0 Thesis MSc Finance
Momentum Investing: a strategy everyone can exploit?
By D.G. VerheulAbstract
This study examines a zero-sum momentum investment strategy in the Amsterdam Euronext stock market for the period of 2001-2016. The study focuses on the trading costs faced by private investors using real-world brokers to calculate the trading costs. We find evidence of momentum within the stock market, but the trading costs faced by the private investor diminish these returns. Results show that the winner portfolio generates the most value to the zero-sum portfolio and the loser portfolio barely adds value. The main drivers of the high trading costs are the turnover ratios and the bid-ask gap of stocks. To narrow the bid-ask gap, the distribution of stocks included in the portfolios are tilted towards the big-cap stocks by means of a restricted sample. The restricted sample generated higher returns, but only one out of twenty-five momentum investment strategies generated significant positive returns.
Keywords: Momentum, private investors, effective bid-ask spreads, stock returns, transaction costs
Name: Derk Gijs Verheul
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1. Introduction
Private investors are constantly looking for a strategy that will steadily yield them significant returns. A private investor is an individual who buys and sells stocks for and his own personal bank account, rather than for a bank or an organization. Imagine that it can be your neighbor. Academics have searched for time series patterns that exist in stock prices, and trying to develop a trading strategy to exploit these time series patterns. It is, however, an extensively debated topic if time series patterns even exist in stocks markets. Some argue that these patterns are a type of apophenia, which is a tendency to perceive a pattern within random data but that’s not actually present. Others argue that these patterns only exist temporarily and these patterns will vanish due to the fact that these patterns are exploited by institutional investors. Others suggest a combination of the aforementioned arguments, that is, a few of the patterns ‘observed’ are real, and these patterns can be exploited by the means of an investment strategy based on these patterns.
Jegadeesh and Titman1 (1993) constructed an investment strategy based on the last mentioned argument. This investment strategy is based on price momentum within a stock. The driver of a momentum strategy lies at the theory that “stocks which performed well (poor) in the past will continue to perform well (poor) in the future” (Jegadeesh and Titman, 1993). In their paper, based on stocks traded on the NYSE and AMEX from 1956-1989, JT found significant results for this momentum investing strategy. The strategy yielded a significant compounded excess annual return of 12.01% on average.
This finding of JT clashed with the idea of an efficient market. The efficient market hypothesis was introduced by Fama (1965) a few decades ago. He stated that in an efficient market, stock prices incorporate all possible information, which means that when the markets are efficient the stock prices follow a random walk. This random walk hypothesis states that it is not possible to predict future prices based on past prices, so stock price changes are not predictable. Subsequent with the efficient market hypothesis all investors have the same information and therefore they cannot achieve an abnormal return. The only way to receive higher expected returns is to take more risk.
Following the study of JT (1993) and Fama and French’s three-factor model (1993), Carhart (1997) enhances the three factor model with an additional factor, namely; the momentum factor. This momentum factor can be calculated by the equal weighted average of the highest performing stocks subtracted by the equal weighted average of the poorest
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performing stocks, lagged one month. This momentum factor is an explanation of the momentum returns. Carhart (1997) only considers a passive momentum strategy (12 months+ holding periods). With the momentum returns explained by Carhart (1997), it is interesting if by following a momentum investment strategy a private investor can indeed beat the market and generate significant excess returns.
A question that may arise is: how it is possible to earn such abnormal returns over a short, 3-12 months, time period. Trying to explain where these abnormal returns are coming from is considered as one of the biggest puzzles in the financial world.
Asset pricing models based on rationality fail to explain these abnormal high returns of momentum investing (see e.g. Fama and French, 1996; Grundy and Martin, 2001). Instead of rational risk models, numerous authors show behavioral models that build on the idea that these momentum profits are present because investors react to information in a biased way (see e.g. Daniel et al., 1998; Hong and Stein, 1999; Barberis and Schleifer, 2003). These studies come up with models that explain short-term momentum returns and long-term return reversals by a delayed overreaction of information by the investors.
Multiple studies find post-cost excess returns for the momentum strategy, however, most of these studies make unrealistic assumptions regarding the trading costs of a private investor. This paper fills this gap by using real-world brokers to estimate the true transaction costs a private investor faces. Although this momentum strategy could generate abnormal returns, one must keep in mind that maintaining this strategy is relative intensive due to the fact that portfolios need to be rebalanced frequently. For a private investor, this frequent rebalancing has an additional downside since high turnover rates are linked with high transaction costs. In this paper, it will be assumed that a private investor can and will hold on to the chosen momentum investment strategy at all times.
We will compare this strategy with a buy-and-hold investment in the AEX during the sample period since we would like to achieve excess returns for this labor-intensive strategy. The returns of the momentum investment strategy should be higher than this particular investment to be interesting for the private investor. Thus, the AEX-investment is considered as a benchmark.
Thus, the main research question of this paper will be: can a private investor, who pursues a momentum investment strategy, yield a significant excess return when trading on the Euronext Amsterdam stock market?
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This paper will calculate the portfolio turnovers of each portfolio and the corresponding transaction costs associated with these turnovers.
The rest of this study is structured the following way: the next section discloses a review of existing literature on momentum strategies and drivers of this momentum. Next, a data and methodology section describes how this study generates its results. This will be followed by the presentation and discussion of these results. Afterward, a conclusion is drawn following these results. Finally, the limitations and recommendations for further research are summed up.
2. Literature Review
2.1 Evidence of momentum
All stock prices should fully reflect all information available. This is the definition of an efficient market, which is suggested by Fama (1965) a few decades ago. This theory is the backbone of a lot of models and theories written by academics. This theory implicates that one can’t predict future returns with historical returns. The stock price should have a random walk distribution. So, if a stock market is efficient, one could not exploit this market following a strategy based on past returns.
However, in past literature, there are strategies developed that contradict with the efficient market theory. In their paper, de Bondt and Thaler (1988) find that, over periods of three to five years, long-term past winners are outperformed by long-term past losers. Thus, they suggest a strategy to buy past losers and sell past winners. This strategy is named a ‘contrarian’ strategy and thus implies that one can get a significant profit following past returns. Lehmann (1990) and Jegadeesh (1990) find supportive evidence of de Bondt and Thaler (1988) and add to this literature that it also true for the short-term, which is one week to a month. All these studies state that this contrarian strategy is profitable due to the fact that stock prices overreact to all available information (de Bondt and Thaler, 1988, Lehmann, 1990 and Jegadeesh, 1990).
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shorting (selling) a portfolio including the worst performing stocks in the past during a particular period, and taking a long position (buying) in a portfolio of equal value that consists of stocks that have out-performed in the same period. Thus, implying that stock prices have ‘momentum’. In order to exploit this momentum, JT (1993) suggested that one should rank all stocks based on their returns and construct two portfolios. One portfolio includes the top decile (highest return) stocks and the other includes the bottom decile (least performing stocks). Then, one should buy (go long) in the first portfolio and sell (go short) in the second one. Following this strategy, JT (1993) find significant returns up to 1% on a monthly basis.
Franck et al. (2013) investigated a momentum strategy in the German mutual funds market. They find weak evidence of momentum in the German market. In their multivariate regression analyses, they did not find a positive effect of momentum investing behavior.
The study of Schiereck et al. (1999) shows that momentum investment strategies can be profitable in the German stock market when considering a short-term period. Moreover, they show that in the long-term a contrarian strategy is more profitable. If this is the case, as private investors maybe don’t have the time or patience to wait for the returns of the contrarian strategy, a momentum strategy seems more appealing for private investors.
In the rest of this literature review and the rest of the paper, the focus will be solely on the momentum strategy since this strategy is more extensively discussed and more evidence is found for this strategy compared to the contrarian strategy.
