The Profitability of Momentum Trading Strategies: a Comparison Between Stock Markets in the Netherlands and Germany

The profitability of momentum trading strategies: A comparison between stock markets in the Netherlands and Germany

Oliver Weil Master’s Thesis International Financial Management (Double Degree) University of Groningen and Uppsala University

Abstract: Can momentum trading strategies beat Dutch or German stock market indices? If so, do those strategies show significant positive net returns? For the period from March 2009 to March 2016 this appears to be the case for only one out of the nine momentum trading strategies investigated with respect to the Dutch stock market and for none of those same momentum trading strategies investigated with respect to the German stock market. Furthermore, this research finds that the net momentum returns seem to be winner- instead of loser-portfolio driven and that the longer the holding period, the higher the net momentum returns realized.

Keywords: Momentum, Efficient markets, The Efficient Market Hypothesis, Transaction costs JEL classifications: G10, G11, G14, G15, G19

Author: O. A. M. Weil Mail: [email protected] Phone number: +31 610155762 Student number: s2021277 Study program: DD MSc International Financial Management Place and date: Groningen, June 2nd 2017 Supervisor: Prof. dr. B. W. Lensink I. Introduction

Managers as well as investors are continuously trying to find ways in which they can generate significant returns. In an efficient market - a market in which security prices always fully reflect available information - the true expected return on any security is equal to its equilibrium expected value, which is, of course, also the market's assessment of its expected value (Fama 1965, 1970). Although the efficient market hypothesis has been tested widely and generally has been found consistent (Jensen, 1978), around the late 1970s, systematic deviations from theoretical expectations, so-called anomalies, were discovered (Frankfurter and McGoun, 2001). These anomalies open up the possibility of profit opportunities by using trading strategies. Research on trading strategies that go against the efficient market hypothesis distinguishes between contrarian trading strategies and momentum trading strategies. This paper focuses on momentum trading strategies. A momentum trading strategy is based on stock price momentum. The underlying expectation is that past stock performance will continue into the future. In other words, stock prices that have appreciated in the past will continue doing so in the future. The same applies to stock prices that have decreased in the past; the momentum trader assumes that they will continue doing so in the future. Making use of the anticipated price trend, a momentum trading strategy involves stocks which have performed well in the past, expecting that a positive return will be made when those stocks are sold at a later date. In the same manner, a positive return is expected to be made by the momentum trader when he short sells stocks1 that have decreased in price in the past.

With respect to the momentum trading strategies the debate continues about what causes the momentum returns and, on the other hand, about whether the momentum strategy is truly profitable. With regard to the cause of the abnormal momentum returns, Fama and French (1996), Grundy and Martin (2001) and Jegadeesh and Titman (2001), show that rational models fail to explain them. Since the rational models fail to explain the abnormal momentum returns, researchers introduced the so-called behavioral models. According to Barberis and Shleifer (2003), Daniel et al. (1998) and Hong and Stein (1999), the behavioral models state that abnormal returns that arise due to a momentum trading strategy occur because of incorrect or delayed information interpretation by the investors. Discussion concerning the profitability of the momentum strategy focuses on the assumptions with respect to the true

1 Short selling is the sale of a stock that is not owned by the seller. It is driven by the assumption that a stock’s price will decrease, enabling it to be purchased back at a lower price to make a profit.

2 transaction costs involved in pursuing such a strategy. Jegadeesh and Titman (1993, 2001) find abnormal returns for the momentum trading strategy by taking into account 0.5% transaction costs. However, more recently, many researchers consider a 0.5% transaction cost too low when pursuing a momentum strategy (Agyei-Ampomah, 2007; Korajczyk and Sadka, 2004; Lesmond et al., 2004; Pavlova et al., 2011).

Previous literature investigated whether momentum returns existed in the United States, the United Kingdom and internationally (e.g. De Bondt and Thaler, 1985; Doukas and McKnight, 2005; Griffin et al., 2003; Jegadeesh and Titman, 1993). To my knowledge little momentum strategy research has been done with respect to continental Europe.

This paper focuses on the profitabilities (on a net basis) of momentum trading strategies with respect to the Dutch and German stock markets from March 2009 to March 2016 (hence, after the financial crisis of 2008) and also attempts to make a comparison between those profitabilities.

This paper seeks to answer two research questions.

The first question is: Can a momentum trading strategy yield significant positive net returns in the Netherlands that exceed the AEX index?

The second question is: Can a momentum trading strategy yield significant positive net returns in Germany that exceed the MDAX index?

The answers to these research questions add to the existing literature in several ways. First, this paper contributes to existing literature by analyzing a new time period (2009-2016), thus avoiding any distortions in the results caused by the financial crisis of 2008. Second, I investigate the profitability of momentum trading strategies in continental Europe, more specifically in the Netherlands and Germany. So far, most momentum trading strategy research has focused on the US and UK stock markets. Third, when calculating the net profitability of the various momentum trading strategies, I endeavor to approximate the actual transaction costs as closely as possible in order to determine whether the application of

3 momentum trading strategies is advantageous. Fourth, I investigate if, and to what extent, the profitability (on a net basis) in the Netherlands exceeds the Dutch stock market AEX index and if, and to what extent, the profitability (on a net basis) in Germany exceeds the German midcap stock market MDAX index. Finally, I investigate the profitability of momentum trading strategies (on a net basis) not only for the research period, but also with respect to six consecutive 12-month periods within the research period. This part of the research aims at providing insight in the development of the profitability of the various momentum trading strategies during the research period.

The results of this research show that, while in the Netherlands five out of the nine momentum trading strategies investigated yield a positive net return that is higher than the Dutch stock market AEX index, in Germany only two out of the corresponding nine momentum trading strategies investigated yield a positive net return that is higher than the German midcap stock market MDAX index. However, only one out of the five Dutch momentum trading strategies that beat the market, yields a significant (positive) net return, while neither of the two corresponding German strategies that beat the market, is robust. With respect to all nine Dutch and German momentum trading strategies, the major part of the net momentum returns, when calculated over the research period, can be attributed to the winner portfolio. With respect to all nine Dutch and corresponding German momentum trading strategies this research shows that the longer the holding period, the higher the net momentum returns realized. For seven out of the nine momentum trading strategies the net momentum returns realized in Germany are lower than the ones realized in the Netherlands, even though for all nine momentum trading strategies applied, the German gross returns are higher than the equivalent Dutch gross returns. Finally, this research shows that for all nine momentum trading strategies the transaction costs in Germany are quite a bit higher than those in the Netherlands. However, the difference between the Dutch and German transaction costs seems to decrease as the length of the holding periods increases.

The remainder of this paper is organized as follows. Section II examines the literature on trading strategies and, more in particular, about momentum strategies. Section III describes the data and methodology used for this research. Section IV provides the empirical results that are found and section V contains a number of conclusions. Finally, section VI provides the reference list and section VII consists of the Appendix.

4 II. Literature review

This section contains an overview of the literature relevant for this paper. In section II.1 the efficient market hypothesis versus the contrarian and momentum trading strategies is discussed. In section II.2 the profitability of the momentum trading strategy is discussed. Section II.3 focuses on the causes of momentum profits and section II.4 reviews the literature on the correlation between Dutch and German stock market returns and between Dutch and German stock market indices.

II.1. Efficient market hypothesis versus the contrarian and momentum trading strategies The efficient market hypothesis is an important theory in the world of finance and is used as starting point in much academic research. As mentioned before, in an efficient market, stock prices fully reflect available information (Fama 1965, 1970). The efficient market actually states that one cannot predict potential returns by making use of past data. Simply said, in an efficient market stocks trade at their fair value, which leads to the situation that it is impossible for managers and investors to either buy stocks that are undervalued or sell stocks which are overvalued. In other words, managers and investors cannot beat the market. Only in an inefficient market will the true expected returns and equilibrium expected returns not necessarily be identical (Fama, 1976). However, around the late 1970s, systematic deviations from theoretical expectations were discovered; that is, there appeared to be predictable opportunities for earning abnormal returns using rather simple trading strategies (Frankfurter and McGoun, 2001). These deviations were labeled anomalies. Anomalies are empirical results that seem to be inconsistent with maintained theories of asset-pricing behavior (Schwert, 2003). They show either market inefficiency (profit opportunities) or inadequacies in the underlying asset-pricing model. After they are recognized and studied in the academic literature, anomalies frequently seem to vanish, reverse, or decrease. This raises the question whether profit opportunities existed historically, but have since been arbitraged away, or whether the anomalies were simply statistical deviations that attracted the attention of researchers (Schwert, 2003).

There have been many papers that tried to confirm the profitability of trading strategies that focus on the predictability of stock returns (Kothari, 2001). For instance, Fama and French (1995) report evidence on the book-to-market effect, De Bondt and Thaler (1985, 1987) report on the long-term contrarian effect, Jegadeesh and Titman (1993) and Rouwenhorst (1998)

5 report on the short-term momentum effect, Moscowitz and Grinblatt (1999) looked at the industry-factor effects to explain the momentum effect, Chan et al. (1996) research the use of the momentum strategy for the US stock market, while Griffin et al. (2003) show that a momentum strategy yields abnormal returns in international stocks. These articles all analyze the contrarian or the momentum strategy as trading strategies that rely on stock market anomalies.

