Stock return seasonality : the january effect in Germany

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Stock return seasonality: the January effect in

Germany

by

Jasper Cornelis Samuel Bakker (10260250)

BSc. Economie en bedrijfskunde

Supervised by: Mark Dijkstra MSc.

University of Amsterdam

June 2016

Abstract

Previous studies found that stock returns are on average higher in January than in other months. This is known as the January effect and it contradicts the Efficient Market Hypothesis. The January effect is mainly researched for American stock markets. Using OLS regressions and monthly returns, this research found a very significant January effect for German stocks between 1987 and 2013. Contrary to earlier research, the effect was found to be stronger for larger firms. Furthermore are the average January returns diverging from the average returns in other months of the year which is also contradictory to previous studies.

JEL clasifications: G140, G120

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Statement of originality

This document is written by Jasper Bakker who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is 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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List of tables and graphs

Table 1: Key figures of the portfolios………... 11

Table 2: Power ratio over time and the influence of macro-economic variables for the complete sample………... 13

Table 3:First week effect………...……….. 14

Table 4:Summary of empirical literature about the January effect ……….... 20

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1. Introduction

The Efficient Market Hypothesis (EMH) states that prices always fully reflect available information (Malkiel and Fama, 1970). Several (seasonal) anomalies considering the EMH have been identified between 1970 and 1991 (Fama, 1991). As Fama (1991, p. 1587) himself states in his review on the literature considering EMH: “the most mystifying seasonal is the January effect. Stock returns, especially returns on small stocks, are on average higher in January than in other months”.

Explanations for the January effect offered so far are firstly the Window dressing hypothesis (Lakonishok, Shleifer, Thaler and Vishny, 1991) which states that institutional investors sell bad performing stock towards the end of the year and reinvest the proceeds in January. Therefore prices and thus returns will rise in January. Secondly the Tax-loss selling hypothesis (Roll, 1983), states that in the last days before the end of the year, individual investors sell securities in which they have losses. This will lower their net capital gains and thus lower the taxes on those net capital gains. Here too, the investors will reinvest the proceeds in January, leading to higher prices and thus higher returns. Finally the Information release hypothesis (Ritter, 1988) states that in the beginning of the year there is an excess information release. However, at first the new information is only available to the managers of a company. Outside investors therefore demand higher returns because of extra risk that is involved due to asymmetric information. Even though the January effect has been a subject of research since 1942, there is still no consensus between academics about what causes the January effect.

In the last two decades some macro-economic variables like GDP growth and inflation growth have been identified to be of importance for the January effect as well. Gu (2003) found that the January effect was weaker during periods of high GDP growth, but Kohers and Koli (1992) had contradictory results. Gu (2003) found that the January effect was weaker during periods of higher inflation growth. Finally, Gu (2003) and Mehdian and Perry (2002) have noted that the January abnormal returns are declining, meaning that the average January return is converging to the average return of the rest of the year.

Most research considering the January effect has been done for American stocks. First this paper is innovating by testing if there is a January effect present among German stocks. Second the question is asked whether the January effect is more present under small firms as has been found by Keim (1983) and Roll (1983). Finally will be tested if the effect is declining and finally what influence of inflation growth and GDP growth are significant as was found by Gu (2003). The central research question for this thesis is the following: Is there a January effect present for stocks listed on German stock exchanges between 1987 and 2013? Monthly data from all listed companies in Germany from 1987 to 2013 are used. Using the following regression model: 𝑅𝑅_𝑡𝑡=∝+ 𝛽𝛽𝐽𝐽𝐽𝐽𝐽𝐽 + 𝜀𝜀𝑡𝑡 a significant January effect is found. Furthermore using a second OLS regression model it is found

that the average January returns are increasing compared to the average return of the rest of the year and the January effect is stronger for larger firms.

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2. Literature review

2.1 Efficient market hypothesis

The Efficient Market Hypothesis (EMH) might be one of the most influential theories in finance. The theory was first introduced in the paper by Malkiel and Fama (1970). They define market efficiency as a market in which prices always fully reflect available information. Several (seasonal) anomalies have been identified between 1970 and 1991 (Fama, 1991). In this paper the focus will be on one of these seasonal anomalies of the EMH, namely the January effect.

2.2 Theories about the January effect

2.2.1 What is the January effect?

Wachtel (1942) who first discovered the January effect states that in January the returns on common stocks tend to be significantly larger than those in other months. This might be, as Boudreaux (1995) mentioned, a violation of the Efficient Market Hypothesis. Because as Haugen and Jorion (1996) explain, if the January effect would be exploitable, and if the market is efficient, the opportunity should have been priced out already. Investors could then exploit the anomaly by selling more in January, which would lower prices and diminish the January returns. More than fifty percent of the January effect occurs within the first week (Keim, 1983). The January effect has been found in many studies, most regarding the American stock market. Empiric literature about the January effect is summarized in table 4. So far there have been many theories trying to explain the January effect, but no academic consensus has been reached yet.

2.2.2 The window dressing hypothesis

There are several possible explanations for the January effect. Chen and Singal (2004) discuss three of the most popular ones in their paper: the tax-selling, the window dressing and the information release hypothesis. In this paper the same hypotheses will be discussed to give insight into possible explanations. Firstly, the window-dressing hypothesis will be explained.

