The profitability of momentum strategies using large and liquid stocks
in the Euro market
Frank Wierink MSc Finance University of Groningen
Using data from the S&P Euro index I examine the profitability of momentum strategies for large and liquid stocks in the Euro market. Using overlapping formation and holding periods I
find that winner portfolios with longer holding periods generate significant positive returns. However none of the momentum portfolios is able to generate a significant positive return. After controlling for market returns and trading costs only the 1 x1 trading cost adjusted portfolio generates significant negative returns. Controlling for risk factors increases the profits for the momentum portfolio and gives significant profits. Adding the momentum factor
completely annihilates these returns.
Keywords: Momentum strategy, Market efficiency, Portfolio theory,
JEL: G10, G11, G14, G15
Name: Frank Wierink
Student number: S2224518
Email: f.s.wierink@student.rug.nl
Date: 10-01-2017
1
1. Introduction
According to the efficient market hypothesis (Fama, 1970) prices should reflect all available information to investors. The past performance of the stocks and new information which arises about stocks is immediately captured in the prices of these stocks. If prices do not reflect all available information the prices react instantly and any possible profits obtainable from these inefficiencies are arbitraged away. However contradicting the efficient market hypothesis there are several inefficiencies which arise in markets and which are not arbitraged away. One of these inefficiencies is the ability to predict future returns on the basis of past returns. A considerable amount of research is written with regards to this inefficiency. The first research which examines this anomaly is conducted by De Bondt and Thaler (1985). They find that that the worst performing stocks (losers) during a period of 3-5 years outperform the best performing stocks (winners) in the subsequent 3-5 years. Jegadeesh (1990) finds that this same phenomenon takes place in the short term, less than a month. This phenomenon where losers during the previous period outperform winners during the coming period is called the contrarian effect. In contrast with these findings, Jegadeesh and Titman (1993) show that in the United States in the medium term, 3-12 months, the winners keep outperforming the losers during the coming 3-12 months. The phenomenon where winners keep outperforming losers is called the momentum effect. Several other studies confirm the findings of Jegadeesh and Titman (1993) and show that the momentum effect is also present in other countries and areas. Rouwenhorst (1998) finds similar results for international stocks, Doukas and McKnight (2005) find momentum returns within 8 out of the 13 European
countries they examine. Besides stocks these returns are also observable in other financial markets. Miffre and Rallis (2007) find profitable momentum strategies in commodity future markets. Although a lot of research is conducted in the area of contrarian and momentum strategies it is not clear what causes these results. Both rational explanations (Conrad and Kaul, 1998) and behavioral explanations (Barberis, Shleifer, and Vishny, 1998; Daniel, Hirshleifer, and Subrahmanyam 1998) are given to explain this anomaly
2 According to several other studies momentum profits are only obtainable using small illiquid stocks and these profits disappear when using large and liquid stocks (Hong, Lim, and Stein, 2000; Doukas and McKnight, 2005). This is contradicted by Rouwenhorst (1998) and Agyei-Ampomah (2007) who argue that momentum strategies using large and liquid stocks are able to generate significant positive returns.
This paper examines the profitability of a momentum strategy on an unadjusted, market adjusted and transaction cost adjusted base for large and liquid Euro stocks in the period from September 2001 till July 2012. In addition I run an out of sample test, during the period august 2012 till September 2016, on the most profitable strategy during the sample period to see what profits an investor could have made following this strategy. This paper uses stocks from the S&P Euro index. The S&P Euro index consists of the stocks from the original 12 Euro countries which are also constituents of the S&P Europe 350. I contribute to the existing literature as I try to answer the question if momentum strategies using large and liquid stocks are profitable in the Euro market. Besides the fact that this paper looks into the profitability of large European stocks it examines European stocks in a time period after the period examined by Rouwenhorst (1998) and Doukas and McKnight (2005). Furthermore to my knowledge there is not a study that examines profitability of momentum strategies in a single
international index which only consists of stocks from the same monetary union. With continuing integration of the European financial markets and especially the financial Euro market it is interesting to see how results found in national indices hold to a single
international index. Especially for large institutional investors it is interesting to see if they can reap benefits from momentum strategies in a single international index. Existence of the monetary index could significantly lower trading costs but in contrast it could also enhance efficiency of the single market.
Therefore my research question is: Are profitable momentum strategies obtainable in the Euro market using large and liquid stocks?
3 standard errors (Newey and West, 1987). In addition I examine the ability of the momentum portfolio to realize returns that exceed the market returns. Furthermore I will test if the momentum returns are robust to trading costs using the method of Agyei-Ampomah (2007). Moreover I test the robustness momentum returns on a risk adjusted base using the Fama-French three factor model (Fama and Fama-French, 1993), the Fama-Fama-French five factor model (Fama and French, 2015), the Carhart four factor model (Carhart, 1997) and the six factor model (Fama and French, 2016). Finally I test the most profitable strategy during the sample period in a subsequent out of sample period.
In this paper I find that profitable momentum strategies do not exist in the Euro market consisting of large and liquid stocks. I do find that Winner portfolio with a long holding period generates positive returns which are significantly different from zero. In contrast to studies of Lesmond, Schill and, Zhou (2004) Doukas and McKnight (2005) and Agyei-Ampomah (2007) which find that the loser portfolio contributes the most to the momentum profits, this study shows that the loser portfolio does not generate significant negative returns and that momentum profits are therefore not obtainable. The highest yet insignificant return of 8.97% is generated by a 12 x 12 portfolio, which is a momentum portfolio using a formation period of 12 months and a holding period of 12 months. The 12 x 12 portfolio also generates the highest market adjusted returns of 1.99%. This return is insignificant as well. When adjusting for transaction costs only the 1 x 1 portfolio generates a significant negative return of -21.09%. The longer term holding returns still have a positive sing although they are not significant as the unadjusted momentum returns were not significant either. After testing the momentum results on a risk adjusted base for the three and five factor model the returns of both the winner and the loser portfolio decrease. However the returns of the loser portfolio react stronger to the risk adjustment and become negative. This results in the fact that the returns of the momentum portfolios increase and become significant for some of the
4 Concluding, because the returns during the sample period are not significantly different from zero I conclude that momentum profits are not present in the Euro area for large and liquid stocks. An investor is therefore unable to earn any profits when he employs a momentum strategy for large and liquid stocks in the Euro market. Therefore the S&P Euro can be seen as an efficient index in the period from September 2001 till July 2012.
This paper continues as follows. The next section will give an overview of the relevant literature. Subsequently section three will elaborate on the methodology and data used. Section four will present the empirical results. Section five will give an overview of the robustness of the momentum returns to the risk adjustments. Section six will give the out of sample analyses for the most profitable strategy. Lastly, section seven will conclude and summarize.