In academic literature two trading strategies may be distinguished, the contrarian trading strategy and the momentum trading strategy. Where the contrarian trading strategy involves buying historical “losers” and selling historical “winners”, the momentum trading strategy involves buying historical winners and selling historical losers. One of the most important articles that confirmed the existence of the contrarian trading strategy for the US stock market is the article by De Bondt and Thaler (1985). They show that, over a three to five year period, past winner stocks are outperformed by past loser stocks and therefore they suggest to buy the historical losers and sell short the historical winners. This contrarian trading strategy was confirmed by, amongst others, Jegadeesh (1990) and Lehmann (1990), who show that the contrarian strategy holds not only for a period of three to five years, but also for a much shorter time period, namely, a week or a month. Besides the contrarian trading strategy, the momentum trading strategy also contradicts the efficient market hypothesis. One of the most important articles that confirmed the existence of the momentum trading strategy is the one by Jegadeesh and Titman (1993). These authors show that buying stocks that performed well historically (three to twelve months) continued to perform well during the next three to twelve months. Within these next three to twelve months, the stocks appear to have a “momentum” that triggers them to keep going in an unchanged direction. The authors demonstrate that abnormal returns can be made by going short on a portfolio consisting of historically losing stocks in a certain period and taking a long position in a portfolio consisting of historically winning stocks in an equal time period. Therefore, they suggest short selling the historical losers and buying the historical winners. In the article by Jegadeesh and Titman (1993), the stocks are ranked based on their returns in the previous ‘J’-months. The formation period, which is also known as the evaluation period or the ranking period, is the period that the stocks are ranked (this period consists of J-months). In the article by Jegadeesh and Titman (1993) J varies between three, six, nine and twelve months. They chose to construct the portfolios in such a way that the winner portfolio consisted of the best performing stocks (top ten percentile) and the loser portfolio consisted of the worst performing stocks (bottom ten

6 percentile). After the portfolios were constructed, they had to be held for a period of ‘K’- months (again; three, six, nine and twelve months), which is named the holding period. Jegadeesh and Titman (1993) conclude that they find significant returns of 1.1% per month.

Not only Jegadeesh and Titman (1993) confirmed the momentum trading strategy to be profitable in the United States, also Chan et al. (1996) did so. Jegadeesh and Titman (2001) evaluated the research they had undertaken approximately eight years earlier and found that the momentum trading strategy continued to be profitable in the United States for the period from 1990 to 1998. Furthermore, Rouwenhorst (1998) shows that also in Central Europe the momentum trading strategy generates significant positive returns. With respect to international stocks, Moskowitz and Grinblatt (1999) and Griffin et al. (2003) show that the momentum trading strategy generates significant positive returns in financial markets all over the world. More recently, Moskowitz, Ooi and Pedersen (2012) and Asness, Moskowitz and Pedersen (2013) find that momentum occurs in exchange traded futures contracts and in bonds too.

II.2. Profitability of the momentum trading strategy Many researchers showed that pursuing a momentum strategy and thereby taking into account transaction costs of 0.5% per trade generated significant positive returns (Jegadeesh and Titman, 1993, 2001; Liu et al., 1999; Rouwenhorst, 1998). They came to this 0.5% transaction cost by taking an average transaction cost. However, more recently, many researchers consider a 0.5% transaction cost too low when pursuing a momentum strategy. Agyei- Ampomah (2007), Korajczyk and Sadka (2004), Lesmond et al. (2004) and Pavlova et al. (2011) consider a transaction cost of 0.5% to be too low, because regular portfolio rebalancing is needed in order to pursue a momentum strategy. One must buy the winner stocks and sell short the loser stocks every time the formation period (consisting of J-months) ends. This comes with transaction costs that, according to the previously mentioned literature, should be higher than 0.5%. Lesmond et al. (2004) even go as far as to state that a momentum strategy is not profitable at all when taking into account the necessary substantial transaction costs. This is also shown by Pavlova et al. (2011), who find that the profits of the momentum strategy vanish entirely when fully taking into account the costs of trading. On the other hand, Korajczyk and Sadka (2004) consider that, although a transaction cost of 0.5% is too low to maintain the momentum strategy, the momentum strategy is still profitable despite the higher transaction costs. Agyei-Ampomah (2007) show that the profitability of momentum strategies

7 with formation and holding periods up to six months is impeded by high transaction costs. The high transaction costs are caused by the high portfolio turnover rate. However, the trading intensity and associated costs of the momentum strategy decreases for longer formation and holding periods. Therefore, investors can profitably trade on momentum strategies with formation and holding periods of six months and more.

II.3. What causes momentum profits? Although Lesmond et al. (2004), as well as Pavlova et al. (2011) clearly state that momentum profits do not occur, many other academics firmly believe that profitable momentum returns do exist. These researchers are mainly interested in the cause of the momentum returns, trying to explain the presence of these excess returns through either rational or through behavioral models.

With respect to the rational models, Fama and French (1996) and Grundy and Martin (2001) show that asset-pricing models based on rationality fail to explain abnormal momentum returns. Conrad and Kaul (1998) suggest that cross-sectional diffusion in expected returns could be a valid source of the momentum returns. Jegadeesh and Titman (2001), however, claim that the findings of Conrad and Kaul (1998) are not the reason behind these profitable momentum returns. MacKinlay (1995) argues that mainly data mining drives the momentum premium, though Grundy and Martin (2001) and Jegadeesh and Titman (2001) reject his finding and state that his arguments do not completely give the explanation to momentum profits.

Since rational models were not able to explain the profitable momentum returns, behavioral models were introduced in order to find an explanation. Daniel et al. (1998) state that trading because of biased self-attribution and overconfidence explains momentum investing. They argue that one will buy a stock if good news supports their own optimistic indication. This also works the other way around; one does not sell the stock if the negative indication is inconsistent with positive news. Barberis et al. (1998) propose that under-reaction is initiated by the conservatism bias over time horizons of one to fourteen months. They explain this conservatism bias as holding on to previous opinions. Thus, investors underreact to the new information that is given, causing the effects of the information on the stock price to be late. More recently, Grinblatt and Han (2005) wrote that the disposition effect is the main reason

8 investors underreact to information. They explain this effect as the trend of investors to sell shares of which the price has increased, while keeping the shares that have decreased in price.

II.4. Correlation between Dutch and German stock market returns and between Dutch and German stock market indices The Netherlands and Germany have close economic, political, social and cultural ties. Economically, Germany is particularly important to the Netherlands. It is its main trading partner, not only for imports, but also for exports2. According to Eun and Resnick (1984), who examined multiple stock markets around the world, the stock market returns of Germany and the Netherlands (and Switzerland) had the highest correlation. Furthermore, Bertero and Mayer (1990) examined share price movements for 23 countries globally. Of the 23 markets examined they report four groups of countries whose stock market indices were particularly closely correlated. One of these groups consisted of Switzerland, Germany and the Netherlands. Likewise, Roll (1992), who examined 24 stock markets worldwide regarding the behavior of international stock market indices, shows that the correlation between Germany and the Netherlands is the highest (again, together with Switzerland). All these findings clearly indicate that German and Dutch stock market returns and stock market indices are highly correlated.

2 https://www.rijksoverheid.nl/onderwerpen/betrekkingen-met-nederland/inhoud/duitsland (accessed on January 19th 2017)

9 III. Data and methodology

This section contains the data and methods used in my research. Section III.1 provides an overview of the framework of my research. Section III.2 explains the source of the data used in my research. Section III.3 provides the research methods used to calculate the returns of the momentum trading strategy. Section III.4 provides the research methods used to calculate the transaction costs and section III.5 provides the research method used to calculate correlations.

III.1. Framework of this research In this paper I analyze the profitability of the momentum trading strategy with respect to the Dutch and German stock markets. In this context I also compare the development of those profitabilities. The research period runs from March 2009 to March 2016, thus avoiding any distortions caused by the financial crisis of 2008. This paper makes use of the momentum trading strategy method as developed by Jegadeesh and Titman (1993, 2001), but deviates from their method as follows: First, with respect to the sample, while I copy their method for the Dutch stock market by taking into account all the stocks listed on the Amsterdam Stock Exchange, I do not copy their method for the German stock market. For the German stock market I make use of a sub- sample of stocks listed on the Frankfurt Stock Exchange. The reason for this is that otherwise the samples would not be comparable in terms of companies’ market capitalization. Second, with respect to portfolio size, where Jegadeesh and Titman (1993, 2001) employ a portfolio size constituted by the best performing 10% or the worst performing 10% of the stocks in their sample (consisting of NYSE and AMEX stocks), this paper employs a portfolio size of 20 stocks for the winner portfolio and 20 stocks for the loser portfolio. Third, with respect to the calculation of transaction costs, these costs are taken into account in line with a method developed by Lesmond et al. (2004). However, while those authors assume a turnover rate of a 100%, this research follows Barber and Odean (2000), who apply the actual turnover rate when calculating transaction costs.

