Seasonal anomalies in Germany : the turn-of-the month effect and liquidity over the past 30 years

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Seasonal anomalies in Germany: The

turn-of-the-month effect and liquidity over the past 30 years

Name: Jesse Koreman Student number: 11038829 Study: Economics and Business Specialization: Economics and Finance

Supervisor: Drs. P.V. Trietsch Date: 26-6-2018 Number of credits thesis: 12

Abstract

This thesis looks into the turn-of-the-month effect on the German stock market from 1988 till 2018. These thirty years are split up in three sub-periods of ten years to examine if the

magnitude of the turn-of-the-month effect changed over time. The DAX index is used to represent the German stock market. The liquidity hypothesis (Ogden, 1990) is examined in attempt to explain the abnormal returns around the turn-of-the-month. In order to examine daily liquidity, daily trading volume is used as a measure of liquidity. Data on trading volume was available from 1999. The liquidity hypothesis is therefore examined from 1999 till 2017, split up in two sub-periods of nine years. The empirical results show that the magnitude of the turn-of-the-month effect decreased over the past thirty years. The seasonal anomaly was no longer present on the German stock market from 2008 till 2018. The regression used to measure the effect of a turn-of-the-month day on liquidity, showed a significant decrease in liquidity on turn-of-the-month days contradicting the liquidity hypothesis.

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Statement of Originality

This document is written by Student Jesse Koreman who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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1. Introduction

To boost the economy after the financial crisis of 2008, the central banks have implemented quantitative easing paired with a low Federal Funds Rate. Quantitative easing and the Federal Funds Rate are tools which are used to lower the interest and savings rates. With lower interest and savings rates borrowing and spending money becomes more attractive, which gives a boost to the economy due to additional spending. An additional effect of the low savings rates, is that people are searching for alternative ways to invest their capital since savings accounts offer low returns.

People want the return on their investment to be as high as possible. Due to risk aversion, people prefer low risk as well. Unfortunately, high returns are paired with high risk according to economic theory. The efficient market hypothesis (hereafter EMH) states that it is impossible to consistently outperform the market without inside information (Fama, 1970). But what if there are ways to consistently beat the market, by gaining higher profits while the risk stays relatively low?

Through the years studies have presented various seasonal anomalies of the EMH. These anomalies are described by abnormal returns; high returns paired with low risk. One seasonal anomaly of the EMH is the turn-of-the-month effect (hereafter TOM effect).

According to this seasonal anomaly the returns on TOM days are significantly higher than the returns on rest-of-the-month days (hereafter ROM days), without a significant increase in risk. The TOM effect describes abnormal returns on both stocks and futures on TOM days

(Lakonishok & Smidt, 1988).

The TOM effect was first discovered on US stocks by Ariel in 1987. Lakonishok and Smidt expanded on his paper by examining the underlying reasons. Possible explanations of the TOM effect are: higher liquidity at the TOM, Window dressing by portfolio managers and the distributions of earnings news (Lakonishok & Smidt 1988). This thesis will examine the liquidity hypothesis as the possible explanation of the TOM effect.

According to the EMH, seasonal anomalies should disappear over time after they get well known (Agrawal & Tandon, 1994; Schwert, 2002). As described by Agrawal and Tandon (1994) the TOM effect disappeared in the 80’s. However, more recent studies show that the TOM is present on the European stock market once again (Kunkel et al., 2003;

McConnell & Xu, 2008). If the TOM effect is in fact present, it might be possible to design an arbitrage strategy to exploit this seasonal anomaly. To gain from such a strategy, a strong TOM effect is preferred. According to previous literature, Germany has had one of the strongest TOM effects (Kunkel et al., 2003; McConnell & Xu, 2008). That is why this thesis attempts to answer the central question: ‘Is the turn-of-the-month effect still present on the

German stock market and does the magnitude change over time?’

In order to answer the central question the following sub questions are answered: (1) What are seasonal anomalies?

