The Effect of the Day of the Week on the Dutch
Stock Returns
Thesis
Master of Science in Business Administration Specialization: Finance
Rijks Universiteit Groningen,
Faculty of Economics and Business, The Netherlands
Author: W.H. van der Werf Student number: S1831550
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The Effect of the Day of the Week on the Dutch
Stock Returns
Abstract
In this paper, the existence of the day-of-the-week effect in the Dutch stock market is researched by studying a sample of 68 firms over the period 2001-2010. The existing literature has found significant day-of-the-week effects in the past. However, the employed methodologies can be questioned. In this paper, I employ the three-factor model of Fama and French (1993) by which returns are adjusted for the market beta, firm size and book-to-market ratio. By performing a GARCH and GJR test, I find significant positive returns on Tuesday and Friday for the AEX index. The AMX and the AScX index do not show a significant day-of-the-week effect. Furthermore, my panel data set does not show unique attributes of individual firms and no universal effects over time. On the basis of my findings, I conclude that the day-of-the-week effect is present in the AEX index. A profitable arbitrage strategy, however, may not exist due to transaction costs and/or limitations on short selling.
Key words: Day of the week effect, three factor model, GARCH, GJR, panel data,
efficient market
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1. Introduction
1.1 Introducing the Day of the Week anomaly
According to the efficient market hypothesis (EMH) (Fama 1965), stocks are priced efficiently so they reflect all available information about the intrinsic value of the security. In an efficient market there are no systematic profitable trading opportunities, because these are eliminated by arbitrage. Researchers have, however, found evidence that challenge this hypothesis1. One anomaly that challenges the EMH is the day-of-the-week effect (DOW-effect), commonly referred to as the Monday effect, weekend effect or Monday seasonal. A DOW-effect is present if stock prices offer significant different daily returns during a week. In this paper I will investigate the presence of the DOW-effect in the Dutch stock market and to what extent it is present.
1.2 Importance of the DOW-effect
The existence of a DOW-effect would be interesting for several reasons. First of all, a significant DOW-effect is an indication of market imperfection. Arbitrageurs could develop a profitable trading strategy from this market imperfection. In effect, a successful forecast of an increase or decrease of returns during a specific day of the week may allow for an arbitrage opportunity. The first evidence of the DOW-effect was provided by Cross (1973). He investigated returns on the Standard and Poors index from 1953 to 1970 and concluded that the returns are significantly negative on Mondays. Moreover, the average return on Mondays equalled -0.001% when the preceding return on Friday was positive and -0.48% when the preceding return on Friday was negative. This result suggests that a systematic profitable trading opportunity may exist. Also, French (1980) found significantly negative returns on Mondays. In order to take advantage of this finding, French argued that an investor could buy on Monday and sell on Friday. However, this advantage is negligible in the presence of transaction costs. An investor could still increase his expected return by timing his trades by delaying stock purchases till after Monday and do stock sales which were scheduled on Monday on the preceding Friday.
Second, a significant DOW-effect could lead to the wrong conclusions in empirical studies that use daily stock returns. Most statistical methods assume that the daily stock returns have a constant expected return through the week. If someone finds a significant
1
4 positive return when a particular event takes place, the abnormal return can disappear when the event takes place on Mondays as the literature show that the returns on Mondays are lower than other days of the week.
Third, it is important for investors to understand the relation between information and stock prices in stock markets. The EMH explains the relationship between information and stock prices. Fama (1970) divides the EMH in three categories of market efficiency, namely weak, semi-strong and strong market efficiency. Investors can more accurately anticipate on the future value of their investments when they know what type of market they are in. The current price of a stock in a market with weak efficiency is based on historical prices only. In a semi-strong efficient market, stock prices are based on current public information in addition to historical prices. In addition to the semi-strong efficient market hypothesis, the strong efficiency hypothesis assumes that unpublished (or insiders) information is also accounted for in the current market price. In general, when company information is freely and easily accessible to investors, the semi-strong market efficiency hypothesis is likely to be true. However, when a significant DOW-effect exists, this suggests that the market is inefficient, since all available market information (the day of the week) is not fully incorporated in the stock price (Schwert 2002).
1.3 Problem statement
5 positive. In order to profit from this, they could buy the stock on Friday before the market closes. Then they are sure that they will profit from the Monday positive return as they got the stock before the market opens on Monday. Due to this trading strategy, the returns on Fridays would be positive as the demand for stocks will rise, which leads to increasing stock prices.
The existing literature has found empirical evidence that stock returns on Mondays tend to be significantly negative as compared to stock returns on the other days of the week. The explanations in the literature are, however, unconvincing and inconsistent. For example, Keim and Stambaugh (1984) stated that high Friday returns reflect measurement errors that are reversed on Friday. Jaffe and Westerfield (1985) stated that the negative Tuesday effect in Japan and Australia are party explainable by the different time zone compared to the New York stock exchange. Furthermore, Rystrom and Benson (1989) stated that people could be less optimistic on Mondays which could cause the negative Monday returns. Wang et al. (1997) concluded that the DOW-effect is affected by the monthly seasonal, as the Monday low returns are mostly present due the last half of the month and that the Monday effect is insignificant due the first half of the month. Draper and Paudyal (2002) concluded that the DOW effect is related to a combination of the fortnight of the month, account settlement day, ex-dividend day, arrival of (bad) news on Fridays, trading activity and the bid-ask spread. On the basis of mixed empirical findings concerning the existence and explanations of the DOW-effect, it appears that the DOW-effect is an unclear empirical finding.
More recently Brusa, Liu and Schulman (2000) found a reverse DOW-effect for the U.S. equity market over the period 1990 - 1994. The returns during that period were significantly positive on Monday and higher than the returns on other days of the week. Later on, studies argued that the DOW-effect seems to have disappeared or at least weakened (Chang and Pinegar (1993) Schwert (2002) Steeley (2001) Kohers et al. (2004) Hui (2005)). This raises the question: Why did the DOW-effect weaken or disappear over time? Were the profitable opportunities arbitraged away? Were the conclusions in the literature of significant abnormal returns based on biased estimates? Or is the DOW-effect different for distinct markets?