2. Literature review
2.1. Momentum and contrarian returns
The research literature finds several anomalies which conflict with the efficient market hypothesis. Two of these anomalies which are related to each other are the contrarian and momentum anomalies. The first researches with relation to these anomalies examined the contrarian effect. De Bondt and Thaler (1985) find evidence for profitable long term
contrarian strategies. They show that the worst performing stocks (losers) during the previous 3-5 years (formation period) outperform the best performing stocks (winners) in the coming 3-5 years (holding period). In addition Jegadeesh (1990) and Lehmann (1990) find evidence for profitable short term contrarian strategies. They both find that using formation and holding periods of less than a month losers outperform winners.
5 period. They use their winner and loser portfolio to construct a zero cost momentum portfolio. This momentum portfolio goes long in the winner portfolio and short in the loser portfolio. Employing this strategy they are able to generate significant positive momentum returns.
The studies of De Bondt and Thaler (1985), Jegadeesh (1990) and Jegadeesh and Titman (1993) are all conducted in the United States. However the contrarian and momentum anomaly are not purely an US or developed market anomaly. Bildik and Gülay (2007) find that zero cost contrarian strategies are profitable in the Turkish market. In addition Baytas and Cakici (1999) find evidence for profitable contrarian strategies in six developed markets. Forner and Marhuenda (2003) report profitable momentum and contrarian strategies in the Spanish market. Agyei-Ampomah (2007) finds positive momentum returns in the United-Kingdom and Bettman, Maher, and Sault (2009) find evidence for momentum profits in the Australian market. Rouwenhorst (1998) finds profitable momentum strategies for
international stocks. Griffin, Ji, and Martin (2003) find profitable momentum strategies for a large number of countries around the world and Doukas and McKnight (2005) find profitable momentum strategies in 8 of the 13 European countries they examine. The Momentum anomaly is not only present in individuals stocks but also in other financial markets. Chan, Hameed, and Tong (2000) find statistically significant momentum profits between equity indices. In addition Miffre and Rallis (2007) find profitable momentum strategies in commodity future markets.
Although there is evidence that economically significant profits are obtainable using a
momentum strategy, it is not clear where these profits come from. First of all there are several rational theories which try to explain the momentum anomaly. Conrad and Kaul (1998) argue that the momentum anomaly is attributable to the cross sectional variation in the returns. MacKinlay (1995) states that momentum returns are the result of datamining. Besides the rational theories there are also several behavioral theories, Grinblatt and Han (2005), Barberis, Schleifer, and Vishny (1998), Daniel, Hirshleifer, and Subrahmanyam (1998) and Hong and Stein (1999) try to explain the momentum profits based on the irrational behavior of investors such as mental accounting, overconfidence, biased self-attribution, anchoring and the
6 2.2. Transaction costs
For an investor using a momentum strategy it does not matter much where the momentum profits stem from. For the investor it is far more important to know if the momentum profits are robust to trading costs. Several different methods are used to take account of the
transaction costs which are incurred when creating a momentum portfolio. Jegadeesh and Titman (1993) assume a one way transaction cost of 0.5%, Rouwenhorst (1998) assumes a maximum roundtrip transaction cost of 2% and Forner and Marhuenda (2003) assume a two way transaction cost of 1.13%. They all argue that momentum results are robust to trading costs. More recent research suggests that transaction costs are well above the costs assumed in early research. Although recent research agrees that the transaction costs are higher than in earlier research they do not agree whether momentum profits are obtainable after adjusting for transaction costs. Lesmond, Schill and Zhou (2004) state that profitable momentum strategies are not present after taking account of trading costs. On the other hand Korajczyk and Sadka (2004) argue that profitable momentum returns are obtainable when using a momentum strategy. In addition Agyei-Ampomah (2007) finds post-cost profitability for holding periods longer than 6 months. Post-cost profitability is present during longer holding periods because the turnover for these portfolios is lower than for the shorter holding periods.
2.3 Stock size and liquidity
The results on the influence of the size and liquidity on the performance of a momentum portfolio are mixed. According to Jegadeesh and Titman (1993) and Liu, Strong, and Xu (1999) the size and liquidity of stocks in the winner and loser portfolio is smaller than the average size and liquidity of the whole market According to Lesmond, Schill, and Zhu (2004) the loser portfolios and also but to a lesser extent the winner portfolios consist of stocks with a low market capitalization and a low price. According to Agyei-Ampomah (2007) the profits of a momentum strategy are mainly driven by the illiquid loser portfolio. However Agyei-Ampomah (2007) also finds that momentum strategies are profitable using only large stocks. This is in accordance with Rouwenhorst (1998) who finds that positive momentum returns are present for large firms, although the returns are higher for small firms. In contrast Hong, Lim, and Stein (2000) find that momentum returns sharply decline when the market capitalization of the stocks increases. According to Doukas and McKnight (2005) size and analysts
7 SDAX. Momentum strategies conducted in the MDAX and DAX, which consist of larger and more liquid stocks, do not generate any significant profits. A momentum strategy in the DAX even generates negative returns.
3. Methodology and data
3.1. Methodology
3.1.1 Unadjusted portfolio returns
The methodology I use in this paper is based on the methodology of Jegadeesh and Titman (1993). Corresponding to their research I also use overlapping formation and holding periods. To compensate for these overlapping periods and the expected autocorrelation I use Newey-West adjusted standard errors (Newey and Newey-West, 1987) throughout the paper. In accordance with Agyei-Ampomah (2007) I use a lag which is equal to the holding period. First I construct the returns of the individual stocks during the formation period, which consist of the previous J months (J= 1, 3, 6, 9, 12). The return over the formation period is calculated as:
Ri ,t,J=
RIi,t−RIi,t−J
RIi,t−j (1)
Where Ri,t,J is the return of stock i on date t over the previous J months. RIi,t,J is the total
return of stock i on date t. RIi,t−j is the total return of stock i on date t-J.
Thereafter I rank the stocks based on their returns during the ranking period. The 10% best performing stocks are assigned to the winner portfolio and the 10% worst performing stocks are assigned to the loser portfolio. Both the winner and the loser portfolio are equally
weighted.
For the stocks in the winner and loser portfolio I calculate the returns during the K month holding period (K= 1, 3, 6, 9, 12). The return in the holding period will be calculated as:
Ri,t,J K=RIi,t+1−RIi,t+1+K
8 Where Ri,t,J K is the return of stock i during the holding period of K months and based on a formation period of J months. RIi,t+1+K is the total return of stock i at time t+1+ K and RIi,t+1 is the total return of stock i at time t+1. To avoid microstructure biases I follow the regular approach to skip one month between the formation and the holding period. This similar to the procedures followed by Rey and Schmid (2007) and Agyei-Ampomah (2007).
