Master Thesis
Finance
Can retail investors exploit the momentum effect?
By W.M. van Lookeren Campagne
Abstract
Existing literature in the field of momentum investing often considers unrealistic assumptions for the retail investor. This paper examines if retail investors can exploit the momentum effect using current competitive transaction fees of two brokerage firms in the Netherlands. Results show that there is a momentum effect on the Dutch stock market over the period of 2000 - 2015, but the potential profitability disappears after accounting for transaction costs and short selling costs. These high costs are a result of high turnover ratios and high spreads, induced by the large proportion of small capitalization stocks found in the momentum portfolios. Retail investors can exploit some of the momentum effect when the sample is restricted, where a higher proportion of large capitalization stocks considerably reduces the spreads and momentum returns exceed the costs of trading.
Key words: momentum strategy, momentum effect, individual investor, retail investor, market
inefficiency, bid-ask spreads, online brokers, transaction cost, contract for differences, CFD
Author: Willemijn Maria van Lookeren Campagne Email: willemijn.campagne@gmail.com
1. Introduction
Momentum investing has received considerable attention in the last few decades. Not only because it challenges the efficient market hypothesis by Fama and French (1996), but also because a vast amount of literature has shown that the momentum effect could prove to be a profitable short-term investment strategy yielding structural significant returns. Price momentum occurs when the price of a stock moves in the same direction for a recognizable period of time. An investor could exploit the momentum effect by buying stocks with a recent history of over-performance (winners) while going short in stocks with a recent history of underperformance (losers). By electing this investment strategy, profits can be obtained by strategically creating long-short portfolios during the momentum phase and closing these positions as the momentum phase ends (Booth et al., 2015). These strategic portfolios are known as a zero-sum investment as the proceeds of selling the loser portfolios are used to buy the winner portfolios.
Although seemingly an effective strategy, it has been argued that momentum returns may not be exploitable in practice due to transaction costs and short selling constraints (Korajczyk and Sadka, 2004; Lesmond et al., 2004; Ali and Trombley, 2006; Thomas, 2006; Li et al., 2009). Momentum investing entails buying and selling stocks more frequently compared to long-term investment strategies, consequently creating higher transaction costs for the investor. Moreover, several papers (Hong et al., 2000; Ali and Trombley, 2006; Agyei-Ampomah, 2007; Siganos, 2012; Booth et al., 2015) show that the momentum return is largely attributable to small capitalization stocks and that these stocks have higher spreads than large capitalization stocks. High spreads, which are part of the transaction costs, could diminish the potential profitability of this investment strategy.
Contracts for Differences (CFDs), are cheaper and provide a feasible short selling possibility for retail investors. Furthermore, this paper examines the potential profitability of momentum effect when small capitalization stocks are excluded.
Results of this paper show that there is a momentum effect to be observed, but the investment strategy cannot be regarded as profitable after all transaction costs are taken into account. The momentum investment strategy is mainly driven by stocks that have over-performed in recent months, where an investor takes a long position, instead of stocks that have underperformed in recent months, where an investor takes a short position. Furthermore, results show high turnover ratios which consequently results in high transaction costs and show a large concentration of small capitalization stocks in the portfolios with high spreads, which diminishes the opportunity to exploit the momentum effect. When the sample is restricted and only half of the stocks with the highest market value are included in the
portfolios, spreads decrease considerably and retail investors can achieve abnormal returns by momentum investing.
The remainder of this paper is structured as follows: Section 2 is ascribed to provide a theoretical framework of momentum investing. Additionally, previous studies are set out and the implications of transaction costs and short selling constraints are discussed. Moreover, the current conditions of the retail investor on the Dutch stock market are defined. Section 3 describes the methodology and the data used to execute the research question of this paper. Section 4 presents and analyses the empirical results of the research, followed by Section 5 which states the main conclusions. Limitations and recommendations for future research are presented in Section 6.
2. Theoretical framework
This section will explain what momentum investing is and provides an overview of the most relevant previous studies concerning the momentum effect. Furthermore, previous literature about transaction costs, short selling constraints and retail investors will be presented.
2.1 Momentum investing
Momentum investing is a short-term investment strategy where an investor
occurs when the price of a stock moves in the same direction for a recognizable period of time. Studies about the momentum effect of individual stocks received substantial attention after Jegadeesh and Titman (1993, 2001). These two authors assert that investors can attain profitable results by holding a zero-sum portfolio that consists of long positions in stocks that have over-performed in the past (so called winners) and short positions in stocks that have underperformed in that same period (so called losers). Their papers show that on average past winners continue to outperform past losers on an intermediate time horizon of three to 12 months.
Several studies have confirmed and extended the findings of Jegadeesh and Titman (1993, 2001). For example, Rouwenhorst (1998) exemplified the existence of momentum profits in European countries. Chan et al., (2000) provide evidence of momentum profits in international equity markets and apply momentum strategies across asset classes and illustrate that very little profit comes from predictability in currency markets. Galariotis (2010) underlines that momentum strategies are significantly profitable in equities, Okunev and White (2003) provide evidence of momentum profits in major currencies. Agyei-Ampomah (2007) examines momentum strategies in the UK market and concludes that the profitability of the momentum strategy disappears on the short horizon due to transaction costs.
Returns of momentum investing are considered a market anomaly. The efficient market hypothesis implies that investors cannot predict future stock prices with historical information, various studies have been done to explain why momentum exists. Bandarchuk and Hilscher (2013) find that firm characteristics are unable to explain momentum
adequately. Several studies (Chan et al., 1996; De Bondt and Thaler, 1987; Jegadeesh and Titman, 2001; Hong et al., 2000) find a behavioural explanation for the momentum effect, in the sense that momentum profits may be a result of a delayed overreaction to information that is subsequently reversed.
Momentum investing is not always considered profitable according to others. Several studies demonstrate that momentum investing is far from risk free (e.g. Grundy and Martin, 2001; Wu, 2002; Johnson, 2002; Hung, 2008; Ho and Hung, 2009; Gu and Huang, 2010). Griffin et al. (2003) revealed unconvincing results concerning momentum strategies in
emerging equity markets. Hameed and Kusnadi (2002) suggest that the contributing factors to the momentum effect in the United States (US) do not prevail in the Asian markets.
Rouwenhorst (1998) was one of the first authors to provide evidence of momentum effects on the Dutch stock market, Liew and Vassalou (2000) also found positive and statistically significant momentum returns for the Netherlands. Karathanasis et al. (2010) showed, amongst other European markets, significant momentum returns although they state that it would be difficult to exploit these returns in the short to medium run, because they are only positive and sizeable in very few years of their sample.