6 ranked 21th in the world - by the end of the year 2009 (CIA world factbook). Despite this rank, the Dutch market is not thoroughly investigated. Only a few studies concerning the DOW-effect in the Netherlands are reported (Chang and Pinegar (1993), Van der Sar (2003) and Apolinario et al. (2006)). This research will update their studies by using a more advanced statistical method, namely the GARCH and panel data method. Most research on the DOW-effect employs only one stock index as the data sample. However using one index does not represent the whole country. Only investigating the AEX will not represent all shares in the Netherlands. Relating this to the DOW-effect, this statement is supported by Keim and Stambaugh (1984) who note that the DOW-effect is stronger with small firms. Therefore this research will focus on the AEX, AMX and AScX. In addition, this paper follows the research of Fama and French (1993), who developed a three factor model. Their model suggests that the market beta, market capitalisation and book-to-market ratio have a high explanatory power of returns. This research will adjust the returns from the Amsterdam Stock Exchange for those three factors by employing Jensens alpha (1968) in the three factor model. Jensens alpha measures the abnormal return that can be gained by only investing on a specific day of the week. Furthermore, the most recent research for the DOW-effect in the Netherlands uses data up to 2004 (Apolinario et al. 2006). Therefore, I will update the DOW-research for the Dutch stock market by using data from 2001 till 2010.
1.4 Overview of this thesis
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2. Literature review
2.1 Discussion of the DOW-effect
Extensive literature documents that weekday returns vary with the day of the week across assets and markets. The literature begins by showing a persistent finding for asset returns to be negative on Mondays. Cross (1973) discovered this between 1953 and 1970. He investigated the S&P composite stock index and compared the Monday and Friday returns. He found that relative increases on Fridays are significant higher than relative increases on Mondays. Cross also found that Monday returns are influenced by preceding trading days. The average Monday return was -0.001% when the preceding Fridays return was positive and -0.48% when the preceding Fridays return was negative.
8 Monday’s closing price). Keim and Stambaugh also related the DOW-effect to the firm size. They discovered that the smaller the firm, the stronger the weekend effect.
Jaffe and Westerfield (1985) first extended the research to the DOW-effect to other markets. They found significant negative Monday return in the U.K, Japan, Australia and Canada, but in contrast to the previous studies they found for Japan and Australia a lowest mean return on Tuesday. Jaffe and Westerfield (1985) show that the lowest weekdays return do not have to be on Monday. The negative Tuesday return could reflect the time zone differences between those markets and the New York stock market. This theory explains some of the Australian seasonal but is unable to explain the Japanese seasonal. Lee et al. (1990) did also found a significant DOW-effect for the Japanese market, but they did not found significant results for the stock exchanges in Hong-Kong, Korea, Taiwan or Singapore. In Europe, seasonal patterns vary across countries and time periods. A negative Monday return is observed on the London Stock Exchange (Theobald and Price 1984, Draper and Paudal 2002). Monday and Tuesday negative returns were observed at the Milan Stock Exchange (Barone 1990). Tuesday and Wednesday negative return were found on the Greek Stock Exchange (Condoyanni et al. 1989), while no significant DOW-effect was found on the stock exchange of Spain and Denmark (Santesmeses 1986, Jennergren and Sorensen 1989). It is obvious that the literature concludes that the DOW-effect is different for each market.
9 Rystrom and Benson (1989) tried to find an explanation for the DOW-effect in the field of behavioral finance. They argue, but did not empirically test, that investors can be influenced by moods, perceptions and emotions that are systematically different on Mondays. After two days of leisure people begin a new long working week with a certain amount of reluctance. On Fridays, people rejoice the weekend gives them a positive attitude. As positive attitude correlate positive with buying, securities should rise at Fridays and decrease on Mondays. However, it is difficult to empirically test this theory. As Rystrom and Benson noticed: “laboratory experiments might be designed to test directly if investors’ perceptions of value or decisions to make risky investments differ across days of the week. Research of this type, although potentially difficult to design and conduct correctly, might lead to more insights into the link between investors’ moods and emotions and the behaviour of financial markets”.
Connolly (1989) questioned the methodology of the DOW-effect in his paper. He argues that much of the empirical work on the DOW-effect rests on a foundation of simple econometric models with strong statistical assumptions. This could lead to biases in the test statistics. Connolly examined the robustness of evidence on the day-of-the-week effect. He found that adjustments for sample size, heteroscedasticity, autocorrelation and leptokurtosis greatly reduce the significance of F- and t-values. Using the standard methodology and GARCH, he found a significant negative return on Mondays till 1974. Connolly concluded that size, strength and stability of the DOW-effect depend on the return measure and the sample period. Therefore, significant negative Monday returns in past research could be present, due the fact of statistical errors and data mining.
10 Balios and Stavaki (2007) investigated the influence of the September’s 2001 attacks in USA on the phenomenon of the DOW-effect in United Kingdom, Germany, France, Spain, Italy and Greece from October 2001 to January 2007. They conclude that the DOW-effect seems to be weaker than it was in previous decades as a result of investors behaviour. Investors became more educated which leads that stock markets become more efficient.
