(Master’s Thesis in MSc Finance) M. Baˇst´aka,∗
aUniversity of Groningen, Faculty of Economics and Business
Abstract
In the thesis, I prove the presence of a short-term reversal and of a medium run continuation in the stock returns in 6 European countries during the period 1993–2012. The long-term reversal was not confirmed during the testing period. I also found that series of negative monthly returns during the one-year period are penalized by lower returns in the following month. However, this consistency does not contribute to the return momentum in a persuasive way. On the other hand, a winner consistency premium is statistically insignificant. Finally, I found a strong seasonality pattern as the short-term reversal is significantly stronger in January and momentum even disappear in this month. I control for risk factors (proxied by size, book-to-market), country and industry influences by means of hedge returns. A method used is Fama-MacBeth type of monthly regressions with controls for all phenomena mentioned above.
Keywords: short-term reversal, momentum, long-term reversal, return consistency, Europe JEL classification:G11, G12, G14
II would like to thank my supervisor, Viola Angelini, for numerous discussions and helpful comments during the thesis writing. ∗Student number: 2089750
Email address: matej.bastak@gmail.com (M. Baˇst´ak)
1. Introduction
Many investors rely on a historical performance of stocks when they construct their portfolios. How-ever, the market efficiency suggests not doing so. The theory states that all information is immediately and correctly incorporated in stock prices. Nevertheless, empirical research has identified three main pre-dictability patterns in stock returns. Short-term reversal is the first among them. It was shown that prices tend to revert during the period of 1 day to 1 month. Stocks with high past returns (winners) usually exhibit significantly lower return that stocks with poor performance (losers) during this short time period. Second, there is a return continuation during the medium time horizon also called momentum which is observed in a way that portfolio consisting of winner stocks outperform portfolio of losers. This phenomenon is mainly determined by past 3 months to 1 year of historical returns. Lastly, returns revert again over the long horizon (usually 2-5 years) which I refer to as long-term reversal.1Another option to predict future returns from the historical performance is to look at the consistency of past returns. My main goal is to test whether these phenomena can be confirmed in Europe during the period 1990–2012.
There are 4 contributions my thesis provides. First, I test all three previously stated phenomena in one single regression which gives us better understanding of the possible link between them. Most of empirical studies focus on the short-term reversal separately from momentum and the long-term reversal. Second, I also include a control for an explanation which has a potential to explain, at least partly, both reversals and momentum — consistency effect. In theory, a stock is considered consistent winner (loser) if it earns steady positive (negative) returns over time and investors consider this return consistency a good predictor for future returns. Up to these days, only very little evidence can be found about the consistency effect in the literature. Third, using European equity markets data also adds some value as no similar study (up to my knowledge) was performed outside the U.S. market. Finally, I use the most recent data available so I can test whether these deviations from efficient markets where ruled out by rational investors during the recent years. This time period also includes the recent financial crisis which might possibly have an influence on investors’ behaviour.
I use a method similar to that ofFama and MacBeth(1973). I run a cross-section regression in which I combine explanatory variables which should capture the short-term reversal, momentum, the long-term reversal, and the consistency effect. For the short-term reversal it is simply a past month stock return. For momentum it is a buy-and-hold return over the last one year, while excluding the most recent month to make it orthogonal to the one-month effect. The long-term reversal is represented in the regression by buy-and-hold returns during the period of past three years without the most recent year. Finally, I include dummy variables indicating if a stock is consistent winner, consistent loser or just non-consistent performer.2 In addition, I use variables for negative past returns (otherwise they are zero) to test whether losers or winners contributes more to the reversals and momentum. By construction, insignificance of these variables indicates the same contribution by both stocks with positive past returns and those with negative
1For evidence on the short-term reversal see for exampleJegadeesh(1990),Lehmann(1990), andSubrahmanyam(2005).
Evi-dence on momentum includes works ofJegadeesh and Titman(1993),Rouwenhorst(1998), andGriffin et al.(2005). Finally, see
DeBondt and Thaler(1985),Richards(1997) for evidence on the long-term reversal effect.
2I consider a stock to be a consistent loser if it records negative return during the past month. A dummy for consistent winners
past returns. To avoid risk factor influences, as well as country and industry effects, I use hedge returns with respect to size, book-to-market, country, and industry as my dependent variable.
My main results are that stocks with poor performance during the previous one month have a strong tendency to outperform other stocks on the market during the following month. On the other hand, past month winners underperform during the following month. I find just opposite results for the one-year horizon. Losers keep their momentum and, on average, earn lower returns that an average stock. Winners also continue to have exceptional returns. The results show that one-year momentum is not reverted back during the following 2-year period. Regarding the consistency effect, I find that if a stock exhibits consistent negative performance in term of steady negative results, it is penalized by investors and earns less than non-consistent performers. I confirm the consistency effect for past one-month horizon and also for the most recent year period. The winner consistency is not really significant during one- and three-year periods.
Besides the previously stated results, I find that nor winners neither losers exclusively stand behind the short-term reversal and momentum. It seems that winners and losers contribute to these two effects by the same portion also during the one-year period (except January). I also confirm a strong seasonal pattern for January when the short-term reversal is the strongest and the momentum strategy is wiped-out by extreme losers’ negative performance.
I do not intend to search for possible explanations of the consistency effect. Before creating any theo-retical background, we need to find enough evidence about the presence and magnitude of the consistency effect. We also need to test for economic significance of the trading strategies based on consistent perfor-mances. Such strategies would imply a short-selling of consistent winners and buying consistent losers over past one-month period, going long in one-year consistent winners and going short in one-year consistent losers, and finally switch back to long position in consistent losers and short position in consistent winners for following months.
The rest of the thesis continues as follows. Section 2 contains an overview of the literature on the predicting of stock returns from historical returns and on the effect of winner and loser consistency. I describe the methodology used in the analysis inSection 3, while I describe the dataset inSection 4. Next, in
Section 5, main results together with some robustness testing can be found. Before concluding inSection 7, I test the economic significance inSection 6.
2. Literature review
2.1. Short-term reversal
The short-term reversal is characterized by negative serial-correlation in stock returns usually find to appear during the period of 1 day to 1 month. Jegadeesh (1990) finds statistically significant short-term returns reversal in monthly stock returns. He uses Center for Research in Security Prices (CRSP) data from the period 1929–1982 and, to test the significance of one month reversal, he employs a method ofFama and MacBeth(1973).3 The results show negative and statistically significant relation between one month past returns and current returns. The economic significance is measured with respect to trading costs of 0.5% per transaction. Although it was a priori questionable due to high trading costs as trading is realised relatively often, the trading strategy earns on average 20.8% of abnormal returns per year. The author tries to find an explanation by testing for 3 different possible reasons: (1) size-based risk; (2) time-varying market risk (beta); and (3) bid-ask spread and thin trading. According to the results, none of these reasons explains the profitability of the trading strategy based on buying past one month losers and on short-selling prior month winners. An extension of the work ofJegadeesh(1990) is provided bySubrahmanyam(2005). First, the period of data used includes successive years to the prior study (1988–1998). Secondly, also the bid-ask bounce effect is controlled for by using mid-point returns (not returns based on the closing prices). The author tries to use beta, book-to-market ratio, size, and longer lags of returns as controls without change in the significance of the reversal effect.
Many other studies find the short term reversal effect in the stock returns. The main interest has gradually moved from testing the presence of this effect to assessing the profitability of the strategy based on the return reversal over the short period.Lehmann(1990) investigates the one week stock return reversal in U.S. data from 1962 to 1986. However, using weekly stock returns can be significantly affected by bid-ask spread. As the author notes, “Eighty per cent of the price movements over successive transactions are between the bid and asked prices, giving the appearance of pronounced negative serial correlation even in daily returns.” (Lehmann,1990, pg. 9) To avoid the influence of successive transactions within the bid-ask range, he uses only 4 trading day returns (omitting Tuesday return and computing a return from Wednesday to Monday). Although this is rather conservative solution, the strategy betting on the reversal still shows high positive returns of 23.74% even when accounting for 0.1% transaction cost4over a half-year period.
