Short-term momentum in Germany

Short-Term Momentum in Germany

Bachelor Thesis in Finance and Organisation submitted by Christoph Rusch 10828958 June 2018

This research has been carried out by Christoph Rusch at the Faculty of Economics and Business at the University of Amsterdam

under the supervision of Pascal Golec

Abstract

We study short-term momentum persistence in Germany and test whether abnormal returns, if any, in momentum trading strategies are due to risk-, size- or book-to-market-factors. We find that strategies that select stocks based on their past 12-month performance and subsequently hold them for three 12-months yield the highest average monthly returns with 1.28 percent between 1980 and 2000, and 2.87 percent between 2000 and 2018. Returns are slightly higher for small-sized firms but still significant across all subsamples. The profits are not explained by market risk or value factors. The results are consistent with prior empirical research. Particularly interesting in this regard is how similar momentum strategy performance is in Germany as compared to the United States. Behavioral biases might play an important role when studying the sources of short-term momentum.

Contents

I. Introduction ... 1

II. Literature Review ... 2

III. Data and Methodology ... 6

A. Portfolio Construction... 6

B. Statistical Significance ... 8

C. Methodology for Regression Analysis ... 8

IV. Returns of Relative Strength Portfolios ... 9

V. Sources of Relative Strength Profits ...13

A. Regression results ... 13

B. Profitability of Relative Strength Strategies Within Size-Based Subsamples ... 14

C. Discussion ... 15

VI. Conclusion ...16

References ...18

1

I. Introduction

The efficient market hypothesis (EMH) claims that stock prices fully reflect all available information and that returns are independent of any past return (Fama & French, 1969). Profits made based on the information should not exceed the cost of acting on such information (Lee, 1977) and investors should therefore not be able to generate any abnormal returns or arbitrage profits. A wide-held view by economists and psychologists, however, is that investors tend to overreact to information, suggesting that selling past winners and buying past losers yield superior returns, which contradicts the EMH. The profitability of these contrarian strategies was proven to be successful by De Bondt and Thaler (1985), showing that poorly performing stocks over a 3- to 5-year horizon achieve higher returns than well-performing stocks over the same period. Critics argue that systematic risk and the size effect explain these results (Chan, 1988; Ball & Kothari, 1989; Zarowin, 1990).

Jegadeesh (1990) and Lehmann (1990), on the other hand, show that well-performing stocks from the previous month generate significant abnormal returns in the subsequent months. Jegadeesh and Titman (1993) point out that these strategies are transaction intensive and based on short-term price movements, claiming that their success may be due to short-term price pressure. By emphasizing the relation between bid-ask spreads and short-term return reversals, Jegadeesh and Titman (1991) support the aforementioned claim. Moreover, Lo and MacKinlay (1990) explain that those abnormal returns were attributable to delayed stock price reactions to common factors rather than to investors’ overreaction.

Contrarian strategies have received a lot of attention in academic literature. Still, early literature on market efficiency investigated preliminary trading strategies based on relative strength portfolios that represent the opposite to contrarian strategies – they buy past winners and sell past losers. These short-term momentum strategies are persistent across markets: Levy (1967), Jegadeesh and Titman (1993), Moskowitz and Grinblatt (1999), as well as Rouwenhorst (1999) show that the momentum effect is significant in the U.S. Various research has been conducted across the globe, including Europe. The German stock market in particular has been investigated by Schiereck, De Bondt and Weber (1999). These authors provide evidence for short-term momentum in Germany and highlight the similarity to results from the U.S.

2

Building up on previous literature, this paper attempts to answer the following research question: Is the short-term momentum effect still persistent in the German stock market? The German economy has grown remarkably during the last two decades, and both domestic investments as well as those from abroad have increased. Since international investors got attracted to the growing and well-performing economy, markets might have become more efficient than they were before, potentially resulting in the disappearance of some market anomalies, such as the momentum effect. The research on the German stock market is motivated by and extends previous analysis in various dimensions. Firstly, Germany represents a large European stock market with different trading practices and institutional environments than those in New York. For example, there are no specialists and no continuous trading for many stocks as well as no explicit bid-ask spreads (Booth, Iversen, Sarkar, Schmidt, & Young, 2010). Additionally, it is always of interest to cross-check in a second market the empirical results first established somewhere else. Another rationale for this study is that German financial markets are of interest in their own right. Many German companies, such as Daimler AG or Siemens, are export-oriented and enjoy a world-wide reputation. Many of these firms represent Europe’s industrial engine. Lastly, a larger sample of stocks and a more recent time period than August, Schiereck and Weber (1999) use is studied. Also noteworthy in this regard is that other stock market anomalies, such as the small-firm effect (first documented by Banz (1981)), have disappeared over time (see Cochrane (2001) and Dimson & Marsh (2000)), and that a more recent study on market anomalies is desirable.

The paper is organized as follows. First, previous literature will be discussed and a background on short-term momentum will be given. Then, the data for this quantitative research will be presented, as well as its methodology. In section IV, momentum and regression results will be presented and analyzed. The subsequent section seeks to find explanations for short-term momentum by analyzing size, value and risk factors. The last section concludes.