Table 1 shows a summary of the researches to the DOW-effect. What can be seen here is that by adjusting hypothesis formulation and statistical methods, opposing results can occur. Statistical methods have been improved through time. This results in outdated literature. Kenourgios and Samitas (2008) improved the research to the DOW-effect by also taking volatility into account. They investigated the Greek stock market and noted that: “It is important to identify whether there are variations in volatility of stock returns
and whether a high (low) return is associated with a high (low) volatility for a given time. If certain patterns in stock return volatility can be identified, then investors would make easier investment decisions based on both return and risk. Uncovering certain volatility patterns in returns might also benefit investors in valuation, portfolio optimization, option pricing and risk management.” Kenourgios and Samitas addressed two drawbacks
about testing the DOW-effect with mean returns and the OLS methodology. The first problem is the autocorrelation in the error term that could bias the results. They address this drawback by including lagged values of the return. The second drawback is that the error variances may not be constant over time. Kenourgios and Samitas used a GARCH (1,1) model, which deals with the two drawbacks, to provide evidence on the DOW-effect in the returns. Further, they employed M-GARCH (1,1) to provide evidence on the DOW-effect for both return and volatility. They found that the DOW-DOW-effect is present in mean returns and volatility for the Greek stock market over the period 1995-2000 but it seems that this stock market anomaly has weakened in both return and volatility during the period 2001-2005.
11 effect which had a return of -0.26% compared with the other days of the week. However, this effect was only significant in the first two weeks of the month. A critical remark can be made on the statistical tests that Chang and Pinegar performed. They conducted an OLS t-test which brings drawbacks with them. The drawbacks of an OLS are also noted by Kenourgios and Samitas (2008). One of them is that the data is assumed to be homoscedastic. However an implication of assuming homoscedastisity would be that standard error estimates could be wrong. Several conditional autoregressive heteroscedastic models (ARCH2) have been developed and applied to deal with this problem. Van der Sar (2003) applied this ARCH model and found slightly positive but not significant Monday returns (0.013%), which argues that there is no weekend effect in returns. However, he found a significant variance which was slightly higher on Monday than on other days of the week (0.014%). This could provide that the information release is higher after the weekend on Mondays than on other days of the week. Van der Sar (2003) performed ARCH tests which deals with non-linear models. Van der Sar (2003) found a significant ARCH (1) effect. However according to Brooks (2001) GARCH3 tests are extremely widely employed in practice. This is because GARCH has some advantages in contrast to ARCH4. While Van der Sar (2003) found an ARCH (1) effect Apolinario et al. (2006) further improved the methodology of the DOW effect and performed the GARCH test. They found insignificant DOW-effect in returns for the AEX, but a significant DOW-effect in volatility on Monday and Thursday with respect to Wednesday. The significant volatility on Monday for the Dutch market is consistent with the findings of Van der Sar (2003). As Chang and Pinegar (1993) found a DOW-effect in returns, Van der Sar and Apolinario et al. did not find a DOW-effect in returns but in volatility.
2
Autoregressive conditionally heteroscedastic (Engle 1982)
3
Generalised autoregressive conditionally heteroscedastic (Bollerslev 1986 and Taylor 1986)
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2.2 Research question
There are still some gaps to fill in for the literature of the DOW-effect in the Dutch stock market. This paper will improve the studies of the DOW-effect on several points.
First, this paper will differ in time period to avoid the data miming problem stated by Connolly (1989). Balios and Stavaki (2007) investigated a time period of 2001 till 2007 and noted that investors became more educated in this period which leads to more efficient stock markets. I will include data from 2001 up to 2010. This 10-year period provides a unique dataset for the Dutch market covering periods of economic distress (internet bubble, credit crisis) which providing more stock experience. The last time the Dutch stock market was examined was by Apolinario (2006), who used data up to 2004. Therefore, this research provides evidence on the presence of the DOW-effect in the recent Dutch stock market by using recent data.
Second, this paper will adjust the returns for the market beta, market capitalisation and book-to-market ratio. Due this adjustment it becomes possible to better compare the firms with each other. This adjustment rest on the literature of Fama and French (1993) three-factor model, which implies that the market beta, market capitalisation and book-to-market ratio have high explanatory power in predicting returns. If this model is correct, a change in those risk factors will influence the returns on every day of the week. The explanation of the significant negative Monday returns found in the existing literature could be there due to a significant decrease of the market capitalization and/or book-to-market ratios on Mondays. Therefore this research will use risk adjusted returns to test the DOW-effect. To my knowledge, the existing literature did not make this adjustment.
14 not performed in the literature on the DOW-effects. However, panel data deals with individual effects, which could bias the results when they are present. I will perform a panel regression to find out if individual effects are present in the data. As can be seen in Table 1, past research concerning the DOW-effect is done on indices and portfolios. This research differs by using individual stocks. The problems that arise by using portfolios or indices based on fundamental attributes (like size or book-to-market ratios) are pointed out by Lo and MacKinlay (1990). They argue that portfolios or indices based on a fundamental attribute may bias test statistics. They provide evidence that sorting on fundamental attributes yields rejections, whereas sorting on theoretically relevant characteristics (like own-variance or dividend yield) does not. Therefore, I will use individual stock returns to prevent bias in the test results. A panel data approach supports the use of individual securities. The panel data approach is more highlighted in the methodology section.
After discussing the literature, several questions remain unanswered. Has the Dutch stock market become more efficient with respect to the DOW-effect? Or, did the past research on the effect create an opposite effect and is the DOW-effect still present in the market? If so, is this an explanation in addition to the required adjustments for firm-size, market capitalization and book-to-market ratio? According to the literature, it is still possible to find a DOW-effect in returns for the Dutch market. However, the literature also suggests that the DOW-effects are too small to profit from. On the basis of the previously discussed literature, this paper will deal with the following research question:
Is the DOW-effect present in returns that are adjusted to the market beta, market capitalization and book-to-market ratio of firms listed on the Dutch stock market between 2001 and 2010?
3. Methodology
This part will first explain the model employed to measure DOW-effects in risk adjusted returns. Thereafter two methods will be discussed to test this model. The first method is a GARCH approach, which deals with statistical problems as heteroscedasticity and autocorrelation in the residuals. The second method uses panel data which allows for a test of individual firm effects.