Lakonishok, Shleifer, Thaler and Vishny (1991) explain the window dressing hypothesis as follows. Portfolio managers who actively manage portfolios are evaluated by comparing their performance to some benchmark, the S&P 500 for instance. However, since stock returns are noisy and the manager might just have been lucky, this might not be enough to evaluate his or her performance. Therefore, the investors might also want to see the actual portfolio holdings. Lakonishok et. al (1991) continue with saying that, to leave a good impression, these fund managers might window dress their portfolio towards the end of each quarter and especially towards the end of the year. The managers do this by overselling bad performing stocks towards the end of the quarter, where a stock’s performance was measured by using its returns. In January the proceeds of these sales are reinvested, which results in larger demand, higher prices and thus higher returns. In their research on 769 American private pension funds Lakonishok et. al (1991) found that every quarter fund managers display window dressing behavior. However, this behavior was stronger in the fourth quarter, which is consistent with

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the January effect. More research considering the window dressing hypothesis is discussed in section 2.3.1. and summarized in table 4.

2.2.3 The tax-loss and tax-gain selling hypotheses

The tax-loss selling hypothesis, first mentioned by Roll (1983), states that before the end of the year, individual investors sell securities in which they have losses. This will lower their net capital gains and therefore lower the taxes on those net capital gains. Because of the selling pressure at the end of December the prices will become lower. When the selling pressure disappears after the turn of the year, the prices rise and this could result in abnormally high returns just after the turn of the year, in January. The tax-loss selling hypotheses are also consistent with the fact that the January effect is particularly strong for small firms, which is discussed in section 2.3.3. Small firms tend to be more volatile and more volatile stocks exhibit a larger tax-gain and tax-loss selling potential (Roll 1983, p.10). Chen and Singal (2006) also mention a tax-gain selling hypothesis, which states that individual investors sell companies on which they have gains in January. In that way they can postpone paying tax on these capital gains by almost a year. More research considering the tax-loss selling hypothesis is discussed in section 2.3.1..

2.2.4 The information release hypothesis

According to the information release hypothesis, the excess January returns are the effect of significant information releases that occur in the first few days of January (Chen and Singal, 2004). This is consistent with Keim (1983) his findings, that the January effect is concentrated in the first week of January. Most firms have a fiscal year following the calendar year; which means that non-public information will be available in early January for managers. Some of these managers might decide to trade on this information. To protect themselves, investors demand a higher required rate of return, hence, the January effect (Ritter, 1988). However this doesn’t explain the notion made by Haug and Hirschey (2006). They state that since the fiscal year in the US has changed in 1986 from a December to a November fiscal year end, fiscal year doesn’t matter concerning the January effect.

Merton (1987) suggests a somewhat different information release hypothesis, also called the investor recognition hypothesis. He suggests that investors might hear about new companies when they release

information. As mentioned above, a lot of information is released in the first few days of January. Because more investors are aware of the company through the information release, more investors are inclined to buy, driving up the price which results in higher returns in January. There have not really been studies that tested this alternative information release hypothesis specifically.

2.3 Empirics of the January effect

2.3.1 Tax-loss selling, window dressing and information release hypothesis

Because many of the predictions considering the tax-loss selling hypothesis the window dressing hypothesis and the information release hypothesis are the same, it is hard to disentangle the possible effect on January returns. This problem has, amongst others, been recognized by Chen and Singal (2004) as well as Starks, Yong and

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Zheng (2006). Chen and Singal (2004) try to disentangle the hypotheses by researching a possible July effect by looking at daily data of common stocks traded on the New York Stock Exchange, The American Stock

Exchange and the NASDAQ. They look for a possible July effect because all mutual funds and similar

institutional investors in the United States are required to also provide a semi-annually report on the value of the securities they own. In June-July there is no tax-loss selling incentive, so abnormal returns in June-July could then be considered due to window dressing or an information release. The insignificant size of abnormal returns for stocks in July which Chen and Singal (2004) found is not in line with the window dressing hypothesis and neither with the information release hypothesis. They also defined a variable: potential for tax-loss selling (PTS). The variable is high for firms that have high capital losses and low for firms that have high capital gains. They found that firms with high PTS display abnormally high turnover rates in December and firms with a low PTS display abnormally high turnover rates in January which is consistent with the Tax-loss and the tax-gain selling hypothesis. They conclude that tax-loss selling probably is the right explanation for the January effect. However, Canada had no capital gains tax before 1972, and research by Berges, McConnel and Schlarbaum (1984) showed that Canadian stocks did display a January effect before 1972. Furthermore, as Haug and Hirschey (2006) mention, since the passage of the Tax Reform Act of 1986 in the United States, which changed the tax deadline for institutional investors from the end of December to the end of October, tax-motivated selling by these investors should not occur at year-end in the US. As Haug and Hirschey (2006) state, many institutions have retained a January–December reporting period despite the new November–October tax period; this favors the window dressing hypothesis again. Then again, as Poterba and Weisbenner (2001) mention, individual investors in the US still have to calculate their taxes based on capital gains for the period from January to December. Individual investors thus still have a reason to sell in December since they can reduce their capital tax gains and thus the taxes imposed on these capital tax gains. These individual investors might still cause a January effect. More empirical work regarding the different hypotheses is summarized in table 4.

