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The Profitability of Momentum Strategies in the
European Markets Including Adjustments for the Fama
and French Effects
Joris Klomp
s2595443
14-01-2016
Master’s Thesis Finance
MSc Finance, University of Groningen
Supervisor: Dr. P.P.M. Smid
Abstract
The purpose of this study is to investigate whether the stock markets of ten European countries are characterized by significant momentum profits. I found that a European winners minus losers portfolio that is based on their past six-months’ returns had a monthly average return of 1.86% between 2000 and 2014. The stock markets of Austria, Belgium, France, Germany, Ireland, Italy, the Netherlands, and Portugal have significant momentum profits during the same time period and the losers portfolios were riskier than the winners portfolios. The results are affected by the three largest markets and especially by the financial crisis. The cumulative average returns are in an upward trend toward time, but in several countries there are periods of negative returns. Fama and French’s (1996) three-factor model explains stock returns in terms of three different factors. The betas of the losers portfolios were significantly higher than those of the winners portfolios. The SMB and HML coefficients of the losers portfolios were significantly lower than the SMB and HML coefficients of the winners portfolios. The time-series
regressions showed a significant market effect but no size or book-to-market effects, which means that the WML returns were only higher when adjusted with the market effect.
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I. Introduction
Graham and Dodd (1934) were the first researchers to suggest that investors extrapolate past stock returns far into the future. Investors drive the prices of stocks that performed well in the previous couple of months to a higher level, and the prices of poorly performing stocks to a lower level. When investors apply the momentum investment strategy, they buy past winners and sell past losers. Momentum investment is based on a winners minus losers (WML) portfolio. Within this strategy, the WML portfolio should have a positive return; when this occurs there are momentum profits. Several researchers have simulated the momentum investment strategy for different countries and time periods. The strategy realized significant momentum profits over the period from 1965 to 2009, but the strategy was less successful in some countries and for some time periods. The purpose of this study is to
investigate whether there are significant momentum profits in the stock markets of ten European countries. If there are significant momentum profits, a momentum investment strategy could be a profitable strategy for investors to partly or broadly implement.
The following question will be answered during this study: How does a sample of ten European countries perform on momentum profits based on zero cost portfolios ranked on their past six-months’ returns and held for six months for the time period from 2000 to 2014? The sub-questions to be answered in this study have been formulated as follows:
1. Which countries have significant momentum profits?
2. How are the returns and standard deviations of each country compared to each other? 3. What are the WML returns, adjusted for the largest markets and crises?
4. How do the cumulative average returns of each WML portfolio move compared to the cumulative returns of the WML portfolio of the total sample?
5. How are the portfolios biased toward conventional risk factors, such as market, size, and book-to-market ratio?
post-3 crisis period from 2009 to 2014. In this study, the stock returns of the following countries are included: Austria, Belgium, Finland, France, Germany, Ireland, Italy, the Netherlands, Portugal, and Spain.
This study provides insight into the momentum investment strategy for a European sample. It provides an answer as to which European stock markets have significant momentum profits. For investors this research will be of interest because they can see which countries have significant
momentum profits with the lowest corresponding risk. Furthermore, the cumulative average returns of each WML portfolio will be calculated. This calculation will provide insight into which countries perform best and which country is best at replicating the total sample. The second part of this study will
investigate the characteristics of the WML portfolio by looking at the sensitivity to the three Fama and French factors: market, size, and book-to-market ratio. This approach is valuable for investors because it is a better tool for evaluating the performance of a strategy than looking only at the risk and return. The Fama and French factors show what kind of firms are in the WML portfolio, which is valuable for
optimally implementing the strategy.
This study is similar to the study by Rouwenhorst (1998). The only differences between the samples in that study and this are that, in this study, Finland, Ireland, and Portugal are included instead of some countries where the Euro is not the home currency. This study will focus on European countries that have the Euro as their home currency, which will immediately eliminate the currency risk within this study.
The paper is organized as follows. Section II presents the literature review. In this section, a review of several theoretical expectations about momentum profits will be discussed, and further on, the empirical results of past implemented momentum investment strategies will be presented. Section III will present the methodology for implementing the strategy and measuring the results. Section IV will provide an overview of the data. Section V will show the results. Finally, Section VI will present the conclusions.
II. Literature review
According to De Bondt and Thaler (1985), stock prices either overreact or underreact to
4 is divided into two different parts. The first part is about the momentum profits, and the second part about the Fama and French factors.
Several researchers have tried to explain momentum profits with risk-based models. Jegadeesh and Titman (2001a) theorize that there are momentum profits because past winners are riskier than past losers, this finding is reversed by Rouwenhorst (1998). According to Fama and French (1996) and Grundy and Martin (2001), momentum profits are higher when adjusted for market, size, and book-to-market effects. According to Nijman et al. (2004), momentum profits are driven by individual stock effects in the European markets, and country momentum plays an unimportant role. The researchers above predict that, with risk-based models, the returns of the winners portfolios should outperform the returns of the losers portfolios.
On the other hand, several studies have tried to explain momentum profits with behavioral models. According to Barberis et al. (1998) and Daniel et al. (1998), momentum profits are based on inherent biases in the way that investors interpret information. They posit that, in these behavioral models, the returns increased because of delayed overreactions or under reactions to information. Barberis et al. (1998) argue that the representative heuristic causes make investors think that stocks that performed well in the past will continue to grow. They found that conservatism bias led to
under-reaction. According to Daniel et al. (1998), the behavior of momentum investors is characterized by self-attribution bias. They found that investors only bought stocks that grabbed their attention. The investors thought that the stocks’ signals were positive and so they would perform well in the future. However, in this case, investors suffered from their own cognitive bias. The investors were overconfident about their ability to pick winners, and thereby overestimated the strength of the positive signals. These two studies found that the prices of the winners were above their long-term values and of the losers were below, which caused negative future returns on portfolios based on high past returns. Thus, the behavioral models predict that the returns of the losers portfolios should outperform the returns of the winners portfolios. In this case, the conclusions of the behavioral models contradicted the results of the risk-based models.
Several researchers have tested the momentum investment strategy to find out which stock markets have significant positive WML returns, and so on which model better fits the data. Some studies used countries from all around the world. Others leaned more toward smaller samples, such as Asian or European countries. There are also researchers who have used other methods, but this study
5 portfolio in some countries showed significant momentum profits, and in other studies and time periods, the strategy did not. These empirical studies showed, with a significance level of 5%, that WML returns are significantly positive 40.8% of the time. In none of these studies did a country have significant negative WML returns, which means that risk-based models better fits the data for these empirical studies.
Rouwenhorst (1998) not only tested monthly returns, but also the associated risk. When graphed, the monthly average standard deviations for the ten equally weighted portfolios were U-shaped. The losers portfolio is the portfolio with the lowest past returns, and the winners portfolio is the portfolio with the highest past returns. The U-shape of the standard deviations showed that the winners and losers portfolios were riskier than the other portfolios. In this case, the portfolios in the middle had the lowest standard deviations. The standard deviation of a European WML portfolio was, on average, about 4% per month, similar to the volatility of a portfolio in the middle, which indicates that an
international momentum portfolio is not well-diversified. The standard deviations of the WML portfolios of the individual countries were two or three times larger than the standard deviation of the total sample. According to Rouwenhorst (1998), this result implies that most standard deviations are country-specific and are diversified away in the total sample. Thus, the risk level of individual countries is lower when they are combined with other countries.