Momentum investing is also explained, by some, as trading because of biased self-attribution and overconfidence (Daniel et al., 1998). This way, an investor will buy a stock if good news supports their own positive signal, and an investor will not sell a stock if their own negative signal with a stock is in contradiction with good news. Thus, they overweight their own signals. Furthermore, Odean (1998) mentioned the ‘disposition effect’ in their study and that this could be one of the reasons that momentum can be observed within stock markets. This effect “describes the tendency of investors to sell past winner stocks while keeping stocks that have lost in value” (Odean, 1998). In his study, Odean (1998) find evidence of superior returns to former winners, which is supported by the findings of JT (1993). This finding of JT (1993) that there was momentum existent in the stock market lead to Carhart’s (1997) extension of the three-factor model introduced by Fama and French (1993) with the additional ‘momentum’ factor. This ‘momentum’ factor is later also accepted and implemented in work of Fama and French (2012).
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higher positive returns than momentum strategies based on recent past performance in the US stock market. Thus, he states that intermediate past performance, not recent performance, is a better predictor of the returns.
2.2 Trading costs
Momentum investing can only be attractive for private investors when returns of the zero-sum portfolio exceed the trading costs. As Carhart (1997) states, the transaction costs consume the generated gains from following a momentum-investment strategy. There are multiple trading costs namely; commission of the broker, bid-ask spreads, and extra short-sale costs. All these costs combined are also named roundtrip costs. In momentum investing, these roundtrip costs are very important, because maintaining a momentum strategy requires a lot of rebalancing of the portfolio. The amount of rebalancing, thus dropping and adding stocks, is called the turnover of a portfolio. A high turnover rate will result in high roundtrip costs. These high roundtrip costs could evaporate the possible profit of momentum investing and thus, should be considered and studied when examining the returns of a private investor who pursues a momentum investment strategy.
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One potentially confounding factor in momentum investing studies is the survivorship bias. This survivorship bias may be present when one deletes the non-surviving stocks from the sample. In his study, Brown et al. (1992) argues that survivorship bias can lead to spurious returns of momentum investment strategies. They find that high-risk stocks tend to generate either more extreme higher or lower portfolio returns compared to low-risk stocks. If the bad performing high-risk stocks are dropped from the sample, and we only look at the survived stocks, the high-risk stocks that survived could consistently outperform the low-risk stocks.
On the other hand, Grinblatt and Titman (1992) work with a dataset that is subject to survivorship bias. They argue that nonacademic clients are only interested in stocks in which they can invest. Moreover, they state, when considering this survivorship bias, their study would be biased towards not finding momentum in a dataset that will only include stocks that survived. Stocks with persistent bad performance are dropped from their sample, while the stocks which changing good and poor performances are included. This leads to the impression that performance reversals are more likely than persistent poor or good performance. Bilson et al. (2005) support the method of Grinblatt and Titman and conclude that the survivorship bias does not affect their results.
Moreover, it can be said that winners could be delisted due to mergers or acquisitions. The news concerning this merger or acquisition is likely to be a driver of a good performance of this stock. On the other hand, bad performance stocks can be delisted because of bankruptcy or liquidation.
Liu et al. (2008) state that an analysis will be statistically more powerful if stocks that are delisted are also included. The returns of a momentum strategy are likely downward biased since it is more likely that delisted stocks included to the loser portfolios since they were already on the edge of bankruptcy or liquidation.
Demir et al. (2004) and Galariotis (2010) deal with the survivorship bias by deleting the stocks that do not survive the holding period. This means that they assume perfect foresight of the investors.
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Brown et al. (1995) develop a model to explain the disappearance of stocks. Results of this study provide support for both Grinblatt and Titman (1992) and Brown et al. (1992) point of view concerning the survivorship bias.
Carhart et al. (2002) find the bias is small (0.07%) for one-year samples, but larger for samples longer than 15 years (1%). Wermers (2007) find that this survivorship bias only accounts for 20 basis points.
Concluding, the survivorship bias is important to consider when conducting a study on momentum investing. It should be clearly stated how one handles this survivorship bias, and if the results could indeed be biased.
2.4 Small-capitalization vs big-capitalization stocks2
A big portion of total trading cost consists from the spread between bid and ask prices. Thus, stocks with a narrow spread will be correlated with lower transaction costs. In their study, Fama and French (2012) find that the spreads are wider for small-cap stocks. They did not incorporate this in their three-factor model, so they state that this three-factor model overestimated the spreads in the big-cap stocks and underestimated the small-cap stocks’ spread. These results of Fama and French (2012) are also found in numerous other studies and widely accepted (see e.g. Siganos, 2012; Novy-Marx, 2012; Booth et al., 2016; Agyei-Ampohmah, 2007).
JT (1993) and Lesmond, Shill and Zhou (2004) both find that their ‘winner’ and ‘loser’ portfolio (formed as previously discussed) are mostly concentrated with illiquid, small-cap stocks. Thus, the main driver of returns derived from following such a strategy are the costly small-cap stocks. Agyei-Ampohmah (2007) makes a restriction for these small-cap stocks and includes only big-cap stocks. In his study, he still finds significant evidence of momentum returns within the big-cap stocks.
On the other hand, Novy-Marx (2012) find that momentum strategies are profitable and that this is especially true for the big-capitalization, most liquid, stocks mainly driven by the smaller spread gap.
Booth et al. (2016) tries different strategies for the corresponding winner and loser portfolio and combines these. A sample of big-cap stocks and small-cap stocks are examined and then combined (e.g. goes short with big-cap stocks only and long with small-cap stocks
2 In the rest of the paper, small-capitalization and big-capitalization might be, for convenience purposes,
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only). He finds if small-cap stocks are in the short portfolio, the returns of these portfolios are consistent and significantly negative, which shows the small-firm effect. This effect in the short portfolio dominates the effect of big-cap stocks in the winner portfolio. Booth et al. (2016) find that small-cap stocks outperform big-cap stocks, but one should keep in mind that these small-cap stocks are generally riskier and that wider spreads are associated with these small-cap stocks.
Resume, small-cap stocks are associated with higher momentum returns than big-cap stocks, but also have a wider spread which is the main driver for transaction costs.
2.5 Momentum investing strategy concerning a private investor
This paper will focus on the possibility, of a private investor, to exploit momentum returns in the Euronext Amsterdam exchange market. Private investors usually buy and sell stocks in amounts smaller than is done by professional or institutional investors. In fact, the average amount Dutch private investors had invested in stocks was €30,000, -3.
In the paper of Siganos (2010), it is argued that a momentum investment strategy is more profitable for professional investors compared to private investors and that one cannot assume that when following this strategy a private investors will generate the same results as previous studies showed for the institutional investors. The professional and private investors are compared to determine if they pursue a momentum investment strategy and then look if these strategies generate positive returns. Siganos (2010) show that momentum investing is not a profitable strategy for the private investor. They find that a reason why professional investors outperform private investors is because they tend to be better informed and disciplined. This is also supported by Pettengill and Schmitt (2006) who state that professional analysts successfully pursue a momentum strategy and private investors do not. Moreover, Siganos (2010) argue that in previous studies large portfolios are constructed and these portfolios aren’t representable for private investors since they generally won’t have sufficient funds to maintain these portfolios.
In The Netherlands, the competition between brokers of the last couple of years drove transaction costs down4. The biggest driver for this competition was when DeGiro entered the market in 20135+6. In 2015, DeGiro tripled their client base to 90.000 investors in The
3http://www.brokertarieven.nl/Nieuws/224/Onderzoek_Beleggingsportefeuille_Monitor_2013/ 4 http://fd.nl/beurs/10355/onlinebrokers-staken-hun-prijzenslag
5 http://www.degiro.nl/over-degiro/
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Netherlands7. Moreover, in 2015, the amount of transaction grew from 1.9 million to 5.9 million Euros. There are multiple surveys done on brokers and a lot state that DeGiro is the cheapest and most competitive one around, with very low transaction costs.8
As stated above, to pursue a momentum investment strategy, one should short the loser portfolio. So, to pursue a momentum strategy, the private investor should be able to go short. In the past, this restriction made it very hard for the private investor to pursue a momentum strategy due to the fact that not many brokers would allow investors to go short. Nowadays, a lot more brokers allow their investors to go short (probably to lure them into the use of their firm). This restriction needs to be taken in mind when considering which brokerage firm to use. Still, not all brokers provide the possibility to go short. DeGiro provides the possibility for a private investor to go short on the Euronext Amsterdam exchange market.