III.2..Data The data used in this research relates to stocks that are traded on the Amsterdam Stock Exchange (AEX) and the Frankfurt Stock Exchange (Deutsche Börse AG) during the period from March 2009 to March 2016. For the Amsterdam Stock Exchange I collect data on all stocks, but for the Frankfurt Stock Exchange I only collect data on a sub-sample of the

10 Frankfurt Stock Exchange, which roughly equals the average market capitalization of the Amsterdam Stock Exchange. I do this in order to make the Dutch sample and the German sample comparable. It is important to do so, as Doukas and McKnight (2005), Hong et al. (2000) and Liu et al. (1999) all found that there exists a strong relationship between companies’ market capitalization and momentum profitability.

The data for both samples used in my research is extracted from DataStream Advance 5.1. All warrants and investment-trusts are eliminated from the two samples. Furthermore, as both samples include surviving and non-surviving stocks, it can be said that the survivorship bias is ruled out (Agyei-Ampomah, 2007). The survivorship bias is a form of the sample selection bias that arises when a sample only includes funds (stocks) that survive until the end of the research period (Carpenter and Lynch, 1999). Finally, in order to prevent this research from being biased regarding the month-end effect (Thaler, 1987), the data is deliberately collected on the 15th day of the month. With respect to the Amsterdam Stock Exchange, during the period from March 2009 to March 2016, all in all 382 different stocks were traded. The maximum number of stocks represented consists of 313 and the minimum number of stocks represented consists of 288. On average 296 stocks are available for analysis. As for the Frankfurt Stock Exchange, during the period from March 2009 to March 2016 all in all 322 stocks were traded, with a maximum of 321 and a minimum of 265. On average 284 stocks are available for analysis.

The data collected from DataStream Advance 5.1 comprises the total monthly returns, also known as the total return index (RI), as well as the stock (share) price, the market capitalization (MV) and the ask and bid price (PA, respectively PB) of all the stocks in the two samples. Furthermore, to be able to compare the momentum trading strategy returns with the Amsterdam Stock Exchange index and the Frankfurt Stock Exchange index, DataStream Advance 5.1 is also used to extract the monthly total returns of these indices.

11 III.3. Research method used calculating the results of the momentum trading strategy In my research, I replicate the method by Jegadeesh and Titman (1993) with respect to constructing the momentum portfolios. That method - also known as the J-month/K-month strategy - is the one most broadly used in the literature.

The stocks in the sample are ranked based on their returns over the formation period J and are held for a period of K. The stocks with the highest returns are called winners and the stocks with the lowest returns are called losers. Here I replicate Jegadeesh and Titman (1993) again, by starting with the holding period K one month after the formation period J has ended. By skipping one month I avoid the effects of bid-ask price pressure and lagged reaction effects, which are found in Jegadeesh (1990) and Lehmann (1990).

Agyei-Ampomah (2007) shows that the profitability of momentum strategies with formation and holding periods of up to six months is impeded by high transaction costs. Those high costs are caused by the high portfolio turnover rate. However, the trading intensity and associated costs of the momentum strategy decreases for longer formation and holding periods. Therefore, he concludes that investors can profitably trade on momentum strategies with formation and holding periods of six months and more. In view of the above, I replicate Agyei-Ampomah (2007) and take formation and holding periods of six, nine and twelve months. By doing so I deviate from Jegadeesh and Titman (1993), who take formation and holding periods of three, six, nine and twelve months.

I take the monthly total returns extracted from DataStream Advance 5.1, to calculate the returns over the formation period J (J = 6, 9, 12). For this calculation I use the following equation:

!"!"! !"!(!!!) �!, !!!,! = (1) !"!(!!!)

In equation 1, �!, !!!,! is the return of stock � for the formation period J, so from time � − � to time �. ��!" is the total return index of stock � at time � and ��!,(!!!) is the total return index of stock � at time � − �. Total return stands for the total growth in value of a stock on

12 the assumption that dividends are used to acquire additional stocks3. I use equation 1 to determine the winner portfolio and the loser portfolio.

By using equation 1 to calculate the returns, this research should be comparable with well- known papers such as Agyei-Ampomah (2007), Chan et al. (1996), Jegadeesh and Titman (1993) and Rouwenhorst (1998). The stocks are ranked based on their returns in the J period. In this research, the winner portfolio consists of the best performing 20 stocks and the loser portfolio consists of the worst performing 20 stocks. These winner and loser portfolios are equally weighted after the formation period at time t and they are held for a period of K months (K = 6, 9, 12). By constructing equally weighted (winner and loser) portfolios I again follow, among others, Jegadeesh and Titman (1993).

In order to avoid the effects of bid-ask price pressure and lagged reaction effects, the holding period will begin one month after the end of the formation period (Jegadeesh, 1990; Lehman, 1990). Using equation 2, I calculate the return per stock, for both the winner and the loser portfolio, for a holding period of K months, using three different holding periods (K = 6, 9, 12). In my research each K-6 will mean that the return of the stock is calculated for a period of six months, starting from time t + 1 up to and including t = 7, K-9 for a period of nine months, starting from time t + 1 up to and including t = 10 and K-12 for a period of twelve months, starting from time t + 1 up to and including t = 13. Furthermore, just as in Jegadeesh and Titman (1993) and in Agyei-Ampomah (2007), the returns of the portfolios are calculated on an overlapping holding period basis.

3 http://findb.aalto.fi/docs/Datastream/datastream_time_series_walkthrough.pdf (accessed on January 26th 2017)

13 In order to calculate the returns per stock over the holding period K, the following equation is used:

!"!,(!!!!!)! !"!,(!!!) �!, !!! (�, �) = (2) !"!,(!!!)

Where �!, !!! (�, �) is the return of stock � over the holding period K. ��!,(!!!!!) is the total return index of stock � at the end of the holding period K and ��!,(!!!) is the total return index of stock � at time t + 1. This calculation is done for every possible combination of formation period J (J = 6, 9, 12) and holding period K (K = 6, 9, 12).

When a manager or investor pursues the momentum strategy, at the end of each formation period (t + 1), the winner portfolio is bought and the loser portfolio is sold (short), thereby holding these portfolios for a period of K months. Different momentum trading strategies can be applied, by using different combinations of the formation period (J) and the holding period (K). This implies that I am examining, for each of the two countries taken into consideration (the Netherlands and Germany), a total of 9 different trading strategies for each winner portfolio and loser portfolio. Each trading strategy represents a different combination of formation period (J) and holding period (K). The different combinations of formation and holding periods are: (J, K) = (6,6), (6,9), (6,12), (9,6), (9,9), (9,12), (12,6), (12,9) and (12,12).

Next, by using equation 3, the average returns for both the winner and the loser portfolio are calculated.

! (!,!) � �, � = !,(!!!) (3) !,(!!!) !

Where �!,(!!!) �, � is the average return of the (winner or loser) portfolio over holding period K, �!,(!!!)(�, �) stands for the return of stock � at time t + 1 and (J, K) stands for respectively the formation and holding periods. N stands for the number of stocks � in the (winner or loser) portfolio; as stated before, in this research, the number of stocks in any winner or loser portfolio is 20.

14 If stocks in the two samples are delisted during the formation period (J), they are not taken into account with respect to the holding period (K). If stocks are delisted during the holding period (K), their return is automatically set to zero. According to Liu et al. (1999), delisting stocks lowers the momentum returns. However, Liu et al. (1999) also observe that this decrease is negligible and momentum returns remain more or less the same. Therefore, I will not use this in my research.

In order to determine the average portfolio profit of the momentum trading strategies for each twelve-month period (�) under consideration, the following equation is used:

�! �, � = ! � �, � (4) !,(!!!) ! !, !!!

! Where �!,(!!!) (�, �) is the average return of the portfolios for a twelve-month period. M stands for the number of 12-month periods that are assessed. Again, (J, K) stands for respectively the formation and holding periods. As this research covers the period from March 2009 to March 2016, a total of six consecutive twelve-month periods are investigated.

Finally, the collective average performance of the winner and the loser portfolio period taken together is calculated by making use of the following equation:

�! �, � = �! �, � − (�! (�, �)) (5) !, !!! ,!" !, !!! ,! !, !!! ,!

Where �! �, � equals the average return of the momentum trading strategy. !, !!! ,!" �! �, � stands for the average return of the winner portfolio and �! (�, �) !, !!! ,! !, !!! ,! stands for the average return of the loser portfolio. (J, K) stands for respectively the formation and holding periods.

15 In order to be sure that the outcomes of the winner and loser portfolios are robust, they are checked on significance by using a t-test as can be seen in equation 6. This t-test can also be used to research whether the momentum trading strategy generates significant excess returns compared to respectively the Amsterdam Stock Exchange and the Frankfurt Stock Exchange indices.

! ! !! t = ! (6) !

Where �̅ is the sample mean, � is the standard deviation, �0 is the tested value, and � is the number of observations.