After the monthly average returns of the WML portfolios are calculated in this study, it will be of interest to see how the returns perform over a longer time period. Griffin et al. (2005) tested the WML returns for the total time period by calculating the cumulative average returns for the total time period. The cumulative average returns were found to be in an upward trend over time. This trend is the strongest in the US followed by Europe. Notably, the cumulative average returns show periods longer than a year where they are not profitable. Jegadeesh and Titman (2001a) showed that, in the U.S. market, the cumulative average returns of the WML portfolio have been profitable since 1965. The figures show some negative outliers where the cumulative average returns were lower, but overall, there is an upward trend visible.
6 positive. Fama and French’s (1996) three-factor model predicts that small cap and value portfolios will have higher expected returns and risk than large cap and growth portfolios; thus, in this case, the SMB and HML coefficients are positive.
Jegadeesh and Titman (2001a) predicted that the firms in the winners and losers portfolios would be small firms. Both portfolios should have higher SMB coefficients than the other portfolios because smaller firms are more volatile than the average firm. Stocks with high standard deviations can earn huge profits one year and the next year have large losses. Therefore, the stocks of smaller firms are in the winners or losers portfolios, because according to Rouwenhorst (1998) these two portfolios have the highest level of risk. If the momentum strategy utilizes stocks from smaller firms, this suggests that implementing the strategy may be difficult and expensive because one has to take many positions in small stocks.
Fama and French (1996) themselves tested whether their three-factor model really explained stock returns. They measured the average difference in returns for 25 U.S. market size and book-to-market portfolios. The results showed that small stocks outperform big stocks and high book-to-book-to-market stocks have higher returns than low book-to-market stocks, therefore the results were in line with their expectations. The regression intercepts should be close to zero if the model accurately describes the expected returns. The results show that smaller stocks and low book-to-market stocks have large negative unexplained returns. The big stocks and low book-to-market stocks show large positive unexplained returns. In most other cases, the intercept is around zero. The adjusted R-squared of these 25 portfolios shows an average explanatory power of 0.93, which means that the model explains the variation in the average returns quite well. Therefore, according to Fama and French (1996), the three-factor model is a good model for predicting the returns on size and book-to-market portfolios. However, they later concluded that the model cannot explain average returns based on only the returns of a past couple of months because the losers are biased positively and the winners negatively on the book-to-market coefficients. In this case, the pattern shows to be a reversal instead of a continuation of the future returns.
7 Rouwenhorst (1998) tested the influence of market and size on the returns of the losers,
winners, and WML portfolios. The results show no market effect because the betas of the winners and losers portfolios are almost the same. The return on the WML portfolio is slightly lower when it is measured for the market effect, but the market effect is not significant. When measuring for the size effect the returns of the WML portfolio were higher than without the effect. Therefore, there is a significant size effect. Rouwenhorst (1998) did not test the book-to-market effect. These results are inconsistent with Fama and French (1996) and Grundy and Martin (2001) because the momentum profits are not higher when they are adjusted for the market effect, but instead are only higher when adjusted for the size effect. In the study of Fama and French (1996) and Grundy and Martin (2001), there is also a significant book-to-market effect.
III. Methodology
The literature review shows mixed results about the momentum profits around the world. In the empirical results, it appears that in just 40.8% of the cases, the WML portfolios have significant positive returns. Therefore, the following hypothesis will be tested with different samples:
H1.0:There are no momentum profits. H1.1: There are momentum profits.
First, the monthly returns of the all stocks indices of the ten individual countries have to be collected. Only stocks with a return history of at least six months will be included in the sample. A monthly overview of the past six-months’ returns of each stock and their future six-months’ returns, will be created. Then, the future six-months’ returns can be sorted based on their past six-months’ returns, resulting in an overview of the past months’ returns from high to low with the corresponding six-months’ future returns.
8 The six-months’ buy-and-hold returns will be converted to an average one-month return to make it comparable to other studies. Furthermore, the strategy of skipping a month between the past six-months’ ranking period and the holding period will be used in order to avoid the effect of one-month return reversals, consistent with Jegadeesh (1990) and Griffin et al. (2005).
The next step is to use overlapping portfolios to increase the power of the tests; the same method is used in Jegadeesh and Titman (2001b). The best way to explain this method is with the timeline of figure I:
Figure I
Timeline to explain methodology
1 Formation period Holding period
Jul Aug Sept Oct Nov Dec Feb Mar Apr May Jun Jul
2 Formation period Holding period
Aug Sept Oct Nov Dec Jan Mar Apr May Jun Jul Aug
The first winners portfolio of January 2000 consists of the stocks with the highest previous six-months’ returns, i.e., the highest returns during the previous July to December period. The six-six-months’ future returns will be from February to July. In the next month, the winners portfolio of February 2000 consists of the highest previous six-months’ returns, from August to January. The future six-months’ returns are from March to August. This study measures a total time period of 15 years, so there will be 180 of these timelines. Every month has an equal weight in this portfolio, and finally, the average monthly returns for the total time period can be calculated. To test if there are significant momentum profits, the t(mean) will be calculated, Rouwenhorst (1998). t(mean) is the mean divided by the standard error. The standard error is the standard deviation divided by the square root of the number of
observations. When the returns of the ten equally weighted portfolios are calculated, it is also possible to calculate the standard deviations of these portfolios. Then, we can see whether the standard
9 With the t(mean) can be calculated whether there are significant momentum profits, but to test whether the results better fits within risk-based or behavioral models two additional tests are necessary. First, whether there are differences between the returns of the ten equally weighted portfolios will be tested. The appropriate method is the ANOVA: Single factor or also called the one-way analysis of variance, Keller (2012). This method analyzes the variance of the data to determine whether one can infer that the population means differ. The F-statistic will show whether there is evidence to infer that the monthly average returns are different in at least two or more portfolios. The next step is to test whether the monthly average returns of the winners outperform the returns of the losers portfolios. Based on the results of the ANOVA: Single factor method, the t-Test: Two-Sample Assuming Unequal Variances is the perfect test, Keller (2012). The test presents a t-statistic and shows whether there is sufficient evidence to infer that, on average, the return of the winners outperform the return of the losers portfolio and when this appears the risk-based models are the appropriate model.
The first hypothesis can also test the momentum profits of the individual countries by calculating the t(mean). Further, it is plausible that one country has been more affected by a crisis than other countries. For example, there was a strong decrease in the Belgian stock prices during the financial crisis relative to the other markets. In this case, the losers portfolio will be over weighted with Belgian stocks relative to stocks from other countries, which could result in a misleading view. Therefore, it is necessary to pick all losers of the ten countries. In this case, the losers of each individual country are also the losers of the total sample. These results make it possible to compare the countries and determine which countries have the highest returns. In this case, the unrestricted relative strength portfolios become country-neutral portfolios. The monthly average returns and risk of each individual country will be calculated for the total time period. Further, a distinction between the WML, winners, and losers
portfolios will be made. Now can be found out whether the standard deviations of the WML portfolios of the individual countries are larger than the standard deviation of the total sample.
According to Rouwenhorst (1998), the returns are very influenced by the three largest countries that contribute the most firms in the sample. In this study, a sample without the three largest markets will be created. The results will undoubtedly be affected by the early recession and by the financial crisis, therefore it will be of interest to discover how the returns are without these crises.