Another broker that provides the possibility for the private investor to go short and claims to have competitive prices is Plus500. Plus500 is also seen as a cheap and reliable broker9. Plus500 does not have commission fees. Instead, they profit from overnight funding premiums10. With Plus500, private investors can pursue a momentum strategy through Contract for Differences (CFD’s). CFD’s are contracts between a buyer and a seller stipulating that the seller or buyer will pay the party the difference in the value of the asset between the beginning of the contract and at maturity. If the difference is positive, the seller will have to pay the buyer and if the difference is negative the money will flow the other way around. These CFD’s make it easy for an investor to go short.
Concluding, there are many papers that researched the ‘momentum phenomenon’. Some academics accept that there is such a phenomenon and some do not. It is a hotly debated topic between multiple researchers and thus interesting to dig a little deeper into this phenomenon. It will be interesting to see if there is a factor ‘momentum’ observable on the stocks of the Euronext Amsterdam stock exchange market. And if so, if private investors can exploit this effect by pursuing a momentum investment strategy. Following the foregoing literature review, a hypothesis is formed namely; there is a momentum effect observable, but private investors can’t exploit this with an intensive momentum investment strategy because of the high trading costs.
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3. Data and methodology
3.1 Data
The sample of stocks which will be used to answer the research question will be all stocks that can be bought or sold on the Euronext Amsterdam stock market gathered from the Thomson Reuters Datastream database from April 2001 to April 2016. As was shown by Agyei-Ampohmah (2007), surviving and non-surviving stocks are included and the dataset excludes all investment-trusts and warrants.
More than half of the sample has either been delisted or has ceased to exist. Therefore, survivorship bias is of great importance in this study.
Following Demir et al. (2004) and Galariotis (2010), the survivorship bias is dealt with by deleting the stocks that do not survive the holding period. This means perfect foresight of the investors is assumed. Moreover, these stocks are not deleted from the sample, they could still be picked at the time before the delisting (unless they are delisted during the holding period).
Our sample includes 338 stocks, not all data is available on each of these stocks. The available data of the stocks ranges between 260 and 313. The average number of stocks available is 289. On average, there are 156 stocks traded on each day during our sample period. The data obtained is collected at the 15th day of each month, this so in order to prevent the data from being biased towards the ‘end-of-the-month’ effect.
For every stock in our sample, information on monthly returns, stock price, bid price, ask price, volume turnover and market value is extracted from Datastream. The commission and premium rates of Plus500 and DeGiro are gathered from their website.
To compare the returns from following a momentum strategy with holding the stock of the AEX index, data of the total return of the AEX is gathered.
3.2 Research Method
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period will be from month -5 to month 0 and the holding period will be from month 1 to month 6. In line with JT, we will call the portfolio with the highest returns the ‘winners portfolio’ which consists of the top decile stocks based on their returns and the portfolio with the lowest the ‘losers’ portfolio’ which consists the decile lowest ranked stocks based on their returns. Moreover, in this paper, an extra ‘one-month’ formation- and holding will be examined. This way, a better comparison can be made between short-term (active) and long-term (passive) momentum strategies. Then, the momentum profit per (three) month(s) will be analyzed. First, without transaction costs, to look if there is a form of momentum existent in the Euronext Amsterdam stock exchange. And in a later stage, the transaction costs of two online brokers are taken into account to examine if private investors can exploit the momentum effect, if there is any.
Following JT (1993), a winner- and loser portfolio is formed based on the returns of each stock in the different formation periods. This formation period is the period that all stocks are analyzed and sorted based on their returns, and assessed if the stock will be in the winner-, loser- or in no portfolio. In other words, with J-3 it is indicated that the 16 stocks that are included in the winner portfolio are in the upper decile of highest returns over the last three months. The returns of each specific stock will be calculated with an arithmetic approach, as we can see in Eq. 1
𝑅𝑅𝑅𝑅𝑅𝑅 =RI𝑖𝑖𝑖𝑖RI− RI𝑖𝑖(t − J) 𝑖𝑖(t − J)
(1) , where 𝑅𝑅𝑅𝑅𝑅𝑅 is the return of the stock i at the time t and RI is the return index of the corresponding stock i at time t, and J is the formation period.
Next, the stocks are ranked and placed in the winner-, loser- or in no portfolio. All stocks will be equally weighted in the portfolios. So, the returns of the corresponding portfolio are calculated as presented in Eq. 2;
𝑅𝑅𝑅𝑅𝑅𝑅(𝐽𝐽; 𝐾𝐾) =𝑁𝑁 𝑅𝑅𝑅𝑅𝑅𝑅 (𝐽𝐽; 𝐾𝐾)1
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, where 𝑅𝑅𝑅𝑅x(J;K) is the return of either the winner- or loser portfolio for the corresponding formation- (J) and holding (K) periods. Rit denotes the return of stock i at time t as calculated in Eq. 1 and N is the amount of stocks that are included in the portfolio, which will be 16 in this paper.
Next, the performance of the zero-sum portfolio is calculated, as was done in the research of JT (1993), using the formula presented in Eq. 3;
𝑅𝑅𝑅𝑅𝑅𝑅(𝐽𝐽; 𝐾𝐾) = 𝑅𝑅𝑅𝑅𝑅𝑅 (𝐽𝐽; 𝐾𝐾) − 𝑅𝑅𝑅𝑅𝑅𝑅 (𝐽𝐽; 𝐾𝐾)
(3) , where Rpn(J;K) is the net zero-sum portfolio, Rpw(J;K) and Rpl(J;K) are the returns of the corresponding winner and loser portfolios, respectively. The returns of each portfolio are estimated based holding period that overlaps, which implies forming a new portfolio within the holding period. This overlapping is in line with previous studies of momentum strategy (see e.g. JT, 1993; Agyei-Ampohmah, 2007). This way, we generate the monthly average returns of K-strategies, which each starts one month apart. JT (1993, 2001) suggest that using these overlapping portfolios instead of non-overlapping portfolios helps to reduce the effect of bid-ask bounce (stock price quickly ‘bounces’ back and forth between the bid- and ask-price) which leads to more robust results. It is very likely that the portfolio returns are auto-correlated, because of the fact that the portfolios are formed on a rolling basis. We can account for this fact, following the research that was done by Agyei-Ampohmah (2007), by estimating the t-stats using the Newey and West (1987) t-test for heteroscedasticity and autocorrelation- consistent standard errors.
To pursue a momentum strategy, a private investor has to frequently rebalance each of the portfolios when the holding period comes to an end. The private investor does this by dropping the stocks that are not in the top or bottom ranked decile returns of stocks anymore and adding the ones who are. The amount of dropping and adding stocks is calculated as a percentage in the turnover ratio. This turnover ratio is important considering the transaction costs, since high turnover ratios equal high transaction costs.
We calculate the turnover ratio as seen in Eq. 4; 𝑇𝑇𝑇𝑇𝑇𝑇𝑅𝑅𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑇𝑇 =𝑁𝑁𝑅𝑅𝑇𝑇𝑅𝑅𝑅𝑅𝑅𝑅𝑁𝑁𝑅𝑅𝑇𝑇𝑅𝑅
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Lee and Ready (1991) argue when using quoted spreads to calculate the actual transaction costs could lead to misleading estimates, this is due to the fact that trades are mostly executed within the bid- and ask-prices. Moreover, private investors could be charged trading prices outside of the spread when an order is much bigger than the normal market size. This is why multiple studies make use of the effective bid-ask spread to calculate the corresponding transaction costs (see e.g. Roll, 1984; Li et al., 2010). When applying a momentum investment strategy and one uses only the bid-ask spread (not the effective bid-ask price), this may lead to consequent incorrect estimates of the trading costs. Therefore, it is necessary to account for the impact of varieties in the quoted spread of the profits of momentum right at the moment of the execution of the trade. How the effective spread is calculated can be seen in Eq. 5;
𝐸𝐸𝐸𝐸𝑖𝑖 = (𝑃𝑃𝑃𝑃𝑖𝑖− 𝑃𝑃𝑃𝑃𝑖𝑖) ((𝑃𝑃𝑃𝑃𝑖𝑖+ 𝑃𝑃𝑃𝑃𝑖𝑖)
2 )
(5) , where ES is the effective spread of stock i, PA is the ask price of stock i and PB denote the bid price of the corresponding stock i.