I only calculate the formation returns for stocks which are in the index at time t and at time t-J. In addition the bid price of one single stock should be above € 5.00. This is in accordance Jegadeesh and Titman (2001) and the guideline of the U.S. Securities and Exchange
Commission (www.sec.gov). I exclude stocks below this price to make sure that small changes in these so called ‘penny stocks’ do not influence the results. I do calculate holding returns for stocks which are not in the index for the entire holding period and for stocks of which the bid price drops below € 5.00 during the holding period. When a delisting occurs due to a merger or acquisition the return for the following months is zero.When a stock delists due to bankruptcy, a bailout or Nationalization the return of the stock is equal to -1. This is in accordance with Liu, Strong, and Xu (1999). Although this can slightly increase the momentum profits obtained by the loser portfolio they argue that the main results are not affected by this.To determine the cause of delisting I use the Orbis database1.
Because all returns are generated over different holding periods the returns have to be annualized to make them comparable. I annualize the returns using the following formula:
Rai,t,J K= Ri,t,J K∗ 12
K (3)
Where Ri,t,J Ka is the annualized return of stock i on time t over a holding period of K months and based on a formation period of J months.
To be able to construct the returns of the momentum portfolio the average returns of the winner and lose portfolio have to be calculated. The average return of both the winner and loser portfolio will be calculated as:
9 RPt,p,J Ka =∑ni=1Ri,t ,J Ka
n (4)
Where RPt,p,J Ka is the annualized average return of the portfolio at time t for a K month holding period and with a J month formation period. P is equal to W for the winner portfolio and equal to L for the loser portfolio. n is equal to the number of stocks which are in the winner or loser portfolio. Since all portfolios are equally weighted I can simply divide the total portfolio returns by the number of stocks in the portfolio.
To construct a zero-cost momentum portfolio an investor should go long in the winner portfolio and short in the loser portfolio (Jegadeesh and Titman, 1993). Therefore the zero cost momentum portfolio is calculated as:
RMt,J Ka = RWt,W,J Ka − RLat,L,J K (5)
Where RMt,J Ka is the annualized return of the momentum portfolio at time t during a holding period of K months and based on a formation period of J months. The return of the loser portfolio is subtracted from the winner portfolio as a result of the fact that the loser portfolio is short.
3.1.2 Market adjusted portfolio returns
I calculate the market adjusted returns for both the winner and loser portfolio to see if the winner and loser portfolio can realize a return in excess of the market. The market adjusted returns are calculated as:
RPt,p,J Kmr = RPt,p,J Ka − Ram,t,K (6)
10 for the market return this paper uses the S&P Euro index. The same index of which all stocks are constituents.
In addition I calculate the market adjusted returns of the momentum portfolio to examine if the momentum portfolio can generate a return that exceeds the market return. The market adjusted return is calculated as:
RMt,J Kmr = RMt,J Ka − Rm,t,Ka (7)
Where RMt,J Kmr is the market adjusted momentum return at time t during a holding period of K months and based on a formation period of J months. It has to be stated that the momentum portfolio is a zero-cost portfolio whereas in order to generate a profit with the market portfolio an initial investment is needed. This discrepancy could bias the results.
3.1.3. Trading costs adjusted portfolio returns
In order to examine if the profits of a momentum strategy are robust to trading costs I follow the method used by Lesmond, Schill, and Zhou (2004) and Agyei-Ampomah (2007). Because constructing a zero-cost momentum portfolio involves short selling the loser portfolio, it is usually not suitable for private investors. However short selling is possible for institutional investors. Therefore I will use transaction costs which are applicable for institutional investors. This is in contrast with Agyei-Ampomah (2007) who use transaction costs applicable to private investors.
Although Lesmond, Schill, and Zhou (2004) and Agyei-Ampomah (2007) use three different methods to calculate the spread I only use the quoted spread method. The spread is calculated over a 12 month period lasting from 18 till 6 months before the start of the holding period. The quoted spread at time t for stock i is calculated as:
Quoted spreadi,t = 1
12∑
PAi,t+τ−PBi,t+τ
(PAi,t+τ+ PBi,t+τ)/2
−6
11 Where PAi,t+τ is the Ask price of stock i at time t + τ, PBi,t+τ is the bid price of stock i at time t + τ and τ ranges from -18 till -6. I only use neutral or positive bid ask spreads. If the ask price is below the bid price I increase the ask price to equalize it with the bid price.
The trading costs of a momentum portfolio do not only depend on the bid ask spread but also on the transaction costs (Agyei-Ampomah, 2007). The total roundtrip costs for stock i are calculated as:
Roundtrip costi = quoted spread + (2 ∗ transacion costs) (9)
Where Roundtrip costsi are the roundtrip costs of buying and selling stock i. The transaction
costs are equal to 0.09% which, according to Lane Clark & Peacock Netherlands B.V. (2016), is the average transaction cost for Dutch pension funds in 2015.
In order to create the roundtrip costs for the winner and loser portfolio. I take the average of the roundtrip costs for the individual stocks in the winner and loser portfolio using the same procedure as for the average of the returns (formula 4).
In order to make the round trip costs applicable to the different holding periods I first annualize the roundtrip costs using formula 3. Afterwards I subtract the roundtrip costs of both the winner and the loser portfolio from the momentum portfolio using the following formula:
RMt,J,Kpa = RMt,J,Ka − (Roundtrip costW+Roundtrip costL) (10)
12 3.1.4. Risk factor adjustments
According to Fama and French (1993) returns of a portfolio are not only based on the excess market return but can also be explained by the size and book to market value of the stocks. To see if these risk factor can capture the variance in the returns of the momentum portfolio I regress the returns of the winner, loser and momentum portfolio on the Fama-French three factor model. In addition I will also adjust the returns of the winner, loser and momentum portfolio for the Fama-French five factor model (Fama and French, 2015). Furthermore I examine if adding the momentum factor to both models can capture the variance of the momentum returns. This will result in the Carhart four factor model (Carhart, 1997). And a six factor model (Fama and French, 2016) which consists of the Fama-French five factor model plus the momentum factor.
First of all I calculate the risk adjusted returns of the winner, loser and momentum portfolio using the Fama-French three factor model (Fama and French, 1993):
RP,t− RFt= ap+ βp(RMt− RFt) + spSMBt+ hpHMLt (11)
Where RP,t− RFt is the return of the portfolio in excess of the risk free rate. RMt− RFt Is the loading on the excess of the market return factor and this is calculated as the market return minus the risk free rate. The second factor, SMBt, is the loading on size factor and is small
size minus big size. The third factor, HMLt, is the loading on the value factor and is high book to market value minus low book to market value.