10 whether the cumulative average returns are in an upward trend toward time or not. Furthermore, these figures will show which country is best at replicating the momentum profits of the total sample and which country has the highest profits during the total time period. These results can help investors by their investment decisions.
In the second part of this study the following hypotheses will be tested: H2.0:There is no market effect
H2.1: There is a market effect
H3.0:There is no size effect H3.1: There is a size effect
H4.0:There is no book-to-market effect H4.1: There is a book-to-market effect
Three methods will be implemented to test whether there are market, size, and book-to-market effects. In the first method, Fama and French (1996) tested whether their three-factor model really explained stock returns on these three factors. They measured the average excess returns on 25 U.S. market size and book-to-market portfolios. The same method will be implemented for this study. With Kenneth R. French’s data library, French (2013), the data can be collected from the 25 portfolios based on their market size and book-to-market values. The only problem is that the sample is larger than the sample in this study. The sample includes all ten sample countries, as well as Denmark, Greece, Norway, Sweden, Switzerland, and the United Kingdom. This bigger sample will even strengthen the results because the hypotheses will be tested on a broader European scale. The following time-series regression will be executed:
Rit - Rf= αit + βit (Rm - Rf) + sitSMB + hitHML + Ɛit (1)
11 Rf = The risk free interest rate is the one-month LIBOR Euro rate at the beginning of the month,
Federal Reserve Bank (2015a). This rate was chosen because the LIBOR is the most widely used reference rate for short-term interest rates. The risk free rate is on a monthly basis.
αit = Alpha, the intercept value. The alpha gives the monthly unexplained return and should be almost zero to measure if the three-factor models describe the expected returns. The reference date is at the beginning of the month.
βit = The slope of the market portfolio, or beta. Beta is a measure of the stock's
market-related (or systematic) risk because it measures the volatility of the stock price related to the overall market volatility. The beta is on a monthly basis, and the reference date is at the beginning of the month.
Rm = The monthly return on the value weighted market portfolio of all stocks in the size and book-to-market portfolios. This will be the value weighted Morgan Stanley Capital International (MSCI) Europe total return index. This index simply tracks the performance of European
companies. The reference date is at the beginning of the month.
sit = The slope of the SMB factor, or the SMB coefficient. The SMB coefficient is on a monthly basis, and the reference date is at the beginning of the month.
SMB = The equally weighted average returns on three European small stock portfolios, minus the average returns on three big stock portfolios. The returns are on a monthly basis, and the
reference date is at the end of the month.
hit = The slope of the HML factor, or the HML coefficient. The HML coefficient is on a monthly basis, and the reference date is at the beginning of the month.
HML = The equally weighted average returns for two European high book-to-market portfolios, minus the average returns of two European low book-to-market portfolios. The returns are on a monthly basis, and the reference date is at the end of the month.
Ɛit = The error term, or residual, shows the difference between the actual return and the return in the model. The error term is on a monthly basis, and the reference date is at the beginning of the month.
12 market equity of all European stocks. These five groups are lower, low, medium, high, and higher book-to-market portfolios. The lower group is based on the bottom 20% of European book-book-to-market stocks. SMB is the difference between the average returns on the five smaller, five small, five middle, five big, and five bigger stock portfolios. On the other hand, HML is the difference between the average of the returns on five lower, five low, five medium, five high, and five higher book-to-market portfolios. This first method tests not only the variation in the average returns, but also whether the European small cap stocks outperform the European large cap stocks and whether the high book-to-market stocks
outperform the low book-to-market stocks.
First, time-series regressions for the characteristics of the 25 market size and book-to-market portfolios will be made. The same time-series regression can be used to measure the characteristics of the ten equally weighted portfolios. Than it is possible to test the betas, SMB and HML coefficients of the winners and losers portfolio compared with each other and compared to the other eight portfolios. A distinction will be made between the unrestricted relative strength portfolios and the country-neutral portfolios. Regression Equation 1 will also be used, but there are some differences. Now, Rit is the actual monthly return of one of the ten equally weighted portfolios. The risk free rate will be the six-months’ LIBOR Euro rate, Federal Reserve Bank (2015b), because the portfolios are based on their past six-months’ returns. The Rm, SMB and HML factors are formed in the same way as the previous method. Some additional calculations are necessary because the returns have to be calculated as the average monthly return based on their future six-months’ returns. When the returns are based on their future six-months’ returns, they are consistent with the returns of the ten equally weighted returns because a monthly portfolio return also contains of an average of the future six-months’ returns. The equality of the betas will be tested with the ANOVA: Single factor method, Keller (2012). The fact that losers have higher SMB and HML coefficients than the winners portfolio will be tested with the t-Test: Two- Sample Assuming Unequal Variances, Keller (2012).
Finally, the last method will be measuring the market, size, and book-to-market effects.
13 the adjusted R-squared to show the variation in the average returns. The t-values test whether the effects are significant, when they are significantly negative then there has been an effect.
IV. Data
The stock prices of the ten European countries were collected from Datastream for the July 1999 to June 2015 time period. The same method as Griffin et al. (2005) was used to prevent any possible data errors. Preferred shares, convertible shares, warrants, investment certificates, participation certificates, units, mutual funds, and foreign-listed shares were excluded from the sample. The other criterion were that stocks with a price lower than one Euro were excluded from the sample. Thus, the results were not driven by extreme price movements in low-priced stocks. The all share index of each individual country were collected because it is a more varied and larger sample than just only the major indices. In the all share index, the liquidity was low but was the most representative measure of how well a stock market of a country had performed. Table III of the Appendix gives an overview of the all share index of each country and the total number of firms involved in each country. The table shows that the sample consists of monthly stock returns of exactly 1100 firms from ten European countries from 2000 to 2014. All returns are in Euros because, since 1 January 1999, the euro has been the de facto currency of all ten countries. The countries with a sample lower than 50 firms were not divided into ten equally weighted portfolios, but rather into five portfolios because of the small number of firms in the sample.
In most cases is the risk free rate the six-months’ LIBOR based on the Euro, and was collected from Federal Reserve Bank (2015b). This rate were chosen because the LIBOR is the most widely used reference rate for short-term interest rates. The six-month period was determined because the
portfolios are also based on their six-months’ past returns. The returns of the 25 size and book-to-market portfolios were collected from Kenneth R. French’s data library, French (2013). The market returns, SMB and HML factors in the European markets were also collected from French’s data library, French (2013). To remain consistent, the returns on the risk free rate, market returns, SMB and HML factors were calculated in the same way as the monthly average returns. Therefore, to be consistent, they are based on their six-months’ future returns and converted to a monthly average rate.
V. Results
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Table IV
Portfolio characteristics of the unrestricted relative strength portfolios
This table reports the average monthly portfolio returns. The sample includes all stocks traded on ten European markets, excluding stocks priced less than €1 at the beginning of the holding period. The momentum portfolios were formed based on their six-months’ past returns and held for six months. The portfolios were adjusted each month. Losers or P1 is the equally weighted portfolio of the 10% of stocks that had the lowest six-months’ returns, and P2 is the equally weighted portfolio of the 10% of stocks with the second lowest returns, and so on. First, the table reports the monthly returns, standard deviations, and t(mean). The returns and standard deviations of the total time period are based on 180 observations; the early recession, pre-crisis, financial crisis, and post-crisis are based on 24, 60, 24, and 72 observations, respectively. Furthermore, t(mean) is the mean divided by the standard error. The standard error is the standard deviation divided by the square root of the number of observations. The t(mean) of the WML portfolio tests whether there are significant momentum profits. The F-statistic tests the equality of the average returns of the ten unrestricted relative strength portfolios. The t-test tests whether the returns of the winners
significantly outperformed the returns of the losers portfolios. ***, **, and * indicate statistical significance at 1%, 5%, and 10%, respectively.