3.1 The model
Fama and French (1993) developed a model for explaining returns. This model adjusts returns for the market beta, market capitalization and book-to-market. A variable that measures the DOW-effect will be included in this model, which results in the following model:
(1) Where are dummy variables which take on the value 1 if the corresponding return for day t is a Monday, Tuesday, Wednesday, Thursday or Friday,
respectively and 0 otherwise. and are the daily return of stock i and risk-free rate. is the market return. SMB and HML are the variables representing the market capitalization and the book-to-market ratio formed by Fama and French (1993). represents the error term consisting of a cross-sectional and time-series dimension.
The excess return of the market portfolio is the premium that will be received for taking additional risk. The foundation of this statement comes from the Capital Asset Pricing Model (CAPM). According to the CAPM5, developed by Sharpe (1964) and Lintner (1965), the expected return is determined by three components; the security beta, the risk premium and the risk free rate. In order to adjust the return for their market beta, two new variables have to be
5
where is the return on security i, is the beta on stock
16 included, namely the market premium and the risk free rate. The beta measures the risk as the volatility of a stock as compared to the volatility of the market as a whole. This volatility risk is also measured by Van der Sar (2003), Apolinario et al. (2006), Balios and Stavaki (2007) and Kenourgios and Samitas (2008). However, according to the three factor model, volatility is not the only risk variable that explains the excess stock returns.
The market capitalization is also a risk variable that Fama and French capture in their model. The literature about the DOW-effect did also mention that market capitalization has influence on the DOW-effects. For instance, Gibbons and Hess (1981) find a significant influence of market capitalization on the DOW-effect by examining the CRSP value weighted and equally weighted index. They reported that the returns on Friday are much larger for the equal weighted index. As the equal weighted index is more influenced by small firms, one could argue that the DOW-effect is stronger in small firms. Keim and Stambaugh (1984) investigated this effect and concluded that smaller firms have a higher DOW-effect. An explanation for this result, however, remains to be found. The three factor model of Fama and French (1993) allows for the opportunity to control for this effect. They included a variable in their model that controls for the influence of the different sizes of firms on the stock returns. The third controlling variable that is incorporated in the three factor model is the book-to-market ratio. The literature did not provide papers of studies to differences in the DOW-effect across firms ranked by to-market ratio. However, Fama and French states that high book-to-market equity (low stock price relative to book value) tend to have low earnings on assets, while low book-to-market equity tend to have high earnings on assets.
17 the returns for the market beta, size and book-to-market ratios by using the Fama and French three factor model.
Furthermore, it should be noted that the model can be easily extended by including other risk variables. Including more risk variables in the model will provide a better fit of the regression coefficients, since the alpha’s will then be influenced by other risks than the beta, market size and book-to-market ratio. However, this research will only focus on the three factors of Fama and French (1993) as they argue that the beta, SMB and HML factors explain the greatest part of stock returns. Therefore I choose to use only those factors in the model. Including other risk variables are left open for future research.
3.2 GARCH approach
This part describes a methodology that is familiar with the methodology of the existing literature on the DOW-effect. According to Table 1, most studies employ a standard OLS model to study the DOW-effect. By employing this model, the results are more comparable and provide additional information on the statistical errors that are made in the literature (Connolly 1989). A common OLS regression to measure the DOW-effect can be specified as:
! (2) where ! is the return of the portfolio, are dummy variables which take on the value 1 if the corresponding return for day t is a Monday, Tuesday, Wednesday, Thursday or Friday, respectively and 0 otherwise. are coefficients which represent the average return for each day of the week and is the error term.
18 use a model that does not assume that the variance of the errors is constant. The presence of heteroscedasticity will be tested in the result section.
Second, the residuals could be autocorrelated. If the residuals are autocorrelated, this implies a tendency of consecutive large (small) changes in asset prices, when a large (small) change in asset prices occurred (volatility clustering). In effect, the current level of volatility tends to be positively correlated with the level during the preceding periods. “This phenomenon, which seems to be
an almost universal feature of asset return series in finance, can be explained by information arrivals which drive price changes themselves occur in bunches rather than being evenly spaced over time” (Brooks 2008). Ignoring this problem
could lead to wrong interpretation of the test results, because the coefficients do not have the minimum variance. This problem can be accounted for by including a lagged value of the conditional variance of the error term into the model (Brooks 2008). The presence of autocorrelation will be tested in the result section.
Bollerslev (1986) and Taylor (1986) developed a model that deals with the problem of heteroscedasticity and autocorrelation, which they termed the GARCH model. This model allows the conditional variance to be dependent on the long-term average value. This conditional variance will consist of the volatility during the previous period and the fitted variance of the model during the previous period. The lags in the model are capturing the volatility clustering in the data, which is common in financial data (Mandelbrot 1963). Apolinario et al. (2006) and Kenourgios and Samitas (2008) also used this GARCH model. Therefore, I will first employ this general GARCH model to keep the methodology comparable. The GARCH (1,1) model is specified as follows:
" # "
# (3)
19 Apolinario et al (2006) note that a drawback of the GARCH model is that it assumes symmetry of volatility for positive and negative shocks. So the GARCH model ignores leverage effects. However, in financial time series, a fall of the stock prices cause volatility to rise by more than an increase of the stock prices. This is explainable due to the leverage effects. A fall of stock prices increases the debt to equity ratio. This leads shareholders to perceive their future cashflow stream relatively more risky (Black 1976, Schwert 1989). Another reason is stated by Pagan and Schwert (1990). They found that negative news have more impact on future volatility than positive news. Therefore, I will test the data for possible asymmetrical effects in the volatility. The GJR (Glosten, Jagannathan and Runkle (1993)) is a model which can test for asymmetric effects. It is an expansion of the GARCH model. It includes an additional term that deals with those asymmetries which results in the following regression:
$% & &'%# ($%# )'%# *%# (4) *%# has the condition that it has the value of 1 when '%# < 0 and 0 otherwise. When + > 0 a leverage effect is present. The GJR model is also used by Apolinario et al. (2006) who found leverage effects for the AEX.