Building on the three-factor model, Fama and French (2015) created a five factor model which is better able to explain returns. The five factor model is calculated as:
Rp,t− RFt= ap+ βp(RMt− RFt)+ spSMBt+ hpHMLt+ rpRMWt+ cpCMAt (12)
13 Besides these models a momentum factor can also be added to the three factor model to create the Carhart four factor model (Carhart, 1997). Adding this factor to the three factor model gives following model:
RP,t− RFt= ap+ βp(RMt− RFt) + spSMBt+ hpHMLt+ upUMDt (13)
This model consist of the original three risk factors from the Fama-French three factor model and adds a fourth factor. This fourth factor is the up minus down factor and tries to capture momentum returns. The factor is constructed as the stocks which go up in the previous year minus the stocks which go down in the previous year (Carhart, 1997).
Building on these models it is possible to create a six factor model (Fama and French, 2016). This model consists of the five factors in the Fama-French three factor model and the
momentum factor from the Carhart four factor model.
Rp,t− RFt = ap+ βp(RMt− RFt)+ spSMBt+ hpHMLt+ rpRMWt
+cpCMAt+ upUMDt (14)
The factor loadings which are downloaded from the website of Kenneth French are monthly factor loadings. In order to use them they have to be calculated over the same period as the holding period. I will calculate these adjusted factors as:
factori,t,K= [∑ (factori,t
100 + 1) − 1 1
t+1 ] ∗ 100 (15)
Where factori,t,K is the monthly factor i (i = Rpt− RFt, SMBt, HMLt, RMWt, CMAt, UMDt or RFt) at time t for period K. After the factors are calculated for the holding period they are annualized using the same approach as the holding returns (formula 3).
3.1.5. Out of sample test
To test how the results of the momentum portfolio hold out of sample I calculate the
14 period starts on August 2012 and the investor opens his first portfolio in the upcoming
months. I do calculate the spread of the portfolio during the sample period as the calculation of the spread does not have any influence on the construction of the portfolios. To come to the annualized unadjusted, market adjusted and transaction cost adjusted results I follow the same methodology as described in section 3.1.1 and 3.1.2.
In addition to these results I also calculate the profits an investor would obtain when he follows the most profitable strategy of the sample period during the out of sample period. To calculate the profits I assume the Investor creates a zero cost momentum portfolio and that he puts the profits of his momentum portfolio in a risk free 1 month German treasury bond.
The returns of the zero cost momentum portfolio are calculated as in formula 1, 2, 4 and 5. I do not use formula 3 because the returns should not be annualized for this purpose. The market adjusted returns are calculated by using formula 7 after the returns of the momentum portfolio are calculated. Thereafter I assume the investor will go long in the winner portfolio with one million Euro and short in the loser portfolio with one million Euro. Therefore the profits during one period for a momentum portfolio are calculated as:
PMt,J,Kα = investment ∗ RMt,J,Kα
(16)
Where PMt,J,Kα is equal to the profits of the momentum portfolio at time t with a formation period of J months and a holding period of K months, PMt,J,Kα is equal to PMt,J,Ku for the unadjusted returns and equal to PMt,J,Kmr for market adjusted returns. Investment is equal to the initial long or short position in the winner or loser portfolio and is always equal to one million Euro. RMt,J,Kα Is equal to RMt,J Ku for the unadjusted returns which is calculated using formula 1,2,4,5. RMt,J,Kα is equal to RMt,J Kmr for the market adjusted returns. Which is calculated using formula 1, 2, 4, 5 and 7.
15 million Euro and over the closing volume which depends on the performance of the portfolio. First I use formula 8, 9, 10 and 3 to calculate the roundtrip costs of the winner and portfolio. As the costs of opening the portfolio are only half of this the opening costs are:
transaction costso,t,P= investment ∗ roundtripcostst,p∗ 0.5 (17)
Where transaction costso,t,Pis the costs of opening the portfolio at time t and p is W for the winner portfolio and L for the loser portfolio. roundtripcostst,p Is the roundtrip costs for the portfolio at time t where p is equal to W for the winner portfolio and equal to L for the loser portfolio.
To calculate the transaction costs of closing the portfolio is use the following formula:
transaction costsc,t,p = investment ∗ (1 + RMt,p,J Ku ) ∗ transactioncostst,p∗ 0.5 (18)
Where transaction costsc,t,Pis the costs of closing the portfolio at time t and p is W for the
winner portfolio and L for the loser portfolio. The total transaction cost adjusted returns at time t are calculated using the following formula:
PMt,J,KP = (invest ∗ RMt,J,Ku ) − (transaction costso,t,W+ transaction costso,t,L + transaction costsc,t,W+ transaction costsc,t,W) (19)
Where PMt,J,KP is equal to the profits of a transaction costs adjusted portfolio at period t based on a formation period of J months and a holding period of K months.
After closing the portfolio the investor will put the profits he generates in a one month risk free German treasury bond. The profits made at time t can be calculated as:
CRt = CRt−1∗ (1 + rft−1) + PMt,J,Kβ (20)
16 on a one month risk free German treasury bond. PMt,J,Kβ is the profit of the momentum
portfolio and equal to PMt,J,Ku , PMt,J,Kmr or PMt,J,Kp . The profit the investor makes is the value of CRt at the end of September 2016.
3.2. Data
The total data sample I use ranges from September 2001 till September 2016. This time period consists of a sample period from September 2001 till July 2012. During this period I test several momentum strategies. The out of sample period ranges from August 2012 till September 2016. During this period I test the strategy which had the highest returns during the first phase. The total sample includes all stocks which are in the S&P Euro. The S&P Euro contains all stocks from the original 12 Euro countries which are also included in the S&P 350.
I obtain all data with regards to the stocks, the market index and the German risk free bond from Datastream. The factor loadings for the Fama-French three factor model, five factor model and the Carhart momentum factor are downloaded from the website of Kenneth French2.