III.4..Research.method.used.calculating.the.transaction.costs In the literature one finds several methods to measure the transaction costs. As mentioned before, Jegadeesh and Titman (1993, 2001) put transaction costs at 0.5%, based on average transaction costs for the United States. They were criticized by many academics (e.g. Agyei- Ampomah, 2007; Korajczyk and Sadka, 2004; Lesmond et al., 2004; Pavlova et al., 2011). Lesmond et al. (2004) indicate that to measure transaction costs more realistically, one needs to determine the total of the bid-ask spread, applicable commissions, price-impact costs, short-sale costs, and other immediacy costs.

With respect to transaction costs, this research replicates the method used by Lesmond et al. (2004). They use the so-called quoted-spread method. This involves examining the bid and ask price spreads of the related stocks. The authors estimate the bid-ask spread during a twelve-month period, starting eighteen months before the transaction has been made and ending six months before that transaction. Lesmond et al. (2004) do so, in order to prevent contamination between the returns realized during the formation and the holding periods and the returns used by the transaction cost estimates. As in Lesmond et al. (2004), for all stocks closing quotes are obtained for a randomly selected day during the third week of each calendar month for a total of 12 estimates per year. This approach mitigates any ‘turn-of-the- month’ effects in quote behavior; it results in a rather evenly spread out quote estimate during the whole period (Lesmond et al., 2004). In this research I do not take into account the short- sale costs. Moreover, I do not take into account any price-impact costs, because it is assumed

16 that the transaction volume of the relevant stocks is high enough to exclude this. The monthly quoted-spread measure is expressed as follows:

!! !"# !,!!! !!"# !,!!! ! �� (!,!) = ! !!!" ! ∗ (7) ∗(!"# !,!!! !!"# !,!!! ) !" !

Where �� is the ask price and �� is the bid price and (�, �) stands for stock � at time �.

In their research Lesmond et al. (2004) use a 100% turnover rate when calculating the transaction costs. However, according to Barber and Odean (2000), portfolios with high turnover rates usually have higher trading activity and therefore higher transaction costs. They deviate from Lesmond et al. (2004) by using the actual turnover rate, instead of the full (100%) turnover rate, when calculating transaction costs. In this paper, in line with Barber and Odean (2000), the actual turnover rate will be used. After all, to pursue the momentum trading strategy, frequent rebalancing of the portfolios is necessary at the end of the holding period (K). This means that at the end of the holding period (K), for the winner portfolio, stocks that are no longer part of the top 20 performing stocks must be dropped and new stocks that now meet the requirement of belonging to the top 20 performing stocks must be added. The same must be done for the loser portfolio. For the loser portfolio, stocks that are no longer part of the bottom 20 performing stocks must be dropped and new stocks that now meet the requirement of belonging to the bottom 20 performing stocks must be added. In this research the frequency of trading is analyzed by the turnover ratio. Namely, the number of new stocks in the portfolio (�!"#) divided by the total number of stocks in the portfolio (�!"!#$). In this research (�!"!#$) is 20.

! �� = !"# (8) !!"!#$

The turnover ratio is used in order to calculate the transaction costs as can be seen in equation 9.

17 Concerning the commission fees, this research distinguishes between transactions in the Dutch stock market and those in the German stock market. I use a commission rate of 0.18% for the Dutch portfolios, as this is the commission rate applied by ABN AMRO Bank4, the largest retail bank in the Netherlands. For the German portfolios I use a commission rate of 0.30%. This commission rate is given by Deutsche Bank Privat- und Geschäftskunden AG5, the largest retail bank in Germany.

Concluding, to calculate the total transaction costs, the turnover ratio is multiplied by the sum of the quoted spread and two times the commission rate:

�� = �� ∗ (�� + �� ∗ 2 ) (9)

III.5. Research method used to calculate correlations Finally, correlations between the net (gross) 12-month returns realized with respect to the Dutch and the German stock market are calculated by making use of the following equation.

!"# �(�, �) = (!") (10) !!∗ !!

Where �(�, �) is the correlation between the net (gross) 12-month returns realized with respect to the Dutch and the German stock market and ��(!") is the covariance between those net (gross) 12-month returns. �! and �! represent the standard deviations of the net (gross) 12-month returns for respectively the Dutch stock market and the German stock market.

4 https://www.abnamro.nl/nl/images/Generiek/PDFs/030_Beleggen/Tarieven/Tarievenkaart_zelf_beleggen.pdf (accessed on April 2nd 2017) 5 https://www.deutsche-bank.de/pfb/data/docs/List-of-Prices-and-Services-Deutsche-Bank-Privat-und- Geschaeftskunden-01042016.pdf (accessed on April 2nd 2017)

18 I also use equation 10, mutatis mutandis, to calculate the correlation between the development of the AEX and the MDAX indices. According to Bertero and Mayer (1990), Eun and Resnick (1984) and Roll (1992), the stock market indices of the Netherlands and Germany are highly correlated. To see if this is also the case for the AEX and MDAX indices during my research period, I extract the total monthly returns with respect to these indices from March 2009 to March 2016 from DataStream Advance 5.1.

19 IV. Empirical results

The results of my research are laid down in tables A - S of the Appendix. Section IV.1 presents a summary and a discussion of the results of this research with respect to the Dutch stock market and is relevant for the response in section V (Conclusions) to the first research question. Section IV.2 presents a summary and a discussion of the results of this research with respect to the German stock market and is relevant for the response in section V (Conclusions).to.the.second.research.question.

IV.1. Summary and discussion of the results of the research with respect to the Dutch stock market Table I contains a summary6 of the results of the research laid down in tables A - I of the Appendix. The results in table I are relevant for the answer to the first research question, which reads as follows: “Can a momentum trading strategy yield significant positive net returns in the Netherlands that exceed the AEX index?”

6 The summary in table I does not include the various t-values, transaction costs and the (net and gross) returns of the separate winner and loser portfolios for the different strategies.

20 Table I Net (average) portfolio returns for various momentum strategies for the Netherlands and their profitability compared to the development of the AEX index

Shown are the net (average) portfolio returns on a 12-month basis for the various momentum strategies, with J = 6, 9 or 12 and K = 6, 9 or 12. P = 1 to P = 6 are six consecutive 12-month periods in my research period, which runs from March 2009 to March 2016. ∑ P = 1-6 is the period covered by all six consecutive 12-month periods taken together. Every month stocks are ranked on their performance over the respective formation period J. The 20 stocks with the highest returns in the formation period form the winner portfolio and the 20 stocks with the lowest returns in the formation period form the loser portfolio. The portfolios are held for K-months (K = 6, 9 or 12), after which their returns are calculated. All stocks are equally weighted in the portfolios. In periods P =1 to P = 6, RWL-N stands for the net 12-month return per strategy, for the winner and loser portfolios taken together. During the period covered by all six consecutive 12-month periods (∑ P = 1-6), RWL-N stands for the net average 12-month return per strategy for the winner and loser portfolios taken together. The t-test shows whether the portfolio returns are significantly different from zero, where *, ** and *** denote, respectively, the 1%, 5% and 10% significance level of the t-test with respect to the portfolio returns. In periods P = 1 to P = 6, AEX stands for the 12-month development of the AEX index and during the period covered by all six consecutive 12-month periods (∑ P = 1-6), AEX stands for the average development of the AEX index on a 12-month basis. Finally, RWL-N / AEX indicates whether, for the six consecutive 12- month periods in my research period, March 2009 to March 2016, the net 12-month profitability of the portfolio returns (winners and losers taken together) is higher than the 12-month development of the AEX index and whether, for period ∑ P = 1-6, the net average 12-month profitability of the portfolios (winners and losers taken together) is higher than the average development of the AEX index on a 12-month basis during that period.

12-month period P J, K P = 1 P = 2 P = 3 P = 4 P = 5 P = 6 ∑ P = 1-6 RWL-N (6, 6) 11.10% -5.17% 9.67% -19.46% -2.58% -1.79% -1.37% (6, 9) 17.40% 7.17% 12.39% -19.62% 5.35% -4.19% 3.08% (6, 12) 26.67% 7.74% 12.81% -12.74% 5.87% -3.67% 6.11%

(9, 6) 9.49% 2.63% 13.91% -19.73% -4.63% 2.34% 0.67% (9, 9) 22.19 13.78% 15.81% -21.93% 1.77% -2.50% 4.85% (9, 12) 30.31% 8.53% 16.34% -17.34% 4.09% -2.08% 6.64%

(12, 6) 11.09% 1.68% 10.96% -20.83% -2.21% 1.76% 0.41% (12, 9) 24.64% 10.69% 13.61% -22.54% 5.44% -0.98% 5.14% (12, 12) 26.87% 5.62% 13.12% -16.12% 8.92% -2.05% 6.06%

Return AEX AEX 12.57% -8.40% 15.28% 12.67% 7.09% -10.57% 4.77%

RWL-N / AEX (6, 6) -1.47% 3.23% -5.61% -32.13% -9.67% 8.78% -6.14%* (6, 9) 4.83% 15.57% -2.89% -32.29% -1.74% 6.38% -1.69% (6, 12) 14.10% 16.14% -2.47% -25.41% -1.22% 6.90% 1.34%

(9, 6) -3.08% 11.03% -1.37% -32.40% -11.72% 12.91% -4.10%*** (9, 9) 9.62% 22.18% 0.53% -34.60% -5.32% 8.07% 0.08% (9, 12) 17.74% 16.93% 1.06% -30.01% -3.00% 8.49% 1.87%***