To test whether it is possible for Dutch private investors to beat the market by pursuing a momentum strategy (exploiting the momentum effect), the transaction costs of brokers that deal in stocks on the Euronext Amsterdam exchange should be taken into account. Because of competition between brokers, the trading fees have declined in the last couple of years. The current trading costs will be used to examine the net profitability of the momentum investing strategy. These costs differ per broker.
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At Plus500, it is possible for a private investor to pursue a momentum strategy by using CFD’s. Here, the investor will pay the effective bid-ask spread and there is an added financial contribution for short positions, and a subtraction of the financial contribution for long positions to cover the revenue/cost of the related transaction.11
With these CFD’s of Plus500, interest premiums have to be paid on the long positions that one holds overnight. This premium is seen as an investment in which Plus500 will lend money to purchase the underlying security. Consequently, the investor will receive a premium when the underlying security is shorted. On average, the stocks that are traded on the Euronext Amsterdam Exchange are debited a 0.03% premium for long positions held per day. The premium for going short is 0.01%. This brings us to the following roundtrip costs of Plus500, which is shown in Eq. 6.1 (long position) and Eq. 6.2 (short position);
𝑃𝑃𝑅𝑅𝑇𝑇𝑃𝑃500 𝑅𝑅𝑇𝑇𝑇𝑇𝑅𝑅𝑅𝑅𝑅𝑅𝑇𝑇𝑅𝑅𝑅𝑅 𝑐𝑐𝑇𝑇𝑃𝑃𝑅𝑅 (𝑅𝑅𝑇𝑇𝑅𝑅𝑙𝑙) = (𝐸𝐸𝐸𝐸 ∗ 𝑇𝑇𝑇𝑇𝑇𝑇𝑅𝑅𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑇𝑇) + (0.03% ∗ 𝑁𝑁𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑) (6.1) 𝑃𝑃𝑅𝑅𝑇𝑇𝑃𝑃500 𝑅𝑅𝑇𝑇𝑇𝑇𝑅𝑅𝑅𝑅𝑅𝑅𝑇𝑇𝑅𝑅𝑅𝑅 𝑐𝑐𝑇𝑇𝑃𝑃𝑅𝑅 (𝑃𝑃ℎ𝑇𝑇𝑇𝑇𝑅𝑅) = (𝐸𝐸𝐸𝐸 ∗ 𝑇𝑇𝑇𝑇𝑇𝑇𝑅𝑅𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑇𝑇) − (0.01% ∗ 𝑁𝑁𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑)
(6.2) , where ES is the effective spread and Ndays is the number of days that the stocks are
held. For convenience matters, all months will be rounded to 30 days.
Online broker DeGiro has a fixed rate of €2.00 for each transaction. The variable rate is 0.02% of the price with a maximum of €30.0012. DeGiro also has some additional costs for going short. These extra shortage costs are 1.00%, annually. If an investor enters or closes a position it will cost them €2.00 each time, so with pursuing a momentum strategy, thus swapping one stock for another will cost them €4.00.
To come up with the roundtrip cost of DeGiro, the fixed costs, variable costs, and effective spread need to be added together. The fixed costs are €4.00 times the Turnover Ratio times the number of stocks included in the portfolio (which in this case is 16). Furthermore, the variable costs are 0.04% and depend on the value of each portfolio. In this case, all stocks have equal weights, so the variable costs are calculated by multiplying the value of the portfolio with the turnover ratio times 0.04%. As mentioned before, the average portfolio value for a Dutch private investor was €30,000, this amount will be used in the rest of the
11 www.plus500.nl/Help/HelpFees.aspx
15
paper as the portfolio value. Similar to Plus500, the private investor has to pay the effective bid-ask spread multiplied by the turnover ratio.
Regarding the shorting of the loser portfolio, an extra premium must be paid to go short. This premium is 1.00% of the total portfolio value on an annual basis. This will be divided by 12 (since our portfolios are formed on a rolling basis) to come up with the monthly premium. Eq. 7.1 and Eq. 7.2 will show the roundtrip costs of DeGiro as was explained above. 𝐷𝐷𝑇𝑇𝐷𝐷𝑅𝑅𝑇𝑇𝑇𝑇 𝑅𝑅𝑇𝑇𝑇𝑇𝑅𝑅𝑅𝑅𝑅𝑅𝑇𝑇𝑅𝑅𝑅𝑅 𝑐𝑐𝑇𝑇𝑃𝑃𝑅𝑅 (𝑅𝑅𝑇𝑇𝑅𝑅𝑙𝑙) = (€4.00 ∗ 𝑇𝑇𝑇𝑇𝑇𝑇𝑅𝑅𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑇𝑇 ∗ 𝑁𝑁) + (0.04% ∗ 𝑇𝑇𝑇𝑇𝑇𝑇𝑅𝑅𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑇𝑇 ∗ 𝑃𝑃𝑃𝑃) + (𝑇𝑇𝑇𝑇𝑇𝑇𝑅𝑅𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑇𝑇𝑅𝑅𝑅𝑅𝑅𝑅𝑇𝑇 ∗ 𝐸𝐸𝐸𝐸) (7.1) 𝐷𝐷𝑇𝑇𝐷𝐷𝑅𝑅𝑇𝑇𝑇𝑇 𝑅𝑅𝑇𝑇𝑇𝑇𝑅𝑅𝑅𝑅𝑅𝑅𝑇𝑇𝑅𝑅𝑅𝑅 𝑐𝑐𝑇𝑇𝑃𝑃𝑅𝑅 (𝑃𝑃ℎ𝑇𝑇𝑇𝑇𝑅𝑅) = (€4.00 ∗ 𝑇𝑇𝑇𝑇𝑇𝑇𝑅𝑅𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑇𝑇 ∗ 𝑁𝑁) + (0.04% ∗ 𝑇𝑇𝑇𝑇𝑇𝑇𝑅𝑅𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑅𝑇𝑇 ∗ 𝑃𝑃𝑃𝑃) + (𝑇𝑇𝑇𝑇𝑇𝑇𝑅𝑅𝑇𝑇𝑇𝑇𝑇𝑇𝑇𝑇 𝑇𝑇𝑅𝑅𝑅𝑅𝑅𝑅𝑇𝑇 ∗ 𝐸𝐸𝐸𝐸) + (1.00% ∗ 𝑃𝑃𝑃𝑃 12� ) (7.2) , where N is the number of stocks included in the portfolio (16), PV is the portfolio value (€30,000).
To give an example of the total roundtrip costs at DeGiro for a long position, consider a month where ten of the sixteen stocks need to be rebalanced. This leads to a turnover ratio of 62.5%, the fixed costs will be ten times €4.00 is €40.00. The variable costs will be €7.50 (0.04%*62.5%*€30,000). Both these numbers will be summed up and added to the turnover ratio multiplied by the effective spread.
The sample includes all listed companies on the Euronext Amsterdam Stock Exchange, and thus some of the stocks in the sample have a very low market capitalization. These firms may be difficult to sell short and , as mentioned before, they tend to have wide bid-ask spreads and lending restrictions. In contrast, medium- or big-cap stocks tend to have more narrow spreads, and thus, it might be interesting to consider these stocks only in a restricted sample.
16 𝑅𝑅2 = �[(𝑁𝑁 ∗ 𝑃𝑃𝑖𝑖) − (𝑁𝑁 ∗ 𝑞𝑞𝑖𝑖)]2 (𝑁𝑁 ∗ 𝑞𝑞𝑖𝑖) 𝑖𝑖 𝑖𝑖=1 (8) , where 𝑅𝑅2 is the chi-square statistic, i is the number of quintiles (which will be five in this case) with i-1 degrees of freedom (so this will be four in our case), si is the fraction of
stocks in each portfolio which are in the i-th quintile, and qi is the proportion of each quintile
when regularly distributed (so 0.200 in this case). We will test for significance at a probability level of 5.00% and a degree of freedom of four, which corresponds with a chi-square critical value of 9.49.