(2) What is the turn-of-the-month effect? (3) What explains the turn-of-the-month effect?

(4) How can the turn-of-the-month effect be measured? (5) How can the daily liquidity be measured?

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To conduct empirical research on the TOM effect four statistical tests are used. The first two tests are used to show whether the TOM is present on the German stock market. First a T-test is run to determine if the mean return on TOM days is significantly higher than the mean return on ROM days. To test if the high TOM returns can be explained by an increase in risk an F-test is used. These tests are run over a total period of 30 years split up in 3 sub-periods of 10 years. To test if the magnitude of the TOM effect changes over time, an OLS regression of TOM days on returns is used. The OLS regression is run three times on periods of 10 years. The regression coefficients are compared to conclude if the magnitude of the TOM effect changes over time. Finally, an OLS regression is used to examine if an increase in liquidity can explain the TOM effect. Trading volume is used as a measure of liquidity, following Ogden (1990).

The DAX index is used to represent the German stock market. The DAX index is made up of the 30 major German companies and measures the performance of the German stock market. Daily closing prices of the DAX index are used starting on 1/1/1988 till 1/1/2018. Trading volume is used as a measure of liquidity through the month. Daily trading volume is used from 1/11/99 till 1/11/2017. Datasets are retrieved from yahoo finance. The next chapter will describe previous studies and possible explanations. Chapter 3 describes data, methodology and hypotheses. Finally, chapter 4 contains conclusions and implications.

2. Literature review

2.1 What are seasonal anomalies?

The EMH has three forms: strong, semi-strong and weak. The semi-strong EMH is considered best to describe reality. The semi-strong EMH states that investors cannot consistently outperform the market without inside information (Fama, 1970). However, research has presented a number of anomalies. These anomalies are described by a pattern in expected returns that cannot be explained by the asset pricing models (Maslov & Rytchkov, 2010). According to the EMH, anomalies should disappear over time after getting well known (Agrawal & Tandon, 1994; Schwert, 2002). A lot of research on seasonal anomalies has been conducted. Some examples of seasonal anomalies are the January effect, the Halloween effect, the Friday the thirteenth effect, the weekend effect, the turn-of-the-week effect, the TOM effect and the turn-of-the-year effect. The growing number of anomalies weakens the validity of the EMH.

2.2 What is the turn-of-the-month effect?

The TOM effect is one of the seasonal anomalies of the EMH. The TOM effect is described by abnormal returns on days around the turn of the month. The most significant TOM days for the European stock market are the last day of the previous month till the third day of the new month, [-1,3] (Lakonishok & Smidt, 1988; Kunkel et al., 2003; McConnell & Xu, 2008). Previous literature describes the TOM effect to be present on both the the stock and futures market. The magnitude of the TOM effect is greater in both low price and small cap stocks (McConnell & Xu, 2008).

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According to the EMH, the TOM effect should decrease, and eventually disappear, over time (Agrawal & Tandon, 1994; Schwert, 2002). The TOM effect was first discovered by Ariel on the US stock market in 1987. Cadsby and Ratner expanded on Ariel’s study by investigating the European and Asian stock market. Cadsby and Ratner (1992) found a

significant TOM effect in most of the European countries but no significant TOM effect in the Asian countries. The research of Agrawal and Tandon (1994) found a TOM effect in the 70’s, however the TOM effect disappeared in in the 80’s. According to more recent studies, the TOM effect has made its return on the American, Asian and European stock market (Kunkel et al., 2003; McConnell & Xu, 2008; Burnett, 2017).

2.3 How can the turn-of-the-month effect be measured?

The seasonal anomaly was first studied by Ariel in 1987. Ariel used a two sample T-test to compare the mean return of the first half of the month to the mean return of the second half. This T-test is used to check if the difference between the mean returns is significantly higher than zero. To compare the risk between the two periods, Ariel used an F-test at a five percent significance level. In 1988 Lakonishok and Smidt expanded on Ariel’s research on seasonal anomalies. Lakonishok and Smidt specified the TOM period as [-1,3], because this window presented the most significant TOM effect. To this day this window seems to

describe the most significant TOM period on the European stock market (Kunkel et al. 2003: McConnel and Xu, 2008).