2.2 Transaction costs
The returns of a momentum investing strategy should exceed the transaction costs to ensure profitability. The various costs incurred during the implementation of a momentum strategy are: bid-ask spread; broker’s commission and short sale costs. Momentum strategies are relatively intensive to maintain, due to frequent rebalancing. These high amounts of turnover, a measure of how frequent stocks are bought and sold, result in high transaction costs. These costs could diminish potential profits from momentum investing so their impact should be carefully considered.
Korajczyk and Sadka (2004) test whether momentum-based strategies that have previously shown to earn high abnormal returns remain profitable after considering price impact induced by trading. They find that momentum investing remains profitable when transaction costs are calculated as proportional costs equal to the effective and quoted spreads. The price impact of trading leads to a large decline in the apparent profitability of some previously studied momentum-based strategies.
Lesmond et al. (2004) find that momentum investing is not profitable when taking into account transaction costs. They show that stocks that generate large momentum returns are generally also the stocks with the highest transaction costs, consequently abolishing potential profits. They state that the profits of momentum investing are non-existent, mainly because the returns associated with momentum investing do not exceed transaction costs.
studying the momentum effect do not consider transaction costs in their design, which consequently reduces turnover and therefore transaction costs.
Most papers assume transaction costs on an estimated averaged one-way cost of 0.5%, such as Jegadeesh and Titman (1993) and Liu et al. (1999). This estimate is based on average transaction costs and thus ignores the kind of stocks that goes into the momentum portfolio or the frequency of trades from rebalancing the portfolio. Grundy and Martin (2001) calculate that at round-trip transactions costs of 1.50%, the profits on a long-short momentum strategy become statistically insignificant. At a round-trip transactions cost of 1.77%, they find that the profits on the long-short momentum strategy are driven to zero. Agyei-Ampomah (2007) estimates transaction costs using three alternative measures: quoted bid-ask spread plus commissions and taxes, effective bid-ask spread plus commissions and taxes, and the limited dependent variable (LDV) measure of implied total transaction costs proposed in Lesmond et al. (1999).
Transaction costs are reliant on the portfolio turnover in momentum investing, a higher turnover implies buying or selling stocks more frequently to maintain the top/bottom decile portfolio of returns in momentum investing. Aygei-Ampomah (2007) shows
significant positive returns for strategies involving longer holding and formation periods. If a stock is evaluated over a longer formation period on its return, these returns are assumed to be more robust, the stock will not be excluded from the portfolio, which consequently would result in a lower turnover ratio. Short holding periods result in higher turnover ratios and longer holding periods are linked to lower turnover ratios. This is relevant for investors because high turnover ratios lead to excessive transaction costs, limiting potential profits of momentum strategy.
Agyei-Ampomah (2007) and Siganos (2012) show that large capitalization stocks tend to have lower transaction costs, as these stocks have a lower spread. Siganos (2012) finds that bid-ask spreads vary significantly among portfolios, spreads are very high for small capitalization firms and for low priced securities. In contrast, spreads are low for large
capitalization firms and high priced companies. Booth et al. (2015) contend that the
2.3 Short selling constraints
Short selling is the sale of a stock that is not owned by the seller or that the seller has borrowed. Short selling is motivated by the belief that the price of a stock will decline, enabling it to be bought back at a lower price to make a profit. Momentum investing strategy involves taking a long position in stocks that have showed recent over-performance and taking a short position in stocks that have showed recent underperformance.
Ali and Trombley (2006) show that momentum profits are largely driven by short sales, using the index by D’Avolio (2002) they show that the magnitude of momentum
returns is positively related to short sales, and loser stocks rather than winner stocks drive this result. Moreover, their results suggest that short sale constraints are an explanation for many of the previously reported momentum returns and find that actual short sales constraints prevent the arbitrage of momentum returns. Furthermore, their results indicate that for momentum-related arbitrage, short selling costs are more important than direct transaction costs. Ali and Trombley (2006) state that direct transaction costs are incurred when buying or selling a stock and that short selling is a cost that continues over the length of the period that the short position is maintained. Assuming that these short positions are maintained for several months, when pursuing momentum investing, short selling costs tend to be larger than direct transaction costs. D’Avolio (2002) argues that the cost of short selling for retail
investors is more than for institutional investors, because retail investors typically receive no interest on their short sale proceeds.
Jones and Lamont (2002) state that in addition to these direct costs, there are other costs and risks associated with shorting, such as the risk that the short position will have to be involuntarily closed due to recall of the stock loan. Also, legal and institutional constraints can inhibit retail investors from selling short. Thomas (2006) also emphasizes the importance of short selling costs and undelines that studies about arbitrage strategies should really
contain appropriate transaction costs, including potentially substantial short selling costs. Moreover, he argues that this has been neglected to date in the literature.
2.4 Momentum investing for the retail investor
institutional investors. Siganos (2010) argues that previous studies in the field of momentum are not representative for retail investors. The majority of these studies revolve around large portfolios that a retail investor would not be able to hold financially. Retail investors are unlikely to be able to buy or short hundreds of companies, this paper examines momentum investing based on a smaller number of stocks in the portfolios. Previously reported
momentum profits may not be available to retail investors who have more trading constraints such as higher transaction costs, product accessibility, short sale constraints and other market imperfections.
Pettengill et al. (2006) argue that the momentum investment strategy is not equally profitable for professional investors and retail investors. They examine and compare professional and retail investors to determine if they appear to engage in momentum investing and if their investment strategies are be profitable, they find that momentum
investing is not a viable strategy for retail investors. They also find evidence that professional investors tend to be more disciplined and well informed which results in a higher profitability compared to the retail investors.
Several studies have investigated the trading behaviour of retail investors. McKay (2005) reasons that retail investors are too slow to “catch the train” when stocks reveal momentum return. He finds that retail investors only purchase these momentum stocks when professional investors have already bought them, creating an adverse effect for retail
investors. Hoffmann and Shefrin (2014) investigate Dutch retail investors who use technical analysis and trade options frequently and find that they make poor portfolio decisions, resulting in lower returns than other investors, because they are more prone to speculation on short-term stock market developments. They state that retail investors that use technical analysis hold more concentrated portfolios, have a higher turnover and are less inclined to bet on reversals.
brokerage firms were able to lower trading fees by becoming online brokers and improve their efficiency.