I choose September 2001 as starting point as constituent information about the S&P Euro is available from that date onwards. The total sample consists of 333 stocks. There is no data available for 12 (3.6%) of the stocks. The total of 333 stocks does not imply that the sample consists of 333 different companies. In September 2008 35 German stocks are replaced with identical stocks which are traded on a different trading system (XETRA). This also happens in July 2013 for eight German stocks. In December 2005 something similar happens with three Irish stocks and in April 2009 with one Dutch stock. To stay consistent with the S&P Euro index I follow their approach and replace these stocks as well. After accounting for these changes 286 different firms are left in the sample. The maximum number of stocks which are included in the S&P Euro during this period is 185 and the minimum is 169. On average 177 firms are included in S&P Euro. The average time a firm is included in the sample is 96 months and 74 firms are part of the S&P Euro during the whole sample period. In addition the testing period which ranges from September 2001 till July 2012 contains 298 firms before adjusting for duplicates and 259 firms after adjusting for duplicates. The second period has a
17 total of 212 firms before adjusting and 204 after adjusting for duplicates. Table I gives an overview of the constituents per country before and after adjusting for the firms which are replaced. Table II gives summary statistics for the total period and the sub periods without taking account of duplicates.
Table I: Constituents of the S&P Euro per country, per period
Panel A Panel B Panel C
All firms Unique Firms All firms Unique Firms All firms Unique Firms Austria 5 5 5 5 4 4 Belgium 15 15 15 15 10 10 Finland 12 12 11 11 10 10 France 61 61 56 56 50 50 Germany 95 52 81 46 52 44 Greece 5 5 5 5 2 2 Ireland 15 12 12 9 8 8 Italy 43 43 40 40 22 22 Luxembourg 5 5 5 5 3 3 Portugal 8 8 8 8 4 4 Spain 32 32 29 29 21 21 The Netherlands 37 36 31 30 26 26 Total 333 286 298 259 212 204
18 A limitation of the data used is that it consists of a relatively short time period. This is due to the fact that the Euro is only shortly in use. Another limitation of the data used is that it consists of a relatively small number of stocks compared with other momentum papers. These limitation could influence the results which are found in this paper.
4. Empirical results
4.1. Unadjusted portfolio returns
4.1.1. Winner and loser portfolio returns
First of all I examine if the winner and loser portfolio generate a return which is significantly different from zero. Table III presents the annualized average return of a winner and loser portfolio constructed with a formation period of J months and a holding period of K months. The t-statistics using Newey-West standard errors are given within parentheses below the corresponding returns. I test if the returns differ from zero at a significance level of 1%, 5%, and 10%.The portfolio with the highest return is a 12 x 9 winner portfolio which is a portfolio with a formation period of 12 months and a holding period of 9 months. This portfolio
generates an annualized average return of 12.71%. Only five winner portfolio returns are significantly different from zero. In table III it is also observable that on average the spread between the winner and loser portfolio increases as the formation or holding period increases.
A significant difference from most research is the fact that the returns of the loser portfolio do not have a negative sign, although the loser portfolio returns are not significantly different
Table II: Summary statistics of all periods
Panel A Panel B Panel C
Total months in the period 181 131 50
Average months a firm is included in the index 96 69 27 Firms included in the index during the entire
period
74 81 151
19 form zero. An explanation for this result could be that this sample only consists of large and liquid stocks. According to Lesmond, Schill and, Zhou (2004) the loser portfolios and also but to a lesser extent winner portfolios consist of stocks with a low market capitalization and a lower price. In addition Agyei-Ampomah (2007) argues that especially the loser portfolio consists of small and illiquid stocks.
Table III: Unadjusted returns of the winner and loser portfolio
K=1 K=3 K=6 K=9 K=12 J=1 WP 1.21% 2.34% 2.73% 3.63% 4.81% (0.17) (0.35) (0.39) (0.52) (0.74) LP 5.70% 1.90% 3.08% 3.82% 3.78% (0.50) (0.20) (0.32) (0.45) (0.50) J=3 WP 4.77% 5.88% 6.67% 7.06% 7.84% (0.79) (0.87) (0.98) (1.07) (1.22) LP 0.62% 0.40% 2.06% 3.67% 3.87% (0.05) (0.04) (0.20) (0.40) (0.48) J=6 WP 3.98% 6.44% 8.07% 9.15% 9.81% (0.65) (1.00) (1.29) (1.46) (1.53) LP -0.27% -0.49% 4.55% 4.52% 4.34% (-0.02) (-0.04) (0.38) (0.43) (0.47) J=9 WP 7.07% 8.55% 9.78% 11.24%* 11.70%* (1.11) (1.48) (1.63) (1.81) (1.77) LP 3.60% 2.77% 5.70% 5.40% 4.39% (0.25) (0.23) (0.46) (0.50) (0.46) J=12 WP 7.01% 8.94% 11.52%* 12.71%* 12.48%* (1.17) (1.57) (1.90) (1.93) (1.78) LP 1.85% 1.69% 6.15% 4.72% 3.51% (0.14) (0.14) (0.49) (0.41) (0.36)
Table III shows the annualized holding returns for a winner (WP) and a loser portfolio (LP) over K months based on a formation period of J months. The corresponding t-values, adjusted for Newey-West standard errors are given below the respective return in parentheses. Returns which are different from zero are indicated with
20 This confirms results found by Liu, Strong, and Xu (1999) who also find that the loser
portfolio consists of more illiquid and small stocks. As small and illiquid stocks are absent in this sample this could explain the inability of the loser portfolio to generate negative returns.
Table IV: Unadjusted returns of the momentum portfolios
K=1 K=3 K=6 K=9 K=12 J=1 -4.48% 0.43% -0.35% -0.19% 1.03% (-0.56) (0.10) (-0.08) (-0.05) (0.37) J=3 4.15% 5.48% 4.61% 3.39% 3.98% (0.45) (0.91) (0.70) (0.60) (0.90) J=6 4.25% 6.93% 3.51% 4.64% 5.47% (0.37) (0.79) (0.36) (0.58) (0.88) J=9 3.48% 5.78% 4.08% 5.84% 7.30% (0.29) (0.58) (0.40) (0.71) (1.19) J=12 5.16% 7.24% 5.37% 8.00% 8.97% (0.45) (0.73) (0.53) (0.93) (1.50)
Table IV shows the annualized holding returns for a winner (WP) and a loser portfolio (LP) over K months based on a formation period of J months. The corresponding t-values adjusted for Newey-West standard errors are given below the respective return in parentheses. Returns which are different from zero are indicated with the superscript *, ** or ***. Which indicates significance at the 10%, 5% or 1% level.
4.1.2 Momentum portfolio returns
21 momentum strategy. Jegadeesh and Titman (1993) finds a maximum annualized return of 17.88%, when skipping one week between the formation and holding period, for a 12 x 3 strategy.