3.3 Panel data approach
20 and across all of the cross-sectional units in the sample. The use of panel data is supported by Bulkley et al. (2004), Hasan and Schmiedel (2004), Minquez-Vera and Martin-Ugedo (2005) and Keef et al. (2009). Panel data allows them to eliminate the unobservable heterogeneity that the different companies of their sample could present. Unobservable heterogeneity (i.e. the same relationship holds for all the data) might result in spurious correlation with the dependent variables, which would bias the coefficients obtained. A panel regression with panel corrected standard errors is used to characterise the way that the DOW-effect systematically varies between countries over the period 2001 to 2010. The literature about the DOW-effects did not use the panel data approach. Reason for could be that the other studies investigated the index as a whole and not per firm. Therefore it would not be possible to investigate the individual firm effects. The term ,will be included in regression (1) to account for the unobservable firm-specific random effect. This term is also included by the model of Martin et al. (2006) who investigate the January effect in stock returns with panel data. They stated that including this term controls for unobserved individual heterogeneity that would otherwise be undetected and could generate biased results.
Equation (1) measures if the intercept for each day of the week is significant different over a period of 10 years. The method for measuring the DOW-effect does not divide the 10-years period is sub periods, as that would result in too small samples that could be affected by other events. Therefore, I assume that the DOW-effect would be the same through the 10-years. Reflecting this to the panel data approach, a fixed effect model will be used. This model supports coefficients that change cross-sectionally, but not over time. It is specified as follows:
(5) -
The difference with equation (1) is that - is included. - measures all variables that affects the risk premium cross-sectionally but not over time.
The Hausman test (Hausman, 1978) is a test of whether fixed or random effects should be used. It verifies the presence of correlations between the
21 the random effects model would be inconsistently estimated and the fixed effects model would be the appropriate model.
Both the GARCH model as the panel data model has some advantages and disadvantages. Where the GARCH model assumes homogeneity in intercepts and slopes in the mean and variance regressions, the panel data approach does not deal with heteroscedasticity and autocorrelation (volatility clustering). According to the results of both approaches a conclusion can be drawn which approach fits the data the best.
4. Data collection
This part provides information about the data used for this paper. It is divided in three subsections. Subsection 4.1 provides information about the formation of the sample. The remaining subsections discuss the forming of the used variables.
4.1 The sample
For employing equation (1) the following data is needed: daily returns, market capitalizations and book-to-market ratios of the firms listed on the AEX, AMX and AScX between 2001 till 2010. This data and time period has not been examined yet in academic literature for the Dutch stock market. Using the most recent data makes this research highly relevant for today’s investors, as they could incorporate a possible significant DOW-effect in their trading strategies. A note has to be made here that for exploiting this trading strategy, the CAPM has to be true. The AScX started in 2005. However, the index value was calculated backwards as far as 2001, allowing for a greater time period analysis than the starting date. Although the Dutch stock market consists of 118 firms in 2010, this paper will only investigate the 75 firms with the highest market capitalization6. These firms are represented by the AEX, AMX and AScX. The 43 firms outside these three indices will not be included as their trading volume can be so small that they could bias the results. This bias would arise due to small or zero stock trades, possibly resulting in many days with zero returns which make it difficult to measure the DOW-effect. What has to be noted here is that my data does not
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22 account for the changes in the composition of the indices. My results are not full representative for the AEX, AMX and AScX. The existing literature provides little guidance on how to deal with this problem and what the effects are. The formation of the indices in this research is based on the index formation of December 2010. Furthermore, it is uncommon that those firms provide data over the whole sample period. Also stocks with low trading volume can suffer from a large bid-ask spread. It is then possible that stocks will not be traded close to the last market price, which may cause large jumps and falls in the stock returns and is therefore unsuitable to include in the sample.
Furthermore, the 75 firms have to satisfy the following criteria, before being included in the sample. First, stocks with a price less than € 1.00 are excluded from the sample. The reason for this criterion is that a little increase or decrease of stock prices below € 1.00, have relative more impact on the returns of the entire sample. This could disturb the data. Excluding firms with stock prices below € 1.00 leaves a total of 68 firms for this paper, consist of 25 AEX firms, 23 AMX firms and 20 AScX firms. Second, a week with less than 5 trading days will be eliminated from the data to prevent interaction between the DOW and holiday effect7 (New Years day, Easter, Labour Day, and Christmas). This criterion rest on the research of Rystrom and Benson (1989) who noted that a non-working day could give investors a positive attitude. As positive attitude correlates positively with buying, i.e. securities prices should rise. Therefore I choose to eliminate the weeks with closing stock market days as they could affect the returns upwards. This elimination is also supported by other DOW studies for the same reason (French (1980), Dubois and Lovet (1996), Brusa et al (2000), Hui (2005), Apolinario et al. (2006), Kenourgios and Samitas (2008)). This will exclude 45 weeks, leaving 475 weeks to investigate the DOW-effect. All stock data is gathered from Thompson Datastream.
When a company pays a dividend, the stock price will decrease. However, I choose to do no adjustments for stocks that pay a dividend. Lakonishok and Smidt (1988) reported that the results in their DOW study remained unchanged for firms from the Dow Jones Industrial Average index between 1896 and 1986 with and without a dividend adjustment. Fishe et al. (1993) confirmed this for the CRSP
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23 index between 1962 and 1986. A bias from dividends is relatively small and is not powerful enough to eliminate the DOW-effect.
Furthermore, Rogalski (1984) stated that negative Monday returns are generated in the non-trading period between Friday close and Monday opening prices. When using open-to-close returns the overnight return is not accounted for. If one would conclude that Monday has a significant positive return, an investor would delay investments till Monday. As a result this includes the overnight return for the investor. Therefore it is more useful to use close-to-close prices to investigate the DOW-effect, which is also used by e.g. French (1980), Draper and Paudal (2002), Van der Sar (2003), Kenourgios and Samitas (2008).