2.3.2 Macro-economic variables

Besides the three discussed hypothesis so far, Kohers and Kohli (1992) documented that macro-economic variables also might explain a part of the January effect. Particularly, they found that the stage of the business cycle influenced the January effect. In expansionary phases, January returns on common stock were

significantly positive, in contractionary phases, none of the months showed stock returns significantly differing from zero. For the research they used monthly data from the S&P 500 composite index from 1948 through 1988. However, several years later, Gu (2003) arrived at an opposite conclusion in his research on American stock indices between 1950 and 2000. He concluded that the effect is weaker during periods of higher real GDP growth and stronger during periods of lower real GDP growth. Furthermore, he tested the influence of some other macro-economic variables on the January effect, expected GDP growth and real and expected inflation growth. For the expected values of the variables he used the next years’ value, assuming rational and accurate investors’ expectations. The other results of the research were that the January effect was weaker for years with higher inflation growth, and stronger for years with lower inflation growth. The expected values of the macro economic factors were both more significant than the actual value. Macro-economic variables might thus influence the January effect, however it is not clear in which direction. It is also not clear why these macro-economic variables might influence the January effect.

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2.3.3 Firm size and the January effect

Banz (1981) found in his study on common stock listed on the New York Stock Exchange that smaller firms have on average a larger risk adjusted return then larger firms: a size effect. Keim (1983) found that nearly fifty percent of the size effect is due to January abnormal returns. Keim (1983) and Roll (1983) also found, amongst others, that the January effect is especially strong for companies with a smaller market capitalization. This means that January small firm returns were significantly larger than large firm return, but not as much during other months of the year. As Easterday and Stephan (2009) state: the January and the size effect probably have a joint nature.

A possible explanation for both phenomena was later found by Keim (1989) in his research on all stocks listed on the New York Stock Exchange and the American Stock Exchange between 1983 and 1988. Small stocks tend to trade at the bid price in late December and trade at the ask price in the beginning of January. Since for small stocks, these spreads can be quite substantial, it can give the illusion of abnormal January returns, while such returns don’t necessarily exist. Clark and McConnel (1992) found in their research on 540 NYSE stocks over the period of 1982-1987 a seasonal pattern, but did not find a significant correlation between the changes in spreads and the January returns. However, both researches had a small sample period which might have influenced their results.

In Gu’s research on the January effect (2003) various American major stock indices between 1950-2000 and between 1988-2000 were used. Among these indices there was a distinction between indices that were comprised of only small stocks and indices that were comprised of larger stocks. He however found that the January effect was less present for the indices comprised of smaller firm stock. As Gu (2003) states himself, this is contradictory to earlier studies on the effect of size on January returns, in general the January effect is found to be more proficient in small stock.

2.3.4 The disappearing January effect

Using major stock indices of the United States, Gu (2003) found that the January effect is disappearing. He constructed a power ratio that indicates how strong the January effect is, and for all the indices he researched, the power ratio was declining. He suggested that the declining January effect may indicate that the market is becoming more efficient. Mehdian and Perry (2002) even found that the effect completely disappears after 1987 for the Dow Jones Composite, the NYSE Composite and the SP500. On the other hand Easterday and Stephan (2009) opposed these findings when studying all stocks listed on the New York Stock Echange (1946-2007) and the NASDAQ (1971-2007). They found that although smaller after 1963-1979, the January returns have returned to earlier levels. It thus isn’t really clear whether the January effect is disappearing or not.

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3. Methodology and Data

3.1 Methodology

Following the example of Haugen and Jorion (1996) to test the null hypothesis of January abnormal returns, regression model one will be used:

𝑅𝑅𝑡𝑡=∝+ 𝛽𝛽𝐽𝐽𝐽𝐽𝐽𝐽 + 𝜀𝜀𝑡𝑡 (1)

Where:

- 𝑅𝑅_𝑡𝑡 is the average monthly return for day t for the portfolio under consideration. - 𝐽𝐽𝐽𝐽𝐽𝐽 is a dummy variable which is 1 if it is January and zero otherwise

- 𝜀𝜀_𝑡𝑡 is an error term that is expected to have a mean of zero.

Like Keim (1983) and Haugen and Jorion (1996), the stocks are divided in ten size portfolios. The portfolios are value weighted and rebalanced at the last trading day of each year. For each portfolio the regression is

performed separately.

A regression coefficient of a dummy variable, as used in model 1 cannot reveal how the January effect moves over time. To identify a possible trend of the effect a power ratio like Gu’s (2003) can be used. The ratio is calculated as follows. First the January and the annual return are calculated. Then the following variables are defined:

𝑅𝑅𝐽𝐽∗= (1 + 𝐽𝐽𝐽𝐽𝐽𝐽𝐽𝐽𝐽𝐽𝐽𝐽𝐽𝐽 𝐽𝐽𝑟𝑟𝑟𝑟𝐽𝐽𝐽𝐽𝐽𝐽)12

𝑅𝑅𝑦𝑦= (1 + 𝐽𝐽𝑟𝑟𝐽𝐽𝐽𝐽𝑦𝑦𝐽𝐽 𝐽𝐽𝑟𝑟𝑟𝑟𝐽𝐽𝐽𝐽𝐽𝐽)