The absence of negative returns for the loser portfolio could be an explanation for the inability of the momentum portfolios to generate a significant positive return. According to Hong, Lim, and Stein (2000), Doukas and McKnight (2005) and Agyei-Ampomah (2007)most of the profits of a momentum strategy are generated by shorting the loser portfolio. As the loser portfolio does not generate negative returns this could seriously obstruct the ability of the momentum portfolios to generate significant positive returns. Although the momentum
returns in this paper are not significant they are more in line with results from Liu, Strong, and Xu (1999) and Bettman, Maher, and Sault (2009) who find that momentum returns are mainly driven by the winner portfolio.
In contrast with findings in this paper Rouwenhorst (1998) finds profitable momentum returns for stocks of all sizes. Furthermore Agyei-Ampomah (2007) argues that even though
momentum results are mainly driven by the loser portfolio they are still obtainable in the UK, using a subsample consisting of only large and liquid stocks. The results in this paper are in accordance with Hong, Lim, and Stein (2000) who find that momentum profits sharply
decline when the market capitalization of the stocks increases and with Doukas and McKnight (2005) who find that momentum profits decrease when size or analyst coverage of the stocks increases.
Therefore I conclude that in accordance with Hong, Lim, and Stein (2000) and Doukas and McKnight (2005) Momentum strategies are not profitable when using large and liquid stocks in the Euro market.
4.2. Market adjusted portfolios
4.2.1. Returns for winner and loser portfolio on a market adjusted base
22 formation period of J months and a holding period of K months. The t-statistics using Newey-West standard errors are given within parentheses below the corresponding returns. The market adjusted returns of the winner and loser portfolio are, as expected, much lower than the unadjusted returns. The largest return of a winner portfolio is still generated by the portfolio based on a formation period of 12 months and a holding period of 9 months, but the return drops from 12.81% to 5.55%.
Table V: Market adjusted returns for the winner and loser portfolio
23 However although all returns decrease the number of significant returns increases. In addition to the returns of the winner portfolios which were significant before adjusting for market returns the 6 x 12, 3 x 3, 3 x 6, 3 x 9 and the 3 x 12 winner portfolios also have a significant returns after adjusting for market returns. This is due to the fact that although the returns of the portfolio decreases the variance of the returns decreases to a greater extinct, increasing the reliability of the returns.
In contrast with the positive returns generated by the unadjusted loser portfolios, all loser portfolios except for the 1 x 1, 1 x 6 and 1 x 9 loser portfolios, underperform the market. And the excess returns of the 1 x 6 and 1 x 9 portfolio are both smaller than 0.2%. These results are consistent with Griffin, Ji, and Martin (2003) who find that a loser portfolio in Europe always underperforms compared to the market and with Agyei-Ampomah (2007) who finds that holding the loser portfolio generates returns lower than those generated by a randomly selected portfolio of stocks in the United Kingdom.
4.2.2 Market adjusted returns of the momentum portfolio
As an increased number of winner portfolios generate market adjusted returns which are significantly different from zero, due to the decrease in variance, it could be the case that the momentum portfolios also generate returns which are significantly different from zero after adjusting for the market return. Therefore table VI shows the returns of the market adjusted momentum portfolio based on a ranking period of J months and a holding period of K months. It can be seen that only 10 out of the 25 momentum portfolios generate a market adjusted return with a positive sign. However none of these returns is significantly different from zero. The market adjusted results are similar with the results of Franz and Regele (2016) who find that profitable momentum strategies are only present in the German SDAX, with smaller stocks and according to them a profitable momentum strategy is not obtainable in the MDAX and DAX which consists of large and liquid stocks.
24
Table VI: Market adjusted returns for the momentum portfolios
K=1 K=3 K=6 K=9 K=12 J=1 -6.97% -1.81% -3.32% -3.83% -3.25% (-0.56) (-0.20) (-0.37) (-0.47) (-0.45) J=3 1.74% 3.25% 1.30% -1.00% -0.86% (0.12) (0.32) (0.12) (-0.11) (-0.11) J=6 1.70% 3.98% -1.34% -0.86% -0.54% (0.10) (0.31) (-0.10) (-0.07) (-0.05) J=9 -1.63% 0.34% -2.12% -1.03% 0.41% (-0.10) (0.02) (-0.15) (-0.08) (0.04) J=12 -0.45% 1.72% -1.72% 0.83% 1.99% (-0.03) (0.12) (-0.12) (0.06) (0.19)
Table VI shows the annualized returns of a momentum portfolio net of trading costs during a holding period of K months and based on a formation period of J months. The corresponding t-values adjusted for Newey-West standard errors are given below the respective returns in parentheses. Returns which are different from zero are indicated with the superscript *, ** or ***. Which indicates significance at the 10%, 5% or 1% level.
4.3. Transaction cost adjusted momentum portfolio returns
25 trading costs cannot explain the existence of momentum returns. And Agyei-Ampomah (2007) who find that momentum returns are robust to trading costs for longer holding periods.
Table VII: Transaction cost adjusted momentum returns
K=1 K=3 K=6 K=9 K=12 J=1 -21.09%*** -5.83% -3.26% -1.49% 0.52% (-2.84) (-1.24) (-0.69) (-0.38) (0.18) J=3 -12.67% -1.61% 1.06% 1.86% 3.74% (-1.35) (-0.24) (0.14) (0.29) (0.79) J=6 -12.13% 0.21% 0.83% 4.43% 6.10% (-1.09) (0.02) (0.08) (0.53) (0.98) J=9 -12.08% -0.42% 1.66% 5.32% 7.42% (-1.05) (-0.04) (0.15) (0.63) (1.23) J=12 -10.36% 0.76% 3.03% 6.84% 8.44% (-0.87) (0.07) (0.29) (0.78) (1.41)
Table VII shows the annualized returns of a momentum portfolio net of trading costs during a holding period of K months and based on a formation period of J months. The corresponding t-values using Newey-West standard errors are given below the respective returns in parentheses. Returns which are different from zero are indicated with the superscript *, ** or ***. Which indicates significance at the 10%, 5% or 1% level.
5. Risk factor adjustments
Fama and French (1993) find common risk factors which are able to describe a lot of the variance in stocks returns. To see if the returns of the momentum portfolio are robust to the common risk factors or can completely be explained by, excess market return, size, and value factors. I test the returns using the Fama-French three factor model (Fama and French, 1993). In addition to this standard model I also test the robustness of the returns to the Carhart four factor model (Carhart, 1997), Fama-French five factor model (Fama and French, 2015) and the six factor model (Fama and French, 2016)
5.1 Three factor model adjustments
First I test the robustness of the results with the three factor model. Table VIII gives an
26 Fama-French three factor model. The returns are given for the winner portfolio (WP) and the loser portfolio (LP) which are based on a formation period of J months and a holding period of K months. Below the returns are the corresponding t-values in parentheses based on Newey-West standard errors.