In the Netherlands there has been a fierce competition1 among brokerage firms with the entrance of DeGiro2 in 2013. DeGiro is an online brokerage where retail investors can buy and sell securities. Several brokerage firm surveys reveal that DeGiro is one of the most competitive brokerage firms on the Dutch market3. DeGiro is growing fast and already has more than 80.000 clients in the Netherlands4, above all: they are planning to launch a free trading platform called DeZiro where investors can trade securities without commission fees and these commission fees are compensated by online advertisements. Currently, brokerage firms are not permitted to wield this type of revenue model according to The Netherlands Authority for the Financial Markets (AFM).5 These development within the brokerages markets have important implications for retail investors and investing strategies such as momentum investing.
As mentioned earlier, momentum investing involves going long in stocks that showed positive returns and shorting stocks with negative returns in the previous months. Short selling has only became available to retail investors in the last few years. Still, only a very limited amount of brokerage firms offer the possibility to sell short for retail investors. DeGiro enables retail investors to sell short, except for American securities6.
Lee and Choy (2014) show that retail investors use Contract for Differences (CFDs) for short selling. A CFD is a tradable instrument that mirrors the movements of the asset underlying it. Consequently, profits and losses of a CFD depend on the movement of the underlying asset, yet the actual underlying asset is never owned by the investor. Siganos (2012) investigates if retail investors can exploit market anomalies, such as the momentum effect, with CFDs. The advantage of CFDs, in comparison to the physical borrowing of shares, is that retail investors can sell short more easily. Another advantage of trading CFDs is pointed out by Leelarthaepin (2006), who states that trading CFDs are cheaper than buying or selling the underlying stocks and could therefore provide a profitable instrument for short-term investment strategies.
Apart from DeGiro, Plus500 is one of the most competitive brokerage firms for Dutch retail investors to trade7. Plus500 offers Dutch retail investors the opportunity to trade CFDs without commission fees. This means that the investor pays the effective spread and an overnight funding premium for long positions and receives a funding premium for short positions. Plus500 has been very popular among Dutch investors8, although the AFM has cautioned retail investors of the great risks associated with the leverages of CFDs9.
To conclude, several papers have demonstrated that stocks show momentum, also on the Dutch stock market. An investor could exploit the momentum effect by strategically creating a zero-sum investment, where he takes a long position in stocks that have over-performed in recent months and takes a short position in stocks that have underperformed in recent months. This short-term investment strategy entails buying and selling stocks frequently, which
consequently results in high transaction cost. Returns of momentum investing should exceed the costs of trading to yield a viable investment strategy. Existing literature in the field of momentum investing assumes unrealistic transaction costs, short selling costs and portfolio volumes for retail investors. This paper examines if Dutch retail investors could exploit the momentum effect by using the current rates of two competitive online brokerage firms that allow retail investors to take a short position. Both physical ownership of stocks and trading through CFDs are analysed. In addition, a second analysis is done where the stocks in the portfolios are double-sorted, first on return and then on market value, to examine the trade-off between returns generated by small capitalization stocks and the relative high spreads they induce.
Following from the literature review, the next hypothesis is formulated:
Significant positive momentum returns are observable in the Dutch stock market, but retail investors cannot exploit these returns due to transaction costs and short selling costs.
3. Data and methodology
This section will present the data and methods used to examine momentum returns in the Dutch stock market. Also, the methods and equations used to determine the winner and loser portfolios will be discussed and the turnover ratios and transaction costs for retail investors are shown and explained.
3.1 Data
The data analysis begins with extracting information from all stocks traded on
Euronext Amsterdam from Datastream (Thomson Reuters), in the time period of June 2000 to August 2015. Following the research done by Agyei-Ampomah (2007), all investment trusts and warrants are excluded. This analysis covers only this 15 year period, since the bid- and ask-price data are needed to estimate the cost of trading and are only sufficiently available from June 2000 onwards. The sample used includes both surviving and non-surviving stocks and is therefore free from survivorship bias, according to Agyei-Amphomah (2007). In total, the sample includes 390 stocks and the number of stocks available ranges between 276 and 363 with an average of 317 stocks. The average amount of stocks traded in the sample period, measured by volume of turnover, is 158. For each stock in the sample, information on
monthly returns (RI), volume turnover (VO), market value (MV), bid price (PB) and ask price (PA) is obtained. All information is collected at the middle of the month, because of the monthly effect investigated by Boudreaux (1995) and Cowell (2013) amongst others. The current rates of DeGiro and Plus500 are extracted from their websites.
3.2 Methodology
The momentum portfolios are formed following the same approach as used by Jegadeesh and Titman (1993). This is the standard technique in the literature on momentum strategies. Jegadeesh and Titman (1993) examine the performance of trading strategies with formation and holding periods between three and 12 months. Their strategy selects stocks based on their returns over the past J months and holds them for K months. Each month, stocks are ranked according to their total returns over the previous J months (J =1, 3, 6, 9 and 12), this is the so-called formation period. Barber and Odean (2011) show that retail investors tend to trade actively also on the very short-term horizon, Demir et al. (2004) find significant momentum effect in Australian equities over both very short-term (one week to one month) horizon and short-term (three to 12 months) horizon. Therefore, this analysis also includes a formation and holding period of one month in addition to the standard holding and formation periods mentioned in the literature.
periods. Logically, a loser portfolio of 16 stocks, the bottom decile of stocks traded, is formed based on the worst returns in the different formation periods. The formation period
symbolizes the period that the return of a stock is assessed to include a stock in either the winner or loser portfolio. For example, J=1 indicates that the 16 stocks in the winner portfolio in August are selected on the highest returns from July to August (t= -1 to t=0).
𝑅𝑖𝑡 =𝑅𝐼𝑖𝑡 − 𝑅𝐼𝑖(𝑡 − 𝐽) 𝑅𝐼𝑖(𝑡 − 𝐽)
The performance of each portfolio is calculated over a holding period of K months, following the formation period (K = 1, 3, 6, 9 and 12). It is common in the literature to start the holding period one month after the formation period, to avoid some of the bid-ask spread, price pressure and lagged reaction effects documented in Jegadeesh (1990) and Lehman (1990). For example, K=1 indicates that the performance of the winner portfolio in August is based on the returns from October to September (t=2 to t=1). In this paper a strategy of, for example, a three month formation period and a six month holding period will be abbreviated to J*K 3*6.
The returns of the portfolios (𝑅𝑝) are measured by Equation 2, where (J*K) stands for the different formation and holding periods respectively at time t. The stocks in each portfolio are all equally weighted, N stands for the amount of stocks in portfolio, which is 16 stocks per portfolio in this analysis.