More recent study byAvramov(2006) shows no evidence of an economic profitability of the contrarian strategy — the strategy based on buying losers and selling winners. After controlling for the bid-ask bounce effect by excluding the last day of the trading week (dropping Tuesday to Wednesday return in their case), profits are overwhelmed by transaction costs which are computed as in the study ofKeim and Madhavan
(1997). The main reason why the transaction costs are too high is the very high turnover caused by rebal-ancing of the winners and losers portfolios. To cope with this,de Groot et al.(2012) propose an alternative trading strategy. The strategy is based on the less frequent rebalancing when an investor keeps stocks previ-ously ranked as extreme losers (bottom stocks) until they are within the lower 50% of loser stocks ranked on past return. The very bottom stocks among losers are bought after these stocks move to the upper 50% and
3This method involves computing monthly cross-section regression estimates and then calculating time-series averages of these
estimates. I describe this method closer inSection 3.
4Lehmann(1990) considers 6 different levels of the transaction cost — 0.05, 0.1, 0.2, 0.3, 0.4, and 1 per cent. The strategy
are sold. Of course, it works in the just opposite way with winner stocks. In addition, the authors find that trading costs are notably lower for companies with large market capitalization.5 Putting large cap stocks together with the new trading strategy, they find the net profit of the short-term reversal strategy to be 30-50 basis points per week.
Although limited in number, very similar results are found in other markets over the world. For example
Chang et al.(1995) find abnormal profits of short-term contrarian strategies in the Tokyo Stock Exchange during the period 1975–1991. Lee et al.(2003) document a negative serial correlation in weekly returns in Australia but without any economic significance after including transaction costs. Hameed and Ting
(2000) find that the stock prices are indeed predictable based on prior week returns also in the Malaysian stock market andKang et al.(2002) find small but statistically significant abnormal profit of the short-term contrarian strategies in the Chinese stock market.
Finally, I look at possible reasons of the profitability of the short-term contrarian strategies. In general, two main opinion streams emerge. One promotes behavioural reasons (overreaction) as the phenomenon explaining most of the profitability, the second group believes in the market microstructure explanation (namely bid-ask bounce and dealers’ inventory effects). However, an overreaction is present in almost every study6only the portion of the explained causality of the short-term negative correlation differs across the studies. By definition, an overreaction is caused by market imperfection when investors first overreact to news (or sudden large price declines)7and then continuously correct their overshooting which causes the reversal effect.
Bid-ask bounce — promoted as the reason of short-term negative serial correlation by Conrad et al.
(1997),Ball et al.(1995), and other authors — means that the negative autocorrelation in the short-term returns is caused by the difference between bid and ask prices.Ball et al.(1995) document that price of the extreme losers portfolio (bottom 10%) closes at a bid 54.7% of the time at the date of portfolio creation. After one week, the frequencies of closing at bid and ask are almost the same (around 37%). This change in closing prices from mainly bid prices to approximately equal proportion of ask and bid prices causes an illusion of correcting the overreaction by the market participants. In addition to the bid-ask bounce,
Jegadeesh and Titman(1995b) explore an inventory-based microstructure model. The authors theorize that when dealers’ inventories are large, dealers try to attract more buyers by setting the midpoints of the bid and ask quotes below its intrinsic values. Jegadeesh and Titman conclude that, “most of the short-horizon return reversals can be explained by the way dealers set bid and ask prices, taking into account their inventory imbalances.” (Jegadeesh and Titman, 1995b, pg. 130) Another study by these authors (Jegadeesh and Titman, 1995a) tests a significance of lead-lag structure in stocks. By definition, the lead-lag occurrence arises because of differences in price adjustments based on the common factors (e.g. macroeconomic news). They find that small cap stocks react with delay comparing to the large cap ones. However, evidence suggests that this effect contributes only weakly to the contrarian profits and that much of this profit is caused by an overreaction.
5They use estimates by Nomura Securities — one of world’s largest stock brokers.
6An example of no overreaction is a work byConrad et al.(1997) who find that all profitability of NASDAQ firms emanates
from the bid-ask bounce.
7For event studies focused on the confirmation of such an overreaction after price declines see for exampleCox and Peterson
2.2. Momentum effect
The phenomenon of momentum is based on continuation of some trends over time. In the field of finance, momentum is characterized by continuance of stock returns mainly during the period of 3 months to 1 year. Jegadeesh and Titman (1993) are among the first who studied the momentum effect in stock
returns. They use CRSP data from the period 1965–1989. Testing 32 relative strength trading strategies (buying past winners and selling past losers) differing in number of ex post months of returns and following monthly returns, the one which picks stocks based on 12 months prior returns and keeps them for 3 months earns the highest return of 1.49% per month when there is a 1-week lag between the formation period and the holding period. Later, many scholars find momentum strategies profitable not only in the U.S but also in many other markets over the globe. I provide just a limited sample of them here. In terms ofRouwenhorst
(1998), during the period 1980–1995, 12 European equity markets exhibit medium-term return continuation even after controlling for country and size effects. In addition, he finds that European markets tend to shows very similar results as U.S. market does.Griffin et al.(2005) study the price momentum effect in 40
countries. They find that, “U.S., African countries, all six American countries, 10 of 14 Asian countries, and 14 of 17 European countries display positive price momentum profits over the period [from February 1976 for U.S., from February 1987 for many other countries].” (Griffin et al.,2005, pg. 25) Moreover, Asian countries exhibit the smallest profits of all countries. Similar results are presented byHameed and Kusnadi(2002) where authors conclude that 6 Asian-Pacific markets8do not possess the magnitude of U.S. momentum effect which leads to no abnormal returns after controlling for size, turnover and country effects. Most recently,Fama and French(2012) discover the return momentum in many countries except Japan.9
Even after vast evidence in favour of momentum effect existence, the main question remains unan-swered: what is the reason behind the profitability of the strategies following simple momentum trading rule? As Fama and French (1996;1998) note, the momentum effect is the only anomaly which cannot be sufficiently explained (until nowadays) by risk factors measured by the market beta factor, size and book-to-market ratio. Main explanations proposed by academics are: behavioural theory (e.g.Barberis et al.,1998;
Daniel et al.,1998,2001); trading volume (Lee and Swaminathan,2000); or different characteristics across countries (Chui et al.,2010).
The model of investor sentiment by Barberis et al. (1998) assumes that representativeness10 causes an overreaction to a series of successive good (or bad) news as they falsely expect that the probability of continuation is higher due to the previous return history. In addition, conservatism is assumed to be behind the underreaction to news as people are conservative in their nature and react only slowly to publicly announced news. On the other hand,Daniel et al.(1998) explain the overreaction in terms of the long-term reversal by overconfidence of individual investors. The authors presume that the underreaction is caused by a biased self-attribution and therefore individual investors assign lower importance to publicly available news. Hong and Stein(1999) employ a different approach. Instead of looking at cognitive biases of an individual investor, they assume a presence of two types of investors. While “newswatchers” cause too slow adjustment of prices based on new information, “momentum traders” bring an overreaction into the model as they can use only very simple momentum strategies.
8These six countries are Hong Kong, Malaysia, Singapore, South Korea, Taiwan, and Thailand. 9The authors take look at the regions of North America, Europe, Japan, and Asia Pacific.
10According toBarberis et al.(1998, pg. 308), “[Representativeness is] the tendency of experimental subjects to view events as
Another reason of the momentum effect — trading volume — is proposed byLee and Swaminathan
(2000). They argue that past trading volume has an ability to predict both the magnitude and persistence of price momentum. Besides others, the authors perform a test similar to that ofJegadeesh and Titman(1993) but with turnover volume analysis by additional sorting on trading volume. They find, even after controlling for risk by considering Fama-French three factor model, that price momentum is higher among high volume stocks (taking the next 12 months into account) and also that low volume stocks generally outperform high volume stocks when momentum is controlled out.