And then the power ratio is calculated by dividing the two:

𝑅𝑅𝐽𝐽∗

𝑅𝑅𝑦𝑦

If 𝑅𝑅𝐽𝐽 ∗

𝑅𝑅𝑦𝑦= 1 then the January return is exactly as good as the return of any other month in a given year. When

𝑅𝑅𝐽𝐽∗

𝑅𝑅𝑦𝑦> 1 then the January return is better than the average monthly return in a given year. When

𝑅𝑅𝐽𝐽∗

𝑅𝑅𝑦𝑦< 1 then January return is below the average monthly return in a given year. The power ratio thus measures the strength of the January effect. This means that when the power ratio converges to 1, the average January return

converges to the average return of the other months. There will be tested if the strength of the January effect is declining by using the following regression, which will be called model 2 in the remainder of the thesis:

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𝑅𝑅𝐽𝐽∗

𝑅𝑅𝑦𝑦= 𝛽𝛽1𝑌𝑌𝑟𝑟𝐽𝐽𝐽𝐽 + 𝛽𝛽2 𝑀𝑀𝐽𝐽𝐽𝐽𝑀𝑀𝑟𝑟𝑟𝑟𝑀𝑀𝐽𝐽𝑀𝑀𝑀𝑀𝑟𝑟𝐽𝐽𝑦𝑦𝑀𝑀𝑀𝑀𝐽𝐽𝑟𝑟𝑀𝑀𝑀𝑀𝐽𝐽 + 𝛽𝛽3𝑀𝑀𝐽𝐽𝐽𝐽𝑀𝑀𝑟𝑟𝑟𝑟𝑀𝑀𝐽𝐽𝑀𝑀𝑀𝑀𝑟𝑟𝐽𝐽𝑦𝑦𝑀𝑀𝑀𝑀𝐽𝐽𝑟𝑟𝑀𝑀𝑀𝑀𝐽𝐽 ∗ 𝑌𝑌𝑟𝑟𝐽𝐽𝐽𝐽 + 𝛽𝛽4𝐸𝐸(𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐽𝐽𝑀𝑀𝐺𝐺𝑟𝑟ℎ𝑡𝑡)

+ 𝛽𝛽5𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐽𝐽𝑀𝑀𝐺𝐺𝑟𝑟ℎ𝑡𝑡+ 𝛽𝛽6𝐸𝐸(𝐼𝐼𝐽𝐽𝐼𝐼𝑦𝑦𝐽𝐽𝑟𝑟𝑀𝑀𝑀𝑀𝐽𝐽𝑛𝑛𝐽𝐽𝑀𝑀𝐺𝐺𝑟𝑟ℎ𝑡𝑡) + 𝛽𝛽7𝐼𝐼𝐽𝐽𝐼𝐼𝑦𝑦𝐽𝐽𝑟𝑟𝑀𝑀𝑀𝑀𝐽𝐽𝑛𝑛𝐽𝐽𝑀𝑀𝐺𝐺𝑟𝑟ℎ𝑡𝑡+ 𝜀𝜀 (2)

Where:

- 𝑌𝑌𝑟𝑟𝐽𝐽𝐽𝐽 is indicating the year, ranging from 0 to 27 where 0 is the year 1987 and 27 is the year 2013. - 𝑀𝑀𝐽𝐽𝐽𝐽𝑀𝑀𝑟𝑟𝑟𝑟𝑀𝑀𝐽𝐽𝑀𝑀𝑀𝑀𝑟𝑟𝐽𝐽𝑦𝑦𝑀𝑀𝑀𝑀𝐽𝐽𝑟𝑟𝑀𝑀𝑀𝑀𝐽𝐽 is calculated by multiplying shares outstanding by the daily closing price - 𝑀𝑀𝐽𝐽𝐽𝐽𝑀𝑀𝑟𝑟𝑟𝑟𝑀𝑀𝐽𝐽𝑀𝑀𝑀𝑀𝑟𝑟𝐽𝐽𝑦𝑦𝑀𝑀𝑀𝑀𝐽𝐽𝑟𝑟𝑀𝑀𝑀𝑀𝐽𝐽 ∗ 𝑌𝑌𝑟𝑟𝐽𝐽𝐽𝐽

- 𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐽𝐽𝑀𝑀𝐺𝐺𝑟𝑟ℎ is the GDP growth in year t

- 𝐼𝐼𝐽𝐽𝐼𝐼𝑦𝑦𝐽𝐽𝑟𝑟𝑀𝑀𝑀𝑀𝐽𝐽𝑛𝑛𝐽𝐽𝑀𝑀𝐺𝐺𝑟𝑟ℎ is the inflation growth measured by the growth percentage of the Consumer Price Index (CPI) using the following formula:

𝐼𝐼𝐽𝐽𝐼𝐼𝑦𝑦𝐽𝐽𝑟𝑟𝑀𝑀𝑀𝑀𝐽𝐽𝑛𝑛𝐽𝐽𝑀𝑀𝐺𝐺𝑟𝑟ℎ =𝐶𝐶𝐺𝐺𝐼𝐼𝑡𝑡_{𝐶𝐶𝐺𝐺𝐼𝐼}− 𝐶𝐶𝐺𝐺𝐼𝐼𝑡𝑡−1

𝑡𝑡−1 ∗ 100%

- 𝐸𝐸(𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐽𝐽𝑀𝑀𝐺𝐺𝑟𝑟ℎ) is the growth of GDP in year t+1. This assumes, like Gu (2003), rational and accurate investors’ expectations.