𝑅𝑝(𝐽∗𝐾) = 1
𝑁 𝑅𝑖𝑡 (𝐽 ∗𝐾)
According to Liu et al. (2009) statistical power is increased if delisted stocks are also included. The momentum returns are likely to be downward biased since delisting, as a result of liquidations, are more likely to be in the loser portfolios. The ‘winner minus loser’
portfolio, abbreviated as W-L, is the zero-sum investment strategy of selling the loser portfolio to buy the winner portfolio and, consistent with Jegadeesh and Titman (1993), the portfolio returns are calculated on an overlapping holding period basis. The monthly portfolio returns are likely to be autocorrelated because the portfolios are calculated on a rolling basis.
Following Agyei-Ampomah (2007), all the t-values are calculated using Newey and West (1987) heteroskedastic and autocorrelation consistent standard errors.
To maintain a momentum strategy, an investor has to rebalance the portfolios at the end of each holding period, excluding stocks that do not belong to the best or worst
performing decile from the winner or loser portfolio respectively and adding the stocks that do meet this criteria. These turnover ratios, calculated as shown in Equation 3, are important because high turnover ratios induce high transaction costs. The turnover ratio (TR) is
calculated by the amount of new stocks in the portfolio (𝑆𝑛𝑒𝑤) divided by the total amount of stocks in the portfolio (N), which is 16 for all the portfolios. The turnover ratio of each portfolio is multiplied with each transaction cost incurred to make a proper estimation of the total transaction costs.
𝑇𝑅 =𝑆𝑛𝑒𝑤𝑁
Lee and Ready (1991) argue that quoted spreads may provide misleading estimates of actual transaction costs because trades are often executed within the bid and ask
quotes. Alternatively, investors may also face trading prices that are outside the spread for orders larger than normal market size. Therefore, several studies use the effective bid-ask spread to measure the ‘true’ transaction costs (see for example, Roll, 1984). Badreddini et al. (2012) also argue that the effective spread is a more appropriate measure than the quoted spread, because the quoted spread suffers from a shortcoming as it employs the bid-ask quotes prior to the portfolio formation and these spreads tend to vary over time. With respect to momentum strategies, using pre-ranking or ranking period bid–ask spreads might consequently incorrectly estimate the cost of trade. It is, therefore, essential to examine the impact of variations in the spread on momentum profits using bid and ask prices at the time of execution of momentum strategies (Badreddini et al., 2012). The effective spread (ES) is the difference between the transaction price and the bid-ask midpoint and calculated according to Equation 4, where PA is the ask price and PB is the bid price.
𝐸𝑆 =(𝑃𝐴 – 𝑃𝐵)
((𝑃𝐴+𝑃𝐵)2 )
To examine whether Dutch retail investors could profit from momentum investing, realistic and current transaction costs of two different online brokerage firms are used. As mentioned earlier, trading fees are declining but to ensure a proper post-cost profitability
(3)
research current fees are used. Furthermore, a retail investor would most likely make use of the cheapest online brokerage firms available, so the rates of DeGiro and Plus500 are used in the scope of this research. Other papers include a stamp duty to their round trip transaction cost, but there is no stamp duty in the Netherlands10.
DeGiro charges a fixed amount of €2.00 per transaction, plus an additional 0.02% of variable costs with an maximum amount of €30.0011. Furthermore, DeGiro charges a 1.00% fee on an annual basis for going short. An average Dutch retail investor has a portfolio of stocks worth approximately €30,000.0012
, this amount is used when calculating the transaction costs for momentum investing. The roundtrip cost for a retail investor trading trough DeGiro for long and short positions are calculated as shown in Equation 5.2 and 5.3 respectively. 𝑅𝑜𝑢𝑛𝑑𝑡𝑟𝑖𝑝 𝑐𝑜𝑠𝑡 𝐷𝑒𝐺𝑖𝑟𝑜 (𝑙𝑜𝑛𝑔) = ( 𝑁 ∗ 𝑇𝑅 ∗ €4.00) + (0.04% ∗ 𝑉𝑃 ∗ 𝑇𝑅) + (𝐸𝑆 ∗ 𝑇𝑅) 𝑅𝑜𝑢𝑛𝑑𝑡𝑟𝑖𝑝 𝑐𝑜𝑠𝑡 𝐷𝑒𝐺𝑖𝑟𝑜 (𝑠ℎ𝑜𝑟𝑡) = ( 𝑁 ∗ 𝑇𝑅 ∗ €4.00) + (0.04% ∗ 𝑉𝑃 ∗ 𝑇𝑅) + (𝐸𝑆 ∗ 𝑇𝑅) + (1% ∗𝑉𝑃 12)
(€4.00 times eight new stocks) and the variable costs are €6.00 (0.04% times €30.000 times 50%), also the effective spread of the new stocks is added to the total costs of trading.
Plus500 is the other brokerage firm used to examine the potential profitability for Dutch retail investors. At Plus500 a retail investor can execute a momentum strategy trough CFDs. A retail investor pays the effective spread and is charged for a funding premium to cover the benefit or cost of the associated funding13.
With CFDs an interest premium is charged on long positions that are held overnight, this funding premium is considered an investment where Plus500 lends money to buy the underlying security. Accordingly, an investor receives the premium when shorting the
security. Stocks traded on Euronext Amsterdam are charged a 0.03% premium on average for long positions held overnight, the average premium for short positions is 0.01%. The
transaction costs for a round trip cost for winner and loser portfolios using Plus500 as brokerage firm are calculated as shown in Equation 6.1 and 6.2 respectively. The number of days for each holding period, K = 1, 3, 6, 9 and 12, are 30, 90, 180, 270 and 360 respectively. In the scope of this research margin requirements are not included.
𝑅𝑜𝑢𝑛𝑑 𝑡𝑟𝑖𝑝 𝑐𝑜𝑠𝑡 𝑃𝑙𝑢𝑠500 (𝑙𝑜𝑛𝑔) = (𝐸𝑆 ∗ 𝑇𝑅) + 0.03% ∗ # 𝑜𝑓 𝑑𝑎𝑦𝑠
𝑅𝑜𝑢𝑛𝑑 𝑡𝑟𝑖𝑝 𝑐𝑜𝑠𝑡 𝑃𝑙𝑢𝑠500 (𝑠ℎ𝑜𝑟𝑡) = (𝐸𝑆 ∗ 𝑇𝑅) − 0.01% ∗ # 𝑜𝑓 𝑑𝑎𝑦𝑠
Several papers (Hong et al., 2000; Ali and Trombley, 2006; Agyei-Ampomah, 2007; Siganos, 2012; Booth et al., 2015) demonstrate that the momentum effect is largely
attributable to small capitalization stocks and that these stocks have higher spreads than large capitalization stocks. Following Agyei-Ampomah (2007), a chi-squared test is done to provide insight into the type of stocks in the winner and loser portfolios, in particular to examine whether the two extreme portfolios are disproportionately weighted towards small capitalization stocks compared to the weight of those stocks in the total sample. The total sample is sorted into five quintile groups based on market value, a decent indicator for market capitalization, hence each quintile has a proportion of 0.2, denoted as 𝑚𝑖. Then, the
proportion of stocks of each portfolio, denoted as 𝑝𝑖, from each market capitalization quintile
13
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is calculated and compared with the total sample. To test whether the distribution of stocks in the portfolio at a point in time is significantly different from the total sample distribution, a chi-squared test (𝑋2) is used as shown in Equation 7. The 𝑋2 is calculated each month and
averaged over the sample period, N is the portfolio size (16 stocks) and I is the number of groups (five groups) with I-1 degrees of freedom.