A very interesting study byChui et al.(2010) reveals a connection between different cultural influences
measured by the cultural dimensions ofHofstede(2001). They assume that one of these cultural dimensions, individualism, is directly correlated with the overreaction in the market (due to overconfidence and an attribution bias). Besides other factors used in the analysis, they find that “individualism is positively associated with trading volume and volatility, as well as to the magnitude of momentum profits.” (Chui et al.,2010, pg. 361)
Although not finding the real underlying reason why momentum appears, Moskowitz and Grinblatt
(1999) find that industries portfolios exhibit strong momentum which preserve even when controlling for size, book-to-market equity ratio, individual stock momentum, the cross-sectional dispersion in mean re-turns, and potential microstructure influences. Nevertheless, there are two differences between individual stock momentum and industry momentum: (1) industry momentum is driven mainly by the long side (win-ners) while individual momentum by the short side (losers); and (2) industry momentum tends to be the strongest during the very short time (1-month horizon).
2.3. Long-term reversal
The long-term reversal is defined as a return reversal over 2 to 5 years which means that stocks with highly positive past performance (winners) underperform the market. On the other hand, losing stocks outperform both winners and the market during this period. Pioneering work by DeBondt and Thaler
(1985) documents a long-time return reversal in U.S. stocks returns during the period 1926–1982 and find substantial abnormal returns of the trading strategies based on the reversal. The methodology is as follows. They compute cumulative excess returns (CR’s) during non-overlapping 3 years period (and other different periods up to 5 years) and then calculate cumulative average residual returns (CAR’s) during following 3 years per portfolios which are created based on previously computed CR — bottom portfolios with the highest negative returns (losers) and top portfolios with highest positive returns (winners) are of highest interest here. Finally, CAR’s are averaged over all non-overlapping periods (denoted as ACAR) and then difference between ACAR’s of losers and winners portfolios is found. The highest abnormal return reported is 24.6% during 3 years. There are also 2 additional findings which draw attention. First, the profitability of zero cost portfolios (losers minus winners) is driven primarily by losers. Therefore we can assume that investors overreact mainly in downward movements so prices correct themselves in greater magnitude. Second, January profits drive most of the total profits of zero cost portfolios which implies high seasonality of the strategy. The authors attribute the results to overreaction by investors.
Richards(1997) documents a significant long-term reversal effect in 16 return indices of countries all
over the globe11during the period 1969–1995. He modifies the methodology ofDeBondt and Thaler(1985)
11The countries are: Australia, Austria, Canada, Denmark, France, Germany, Hong Kong, Italy, Japan, the Netherlands, Norway,
in few ways — buy-and-hold returns are used rather than averages of monthly residuals returns; time pe-riods overlap to increase the number of observations; and he simulates the critical values to assess the statistical significance of the return on the contrarian portfolio (in contrast with theoretically derived critical values).Schiereck et al.(1999) test the profitability of long-term contrarian strategies in the Frankfurt stock exchange during the years 1961–1991. Although the functioning of the German main stock exchange is different in many aspects, the authors find very similar results as are found in U.S. financial markets. The conclusions are that the long-term reversal is weaker during the first half of the testing period and that, including relatively low transaction costs, the strategies outperform passive strategies by modest amount.
Conrad and Kaul(1993) try to disprove the results ofDeBondt and Thaler(1985). The main concerns are about the way the profitability of the strategy is assessed. The authors argue that bid-ask errors, nonsyn-chronous trading, and/or price discreteness cause upward bias in portfolio returns. Moreover, this problem is magnified due to computing cumulative returns over longer time period (i.e. 3 to 5 years) resulting in cumulating also the bias which can account for seemingly significant profits.Conrad and Kaul(1993) pro-pose computing a buy-and-hold return as a solution to this problem.12 Apart from this,Conrad and Kaul
(1993) also find that January effect is caused by a low price phenomenon and not by the overreaction as was previously thought.
In addition to technical issues of the model used byDeBondt and Thaler(1985), there are arguments against the fundamental reasons why the the long-term reversal is found. For example Ball and Kothari
(1989) reject the hypothesis of overreaction by markets. They argue that this deviation from market
effi-ciency is caused by higher risk of the extreme portfolios (both winners and losers).Ball and Kothari(1989) find that abnormal returns generally are less than 2% per year after controlling for varying betas over time (versus 12–14% in the extreme portfolios, if betas are assumed constant). The methodology used is based on the yearly ranking of stocks based on past 5-year returns or size into 20 portfolios. After that, buy-and-hold returns over successive 5 years are measured. Fama and French(1992) add book-to-market equity as another proxy for risk and later (Fama and French,1996) present a comprehensive study showing that the long-term reversal can be explained by their three factor model.
2.4. Consistency
Up to now, I did not mention one possible explanation of predictability of stock returns from the past returns — return consistency. This phenomenon is less documented and there are still uncertainties about its underlying source.Watkins(2003) argues that consistency has a strong predictive power with economically and statistically significance. First, he creates dummies for consistent losers and for consistent winners. In the study, stocks with 6 positive returns out of consecutive 6 months are labelled as consistent winners and those with 6 negative returns as consistent losers. Then, average returns of non-consistent performers are deducted from average returns of both consistent performers’ portfolios. This simple analysis shows that there indeed is a correlation between consistency and returns. Later in the study, he considers also a cross-section regression of 3 factors of Fama and French with momentum and January dummy added to test what drives the consistency effect. A weaker form of consistency is used here — 4 out of 6 days of positive or negative returns is enough for consistency. Also this test confirms his hypothesis of the consistency effect
12Later,Fama(1998) argues just the opposite, that using buy-and-hold returns does not provide much improvement over average
on returns, concluding that the effect is stronger in the negative direction than the positive. Finally, he notes that the consistency effect tends to revert after two years for consistent winners, but not for consistent losers.
Grinblatt and Moskowitz(2004) find slightly different results. Namely, losers consistency is not always
significant. The consistency effect of winners is confirmed also in their study. I do not pay much attention to the methodology used here as I use it in my thesis (slightly modified) and thus I describe it closely in
Section 3.
According toWatkins(2003), there are three theories which are possibly able to explain the presence of the consistency effect in medium run. First, managers have a tendency to smooth earnings and market can consider consistency over the time as signal of reduced risk. Lower perceived risk may lead to higher valuation of a company. Second, there is a possibility that the sufficiently high number of investors is just irrational or too many investors believe that the rest of the investors are not fully rational. Finally, the manner in which information is incorporated into stock returns may tend to lead to a series of positive price movements. That cause negative skewness in the returns and investors might require a compensation for the skewness risk.
Watkins (2006) and Gutierrez and Kelley (2008) look at consistency during the short-term period.
Watkins(2006) creates dummies for consistent performers based on the previous 5 days (5 returns of the same sign indicate consistency). Then, he measures the buy-and-hold profit but skips first day after portfo-lio creation and in addition, he repeats this procedure after 20 trading days only, to make the results more robust to the market microstructure. Otherwise the same analysis as has been done by him previously, yields expected results, based on the short-term reversal evidence, that consistent winners earn lower returns that consistent losers. Gutierrez and Kelley (2008) consider 1- and 4-week horizons. Consecutive 5 positive (negative) returns out of 5 days are needed to categorize a stock as consistent winner (loser) while taking the one-week formation period and 14 out of 20 days for 4 trading weeks. The authors perform only a cross-sectional regression analysis similar to that ofFama and MacBeth(1973) with slightly different con-struction of the dummy variables — dummy variable becomes 1 if a stock is consistent winner, -1 if it is consistent loser, and 0 otherwise. They find that consistency over the 1-week period is not a significant predictor of the future returns. However, 4-week consistency is related to return reversal in the following week according to this study.