- 𝐸𝐸(𝐼𝐼𝐽𝐽𝐼𝐼𝑦𝑦𝐽𝐽𝑟𝑟𝑀𝑀𝑀𝑀𝐽𝐽𝑛𝑛𝐽𝐽𝑀𝑀𝐺𝐺𝑟𝑟ℎ) is the inflation growth in year t+1. This assumes, like Gu (2003), rational and accurate investors’ expectations.

- 𝜀𝜀_𝑡𝑡 is an error term that is expected to have a mean of zero.

3.2 Data

Data on daily stock prices and the number of shares outstanding have been obtained through Compustat Global Securities. With this data monthly returns were calculated. However, the data exposed numerous flaws. For example the closing price of Bayer Motoren Werke (BMW) changed in one month from €71.26 to €1533.65 and two months after that it returned to a level of €93.36. After verification through Yahoo finance, the closing prices did not have such a large fluctuations at all. The magnitude of the problem in the dataset is hard to ascertain, but when all observations were dropped arbitrarily in case that the power ratio is higher than five, 21024 of the 165463 monthly observations were dropped. If the power ratio would be bigger than five this would mean that the January return would be 5 times larger than the average yearly return, which should be very unlikely, especially in a developed market such as Germany.To clean the dataset, the daily closing price was trimmed at the 5% level for the entire dataset. This means that the extreme values below the 2.5th and above the 97.5th percentile were ignored (Tukey, 1977). To reduce the impact of the extreme values, winsorizing is also an option. Winsorizing at the 5% level would mean that the extreme values below the 2.5th and above the 97.5th percentile would have been set at the values of the 2.5th and above the 97.5th percentile (Tukey, 1977).

Winsorizing or trimming data is common (Tukey, 1977). In this dataset however, it is not known which values are wrong and which are not. If in the example of BMW the price went from €71.26 to €70,- for instance, winsorizing would set the price would the level of the 97.5 th percentile generating a large return instead of a minor loss. Therefore, it is better in this case to trim instead of winsorize so the faulty prices have as little

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influence as possible. Before trimming the skewness of the daily closing prices was 118.15 and the Kurtosis 17195.18. After trimming the Skewness was 2.57 and the Kurtosis 9.09.

Despite that utmost care has been carried out when cleaning the dataset it is possible that the results might still be affected by the imperfect dataset. Hence this stipulation should be kept in mind when interpreting the results. The data on GDP growth and Inflation was obtained through the database of the World Bank where inflation is measured by the Consumer Price Index (CPI). 1990 Is the base year for the CPI.

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4. Results

4.1 Results model 1 and model 2

In table 1 key figures concerning the portfolios are summarized. Model one was used to test whether the mean January return was significantly different from the mean return in other months. For the complete sample the average January return is found to be significantly larger than the average return of the other months. In accordance with earlier research concerning the American stock market (Wachtel, 1942; Haug and Hirschey, 2006) a January effect is also present in Germany from 1987 to 2013. The only portfolio that has larger returns in other months than January is portfolio two, containing the second decile smallest firms. However, this difference is not significant. Keim (1983) and Roll (1983) found that the January effect is stronger among small firms. When assuming that market capitalization and balance sheet total don’t differ too we can follow the classifications the European Union has made about size. Following that definition only the smallest three portfolios could be called small or medium sized, since only these have a smaller market capitalization than 50 million euros (European Commission, 2016). Portfolios four to eight can than already be considered being formed of large companies, but they still have a significant January effect. Furthermore, when the January return is compared to the mean monthly return for the rest of the year it is about twice as high for portfolio one, but it is more than seven times as high for portfolio six and more than five times as high for portfolio five which are both large firm portfolios.

Table 1: Key figures of the portfolios

Portfolio Avg. Market Cap

(in € 1.000.000)

Mean return January

Mean monthly return rest of year

Number of observations Complete sample 1452.4 2.18%* 1.53% 142,097 Smallest firms 14.0 13.65%** 6.76% 8,597 Portfolio 2 31.1 3,53% 6.13% 12,777 Portfolio 3 41.3 1.20%** 0.42% 14,337 Portfolio 4 57.3 2.03%** 0.70% 14,484 Portfolio 5 86.0 0.40%** 0.07% 14,818 Portfolio 6 128.6 1.88%** 0.26% 14,898 Portfolio 7 325.4 0.98%* 0.53% 14,892 Portfolio 8 443.9 0.53%* -0.25% 14,822 Portfolio 9 1166.2 0.27% 0.13% 15,257 Largest firms 10325.4 0.15% 0.07% 16,719

* Significant with α=10% (one-sided) **Significant with α=5% (one-sided)

*** Significant with α=1% (one-sided) Model: 𝑅𝑅𝑡𝑡=∝+ 𝛽𝛽𝐽𝐽𝐽𝐽𝐽𝐽 + 𝜀𝜀𝑡𝑡

It should be noted that the number of observations per portfolio differs per portfolio where on average the smaller portfolios have less observations than the larger. This is due to the fact that if a company has its IPO there will be missing values prior to the IPO. Since the average IPO volume in Germany was about € 102