𝑋2 = ∑(𝑁𝑝𝑖− 𝑁𝑚𝑖)2
𝑁𝑚𝑖
𝐼
𝑖=1
To illustrate, suppose there are 16 stocks in portfolio P at time t and suppose that five out of 16 stocks in the portfolio come from the first size quintile, then 𝑝1 for Portfolio P is
0.313 (i.e. 5/16). In this case the weight of Size Quintile 1 in portfolio P is 31.3% compared to 20% in the total sample.
The methods and equations described above are also performed on the restricted sample. In the restricted sample the stocks in each portfolio are selected on their returns in previous J months, identical to the method described above for the unrestricted sample, and then ranked on their market value. The stocks in the portfolios of the restricted sample are the eight stocks that show the highest (lowest) return and the highest (highest) market value for each winner (loser) portfolio. So, the number of stocks (N) in the equations above is eight for the restricted sample.
4. Empirical results
This section shows and analyses the post-cost profitability of momentum investing for the Dutch retail investor between 2000 and 2015. First, the annualized returns without transaction costs are discussed and the turnover for each formation and holding period are examined. Then, the returns of momentum investing when using Plus500 and DeGiro as brokerage firms are analyzed and compared. In addition, the results of the chi-squared test are shown to examine if the stocks are disproportionally weighted to small capitalization stocks compared to the sample. Moreover, the same analysis is performed on the restricted sample, where the stocks in each portfolio are double-sorted, first on return and then on market value. The restricted sample includes the stocks with the highest market value.
4.1 Unrestricted sample
The unrestricted sample includes all stocks in the sample.
4.1.1 Momentum investing without transaction costs
Table 1 shows the returns of the portfolios, without transaction costs, between 2000 and 2015. As described in Section 3, the same technique as Jegadeesh and Titman (1993) is used where the portfolios are ranked during the formation period (J = 1, 3, 6, 9 and 12 months) and the returns of different holding periods (K = 1, 3, 6, 9 and 12 months) are shown. For example, a strategy with a six months formation period and a three months holding period will be abbreviated to J*K 6*3. Momentum investing involves creating a long-short portfolio, denoted as W-L, of the so-called winner and loser portfolio. The winner portfolio consists of the 16 stocks, the top decile of stocks traded, with the highest returns in the previous J months. Naturally, the loser portfolio consists of the 16 stocks, the bottom decile of stocks traded, with the lowest returns in the previous J months. The portfolios are equally weighted and created on a rolling basis. To avoid autocorrelation, due to overlapping months, all the t-values are calculated using Newey and West (1987) heteroskedastic and autocorrelation consistent standard errors. In every table the returns are annualized to make the returns easily comparable with other papers. Table 1 examines whether there is
momentum effect on the Dutch stock market between 2000 and 2015, without considering transaction costs. Table 3 and Table 4 show the returns of performing a momentum strategy on the Dutch stock market when using two different online brokerage firms. These online brokerage firms are easy accessible for Dutch retail investors and allow for short selling. Table 5 shows the momentum returns net of effective spread, without considering short selling costs or commission fees.
Table 1 shows that, without considering transaction costs, there are several significant momentum investing profits attainable on the Dutch stock market between 2000 and 2015. The highest zero-sum strategy, that is W-L, generates a 14.03% annualized return for strategy
J*K 6*9, significant at the 10% level. Eight (out of 25) strategies show significant profits for
1989. Rouwenhorst (1998) finds 16.20% as highest attainable return of momentum investing for the European stock market between 1980 and 1995. More recent evidence, such as Chaves (2012) finds momentum profits up to 35.43%, 22.04% and 23.23% in France, Germany and the UK respectively between 1927 and 2011.
It is remarkable that the significant W-L returns are solely driven by the winner
portfolios, there are no significant returns in the loser portfolios where an investor can profit from short selling. Griffin et al. (2003) find that returns from the W-L portfolio in European markets are largely driven by the loser portfolios. Similar findings have been reported by Hong et al. (2000), Grinblatt and Moskowitz (2003) and Doukas and McKnight (2005) for other markets. They conclude that any restrictions on short selling would affect the viability of the strategy, this would not be the case in the scope of this research since profits are driven by the winner portfolios.
The most profitable winner portfolio is for strategy J*K 9*6, which shows an annueal return of 14.92%. Here, an investor would generate a higher return with a long only portfolio instead of pursuing a long-short strategy. There is not a significant profitable loser portfolio, strategy J*K 3*9, 3*12 are the only significant returns for the loser portfolios but here the returns of the stocks in the loser portfolio increased, while a profit is only made with short selling when a stocks return decreases. As mentioned above, this is in contradiction with most other studies that find profitable loser portfolios.
Table 1.
Average annualized portfolio returns without transaction costs, 2000 – 2015 (unrestricted sample).
Each month stocks are ranked in ascending order based on previous J months performance. The stocks in the top decile are assigned to the winner portfolio, the stocks in the bottom decile are assigned to the loser portfolio. Both portfolios contain 16 stocks. The portfolios are equally weighted and the annualized returns of each portfolio after holding for K months are displayed for each formation period. W-L shows the return of the zero-sum strategy where an investor goes long in the winner portfolio and goes short in the loser portfolio. For each return, the t-values of the Newey-West standard errors test are shown to check whether the returns of the portfolios are significantly different from zero. *, ** and *** denotes significance at the 1%, 5% and 10% level respectively.