II. Literature Review

Previous literature on asset pricing has focused preliminary on stock market anomalies and proofs of the efficient market hypothesis. Fama and French (1969) present the EMH in three forms: the strong, the semi-strong and the weak form while each implies that information of different levels is impounded into stock prices. The paid amount for a

3

stock or another security and ultimately its return, when discounted based on the appropriate amount of risk, should, according to the EMH, give a net present value of zero.

The strongest EMH form claims that all public and private information is impounded in the price of a stock. That means that even if inside information was available to an investor, the market could still not be beaten. The second form is the semi-strong form in which all information is impounded in the security price. Information in this case means historic information on annual reports, anything in the news that has been published, or anything that was announced publicly by companies. The last form explains that historic prices have no information on where the future goes. According to this assumption, it is next to impossible to make any consistent gains in mispricing and guessing what the markets are going to be, using historic price patterns. Eventually, there might be some gains to be made by following certain trading strategies based on past prices. But once transaction costs are applied, profits will disappear quickly. In conclusion, the EMH claims that securities are fairly priced based on most of the information that is in the marketplace and the behavior of common stock, and other speculative prices could be well approximated by a random walk (Fama & French, 1969).

Having a closer look at the random walk assumption, it is apparent that the only price changes that would occur are those that result from new information. Since there is no reason to expect that information to be non-random in appearance, the period-to-period price changes of a stock should be random movements, statistically independent of one another (Cootner, 1964). Despite the EMH’s popularity, however, theories that contradict the random walk assumption have been published early on.

The vast majority of previous literature on stock market anomalies has focused on international contrarian and momentum strategies. Levy (1967) was the first one attempting to prove short-term momentum which relies on historic price patterns. He studied relative strength strategies, has found positive returns with momentum strategies and attributes this to investors’ underreaction to information. Following De Bondt and Thaler (1985) who discuss the stock market’s overreaction to new information, Jegadeesh and Titman (1993) provide evidence for momentum persistence on the U.S. stock market. They rank stocks based on past performance during the formation period. Jegadeesh and Titman (1993) find that winner portfolios of the past six months outperform the market by an average cumulative return of 9.50 percent per annum between 1965 and 1989. Overall, momentum profits are highest and most significant over the medium-term, a ranking period of six

4

months and a holding period of six months. As opposed to their EMH, Fama and French (1996) also found support for short-term winners’ profitability.

Rouwenhorst (1998) has performed research on momentum strategies in international stock markets, following Jegadeesh and Titman’s (1993) methodology. He uses a sample of 2190 stocks from 12 European countries (including Germany) between 1980 and 1995 and includes two sets of strategies: one that is formed at the end of the formation period and a second that skips a month between the formation and holding period. The main findings are that an internationally diversified relative strength portfolio that invests in past medium-term winners and shorts past medium-term losers gives a positive return of approximately one percent per month. The author further finds that the significant momentum results are not due to country-specific momentum as return continuation is analyzed separately for each country. Although the momentum effect seems to be stronger for smaller firms, Rouwenhorst (1998) shows that risk factors do not explain momentum returns and that the return continuation is present for both small and large stocks. Interestingly, he finds that, when controlling for market risk or size, the good performance of relative strength strategies increases.

In his following publication, Rouwenhorst (1999) investigates whether those return patterns which he found in developed countries are also true for emerging economies. The new sample consists of 20 emerging markets and 1750 stocks in total with monthly closing prices and a sample period from 1975 onwards, including more stocks over time as more data became available. Methodology and strategies again follow Jegadeesh and Titman’s (1993) paper, but having a one month gap between formation and holding period while using equally weighted portfolios. The average return from zero-cost portfolios across all 20 markets is 0.39 percent per month which is relatively low compared to previous research done in developed countries. Solely investing in winners, however, would provide a return of 2.13 percent per month. Moreover, Rouwenhorst (1999) does provide evidence that short-term momentum is cross-sectional correlated with turnover in emerging markets, but does not find a significant relation between share turnover and expected return.

Rouwenhorst’s (1999) findings are complemented by Griffin, Ji and Martin (2003) by including macroeconomic risk factors in their research. The data sample includes monthly returns for NSYE stocks with an extended time period of 74 years (1926 to 2000). They include 39 non-U.S. countries with a minimum of 50 stocks available. Griffin et al. (2003) select stocks based on their performance from the past six months and use

5

overlapping holding periods. They allocate the top 20 percent best-performing stocks and bottom 20 percent worst-performing stocks to the winner and loser portfolios, respectively, and hold them for six subsequent months. The authors document significant momentum profits across the entire sample with an average zero-cost profit of 0.77 percent for Europe, 0.78 percent for continental America (U.S. being excluded) and 1.63 percent for Africa. An abnormal return with 0.32 percent is also documented for Asia but it is not significant. Intraregional and interregional correlation between momentum returns are low, implying that those returns are not driven by a global risk factor. The authors further document that excess returns during positive GDP growth compared to negative GDP growth are non-significant and therefore conclude that momentum strategies are robust both during good and bad economic states, thus not being related to risk arising from macroeconomic states.