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million between 1990 and 2000 (Franzke, Grohs and Laux, 2003), the portfolios containing smaller firms should have less observations. Also there are companies in the dataset that have gone bankrupt, have been acquired, merged or taken over. For these firms there is no data after that specific moment. In general young and small firms go bankrupt more often than larger firms (Thornhill and Amit, 2003), whereas 60% of the small firms are likely to disappear within 5 years, compared to 30% of the large firms (Kothari, Sabino and Zach, 2006). Furthermore it is per definition harder to take over or acquire a larger firm since more capital is needed, so the larger firms will take over smaller firms more easily than vice versa. These factors all contribute to the fact that there are fewer observations for the smaller portfolios. When forming the portfolios, the firms without data for the complete period were kept in on purpose. If only the firms of which data is available for the full period would have been included, a survivorship bias would have occurred. This potential of survivorship bias could lead to biased results, since smaller firms are more likely to go bankrupt and previous studies (Keim, 1983; Roll, 1983) found that the January effect is more prevalent among smaller firms.

Table 2 shows various forms of regression model 1, all regression coefficients are significant at the 1% level. Contrary to what has been found by Gu (2003), the power ratio increases over the years, meaning that the January returns are diverging from the mean returns of the other months in all columns. For the coefficients of market capitalization can be concluded that the power ratio is increasing for larger firms. This is in accordance with Gu (2003) who found that the January effect is larger for larger firms. It is however contradictory to what Keim (1983) and Roll (1983) found, since they both found that the January effect is stronger for small firms. In regression three and four the coefficient of year times market capitalization is added and has a negative sign in both cases. This means that when time passes, the power ratio is becoming smaller given a certain market capitalization and that for a given year, the power ratio is smaller for large firms. This can be explained since the coefficients for market capitalization and year both increase enough, compared to regression one and two, to offsets the negative coefficient of year times market capitalization. In the last column the macro economic variables are added. Contrary to Gu’s (2003) findings, the absolute values of the coefficients of GDP growth and inflation growth are larger than the values of expected GDP growth and expected inflation growth respectively. Furthermore Gu (2003) found that all macro-economic variables have a negative relation to the power ratio, this research found however a positive relation to the expected GDP growth. Finally all variations of the regression model have a low adjusted 𝑅𝑅2. The model thus does not explain the power ratio very well. This is in accordance with Gu (2003) his findings, who found low adjusted 𝑅𝑅2’s as well. He used a similar model where the factors market capitalization and year times market capitalization where omitted but which were conducted on indices containing firms of different sizes.

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Table 2: Power ratio over time and the influence of macro-economic variables for the complete sample Regressor (1) (2) (3) (4) Year 1.34%*** (.0007) 1.36%*** (.0007) 1.50%*** (.0007) 1.73%*** (.0007) Market cap. (in € 1.000.000.000) .56%*** (.0005) 1.43%*** (.2137) 1.20%*** (.2131)

Year * Market cap. (in € 1.000.000.000) -.07%*** (.0001) -.06%*** (.0002) Inflation growth -3.02%*** (.0016) GDP growth -3.14%*** (.0018) E(Inflation growth) -2.92%*** (.0016) E(GDP growth) 1.78%*** (.0018) Intercept 1.157*** (.0130) 1.142*** (.0131) 1.118*** (.0135) 1.177*** (.0142) Summary statistics Adj. 𝑹𝑹𝟐𝟐 _.0030 _.0037 _.0037 _.0119 n 142,097 142,097 142,097 142,097

* Significant with α=10% (two-sided) **Significant with α=5% (two-sided) *** Significant with α=1% (two-sided)

Standard errors are denoted in parentheses under the coefficients dependent variable: 𝑅𝑅𝐽𝐽

∗

𝑅𝑅𝑦𝑦

4.2 Robustness

In the results section above is described that portfolio two, nine and ten don’t display a significant January effect and that the January effect is actually larger for larger firms. However, Keim (1983) found that the January effect can mostly be ascribed to the returns of the first week and Roll (1983) and Keim (1983) found that the January effect is stronger for small firms. To test whether there was first week effect and whether there is a difference per portfolio, the following model was tested per portfolio:

𝑅𝑅𝑡𝑡=∝+ 𝛽𝛽𝐼𝐼𝑀𝑀𝐽𝐽𝑓𝑓𝑟𝑟𝐺𝐺𝑟𝑟𝑟𝑟𝑀𝑀 + 𝜀𝜀𝑡𝑡

Where 𝐼𝐼𝑀𝑀𝐽𝐽𝑓𝑓𝑟𝑟𝐺𝐺𝑟𝑟𝑟𝑟𝑀𝑀 is a dummy variable, one for the first five business days of a year and 0 otherwise. Table 3 summarizes the results. For the complete sample there is a significant first week effect, meaning that the first week’s returns are higher than the returns for the rest of the year. The returns in the first week for the complete sample is 213% higher than the January return and 421% higher than the monthly return during the rest of the year. Which means that on average the returns substantially decrease after the first week. This strong first week

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effect can primarily be ascribed to the high first week returns of the two portfolios containing the smallest firms. These portfolios both have higher significance and higher first week returns compared to the rest of the year than the other portfolios. This is in agreement with Keim (1983) and Roll (1983) who stated that the January effect is stronger for small firms and with Keim (1983) whom stated that the high January returns are primarily formed within the first week. Compared to the findings in table 1, where there is no January effect for portfolio two, there is a significant and large first week effect. This means that rest of January has very low returns compared to the first week.