Table VIII: Winner and loser portfolio returns after three factor model risk adjustment
K K=1 K=3 K=6 K=9 K=12 J=1 WP -4.43% -4.34% -4.23% -3.79% -3.29% (-1.00) (-1.41) (-1.64) (-1.44) (-1.30) LP -4.85% -7.59%* -7.26% -6.35% -6.66%* (-0.78) (-1.69) (-1.48) (-1.48) (-1.84) J=3 WP -1.36% -0.74% 0.04% -0.42% -0.27% (-0.35) (-0.25) (0.01) (-0.14) (-0.11) LP -10.00% -9.55%* -9.07% -7.91%* -7.69%** (-1.54) (-1.73) (-1.59) (-1.71) (-2.01) J=6 WP -1.64% 0.09% 1.00% 1.49% 1.35% (-0.42) (0.03) (0.32) (0.50) (0.55) LP -11.97% -12.30%** -9.31% -9.17%* -9.15%** (-1.50) (-2.01) (-1.57) (-1.97) (-2.58) J=9 WP 0.01% 1.61% 2.32% 3.25% 3.16% (0.00) (0.50) (0.74) (1.16) (1.30) LP -9.67% -11.38%* -8.75% -8.97%** -9.24%*** (-1.21) (-1.84) (-1.53) (-2.14) (-3.13) J=12 WP -0.33% 2.25% 3.93% 4.77% 3.90% (-0.08) (0.66) (1.22) (1.52) (1.46) LP -12.37%* -12.62%** -8.35% -9.44%** -9.49%*** (-1.78) (-2.10) (-1.56) (-2.19) (-3.41)
27 As expected the adjusted returns of both the winner and loser portfolio are lower than the unadjusted returns. The highest return is still generated by the 12 x 9 portfolio however the return decreases from 12.71% for the unadjusted return to only 4.77% for the risk adjusted return. It is interesting to see that the returns of the loser portfolio react much stronger to the three factor adjustments than the returns of the winner portfolio. Besides the fact that the loser portfolios react much stronger to the three factor model, the loser portfolios all generate a negative returns after the risk adjustment. In contrast the winner portfolios still realize a positive return. A very remarkable result that appears, and can be seen in table IX, is that due to the fact that the returns of the loser portfolio react stronger to the risk factors, the risk adjusted momentum returns increase compared with the unadjusted momentum returns.
Table IX: Momentum portfolio returns after three factor model risk adjustment
K=1 K=3 K=6 K=9 K=12 J=1 -1.25% 1.59% 1.36% 0.86% 1.64% (-0.19) (0.45) (0.36) (0.27) (0.72) J=3 6.98% 7.15% 7.44% 5.80% 5.67%* (0.96) (1.35) (1.39) (1.32) (1.76) J=6 8.66% 10.72% 8.61% 8.93%* 8.73%** (0.96) (1.49) (1.27) (1.7) (2.09) J=9 8.00% 11.31% 9.34% 10.44%* 10.59%** (0.89) (1.52) (1.39) (1.94) (2.49) J=12 10.36% 13.17%* 10.50% 12.39%** 11.54%*** (1.24) (1.95) (1.61) (2.11) (2.71)
Table IX shows the returns of momentum portfolios, adjusted for the Fama-French three factor model, over a holding period of K months and based on a formation period of J months. The corresponding t-values are given within parentheses. The t statistic are adjusted for Newey-West standard errors. Returns which are different from zero are indicated with the superscript *, ** or ***. Which indicates significance at the 10%, 5% or 1% level.
The highest risk adjusted momentum return is generated by the 9 x 12 portfolio this return is 12.39% whereas the highest unadjusted momentum return is generated by the 12 x 12 portfolio and is only 8.97%. Agyei-Ampomah (2007) finds similar effects for several
28 exposure to a size factor increase the returns of momentum strategies. In addition Fama and French (1996) find that their three factor model in unable to explain the momentum anomaly.
Table X: Winner and loser portfolio after five factor model risk adjustments
29 5.2 Fama French five factor model
Besides the three factor model the robustness of the momentum results can also be tested using the more recent Fama-French five factor model (Fama and French, 2015). The five-factor model adds a profit five-factor and investment five-factor to the model. Table XI gives the results of the winner and loser portfolio adjusted for the five factor model. The returns are based on a formation period of J months and a holding period of K months. The t-values of the corresponding returns, adjusted for Newey-West standard errors are given below the returns in parentheses. Results of this model are very similar to the results of the three factor model. However compared with the unadjusted returns not all returns of the winner and loser portfolio decrease when adjusted for the factors in the five factor model. The excess return of the 1 x 1 winner portfolio the 1 x 1, 3 x 1, 6 x 1 and 9 x 1 loser portfolios increase compared with the unadjusted returns. In addition the returns of the winner portfolio adjusted with the five factor model decrease less than returns adjusted with the three factor model.
Table XI: Momentum returns adjusted with five factor model
K=1 K=3 K=6 K=9 K=12 J=1 -12.68%* -0.94% 2.50% 4.78% 5.61%** (-1.79) (-0.22) (0.50) (1.44) (2.24) J=3 -6.58% 4.43% 10.23% 11.77%*** 13.54%*** (-0.75) (0.67) (1.61) (2.93) (2.91) J=6 -7.08% 7.22% 16.04%*** 16.86%*** 19.36%*** (-0.64) (0.92) (2.65) (3.31) (2.80) J=9 -7.49% 5.39% 12.92%** 15.43%*** 19.21%*** (-0.70) (0.65) (2.00) (2.73) (2.71) J=12 -4.44% 6.07% 13.23%** 18.26%*** 20.85%** (-0.41) (0.75) (2.37) (3.64) (2.51)
Table XI shows the returns of momentum portfolios over a holding period of K months and based on a formation period of J months adjusted using the Fama-French five factor model. The corresponding t-values are given within parentheses. The t statistic are adjusted for Newey-West standard errors. Returns which are different from zero are indicated with the superscript *, ** or ***. Which indicates significance at the 10%, 5% or 1% level.
30 to Fama and French (2016) their model is built to explain longer term anomalies and it is not able to explain the short term momentum anomaly. In their paper they also find that the five factor model is unable to explain the short term momentum anomaly.