4.2 Returns
Daily stock returns are required to investigate the DOW-effect in the Dutch stock market. I will adjust the returns by calculating them as logarithmic returns. By applying logarithmic returns instead of arithmetic returns a more even distribution is obtained. The logarithmic daily returns will be calculated as:
! ./0 #1 (6)
where ! is the daily stock return and the closing stock value on day t.
24 normal distribution. I exclude the stock day return of -99,5% of Ahold. This drop in February 2003 was caused when the accounting fraud of Ahold came to light. Excluding this return results in a drop of the kurtosis from 58 to 14. Day-of-the-week effects are expected to influence stock variables only to a relatively small extend, so I will exclude this large outlier as this is not caused by DOW-effects. Further, using a model with asymmetric effects could deal with the high kurtosis8. At last, the Jarque-Bera test provides a p-value of zero implying non-normality.
Table 2: Summary statistics. This table shows the statistics of the logarithmic average daily
returns of stocks over the period January 2001 to December 2010. Firms are used who are listed on the AEX, AMX and AScX Index and have a market price that is higher than € 1.00.
AEX AMX AScX
Mean -0.024% -0.022% -0.032% Median 0.000% 0.000% 0.000% Maximum 30.219% 44.145% 45.667% Minimum -32.136% -35.721% -46.649% Standard Deviation 2.437% 2.562% 2.42% Skewness -0.166 0.140 0.552 Kurtosis 14.19 15.64 36.37 Observations 297500 273700 238000
Jarque Bera test statistic 304990 336357 2211427
P-value Jarque Bera test 0.000 0.000 0.000
4.3 Three factor model
According to the three factor model, developed by Fama and French (1993), the expected return is determined by three components; the market premium, SMB factor and HML factor. The market premium is calculated as the market returns minus the risk-free rate. Therefore we also have to determine an appropriate bench mark for the Netherlands and set a risk free rate. The most important stocks of the Dutch stock market are found to be those of the largest companies, which are listed on the AEX. However, using the AEX will show a correlation that is biased upwards as the analysed companies make up the AEX. Therefore I choose to use a broader index, namely the MSCI EMU. This index measures the performance of stocks in the countries that use the Euro (EMU). The MSCI EMU index is a good
8
25 proxy for the bench mark, since the firms from my sample are participants in this index.
The risk free rate has to be a guaranteed interest rate. In this paper the Euribor 3 month rate is the proxy for the risk free rate. This is the Euro Interbank Offered Rate; the average interest rate at which banks borrow funds from one another. The Euribor rate provides a basis for the price and interest rates of all kinds of financial product used by prime banks that are willing to lend funds in euros. Because this rate is used by a lot of prime banks it can function as an appropriate risk free rate.
The factor SMB measures the influence of market capitalization on return explanation. Fama and French (1993) define market capitalization as number of shares outstanding times the stock price. SMB measures the difference between the returns on small and big stocks as per the Fama and French methodology. The median of the size measure of the whole sample is used as the breakpoint to establish two groups of firms, which results in a group with small firms and a group with large firms (Bundoo 2008). Next, the average returns of the small group will be subtracted from the average return of the large group to receive the factor SMB, which I use in the model. Fama and French divided the firms in three groups ranked by book-to-market ratio. However they pointed out that there was no reason that tests should be sensitive to this choice. Because I use a small sample size, I choose to divide the sample in only two groups. Again, the average returns of the group with the high book-to-market ratio minus the average return of the group with the low book-to-market ratio results in the HML factor.
5. Results
This section presents the estimation results of the two employed methods. In Section 5.1, the day of the week effect is tested by the GARCH approach. Section 5.2 presents and discusses the results of the panel data approach.
5.1 GARCH results
26 since the p-values of the three Dutch indexes are zero (Appendix A). The Durbin-Watson (1951) test shows no autocorrelation in the residuals of the three indexes (Appendix B). The Breusch-Godfrey test is more advanced than the Durbin-Watson test as it can include more lagged values. Surprisingly, the Breusch-Godfrey test strongly rejects the null of no autocorrelation (Appendix C). If financial markets are efficient, stock market prices should respond quickly to new information. This suggests that there should be no autocorrelation in financial time series. However, the Breusch-Godfrey test indicates that the residuals are autocorrelated, which is evidence for an inefficient market.
Consistent with Connolly (1989), Apolinario et al (2006), Kenourgios and Samitas (2008), who also found evidence of heteroscedasticity and autocorrelation, a GARCH model will be employed. This model captures certain dynamics in the volatility and heteroscedasticity. The Engle (1982) test is performed to make sure that the GARCH model is appropriate for the data. This test seems to be significant, indicating the presence of ARCH effects (Appendix D). Also, the result of significant ARCH effects is consistent with the findings of ARCH effects by Van der Sar (2003) for the Dutch market. Results of the GARCH model are shown in Table 3. This model includes quasi-maximum likelihood covariances and standard errors as discussed by Bollerslev and Wooldridge (1992). This inclusion deals with the non-normal distribution of the residuals as concluded from the Jarque-Bera test.
Table 3. Regression results GARCH(1,1)model. GARCH (1,1) regression results including
quasi-maximum likelihood correction for Day of the Week effects in firms listed on the AEX, AMX, AScX. AEX based on 297500 observations, AMX based on 273700 observations and AScX based on 238000 observations during the period 01-01-2001 till 31-12-2010. Results are on a daily basis. Weeks with stock market holidays and stocks with a price lower than € 1.00 are excluded.