To my knowledge, the literature misses a comprehensive explanation of the short-term return consis-tency effect. Usually, the scholars test this effect only as an addition to some another topics of interest and do not pay much attention to explanations.
2.5. How does my study fit in?
My thesis contributes to the financial literature in fourfold way. First, until now, very few studies focus on all three types of trading strategies based on the past returns (one example isGrinblatt and Moskowitz,
pre-dictability is scarce. I provide evidence that loser consistency indeed possesses a predicting power. And finally, I use most recent data available including an interesting period of the financial crisis of 2008.
3. Methodology 3.1. Main regression
To test the dependency of stock returns on the past performance together with the return consistency effect, I employ a widely used method ofFama and MacBeth(1973). I run a cross-section ordinary least square (OLS) regression within every month. Using similar notation as inGrinblatt and Moskowitz(2004), the regression of my main interest is
rt( j) − RtB( j) = αt+ β1trt−1:t−1( j)+ β2trt−1:t−1L ( j)+ β3tDCWt−1:t−1( j)
+ γ1trt−12:t−2( j)+ γ2trLt−12:t−2( j)+ γ3tDCWt−12:t−2( j)+ γ4tDCLt−12:t−2( j)
+ δ1trt−36:t−13( j)+ δ2trt−36:t−13L ( j)+ δ3tDCWt−36:t−13( j)+ δ4tDCLt−36:t−13( j)+ ˜εt( j), (1)
where rt( j) is stock j’s return in month t; RBt( j) stock j’s benchmark portfolio return in month t;
rt−t2:t−t1( j) the stock j’s buy-and-hold cumulative return from month t − t2 to month t − t1; rt−t2:t−t1L ( j) is the min(0, rt−t2:t−t1( j)), the cumulative return from month t − t2 to month t − t1 for negative (loser) returns
only (otherwise it is zero), DCWt−1:t−1( j) a dummy variable that is one if stock j is a consistent winning stock over the horizon t − t2:t − t1; and Dt−2:t−1L ( j) a dummy variable that is one if stock j is a consistent losing stock over that horizon.
I store the estimates of equation (5) to create a time-series of 240 observations spanning from January 1993 to December 2012. Data from years 1990–1992 are not used for regression as I need the stocks’ past performance during the recent three years to measure the long-term reversal effect. Then I calculate time-series averages of the estimated coefficients. To assess the significance of the coefficients’ estimates I find T-statistics as t( ¯ˆθi)= ¯ˆθi s( ˆθi)/ √ n, (2)
where ˆθ is a vector consisting of values of regression coefficients, ¯ˆθ is time-series average of a coefficient θi, s( ˆθi) is a standard deviation of monthly estimates and n is a number of months in the testing period.
for the return consistency I followGrinblatt and Moskowitz(2004) in a way that approximately top 10% from distribution of number of positive/negative returns is covered.
Variables controlling for negative past returns (rt2:t1L ( j)) are constructed to capture different behaviour for stocks with, on average, a positive past performance (winners) and those with negative returns (losers). To test an effect of past returns on the predictability of future returns for winners we have to look at the single coefficient of past returns only (rt2:t1( j)). On the other hand, sum of the coefficients for both past return
and negative past returns determine the effect for losers. If the latter is insignificant, losers and winners contribute to momentum by the same portion. Results on different contribution by winners versus losers are not consistent in the literature. For example a study byJegadeesh and Titman(2001) shows approximately equal contribution to momentum strategies by both winners and losers portfolios. In the contrary, Hong et al.(2000) find that losers create most of the momentum profitability. DeBondt and Thaler (1985) and
Atkins and Dyl(1990) conclude the same for the long-term reversal. 3.2. Dependent variable and testing for country effect and industry effect
The dependent variable in this study is a hedge return which controls for book-to-market and size effect as presented byFama and French(1993), and also for possible country and industry influences. The size and book-to-market effects are well documented in the literature.Banz(1981) first documents a size effect on the NYSE stock exchange during the period 1936–1975. He finds that common stocks of small firms show higher returns adjusted for risk (measured by the market β factor) than stocks of larger firms.Stattman
(1980) is the first who found a significant negative relationship between the market-to-book ratio and stock returns. Stocks with the low market-to-book ratio (also called value stocks) have higher returns than those with the high market-to-book ratio (growth stocks). Finally, in one of the most famous articles in finance,
Fama and French(1992) find that size together with book-to-market equity have an ability to capture the cross-sectional variation of stocks. They consider market capitalization (size) and book-to-market ratio as proxies for two different risk dimensions. Also evidence of the country and industry specific factors can be found in the literature. For exampleLessard(1976),Heston and Rouwenhorst(1995), andTessitore and Usmen(2005) find that, from the perspective of an investor, the country effect is more important and should
be considered as the first choice when it comes to hedging of an international portfolio.
To see if the hedging really removes all factors considered, I run a very simple cross-sectional OLS regression on the whole sample of the form
rt( j)= αt+ β1t
rtM− rRFt + β2tSMBt+ β3tHMLt+ β4tMOMt+ γtDC( j)+ δtDI( j)+ ε, (3)
where rt( j) is a return of stock j (closely specified later),
rtM− rRFt
is a market premium (market return minus risk-free rate), SMB (small minus big) and HML (high minus low) are factors fromFama and French
(1993), MOM (momentum) is a measure of momentum as used byCarhart(1997), DC stands for a vector of dummies indicating countries, and DI for dummies based on industries.
I use main stock exchange indices as a proxy for market rates when calculating market premium.13 As FTSE MIB Index (Italy) is not available before 1996, I use a value-weighted average of all Italian stocks
13Euronext BEL-20 Index for Belgium, CAC 40 Index for France, DAX Index for Germany, FTSE MIB Index for Italy,
AEX-Index for the Netherlands, and Ibex 35 Index for Spain. Monthly closing prices for calculating log-returns are taken fromR
in the dataset instead. Before acquiring euro currency, I use 3 month LIBOR (London Interbank Offered Rate) rate in the corresponding currency as a risk-free rate. Later, 3 month EURIBOR (Euro Interbank Offered Rate) is used for all countries after January 1999. SMB and HML are calculated as follows. Every month, stocks are assigned to two portfolios based on the median of market capitalization. Independently on the previous step, I also create three portfolios every month based on the 30thand 70thpercentiles of book-to-market ratio. Every stock is thus uniquely identified within one of the six portfolios.
Let assign S to those portfolios containing small cap companies, B to those containing large cap compa-nies, H to portfolios composed from stocks with high BE/ME value, M (middle) to portfolios with average BE/ME stocks and L to those with low BE/ME stocks. Then we have portfolios denoted as SH, SM, SL, BH, BM, and BL for which value-weighted mean return is calculated. SMB is then found as a difference between equal-weighted mean return of 3 portfolios with market capitalization under the median value (SH, SM, SL) and 3 portfolios which were categorized as big (BH, BM, BL). Similarly, HML is the difference of equal-weighted average returns of 2 portfolios with the high book-to-market ratio (SH, BH) and those 2 with the low book-to-market value (SL, BL). To come up with value of MOM, I first create, in monthly intervals, portfolios based on 30th(so called loser portfolio) and 70th(winner portfolio) percentiles of buy-and-hold returns over the previous year. I skip the most recent month to make the value orthogonal to the possible one month reversal effect. MOM is then calculated as the value-weighted mean return of the winners portfolio minus the value-weighted mean return of the portfolio of losers.
I use 6 different returns inEquation 3. The goal of this analysis is to find out which return eliminate the effects of size, book-to-market, country, and industry influences in the best possible way. In theory, all independent variables’ coefficients should not be significantly different from zero after the hedging. First, I consider the excess return over the risk free rate.14 To find the second type of return, I sort the data every month by previous month value of ME and 5 portfolios are created based on quintiles.