5.3 Carhart four factor and six factor model
Besides the three and five factor models a four and six factor model can be constructed by adding Carhart’s (1997) momentum factor to the three and five factor models. Table XII gives an overview of the momentum portfolio returns adjusted for risk using the Carhart four factor model and the six factor model. Panel A shows the results of the momentum portfolio
adjusted for risk using the four factor model and panel B show the results of the momentum portfolio adjusted for risk using the six factor model. The returns are based on a formation period of J months and a holding period of K months. The t-values of the corresponding returns are given below the returns and are adjusted for Newey-West standard errors. As can be seen in Panel A, all significant positive returns from de Fama-French three factor model disappear when adding the momentum factor. Which is not surprisingly as this factor tries to captures exactly the abnormal returns which this paper tries to measure. In addition the returns which are significantly different from zero are all negative returns. The most negative returns are associated with portfolio with short formation and holding periods. This can be explained by the fact that the momentum factor is based on the previous 12 months returns (Carhart, 1997). Whereas the holding portfolio in is based on shorter formation periods, the Carhart four factor model is therefore better able to explain the longer term momentum portfolios.
Panel B shows that the significant positive momentum returns of the Fama French five factor model completely disappear when adding the momentum factor. None of the momentum portfolios earns a positive return. The 12 x 12 momentum portfolio earns a negative return of 0.05% where in the five factor model this returns was 20.85%. This large drop can be
explained by the fact that the momentum factor exactly measures the return over the
formation and holding period as specified by that portfolio (Carhart, 1997). These results are in line with the results found by Fama and French (2016). Who argue that when adding the momentum factor to their five factor model, the model is able to explain a lot of the
momentum returns. According to them their model only has problems explaining momentum returns for small stocks. As this sample does not include small illiquid stocks it is not
31 Concluding, Adjusting for risk using the Fama-French three and five factor models lowers the returns of both the winner and loser portfolio. Because the returns of the loser portfolio react stronger to the risk adjustment than the returns of the winner portfolio, and even become negative, the surprising result emerges that the momentum returns increase after the risk adjustment. The Three and five factor model are therefore not able to explain the suggested positive returns of the unadjusted momentum portfolios. However when the momentum factor is added to both models all significant positive results completely disappear. The few
3
2
Table XII: Momentum portfolio returns adjusted for four and six factor model
33
6. Out of sample analysis
Although the momentum portfolios do not generate significant positive returns an investor could argue that he still wants to follow the most profitable momentum strategy as
Rouwenhorst (1998) and Agyei-Ampomah (2007) find positive returns for large and liquid stocks. The investor would choose the momentum strategy which, although not significant, earns the highest return. For all momentum portfolios, raw; market adjusted; transaction cost adjusted, the highest return is generated by the 12 x 12 portfolio. Therefore an investor who after calculating the model up to July 2012 starts to run a momentum strategy from August 2012 onwards. Would buy his first portfolio at the end of September 2013 and sell his last portfolio at the end of September 2016. Table XIII gives and overview of returns of the investor. Panel A shows the annualized returns of the investor using the same methodology as during the sample period. Panel B shows the profits the investor would have made using the strategy described in the methodology 3.1.5, generating a zero costs momentum portfolio and putting the profits of this portfolio into a risk free German one month treasury bond.
Table XIII: Returns and profits of out of sample 12 x 12 momentum portfolio
Panel A Panel B
Unadjusted momentum portfolio 4.75%** € 1,118,629
2.11
Market adjusted momentum Portfolio -0.90% € -162,707
-0.14
Transaction cost adjusted momentum portfolio 3.88%* € 906,327 1.71
Table XIII shows the results of a 12 x 12 momentum portfolio during the out of sample period. Panel A shows the annualized returns of a momentum portfolio. The corresponding t-values are given below the respective returns in parentheses and are adjusted using Newey-West standard errors. Returns which are different from zero are indicated with the superscript *, ** or ***. Which indicates significance at the 10%, 5% or 1% level. Panel B show the profits an investor would have made using the 12 x 12 strategy when going long in the winner portfolio with one million Euro and short in the loser portfolio with one million Euro.
34 sign compared with a positive sign during the sample period, but both results are insignificant. The transaction cost adjusted return is comparable with the sample period, 3.88% compared to 8.44%. Although lower due to the fact that the unadjusted momentum return is lower. An explanation for the significance of the returns is the fact that the out of sample period mostly consists of a bull market whereas the in sample period consists of both bear and bull markets as can be seen in figure I. First of all when there are several market states the variance between the returns is probably larger which decreases the reliability of the returns. In addition according to Rey and Schmid (2007) and Siganos and Chelley-Steeley (2005) momentum returns are higher following a bear market.
Panel B shows the profits an investor would have made when following through with the 12 x 12 strategy. In excess of transaction costs the investor would have made a profit of € 906,327 during the period from August 2012 till September 2016 In contrast, the momentum return adjusted for the market return results in a loss of € 162,707. Although it has to be stated that the momentum portfolio is a zero investment portfolio. In contrast buying the market portfolio involves an initial investment.
Concluding, an investor who would continue to pursue the momentum portfolio during the period august 2012 till September 2016, even though the momentum returns during the sample were not significant would generate a profit a profit of € 906,327 in excess of
transaction costs when constructing a momentum portfolio which goes long for one million in the winner portfolio and short for one million in the loser portfolio.
0 500 1000 1500 2000 2500 3000 se p -0 1 se p -0 2 se p -0 3 se p -0 4 se p -0 5 se p -0 6 se p -0 7 se p -0 8 se p -0 9 se p -1 0 se p -1 1 se p -1 2 se p -1 3 se p -1 4 se p -1 5 se p -1 6
35
7. Conclusion
This paper examines momentum strategies for large and liquid stocks In the S&P Euro index in the period from September 2001 till August 2012. I find that profitable momentum
strategies do not exists in the Euro market for large and liquid stocks. The highest unadjusted returns can be obtained using a 12 x 12 strategies and is 8.97%. However this return does not significantly deviate from zero. A possible explanation for the fact that no positive
36 significant returns for both the unadjusted and transaction cost adjusted returns during the period August 2012 till September 2016. Nevertheless I conclude that profitable momentum strategies are not present in the Euro market for large and liquid stocks.
Although the evidence indicates that momentum returns are not obtainable for large and liquid stocks in the Euro area further research could elaborate on this by using a larger sample of Euro stocks and not only stocks which are present in the S&P Euro index, an example of this could be the Euro 600 index. In addition it would be interesting to see how the results in this paper compare with research which includes large and liquid stocks from all Euro countries and not only stock from the 12 original Euro countries. Because countries which joined the Euro later may have a less efficient market. Using high capitalization stocks from these less developed Euro countries could greatly adjust the results. In addition it would be interesting to see how these results hold between time periods. A paper which splits results in accordance to different markets states could find that momentum returns are obtainable after down markets as suggested by the evidence in the out of sample analysis. Furthermore, it would be very interesting to see how these results hold over a longer time period. However this is only a possibility for future research in several years.
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