Rouwenhorst’s (1998) findings for Germany (0.72 percent excess return for momentum strategies per month) are in line with the results from Schiereck, De Bondt and Weber (1999). The authors study all major companies listed on the Frankfurt stock exchange between 1961 and 1991 and use a non-overlapping approach. They find that winners are as likely to outperform the market as losers to underperform the market (63 percent of the times). The authors suggest that, if momentum strategies succeed because the market underreacts to news, then one would expect that the effect would have been stronger if past performance had been more extreme. To investigate this point, they form portfolios of two times ten stocks (rather than two times 20 stocks) which earned, on average, 1.9 percent. Portfolios of two times 40 stocks earned only one percent on average. Hence, in agreement with underreaction, momentum performed better if the rank period was longer. Moreover, Schiereck, De Bondt and Weber (1999) find that over a rank period of three months, average past winner portfolios of 20 stocks gained 21 percent and average loser portfolios gave up 20 percent. During another test period, winners yielded abnormal performance of 2.50 percent after 12 months while loser portfolios lost 2.10 percent.

Considering the success of previous research in attempting to prove short-term momentum persistence across emerging and developing (U.S., European and particularly German) markets, the results from this research are expected to be significant both for the time-period before 2000 and after 2000, even after controlling for risk, size and book-to-market factors.

6

III. Data and Methodology

This section explains how the aforementioned hypothesis will be tested. The sample consists of monthly total returns in local currency (EUR) for all German firms that were publicly listed on the Frankfurt Stock Exchange between 1980 and 2018. The data was downloaded from Datastream. The sample covers more than 95% of the country’s market capitalization, counts exactly 2000 stocks (active and dead or delisted stocks) in total and is representative for the German stock market with its size. Survivorship bias is mitigated since all stocks, that are currently not trading anymore, are taken into account as well. This research has attempted to use a long sample period as possible. Datastream’s records give data for the German stock market from 1973 onwards. The time span, however, was decreased as accounting data such as book-to-market ratios are solely available from 1980 onwards. The matching data is needed for the regression analysis in section V. Data and sample period are therefore exposed to two restrictions in total: First, portfolios only include stock returns of companies with a return history of at least 12 months which is consistent with previous research (see Rouwenhorst, 1999). Second, company return data is only taken into account if other relevant accounting data is available for the matching time period.

A. Portfolio Construction

The construction of relative strength portfolios is based on Jegadeesh and Titman’s (1993) approach. Stocks with a return history of at least 12 months are ranked based on their past F-month return (F equals 3, 6, 9, or 12) into deciles at the end of each month and assigned to one of the relative strength portfolios (portfolio 1 contains the stocks with the lowest past performance, portfolio 10 contains the stocks with the highest past performance). The portfolios are equally weighted at formation and subsequently held for H months (H equals 3, 6, 9, or 12) without rebalancing. Since no explicit bid-ask spreads are assumed, the strategies do not skip a month between the formation and holding period. This research follows an overlapping portfolio approach to include as many portfolios as possible. Overlapping holding periods are revised every 1/H month and returns of strategies with H months are reported each starting one month apart. The portfolios construction approach gives 16 strategy combinations. The combinations are hereafter referred to as F-month/H-month strategies.

7

To calculate the stocks’ and portfolios’ returns, either discrete or continuously compounded returns can be used. A disadvantage of continuously compounded returns, or the log-returns, is that they are a nonlinear function of a portfolio’s component weight which would actually be the case with simple or discrete returns. With discrete returns, the portfolio-weighted return is the sum of the component or asset returns. For this research, however, continuously compounded returns are used due to two advantages. First, log-returns are time-additive, or time consistent. A two-period log-return for an asset or total portfolio turns out to be the same as adding the one-period log-returns. Second, the normal distribution of log-returns represents another desirable property. That log-returns are normally distributed is a common assumption over shorter periods (Barakat, 1976). Adding these normally distributed variables produces an n-period log-return that is also normally distributed. The log-return is calculated as follows. The natural logarithm of the price at the end of period two divided by the prior period’s price is taken. Hence, for the one-period log-return, it is the natural logarithm of the price in period two divided by the price in period one. The one-period log-return, r_i,t, for a stock i in period t is calculated as

r_i,t= ln&Pi,t

Pi,t-1', where P_i,t equals eri,t × P

i,t-1. Compounded returns for portfolios in the formation period (F)

as well as the holding period (H) consist of the added monthly log-returns: Cr_it(k)= / r_i,t

k

t=1

The stocks are subsequently ranked based on their compounded return Crit(k). As

mentioned above, winner and loser portfolios consist of each period’s ten percent best and worst performing stocks, respectively. Portfolios’ returns with equally weighted stocks N are calculated as follows:

CrP,t(k)= 0 1 N/ Cri,t(k) N t=1 11 H

The momentum strategy’s return r_M,t is computed by subtracting the loser portfolio’s return rL from the winner portfolio’s return rW (CrM,t(k)=CrW,t(k) - CrL,t(k)). Each

strategy’s average log-return per month is computed by averaging all zero-cost portfolio returns throughout the sample period. The illustrated calculations are applicable to each of the 16 momentum strategies.