Ogden (1990) introduced an OLS regression model to directly test the effect of TOM days on returns. In 1992 Cadsby and Ratner developed the most commonly used OLS regression model to estimate the TOM effect.

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2.4 What explains the turn-of-the-month effect?

Previous literature attributes four possible explanations to the TOM effect: the liquidity hypothesis, the window dressing hypothesis, the distribution of earnings news and higher risk. Only the liquidity hypothesis and the window dressing hypothesis are seen as possible explanations in this thesis. Since the distribution of earnings news can only explain the TOM effect for turn-of-the-quarter months. In addition, an increase in risk violates the definition of abnormal returns. Therefore, these theories cannot be an explanation of the TOM effect.

Diagram 1: Variables influencing the TOM effect

Diagram 1 shows the influences of some variables on the TOM effect according to different theories. An indicates a positive influence on the TOM effect. An indicates a negative influence on the TOM effect.

TOM EFFECT Efficient Market Hypothesis

Liquidity Hypothesis

Window Dressing Hypothesis

Portfolio rebalancing at the TOM

Reinvestment at the TOM

Distribution of earnings news

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2.4.1 Liquidity hypothesis

Ogden (1990) was one of the first to describe the liquidity hypothesis as the

underlying reason for the TOM effect. The liquidity hypothesis explains the TOM due to a concentration of cash flows at the end of the month. These cash flows consist of wages, interest payments, dividends, principal payments and other liabilities who are typically paid just before the TOM. As a result of these payments before the TOM, investors are looking for new projects to reinvest their capital. Ogden links the increase in the search of projects for reinvestment, to the increase in the stock prices by making use of the supply and demand mechanism. He reasons that when the demand for stocks increases, because investors try to reinvest their capital, the prices of the stocks increase. This buying pressure would explain the increase in the stock prices and thereby increase the returns during the TOM (Ogden, 1990). Ogden (1990) found a significant increase in liquidity at the TOM. Ziemba (1991) describes buying pressure, caused by salaries paid on day 20-25, to be a plausible explanation for the TOM effect as well. Burnett (2017) added to the liquidity hypothesis by including investors confidence. His paper states: “A TOM regularity is present during high liquidity months, but only when it is accompanied by high investor confidence.’’ (Burnett, 2017). However not all research points in the same direction. McConnell and Xu (2008) could not find evidence supporting the liquidity hypothesis as the underlying reason for the TOM effect. According to the liquidity hypothesis, the trading value and volume should be higher on TOM days (Ogden, 1990). McConnel and Xu (2008) examined this theory by comparing the trading volume on TOM days to that on ROM days using a T-test. Kayacetin and Lekpek (2016) conducted a T-test on the trading volume ratio. Wiley and Zumpano (2009) used REIT’s to conduct research on the influence of liquidity and institutional investment on the TOM effect. Kayacetin & Lekpek and McConnel & Xu couldn’t find evidence supporting the liquidity hypothesis. The paper of Wiley and Zumpano however, concludes that an increase in liquidity at the TOM is the most plausible explanation of the TOM effect.

2.4.2 Window dressing hypothesis

The window dressing hypothesis was initially used to explain the January effect, another seasonal anomaly, but nowadays the theory is widely accepted as a possible explanation of the TOM effect. This theory (initially called the portfolio rebalancing hypothesis) states that fund managers rebalance their portfolios right before the reporting date, by selling off underperforming stocks and buying stocks that perform well. This strategy is applied by institutional investors, for example mutual fund managers. Fund managers apply this strategy so they can satisfy their investors by showing them the funds they invest in consist of well performing stocks. As soon as the report date passes, institutional investors rebalance again, by investing in riskier assets (Ritter & Chopra, 1989).