Then, also monthly, the dataset is — independently on previous step — sorted by previous month value of book-to-market ratio (BE/ME) and another 5 portfolios are created. Every single stock in every month thus uniquely belongs to one of 25 portfolios for which I compute value-weighted mean returns which I deduct from single security monthly return. This process gives me the size and BE/ME hedge returns (HRME,BE/ME). Then, I consider country and industry effect in the following columns. I calculate an
average size and BE/ME hedge returns per country and deduct it from a regular stock’s return (in addtion to hedge return of corresponding size and BE/ME benchmark portfolio). Similar procedure is performed for industry effects in the fourth column. In the fifth column, I substract both country and industry effects used previously. The last column uses dependant country and industry hedging. I calculate average size and BE/ME hedge returns for every industry within every country to cope with different covariances between countries’ industries.
As can be seen in the first column ofTable 1, when using the excess return as the dependent variable in (3), all country dummies, two industry dummies, the constant, and all but HML factors are statistically significant.15 I must admit that the economic significance is somewhat debatable here. Due to the very high number of observations, even really small and economically not significant coefficients might appear
14As mentioned before, I use 3 month LIBOR rates for years 1990–1998 and 3 month EURIBOR afterward. I also tried to
use government bonds which were used for convergence criteria of corresponding countries. The results were without significant changes.
correla-Table 1: Testing goodness of different types of hedging (standard errors clustered across months)
I run a regression of 6 different hedge returns on factors of Fama-French three factorial model, momentum (as inCarhart(1997)), and dummies indicating which country and industry a stock belongs to. I divide all stocks into 2 groups based on the median value of market capitalization and then independently into 3 groups based on 30thand 70thBE/ME percentiles. Six portfolios are then
created as a combination of these groups. SMB (small minus big) factor is calculated as an average return of portfolios comprising small cap companies minus an average return of those with large capitalization. HML factor is found as difference between average returns of portfolios with high BE/ME stocks and average returns of portfolios containing low BE/ME stocks. I find momentum (MOM) as a difference between an average return of winners portfolio and an average return of losers portfolio. Winners and losers are based on the past one year returns, skipping the most recent month to avoid the bid-ask bounce. Market premium is a difference between market monthly return measured by a corresponding stock exchange index and risk-free rate (3 month interbank interest rate). ER is an excess return of a stock j over risk-free rate. There are five hedge returns denoted by HR. First, HRME,BE/MEis
hedge return with respect to size and BE/ME ratio, HRCwith respect to size, BE/ME, and country effect, HRIhedges size, BE/ME,
and industry effects, HRi
C,Iincludes both country and industry effect independently, and finally HRdC,Iconsiders dependent country
and industry hedging. Dummies for Germany and Oil&Gas industry are omitted to avoid multicollinearity.
ER HRME,BE/ME HRC HRI HRC,Ii HRdC,I
Market Premium 0.7043*** 0.0533*** 0.0068 -0.0776*** -0.1241*** -0.1183*** (0.028) (0.010) (0.012) (0.008) (0.011) (0.010) SMB 0.4011*** 0.1079*** 0.1016*** -0.0102 -0.0165 -0.0165 (0.058) (0.012) (0.019) (0.012) (0.020) (0.017) HML -0.0526 0.0295*** 0.0164 -0.0164 -0.0295 -0.0422** (0.044) (0.009) (0.016) (0.015) (0.018) (0.017) MOM -0.1141*** 0.0389*** 0.1057*** -0.0454*** 0.0215 0.0206 (0.034) (0.010) (0.017) (0.010) (0.015) (0.013) France 0.0082*** 0.0052*** 0.0049*** 0.0024 0.0021 0.0025* (0.002) (0.002) (0.002) (0.001) (0.001) (0.001) Spain 0.0070*** 0.0023 0.0021 -0.0004 -0.0006 -0.0003 (0.003) (0.002) (0.002) (0.002) (0.002) (0.001) Belgium 0.0094*** 0.0039** 0.0038** 0.0027 0.0025 0.0031** (0.002) (0.002) (0.002) (0.002) (0.002) (0.001) Italy 0.0058** -0.0004 -0.0006 -0.0014 -0.0016 -0.0004 (0.002) (0.002) (0.002) (0.002) (0.002) (0.001) Netherlands 0.0083*** 0.0047*** 0.0047*** 0.0021 0.0021 0.0011 (0.002) (0.002) (0.002) (0.002) (0.002) (0.002) Basic Materials 0.0026 0.0005 0.0035 0.0011 0.0041 0.0005 (0.003) (0.003) (0.004) (0.003) (0.004) (0.002) Industrials 0.0021 0.0018 0.0065* 0.0026 0.0073* 0.0030 (0.003) (0.003) (0.004) (0.003) (0.004) (0.002) Consumer Goods 0.0027 0.0021 0.0040 0.0028 0.0048 0.0007 (0.003) (0.003) (0.004) (0.003) (0.004) (0.002) Health Care 0.0004 0.0030 0.0001 0.0039 0.0010 -0.0034 (0.003) (0.003) (0.004) (0.003) (0.004) (0.003) Consumer Services -0.0016 -0.0008 0.0040 -0.0001 0.0047 0.0017 (0.003) (0.003) (0.004) (0.003) (0.004) (0.002) Telecommunications -0.0057 -0.0043 -0.0004 -0.0043 -0.0005 -0.0011 (0.006) (0.005) (0.004) (0.005) (0.004) (0.004) Utilities 0.0067** 0.0049* 0.0074** 0.0058** 0.0084** 0.0029 (0.003) (0.003) (0.003) (0.003) (0.003) (0.002) Financials 0.0033 0.0002 0.0069* 0.0010 0.0077* 0.0034 (0.003) (0.003) (0.004) (0.003) (0.004) (0.003) Technology -0.0122** -0.0054 0.0049 -0.0048 0.0056 0.0019 (0.006) (0.005) (0.005) (0.005) (0.005) (0.003) Constant -0.0064* -0.0042 -0.0092** -0.0020 -0.0070** -0.0030 (0.004) (0.003) (0.004) (0.003) (0.004) (0.002) Observations 330,087 330,087 330,087 330,087 330,087 330,087 Adjusted R-squared 0.1131 0.0016 0.0025 0.0019 0.0050 0.0045
Robust standard errors clustered across months in parentheses; *** p<0.01, ** p<0.05, * p<0.1
as statistically highly significant. Nevertheless, this analysis sheds some light on the different types of the hedging. When I compare each dummy coefficient step-by-step across all columns, the hedging with dependent influence of country and industry yields the smallest deviation from zero (Column 6). Therefore I choose this type of hedging for the further testing purposes.16 There is however one disadvantage — it does not lower the effect of the market risk factor measured by β in the best way.
An interesting result can be seen in the second column. It seems that hedging with respect to size and BE/ME eliminates substantial part of country and industry effects. One of the possible reasons is that size and book-to-market values are not homogeneous across countries and creating size and BE/ME neutral portfolios eliminate correlations between these variables among countries.
4. Data
4.1. Description of dataset
I use data from Datastream and World Scope databases comprising virtually all equity securities traded on the main stock exchanges in Germany, France, the Netherlands, Spain, Italy, and Belgium17during years 1990–2012. I deliberately choose countries with the highest number of securities traded in euro currency. Although the United Kingdom and Switzerland would satisfy the size of stock exchange condition, an exchange rate risk can cause severe problems in finding causality in the stock return behaviour. Using only euro denominated securities, I intend to eliminate the exchange rate risk.