Early recession Pre-crisis period Financial crisis Post-crisis period Total time period
15 Each column shows the results of the ten equally weighted portfolios for the total time period and also for the four sub-periods. The most important finding is that significant momentum profits were found in all four sub-periods and in the total time period because the t(mean) of the WML portfolios were all significant at the 1% level. There were significant momentum profits, so these results were consistent with Landis and Skouras (2012), Griffin et al. (2005) and Rouwenhorst (1998). The WML portfolio of the total time period had an average monthly return of 2.05%. Notably, the WML portfolios of the early recession and financial crisis periods, by far, had the highest monthly average returns, which means that the momentum profits were quite dependent on the crises periods. The high WML returns were due to the high negative returns of the losers portfolios.
In most cases the returns increased from one portfolio to the next. This increase did not occur in the early recession and financial crisis time period. In these two time periods, the returns of the winners portfolio were lower than in some previous portfolios. The results of the F-statistic were mixed between the different time periods. The results are insignificant in the pre-crisis and post-crisis period, which means that there is not enough evidence to infer that the returns of these time periods are different from each other. In the other time periods were the F-statistic significant at the 1% level, which means that the returns differ. The t-test tested whether the returns of the winners portfolio were significantly higher than the returns of the losers portfolio. This test is different from the t(mean) because t(mean) only measure whether the WML portfolios have significant momentum profits. The t-statistic is
16 the ten equally weighted portfolios in each individual sub-period, but only lower in the total time period, which means that only the WML portfolio of the total time period can be used to diversify.
Table V provides an overview of the monthly average returns, the standard deviations, and t(means) of the country-neutral portfolios. This table shows similar findings as Table IV. The most important finding is that the momentum profits are significant in all four sub-periods and the total time period, because the t(mean) of the WML portfolios are significant at the 1% level. The WML portfolio of the total time period had an average monthly return of 1.86%. The results of the F-statistic shows less significant results compared to Table IV . The returns of the ten equally weighted portfolios in the pre-crisis, financial pre-crisis, and post-crisis periods are not significantly different. The results of the t-test were mixed between different time periods. In the early recession, pre-crisis, and total time periods the results are significant at the 1% level, which means that during these periods the returns of the winners outperforms the returns of the losers portfolio. In the post-crisis period, the result is significant at the 10% level. The findings with the standard deviations are similar to the sample of Table IV. The standard deviation of the country-neutral WML portfolio is 3.46% per month.
In most cases, there were small differences between the average returns of Table IV and Table V. The average returns of the WML portfolios showed that, with country-neutral portfolios, the average return was slightly lower from 2.05% to 1.86% per month, because the returns were not influenced anymore by the results of one or more individual countries, which had for example a large part of stock returns within the losers portfolio of the total sample. This result means that the differences between the returns are lower. According to Rouwenhorst (1998), this result suggests that country momentum is not really important for explaining the continuation effect because of the small differences between the WML returns of the unrestricted relative strength portfolios and the country-neutral portfolios. The standard deviations of the WML portfolios show that, with country-neutral portfolios, the risk is lower because the standard deviation decreases from 3.91% to 3.46% percent per month. The result of lower standard deviations has the same reason as with the returns.
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Table V
Portfolio characteristics of the country-neutral portfolios
This table reports the average monthly portfolio returns. The sample includes all stocks traded on ten European markets, excluding stocks priced less than €1 at the beginning of the holding period. The momentum portfolios were formed based on their six-months’ past returns and held for six months. The portfolios were adjusted each month. Losers or P1 is the equally weighted portfolio of the 10% of stocks that had the lowest six-months’ returns, and P2 is the equally weighted portfolio of the 10% of stocks with the second lowest returns, and so on. First, the table reports the monthly returns, standard deviations, and t(mean). The returns and standard deviations of the total time period are based on 180 observations; the early recession, pre-crisis, financial crisis, and post-crisis are based on 24, 60, 24, and 72 observations, respectively. Furthermore, t(mean) is the mean divided by the standard error. The standard error is the standard deviation divided by the square root of the number of observations. The t(mean) of the WML portfolio tests whether there are significant momentum profits. The F-statistic tests the equality of the average returns of the ten country-neutral portfolios. The t-test tests whether the returns of the winners significantly outperformed the returns of the losers portfolios. ***, **, and * indicate statistical significance at 1%, 5%, and 10%, respectively.
Early recession Pre-crisis period Financial crisis Post-crisis period Total time period
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Table VI
Portfolio returns of the total sample compared to a sample without the three largest markets and to a sample without the early recession and financial crisis
This table reports the monthly average portfolio returns. The sample includes all stocks traded on ten European markets, excluding stocks priced less than €1 at the beginning of the holding period. The sample without the three largest markets includes all stocks, excluding stocks from France, Germany, and Italy. The sample without crises includes all stocks, excluding the returns of year 2000, 2001, 2007, and 2008, i.e., the early recession and the financial crisis. The portfolios were formed based on their six-month past returns and held for six months. The portfolios were adjusted each month. Losers or P1 is the equally weighted portfolio of the 10% of stocks that had the lowest six-months’ returns, and P2 is the equally weighted portfolio of the 10% of stocks with the second lowest returns, and so on. First, the table reports the monthly returns, standard deviations, and t(mean). The returns and standard deviations of the normal sample and the sample without the three largest markets are based on 180 months. The sample without the crises are based on 132 months. Furthermore, t(mean) is the mean divided by the standard error. The standard error is the standard deviation divided by the square root of the number of observations. The t(mean) of the WML portfolio tests whether there are significant momentum profits. The F-statistic tests the equality of the average returns of the ten equally weighted portfolios. The t-test tests whether the returns of the winners outperformed the returns of the losers portfolios. ***, **, * indicate statistical significance at 1%, 5%, 10%, respectively.
Normal sample Sample without three largest markets Sample without crises
Return St. dev. t (mean) Return St. dev. t (mean) Return St. dev. t (mean)
19 The return of the WML portfolio without the three largest markets is lower than the normal sample. Therefore, the results are affected by the largest markets. When excluding the early recession and financial crisis the return of the WML portfolio even becomes lower than in the sample without the three largest markets, which means that the returns are more affected by crises than by the three largest markets. Notably, all ten equally weighted portfolios have positive returns in the sample without crises. The standard deviations of the different samples indicate that the standard deviations of the normal sample and the sample without the three largest markets are, in most cases, similar. The standard deviation of the winners portfolios in both samples shows the greatest difference because, the standard deviation of the sample without the three largest markets is almost 1% riskier. The standard deviations of the sample without crises are considerably lower than the normal sample because, when a crisis appears, the markets become more volatile. The results of the F-statistic are no longer significant
without the three largest markets, which means that the returns are not significantly different. The t-test shows that, with a sample without the three largest markets, the returns of the winners portfolio only outperformed the returns of the losers portfolio at a 10% level instead of a 1% level, this is because the differences in returns of both portfolios are smaller than within the normal sample. The F-statistic and t-test of the sample without the crises are also significant at the 1% level.