The TOM effect could possibly be explained by the window dressing hypothesis “since the reporting dates presumably coincide with natural calendar dates” (Thaler, 1987). Because the reporting dates coincide with the TOM, window dressing could explain the abnormal increase in returns at the TOM. Lakonishok & Smidt (1988) were one of the first to attribute the window dressing hypothesis to the TOM effect. Wiley and Zumpano were the first to provide an empirical test on the window dressing hypothesis. Their findings support

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2.4.3 Distribution of earnings news

In his paper Penman (1987) describes the distribution of earnings news as a possible explanation of seasonal anomalies such as the TOM effect. Good news is published almost directly, while bad news is usually published with a delay (Penman, 1987). “Earnings reports published in the first two weeks of calendar quarters 2, 3 and 4 on average convey good news, in the sense that they affect stock prices of reporting firms positively, whereas reports

appearing later in the quarter are more likely to carry bad news, in the sense that they affect stock prices negatively.” (Penman, 1987). The findings of Michaely, Rubin, & Vedrashko (2016) are in line with the theory of delaying news. Their research concludes that managers publish good news quickly, often on Mondays, and delay bad news, often till Fridays. The distribution of earnings news occurs every quarter, not every month. The TOM effect however, is present in all months. Therefore, the distribution of earnings news might have a positive influence on the TOM effect on turn-of-the quarter months but it cannot be the single explanation of the TOM effect.

2.4.4 Higher risk

Previous studies describe an increase in risk at the TOM as a fourth explanation. The CAPM model describes the relationship between risk and expected return. The CAPM model states that an investor should be compensated if he takes on additional systematic risk.

Therefore, an increase in risk at the TOM should be compensated with higher expected returns. This leads to the conclusion that an increase in risk is not an explanation of the TOM effect since there are no abnormal returns.

Even so, previous studies don’t show an increase in risk at the TOM. Ariel (1987) didn’t find enough evidence to reject the null hypothesis of equal risk. Lakonishok and Smidt state that it is very unlikely that an increase in risk creates the pattern of increased returns (Lakonishok & Smidt, 1988). Agrawal & Tandon (1994) find a low variance on the last trading days of the month for most countries. The findings of McConnell and Xu even contradict this theory by stating: “This analysis shows that volatility is not unusually high at turns of the month. Indeed, if anything, volatility of returns is somewhat lower over the four-day turn-of-the-month period than over other four-days” (McConnell & Xu, 2008).

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Research (Year) Country Period Result Research method

Measure Index TOM

days

Burnett (2017) United States

1973-2007 +1 T-test difference >0 Stocks CRSP, S&P500 [-1,3] Wiley & Zumpano (2009) United States 1980-2004 +5 _OLS/LAD/ GARCH & T-test difference>0 REIT's CRSP [-4,1] McConnell & Xu (2008) Australia, Austria, Belgium, Canada, Chile, Denmark, Finland, France, Germany,

Greece, Hong Kong, Indonesia, Ireland, Japan, Mexico, The Netherlands, New Zealand, Norway, Philippines, Portugal, Singapore, South Africa, South Korea, Spain, Sweden, Switzerland, Taiwan, Thailand, Turkey, UK

1987-2005

+10** _{OLS & T-test}

difference >0 Stocks CRSP [-1,3] Argentina, Colombia, Italy, Malaysia - Kunkel, Compton & Beyer (2003) Australia, Austria, Belgium, Canada, Denmark, France ,Germany, Japan, Mexico,

The Netherlands, New Zealand, Singapore, South Africa, Switzerland, UK, United States 1988-2000

+10** _{OLS & T-test}

difference >0

Stocks Yahoo Finance [-1,3]

Brazil, Hong Kong, Malaysia - Agrawal & Tandon (1994) Australia, Belgium, Brazil, Canada, Denmark, France, Germany, Italy, Japan, Luxembourg, Mexico, New Zealand, Singapore, UK 1971-1987 +10** ***