I show the composition of the dataset over time by countries and by industries in Figure 1. The per-centages are relatively stable over time. The only serious kink occurred in the last year during the testing period where many German companies do not report book value of shareholders’ equity. The highest av-erage number of stocks across time comes from France (592), the smallest avav-erage is that of Spain (97.4). Looking at the right part ofFigure 1, we can analyse relative size of industry portfolios and their changes as time has been passing out. I use the FTSE/DJ Industry Classification Benchmark (ICB) hierarchy18where 10 different types of business are specified (as shown in the figure). The highest number of companies is classified in Industrial and Financial industries while Telecommunications industry has the lowest share. The major increase in percentage occurred in Technology industry after the mid-1990s. As both country and industry portfolios do not change their compositions substantially, I later assume that the return generating process in not significantly affected by these changes. Average frequencies of stocks based on industries within countries can be found inTable B.2. Total return index data (later used for calculating returns) start on January 1990 and end on December 2012. Choosing also data before January 1990 would cause too small sample size for countries with stock exchanges with smaller number of stocks listed. As I calculate also returns during the prior 3 years, the final dataset is within the period January 1993 – December 2012,
16I also performed testing for the presence of reversals and momentum, as well as for consistency effects, with simple size
and BE/ME hedging. The results are almost the same as when I include hedging with respect to country and industry. The only noticeably difference is in the effect of winners consistency over prior one year period where size and BE/ME hedging causes this effect to be stronger. This similarity of results is caused by relatively small differences in the magnitude of the two hedged returns.
17Frankfurt Stock Exchange is the main stock exchange for Germany, Euronext Paris for France, Euronext Amsterdam for the
Netherlands, Madrid Stock Exchange for Spain, Milan Stock Exchange for Italy, and Euronext Brussels for Belgium.
Figure 1: Composition of country and industry portfolios during the time
The left panel of the figure depicts a time variation of country portfolios. The areas represent countries’ shares as of the total dataset. Every month, I calculate a ratio of number of shares within a country to the total number of shares. The panel on the right-hand side shows the same information for industries as defined by FTSE/DJ Industry Classification Benchmark (ICB).
starting with 930 stocks and ending with 323 companies in total.19The highest number of stocks present in the dataset was 2,146 in December 2000.
Figure 2shows a time pattern of stock returns for all 6 countries. I first set an index at the initial value of 100 basis points at the beginning of the test period (January 1990) and then I recalculate the index every month for every country based on the value-weighted average stocks’ return of that country. In general, all indices show peaks prior to two crises which occurred in the last 20 years. Stocks of three countries — Germany, Spain and Italy — ended within the test period with lower value comparing with the point where they started, while Italian index felt during the period approximately by 20%. However, these three indices seem to be the least volatile within the sample. On the other hand, the Dutch index both reached the highest peak and also kept the highest value until the last day. This simple visual analysis indicates that stocks do not move together perfectly, so taking country effects on returns into account seems to be appropriate here. To avoid an influence of illiquidity and a possible bid-ask bounce (seeSubsection 2.1for more on this issue), I exclude securities with the price lower thane5.20 The number of stocks undere5
19The lower number of stocks closer to the end of the testing period is caused mainly by a lack of financial reports on
sharehold-ers’ equity book value and partially by higher default rate in the economies across Europe during the recent crisis years.
Figure 2: Time-series patterns of returns per country
The value-weighted index is calculated assuming a base value of 100 basis points at the beginning of the testing period (January 1990). Then the index is recalculated every month based on value-weighted mean of monthly return within a country.
represents approximately 30% of the total dataset. I also drop observations with price higher thane1,500 due to possible lower liquidity as well. A value of 1,500 is located around the 99.5thpercentile.
I compute logarithmic return of a stock as rt( j)= ln
TRIt+1( j)
TRIt( j)
, (4)
where ln is a natural logarithm, TRIt+1( j) is a total return index21 value of a stock as of the first day of
next month and TRIt( j) as of the present month. Book-to-market equity value (BE/ME) is book value of
a common equity of a company divided by its market capitalization, measured in millions of euros. Both market equity values and market capitalization values are figures observed during the previous month. This correspond to investor’s situation when she is about to construct a portfolio based on size, book-to-market ration, and past returns. Technically, market capitalization is simply a number of ordinary shares outstanding multiplied by the share price. I calculate turnover as a ratio of total shares traded per the most recent month
Peterson (1994) use $10 as their lower threshold orLee and Swaminathan(2000) excludes stocks with the price under $1.
21DataStream definition: Total Return Index shows a theoretical growth in value of a share holding over a specified period,
Table 2: Time-series summary statistics
The first column shows averages of equally weighted monthly means of hedge returns and variables used in the regression. The sec-ond column contains time-series averages of monthly value-weighted average values and time-series averages of monthly standard deviations are presented in the third column. Finally, I provide averages of values on skewness and kurtosis over time.
Time-series means
Equal-weighted mean Value-weighted mean Standard deviation Skewness Kurtosis Monthly return -0.0023 0.0009 0.1074 -0.6096 25.6527 Hedge return (ME and B/M) -0.0004 0.0000 0.1050 -0.5413 25.5219 Hedge return (C+I indep.) 0.0001 0.0000 0.1058 -0.5233 25.0227 Hedge return (C+I dep.) 0.0002 0.0000 0.1060 -0.4896 24.5338
r−1:−1 0.0010 0.0079 0.1024 -0.0232 17.8979 rL −1:−1 -0.0354 -0.0285 0.0616 -4.4840 49.1470 DCW −1:−1 0.4764 0.5486 0.4734 0.1348 1.5877 r−2:−12 0.0353 0.0992 0.3234 -0.3491 6.7409 rL −2:−12 -0.0986 -0.0686 0.1795 -4.1738 33.3711 DCW −2:−12 0.1400 0.2226 0.3202 2.7918 12.3463 DCL −2:−12 0.0886 0.0502 0.2608 3.7730 18.7828 r−13:−36 0.1170 0.2242 0.4448 -0.3437 5.5786 rL −13:−36 -0.0906 -0.0713 0.1964 -4.9950 44.5593 DCW −13:−36 0.1309 0.2357 0.3068 3.0296 14.7456 DCL −13:−36 0.0988 0.0483 0.2763 3.3855 14.9142
to the average number of total shares outstanding during this period. 4.2. Summary of other regression variables and firm characteristics
Table 3: Time-series averages of percentile ranks
The figures are computed as time-series averages of percentile ranks. I calculate ranks every month as percentile rank of an average stock within corresponding decile portfolio (to find an average stock I use both value- and equal-weighted means). Ranks are reported for market capitalization, book-to-market ratio, turnover, and total assets. The decile portfolios are based on past returns during the three historical periods — 1 month, 12 months (first month omitted), and 36 months (first year omitted). Decile 1 stands for the portfolio with lowest prior returns; decile 10 contains companies with the highest past returns. The last two columns contain percentages of consistent winners and losers in the corresponding decile portfolio, respectively. NOTE: Turnover data are available only in 84.38 per cent of observations. In general, the dataset misses mainly turnover data of German companies therefore we must be careful in interpreting the results based on turnover as data availability is not homogenous across countries.