For the restricted sample, the specific stocks in each of the portfolios (identical method as in the unrestricted sample) are sorted on their market value. Then, the top 8 ranked stocks for both the loser and winner portfolio are considered in the new restricted portfolio. Thus, the stocks will be double sorted. First, we sort them on with regards to their returns. Secondly, they will be sorted based on their market value (highest will be picked). When implementing this method, there are probably lower transaction costs both due to the fact that there are fewer stocks to rebalance and that we are dealing with medium/large cap stocks. Dealing with portfolios of eight stocks might also be considered more convenient to maintain for a private investor. Moreover, the restricted sample is examined the same way as the aforementioned methodology, only the number of stocks will change from 16 to eight.
This approach is different than the approach of e.g. Agyei-Ampohmah (2007). In his study, the top 30% biggest capitalization stocks are considered in his restricted sample. After this sorting method, he formed the portfolios the same way as before (selecting the top 10% stocks based on their returns) which would lead to eight stocks per portfolio. If we would reproduce this method, we would only have to include four stocks in each of the portfolios.
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4. Empirical Results
4.1 Empirical results unrestricted sample
The next section will discuss the results of this study regarding the sample including all stocks (the unrestricted sample).
4.1.1 Returns from a momentum strategy ex-ante roundtrip costs
Table 1 presents the returns of all portfolios held within the mentioned sample time frame ranging from April 2001 until April 2016, without transaction costs. As mentioned in the methodology section, all portfolios are formed the way JT (1993) showed us; ranking the portfolios during the Jth period based on their total returns and holding them for K-months. For each strategy, results are given for both the winner and the loser portfolio. Moreover, the results of the zero-sum portfolio are also given. This is simply holding a long position in the winner portfolio and a short position in the loser portfolio. So, to calculate the returns of the zero-sum portfolios, the returns of the winner portfolio is subtracted by the returns of the loser portfolio of the same corresponding strategy. As done by other studies, thus to make it easy comparable, all returns are annualized and averaged. Below each return, the t-stats are estimated with the Newey-West (1987) approach to show the statistical significance of the results.
To illustrate, for the strategy that is formed in the 3rd month (J-3) and is held for 12 months (K=12) it is seen that the winner portfolio generates a return of 12.75% and the loser portfolio a return of 2.69%. The corresponding return of the zero-sum portfolio of that particular period will be 10.07% (winner- minus loser portfolio).
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the results found in the study of Agyei-Ampohmah (2007) who finds a highest return of a whopping 44.64%.
Moreover, it can be noted that pursuing an active momentum strategy (short holding period) doesn’t necessarily generate higher returns than a more passive momentum strategy (longer holding period). However, there is a slight increase in returns for the longer formation periods compared to the shorter ones. This can be explained due to the fact that with longer formation periods more information is reflected in the returns thus, the stocks included in these portfolios tend to be more robust.
Furthermore, comparing these results with other papers show us some contrast. The studies done by Agyei-Ampohmah (2007), JT (1993), Grinbaltt and Moskowitz (2003) and Rouwenhorst (1998) find results that most of the momentum returns are attributable to the short position in the loser portfolio, which is the opposite of what is found in this sample. A possible conclusion of this fact is that short selling is less critical in the Euronext Amsterdam exchange market than in other markets.
These results should be compared with our benchmark, the buy-and-hold investment strategy in the AEX during our sample period. An investment in the AEX during our sample period would generate a return of 6,84%. Seven significant ‘zero-sum’ portfolios are found, of which six have out-performed the AEX investment. The only ‘zero-sum’ portfolio that did not out-perform the AEX investment was the J-1, K=12 momentum strategy.
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Table 1. Annualized portfolio returns with no transaction costs - Unrestricted sample, 2001-2016.
Every month the stocks in this sample are ranked in an ascending order, based on their past returns in the formation period. The 16 best performing stocks are included in the winner portfolio, and the 16 worst performing stocks are included in the loser portfolio. The zero-sum portfolio consists of one a long position in the winner portfolio and shorting the loser portfolio. All stocks are weighted equally in each portfolio. K=1,3,6,9,12 denotes the holding period in months. Returns are calculated for each portfolio by averaging and annualizing all portfolio returns. The t-stats are calculated using the Newey-West (1987) standard error test. All t-stats are denoted between parentheses. *, **, *** denotes the significance of these t-stats at the 10%, 5%, and 1% level, respectively.
20 4.1.2 Portfolio Turnover Ratios
To calculate the trading costs, it is necessary to estimate the turnover ratios of each portfolio. Table 2 show the turnover ratio for each portfolio, calculated as shown in Eq. 4. The turnover rates are averaged and then annualized. The results indicate that maintaining a momentum investing strategy requires rebalancing a portfolio frequently. As expected, the J-1;K=1 strategy has the highest turnover ratios. The higher the holding and formation period, the lower the turnover ratios. This could be explained by the theory that, with a longer formation period, stocks are better judged so it can be classified more appropriate to a loser or winner stock (these stocks are more ‘robust’). Because of the better rankings with the longer formation periods, the portfolios need to be less rebalanced compared to the shorter formation periods. The winner portfolio has the highest annualized turnover ratio, with a 1034,1% annualized turnover ratio. This indicates that the entire winner portfolio would change 10 times a year. In all strategies, the winner portfolio has a higher average turnover than the corresponding loser portfolio. This is also found by the research done by Agyei-Ampohmah (2007).
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Table 2. Portfolio Turnover – Unrestricted sample, 2001-2016.
The following table presents the average turnovers of both the winner- and loser portfolio as a percentage for each different momentum strategy. All turnovers are averaged. The percentage between brackets [] is the corresponding annualized turnover rate.
Formation Period Portfolio Holding Period
k=1 k=3 k=6 k=9 k=12 Average J-1 Winner 86.2% 84.4% 86.9% 86.0% 87.1% 86.1% [Annualized] [1034.1%] [337.4%] [173.7%] [114.7%] [87.1%] [349.4%] Loser 79.2% 77.7% 80.7% 81.4% 81.5% 80.1% [Annualized] [949.9%] [310.9%] [161.4%] [108.6%] [81.5%] [322.4%] J-3 Winner 51.3% 85.4% 86.1% 84.7% 86.6% 78.8% [Annualized] [615.3%] [341.7%] [172.2%] [112.9%] [86.6%] [265.7%] Loser 46.4% 75.4% 76.2% 76.4% 77.1% 70.3% [Annualized] [557.0%] [301.7%] [152.3%] [101.9%] [77.1%] [238.0%] J-6 Winner 35.8% 62.1% 84.4% 84.9% 87.1% 70.8% [Annualized] [429.7%] [248.3%] [168.7%] [113.2%] [87.1%] [209.4%] Loser 30.8% 52.0% 71.6% 72.4% 74.4% 60.2% [Annualized] [369.8%] [208.1%] [143.2%] [96.5%] [74.4%] [178.4%] J-9 Winner 30.5% 51.5% 71.2% 86.0% 86.8% 65.2% [Annualized] [365.8%] [205.9%] [142.4%] [114.7%] [86.8%] [183.1%] Loser 23.8% 39.8% 55.8% 68.1% 70.0% 51.5% [Annualized] [285.1%] [159.3%] [111.7%] [90.7%] [70.0%] [143.4%] J-12 Winner 26.8% 45.5% 63.8% 76.3% 87.2% 59.9% [Annualized] [321.9%] [182.1%] [127.7%] [101.8%] [87.2%] [164.1%] Loser 20.3% 33.5% 48.1% 58.6% 68.4% 45.8% [Annualized] [244.2%] [133.9%] [96.2%] [78.1%] [68.4%] [124.2%] Average per
holding period Monthly 43.1% 60.7% 72.5% 77.5% 80.6%
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4.1.3 Returns from a momentum strategy including roundtrip costs of Plus500
After calculating the turnover ratios per portfolio, the next step is to calculate the transaction costs. Table 3 depicts the returns of a private investor when he/she would use Plus500 as broker. The returns are the returns of a momentum investment strategy subtracted by the roundtrip costs of Plus500 as calculated in Eq. 6.1 (winner) and Eq. 6.2 (loser). At Plus500, through CFD’s, private investors can take a long or short position in a stock. Plus500 doesn’t have additional commission fees, but the investor has to pay the effective bid-ask spread and receives (pays) a funding premium for the short (long) position.