OLS & T-test difference >0

Stocks London Financial Times [-1,3]

Hong Kong, The Netherlands, Sweden, Switzerland, United States

-

Cadsby & Ratner (1992) Australia, Canada, Switzerland, UK, United States, West Germany 1962-1987* +5** _{OLS + T-test} difference >0

Stocks CRSP, Toronto stock exchange, NIKKEI, Hang Seng index, FT500, All Ordinaries index, Banca Commerciale index, Swiss Bank Corporation Industrials index, Commerzbank index, Compagnie des Agents de Change General index

[-1,3]

Japan, Hong Kong, Italy, France - Ziemba (1991) Japan 1949-1988 +5 _T-test difference >0 Stocks TOPIX [-5,2]

Ogden (1990) United States

1969-1986 +1 _{OLS + T-test} difference >0 Stocks CRSP [-1,3] Lakonishok & Smidt (1988) United States 1897-1986 +1 _T-test difference >0 Stocks DJIA [-1,3]

Ariel (1987) United States

1963-1981

+1 _T-test

difference >0

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3. Data analysis

3.1 How is the the turn-of-the-month effect measured in this thesis?

To answer the question: ‘How is the turn-of-the-month effect measured in this thesis?’ the buy and hold returns will be calculated making use of the DAX index. First off a T-test is used to examine if the mean return on TOM days is significantly higher than the mean return on ROM days. Secondly the risk of TOM and ROM days is compared by an F-test. Finally a regression is used to measure the magnitude of the TOM effect.

The first test compares the returns on TOM days to those on ROM days. This T-test examines if the mean returns on TOM days are significantly higher than the mean returns on ROM days. If the T-tests shows significant t-values, the returns on TOM days are

significantly higher than those on ROM days. Therefore, investors would prefer owning stocks on TOM days over ROM days if there is no significant increase in risk.

A possible explanation for the higher returns at the TOM is higher risk. Standard deviation is used as a measure of risk following Lakonishok and Smidt (1988). High standard deviations during TOM days might be an explanation for abnormal returns since investors should be compensated for taking on additional systematic risk according to the CAPM model. To examine the possible explanation of higher risk at the TOM, an F-test is used. This test is applied on the standard deviation of the return on TOM and ROM days. The F-test tests whether the variance, the standard deviations squared, on TOM days is significantly higher than on ROM days. If the test does not show a significant increase in standard deviations for TOM days, the risk on TOM days does not exceed the risk on ROM days.

Combining the outcome of the first two tests leads to the conclusion of the presence of the TOM effect. If the returns on TOM days are significantly higher than those on ROM days, paired with the absence of an increase in risk on TOM days, the TOM effect is present on the German stock market.

The final test is an OLS regression which measures the magnitude of the TOM effect by examining the effect of a TOM day on returns. Following Lakonishok & Smidt (1988) and Kunkel et al. (2003) the following OLS regression is run on the DAX index:

𝑅_" = 𝛽_%+ 𝛽₍𝐷_*+,+ 𝜖_"

Where Rt is the dependent variable and stands for the return on day t. β0 is the the mean return

for the ROM days. DTOM is a dummy variable for the TOM days, taking on the value 1 on the

TOM days and 0 otherwise. The TOM days used in this thesis are the last day of the previous month and the first 3 days of the new month, [-1,3]. This period is chosen because the

literature found the most significant TOM effect during this period on the European stock market (McConnel & Xu, 2008). β1 represents the difference between the mean TOM returns

and the mean ROM returns. et represents the error term (Kunkel et al., 2003).

As described by the EMH, the TOM effect should decrease over time and eventually disappear after getting well known. The TOM effect was first described late in 1987, therefore this thesis examines the magnitude of the TOM effect from 1/1/1988 till 1/1/2018. This period is split up into three sub-periods of ten years. The regression is run on those three periods of ten years to estimate the magnitude of the TOM effect. The three β1 coefficients are compared

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3.2 How is the daily liquidity measured in this thesis?