Table 3: First week effect

Portfolio Mean return

first week

# of observations Mean return January

Mean monthly return rest of year

Complete sample 5.05%*** 50.608 2.18% 1.2% Smallest portfolio 23.35%*** 3027 13.65% 6.76% Portfolio 2 34.14%*** 4372 3,53% 6.13% Portfolio 3 .78% 5182 1.20% 0.42% Portfolio 4 1.14%* 5124 2.03% 0.70% Portfolio 5 .43%** 5344 0.40% 0.07% Portfolio 6 .73%** 5351 1.88% 0.26% Portfolio 7 .49%** 5328 0.98% 0.53% Portfolio 8 .23% 5202 0.53% -0.25% Portfolio 9 1.1% 5410 0.27% 0.13% Largest Portfolio 2.1% 5982 0.15% 0.7%

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5. Conclusion and Discussion

In this paper the January effect has been researched for all stocks listed on German stock exchanges for the period of 1987 to 2013. It has been found that for the full sample a significant January effect is present. This might indicate that the German stock market is not efficient. Contrary to Gu (2003) his findings, the January effect is becoming stronger. In accordance with Gu (2003) his findings but opposing the general view expressed by Keim (1983) and Roll (1983): the January effect is stronger for larger firms than for small firms. As earlier found by Keim (1983) for the New York Stock Exchange, the January effect is primarily a first week effect for German stocks as well. For the complete sample the returns after the first week decrease drastically. The smaller firms displayed the strongest first week effect, both in terms of significance as well how high the return was in the first week compared to the rest of the year. This is in accordance with the findings of Keim (1983) and Roll (1983) who stated that the January effect is stronger for small firms where Keim (1983) also stated that the January effect is primarily formed within the first five business days. The factors (expected) GDP growth and (expected) inflation growth have a significant influence on the January effect as earlier research by Gu (2003) found as well. Where Gu (2003) found that all these factors have a negative effect on the January effect, this paper finds that the expected GDP growth has a positive effect on the January effect.

A serious limitation to this research is that the dataset exposed numerous flaws. Even though the dataset was cleaned with the utmost care, the results might have been influenced by the imperfect dataset. Furthermore firms that had high daily closing prices have been thrown out. Observations were non-randomly deleted by trimming the data this, might have led to biased inferences, as Kothari, Sabino and Zach (2006) point out. They found that such biases are in favor of finding systematic mispricing. The significant January effect that has been found might thus be a biased result because of the data trimming. Further research might use another data source when trying to replicate the results of this research so trimming the data is not necessary.

The significant January effect might indicate that the German stock market is not efficient and the significant positive year coefficient might indicate that it is even becoming less efficient. Bhardwaj, Ravinder and Brooks (1992) mention that the January effect might not be exploitable due to transaction costs. It is hard to get data on total transaction cost (Roll, 1983), but further research might include bid-ask spreads to partially control for the transaction costs. Finally Sullivan, Timmerman and White (2001) describe how in general, economics is a non-experimental science: there is normally no possibility to generate new data sets to test hypotheses

independently. They continue by saying that by using the same data set to formulate and test hypotheses, data-mining biases are introduced. Furthermore, they call the data-driven discovery of calendar effects in stock returns a striking example. Haug and Hirschey (2006) tested the January effect specifically they controlled for the bias by employing decision cones, which is a different form of using critical values. They also tested both equal-weighted and value-weighted portfolios since Sullivan et. al (2001) state, amongst others, that value weighted portfolios do not provide robust support for the January effect hypothesis. When using this altered method Haug and Hirchey (2006) still found a significant January effect. Considering the fact that none of the hypotheses discussed seem to explain the January effect to a large extent, it is interesting to conduct further research on datasets that haven’t been used yet to test whether there is a January effect or that the January effect might be the result of a datamining bias. It also interesting to adopt the methodology of Haug and Hirschey to control for the datamining bias on datasets that have been used already.

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7. Appendix

In table 4 below a summary about the empirical literature on the January effect can be found. The table is clustered per category of literature about the January effect. Some studies are mentioned multiple times because they have interesting findings about multiple subjects concerning the January effect.

Table 4: Summary of empirical literature about the January effect

Author and year

Sample and period Result Concerning

Gu (2003) Russel 1000 (1988-2000) Russel 2000 (1988-2000) Russel 3000 (1988-2000) Dow 30 (1929-2000) S&P 500(1950-2000)

The strength of the january effect is declining

Declining January effect

Mehdian and Perry (2002)

Dow Jones Composite , NYSE Composite and the SP500. All from 1964-1998

A January effect was present until 1987. After the 1987 market crash no significant January effect is

Easterday and Stephan (2009)

All stocks listed on the New York Stock Echange (1946-2007) NASDAQ (1971-2007)

January returns are smaller after 1963–1979, but have simply reverted to levels that existed before that time. They also show that the January effect is not limited to mature markets but also appears in firms trading on the relatively new NASDAQ exchange in the 1970s

Haug and Hirschey (2006) Combined dataset on American stock markets (1802-2004)

The January effect was more present under small stock.