Formation
period Portfolio Holding period
Table 1 continued Formation
period Portfolio Holding period
K=1 K=3 K=6 K=9 K=12 J=3 Winner 9.858% 8.562% 10.706%** 12.766%* 11.859%* (t-value) (1.364) (1.435) (2.061) (2.851) (2.846) Loser -2.198% -4.732% -5.677% -6.597%** -6.164%** (t-value) (0.382) (0.874) (1.490) (2.000) (2.010) W-L 7.661% 3.830% 5.030% 6.169%** 5.695%*** (t-value) (1.328) (0.663) (1.388) (2.076) (1.904) J=6 Winner 11.407%*** 12.146%** 14.767%* 14.678%* 12.378%* (t-value) (1.747) (2.101) (2.996) (3.331) (3.110) Loser 0.961% 0.812% -1.198% -0.641% -1.393% (t-value) (-0.071) (-0.055) (0.113) (0.085) (0.215) W-L 12.368% 12.958% 13.569% 14.037%** 10.985%*** J=9 Winner 12.832%** 14.376%* 14.924%* 13.219%* 11.692%* (t-value) (2.187) (2.731) (3.191) (3.198) (3.055) Loser 3.918% -0.317% -2.904% -1.237% -2.250% (t-value) (-0.270) (0.020) (0.261) (0.166) (0.360) W-L 16.75% 14.06% 12.02% 11.98%*** 9.44% (t-value) (1.267) (0.922) (1.112) (1.675) (1.570) J=12 Winner 13.429%** 12.875%* 12.611%* 11.761%*** 11.195%* (t-value) (2.341) (2.698) (2.959) (2.883) (2.786) Loser -2.958% -6.845% -6.271% -3.750% -4.980% (t-value) (0.191) (0.413) (0.543) (0.497) (0.807) W-L 10.471% 6.030% 6.340% 8.011% 6.214% (t-value) (0.700) (0.370) (0.563) (1.086) (1.010) 4.1.2 Turnover ratios
Table 2 shows the turnover ratios per holding period and annualized for each strategy. Recall that the turnover ratio is calculated by the amount of new stocks in a portfolio divided by the total amount of stocks in the portfolio for each winner and loser portfolio. Turnover ratios are important to consider for momentum investing because a higher turnover results in higher transaction costs, due to frequent rebalancing, which could diminish the potential profitability of momentum investing.
(2007) also calculates the turnover ratios for his UK sample and finds lower turnover ratios. His highest annualized turnover is 614%, his lowest annualized turnover is 80.2%.
A formation period of 12 months (J=12) for the loser portfolio shows the lowest average turnover of 47.7% compared to other formation months. This could indicate that assessing stocks over a longer amount of time (12 months in this case) could result in a lower turnover because the returns of the stocks are more robust. Moskowitz and Grinblatt (1999) research the momentum effect by industries and find that holding on to long and short positions for an additional six months beyond the initial holding period does not reduce the average monthly return while reducing turnover to 100% per year, greatly reducing transaction costs.
A formation period of 3 months (J=3) for the loser portfolio shows the highest average turnover of 90.8% compared to other formation periods. When comparing the average turnover ratio per holding period, K=12 shows an average turnover ratio of 83.9% compared to an average turnover ratio of 48.0% for K=1. These results differ greatly when assessed on an annual basis: K=1 shows an annualized average of 576.4%. Furthermore, it is interesting that on average winner portfolios show a higher turnover ratio than loser portfolios, this is in line with the results of Agyei-Ampomah (2007).
Lee and Swaminathan (2000) and Hvidkjaer (2006) find that high turnover losers underperform low turnover losers, while little difference exists in the returns of low and high turnover winners. Comparing Table 1 and Table 2 similar results are found: the return of strategy J*K 3*12 (highest turnover loser) is lower than the return of strategy J*K 12*1 (lowest turnover loser), although these returns are not significant. The return for strategy J*K
12*1 (lowest turnover winner) is higher than the return for the highest turnover winner
strategy J*K 12*12 (highest turnover winner).
Momentum investing has very high annual turnovers compared to long-term investment strategies. Barber and Odean (2000) and Barber et al. (2009) research the stock trading behavior of retail investors. They find that individuals with higher turnover ratios underperform compared to individuals with lower turnover ratios with approximately 7% on an annual basis. A retail investor should be aware of the findings of Barber and Odean (2000) and Barber et al. (2009), although, as will be described later in this paper, the negative
Table 2.
Turnover ratios (unrestricted sample).
This table shows the average percentage turnover of both the winner and loser portfolios for the different J and K periods. For each row, the top number is the average turnover per holding period; the bottom row in italic is the corresponding percentage annualised turnover. The average turnover ratio per formation period and holding period are shown in bold.
Formation
period Portfolio Holding period
4.1.3 Momentum investing with Plus500 as brokerage firm
Table 3 shows the returns if a Dutch retail investor would pursue a momentum investing strategy using Plus500 as an online brokerage firm. The same technique is used to form the portfolios as described earlier, Table 3 shows the returns of momentum investing net of transaction costs. Plus500 offers retail investors to go either long or short in the underlying of a stock, through CFDs. Plus500 does not charge commission fees, although the retail investor does pay the effective spread and receives or pays a funding premium for going short or long respectively. For every winner and loser portfolio the transaction costs are calculated based on the effective spread and the funding premium, such as described in Equations 6.1 and 6.2. Since the actual turnover ratios are multiplied with the effective spread for each portfolio between 2000 and 2015, the estimated transaction costs are very realistic.
Table 3 shows there is no profitable strategy available for a retail investor using Plus500 as brokerage firm. This indicates that the costs accompanying momentum strategies are very high and destructive in generating any potential profit from the momentum effect. Even worse: trading with CFDs has unlimited downside risk and a retail investor could generate losses greater than 100%, such as strategy J*K 3*1. Strategy J*K 1*12 would generate an annualized loss of 9.66%, which is the lowest significant loss a retail investor could produce with a zero-sum investment. Also, among the winner and loser portfolios individually there is not a strategy that would provide a profit due to the high transaction costs.
Bauer et al. (2009) also use derivatives to study the returns of retail investors, they find that retail investors incur substantial losses and attribute these losses to transaction costs. Lee and Choy (2014) find that retail investors can generate a profit when using CFDs net of bid-ask spread of up to a week holding period. Moreover, they find that investors earn
negative returns for holding periods from one month to one year as a result of financing costs. Siganos (2012) investigates if retail investors can exploit the momentum effect with CFDs and finds only profitable strategies when selecting stocks on an earnings/price strategy, overall he finds that no profitable strategy after adjusting for transaction costs. Siganos (2012) shows that these high transaction costs are largely attributable to high spreads caused by small capitalization stocks. Menkveld and Wang (2013) show that the Dutch stock market has a substantial amount of small capitalization stocks. The large amount of small
capitalization stocks that have a higher effective spread could explain the large differences between the returns presented in Table 3 and the papers mentioned earlier, this will be examined more extensively in the restricted sample.
Table 3.
Average annualized portfolio returns with Plus500 as brokerage firm, 2000 – 2015 (unrestricted sample).