The liquidity hypothesis states that the TOM effect is caused by an increase in liquidity on TOM days. Therefore, trading value and or volume should be higher on TOM days (Ogden, 1990). In this thesis trading volume is used to measure liquidity. To examine if the TOM effect can be explained by an increase in liquidity, the first step is to check if the TOM effect is present. Thereafter the liquidity on TOM days is measured by the following OLS regression which estimates the effect of a TOM day on liquidity:

𝑇𝑟𝑎𝑑𝑖𝑛𝑔 𝑉𝑜𝑙𝑢𝑚𝑒 = 𝛽_% + 𝛽₍𝐷_*+,+ 𝜖_"

Where trading volume is the dependent variable. β0 is the the mean trading volume for a

ROM day. DTOM is a dummy variable for the TOM days, taking on the value 1 on the TOM

days [-1,3] and 0 otherwise. β1 represents the difference between the mean TOM trading

volume and the mean ROM trading volume. et represents the error term.

The data on trading volume starts on 1/11/1999. Therefore, two periods of 9 years are examined. The first period starts at 1/11/1999 and ends at 1/11/2008. The second period starts at 1/11/2008 and ends at 1/11/2017. The β1 coefficient is examined to determine if the

liquidity is significantly higher on TOM days. If the TOM effect is present paired with an increase in liquidity on TOM days, evidence in favour of the liquidity hypothesis is present.

3.3 Hypotheses

The first couple of tests are run to answer the sub-question: ‘Has the turn-of-the-month

effect been present on the German stock market over the past 30 years?’ The 30-year period

is split up in three sub-periods of 10 years. This approach has been chosen because 30 years is a large period, in which a lot can change. Therefore, this method gives a better overview of the TOM effect through the years.

After examining if the TOM effect is present, an OLS regression is run on returns to measure the significance and the magnitude of the TOM effect. The regression examines the effect of a TOM day on the return. The final tests are used to answer the sub question: ‘Can the TOM effect be explained by the liquidity hypothesis?’ A regression is used to examine whether the liquidity on TOM days is significantly higher than the liquidity on ROM days.

Table 2: Hypotheses

TOM effect in Germany over the past 30 years

Hypothesis 1: The returns on TOM days are significantly higher than the returns on ROM days for all three sub-periods.

Hypothesis 2: In all three sub-periods the mean standard deviation on TOM days is not significantly higher than the mean standard deviation on ROM days.

Hypothesis3: The TOM effect is present in all three sub-periods. Significance of

the TOM effect

Hypothesis 4: A TOM day has a significant positive effect on returns in all three sub-periods.

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3.4 Data summary

Data is retrieved from yahoo finance. The closing prices of the DAX index are adjusted for splits and dividends. Data used for closing prices starts on 1/1/1988 and ends at 1/1/2018. The data used for trading volume starts on 1/11/99 (earlier data was not available) and ends at 1/11/2017.

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Table 3: Data summary

Observations Mean Std. Dev. Maximum Minimum

TOM Return 88-98 479 0,232% 1,120% 5,850% -5,110% ROM Return 88-98 2023 0,028% 1,156% 6,585% -13,143% TOM Return 98-08 481 0,186% 1,644% 7,343% -7,590% ROM Return 98-08 2058 0,003% 1,560% 7,845% -8,482% TOM Return 08-18 480 0,018% 1,496% 6,072% -5,882% ROM Return 08-18 2057 0,032% 1,452% 11,402% -7,164% TOM Return 99-08 433 0,190% 1,553% 7,343% -5,830% ROM Return 99-08 1860 -0,033% 1,632% 11,402% -8,492% Trading Volume 99-08 2293 1,01e+08 5,53e+07 5,10e+08 6569700