(12, 6) -1.48% 10.08% -4.32% -33.50% -9.30% 12.33% -4.36%*** (12, 9) 12.07% 19.09% -1.67% -35.21% -1.65% 9.59% 0.37% (12, 12) 14.30% 14.02% -2.16% -28.79% 1.83% 8.52% 1.29%

21 Is the Dutch net average return of the momentum trading strategy (RWL-N) significantly higher than the development of the AEX index on a 12-month basis? Table I shows that, for five out of the nine momentum trading strategies, the Dutch net average returns (RWL-N), calculated over the whole period ∑ P = 1-6, are higher than the average 12-month development of the AEX-index for the same period. This means that in my research five out of the nine momentum trading strategies beat the market. The four trading strategies which do not beat the market are the three trading strategies with the shortest holding period (J, K = 6,6; J, K = 9,6 and J, K = 12,6) and the trading strategy with the formation and holding period J, K = 6,9. Application of the t-test shows that of the nine strategies only the J, K = 6,6 strategy is significant at the 1% significance level. Furthermore, the J, K = 9,6; J, K = 9,12 and J, K = 12,6 strategies are significant at the 10% significance level. However, of the five strategies that beat the market, only the J, K = 9,12 strategy is significant (at the 10% significance level).

Profitability of the RWL-G and the RWL-N when calculated over the whole period ∑ P = 1-6 Tables A - I of the Appendix show that all nine momentum trading strategies, applied with respect to the Dutch stock market, realize a gross average return (RWL-G) that is positive. Table I shows that only one out of nine momentum trading strategies applied with respect to the Dutch stock market realize a net average return (RWL-N) calculated over the whole period ∑ P = 1-6 that is negative.

RWL-N and duration of the holding period Table I also shows that for the three Dutch trading strategies with the shortest holding period (J, K = 6,6; J, K = 9,6 and J, K = 12,6), the net average returns (RWL-N) calculated over the whole period ∑ P = 1-6, are quite low. For J, K = 6,6 it is -1.37%, for J, K= 9,6 it is 0.67% and for J, K = 12,6 it is 0.41%. The six Dutch trading strategies with longer holding periods show relatively higher net returns. For J, K = 6,9 it is 3.08%, for J, K = 9,9 it is 4.85% and for J, K = 12,9 it is 5.14%. For J, K = 6,12 it is 6.11%, for J, K = 9,12 it is 6.64% and for J, K = 12,12 it is 6.06%. These empirical results seem to imply that in the Netherlands the longer the holding period (K), the higher the net average return realized over the whole period ∑ P = 1-6. A possible (and probably only partial) explanation for this phenomenon may be that the transaction costs are relatively higher for momentum strategies with a short holding period. Indeed, table S in the Appendix shows that for all Dutch momentum trading strategies, the

22 transaction costs (WL-TC) decline as the holding period (K) increases, possibly due to the lower turnover ratios (frequency of trading) involved with longer holding periods.

Composition of the RWL-N The results of this research as included in the Appendix, tables A - I, also show that for every Dutch momentum strategy, the major part of the net average return realized during the whole period ∑ P = 1-6, has been contributed by the winner portfolios (RW-N). These results differ from the results shown in the research done by Agyei-Ampomah (2007), Doukas and McKnight (2005) and Jegadeesh and Titman (1993, 2001). These authors find that the major part of the momentum strategy returns are realized with the short position in the loser portfolios, which is clearly not the case with respect to the Dutch stock market in my research period.

RWL-N and duration of the application period of the momentum trading strategy Finally, table I shows that for eight out of nine Dutch momentum trading strategies the net average return (RWL-N) is profitable when calculated over the whole period (∑ P = 1-6). However, the net 12-month returns of the separate consecutive 12-month periods of these eight trading strategies show quite some fluctuation. For instance, while the momentum trading strategy J, K = 9,12 shows the highest net average return (RWL-N = 6.64%) when calculated over the whole period ∑ P = 1-6, application of this strategy shows a net 12-month return of 30.31% in P = 1, a net 12-month return of -17.34% in P = 4 and a net 12-month return of -2.08% in P = 6. These results demonstrate that application of these eight momentum trading strategies over a longer period of time will eventually show a positive net average return, because, over time, negative net 12-month returns will be compensated by positive net 12-month returns.

IV.2. Summary and discussion of the results of the research with respect to the German stock market Table II contains a summary7 of the results of the research laid down in tables J - R of the Appendix. The results in table II are relevant for the answer to the second research question, which reads as follows: “Can a momentum trading strategy yield significant positive net returns in Germany that exceed the MDAX index?”

7 The summary in table II does not include the various t-values, transaction costs and the (net and gross) returns of the separate winner and loser portfolios for the different strategies.

23 Table II Net (average) portfolio returns for various momentum strategies for Germany and their profitability compared to the development of the MDAX index

Shown are the net (average) portfolio returns on a 12-month basis for the various momentum strategies, with J = 6, 9 or 12 and K = 6, 9 or 12. P = 1 to P = 6 are six consecutive 12-month periods in my research period, which runs from March 2009 to March 2016. ∑ P = 1-6 is the period covered by all six consecutive 12-month periods taken together. Every month stocks are ranked on their performance over the respective formation period J. The 20 stocks with the highest returns in the formation period form the winner portfolio and the 20 stocks with the lowest returns in the formation period form the loser portfolio. The portfolios are held for K- months (K = 6, 9 or 12), after which their returns are calculated. All stocks are equally weighted in the portfolios. In periods P =1 to P = 6, RWL-N stands for the net 12-month return per strategy, for the winner and loser portfolios taken together. During the period covered by all six consecutive 12-month periods (∑ P = 1-6), RWL-N stands for the net average 12-month return per strategy for the winner and loser portfolios taken together. The t-test shows whether the portfolio returns are significantly different from zero, where *, ** and *** denote, respectively, the 1%, 5% and 10% significance level of the t-test with respect to the portfolio returns. In periods P = 1 to P = 6, MDAX stands for the 12-month development of the MDAX index and during the period covered by all six consecutive 12-month periods (∑ P = 1-6), MDAX stands for the average development of the MDAX index on a 12-month basis. Finally, RWL-N / MDAX indicates whether, for the six consecutive 12-month periods in my research period, March 2009 to March 2016, the net 12-month profitability of the portfolio returns (winners and losers taken together) is higher than the 12-month development of the MDAX index and whether, for period ∑ P = 1-6, the net average 12-month profitability of the portfolios (winners and losers taken together) is higher than the average development of the MDAX index on a 12-month basis during that period.

12-month period P J, K P = 1 P = 2 P = 3 P = 4 P = 5 P = 6 ∑ P = 1-6 RWL-N (6, 6) -11.52% -6.68% -5.02% -11.06% -25.64% -12.45% -12.06% (6, 9) -2.46% 1.69% 3.19% 7.93% -10.98% 0.02% -0.10% (6, 12) 8.33% 7.12% 8.99% 12.30% -9.94% -1.65% 4.19%

(9, 6) -11.58% -5.32% -8.49% 0.53% -9.95% -10.36% -7.53% (9, 9) 4.04% 5.46% 2.76% 11.32% -4.30% -13.76% 0.92% (9, 12) 4.85% 10.14% 14.28% 19.21% 14.69% -17.10% 7.68%

(12, 6) -6.57% 1.70% -5.63% 3.90% -17.91% -8.13% -5.44% (12, 9) 1.71% 6.32% 5.46% 12.41% 0.65% -12.07% 2.41% (12, 12) -1.57% 14.05% 16.36% 17.24% 12.81% -16.35% 7.09%

Return MDAX MDAX 13.41% -1.57% 13.09% 16.58% 3.96% -4.00% 6.91% RWL-N / MDAX (6, 6) -24.93% -5.11% -18.11% -27.64% -29.60% -8.45% -18.97%* (6, 9) -15.87% 3.26% -9.90% -8.65% -14.94% 4.02% -7.01%* (6, 12) -5.08% 8.69% -4.10% -4.28% -13.90% 2.35% -2.72%***

(9, 6) -24.99% -3.75% -21.58% -16.05% -13.91% -6.36% -14.44%* (9, 9) -9.37% 7.03% -10.33% -5.26% -8.26% -9.76% -5.99%** (9, 12) -8.56% 11.71% 1.19% 2.63% 10.73% -13.10% 0.77%

(12, 6) -19.98% 3.27% -18.72% -12.68% -21.87% -4.13% -12.35%* (12, 9) -11.70% 7.89% -7.63% -4.17% -3.31% -8.07% -4.50%*** (12, 12) -14.98% 15.62% 3.27% 0.66% 8.85% -12.35% 0.18%