Results show no significant momentum strategy that is profitable for the private investor when Plus500 is used as broker. Moreover, there was not one portfolio with significant positive results. The only zero-sum portfolio that generated a positive return was that of J-6;K=9, but this result is close to zero and was not found significant. The highest significant loss for the zero-sum portfolio is for the strategy of J-1;K=1, which generated a loss of -56,78% significant at the 1% level. The lowest significant loss for the zero-sum portfolio was with the strategy J-1;K=12. This is in line with the expected since there will be fewer transactions for longer holding periods.
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Table 3 – Annualized portfolio returns including transaction costs of Plus500 – Unrestricted sample, 2001-2016
The following table shows all post-transaction costs returns when a private investor uses Plus500 as broker. Each portfolio is constructed the same way as mentioned before. The transaction costs are calculated by multiplying the average effective spread by the corresponding portfolio turnover for each portfolio. Moreover, the costs also include a premium that is charged by Plus500.for holding stocks overnight. Thus, the returns seen are the returns post-costs charged by Plus500. Again, t-stats are calculated using the Newey-West (1987) approach. T-stats are depicted between parentheses. ***, **, * denotes the significance of these t-stats at the 1%, 5%, and 10% level, respectively.
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4.1.4 Returns from a momentum strategy including roundtrip costs of DeGiro
Obtained in a similar fashion as was shown in the previous section regarding Plus500, the returns including the roundtrip costs of broker DeGiro are shown in Table 4. Plus500.and DeGiro have different roundtrip costs. Online broker DeGiro has a fixed rate of €2.00 per transaction. The variable rate is 0.02% of the costs with a maximum of €30.0013. In this study a constant portfolio value of €30,000 is assumed, so this variable costs will be €12.00 times the portfolio’s turnover ratio. DeGiro also has some additional costs for going short. These extra shortage costs are 1.00% annually.
It can be seen in Table 4 that there is no significant positive zero-sum portfolio. When pursuing the J-1;K=1 strategy, one would have the highest loss, namely a 55.68% loss significant at the 1% level. Again, this is as expected the most expensive strategy. In contrary to the results of Plus500, there are some strategies that yielded significant positive results. The highest positive result will be that with a strategy of going long in the winner portfolio of J-6;K=9, this will result in a return of 11,68% significant at the 1% level.
Other studies, like JT (1993) and Agyei-Ampohmah (2007), show significant positive returns of a momentum strategy minus the roundtrip costs. However, unlike this sample, the returns are mostly driven by the shortage of the loser portfolio. Moreover, they base the roundtrip costs on a percentage, while at DeGiro it is a combination of variable and fixed costs.
If we compare Table 3 with Table 4, which both represent the returns of a private investor pursuing a momentum strategy on the Euronext Amsterdam exchange market with the online brokers Plus500 and DeGiro, respectively. It is clear that when the private investor uses DeGiro as broker, it will generate higher returns than when the private investor uses Plus500. This shows that the roundtrip costs of Plus500 are higher than the roundtrip costs of DeGiro. Furthermore, a private investor will be more at risk through the CFD’s traded at Plus500. There is also a positive correlation between the turnover ratios depicted in Table 2 and the returns displayed in Table 3 and Table 4, this is because the turnover ratios are a huge driver of the roundtrip costs. Moreover, the momentum effect is mostly driven by the long position in the winner portfolios and not by shorting the loser portfolios.
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Table 4 – Annualized portfolio returns including transaction costs of DeGiro – Unrestricted sample, 2001-2016
The following table shows all post-transaction costs returns when an investor uses DeGiro as a broker. Each portfolio is constructed the same way as mentioned before. The roundtrip costs of broker DeGiro are calculated by adding the effective spread with the fixed and variable costs charged by DeGiro. A portfolio value of €30,000 is assumed, as this is the average portfolio value of which a Dutch private investor has invested in stocks. Returns are annualized and given as a percentage. These returns are tested with the Newey-West (1987) test. The t-stats are presented between parentheses. *, **, *** denotes the significance of the t-test at the 10%, 5%, and 1% level, respectively.
Formation
period Portfolio Holding period
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4.1.5 Distribution of stocks based on market capitalization
As we can see in the results presented above, a private investor can’t generate abnormal high post-transaction costs returns following a momentum strategy. In fact, they can’t even generate a significant positive return. Thus, the costs that should be made to continue a momentum strategy are too high. An important driver of these costs is the effective spread. As mentioned in the literature review, multiple academics show that this bid-ask spread is particularly wide for small-cap stocks (see e.g. Agyei-Ampohmah, 2007; Novy-Marx, 2012; Booth et al., 2016). Furthermore, these small-cap stocks tend to be a lot more volatile than big-cap stocks. Because of this high volatility, it can be argued that the small-cap stocks tend to be more in the loser or winner portfolios. To check whether both portfolios are biased towards small-cap stocks, a chi-squared test is done. Results of this test are presented in Table 5. This table shows that a significant percentage of portfolios are normally distributed concerning the market cap of the stocks included in the portfolio. However, if we take a closer look at the distribution, we see that the portfolios, on average, are slightly tilted towards the small-cap stocks as was expected (see e.g. the loser portfolio of the J-12 strategy, which has a proportion of 43.50% in the lowest-cap stocks). Moreover, we see that especially the loser-portfolios are tilted towards the small-cap stocks.
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Table 5 – Market capitalization – Unrestricted sample, 2001-2016
Following Jegadeesh and Titman (1993) winner (W) and loser (L) portfolios are formed. Both portfolios include an amount of 16 stocks. The stocks are then categorized, based on their market value. The categories are based on five quintiles ranging van small-cap stocks (Q1) to big-cap stocks (Q5) for each formation period. A chi-squared test for normality calculated by 𝑅𝑅2= ∑ [(𝑁𝑁∗𝑑𝑑𝑖𝑖)−(𝑁𝑁∗𝑞𝑞𝑖𝑖)]2
(𝑁𝑁∗𝑞𝑞𝑖𝑖) 𝑖𝑖
𝑖𝑖=1 with a degrees of freedom of four, and a critical value of 9.49 (5%
level). The significance percentage shown is the number of times the chi-squared test was reject. Furthermore, the effective spreads of each portfolio is also presented.
Formation period J-1 J-3 J-6 J-9 J-12
Quintile Market capitalization W L W L W L W L W L
1 Small-capitalization 0.205 0.326 0.187 0.359 0.165 0.395 0.216 0.251 0.153 0.435 2 Capitalization quintile 2 0.206 0.219 0.203 0.219 0.196 0.201 0.192 0.213 0.196 0.201 3 Capitalization quintile 3 0.180 0.158 0.175 0.144 0.178 0.135 0.125 0.157 0.186 0.128 4 Capitalization quintile 4 0.212 0.165 0.207 0.147 0.203 0.128 0.163 0.152 0.190 0.105 5 Large capitalization 0.201 0.146 0.214 0.125 0.206 0.103 0.186 0.112 0.202 0.062 Chi-test 23.02 24.95 20.31 25.01 17.88 29.46 15.12 14.42 17.31 37.51 Significance 70.72% 72.93% 78.65% 80.34% 68.00% 85.71% 62.79% 70.35% 68.05% 93.49%
28 4.2 Results of the restricted sample
The next section will discuss the results regarding the restricted sample. This restricted sample is formed by first, doing the exact same thing as was done with the unrestricted sample as described in the methodology. Secondly, the stocks will be ranked based on their market capitalization (which is based on the market value). After this, the 50% (eight) stocks which have the highest market value will be included in the restricted winner- and loser portfolio. Thus, the stocks will be sorted twice. Moreover, one should note that the number of stocks (N) in all equations displayed in the methodology section will change from sixteen to eight.