TOM Return 08-17 433 0,023% 1,512% 6,072% -5,882%

ROM Return 08-17 1849 0,060% 1,350% 10,344% -6,838%

Trading Volume 08-17 1786 1,20e+08 5,05e+07 2,87e+07 4,36e+08

3.5 Results

The tests for the 30-year span have been divided in three sub-periods of ten years. Tests for sub-period 1988-1998: The T-test, of the difference between mean TOM return and mean ROM return, shows that the mean TOM return is significantly higher than the mean ROM return at a one percent significance level. Therefore, the null hypothesis is rejected: (mean TOM) – (mean ROM) equals zero. An F-test between the two sample variances shows that the variance of the returns on ROM days exceeds the variance of the returns on TOM days. At a five percent significance level the null hypothesis is rejected: (variance of returns on TOM days) – (variance of returns on ROM days) equals zero. The regression of TOM days on returns shows that the return on TOM days is significantly higher at a one percent

significance level.

Tests for sub-period 1998-2008: The T-test, of the difference between mean TOM return and mean ROM return, shows that the mean TOM return is significantly higher than the mean ROM return at a five percent significance level. Therefore, the null hypothesis is rejected: (mean TOM) – (mean ROM) equals zero. The F-test between the two sample

variances shows that the variance of the returns on TOM days does not exceed the variance of the returns on ROM days. At a five percent significance level there is not enough evidence to reject the null hypothesis: (variance of returns on TOM days) – (variance of returns on ROM days) equals zero. The regression of TOM days on returns shows that the return on TOM days is significantly higher at a significance level of one percent. Therefore, the null hypothesis is rejected at a one percent significance level: β1 equals zero.

Tests for sub-period 2008-2018: The T-test, of the difference between mean TOM return and mean ROM return, shows that the mean TOM return is not significantly higher than the mean ROM return. At a ten percent significance level there is not enough evidence to reject the null hypothesis: (mean TOM) – (mean ROM) equals zero. An F-test between the two sample variances shows that the variance of the returns on TOM days does not exceed the variance of the returns on ROM days. At a five percent significance level there is not enough

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The tests for examining liquidity on TOM days are divided in two sub-periods of nine years each. Tests for sub-period 1999-2008: The T-test, of the difference between mean TOM return and mean ROM return, shows that the mean TOM return is significantly higher than the mean ROM return at a one percent significance level. Therefore, the null hypothesis is rejected: (mean TOM) – (mean ROM) equals zero. The F-test between the two sample

variances shows that the variance of the returns on TOM days does not exceed the variance of the returns on ROM days. At a five percent significance level there is not enough evidence to reject the null hypothesis: (variance of returns on TOM days) – (variance of returns on ROM days) equals zero. The regression of TOM days on trading volume shows that the trading volume on TOM days is significantly lower than on ROM days at a one percent significance level. Therefore, the null hypothesis is rejected: (trading volume on TOM days) – (trading volume ROM days) equals zero.

Tests for sub-period 2008-2017: The T-test, of the difference between mean TOM return and mean ROM return, shows that the mean TOM return is not significantly higher than the mean ROM return. At a ten percent significance level there isn’t enough evidence to reject the null hypothesis: (mean TOM) – (mean ROM) equals zero. An F-test between the two sample variances shows that the variance of the returns on TOM days does not exceed the variance of the returns on ROM days. At a five percent significance level there isn’t enough evidence to reject the null hypothesis: (variance of returns on TOM days) – (variance of returns on ROM days) equals zero. The regression of TOM days on returns shows that returns on TOM days are significantly lower than on ROM days at a ten percent significance level. Therefore, the null hypothesis is rejected: (trading volume on TOM days) – (trading volume ROM days) equals zero.