Table VII shows the summary statistics of the WML portfolios of the total sample and of each individual country. These results are based on 180 months and can help investors make predictions about the future. The returns of the individual countries were between 0.31% and 4.24% per month. In this study, the WML portfolios of France, Germany, and Ireland had the highest returns. The results are inconsistent with Landis and Skouras (2012), Griffin et al. (2005), and Rouwenhorst (1998). In this study, France and Germany are in the top three instead of Belgium and the Netherlands. The standard
20
Table VII
Summary statistics of WML portfolios by country
This table presents the summary statistics of the WML portfolios of the total sample and the ten individual European countries. First, the most important numbers are the mean and standard deviations. Furthermore, this table show the results of the median, maximum, and minimum values. To test for normality, the skewness and kurtosis were calculated. Additionally, the Jarque-Bera test, which tests for normality, was implemented. ***, **, * indicate statistical significance at 1%, 5%, and 10%, respectively.
TOTAL A B F FIN G I IRL NL P S
Mean 0.0186 0.0126 0.0195 0.0240 0.0033 0.0295 0.0144 0.0424 0.0220 0.0231 0.0031 Median 0.0144 0.0133 0.0171 0.0178 0.0120 0.0159 0.0145 0.0067 0.0111 0.0100 0.0061 Max. 0.2526 0.2414 0.5505 0.4853 0.1313 0.5670 0.0909 0.9678 0.5538 0.4115 0.1614 Min. -0.0738 -0.1209 -0.1000 -0.0750 -0.3585 -0.0843 -0.0594 -0.1044 -0.1301 -0.2972 -0.3348 Std. Dev. 0.0346 0.0387 0.0553 0.0552 0.0536 0.0710 0.0239 0.1526 0.0772 0.0730 0.0509 Skewness 3.0967 1.5102 5.1831 4.1187 -3.9787 4.2860 -0.0014 4.3326 4.1378 1.4216 -2.7130 Kurtosis 21.8939 12.8225 49.8646 30.9066 27.2204 27.4646 4.2296 24.1052 25.9593 10.4475 19.7730 Normality 2965*** 792*** 17278*** 6350*** 4875*** 5040*** 11*** 3904*** 4467*** 477*** 2331***
The WML portfolios of Belgium and France show the highest peaks. These two numbers are displayed in Figure 2 of the Appendix, showing the distribution of the monthly average returns of the WML portfolio over the total time period. The figure shows that most returns are between 2% and 4% per month and clearly has a peak and fat tails. To test for normality, the Jarque-Bera test was executed, which show significant results at a 1% level, which implies that the distributions are non-normal. However, since the number of observations is large enough, non-normality is not a problem for executing the F-statistic and t-test.
21
Table VIII
Portfolio characteristics of country-neutral portfolios by country
This table reports the average monthly portfolio returns and standard deviations of the WML portfolios, the winners, and losers
portfolios of the individual countries. The sample includes all stocks traded on ten European markets, excluding stocks priced less than €1 at the beginning of the holding period. The portfolios were formed based on their six-months’ past returns, and held for six months for each individual country. The portfolios were adjusted each month. First, the table reports the monthly returns, standard deviations, and t(mean). The returns and standard deviations are based on 180 observations; t(mean) is the mean divided by the standard error. The standard error is the standard deviation divided by the square root of the number of observations. The t(mean) of the WML portfolio tests whether there are significant momentum profits. The F-statistic tests the equality of the average returns of the ten equally weighted portfolios of each individual country. The t-test tests whether the returns of the winners significantly outperformed the returns of the losers portfolios. ***, **, * indicate statistical significance at 1%, 5%, and 10%, respectively.
WML Winners Losers Equality W>L
Return Std. Dev t (mean) Return Std. Dev t (mean) Return Std. Dev t (mean) F-statistic t-test
22 Because of the short position, Ireland’s losers portfolio had the highest return: -5.29% per month. Spain’s losers portfolio had the lowest return: -0.97% per month. The standard deviations of the winners
portfolios varied between 11.66% and 4.34% per month. The standard deviations of the losers portfolios varied between 20.21% and 5.59% per month. Thus, the losers portfolios have higher standard
deviations than the winners portfolios, which means that the losers portfolios load more towards risk. The fact that losers load more toward risk than the winners portfolios is reinforced by the fact that in eight out of ten countries the losers portfolios have higher standard deviations than the winners portfolios. The only exceptions are Finland and Spain, but these countries had insignificant momentum profits. In this study, Ireland had the highest risk, and Italy had the lowest risk within their WML
portfolios. The WML portfolio of Ireland had the highest risk and also the highest return, but the sample of Ireland was also small which could give a misleading view. On the other hand, the standard deviation of the WML portfolio of Italy was even lower than the standard deviation of the WML portfolio of the total sample because of the low standard deviation in the losers portfolio compared to the total sample. This result is inconsistent with Rouwenhorst (1998) because there the standard deviation of the all stocks sample is lower than the standard deviations of each individual country.
The F-statistic shows that, in six countries, there are significant results at the 1% level. There is little evidence in Italy at the 10% level, which means that there is enough evidence to infer that the returns of these countries are different among the ten relative strength portfolios. Notably, both countries that have insignificant momentum profits also have insignificant differences between their returns, just like the WML portfolio of Austria.
The t-test showed significant results in five countries at the 1% level, in Ireland at the 5% level, and in the Netherlands at the 10% level. In these seven countries the returns of the winners portfolios outperformed the returns of the losers portfolios, which means that the risk-based models better fits the data. Also in this case, the results were insignificant for the stocks of Finland and Spain. The stocks of Austria showed insignificant results on both the F-statistic and t-test, through the lower returns than the other countries especially within the losers portfolio.
23
Figure 3
Cumulative average returns of the WML portfolios by country
The light grey line is the cumulative average return of the WML portfolios of each individual country, and the dark grey line is the cumulative average return of the WML portfolio of the total sample. The y-axis represents the total return, and the x-axis the years.
24
Germany Ireland
Italy the Netherlands
25
Portugal Spain
In the other countries, especially in Ireland and the Netherlands, the financial crisis actually contributed to the momentum profits. The total cumulative average returns of the WML portfolios of Belgium, France, Germany, Ireland, the Netherlands, and Portugal were, in the end, above the cumulative average returns of the WML portfolio of the total sample. The WML portfolio of Belgium showed the least differences compared to the total sample. The cumulative average returns of the WML portfolios of Finland, the Netherlands, Portugal, and Spain showed many more fluctuations than the total sample. When the momentum investment strategy was implemented for the country-neutral portfolios and the total time period, one earned a return of 335.3%. The WML portfolio of Ireland had the highest return with 763.2%, and the WML portfolio of Spain had the lowest with a return of only 55.4%.
The second part of this study does not only examine the risk and return of the portfolios, but also the market, SMB and HML factors. Table IX presents the results of the time-series regressions of 25 market size and book-to-market portfolios. The most important finding of this table is that small stocks outperformed big stocks and high book-to-market stocks had higher returns than low book-to-market stocks, these findings are consistent with Fama and French (1996). The small stocks with low market values are riskier than the big stocks with low market values, but with higher book-to-market values this reversed. This results is inconsistent with Fama and French (1996), which means that bigger stocks becomes more riskier than smaller stocks with higher book-to-market values.