Market Value
Book-to-Market Turnover Total Assets
Consistent Winners
Consistent Losers
Panel A: Number of months back: 1 Equally weighted Decile 1 (Low) 42.50 50.49 51.57 42.88 . 100.00 Deciles 2-9 51.56 50.72 48.31 51.89 86.15 90.29 Decile 10 (High) 47.78 45.00 56.63 44.99 99.69 22.67 Value weighted Decile 1 (Low) 86.42 44.03 64.82 82.16 . 100.00 Deciles 2-9 91.94 40.78 66.23 88.38 86.15 90.29 Decile 10 (High) 88.36 38.16 66.96 82.89 99.69 22.67
Panel B: Number of months back: 12 Equally weighted Decile 1 (Low) 38.31 55.52 51.99 42.61 0.96 39.67 Deciles 2-9 53.05 52.34 47.73 54.05 15.60 10.36 Decile 10 (High) 53.90 39.53 52.62 48.16 44.41 0.94 Value weighted Decile 1 (Low) 83.72 50.13 63.27 81.11 0.96 39.67 Deciles 2-9 91.99 42.10 67.12 88.97 15.60 10.36 Decile 10 (High) 89.68 32.54 61.54 83.37 44.41 0.94
Panel C: Number of months back: 36 Equally weighted Decile 1 (Low) 38.11 60.60 48.63 44.70 1.30 44.22 Deciles 2-9 55.08 54.41 47.02 57.06 14.33 10.72 Decile 10 (High) 57.12 40.65 49.55 52.93 40.45 1.57 Value weighted Decile 1 (Low) 83.10 52.29 59.58 81.22 1.30 44.22 Deciles 2-9 91.91 42.70 66.51 89.32 14.33 10.72 Decile 10 (High) 89.73 31.37 62.05 83.23 40.45 1.57
periods have smaller market capitalization than winners and companies in the middle. The relation between winners portfolio and middle companies changes slightly over the three time horizons when we consider equally weighted averages. Gradually, bigger companies are becoming more common in the top decile. The book-to-market value is highest for decile 1 companies, while companies in deciles 10 have the lowest book-to-market value. This can be seen as indication of higher returns for value rather than growth com-panies. The pattern is stable when considering three different periods. Results on turnover are not truly conclusive.22 Although equally weighted averages show slightly higher turnover both for deciles 1 and
22Turnover data are available only in 84.38 per cent of observations. In general, the dataset misses mainly turnover data of
10, averages weighted by market capitalization document just the opposite relation. The last two columns show average percentages of consistent winners and consistent losers within reported deciles. As expected, consistent performers are located mainly in top and bottom deciles.
5. Regression results
The main results of the thesis can be found inTable 4. In the table, I present results for all months in aggregate, for January and December separately, and finally for the rest of the year. Many studies show that seasonality of stock returns is significant almost from the beginning of trading on stock exchanges.
Rozeff and Kinney Jr.(1976) document this phenomenon in stocks traded on the New York Stock Exchange (NYSE) during the periods 1904–1928 and 1941–1974. They do not find any consistent seasonal pattern and provide no explanation of possible reasons behind the seasonality. The theory of efficient markets implies that such an anomaly should disappear quickly after its revelation. Though, the January effect, as the most famous seasonal pattern is reported to be present many years after its discovery.Haugen and Jorion
(1996) confirm that small stocks greatly outperform large cap companies during the beginning of the year (also on the NYSE). They consider two different views at the problem: (1) markets are still efficient as this anomaly is not economically feasible due to high trading costs of small cap stocks; and (2) markets are indeed inefficient as there are too few rational investors who exploit this anomaly and therefore the effect is not eliminated by arbitrage. Nevertheless, there is no generally accepted explanation why January effect is still out there. Haug and Hirschey(2006) summarize that it might be caused by behavioural biases of investors, tax-selling, or just simple chance when only data-snooping causes statistical significance. 5.1. Results on past returns
Statistically significant and negative average of coefficients for past month return (rt−1:t−1) implies a
short-term reversal of prices. The magnitude of the effect is smallest in December. Coefficients of past negative returns are significant during the period from February–November and in December only. For the first case, the sign is opposite to the past return coefficient which implies that winners contribute more to the momentum effect. However, there is different relation during December where losers drive substantial part of momentum. In general, the appearance of short-term returns’ reversal confirms previous results found in the literature (e.g.Jegadeesh,1990).
Averages of coefficient estimates for past one-year returns (rt−12:t−2) are significant in almost all periods
of year but in December. There is a strong seasonality effect during the one year period. On average over the year, winners and losers show similar continuation in returns. However, everything changes at the end of the year. The absolute value of losers’ negative returns is higher than profits of winners in December. The pattern switches in January and returns of losers bounce back significantly to offset the momentum effect of winners. The magnitude of winners’ momentum is significantly stronger than during the rest of the year. These two facts — strong momentum of winners and return reversal of losers — imply the strong January effect when the highest returns are recorded during the beginning of year. These conclusions are well grounded in the literature. The theory on momentum (e.g.Jegadeesh and Titman,1993;Rouwenhorst,
Table 4: The averages of coefficient estimates
I run a cross-section OLS regression for every month which creates time-series of coefficient estimates. Data used span from January 1993 to December 2012 and consist of 6 major euro-currency markets. The equation is of form
rt( j) − RBt( j) = αt+ β1trt−1:t−1( j)+ β2trt−1:t−1L ( j)+ β3tDCWt−1:t−1( j)
+ γ1trt−12:t−2( j)+ γ2trt−12:t−2L ( j)+ γ3tDCWt−12:t−2( j)+ γ4tDCLt−12:t−2( j)
+ δ1trt−36:t−13( j)+ δ2trt−36:t−13L ( j)+ δ3tDCWt−36:t−13( j)+ δ4tDCLt−36:t−13( j)+ ˜εt( j).
The dependant variable is a hedge return which controls for risk (by means of size and book-to-market effects), country, and industry effects. The explanatory variable rt2:t1( j) is the stock j’s buy-and-hold cumulative return during the period t2-t1; rLt2:t1( j)
is the min(0, rt2:t1( j)) representing negative return or zero otherwise. Variables DCWt1:t2and DCLt1:t2are dummies for consistent winners
and consistent losers over the 3 different periods, respectively. A stock is considered a consistent loser if it records a negative return during the past month (DCL
t−1:t−1); if it records 8 positive (8 negative) monthly returns out of 11 months (D CW
t−12:t−2and D CL t−12:t−2); or
if it records 16 positive (15 negative) monthly returns out of 24 months (DCW
t−36:t−13and D CL
t−36:t−13). Average values of the estimates
are shown for all 12 months, for January and December separately, and for 10 other months. Fama and MacBeth(1973) type of t-statistics are computed as t(¯ˆθ)= s(ˆθ)/¯ˆθ√
n, where θ is a vector of coefficients and n is the number of months in the period (also
number of estimates ˆθ).
All Months January February-November December
r−1:−1 -0.0900*** -0.1487*** -0.0885*** -0.0464* (-11.15) (-5.42) (-11.27) (-1.53) rL −1:−1 0.0111 -0.0136 0.0224* -0.0768* (0.79 ) (-0.37) (1.29 ) (-1.72) DCL −1:−1 -0.0052*** -0.0032 -0.0053*** -0.0063** (-7.20) (-1.31) (-6.78) (-2.40) r−2:−12 0.0141*** 0.0349*** 0.0127*** 0.0069 (5.17 ) (4.26 ) (5.08 ) (0.97 ) rL −2:−12 0.0012 -0.0704*** 0.0065 0.0200* (0.24 ) (-4.51) (-0.10) (1.42 ) DCW −2:−12 0.0009 -0.0016 0.0009 0.0036 (0.97 ) (-0.32) (0.68 ) (1.06 ) DCL −2:−12 -0.0036** -0.0099*** -0.0033** -0.0000 (-2.40) (-3.23) (-2.46) (-0.01) r−13:−36 0.0008 -0.0004 0.0008 0.0019 (0.55 ) (-0.07) (0.45 ) (0.43 ) rL −13:−36 0.0052* 0.0076 0.0046* 0.0093 (1.80 ) (0.63 ) (1.57 ) (1.23 ) DCW −13:−36 -0.0014 0.0033 -0.0019* -0.0004 (-1.34) (1.17 ) (-1.33) (-0.17) DCL −13:−36 0.0000 0.0076* -0.0003 -0.0048 (0.01 ) (1.47 ) (0.35 ) (-1.01) Constant 0.0033** -0.0085* 0.0046** 0.0025 (2.10 ) (-1.76) (2.03 ) (0.54 )
Note: t-values in parenthesis; *** p<0.01, ** p<0.05, * p<0.1
5.2. Results on consistency
Based on the sign and significance of the coefficient of the dummy variable Dt2:t1L in Table 4 I find that consistent losers are, in general, penalized in terms of returns within the one-month past horizons. Though, the consistency effect is not observed during January. Being a consistent loser during the prior month causes a return lower by approximately 0.5% compared to other stocks. The consistency effect of losers can be found in all months except December while looking at the most recent year performance. On average during the year, the penalty for being a consistent loser is -0.36%. Effects of consistency over 3-year period are much weaker. There is only small positive effect of consistent losers during January and even weaker negative effect of consistent winners during the period February–December. Results are similar to
Watkins(2003) in the way that effect of consistent losers is higher than that of consistent winners. However, Grinblatt and Moskowitz(2004) come to the just opposite conclusion.