Table 4: Summary test statistics

1988-1998 1998-2008 2008-2018 1999-2008 2008-2017 T-test mean return TOM >mean return ROM p-value 0,0003*** 0,0131** 0,5588 0,0038*** 0,6812 F-test**: Fobs>Fcritical Fobs exceeds Fcritical (Variance ROM>TOM) Fobs does not exceed Fcritical Fobs does not exceed Fcritical Fobs does not exceed Fcritical Fobs does not exceed Fcritical OLS TOM on return coefficient 0,0020*** 0,0018** -0,0001 0,0022**** -0,0004 OLS TOM on trading volume coefficient - - - -7538776*** -4966394*

- Indicates that the trading volume is not examined in this period. * Indicates significance level at 10 percent.

** Indicates significance level at 5 percent. *** Indicates significance level at 1 percent.

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4. Conclusions and implications

This thesis attempts to answer the central question: ‘Is the turn-of-the-month effect still

present on the German stock market?’ The previous literature describes a return of the TOM

effect on the European stock market after it briefly disappeared in the 80’s. After the disappearance of the TOM effect, described by Agrawal and Tandon, the seasonal anomaly was present on the German stock market up to 2008 according to every published study. The empirical test conducted in this thesis shows that there was a significant TOM effect present from 1988 till 1998 at a one percent significance level. From 1998 till 2008 the TOM effect was present at a five percent significance level. In the period of 2008 till 2018 however, the seasonal anomaly was no longer present on the German stock market.

This leads to the conclusion that the TOM is no longer present on the German stock market. These test outcomes also lead to the conclusion that the magnitude of the TOM effect decreases over time.

In addition to examining if the TOM effect is present on the German stock market, the liquidity on TOM days is examined to check if the TOM effect can be explained by the liquidity hypothesis. To examine the liquidity on TOM days two periods of nine years each were examined. The first period, starting on 1/11/1999, had a significant TOM effect. The second period starting on 1/11/2008 did not have a significant TOM effect. Therefore, the liquidity hypothesis could only be an explanation for the TOM effect in the first period. In contrast to the liquidity hypothesis, the trading volume was significantly lower on TOM days at a one percent significance level. Consequently, the liquidity hypothesis cannot explain the TOM effect. These findings are in line with the findings of McConnell and Xu (2008).

With these findings the answer to the central question: ‘Is the turn-of-the-month effect

still present on the German stock market and does the magnitude change over time?’, is that

the the magnitude of the TOM effect has diminished over the past 30 years and is no longer present on the German stock market. Therefore, it is impossible to design a strategy to exploit the seasonal anomaly and consistently outperform the market. This leads to the conclusion that the semi-strong version of the EMH still holds.

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Discussion

As stated by McConnel and Xu (2008) the magnitude of the TOM effect is greater in low price and small cap stocks. The DAX index, used to represent the German stock market, is made up of the thirty biggest companies of Germany. Consequently, the magnitude of the TOM effect might be underestimated. This also implies that the TOM effect might have been present in the period from 2008 till 2018.

In this thesis the assumption is made that the TOM effect is present on days [-1,3]. According to previous literature the TOM effect is strongest for the European stock market in this period. This window may have changed since the most recent paper on the TOM effect in the European stock market was published in 2008. If the TOM window is in fact wider, this would lead to an increase in the mean ROM return calculated. Consequently, the TOM effect would be underestimated due to the decrease in the difference between the mean TOM and mean ROM returns. Following the same reasoning, the TOM effect might be underestimated if the TOM window is in fact smaller than [-1,3]. Due to the smaller TOM window the mean TOM return calculated decreases, which leads to a decrease in the difference between the mean TOM and the mean ROM returns.

Due to the absence of the anomaly over the past 10 years, this study has not looked into possible strategies that exploit the TOM effect. For previous periods, where the TOM effect was in fact present, it might still be impossible to exploit the TOM effect due to transaction costs. If these transaction costs lead to the conclusion that the TOM effect cannot be exploited when present, the EMH would still hold even when the TOM effect is present. Additional research is needed to conclude if the EMH is violated when the TOM effect is present.

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Seasonal anomalies in Germany : the turn-of-the month effect and liquidity over the past 30 years