Firm Size Athanassakos (1992) Toronto Stock Exchange (1960-1989)

The January effect was more present under small stock.

Firm size

Clark and McConnel (1992)

Common stock listed on the New York Stock Exchange (NYSE) (1982-1987)

Changes in bid ask spreads are not correlated with the January effect

Firm size

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2000) Russel 2000 (1988-2000) Russel 3000 (1988-2000) Dow 30 (1929-2000) S&P 500(1950-2000)

firms have a stronger January effect than indices formed of all firm sizes or small firm sizes

Keim (1984) All stocks listed on the New York Stock Echange (1962-1979)

January effect is especially strong for smaller firms

Firm Size

Roll (1984) All stocks listed on the New York Stock Echange (1963-1980) and the American Stock Exchange (1963-1980)

January effect is especially strong for smaller firms

Firm Size

Keim (1989) All stocks listed on the New York Stock exchange (1983-1988) and the American Stock exchange (1983-1988)

Small stocks tend to trade at the bid price in late December and trade at the ask price in the beginning of January. Since for small stocks, these spreads can be quite

substantial, this can give the illusion of abnormal January returns

Firm size

The January effect is concentrated in the first week

First week effect

Chen and Singal

All stocks listed on the New York Stock Exchange (1993-1999), The American Stock (1993-1999) Exchange and the NASDAQ (1993-1999)

In June-July there is no tax-loss selling incentive, so abnormal returns in June-July could then be considered due to window dressing or an information release. No effect was found. Information hypothesis Haug and Hirschey (2006) Combined dataset on American stock markets (1802-2004)

The January effect was still present after the tax reform act of 1987. Contrary to what the information release hypothesis would have

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predicted. Haug and Hirschey (2006) Combined dataset on American stock markets (1802-2004)

A January effect was present. January effect

Rozeff and Kinney (1976)

Common stock listed on the New York Stock Exchange (1904-1974)

A January effect was present January effect

Wachtel (1942)

Dow Jones Industrial Average(1927-1942)

Athanassakos (1992)

All stocks listed on the Toronto Stock Exchange (1960-1989)

A January effect was present January Effect

Roll (1984) All stocks listed on the New York Stock Echange (1963-1980) and the American Stock Exchange (1963-1980)

Haugen and Jorion (1996)

All stocks listed on the New York Stock Exchange (1926-1993)

Berges, McConnel and Schlarbaum (1984) Canadian Stocks (1951-1980)

Chen and Singal

All stocks listed on the New York Stock Exchange (1993-1999), The American Stock (1993-1999) Exchange and the

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NASDAQ (1993-1999) Starks, Yong and Zheng (2006) 168 American municipal bond closed-end funds over the 1990 to 2000 sample period

Gu (2003) Russel 1000 (1988-2000) Russel 2000 (1988-2000) Russel 3000 (1988-2000) Dow 30 (1929-2000) S&P 500(1950-2000)

(expected) inflation and (expected) GDP growth all have a negative influence on the strength of the January effect Macro-economic variables Kohers and Kohli (1992) S&P Composite index (1948-1988)

GDP growth has a positive effect on the strength of the January effect

Macro-economic variables Haug and Hirschey (2006) Combined dataset on American stock markets (1802-2004)

The January effect was still present after the tax reform act of 1987. Contrary to what the Tax loss selling hypothesis would have predicted. Tax-loss selling hypothesis Berges, McConnel and Schlarbaum (1984) Canadian Stocks (1951-1980)

Canada introduces no capital gains tax until 1973 and the paper reports that January returns in Canada exceed returns for other months of the year before and after this date. Contrary to what the Tax loss selling hypothesis would have predicted.

Tax-loss selling hypothesis

Chen and Singal

Firms with high Potential for Tax loss Selling (PTS) display abnormally high turnover rates in December and firms with a low PTS display abnormally high turnover rates in January which is consistent with the Tax-loss and the tax-gain selling hypothesis.

Tax-loss selling hypothesis Starks, Yong and Zheng (2006) 168 American municipal bond closed-end funds

They assume that closed end municipal bonds are primarily bought by people who are tax

Tax-loss selling hypothesis

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over the 1990 to 2000 sample period

sensitive since these bonds have a tax-exempt status. They found that abnormal returns of these funds in January are positively correlated with the year-end trading volumes. They also found that the year-end volumes are negatively related to the current and the previous year returns. Their findings support the tax-loss selling hypothesis. Athanassakos

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Fund managers window dress Window dressing hypothesis Lakonishok, Shleifer, Thaler and Vishny (1991) 769 American private pension funds (1985-1989)

Fund managers window dress Window dressing hypothesis

Athanassakos (1992)

Fund managers do not window dress

Window dressing hypothesis

Griffith and White (1993)

Fund managers do not window dress

Chen and Singal

In June-July there is no tax-loss selling incentive, so abnormal returns in June-July could then be considered due to window dressing or an information release. No effect was found.

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Stock return seasonality : the january effect in Germany