Each month stocks are ranked in ascending order based on previous J months performance. The stocks in the top decile are assigned to the winner portfolio, the stocks in the bottom decile are assigned to the loser portfolio. Both portfolios contain 16 stocks. The portfolios are equally weighted and the annualized returns of each portfolio after holding for K months are displayed for each formation period. W-L shows the return of the zero-sum strategy where an investor goes long in the winner portfolio and goes short in the loser portfolio. For each portfolio the average effective spread is calculated and multiplied with the turnover ratio. The transaction costs are corrected for a daily funding premium charged by Plus500 for holding overnight positions. The returns shown are the net returns adjusted for transaction costs. For each return, the t-values of the Newey-West standard errors test are shown to check whether the returns of the portfolios are significantly different from zero. *, ** and *** denotes significance at the 1%, 5% and 10% level respectively.
Formation
period Portfolio Holding period
Table 3 continued Formation
period Portfolio Holding period
K=1 K=3 K=6 K=9 K=12 J=6 Winner -18.592%* -9.534% -3.574% -1.268% -2.388% (t-value) (2.636) (-1.588) (-0.719) (-0.289) (-0.602) Loser -23.140% -15.025% -8.667% -4.588% -3.661% (t-value) (1.573) (0.952) (0.767) (0.573) (0.538) W-L -41.731%* -24.560% -12.241% -5.856% -6.049% (t-value) (-3.005) (-1.644) (-1.173) (-0.773) (-0.925) J=9 Winner -15.181%** -5.676% -2.503% -2.935% -3.169% (t-value) (-2.383) (-1.048) (-0.525) (-0.691) (-0.807) Loser -13.655% -13.629% -8.248% -5.119% -4.457% (t-value) (0.884) (0.791) (0.696) (0.636) (0.668) W-L -28.836%*** -19.305% -10.751% -8.054% -7.626% (t-value) (-1.967) (-1.154) (-0.919) (-1.025) (-1.170) J=12 Winner -13.198%** -7.051% -4.116% -3.679% -3.533% (t-value) (-1.996) (-1.340) (-0.909) (-0.855) (-0.834) Loser -18.932% -18.892% -10.790% -6.882% -7.401% (t-value) (1.156) (1.053) (0.880) (0.848) (1.109) W-L -32.130%*** -25.942% -14.906% -10.561% -10.934% (t-value) (-1.928) (-1.423) (-1.212) (-1.298) (-1.605)
4.1.4 Momentum investing with DeGiro as brokerage firm
Table 4 shows the returns of momentum investing for a Dutch retail investor using DeGiro as brokerage firm. A retail investor who wishes to execute a momentum investing strategy is likely to choose a brokerage firm that allows short selling and offers competitive prices for frequent trading. At the time of this analysis, DeGiro would be the logical choice for a Dutch retail investor. The transaction costs are based on the transaction costs stated on the website of DeGiro. DeGiro charges a fixed amount of €2.00 per transaction, so the fixed cost of a round trip transaction is €4.00. In addition to the fixed costs, DeGiro charges a 0.02% fee of the amount bought or sold. In order to make realistic calculations, the value of the portfolio is assumed to be €30,000.00, which is the average value that Dutch retail investors have invested in stocks. All costs incurred with trading (the effective spread, variable and fixed costs per transaction) are multiplied with the turnover ratio of each portfolio to make a realistic estimate of the total transaction costs.
Table 4 shows that there is not a significant profitable zero-sum strategy, net of transaction costs, attainable for the Dutch retail investor between 2000 and 2015 based on the current rates of DeGiro. The worst significant strategy available would generate an
be made, which is the lowest loss available for the W-L portfolios. It is remarkable that Table 4 shows there are several long only strategies profitable: such as the winner portfolio of strategy J*K 6*9 which could generate an annual return of 9.24%.
As mentioned earlier, other papers such as Jegadeesh and Titman (1993),
Rouwenhorst (1998) and Agyei-Ampomah (2007) show profitable results net of transaction costs when researching momentum investing. These returns might differ as a result of lower spreads, lower turnover ratios and the fact that the W-L portfolio is largely driven by the loser portfolio. Nevertheless, they all base the transaction costs on a percentage while the
transaction costs of DeGiro are determined by both fixed and variable costs. Jegadeesh and Titman (1993), for example, base their estimate of transaction costs on the trade-weighted mean commission and market impacts. Stoll and Whaley (1983) and Bhardwaj and Brooks (1992) produce estimates of "spread plus commission" costs by directly examining quoted market bid-ask spread data and prevailing commission schedules, but Seppi (1997), amongst others, state that these quoted measures are likely to be inaccurate since trades frequently occur off the quoted prices and commission fees change frequently. Lesmond et al. (2004) use a discount brokerage schedule that reflects the competitive commission rate for their sample period and find little evidence that momentum strategies provide positive abnormal return opportunities net of transaction costs. This is interesting, as mentioned earlier, because commission rates have sharply declined since their paper. Furthermore, they acknowledge that the magnitude of the commission schedule used appears high with respect to the online commission rates offered in the later part of their sample period. Even with a more
competitive commission rate, the results of Table 4 are in line with the results found by Lesmond et al. (2004).
It is interesting to compare the returns of Table 3 and Table 4, because these returns represent the returns if a retail investor would pursue momentum investing on the Dutch stock market with the current rates of the most competitive brokerage firms. It shows that a Dutch retail investor cannot profit from the momentum effect by creating a zero-sum
Table 4.
Average annualized portfolio returns with DeGiro as brokerage firm, 2000 – 2015 (unrestricted sample).
Each month stocks are ranked in ascending order based on previous J months performance. The stocks in the top decile are assigned to the winner portfolio, the stocks in the bottom decile are assigned to the loser portfolio. Both portfolios contain 16 stocks. The portfolios are equally weighted and the returns of each portfolio after holding for K months are displayed for each formation period. W-L shows the return of the zero-sum strategy where an investor goes long in the winner portfolio and goes short in the loser portfolio. For each portfolio the current fixed and variable costs of entering and closing a position through DeGiro are calculated based on a portfolio of €30.000, the average value of Dutch retail investor portfolios in stocks. The returns are adjusted for the transaction costs of DeGiro and the effective spread and expressed in percentages. For each return, the t-values of the Newey-West standard errors are shown to test whether the returns of portfolios are significantly different from zero. *, ** and *** denotes significance at the 1%, 5% and 10% level respectively.
