634170 (0.1630) 0.715846 (0.5811) 1.805538 (0.1251)

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8.3 After crisis period

C 0.000566 (0.3192) 0.001604 (0.0022) *** 0.000662 (0.4497) 0.000607 (0.3841) 0.001903 (0.0031) *** -0.001176 (0.4132) 0.001947 (0.0717) * 0.000336 (0.4681) 0.001148 (0.0333) ** Tuesday 0.000444 (0.6004) -0.000654 (0.4205) -0.000781 (0.5475) 0.001614 (0.2147) -0.001034 (0.2588) 0.002393 (0.2221) -0.002023 (0.1528) 0.001634 (0.0259) ** -0.000106 (0.8974) Wednesday 0.000127 (0.8681) -0.001056 (0.1965) 0.000521 (0.6695) 0.000012 (0.9910) -0.000878 (0.4239) 0.003331 (0.0717) ** -0.001533 (0.3097) 0.000451 (0.5292) -0.001002 (0.1946) Thursday 0.000421 (0.6125) -0.002330 (0.0085) *** -0.000289 (0.8365) -0.000314 (0.7664) -0.001495 (0.1112) 0.004211 (0.0327) ** -0.001379 (0.3288) -0.000856 (0.3259) -0.000638 (0.4952) Friday -0.000544 (0.4626) -0.001080 (0.1730) 0.000087 (0.9415) -0.000199 (0.8459) -0.002965 (0.0012) *** 0.000569 (0.7738) -0.002010 (0.1405) -0.000594 (0.3964) -0.001317 (0.1018) Wald test 0.580521 (0.6768) 1.784345 (0.1294) 0.275846 (0.8937) 0.575693 (0.6803) 2.752442 (0.0268) ** 1.847147 (0.1173) 0.671051 (0.6121) 2.637273 (0.0325) ** 0.971292 (0.4221)

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Calendar effects in the Dutch stock market