24 Is the German net average return of the momentum trading strategy (RWL-N) significantly higher than the development of the MDAX on a 12-month basis? Table II shows that for only two out of the nine momentum trading strategies, the German net average returns (RWL-N), calculated over the whole period ∑ P = 1-6, are higher than the average 12-month development of the MDAX-index for the same period. This means that in my research with respect to the German stock market only two out of the nine momentum trading strategies (J, K = 9,12 and J, K = 12,12) beat the market. Out of the seven trading strategies which do not beat the market, three trading strategies are those with the shortest holding period (J, K = 6,6; J, K = 9,6 and J, K = 12,6). This outcome is the same as the outcome of my research with respect to the Dutch stock market. As is the case in the Netherlands, the fourth trading strategy, applied with respect to the German stock market, which does not beat the market, is the trading strategy with the formation and holding period J, K = 6,9. Finally, the trading strategies with the formation and holding periods J, K = 6,12 and J, K = 9,9 when applied with respect to the German stock market, also do not beat the market. While for Germany only two of the nine momentum trading strategies beat the market, for the Netherlands five out of the nine do so. This seems to imply that there is a bigger chance to beat the market with the application of a momentum trading strategy with respect to the Dutch stock market than there is when trading strategies are applied with respect to the German stock market. Application of the t-test shows that of the nine strategies four strategies are significant at the 1% significance level (J, K = 6,6; J, K = 6,9; J, K = 9,6 and J, K = 12,6). Furthermore, the J, K = 9,9 strategy is significant at the 5% significance level and the J, K = 6,12 and J, K = 12,9 strategies are significant at the 10% significance level. The two strategies that generate a positive return relative to the MDAX index (J, K = 9,12 and J, K = 12,12) are not significant.

Profitability of the RWL-G and the RWL-N when calculated over the whole period ∑ P = 1-6 Tables J - R of the Appendix show that, as is the case in the Netherlands, all nine momentum trading strategies, applied with respect to the German stock market, realize a gross average return (RWL-G) that is positive. While only one out of nine of the momentum trading strategies, applied with respect to the Dutch stock market, realizes a net average return (RWL- N) calculated over the whole period ∑ P = 1-6 that is negative, momentum trading strategies applied with respect to the German stock market show a different picture. Table II shows that for the German stock market four out of nine strategies realize a net average return (RWL-N) calculated over the whole period ∑ P = 1-6 that is negative.

25 RWL-N and duration of the holding period The results of table I show that for the momentum trading strategies with the shortest holding period (K = 6), when applied with respect to the Dutch stock market, the net average returns (RWL-N) calculated over the whole period ∑ P = 1-6, are quite low. Table II also shows that this is the case in Germany. Indeed, for the German stock market all three momentum trading strategies with the shortest holding period (J, K = 6,6; J, K = 9,6 and J, K = 12,6) show net average returns (RWL-N) calculated over the whole period ∑ P = 1-6, that are negative. For J, K = 6,6 it is -12.06%, for J, K = 9,6 it is -7.53% and for J, K = 12,6 it is -5.44%. Moreover, two of the three momentum trading strategies with a holding period of nine months (J, K = 6, 9 and J, K = 9,9) also show a net average return that is quite low, even though higher than the net average returns of the three German trading strategies mentioned above. For J, K = 6,9 it is -0.10% and for J, K = 9,9 it is 0.92%. The remaining four German trading strategies show higher net average returns. For J, K = 12,9 it is 2.41%. For J, K = 6,12 it is 4.19%, for J, K = 9,12 it is 7.68% and for J, K = 12,12 it is 7.09%. These empirical results seem to imply that the longer the holding period (K), the higher the net average return realized over the whole period ∑ P = 1-6. As said above with respect to the Netherlands, a possible (and probably only partial) explanation for this phenomenon may be that the transaction costs are relatively higher for momentum strategies with a short holding period. Indeed, table S in the Appendix shows that for all German momentum trading strategies, the transaction costs (WL-TC) decline as the holding period (K) increases, possibly due to the lower turnover ratios (frequency of trading) involved with longer holding periods. Comparison of the Dutch and the German transaction costs (see tables A - R of the Appendix and table S of the Appendix) further shows that, for all momentum trading strategies applied with respect to the German stock market, the German transaction costs are quite a bit higher than the corresponding Dutch transaction costs. This difference between the Dutch and German transaction costs could perhaps partially explain why in most cases the German net average 12-month returns are lower than the Dutch ones. In my research only in two cases, the momentum trading strategies J, K = 9,12 and J, K = 12,12, is the German net average return calculated over the whole period ∑ P = 1-6 higher than the Dutch equivalent possibly because the difference between the Dutch and German transaction costs seems to decrease as the length of the holding periods increases.

26 Composition of the RWL-N The results of this research as included in tables J - R of the Appendix also show that for every German momentum strategy the major part of the net average return, realized during the whole period ∑ P = 1-6, has been contributed by the winner portfolios (RW-N). This outcome is the same as the outcome of the trading strategies applied with respect to the Dutch stock market. These empirical results seem to imply that during my research period, the RWL-N is “winner” driven and not “loser” driven, as is the case in earlier research (Agyei-Ampomah, 2007; Doukas and McKnight, 2005; Jegadeesh and Titman, 1993, 2001).

RWL-N and duration of the application period of the momentum trading strategy Finally, table II shows that five out of nine momentum trading strategies show a net average return (RWL-N) that is positive when calculated over the whole period ∑ P = 1-6. However, as is the case in the Netherlands, the German net returns of the separate consecutive 12-month periods of these five trading strategies show quite some fluctuation. For instance, while the German momentum trading strategy J, K = 9,12 shows the highest net average 12-month return (RWL-N = 7.68%), when calculated over the whole period ∑ P = 1-6, application of this strategy shows a net 12-month return of 4.85% in P = 1, a net 12-month return of 19.21% in P = 4 and a net 12-month return of -17.10% in P = 6. As can be seen in tables I and II, the fluctuations of the Dutch and those of the German net 12-month returns realized during the six consecutive 12-month periods do not move in the same direction. This seems to imply that there is little chance of a strong positive correlation between the net 12-month returns realized with respect to the Dutch stock market and those realized with respect to the German stock market. Furthermore, as has been found with respect to the Dutch stock market, the results demonstrate that, due to a compensation of negative net 12-month returns by positive net 12- month returns, application of these five momentum trading strategies over a longer period of time will eventually show a positive net average return.

Correlation between the development during the research period of the net 12-month returns of the momentum trading strategies applied with respect to the Dutch and German stock market, respectively Tables I and II show quite different fluctuations in the development of the net 12-month returns of the Dutch and of the corresponding German momentum trading strategies. As said above, this outcome seems to imply that there is little chance of a strong positive correlation between the net 12-month returns realized with respect to the Dutch stock market and those

27 realized with respect to the German stock market. This seems remarkable, since previous literature indicates a high positive correlation between Dutch and German stock market returns and between indices of the two stock markets (Bertero and Mayer, 1990; Eun and Resnick, 1984; Roll, 1992). As the AEX index and the MDAX index are benchmarks for, respectively, the Dutch stock market and the German midcap stock market, and as the momentum returns are being realized with portfolios consisting of stocks trading on those stock markets, I initially, at the beginning of my research, expected the development of the net profitabilities of all nine Dutch and corresponding nine German momentum trading strategies during the research period to be similar to the development of the AEX and MDAX indices during that period. Hence, I initially expected that the net 12-month returns would show a similar correlation as those two indices. Therefore I decided to investigate how the net 12-month returns of the Dutch and German momentum trading strategies are correlated.

To this end I started out by investigating whether, in line with Bertero and Mayer (1990), Eun and Resnick (1984) and Roll (1992), the AEX and MDAX indices indeed show a strong positive correlation during the research period of this paper (2009-2016). Table III presents the percentage increase or decrease of these indices in six consecutive 12-month periods of my research.

Table III Development of the AEX and MDAX indices

Shown is the development of the AEX index and that of the MDAX index, both on a 12-month basis. P = 1 to P = 6 are six consecutive 12-month periods in my research, which runs from March 2009 to March 2016. AEX stands for the percentage increase or decrease of the AEX index on a 12-month basis. MDAX stands for the percentage increase or decrease of the MDAX index on a 12-month basis.

12-month period P Index P1 P2 P3 P4 P5 P6

AEX 12.57% -8.40% 15.28% 12.67% 7.09% -10.57%

MDAX 13.41% -1.57% 13.09% 16.58% 3.96% -4.00%

As expected, during my research period, the development of the AEX index and that of the MDAX index show a strong positive correlation, i.e. 0.93. This strong correlation can clearly be seen when the results of table III are presented graphically (see figure I).

Figure I Development of the AEX and MDAX indices

Shown is the development of the AEX index and that of the MDAX index, both on a 12-month basis. The horizontal line consists of six consecutive 12-month periods in my research, which runs from March 2009 to March 2016. The vertical line shows the percentage increase of the AEX index and that of the MDAX index.

20,0% AEX MDAX

15,0%

10,0%

5,0%

0,0% 1 2 3 4 5 6 -5,0%

-10,0%

-15,0%

Next, I calculated the correlation between the 12-month returns of the momentum trading strategies applied with respect to the Dutch and German stock market, respectively. Table IV presents the correlation8 between the net as well as between the gross 12-month returns of the

various Dutch and German momentum trading strategies.