AEX AMX AScX
Coefficient P-value Coefficient P-value Coefficient P-value
27 The findings in Table 3 support the model of Fama and French (1993). As can be seen, the risk factors Beta and SMB are significant at a 1% level for all three indices. The HML factor is only significant for the AMX and the AScX. The result of the HML factor for the AEX is marginally significant at a 10% level. However, the coefficients SMB and HML are negative for the AEX, where they are positive for the AMX and AScX. Fama and French (1993) argue that companies with a high market ratio (value stocks) outperform those with a low book-to-market ratio (growth stocks). However, the significant negative HML factor for the AEX indicates the opposite. A high book-to-market ratio indicates a buying opportunity: the stocks look cheap. However, when believing in the Efficient Market Hypothesis the stocks are cheap because investors could think they are more risky. Furthermore, according to Cross (1973) and French (1980), the DOW-effect should be significantly negative on Mondays and significantly positive on Fridays. Results from Table 3 show, however, significant positive Tuesday and Friday effects at a 1% level for the AEX and a significant positive Monday effect at the 5% level. These findings are inconsistent with the findings of Apolinario et al. (2006). Using the GARCH model, they found no significant DOW-effects in the returns. The difference between the test statistics of Apolinario et al. (2006) and my test statistics for the AEX could be due to the inclusion of the three factors of Fama and French in the model used in this paper. As stated by Fama and French, the returns are influenced by the market beta, firm size and book-to-market ratio. So the exclusion of those factors by Apolinario et al. could have biased the results. The three factors could affect the returns on each day, by which it was not possible to find a significant DOW-effect. According to Appendix E, the coefficients of the lagged squared residual and the lagged conditional variance are highly significant. The sum of those coefficients is close to one. This implies that the current level of volatility tends to be correlated with the level during the preceding period
(volatility clustering). This indicates that the return on the previous day has an impact on the current return.
According to Table 3 the DOW-effect on Tuesdays is 0.041% and on Friday
28 Transaction costs are minimal 0.06% of the total transaction price9. So buying and selling a stock on Tuesday or Friday would already involve two transactions, which let the transaction costs exceeds the profit gained due the DOW-effect.
The kurtosis and the skewness in Table 2 provides evidence of asymmetry in the data. Therefore the GJR model is used to adjust for those asymmetric effects. The variance equation of the GJR model is presented in Appendix F. It presents a significant positive leverage coefficient, indicating that a leverage effect is present in the three stock markets. The positive coefficients suggest that negative shocks imply a higher next period conditional variance than positive shocks of the same sign. This positive significant coefficient is also found by Apolinario et al (2006) for the AEX. Consistent with Apolinario et al. the gains and losses in the stock markets in our sample affect volatility in a different way. This leads to different results than the symmetric GARCH model.
Table 4: GJR regression results. GJR regression results including quasi-maximum likelihood
correction for Day of the Week effects for firms listed on the AEX, AMX, AscX. AEX based on 297500 observations, AMX based on 273700 observations and AScX based on 238000
observations during the period 01-01-2001 till 31-12-2010. Results are on a daily basis. Weeks with stock market holidays and stocks with a price lower than € 1.00 are excluded.
AEX AMX AScX
Coefficient P-value Coefficient P-value Coefficient P-value
Monday 0.023% 0.101 0.029% 0.144 -0.005% 0.819 Tuesday 0.031% 0.038 0.028% 0.185 0.009% 0.649 Wednesday 0.006% 0.679 0.032% 0.097 0.019% 0.355 Thursday -0.011% 0.495 -0.031% 0.105 -0.031% 0.179 Friday 0.031% 0.030 0.021% 0.341 0.028% 0.166 Beta 0.756 0.000 0.711 0.000 0.492 0.000 SMB -0.103 0.000 0.6 0.000 0.625 0.000 HML -0.022 0.084 0.126 0.000 0.242 0.000
The GJR results present a significantly positive Tuesday and Friday effect at a 5% level for the AEX. The AMX shows no significant DOW-effect, neither the AScX. Further, the significant coefficients of Tuesday and Friday are 0.031% for both days. This indicates that investing on Tuesdays or Friday only, provides an extra return of 0.031%. Knowing those numbers, the same conclusion can be drawn as
9
29 French (1980). The abnormal return gained due the DOW-effect is too little to make profit from an arbitrage strategy. Again, the transaction costs are higher than the abnormal return. Although, when an investor wants to invest in a firm listed on the AEX he gains some more return by delaying his investments till Tuesdays or Fridays.
5.2 Panel data results
The panel data methodology is used to carry out this study. This allows eliminating the unobservable heterogeneity that the different companies of the sample could present (Himmelberg et al. 1999, Minguez-Vera and Martin-Ugedo 2005). The White test did show evidence of heteroscedasticity, indicating there is no need to pool the data. The Hausman test allows verifying the presence of correlations between the unobservable heterogeneity and the explanatory variables. This consists of comparing the coefficients of the estimates for fixed effects and the estimates for random effects. Results of the Hausman test conclude that the random effects estimate of the cross-section variance term is zero, so that there is no evidence of individual effects in the data. This conclusion is supported by Keef et al. (2009) who investigated the Monday-effect. They stated that a random effects model is not feasible due to lack of degrees of freedom in the between-firm regression10. Thus, a between-firm covariate cannot be incorporated in the model. Next, it is worth determining whether the fixed effects are necessary or not by running a redundant fixed effects test. Both the 2² and F-test for restricting the cross-section fixed effects to zero do not show significant results. This indicates that the restriction is not rejected by the data and that a pooled sample could also be employed. Now equation (5) will be applied to the subsection of firm data over all ten trading years and with a cross-sectional fixed effects model to allow for firm-specific differences in stock returns. The regression results are documented in Table 5. As the redundant fixed effect test concluded that this test could also be employed with pooled data the results from Table 5 can also be interpreted as the results from an ordinary least square regression.
10
30
Table 5. Panel least squares regression with cross-sectional fixed effects. Firms listed on the
AEX, AMX, AscX. AEX based on 297500 observations, AMX based on 273700 observations and AScX based on 238000 observations during the period 01-01-2001 till 31-12-2010. Results are on a daily basis. Weeks with stock market holidays and stocks with a price lower than € 1.00 are excluded.