8

B. Significance

To judge whether the obtained results are statistically significant, a two-sample t-test is used. For the zero-cost portfolios, the t-values will be evaluated against critical values given by the student t-distribution at 1, 5, and 10 percent significance levels. This is the two-sample t-statistic used for monthly mean log-returns:

t=(x21-x22)-(µ1-µ2) 3s12 n₁+s2 2 n₂ ,

where s2=∑i=1n1(xi-x21)2+ ∑n2i=1(xi-x22)2

n1+n2-2 .

C. Methodology for Regression Analysis

In case abnormal returns for different strategies will be documented and proven to be statistically significant, it makes sense to find out whether these abnormal returns are explained by factors that usually explain more than 90 percent of a stock’s return (Fama & French, 1993). Fama and French’s 3-factor model will be used to assess the aforementioned ideas:

R_it - R_Ft = α_i + b_iMkt_t + s_iSMB_t + h_iHML_t + e_it,

where Rit is the portfolio’s return, Mktt is the market return above the risk-free rate, SMBt

is the size factor and HMLt is the book-to-market factor. The DAX, an index of Germany’s

30 largest companies, is used as a market proxy and returns on German government bonds are used for the risk-free rate (with H-month bond yields). Unlike data on U.S. stocks, such as the S&P 500, SMB and HML values are not recorded in any (publicly available) database for the German stock market. Therefore, the entire regression input, apart from historic return data of course, had to be calculated manually. As for the second step, six portfolios were constructed: S/L, S/M, S/H, B/L, B/M and B/H, where S stands for small size, B for big size, L for low, M for medium, and H for high book-to-market ratio (size is measured by market capitalization). For example, S/L represents a portfolio of small-size companies that have a low book-to-market ratio. The next step includes the calculation of each

9

observed stock’s average return as well as the calculation of the six constructed portfolios’ average return. Then, to get the SMB value for each period, ⅓ (Big Low + Big Medium + Big High) is subtracted from ⅓ (Small Low + Small Medium + Small High). Similarly, in order to get each period’s HML value, ½ (Small Low + Big Low) is subtracted from ½ (Small High + Big High). Subsequently, the corresponding risk-free rate is subtracted from the average market return for each period to get each period’s Mkt value. Lastly, the regression will be run on the returns from the most significant portfolio strategy.

The following Least Squares Assumptions are expected to hold: (1) The conditional distribution of u_i given X_i has a mean of zero; (2) (X_i, Y_i), i=1,…,n, are independently and identically distributed; and (3) large outliers are unlikely.

IV. Returns of Relative Strength Portfolios

This section provides momentum results for three momentum portfolio sets. First, results for the entire period between 1980 and 2018 will be analyzed. Then, to see if the hypothesis can be rejected or not, the periods of 1980 to 2000 and 2000 to 2018 will be compared.

Table I reports the profits and losses of relative strength portfolios contructed between January 1980 and May 2018. The results clearly indicate that short-term momentum persistence does exist for this sample. The 16 stratregies are statistically significant at a 1% significance level. Selecting stocks based on their performance over the past 12 months and then holding them for 3 months gives the strongest zero-cost profit of 2.03 percent per month on average. As for the other strategies based on the same formation period, the returns diminish as the holding periods increase. While the 12-month/3-month strategy gives a return of 2.03 percent per month, the 12-month/6-month, 12-month/9-month and 12-12-month/9-month/12-12-month/9-month strategies yield 1.86 percent, 1.70 percent and 1.57 percent, respectively. Interestingly, the observation that all zero-cost portfolios perform better the longer the formation period is, seems to be present across all holding periods.

Considering a formation period of three months, holding the stocks for the subsequent three months gives relatively low profits of 0.30 percent per month, while holding the selected stocks for one year gives 1.15 percent per month. Selecting stocks based on their past six-month performance and holding them over the medium-term, i.e. six and nine months, yields average returns of 1.55 percent, which are higher than it is the case for

10

holding periods of three and twelve months, with 1.44 and 1.43 percent return on average, respectively. Similarly, for a formation period of nine months, the highest average returns for the zero-cost portfolio are made if the selected stocks are held for six subsequent months (1.80 percent per month). Taking the aforementioned observations together, it is noteworthy that the holding period with the highest return decreases as the corresponding formation period increases, and that strategies with longer formation periods are more profitable than those with shorter ones. In particular, the 3-month/12-month, 6-month/6- or month, 9-month/6-month and 12-month/3-month strategies are the most successful ones in this sample. This observation confirms Rouwenhorst’s (1999) findings for emerging markets as well as for European stocks (Rouwenhorst, 1998). One explanation for this pattern could be that returns over the next three months after formation tend to be much closer to the average of the past 12 months than to the average the past 3-month returns, especially in more volatile periods.