4.2.1 Distribution of stocks based on market capitalization
Implying such a restriction on the sample will lead to a higher distribution of big-cap stocks within the portfolios. This can be seen in Table 6. We see that only the loser portfolios of the J-3 and J-6 formation periods are not 100% rejected for each chi-squared test, but they are close to. We see that all portfolios are, as expected, tilted toward the big-cap stocks. The proportion of the biggest cap stocks (Q5) ranges between 19.3% and 42.0%. There are still some included in the portfolio that belong in the small-cap category (Q1), ranging from 0.3% to 5.8%. In general, we see that the loser portfolios are still more tilted towards the small-cap stocks when comparing this with the winner portfolios.
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Table 6 – Market capitalization – Restricted sample, 2001-2016
Following Jegadeesh and Titman (1993) winner (W) and loser (L) portfolios are formed. Both portfolios include an amount of 16 stocks. The stocks are then categorized, and sorted, based on each stock’s market value. The categories are based on five quintiles ranging van small-cap stocks (Q1) to big-cap stocks (Q5) for each formation period. A chi-squared test for normality calculated by 𝑅𝑅2= ∑ [(𝑁𝑁∗𝑑𝑑𝑖𝑖)−(𝑁𝑁∗𝑞𝑞𝑖𝑖)]2
(𝑁𝑁∗𝑞𝑞𝑖𝑖) 𝑖𝑖
𝑖𝑖=1 with a degrees of freedom of four, and a critical
value of 9.49 (5% level). The significance percentage shown is the number of times the chi-squared test was rejected. Furthermore, the effective spreads of each portfolio is also presented.
Formation period J-1 J-3 J-6 J-9 J-12
Quintile Average market capitalization W L W L W L W L W L
1 Lowest 0.014 0.015 0.010 0.030 0.004 0.058 0.003 0.052 0.003 0.035 2 2nd lowest 0.075 0.177 0.064 0.223 0.050 0.149 0.048 0.173 0.041 0.140 3 Medium 0.182 0.218 0.162 0.251 0.175 0.263 0.159 0.232 0.151 0.232 4 2nd highest 0.344 0.288 0.330 0.302 0.341 0.238 0.337 0.227 0.318 0.195 5 Highest 0.361 0.280 0.412 0.193 0.420 0.271 0.381 0.250 0.381 0.299 Chi-test 87.05 67.43 89.71 54.74 89.30 58.24 90.66 64.98 92.82 69.84 Significance 100.00% 100.00% 100.00% 98.88% 100.00% 98.25% 100.00% 100.00% 100.00% 100.00%
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4.2.2. Returns of the momentum investment strategy ex-ante trading costs
In the next section, results of the restricted sample will be discussed and presented in tables. These results will be compared with the results of our unrestricted sample. The same steps as in the unrestricted sample are taken to come up with the results of the unrestricted sample.
Table 7 displays the returns each portfolio ex-ante transaction costs. We find multiple significant positive returns of a zero-sum portfolio, the highest for the J-1;K=9 strategy (8.87%). What’s interesting to see is that not a single loser portfolio generates extra returns for the zero-sum portfolio. The main drivers of the returns are, as was in the unrestricted sample, the winner-portfolios. In general, the returns of the zero-sum portfolios are comparable to the returns of the unrestricted sample. The returns of our restricted sample are slightly lower than the returns of our unrestricted sample. This result is supported by several studies who find that high returns are mostly attributable to small-cap stocks (see e.g. Agyei-Ampohmah, 2007; Novy-Marx; 2012; Booth et al., 2016).
Table 7 – Annualized portfolio returns with no transaction costs – Restricted sample, 2001-2016
All portfolios are constructed the same way as in the unrestricted sample. A restriction is made within these portfolios; the top eight highest market value stocks of the unrestricted sample portfolio are included in the restricted sample’s portfolio. The table presents the annualized returns of every momentum strategy without considering transaction costs. To check whether each return significantly differs from zero, the t-stat of Newey-West’s (1987) standard errors test is calculated. *, **, *** denotes the significance of the t-tests at the 10%, 5%, and 1% level, respectively.
31 Table 7 – Continued Formation period Portfolio Holding period k=1 k=3 k=6 k=9 k=12 J-6 Winner 6.20% 8.84% * 9.20% ** 10.13% *** 11.60% *** (t-stat) (1.043) (1.678) (2.138) (2.615) (3.174) Loser 5.28% 4.28% 7.23% 11.18% 12.10% (t-stat) (0.396) (0.299) (0.657) (1.108) (1.332) Zero-sum 0.92% 4.56% 1.97% -1.05% -0.50% (t-stat) (0.071) (0.332) (0.197) (-0.116) (-0.061) J-9 Winner 9.05% * 7.75% 9.54% ** 11.22% *** 12.41% *** (t-stat) (1.706) (1.573) (2.079) (2.747) (3.182) Loser 9.80% 9.76% 10.87% 10.08% 10.34% (t-stat) (0.769) (0.932) (1.304) (1.398) (1.617) Zero-sum -0.75% -2.00% -1.32% 1.14% 2.07% (t-stat) (-0.063) (-0.221) (-0.200) (0.204) (0.434) J-12 Winner 16.60% * 10.38% * 12.68% ** 12.89% *** 11.97% *** (t-stat) (1.887) (1.673) (2.352) (2.709) (2.810) Loser 6.81% 5.95% 3.98% 4.28% 5.01% (t-stat) (0.786) (0.796) (0.651) (0.821) (1.127) Zero-sum 9.78% 4.43% 8.70% * 8.61% ** 6.95% ** (t-stat) (1.064) (0.845) (1.974) (2.371) (2.029)
4.2.3 Portfolio turnover ratios
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Table 8 – Portfolio turnover - Restricted sample, 2001-2016
The following table presents the average turnovers of both the winner- and loser portfolio as a percentage for each different momentum strategy for the restricted sample. All turnovers are averaged. The percentage between brackets “[]” is the corresponding annualized turnover rate.
Formation period Portfolio Holding period k=1 k=3 k=6 k=9 k=12 Average J-1 Winner 60.38% 89.43% 89.68% 87.50% 90.44% 83.49% [Annualized] [724.58%] [357.71%] [179.36%] [116.67%] [90.44%] [293.75%] Loser 57.91% 87.43% 86.34% 85.95% 87.88% 81.10% [Annualized] [694.92%] [349.71%] [172.67%] [114.60%] [87.88%] [283.96%] J-3 Winner 59.32% 89.36% 89.32% 87.43% 90.44% 83.17% [Annualized] [711.86%] [357.43%] [178.63%] [116.57%] [90.44%] [290.99%] Loser 91.29% 95.50% 95.35% 94.67% 95.18% 94.40% [Annualized] [1095.43%] [382.00%] [190.70%] [126.23%] [95.18%] [377.91%] J-6 Winner 43.64% 70.39% 89.37% 89.77% 91.20% 76.88% [Annualized] [523.70%] [281.58%] [178.74%] [119.70%] [91.20%] [238.98%] Loser 42.27% 66.23% 84.45% 86.59% 88.43% 73.59% [Annualized] [507.23%] [264.91%] [168.90%] [115.45%] [88.43%] [228.98%] J-6 Winner 43.16% 69.64% 89.02% 90.05% 91.43% 76.66% [Annualized] [517.94%] [278.57%] [178.03%] [120.06%] [91.43%] [237.21%] Loser 41.84% 66.89% 85.61% 86.50% 87.74% 73.71% [Annualized] [502.06%] [267.56%] [171.21%] [115.33%] [87.74%] [228.78%] J-12 Winner 42.59% 68.40% 88.22% 88.88% 90.81% 75.78% [Annualized] [511.11%] [273.60%] [176.43%] [118.51%] [90.81%] [234.09%] Loser 42.36% 66.80% 86.23% 86.12% 82.92% 72.88% [Annualized] [508.33%] [267.19%] [172.45%] [114.83%] [82.92%] [229.14%] Average per
holding period Monthly 52.48% 77.01% 88.36% 88.35% 89.65%
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4.2.4 Returns of the momentum strategy post transaction costs of two brokers
Both Table 9 and Table 10 show the returns of each portfolio post-transaction costs of both Plus500 and DeGiro, respectively. When looking at the returns of Plus500 in Table 9 we find that there is still no significant positive return for the zero-sum portfolio. The significant returns from the zero-sum portfolio range from -41.32% (J-3;K=1) to -5.11% (J-3;K=12). The losses are mostly due to the fact that almost all loser portfolios generated a positive return (to add value the
short portfolios should yield a negative return). In general, when we compare the results of
the restricted sample with the unrestricted sample, we find higher returns from the restricted sample. This is mainly attributable due to the fact that the effective spreads are narrower for the restricted sample as is presented in Table 5 and Table 6.