8 Correlation is strong between the values 0.5 to 1 (-0.5 to -1), moderate between the values 0.3 to 0.5 (-0.3 to -0.5) and weak between the values 0 to 0.3 (0 to -0.3).

29 Table IV Correlation between the net as well as gross 12-month returns of the various Dutch and German momentum trading strategies, between the Dutch net 12-month returns and the development of the AEX index, and between the German net 12-month returns and the development of the MDAX index

Shown is the correlation between the development of the net 12-month returns of the various momentum strategies with respect to the Dutch and the German stock markets, as well as the correlation between development of the gross 12- month returns, between the development of the Dutch net 12-month returns and the development of the AEX index, and between the development of the German net 12-month returns and the development of the MDAX index. C-N stands for correlation between the development of the Dutch and German net 12-month returns (RWL-N) and C-G stands for the development of the Dutch and German gross 12-month returns (RWL-G). C-NL / AEX stands for correlation between the development of the Dutch net 12-month returns (Dutch RWL-N) and the development of the AEX index. C-GE / MDAX stands for correlation between the development of the German net 12-month returns (German RWL-N) and the development of the MDAX index. J, K stands for the different formation and holding periods of the various trading strategies.

Holding period Formation period K = 6 K = 9 K = 12 J = 6 C-N 0.15 -0.48 0.05 C-G -0.47 -0.72 0.24 C-NL / AEX 0.10 -0.27 0.04 C-GE / MDAX 0.20 -0.74 0.08 J = 9 C-N -0.75 -0.06 -0.07 C-G -0.76 -0.03 0.05 C-NL / AEX -0.30 -0.04 -0.08 C-GE / MDAX -0.18 -0.10 -0.14 J = 12 C-N -0.38 -0.24 -0.14 C-G -0.54 -0.84 -0.02 C-NL / AEX -0.26 -0.17 -0.17 C-GE / MDAX -0.52 -0.44 -0.24

Table IV indicates that of the nine momentum trading strategies analyzed, the development of the net 12-month returns of two momentum trading strategies (J, K = 6,6 and J, K = 6,12) applied with respect to the Dutch and German stock markets during six consecutive 12-month periods shows a weak positive correlation, that the development of the net 12-month returns of one momentum trading strategy (J, K = 9,6) shows a strong negative correlation, that the development of the net 12-month returns of another two (J, K = 6,9 and J, K = 12,6) shows a moderate negative correlation and that the development of the net 12-month returns of the remaining four momentum trading strategies (J, K = 9,9; J, K = 9,12; J, K = 12,9; J, K = 12,12) shows a weak negative correlation between the net returns.

These results are not what I had initially expected. As said above, at the beginning of my research, I expected that the development of the net profitabilities of Dutch and German momentum trading strategies would be similar to the development of the AEX and MDAX

30 indices during that period. Hence, I expected that the net profitabilities show a similarly strong positive correlation as those two indices.

In order to ascertain that the difference between the Dutch and German transaction costs is not the cause of this result, I also analyzed the correlation between the development of the gross 12-month returns, thus excluding any influence of the difference between transaction costs. As can be seen in table IV, also most of the gross 12-month returns are negatively correlated and therefore also do not show a strong positive correlation as shown by the AEX index and the MDAX index. Therefore, one can conclude that the difference between transaction costs is not the reason why the correlation between the net returns of the Dutch and German momentum trading strategies is not similar to the correlation between the Dutch and German indices. A possible explanation for the difference of these correlations could be that the sample of the AEX index does not coincide with the Dutch sample for this research, i.e. the stocks listed on the Amsterdam Stock Exchange, and that the sample of the MDAX index does not coincide with the German sample of this research, i.e. the stocks listed on the Frankfurt Stock Exchange. The AEX-index consists of the 25 biggest companies in terms of market capitalization that are traded on the Amsterdam Stock Exchange, while the MDAX consists of the 26th to 75th biggest companies in terms of market capitalization that are traded on the Frankfurt Stock Exchange. This research, however, includes 382 stocks for the Dutch sample and 322 stocks for the German sample. Comparison of the relevant samples has shown that the stocks included in the AEX index and those included in the MDAX index represent only 6.5% and 15.5%, respectively, of the Dutch and German samples. Therefore, the samples in this research are not mainly driven by the stocks that are included in the AEX index and the MDAX index. Since the bases of the two correlations differ, there is really no reason why the two correlations should correspond. This becomes more evident when analyzing which percentage of the Dutch winner and loser portfolios used in the six consecutive 12-month periods of this research consisted of stocks included in the AEX index and which percentage of the German winner and loser portfolios consisted of stocks included in the MDAX index9. The results presented in table V indicate that the stocks that are included in the AEX index and in the MDAX index, respectively, are not the main drivers of the winner and loser portfolios in the Dutch and German samples.

9 I took into account the yearly revision of the AEX and MDAX indices where stocks are added and dropped based on their performance in the previous year.

31 Table V Percentage of the Dutch winner and loser portfolios consisting of stocks included in the AEX index and percentage of the German winner and loser portfolios consisting of stocks included in the MDAX index

Shown is the percentage of the AEX index stocks in the Dutch winner and loser portfolios and the percentage of the MDAX index stocks in the German winner and loser portfolios. P = 1 to P = 6 are six consecutive 12-month periods in the research period, which runs from March 2009 to March 2016. ∑ P = 1-6 is the period covered by all six consecutive 12- month periods taken together.

12-month period P P1 P2 P3 P4 P5 P6 ∑ P = 1-6 % AEX-index-stocks in the winner and loser ± 9% ± 8% ± 11% ± 12% ± 12% ± 14% ± 11% portfolio

% MDAX-index- stocks in the winner ± 16% ± 19% ± 17% ± 17% ± 16% ± 19% ± 17% and loser portfolio

Table V shows that approximately 11% of the stocks in the Dutch winner and loser portfolios consisted of stocks that are included in the AEX index and approximately 17% of the stocks in the German winner and loser portfolios consisted of stocks included in the MDAX index. The higher percentage of MDAX-index-stocks in the winner and loser portfolios of the German sample was to be expected, since 15.5% of the German sample consisted of MDAX- index-stocks versus only 6.5% of the Dutch sample consisted of AEX-index-stocks.

In view of the above, my initial reasoning as to why the development of the net 12-month returns realized with the various momentum trading strategies in the Netherlands and Germany would be similar to the development of the AEX and MDAX index, respectively, is incorrect. This is supported by the results presented in table IV, which show that correlation between the development of the Dutch net 12-month returns and the development of the AEX index is weakly positive for two out of the nine momentum trading strategies and negative for the remaining seven strategies. Likewise, correlation between the development of the German net 12-month returns and the development of the MDAX index is weakly positive for two out of the nine momentum trading strategies and negative for the remaining seven strategies.

More importantly, however, (a) since momentum trading strategies are based on the premise that past stock performance (during the formation period) will continue into the future (during the holding period), and (b) since profitability (positive or negative) of the winner portfolios depends on the actual development during the holding period of the micro price trend of the individual winner

32 stocks included, and profitability (positive or negative) of the loser portfolios depends on the actual development during the holding period of the micro price trend of the individual loser stocks included, and (c) since in my research, which replicates the method used by Jegadeesh and Titman (1993), momentum returns are defined as the sum formed by the returns realized with the winner portfolios and the returns realized with the loser portfolios, the development of momentum returns over time is unpredictable and need not - other than coincidentally - move in the same direction as the AEX index and the MDAX index, respectively. Therefore, my initial expectation that Dutch and German momentum returns might show a similar correlation as that between the AEX and MDAX indices is unfounded. Since this part of my research has turned out not to be relevant, its outcomes will not be further discussed in section V (Conclusions).

33 V. Conclusions

This paper investigates the returns of the various momentum trading strategies (on a net basis) with respect to the Dutch stock market and the returns of the same momentum trading strategies with respect to the German stock market. These returns are investigated for the period from March 2009 to March 2016. To this end I analyzed the momentum returns on a gross basis (i.e. before subtracting the transaction costs), the transaction costs and the momentum returns on a net basis (i.e. after subtracting the transaction costs) of the various momentum trading strategies, realized during the research period mentioned above. The results of this investigation are used to answer the following research questions.

First research question: Can a momentum trading strategy yield significant positive net returns in the Netherlands that exceed the AEX index?

This paper shows that, when calculated over the research period, all nine momentum trading strategies applied with respect to the Dutch stock market, yield a positive gross return, i.e. before subtraction of transaction costs. Further investigation shows that eight out of the nine momentum trading strategies applied with respect to the Dutch stock market, yield a positive net return, i.e. after subtraction of transaction costs. Finally, the research with respect to the Dutch stock market shows that only five out of the nine momentum trading strategies yield a positive net return that is higher than the Dutch stock market AEX index. This means that in my research regarding the Dutch stock market only five out of the nine momentum trading strategies beat the market. However, when investigating whether the result of this part of my research is robust, it turns out that only one out of the five momentum trading strategies that beat the market, yields a significant (positive) return. Contrary to previous research (Agyei- Ampomah, 2007; Doukas and McKnight, 2005; Jegadeesh and Titman, 1993, 2001), my research regarding the Dutch stock market shows that the major part of the net momentum returns, when calculated over the research period, can be attributed to the winner portfolio instead of the loser portfolio. Finally, this paper shows that the longer the holding period, the higher the net momentum return realized. A possible (and probably only partial) explanation for this phenomenon may be that for the Netherlands the transaction costs decline as the

34 holding period increases, possibly due to the lower turnover ratios (frequency of trading) involved with longer holding periods.