Table I

Momentum Results

In this table, 16 strategy combinations are presented. The formation periods F and the holding periods H are indicated in the first column and in the second row, respectively. Stocks for each portfolio combination are selected based on their F-month past performance and ranked in ascending order. The long portfolio includes stocks from the highest return decile (with return rW) and the short portfolio includes stocks from the lowest return decile (with return rL) The stocks within these portfolios are equally weighted. The sample period is January 1981 to May 2018.

Holding Period (H) F Strategy 3 6 9 12 3 Winner -0.14% -0.25% -0.18% -0.10% Loser -0.44% -1.36% -1.28% -1.26% Zero-cost 0.30% 1.11% 1.11% 1.15% (t-stat)a _{(2.81) (4.40) (4.99) (5.83)} 6 Winner -0.07% 0.06% 0.12% 0.10% Loser -1.51% -1.49% -1.44% -1.33% Zero-cost 1.44% 1.55% 1.55% 1.43% (t-stat)a _{(4.51) (6.13) (7.08) (7.31)} 9 Winner 0.16% 0.24% 0.17% 0.14% Loser -1.56% -1.56% -1.46% -1.36% Zero-cost 1.72% 1.80% 1.63% 1.50% (t-stat)a _{(5.32) (7.03) (7.45) (7.63)} 12 Winner 0.40% 0.31% 0.27% 0.24% Loser -1.64% -1.55% -1.43% -1.33% Zero-cost 2.03% 1.86% 1.70% 1.57% (t-stat)a _{(6.30) (7.36) (7.84) (8.05)}

a_{The one-sided two-sample t-test is applied to test if the difference between r}

11 Table II

Momentum Results before and after 2000

Panel A shows results for the time-period before 2000, Panel B for the time-period after 2000. Portfolios are constructed in the same way as before. The best-performing stocks from the formation period F will be held for the subsequent H-months. Each row shows a different ranking period whereas each column shows a different holding period.

Panel A Panel B

Holding Period (H) Holding Period (H)

F Strategy 3 6 9 12 3 6 9 12 3 Winner 0.57% 0.61% 0.65% 0.68% -1.49% -1.17% -1.08% -0.97% Loser 0.42% 0.26% 0.18% 0.05% -3.16% -3.11% -2.88% -2.70% Zero-cost 0.15% 0.35% 0.47% 0.63% 1.67% 1.93% 1.80% 1.73% (t-stat)a _{(0.48) (1.48) (2.40) (3.66) (3.20) (4.60) (4.84) (5.19)} 6 Winner 0.79% 0.78% 0.80% 0.71% -0.99% -0.73% -0.64% -0.59% Loser 0.22% 0.06% -0.08% -0.11% -3.36% -3.17% -2.93% -2.70% Zero-cost 0.57% 0.73% 0.88% 0.82% 2.36% 2.44% 2.29% 2.11% (t-stat)a (1.75) (2.98) (4.38) (4.50) (4.51) (5.81) (6.18) (6.41) 9 Winner 0.96% 0.92% 0.79% 0.68% -0.70% -0.51% -0.52% -0.48% Loser 0.10% -0.10% -0.18% -0.16% -3.36% -3.18% -2.90% -2.73% Zero-cost 0.86% 1.02% 0.97% 0.84% 2.66% 2.67% 2.37% 2.25% (t-stat)a (2.53) (3.95) (4.51) (4.19) (4.99) (6.26) (6.48) (7.00) 12 Winner 1.10% 0.88% 0.78% 0.67% -0.38% -0.33% -0.31% -0.27% Loser -0.18% -0.29% -0.27% -0.23% -3.25% -2.97% -2.76% -2.61% Zero-cost 1.28% 1.17% 1.04% 0.90% 2.87% 2.64% 2.45% 2.34% (t-stat)a _{(3.71) (4.39) (4.60) (4.21) (5.34) (6.28) (6.82) (7.49)}

a_{The one-sided two-sample t-test is applied to test if the difference between r}

W and rL is positive and significant.

As previously pointed out, the economic situation in Germany has considerably changed since 2000. To see whether short-term momentum persistence is still present in the German stock market, the earlier introduced sample will be split into two portfolio sets: one for the time-period before 2000, and one for the time-period after 2000. Table II reports the average returns of the different buy and sell portfolios as well as the zero-cost (winners minus losers) portfolios for the 16 strategies, comparing the time-periods from January 1980 to December 1999 and January 2000 to May 2018. All the zero-cost portfolios give positive and statistically significant returns except for the 3-month/3-month strategy in Panel A, which produces a non-significant return of 0.15 percent per month. All other log-returns for the same time-period are significant at a 1% significance level, except those in the 3-month/6-month and 6-month/3-month portfolios which are significant at 10% and 5% with monthly log-returns of 0.35 and 0.57 percent, respectively.