AEX AMX AScX
Coefficient P-value Coefficient P-value Coefficient P-value
C 0.021% 0.269 -0.013% 0.554 -0.027% 0.312 Tuesday -0.023% 0.386 0.030% 0.350 -0.020% 0.602 Wednesday -0.015% 0.569 0.021% 0.502 0.036% 0.341 Thursday -0.028% 0.299 -0.012% 0.697 -0.023% 0.545 Friday 0.020% 0.456 0.030% 0.345 0.075% 0.044 Beta 0.903 0.000 0.866 0.000 0.669 0.000 SMB -0.110 0.000 0.741 0.000 0.838 0.000 HML 0.055 0.000 0.145 0.000 0.279 0.000
What has to be noticed in Table 5, the name of the Monday variable is replaced by the C variable. The reason of this is that this avoids the dummy variable trap as the statistical software always includes a C (the intercept) in the panel regressions. The consequence of this is that the statistics has to be interpreted in another way. The C variable is calculated without a dummy variable. Therefore, the C variable is just the abnormal return on Mondays. The abnormal returns on the other days have to be adding with the coefficient of C to get their abnormal returns. Results show the significant influence of the Beta, SMB and HML risk factors, as consistent with Fama and French (1993). Further, the return for the AScX on Friday is significantly 0.075% more than the return on Monday on a 5% significance level. Also, the returns for the AEX and AMX on Fridays are higher than the returns of the other days of the week. However, those are not significant. Summarizing, only the AScX shows a significant Friday effect with the panel data method.
5.3 Main findings
32
6. Conclusion, recommendation and future research
In this paper the day-of-the-week effect on the Dutch stock market is investigated. This contributes to a better understanding of the Dutch stock market. Unlike other studies, in this paper firm returns are adjusted for the market beta, market capitalization and the book-to-market ratio. According to Fama and French (1993) these factors have a significant influence on the stock returns. The sample period is from January 2001 to December 2010. Furthermore, two methods are used to find the most appropriate methodology for investigating the day-of-the-week effect.Using this data and methodology I have found an answer to the research question: Is the DOW-effect present in returns that are adjusted to the market beta,
market capitalization and book-to-market ratio of firms listed on the Dutch stock market between 2001 and 2010? I find that the GARCH test suffers from an
asymmetric effect. Therefore, I employ a GJR test. My results show a significant positive return of 0.031% on Tuesday and Friday for the AEX. However this positive return will disappear when transaction costs will be included. The AMX and AScX do not show significant results. The second method uses panel data. The panel regression accounts for individual effects in firm stocks. Conducting a panel least squares regression with cross-sectional fixed effects result in a significant Friday effect for the AScX. However the redundant fixed effects test concludes that there are no individual effects in the firm stocks and the regression can also be performed without panel data. I conclude that there are DOW-effects present on Tuesday and Friday in firm returns for the AEX.
34
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Appendix
Appendix A: White’s heteroscedasticity test. Results from the White’s test, using three different
types of tests for heteroscedasticity. The following information is needed to determine whether the assumption of homoscedasticity is valid or not. Since the p-values are below 0.05 for all three indexes and the three tests it can be concluded that there is evidence of heteroscedasticity.
AEX AMX AScX
Coefficient P-value Coefficient P-value Coefficient P-value
F-statistic 316.228 0.000 142.013 0.000 86.378 0.000
Observations*R-squared
(chi-Square) 2133.111 0.000 975.060 0.000 596.172 0.000
Scaled explained sum of squares
(chi-Square) 17152.270 0.000 8755.965 0.000 13197.080 0.000
Appendix B: Durbin-Watson test for autocorrelation. Results from the Durbin-Watson test that
test for first order autocorrelation. For all three indexes the Durbin-Watson statistic falls between the upper critical value and 4 minus the upper critical value, which indicates that there is no significant residual autocorrelation.
AEX AMX AScX
DW statistic 2.023 1.955 2.003
Appendix C: Breusch-Godfrey test for autocorrelation. Results from the Breusch-Godfrey test,
using two different types of tests and including 5 lags. Since the p-values are below 0.05 for all three indexes and the three tests it can be concluded that the null hypothesis of no autocorrelation should be rejected.
AEX AMX AScX
Coefficient P-value Coefficient P-value Coefficient P-value
F-statistic 11.849 0.000 6.200 0.000 8.568 0.000
Observations*R-squared
(chi-Square) 118.294 0.000 61.949 0.000 85.543 0.000
Appendix D: Engle test for ARCH effects. Results from the Engle test, using two different types
of tests and including 5 lags. Both tests are significant for all three indexes suggesting the presence of ARCH effects.
AEX AMX AScX
Coefficient P-value Coefficient P-value Coefficient P-value
F-statistic 1083.772 0.000 271.021 0.000 466.627 0.000
40
Appendix E: Results of the variance equation GARCH (1.1) model. Results shows statistically
significant lagged squared residuals and lagged conditional variances. The sum of the ARCH and GARCH coefficients are close to 1 which implies that shocks to the conditional variance will be highly persistent.
AEX AMX AScX
Coefficient P-value Coefficient P-value Coefficient P-value
C 3.48E-06 0.000 6.36E-06 0.001 2.05E-06 0.000
ARCH 0.079 0.000 0.049 0.000 0.045 0.000
GARCH 0.916 0.000 0.939 0.000 0.955 0.000
Appendix F: Results of the variance equation GJR model. Results shows statistically
signifi-cant lagged squared residuals and lagged conditional variances. The sum of the ARCH and GARCH coefficients are close to 1 which implies that shocks to the conditional variance will be highly persistent. The positive leverage coefficient suggests that negative shocks imply a higher next period conditional variance than positive shocks of the same sign.
AEX AMX AScX
Coefficient P-value Coefficient P-value Coefficient P-value
C 3.70E-06 0.000 6.60E-06 0.000 2.14E-06 0.000
ARCH 0.061 0.000 0.033 0.000 0.030 0.000
Leverage 0.035 0.000 0.031 0.000 0.024 0.000