26
Table IX
Three-factor regressions for 25 portfolios formed on size and book-to-market ratios
This table shows the returns and standard deviations of 25 market size and book-to-market portfolios. The portfolios are based on five different size portfolios (smaller, small, middle, big, bigger) and five different book-to-market portfolios (lower, low, medium, high, higher). Furthermore, the table shows, with time-series regressions, the alphas, betas, SMB coefficients, HML coefficients, and the adjusted R-squares of these 25 portfolios. Additionally, t() is the t-statistic and s(e) is the standard error. The sample period is from January 2000 to December 2014 and so counts for 180 months. ***, **, * indicate statistical significance at 1%, 5%, and 10%, respectively.
Book-to-market Equity (BE/ME) Quintiles
Size Low 2 3 4 High Low 2 3 4 High Panel A: Summary Statistics
Returns Standard Deviations
Small -0.0032 0.0024 0.0050 0.0075 0.0097 0.0646 0.0603 0.0578 0.0557 0.0549 2 0.0016 0.0063 0.0084 0.0098 0.0116 0.0651 0.0616 0.0572 0.0592 0.0613 3 0.0040 0.0064 0.0077 0.0094 0.0106 0.0677 0.0606 0.0587 0.0598 0.0638 4 0.0052 0.0078 0.0089 0.0089 0.0086 0.0623 0.0562 0.0571 0.0608 0.0669 Big 0.0027 0.0052 0.0049 0.0068 0.0056 0.0525 0.0527 0.0587 0.0631 0.0734
Panel B: Regressions: Ri - Rf= αi + bi(Rm - Rf) + siSMB + hiHML + ei
27 The findings on the alphas of this study were inconsistent to Fama and French (1996). The differences are that, in this study, the portfolios with lower, low or medium book-to-market values, in most cases, had positive unexplained returns instead of negative returns. All intercepts are around zero. The betas with smaller and small stocks showed that, with higher book-to-market values, the betas are lower. The middle stocks have higher betas than the bigger stocks with low book-to-market values, but there is a reversal. The portfolios with bigger stocks and high book-to-market values have higher betas than the smaller stocks. The findings with the betas are similar to Fama and French (1996). The adjusted R-squared showed an average explanatory power of 0.95, which means that the model almost perfectly explains the variation in the average returns. The intercepts showed significant results in most cases but were insignificant or less significant with the portfolios with small stocks and low book-to-market values and with portfolios with big stocks and high book-to-market values, which means that the intercepts were not significantly different from zero. The beta and SMB coefficients had significant results in all 25 portfolios. The HML coefficients were all significant, except the portfolio of big stocks with low book-to-market values. The results of the regressions showed inconsistent results with the standard deviations and the alphas compared to Fama and French (1996), which means that there could be some differences in the empirical results of other studies.
Table X describes the characteristics of the market portfolio, SMB, and HML factors. These results are on a monthly basis. The HML factor had the highest return and the market factor had the highest risk. Furthermore, this table shows the correlations between these three factors and the associated WML portfolio. Panel B shows the correlations of the Fama and French factors with each other and with the WML portfolio of the unrestricted relative strength portfolios. This correlation matrix indicates that the market and SMB factors have a negative relationship, and the HML factor a slightly positive relationship with the WML portfolio. The relationships of the WML portfolio with the SMB and HML factors are weak but with the market factor is strongly negative. Panel C shows the same results as Panel B but for the country-neutral portfolios. This correlation matrix indicates that all three Fama and French factors have negative relationships with the WML portfolio. The relationships of the WML
28
Table X
Summary statistics of Fama and French factors and associated correlations
Panel A shows the summary statistics of the Fama and French market, size, and book-to-market factors. Mkt – RF is the return on the market portfolio. SMB is Small Minus Big and represents the difference between the return on a small stock portfolio and the return on a big stock portfolio. HML is high minus low and represents the difference between the return on a high book-to-market portfolio and the return on a low book-to-market portfolio. Panel B and Panel C show the correlations between these three factors and with the associated WML portfolio.
Panel A: Summary statistics of Fama and French Factors
Mkt-Rf SMB HML Mean 0.0019 0.0010 0.0055 Median 0.0080 0.0024 0.0050 Maximum 0.0672 0.0180 0.0544 Minimum -0.1455 -0.0219 -0.0283 St. Dev. 0.0308 0.0079 0.0145
Panel B: Correlation matrix unrestricted rel. str. portfolios
WML Mkt -Rf SMB HML WML 1.0000 Mkt-Rf -0.6861 1.0000 SMB -0.1888 0.5078 1.0000 HML 0.0345 0.1607 0.1442 1.0000
Panel C: Correlation matrix country-neutral portfolios
WML Mkt -Rf SMB HML
WML 1.0000
Mkt-Rf -0.7215 1.0000
SMB -0.2234 0.5078 1.0000
HML -0.0288 0.1607 0.1442 1.0000
29
Table XI
Fama and French three-factor regressions of the ten equally weighted portfolios of the unrestricted relative strength portfolios
Alpha is the intercept value, and beta represents the systematic risk. SMB is Small Minus Big and represents the difference between the return on a small stock portfolio and the return on a big stock portfolio. HML is high minus low and represents the difference between the return on a high book-to-market portfolio and the return on a low book-to-book-to-market portfolio. The table shows the results of the regressions with the unrestricted relative strength portfolios. Losers or P1 is the equally weighted portfolio of the 10% of stocks that had the lowest six-months’ returns, and P2 is the equally weighted portfolio of the 10% of stocks with the second lowest returns, and so on. The regressions were made for all ten equally weighed portfolios and the WML portfolio. The table shows the intercept value, beta, SMB, and HML coefficients. The t-value is the t-statistic. The F-statistic tests whether the beta of the winners and losers portfolios are equal. The t-test tests whether the betas, SMB and HML coefficients of the losers portfolio are significantly higher than the winners portfolio. ***, **, * indicate statistical significance at 1%, 5%, and 10%, respectively.