The returns and their significance before 2000 are relatively low compared to the results from after 2000. The average return difference between these two portfolio sets is 1.49 percent per month, peaking at 1.80 percent for the 9-month/3-month strategy. All

12

strategies with a formation period of at least 6 months generate returns higher than two percent per month after 2000 in all cases, more than twice as much as for the results from the period between 1980 and 2000. This observation is probably explained by Germany’s remarkable economic growth during the last two decades. However, very similar return patterns occur across all three sample periods. Looking at the best performing strategies for each formation period, it again applies that the higher the formation period is, the lower is the holding period. As it is the case for the entire time-span between 1980 and 2018, selecting stocks based on their returns over the previous 12 months and holding the portfolio for the subsequent three months produces the highest returns, as compared to the other strategies. This strategy yields 1.28 percent per month before 2000 (shown in Panel A) and it yields 2.87 percent per month after 2000 (shown in Panel B).

To illustrate the payoff of buying past winners and short-selling past losers over the short-term, the 6-month/6-month strategy, which is representative for all other strategies, will be compared to the market. Figure I plots the returns of the 6-month/6-month strategy and those of the DAX as a market proxy from 2000 up to 2018 since the focus of this research is on this particular time-period. The graphs show how well an investor would have done with investments in different assets. Investing one Euro in common stocks would have yielded 1.22 Euros. In contrast, if one Euro was invested into the momentum portfolio, one would have been up to 134.40 Euros. This remarkable momentum profitability can be further illustrated by looking at the reward-per-unit-risk, or the Sharpe ratio. Specifically, with a mean return of 3.18 percent per year and a standard deviation of 26.03 percent, the market’s Sharpe ratio was 0.12 after 2000, assuming a risk-free rate of zero percent. The zero-cost portfolio’s mean return per year for the 6-month/6-month strategy is 29.50% and its standard deviation equals 35.51 percent, giving a Sharpe ratio of 0.83. Building a portfolio that has the same volatility as the market and consists of investments into the momentum as well as the market portfolio, one would be up to a Sharpe ratio of 1.01, with a remarkably successful mean return of 26.4 percent per year and a standard deviation of 26.03 percent.

Having established that the relative strength strategies are on average quite profitable, the 6-month/6-month strategy will be examined in detail in the next two sections. The following analysis attempts to provide explanations about the source of the observed momentum profits. Rouwenhorst (1999) has shown that internationally diversified relative

13 Figure I

Market and Momentum Returns after 2000

This figure compares log-returns from the 6-month/6-month investment strategy and log-returns from investments into the market index, in this case the DAX. The graphs show how well these two investment strategies would have done, if one Euro was invested into each in the beginning of 2000. The y-axis is presented in logs and shows the amount of Euros earned. Time in yearly gaps is plotted on the x-axis. The solid line represents the performance of the market, and the dashed line represents the performance of the momentum portfolio.

strength portfolios in developed markets depends on firm size and partly on market risk factors, and the next section will focus on these factors.

V. Sources of Relative Strength Profits

To identify factors that help to explain momentum profits, the 3-factor regression model by Fama and French (1993) will be used, which is usually widely applied in asset pricing.

A. Regression results

Three regressions will be run: One for the period between 1980 and 2018, one for the period before 2000 and another one for the period after 2000. Table III reports the regression results. Considering the R-squared for each model, the multi-factor model does not seem to explain momentum profits, or at least does not include relevant explaining factors. The linear regression model only explains 4.68 percent of the variance in momentum profits between 1980 and 2018, 0.39 percent before 2000 and 5.27 percent after 2000. The alphas (or intercepts), however, are statistically significant at 1% for all portfolio sets. Looking at the HML factor, profits earned with momentum portfolios are not explained by the values of book-to-market ratios–the positive coefficients give p-values of 0.252, 0.405 and 0.670. The size factor, on the other hand, is statistically significant for the period

0,1 1 10 100 1000 01.02.00 01.02.02 01.02.04 01.02.06 01.02.08 01.02.10 01.02.12 01.02.14 01.02.16

14 Table III

Results for 3-Factor-Model – Zero-Cost Portfolio

This table gives results for three regression analyses–one for each time-period of interest for this research. The portfolios’ return for the 6-month/6-month strategy represents the dependent variable. The relative strength portfolios are formed selecting the past 6-month winners and subsequently held for 6 months. Mkt, SMB and HML are the independent variables and stand for the excess market return over the risk-free rate, the size factor and book-to-market factor, respectively. The intercept represents Jensen’s alpha.

OLS Parameter Estimates

Parameter Estimate Standard Error t-value p-value R2

A. 1980 to 2018 0.0468 Intercept .0126918 .0018196 6.97 0.000 Mkt -.0055003 .0244249 -0.23 0.822 SMB -.2486525 .0551965 -4.50 0.000 HML .0610988 .053216 1.15 0.252 B. Before 2000 0.0039 Intercept .0073376 .0014968 4.90 0.000 Mkt -.0042728 .0237008 -0.18 0.857 SMB .0287768 .0650209 0.44 0.658 HML .0456074 .0547016 0.83 0.405 C. After 2000 0.0527 Intercept .0218295 .0036456 5.99 0.000 Mkt .002199 .0405719 0.05 0.957 SMB -.2503258 .0881736 -2.84 0.005 HML .0159758 .0866586 0.18 0.670

between 1980 and 2018, and for the period after 2000 with coefficients of -0.249 (p-value: 0.000) and -0.250 (p-value: 0.005), respectively. Between 1980 and 2000, firm size is non-significant (p-value: 0.658).