Furthermore, we consider the momentum investment returns post transaction costs of DeGiro as presented in Table 10. The significant returns of the zerosum portfolios range from -38.14% (J-3;K=1) to 6.15% (J-12;K=9). As in the restricted sample, the returns of the zero-sum portfolios are all driven by the winner- portfolio. Moreover, there is not a single loser portfolio that added value to the zero-sum portfolio since all these returns are positive. In fact, we find a significant positive return of a zero-sum portfolio. On average, the returns of the restricted sample produce higher returns than the unrestricted sample. Which, again, is due to the fact that the spreads are lower and we include fewer numbers (so N becomes 50% smaller) of stocks in our portfolios.
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Table 9 –Returns post transaction costs of Plus500, restricted sample
The following table shows all post-transaction costs annualized returns when a private investor uses Plus500 as a broker for the restricted sample. Each portfolio is constructed following JT (1993). The transaction costs are calculated by multiplying the average effective spread by the corresponding portfolio turnover for each portfolio. Moreover, the costs also include a premium that is charged by Plus500ifor holding stocks overnight. Again, t-stats are calculated using the Newey-West (1987) approach. T-stats are depicted between parentheses. ***, **, * denotes the significance of these t-stats at the 1%, 5%, and 10% level, respectively.
Formation period Portfolio
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Table 10 – Annualized portfolio returns post transaction costs of DeGiro, restricted sample
The following table shows all post-transaction costs returns when an investor uses DeGiro as a broker, for the restricted sample. Each portfolio is constructed following JT (1993). The roundtrip costs of broker DeGiro are calculated by adding the effective spread with the fixed and variable costs charged by DeGiro. A portfolio value of €30,000 is assumed, as this is the average portfolio value of which a Dutch private investor has invested in stocks. Returns are annualized and given as a percentage. These returns are tested with the Newey-West (1987) test. The t-stats are presented between parentheses. *, **, *** denotes the significance of the t-test at the 10%, 5%, and 1% level, respectively.
Formation period Portfolio
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5. Conclusion
This study tested if a private investor could generate significant returns following a momentum investment strategy using real-world brokers. The sample consisted of stocks traded on the Euronext Amsterdam exchange market for the period ranging from 2001 to 2016. Pursuing a momentum investment strategy implies holding a zero-sum portfolio. This zero-sum portfolio is obtained by taking an equal long position in a ‘winner’ portfolio as a short position in a ‘loser’ portfolio. The ‘winner’ portfolio includes stocks with the highest return of the past J-months and subsequently a ‘loser’ portfolio includes stocks with the lowest return of the past J-months. This strategy is extensively researched (see e.g. Agyei-Ampohmah, 2007; JT, 1993,2011), and abnormal excess returns were found using this type of investment strategy. Previous literature regarding momentum investing for the private investor entail unrealistic assumptions concerning short-selling and transaction costs (see e.g. Lee and Choy, 2014; Siganos, 2012; Agyei-Ampohmah, 2007).
To deal with these unrealistic assumptions, this paper incorporates trading costs with real world examples. Two different brokers are taken into account so that we can also make a comparison between these two brokers. The two brokers that are found to be the most competitive are Plus500 and DeGiro. With both brokers, a short position can be taken (which is a necessity for obtaining a zero-sum portfolio). The current trading/ commission rates of Plus500 and DeGiro are obtained in order to come up with the trading costs. By doing this, it will give us a realistic view of the actual costs.
Results of this study show that, with no transaction costs, a significant positive return is found pursuing a momentum investing strategy. So, it can be said that a momentum effect is observable on the Amsterdam Euronext stock exchange. This return is, in contrary to other papers, mostly attributable to the winner-portfolio. Thus, a momentum effect is observed and, without roundtrip costs and constraints regarding short-selling, these effects are exploitable. But, because the analysis was done regarding a private investor and this investor faces trading costs, these costs need to be taken into account. When these costs are considered, the positive returns of the ex-ante transaction costs portfolios diminish. There is no significant positive zero-sum portfolio found for the unrestricted sample, which is a result of the high transaction costs. However, there are some winner portfolios found that are significantly positive when the private investor chooses DeGiro as a broker.
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rebalancing of a portfolio. This frequent rebalancing leads to high turnover rates which in their turn imply high trading costs. The other main driver for high trading costs is the wide effective spreads. Wide spreads are often associated with small-cap stocks and the distribution of the portfolios is tilted towards these small-cap stocks. So, to narrow this gap, this study made a restriction on the capitalization of stocks included in the portfolio.
Regarding this restricted sample, the stocks were first sorted on their returns (same as in the unrestricted sample) and then the 50% of stocks with the largest market value are included in the new restricted portfolios. With this approach, a significant drop in the effective spread was observed, just like we want to achieve by imposing this restriction. The results of this restricted sample are collected in a comparable fashion as was done by the unrestricted sample. Only one positive post-cost return was found for the zero-sum portfolio namely for the J-9;K=12 momentum strategy when making use of DeGiro as broker. A significant return of 6.15% was generated by following this strategy. On average, online broker DeGiro yielded higher returns when comparing this to Plus500. This is mainly explained by the fact that DeGiro’s fixed and variable costs added together is almost every time lower than the extra premium you have to pay for holding a position per day at Plus500. Concluding, we analyzed 25 different momentum strategies and obtained returns pre- and post- trading costs. We find that there is a momentum effect on the Euronext Amsterdam stock market. However, due to the trading costs, this effect can’t be exploited by using a zero-sum momentum investment strategy. This finding supports our hypothesis.
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6. Limits and recommendations
The next section will discuss the limitations this study had, and come up with suggestions for further research. First, the biggest assumption, the perfect foresight, will be discussed. This assumption is an offspring of the survivorship bias. Other studies deal with this bias in a lot of different ways. Multiple studies show that this survivorship bias only counts for less than 1%, or just 20 basis points. In our sample, a technique to deal with this bias was tested by giving the delisted firms a one-time hit of -100% and 0% afterwards, but this technique influenced the results with more than 250 basis points, which is a lot more than is found in other studies. So, this is probably not the best way to deal with the survivorship bias on the Amsterdam Euronext stock market. Other techniques or risk-adjusted returns with regards to this survivorship bias could improve this study.
This study doesn’t incorporate risk-adjusted returns. This could be done for example the market risk and liquidation risk. Carhart’s (1997) model could be used to make adjustments to the risk returns or this model could be used to generate an alpha for excess returns.
Furthermore, we find the post-cost returns by first generating ex-ante returns and at a later phase incorporating the transaction costs. It would also be interesting to already incorporate the transaction costs before forming the portfolios. This would probably lead to portfolios that are biased towards big-cap stocks, which this study also tried to obtain by making a restriction on the market value of stocks.
Something else to consider is the overlapping holding periods. This study examined the returns by using an overlapping holding period. This helps to reduce the effect of bid-ask bounce bias. However, it is not likely that a private investor would use these overlapping holding periods. So, one could also study the effect without an overlapping holding period and actually generate returns of how a private investor would act in the real world.
In this study, all stocks included in the portfolios are equally weighted. It might be interesting to examine if it is possible to produce a strategy that leads to an optimally-weighted portfolio.