5.3. Robustness checks
Table 5 contains results of various robustness checks I did to investigate influences which are found in the literature. FollowingFama and French(1993) I exclude companies with the negative book value of shareholders’ equity. Nevertheless, the exclusion of 12,408 monthly observations (13 companies during the entire test period never reached a positive book-to-market ratio) does not cause virtually any impact on the results. There is only a very small change in the t-statistic for loser consistency in December which causes that this effect is not significant any more.
More interesting results are found when we look at the lower part of the price distribution. As was noted byConrad and Kaul(1993), low-price stocks cause much of the bias in the results ofDeBondt and Thaler(1985). When I exclude approximately 30% of all observations due to price lower than e5, the results change noticeably. First, the short-term reversal effect is less significant in December. Furthermore, it seems that penalty in returns of consistent losers in January is driven by low-price stocks as the effect of consistent losers disappear with the exclusion of these stocks. Finally, the similar result is observed for consistent winners during the prior year period where statistical significance of consistent winners’ premium disappears completely. On the other hand, dropping observations with price over 1,500 euros makes almost no difference. There is a change only in the second row ofTable 5 as the consistency effect for becomes slightly significant again.
Table 5: Various checks of results’ robustness
The table shows significance of effects of a short-term reversal, momentum, a long-term reversal, and consistency over the three horizons of interest after controlling for various restrictions on data. Rows indicates the effects where variables rt1:t2are past returns
over past periods of 1, 12, and 36 months, respectively. I skip the most recent month from the one year period and also the most recent year in the 3-year period to make the effects orthogonal to each other. Variables DCW
t1:t2and D CL
t1:t2are dummies for consistent
winners and consistent losers over the 3 different periods, respectively. A stock is considered a consistent loser if it records a negative return during the past month (DCL
t−1:t−1); if it records 8 positive (8 negative) monthly returns out of 11 months (D CW t−12:t−2and
DCL
t−12:t−2); or if it records 16 positive (15 negative) monthly returns out of 24 months (D CW
t−36:t−13and D CL
t−36:t−13). The letter J is used
if the effect is significant in January, F-N if it is significant during February to November, and D stands for December significance. Finally, Y indicates significance during the entire year. I use 10% significance level for this analysis.
Past return variables No restriction BE/ME > 0 Price >e5 e5 < Price <
e1,500 All before Before09/2008
09/2008 and after rt−1:t−1 Y, J, F-N, D Y, J, F-N, D Y, J, F-N, D Y, J, F-N, D Y, J, F-N, D Y, J, F-N, D Y, J, F-N, D‡ DCLt−1:t−1 Y, J, F-N, D Y, J, F-N, D Y, F-N, D Y, J, F-N, D Y, F-N, D Y, J, F-N, D Y, F-N, D rt−12:t−2 Y, J†, F-N, D Y, J†, F-N, D Y, J†, F-N Y, J†, F-N Y, J†, F-N Y, J†, F-N Y‡, J†, F-N‡ DCW t−12:t−2 Y, F-N, D Y, F-N, D - - - Y -DCL t−12:t−2 Y, J, F-N, D Y, J, F-N Y, J, F-N Y, J, F-N Y, J, F-N Y, J, F-N -rt−36:t−13 - - Y‡, F-N‡ Y‡, F-N‡ Y‡, F-N‡ Y‡, F-N‡, D‡ -DCW t−36:t−13 J J F-N F-N F-N - -DCL t−36:t−13 J - J J J - -# of companies 3,579 3,566 3,285 3,279 3,270 3,230 1,645 # of observations 490,064 477,656 346,867 344,454 339,967 287,368 52,599 †
opposite signs for winners and losers, losers have higher effect;‡driven by losers only
6. Economic interpretation of the results
Another look at the relationship between momentum and the consistency effect is presented inTable 6. I construct portfolios based on the past year performance measured by buy-and-hold returns during the period t −12 : t − 2. Decile 1 portfolios contain companies with the poorest performance (let’s call them extreme losers) while companies assigned to decile 10 portfolios have the strongest past performance (extreme winners). Deciles are shown in columns of the table and “All” indicates the total average return of all stocks. Different periods of year are presented in rows.
Panel A confirms that, on average, momentum strategy yields a positive hedge profit. Extreme winners portfolio outperforms extreme losers by 1.4% (2.41% when equal weighted) during the test period. In general, value-weighting is more relevant in the analyses of the similar type. Fama (1998) puts forward two main reasons why. First, an investors’ total wealth effect is captured better by the value weighting. Secondly, more important according to the author, is a bad-model problem. This problem can arise when a model is not fully able to capture small stocks’ behaviour. Equal weights intensify the impact of this misspecification compared to value-weighting.
stocks together, in the first column, we can see that there is a small premium for being a consistent winner. The difference in the average hedge returns of consistent winners and other stocks is 0.34%. Altogether, this is not a really significant difference which can be, from statistical point of view, attributed to chance. This result is in line with the result in Table 4 where coefficient for the consistent winners dummy is, on average over time, not significant. Looking at the deciles 9 and 10 where the majority of consistent stocks are allocated, I find that the effect of consistent winners is even weaker. When value-weighted, consistent winners earn on average only 0.1% higher hedge returns than non-consistent stocks. One possible explanation is that stocks which records consistent positive returns after substantial losses contribute to the consistency effect more significantly than stocks with rare but high positive returns. Focusing on different year periods, only January differs as there is no distinction between average consistent winners and other stocks. Other months show very similar results as for the entire year. Explaining the difference between deciles 1 and 2 portfolios has no theoretical justification as virtually no consistent winners are found within these portfolios. Very similar results are found for the right-hand side of the table where equal-weighted average hedge returns are shown. Only the magnitude of the consistency effect is slightly higher due to higher impact of companies with smaller market capitalization.
The bottom panel ofTable 6contains the analysis of the consistent losers effect. As expected based on the previous results, the importance of loser consistency is higher than that of winners. Consistent losers earn 0.57% less than non-consistent performers over the entire year. However, decomposition of this effect is not as straightforward as portfolios with a high number of consistent losers (deciles 1 and 2) almost do not differ in time-series average of hedge returns. Neither using equal weights does not help to find any clue. I have to conclude that the consistency effect of losers cannot be clearly explained by stocks with the lowest returns but rather by stocks in the middle of the returns distribution. Anyhow, inferring from evidence based on stocks in the middle return portfolios would be impossible as they are not representative due to the too low number of consistent losers within them. Seasonal patterns are not as coefficients in
Table 4suggest. Although the coefficient for losers consistency is the highest, the extreme losers portfolio
of consistent losers shows better performance than non-consistent performers. One possible explanation is that investors are probably more prone to buy consistent losers with less extreme losses recorded over the prior one-year period.
I have also calculated standard deviations of the decile portfolios but results are not shown here due to combination of space saving and low addition value to the analysis. In general, extreme losers (decile 1 portfolios) exhibit higher standard deviation. This is logical as these portfolios contain the worst companies and firms which have undergone severe financial problems. The risk of winners is not significantly higher than the risk of an average firm. This is in line with conclusions drawn in literature that momentum strategies profitability is not driven by (known) risk factors.