Although the tested 3-factor model does only explain a relatively small fraction of the variability in momentum profits, it makes sense to have a closer look at the size factor. This is the only factor that is significant for two out of the three regressions and it was earlier emphasized by Jegadeesh and Titman (1993) and Rouwenhorst (1999) that momentum returns are correlated with firm size.

B. Profitability of Relative Strength Strategies Within Size-Based Subsamples

This section will examine the 6-month/6-month strategy’s profitability within subsamples stratified on the basis of firm size. Specifically, this strategy will be implemented on three size-based subsamples with small, medium-sized and large firms. Since existing literature suggests that firm size is related to expected returns (Fama & MacBeth, 1973; Banz, 1981), the dispersion in expected returns should be less within subsamples than in the full sample. If the relative strength profits are related to differences in expected returns, then they will be less within each subsample. In fact, if momentum

15

profits are not factor-related, the strategies are likely to generate higher returns when they are implemented within the small-firm subsample that consists of less actively traded stocks and to generate lower returns when they are implemented within the large-firm subsample. Table IV contains the average returns of the strategy in question for each of the subsamples. The results show that the observed log-returns are of roughly the same value when the strategies are implemented on the entire sample as when they are arranged into subsamples. They do, however, appear to be related to firm size to some extent; the zero-cost portfolio S1 gives relatively lower returns than the other subsamples. But returns from all subsamples are significant, except for the loser portfolio of medium-sized firms. This shows that short-term momentum is not dependent on any particular subsample of stocks. Banz (1981) was the first one emphasizing that small-firm effects slowly disappear over time. For momentum trading strategies, however, this effect is still present.

C. Discussion

As sections IV and V show, momentum is a persistent force in market behavior. One major theory to explain why this effect occurs is that there might be a behavioral bias. First, investors may underreact to new information because they anchor their investment behavior to information they already know and may not fully appreciate the magnitude of new

Table IV

Momentum Portfolios Based on Size and Their Returns

Stocks for each strategy combination are selected based on their F-month past performance and ranked in ascending order. The long portfolio includes stocks from the highest return decile (portfolio P10) and the short portfolio includes stocks from the lowest return decile (portfolio P1). The stocks within these portfolios are equally weighted. Average monthly returns of portfolios P1 through P10, which include all stocks, are reported here. Additionally, relative strength portfolios that are formed using subsamples based on firm size are reported as well, where S3 provides results for the largest firms, S2 for medium-sized firms, and S1 for small-sized firms. Sizes are ranked based on market capitalization, where the smallest firms are from the lower 30 percent, medium-sized firms from the middle 40 percent, and large firms from the upper 30 percent.

Average Monthly Returns

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 P10-P1 F-Statistics a All -.0149 -.0135 -.0122 -.0121 -.0116 -.0101 -.0095 -.0077 -.0012 .0006 .0155 2.73 (1.56) (2.78) (3.40) (3.59) (3.87) (4.14) (4.19) (4.30) (4.36) (4.33) (3.07) (p-value: 0.00) S1 -.0146 -.0112 -.0076 -.0063 -.0051 -.0037 -.0029 -.0016 -.0009 .0013 .0159 2.75 (1.35) (2.29) (3.23) (3.59) (3.74) (4.08) (4.13) (4.11) (4.28) (3.99) (2.77) (p-value: 0.00) S2 -.0181 -.0171 -.0155 -.0141 -.0101 -.0067 -.0043 -.0028 -.0009 .002 .0201 4.39 (0.99) (2.54) (3.34) (3.58) (3.83) (4.22) (4.12) (4.16) (4.11) (4.11) (4.57) (p-value: 0.00) S3 -.0145 -.0129 -.0105 -.0095 -.0089 -.0062 -.0049 -.0021 -.0016 -.0006 .0139 4.21 (2.22) (3.08) (3.53) (3.66) (3.85) (3.66) (3.90) (3.86) (4.17) (4.41) (3.03) (p-value: 0.00)

16

information as it gets released into the market. This can potentially cause market prices to react more slowly than they should. Second, investors might be reluctant to sell stocks that have gone down in price, in the hopes of breaking even. A third effect may be that investors, once a pricing pattern has been established, they pile into this strategy, hoping to benefit from it which may potentially push prices away from their value, and potentially leading to longer-term reversials with the value effect. There are different driving forces of short-term momentum that could work but it seems to be persistent that initial underreaction and longer-term overreaction exists. The same effect has been observed in international markets–not only in stocks but also in other asset classes. Despite the short-term momentum’s prominence in domestic as well as international markets, the findings from this research should be viewed with caution. As Daniel and Moskowitz (2016) recently pointed out, momentum strategies can experience infrequent strings of negative returns, such as during the financial crisis of 2008 when winner and loser portfolio returns actually reversed across numerous markets and asset classes. In March 2008, when the market started to turn around, past losers started doing relatively well as compared to past winners. One should keep in mind that this research has focused on average momentum returns over time-periods of minimum 17 years and that momentum strategies tend to crash during economic downturns (Daniel & Moskowitz, 2016). The 12-month/3-month strategy in particular might be the worst performing strategy during bad economic states since those strategies that have longer formation periods and shorter holding periods suffer logically the most when winner and loser stocks start reversing–strategies with shorter ranking periods adjust themselves more quickly to reversed return patterns.