Alpha t-value Beta t-value SMB t-value HML t-value Losers -0.0368 -14.2629*** 2.3573 25.8309*** -0.3775 -1.0684 -0.2511 -1.4900* P2 -0.0265 -13.0070*** 1.6462 22.8366*** -0.0491 -0.1761 0.1255 0.9431 P3 -0.0238 -11.8999*** 1.5560 22.0258*** -0.1444 -0.5279 0.2171 1.6646** P4 -0.0217 -12.2039*** 1.3670 21.6855*** 0.1634 0.6694 0.2395 2.0578** P5 -0.0200 -11.7766*** 1.2542 20.8339*** 0.1383 0.5936 0.2770 2.4921*** P6 -0.0203 -11.5260*** 1.2576 20.1576*** 0.2327 0.9634 0.3525 3.0601*** P7 -0.0186 -11.1484*** 1.1655 19.7132*** 0.3049 1.3319* 0.3388 3.1033*** P8 -0.0177 -11.3782*** 1.1178 20.3298*** 0.3211 1.5083* 0.2382 2.3466** P9 -0.0174 -10.4088*** 1.1462 19.3769*** 0.4451 1.9434** 0.1467 1.3434* Winners -0.0173 -9.9016*** 1.3289 21.4811*** 0.6248 2.6085*** 0.1131 0.9900 WML 0.0195 8.9469*** -1.0284 -13.3528*** 1.0023 3.3613*** 0.3641 2.5607*** F-statistic 20.0334*** t-test W<L 5.6995*** -2.2735** -6.7137***
Regarding the country-neutral portfolios, the losers had an SMB coefficient of -0.2437, and the winners portfolio of 0.5667. In both Table XI and Table XII, within the losers portfolios, the big stocks
30
Table XII
Fama and French three-factor regressions of the ten equally weighted portfolios of the country-neutral portfolios
Alpha is the intercept value, and beta represents the systematic risk. SMB is Small Minus Big and represents the difference between the return on a small stock portfolio and the return on a big stock portfolio. HML is high minus low and represents the difference between the return on a high book-to-market portfolio and the return on a low book-to-book-to-market portfolio. The table shows the results of the regressions with the country-neutral portfolios. Losers or P1 is the equally weighted portfolio of the 10% of stocks that had the lowest six-months’ returns, and P2 is the equally weighted portfolio of the 10% of stocks with the second lowest returns, and so on. The regressions were made for all ten equally weighed portfolios and the WML portfolio. The table shows the intercept value, beta, SMB, and HML coefficients. The t-value is the t-statistic. The F-statistic tests whether the beta of the winners and losers portfolios are equal. The t-test tests whether the betas, SMB and HML coefficients of the losers portfolio are significantly higher than the winners portfolio. ***, **, * indicate statistical significance at 1%, 5%, and 10%, respectively.
Alpha t-value Beta t-value SMB t-value HML t-value Losers -0.0361 -14.3966*** 2.2623 25.5205*** -0.2437 -0.7101 -0.0625 -0.3818 P2 -0.0270 -12.9119*** 1.7360 23.4500*** -0.1314 -0.4585 0.0626 0.4580 P3 -0.0258 -10.5049*** 1.7632 20.3006*** -0.1155 -0.3435 0.2466 1.5379* P4 -0.0216 -12.2157*** 1.3494 21.5751*** 0.0393 0.1621 0.2537 2.1972** P5 -0.0206 -11.9183*** 1.3014 21.3238*** 0.2111 0.8932 0.2557 2.2692** P6 -0.0193 -12.1925*** 1.1610 20.7468*** 0.2709 1.2503 0.3153 3.0518*** P7 -0.0185 -11.3132*** 1.1617 20.0471*** 0.2867 1.2780 0.2500 2.3363** P8 -0.0177 -11.2809*** 1.1218 20.2443*** 0.3379 1.5747* 0.1941 1.8970** P9 -0.0174 -10.4333*** 1.1633 19.7411*** 0.3860 1.6916** 0.2056 1.8899** Winners -0.0175 -9.8723*** 1.3335 21.3113*** 0.5667 2.3391** 0.1216 1.0526 WML 0.0186 9.9973*** -0.9288 -14.1015*** 0.8104 3.1780*** 0.1841 1.5138* F-statistic 12.2425*** t-test W<L 4.8145*** -2.1753** -6.8358***
31 smaller stocks. Thus, in this study, the smallest firms are within the winners portfolios and the biggest firms are within the losers portfolios. Table XI and Table XII show positive HML coefficients, except in the losers portfolio. The losers portfolio in the unrestricted relative strength portfolios sample shows an HML coefficient of -0.2511, and in the winners portfolio of 0.1131. Regarding the country-neutral portfolios, the HML coefficient of the losers portfolio is -0.0625, and that of the winners portfolio is 0.1216. In this case, only the HML coefficient of P2 of the country-neutral portfolios is lower than the winners portfolio. In the other cases, the HML coefficients of the winners and losers portfolios are lower than the other portfolios, which is consistent with the empirical results of Table II. In both Table XI and Table XII within the losers portfolio, the growth stocks outperformed the value stocks. These findings are inconsistent with Fama and French (1996) and Jegadeesh and Titman (2001b), this is because the fact that within Table X not only the lowest book-to-market values has negative values, but also the portfolios with low book-to-market values. To test the results of this study with the empirical results, the F-statistic test and t-test were executed. The F-statistic tests whether the betas of the winners are equal to the betas of the losers portfolios. Both Table XI and Table XII show significance at the 1% level, which means that the betas of the winners and losers portfolios are unequal. The t-test test whether the Fama and French coefficients of the losers portfolios outperformed the coefficients of the winners portfolios. The results of the t-tests show that the betas of the losers portfolios are significantly higher than the betas of the winners portfolios at a 1% level, which is inconsistent with Jegadeesh and Titman (2001b) and
Rouwenhorst (1998), because both their betas are almost the same. Furthermore, the betas are further away from unity than in Rouwenhorst (1998), which means that the equally weighted portfolios of this study are more volatile to the market than in Rouwenhorst (1998). These results of the betas can be clarified by the following facts; the monthly average return on the market is low compared to the return on the WML portfolios, the losers portfolios are riskier than the winners portfolios, and the WML portfolio and the market factor have a strongly negative relationship. The results of this study’s t-tests show that the SMB coefficients of the losers are significantly lower than the SMB coefficients of the winners portfolios at the 5% level. The results of the t-tests show that at a 1% level the HML coefficients of the losers are significantly lower than the HML coefficients of the winners portfolios. The results of the t-test can be compared with the empirical results in Table II. It appears that the betas are not equal, and the losers portfolio has a significantly higher beta than the winners portfolio. The results of the SMB and HML coefficients are reversed compared to the empirical results.
32
Table XIII
Returns adjusted with market, size, and book-to-market effects for the unrestricted relative strength portfolios and country-neutral portfolios
The returns of the unrestricted relative strength portfolios and country-neutral portfolios are used in this table. This table presents the results from the regressions of the monthly returns of the losers, winners, and WML portfolios in excess of the risk free rate. The alpha is the intercept of the regression. The beta is measures the volatility of a portfolio compared to the market, while s is Small Minus Big and
represents the difference between the return on a small stock portfolio and the return on a big stock portfolio. Furthermore, h is high minus low and represents the difference between the return on a high book-to-market portfolio and the return on a low book-to-market portfolio, and t-value is the t-statistic and measures the significance of the coefficients. The adjusted R-square measures whether the model fits the data. ***, **, * indicate statistical significance at 1%, 5%, and 10%, respectively.