Second research question: Can a momentum trading strategy yield significant positive net returns in Germany that exceed the MDAX index?

This paper shows that, when calculated over the research period, all nine momentum trading strategies applied with respect to the German stock market, yield a positive gross return, i.e. before subtraction of transaction costs. Further investigation shows that five out of the nine momentum trading strategies applied with respect to the German stock market, yield a positive net return, i.e. after subtraction of transaction costs. Finally, the research with respect to the German stock market shows that only two out of the nine momentum trading strategies yield a positive net return that is higher than the German midcap stock market MDAX index. This means that in my research regarding the German stock market only two out of the nine momentum trading strategies beat the market. However, when investigating whether the result of this part of my research is robust, neither of the two momentum trading strategies that beat the market, yields a significant (positive) return. Like the research regarding the Dutch stock market, the research regarding the German stock market shows that the major part of the net momentum returns, when calculated over the research period, can be attributed to the winner portfolio and not to the loser portfolio.

Furthermore, as is the case for the Netherlands, the research shows that in the case of Germany, the longer the holding period, the higher the net momentum return realized. A possible (and probably only partial) explanation of this phenomenon may be that also in Germany the transaction costs decline as the holding period increases. Finally, comparison of the Dutch and the German transaction costs shows that, for all momentum trading strategies applied, the transaction costs in Germany are quite a bit higher than those in the Netherlands. This difference could perhaps partially explain why in most cases the net momentum returns realized in Germany are lower than the ones realized in the Netherlands, even though for all nine momentum trading strategies applied, the German gross momentum returns realized are higher than the equivalent Dutch gross momentum returns. In my research only two German momentum trading strategies realize a net return that is higher than that of their Dutch

35 equivalents, possibly because the difference between the Dutch and German transaction costs seems to decrease as the length of the holding periods increases.

Further.research First, this research does not take into account short-selling costs and it would therefore be interesting for future research to include these costs. Second, this research does not take into account the “January effect” that has a significant negative impact on momentum returns according to Haug and Hirschey (2006). It would be interesting to examine the influence of the January effect on momentum returns. Third, the results indicate that the longer the holding period (K), the higher the net returns. Therefore, it would be interesting to see if longer holding periods than K = 12 (months) would lead to even higher net returns. In addition, the use of longer holding periods could perhaps reveal a higher number of significant positive net returns that beat the market than were found in this research. Fourth, this research took into account winner and loser portfolios with a size of 20 stocks each. According to Siganos (2007) a portfolio size of 40 different stocks maximizes momentum returns. Therefore, future studies could use this return-maximizing portfolio size. Finally, it could be interesting to look at what kind of stocks were mainly present in both the winner and loser portfolios (liquid versus illiquid, high share price versus low share price). This is especially interesting because stocks with certain features come along with different transaction costs (Lesmond et al., 2004).

36 VI. Reference list

Agyei-Ampomah, S., 2007. The post-cost profitability of momentum trading strategies: Further evidence from the UK. European Financial Management 134, 776-802.

Asness, C., Moskowitz, T., Pedersen, L., 2013. Value and momentum everywhere. Journal of Finance 68, 929-985.

Barber, B., Odean, T., 2000. Trading is hazardous to your wealth: The common stock investment performance of individual investors. Journal of Finance 55, 773-805.

Barberis, N., Shleifer, A., 2003. Style investing. Journal of Financial Economics 68, 161-199.

Barberis, N., Shleifer, A., Vishny, R., 1998. A model of investor sentiment. Journal of Financial Economics 49, 307-343.

Bertero, E., Mayer, C., 1990. Structure and performance: Global interdependence of stock markets around the crash of October 1987. European Economic Review 34, 1155-1180.

Carpenter, J., Lynch, W., 1999. Survivorship bias and attrition effects in measures of performance persistence. Journal of Financial Economics 54, 337-374.

Chan, L., Jegadeesh, N., Lakonishok, J., 1996. Momentum strategies. Journal of Finance 51, 1681-1713.

Conrad, J., Kaul, G., 1998. An anatomy of trading strategies. Review of Financial Studies 11, 489-519.

Daniel, K., Hirshleifer, D., Subrahmanyam, A., 1998. Investor psychology and security market under- and overreactions. Journal of Finance 53, 1839-1885.

De Bondt, W., Thaler, R., 1985. Does the stock market overreact? Journal of Finance 40, 793- 805.

37 De Bondt, W., Thaler, R., 1987. Further evidence on investor overreaction and stock market seasonality. Journal of Finance 42, 557-581.

Doukas, J., McKnight, P., 2005. European momentum strategies, information diffusion, and investor conservatism. European Financial Management 113, 313-338.

Eun, C., Resnick, B., 1984. Estimating the correlation structure of international share prices. Journal of Finance 39, 1311-1324.

Fama, E., 1965. The behavior of stock-market prices. Journal of Business 38, 34-105.

Fama, E., 1970. Efficient capital markets: A review of theory and empirical work. Journal of Finance 25, 383-417.

Fama, E., 1976. Efficient capital markets: Reply. Journal of Finance 3, 143-45.

Fama, E., French, K., 1995. Size and book-to-market factors in earnings and returns. Journal of Finance 50, 131-155.

Fama, E., French, K., 1996. Multifactor explanations of asset pricing anomalies. Journal of Finance 511, 55-84.

Frankfurter, G., McGoun, E., 2001. Anomalies in finance: What are they and what are they good for? International Review of Financial Analysis 10, 407-429.

Griffin, J., Ji, X., Martin, J., 2003. Momentum investing and business cycle risk: Evidence from pole to pole. Journal of Finance 58, 2515-2547.

Grinblatt, M., Han, B., 2005. Prospect theory, mental accounting and momentum. Journal of Financial Economics 78, 311-339.

Grundy, B., Martin, J., 2001. Understanding the nature of the risks and the source of the rewards to momentum investing. Review of Financial Studies 14, 29-78.

38 Haug, M., Hirschey, M., 2006. The January effect. Financial Analysts Journal 62, 78-88.

Hong, H., Stein, J., 1999. A unified theory of underreaction, momentum trading, and overreaction in asset markets. Journal of Finance 54, 2143-2184.

Hong, H., Kim, T., Stein, J., 2000. Bad news travels slowly: Size, analyst coverage, and the profitability of momentum strategies. Journal of Finance 55, 265-295.

Jegadeesh, N., 1990. Evidence of predictable behavior of security returns. Journal of Finance 45, 881-898.

Jegadeesh, N., Titman, S., 1993. Returns to buying winners and selling losers: Implications for stock market efficiency. Journal of Finance 48, 65-91.

Jegadeesh, N., Titman, S., 2001. Profitability of momentum strategies: An evaluation of alternative explanations. Journal of Finance 56, 699-720.

Jensen, M., 1978. Some anomalous evidence regarding market efficiency. Journal of Financial Economics 6, 95-102.

Korajczyk, R., Sadka, R., 2004. Are momentum profits robust to trading costs? Journal of Finance 593, 1039-1082.

Kothari, S., 2001. Capital markets research in accounting. Journal of Accounting and Economics 31,105-231.

Lehmann, B., 1990. Fads, martingales and market efficiency. Quarterly Journal of Economics 105, 1-28.

Lesmond, D., Schill, M., Zhou, C., 2004. The illusory nature of momentum profits. Journal of Financial Economics 712, 349-380.

Liu, W., Strong, N., Xu, X., 1999. The profitability of momentum investing. Journal of Business Finance & Accounting 26, 1043-1091.

39 MacKinlay, A., 1995. Multifactor models do not explain deviations from the CAPM. Journal of Financial Economics 38, 3-28.

Moskowitz, T., Grinblatt, M., 1999. Do industries explain momentum? Journal of Finance 54, 1249-1290.

Moskowitz, T., Ooi, Y., Pedersen, L., 2012. Time series momentum. Journal of Financial Economics 104, 228-250.

Pavlova, I., Parhizhari, A., 2011. In search of momentum profits: Are they illusory? Applied Financial Economics 21, 1617-1639.

Roll, R., 1992. Industrial structure and the comparative behavior of international stock market indices. Journal of Finance 47, 3-41.

Rouwenhorst, G., 1998. International momentum strategies. Journal of Finance 53, 267-284.

Schwert, G., 2003. Anomalies and market efficiency. Handbook of the Economics and Finance 1, 939-974.

Siganos, A., 2007. Momentum returns and size of winner and loser portfolios. Journal of Applied Financial Economics 17, 701-708.

Thaler, R., 1987. Seasonal movements in security prices II: Weekend, holiday, turn of the month, and intraday effects. Journal of Economic Perspectives 1, 169-177.

40 VII. Appendix Table A The Netherlands, formation period J = 6 and holding period K = 6