VI. Conclusion

This paper documents return continuation in the German stock market in a sample of 2000 stocks, active or dead, trading on the Frankfurt stock exchange. A portfolio of past winners outperformed a portfolio of past losers by roughly 1.50 percent per month on average between 1980 and 2018. The effect of buying winners and selling losers was stronger for portfolios formed after 2000, with approximately 2.30 percent on average, than it was for the period between 1980 and 2000 with 0.80 percent. These results are negatively correlated with firm size. Small-sized firms produce slightly higher returns than big-sized

17

firms, but all results are significant at a 1% level. The payoffs are therefore inconsistent with the joint hypotheses of market efficiency and commonly used asset pricing models. The German evidence is remarkably similar to findings for the United States by Jegadeesh and Titman (1993) and for Europe by Rouwenhorst (1998). Topics for future research in the German market could be seasonality (due to the January effect which was observed in earlier literature) of momentum profits. Moreover, industries could play an important role in the sources of short-term momentum profitability, as well as behavioral factors, and especially how they differ between Germany and other developed and emerging markets.

Considering the aspects of behavioral finance, the most surprising observation is that the results for Germany are very similar to the findings fin the United States–although there are differences in the cultural as well as economic environment, and although equity markets are organized differently. General traits in human behavior probably overcome the observed differences and drive the dynamics of world financial markets’ asset prices.

18 References

Ball, R., & Kothari, S.P. (1989). Nonstationary expected returns: Implications for tests of market efficiency and serial correlation in returns. Journal of Financial Economics,

25, 51-74.

Barakat, R. (1976). Sums of independent lognormally distributed random variables. Journal

of the Optical Society of America, 66(3), 211-216.

Booth, G.G., Iversen IV, P., Sarkar, S.K., Schmidt, H., & Young, A. (2010). Market structure and bid-ask spreads: IBIS vs Nasday. The European Journal of Finance,

5(1), 51-71.

Chan, K.C. (1988). On the contrarian investment strategy. Journal of Business, 61, 147-163.

Conrad, J., & Kaul, G. (1998). An Anatomy of Trading Strategies. The Review of Financial

Studies, 11(3), 489-519.

Cootner, P. (1964). The Concept of Yield on Common Stock: Discussion. The Journal of

Finance, 19(2), 201-204.

De Bondt, W.F.M., & Thaler, R. (1985). Does the Stock Market Overreact? The Journal of

Finance, 40(3), 793-805.

Fama, E.F. (1969). Efficient Capital Markets: A Review of Theory and Empirical Work.

The Journal of Finance, 25(2), 383-417.

Griffin, J.M., Ji, X., & Martin, J.S. (2003). Momentum Investing and Business Cycle Risk: Evidence from Pole to Pole. The Journal of Finance, 58(6), 2515-2547.

19

Ising, J., Schiereck, D., Simpson, M.W., & Thomas, T.W. (2006). Stock returns following large 1-month declines and jumps: Evidence of overoptimism in the German market.

The Quarterly Review of Economics and Finance, 46(4), 598-619.

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. The Journal of Finance, 48(1), 65-91. Jegadeesh, N., & Titman, S. (2001). Profitability of Momentum Strategies: An Evaluation

of Alternative Explanations. The Journal of Finance, 56(2), 699-720.

Jegadeesh, N., & Titman, S. (2002). Cross-Sectional and Time-Series Determinants of Momentum Returns. The Review of Financial Studies, 15(1), 143-157.

Lee, C.M.C., & Swaminathan, B. (2002). Price Momentum and Trading Volume. The

Journal of Finance, 55(5), 2017-2069.

Lehmann, B. (1990). Fads, martingales and market efficiency. Quarterly Journal of

Economics, 105, 1-28.

Lo, A.W., & MacKinlay, A.C. (1990). An econometric analysis of nonsynchronous trading.

Journal of Econometrics, 45(1-2), 181-211.

Moskowitz, T., & Grinblatt, T.J. (1999). Do Industries Explain Momentum? The Journal of

Finance, 54(4), 1249-1290.

Rouwenhorst, K.G. (1998). International Momentum Strategies. The Journal of Finance,

53(1), 267-284.

Rouwenhorst, K.G. (1999). Local Return Factors and Turnover in Emerging Markets. The

20

Schiereck, D., De Bondt, W., & Weber, M, (1999). Contrarian and Momentum Strategies in Germany. Financial Analysts Journal, 55(6), 104-116.

Yao, Y. (2012). Momentum, contrarian, and the January seasonality. Journal of Banking &

Finance, 36(10), 2757-2769.

Zarowin, P. (1990). Size, seasonality, and stock market overreaction. Journal of Financial