Portfolio α t(α) β t(β) s t(s) h t(h) R2
Panel A.1: Unrestricted Relative Strength Portfolios
Losers -0.0340 -5.8574*** 1.0000
Winners -0.0135 -3.6842*** 1.0000
WML 0.0205 7.0083*** 1.0000
Panel A.2: Returns adjusted with Market, Size, and Book-to-market effects
Losers -0.0368 -14.2629*** 2.3573 25.8309*** -0.3775 -1.0684 -0.2511 -1.4900* 0.8273 Winners -0.0173 -9.9016*** 1.3289 21.4811*** 0.6248 2.6085*** 0.1131 0.9900 0.8013 WML 0.0195 8.9469*** -1.0284 -13.3528*** 1.0023 3.3613*** 0.3641 2.5607*** 0.5147
Panel B.1: Country-neutral Portfolios
Losers -0.0323 -5.7310*** 1.0000
Winners -0.0137 -3.7233*** 1.0000
WML 0.0186 7.2076*** 1.0000
Panel B.2: Returns adjusted with Market, Size, and Book-to-market effects
Losers -0.0361 -14.3966*** 2.2623 25.5205*** -0.2437 -0.7101 -0.0625 -0.3818 0.8271 Winners -0.0175 -9.8723*** 1.3335 21.3113*** 0.5667 2.3391** 0.1216 1.0526 0.7969 WML 0.0186 9.9973*** -0.9288 -14.1015*** 0.8104 3.1780*** 0.1841 1.5138* 0.5463
33 losers, winners, and WML portfolios in panel A.2 and panel B.2 are lower than the alphas in panel A.1 and panel B.1, except the WML portfolio of the country-neutral portfolios that is equal to panel B.1. This result shows that the WML returns are not higher when adjusted with these three effects, which is inconsistent with Fama and French (1996) and Grundy and Martin (2001). The market effects of both WML portfolios are significantly negative, which means that, when measuring for the market effect, the WML returns are higher, which means there is a significant market effect. According to Rouwenhorst (1998), there is no market effect because the betas of the winners and losers portfolios are almost the same. In this study, the betas are significantly different and of the losers portfolios higher than the winners portfolios, which means that there is a significant market effect. The SMB and HML coefficients of both WML portfolios are significantly positive at the 1% level, except the HML coefficient of the country-neutral portfolios at the 10% level. Because these coefficients are positive, the returns adjusted with these effects are not higher but lower, which means that there are no significant size or book-to-market effects. The SMB and HML coefficient are significantly positive within the WML portfolio because the SMB and HML coefficients of the winners outperformed the SMB and HML coefficients of the losers portfolios according to Table XI and Table XII. These results show that the WML returns are higher when adjusted with the market effect and lower by the size and book-to-market effects.
VI. Conclusion
This paper shows significant momentum profits in a sample of ten European countries during the 2000 to 2014 period. An internationally diversified WML portfolio based on past six-months’ returns has a return of 2.05% per month. When the portfolios are based on country-neutral portfolios there are significant momentum profits of 1.86% per month, which is consistent with Rouwenhorst (1998) and Nijman et al. (2004) because momentum profits are not driven by country momentum but more by individual stock effects. The momentum profits are affected by the three largest markets and also by crises. Regarding the sample without the crises, the returns of the ten equally weighted portfolios were all positive, but the return of the WML portfolio was lower. The losers portfolios were riskier than the winners portfolios. The standard deviation of a European WML portfolio was, on average, about 4% per month, which is lower than the volatility of the ten equally weighted portfolios. This result indicates that an international momentum portfolio can be used to diversify.
34 France, Germany, Ireland, Italy, the Netherlands, and Portugal had significant momentum profits, while the WML portfolios of Finland and Spain did not. In this model, the returns of the winners outperform the returns of the losers portfolios, which means that the results of this study are in accordance with the risk-based models. In eight countries, the losers portfolios were riskier than the winners portfolios; also in this case, the WML portfolios of Finland and Spain were the exceptions. Only in Italy were the standard deviation of the WML portfolio lower than the standard deviation of the total sample, which implies that, in the other countries, the standard deviations are country-specific and can be diversified away in the total sample.
The cumulative average returns were in an upward trend toward time, which is consistent with Griffin et al. (2005). In most countries, except the WML portfolio of Finland and Spain, the cumulative average returns were in an upward trend. The momentum profits in Finland and Spain were negatively affected by the financial crisis. In the end, the total cumulative average returns of Belgium, France, Germany, Ireland, the Netherlands, and Portugal were above the cumulative average returns of the total sample.
The 25 European size and book-to-market portfolios show small stocks outperform big stocks and high book-to-market stocks have higher returns than low book-to-market stocks. The results of the Fama and French three-factor model are as follows. The betas of the winners and losers portfolios are unequal, and the betas of the losers portfolios are significantly higher than the betas of the winners portfolios. The SMB and HML coefficients of the losers are significantly lower than the SMB and HML coefficients of the winners portfolios. The results of these three factors are inconsistent with the empirical results of comparable studies, but because the results of the HML coefficients are the other way around the model can explain the average returns based on the past couple of months’ returns according to Fama and French (1996). The results indicate that the winners load more to risk than the losers portfolio because they are more sensitive to the SMB and HML factors, this is inconsistent with Fama and French (1996). The output of the regressions show that momentum profits are not higher when adjusted for these three effects. Both WML returns are only significantly higher when adjusted with the market effect and lower when adjusted with the size and book-to-market effects.
35 realized the highest profits especially during the financial crisis, which is inconsistent with other studies. Furthermore, the samples of Ireland and Portugal were small, therefore extremely influenced by outliers, which made them not a good comparison to other countries. The Fama and French factors included more countries compared to this study, which caused that the results were not a good comparison to the empirical results. The results suggest that the momentum investment strategy is a profitable strategy for investors. However, in this study, the number of positions and the corresponding transaction costs are not considered.
36
References
Barberis, N., Shleifer, A., & Vishny, R. (1998). A model of investor sentiment. Journal of financial economics, 49(3), 307-343.
Chui, A. C., Wei, K. C., & Titman, S. (2000). Momentum, legal systems and ownership structure: An analysis of Asian stock markets. Sheridan, Momentum, Legal Systems and Ownership Structure: An Analysis of Asian Stock Markets (December 2000).
Daniel, K., Hirshleifer, D., & Subrahmanyam, A. (1998). Investor psychology and security market under‐and overreactions. The Journal of Finance, 53(6), 1839-1885.
De Bondt, W. F., & Thaler, R. (1985). Does the stock market overreact?. The Journal of Finance, 40(3), 793-805.
Fama, E. F., & French, K. R. (1996). Multifactor explanations of asset pricing anomalies. The Journal of Finance, 51(1), 55-84.
Federal Reserve Bank of St. Louis (2015a). 1-Month London Interbank Offered Rate (LIBOR), based on Euro. Retrieved from https://research.stlouisfed.org/fred2/series/EUR1MTD156N#
Federal Reserve Bank of St. Louis (2015b). 6-Month London Interbank Offered Rate (LIBOR), based on Euro. Retrieved from https://research.stlouisfed.org/fred2/series/EUR6MTD156N#
French, K. R. (2013). Data library. Tuck School of Business at Dartmouth faculty web profile for Kenneth R.
French, available at http://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library. html.
Graham, B., Dodd, D. L. F., & Cottle, S. (1934). Security analysis (pp. 44-45). New York: McGraw-Hill. Griffin, J. M., Ji, X., & Martin, J. S. (2005). Global momentum strategies. The Journal of Portfolio
Management, 31(2), 23-39.
Grundy, B. D., & Martin, J. S. (2001). Understanding the nature of the risks and the source of the rewards to momentum investing. Review of Financial Studies, 14(1), 29-78.
Hameed, A., & Kusnadi, Y. (2002). Momentum strategies: Evidence from Pacific Basin stock markets. Journal of Financial Research, 25(3), 383-397.
Jegadeesh, N. (1990). Evidence of predictable behavior of security returns. Journal of Finance, 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. (2001a). Momentum.Annu. Rev. Financ. Econ., 3(1), 493-509
Jegadeesh, N., & Titman, S. (2001b). Profitability of momentum strategies: An evaluation of alternative explanations. The Journal of Finance, 56(2), 699-720.