Formation
period Portfolio Holding period
4.1.5 Spread and market capitalization
The results shown in Table 3 and Table 4 suggest that retail investors cannot exploit the momentum effect after considering transaction costs. Several papers (Hong et al., 2000; Ali and Trombley, 2006; Agyei-Ampomah, 2007; Siganos, 2012)demonstrate that these high transaction costs can also be a result of high spreads which are often related to small
capitalization stocks. Furthermore, Booth et al. (2015) suggest that small capitalization stocks generate the highest volatility in returns and are therefore more likely to be in the either winner or loser portfolio.
Table 5 shows the returns net of the effective spread, without considering any other commission fees or transaction costs. As mentioned earlier, DeGiro stated that they are planning to launch DeZiro14, where retail investors can trade securities without transaction costs, as displayed in Table 5, where only the spreads are incurred. Table 5 shows that there are several profitable strategies for the winner portfolio when having a holding period of nine or 12 months. However, there is no significant profitable strategy for any of the W-L
strategies, indicating that either the return of the loser portfolios is not profitable or the spreads of the stocks in the loser portfolio are too high.
14
Table 5.
Average annualized portfolio returns minus spreads, 2000 – 2015 (unrestricted sample). Each month stocks are ranked in ascending order based on previous J months performance. The stocks in the top decile are assigned to the winner portfolio, the stocks in the bottom decile are assigned to the loser portfolio. Both portfolios contain 16 stocks. The portfolios are equally weighted and the returns of each portfolio after holding for K months are displayed for each formation period. W-L shows the return of the zero-sum strategy where an investor goes long in the winner portfolio and goes short in the loser portfolio. The returns are adjusted for the effective spread and expressed in percentages. For each return, the t-values of the Newey-West standard errors are shown to test whether the returns of portfolios are significantly different from zero. *, ** and *** denotes significance at the 1%, 5% and 10% level respectively.
Formation
period Portfolio Holding period
Table 6.
Market capitalization (unrestricted sample).
Each month stocks are ranked in ascending order based on previous J months performance. The stocks in the top decile are assigned to the winner portfolio, the stocks in the bottom decile are assigned to the loser portfolio. Both portfolios contain 16 stocks. Stocks in the total sample are then categorized into 5 quintiles (Q) based on market capitalization (measured as market value), hence the proportion of each size quintile in the total sample is 0.2; for each formation period the average proportion of stocks for the winner and loser portfolio are shown. CHI is the average 𝑋2value and % significant is the percentage of times the 𝑋2test was rejected. The average effective spread for
each winner and loser portfolio per formation period is also shown.
Sample J=1 J=3 J=6 J=9 J=12
Winner Loser Winner Loser Winner Loser Winner Loser Winner Loser
4.2 Restricted sample
In this section, the analysis described in Section 3 is replicated for the restricted sample. In the restricted sample the stocks in each portfolio are selected on their returns in previous J months, identical to the method described for the unrestricted sample, and then ranked on their market value. The stocks in the portfolios of the restricted sample are the eight stocks that show the highest (lowest) return and the highest (highest) market value for each winner (loser) portfolio.
4.2.1 Spread and market capitalization
First, it is interesting to examine how the proportion of stocks is distributed in the restricted sample. Agyei-Ampomah (2007) creates a sub-sample of stocks that are in the top 30th percentile based on market capitalization. This paper follows a different approach by selecting eight stocks of the highest (lowest) return decile that show the highest (highest) market value. Replicating the approach proposed by Agyei-Ampomah would limit each portfolio to five stocks only. Secondly, the spreads of the restricted sample are compared with the spreads of the unrestricted sample.
Table 7.
Market capitalization (restricted sample).
Each month stocks are ranked in ascending order based on previous J months performance. The stocks in the top decile are assigned to the winner portfolio, the stocks in the bottom decile are assigned to the loser portfolio. The portfolios are restricted by only including half of the stocks that have the highest market value, both winner and loser portfolios contain 8 stocks each. Stocks in the total sample are then categorized into 5 quintiles (Q) based on market capitalization (measured as market value), hence the proportion of each size quintile in the total sample is 0.2; for each formation period the average proportion of stocks for the winner and loser portfolio are shown. CHI is the average 𝑋2value and % significant is the percentage of times the 𝑋2test was rejected. The average effective spread for each winner and loser portfolio per formation period is
also shown.
Sample J=1 J=3 J=6 J=9 J=12
Winner Loser Winner Loser Winner Loser Winner Loser Winner Loser
4.2.2 Results restricted sample
First, the annualized returns without transaction costs of each strategy for the
restricted sample are examined in Table 8. It is noteworthy that six zero-sum strategies (such as J*K 1*1, 1*9, 6*3, 9*1, 9*3 and 9*6) of the restricted sample show higher significant returns compared to the same significant strategies of the unrestricted sample. However, some strategies, such as J*K 3*12,6*9 and 9*9, generate a higher significant return in the unrestricted sample. As with the unrestricted sample, the potential profits of the zero-sum investment portfolio are solely driven by the winner portfolios, and not the loser portfolios. Strategy J*K 9*1 generates the highest return of 20.75% in the restricted sample, while the highest zero-sum strategy in the unrestricted sample generates an annualized return of 14.03% . These results are surprising, since several authors (Agyei-Ampomah, 2007, Booth et al. 2015; Ali and Trombley, 2006; Hong et al., 2000) find that small capitalization stocks generate higher returns. The results in this paper are in contradiction with other papers as the unrestricted sample shows a higher proportion of small capitalization stocks while generating lower returns than the restricted sample, which shows a higher proportion of large
capitalization stocks.
Table 8.
Average annualized portfolio returns without transaction costs, 2000 – 2015 (restricted sample).
Each month stocks are ranked in ascending order based on previous J months performance. The stocks in the top decile are assigned to the winner portfolio, the stocks in the bottom decile are assigned to the loser portfolio. The portfolios are restricted by only including half of the stocks that have the highest market value, both winner and loser portfolios contain 8 stocks each. The portfolios are equally weighted and the annualized returns of each portfolio after holding for K months are displayed for each formation period. W-L shows the return of the zero-sum strategy where an investor goes long in the winner portfolio and goes short in the loser portfolio. For each return, the t-values of the Newey-West standard errors test are shown to check whether the returns of the portfolios are significantly different from zero. *, ** and *** denotes significance at the 1%, 5% and 10% level respectively.
Formation
period Portfolio Holding period
Table 9 shows the turnover ratios for the restricted sample, obtained in a similar fashion as for the unrestricted sample. Overall, the turnover ratios of the restricted sample are slightly higher than the turnover ratios of the unrestricted sample. This is noteworthy since Eun et al. (2008) show that small capitalization stocks have greater return volatility and hence a higher turnover ratios would be expected in the unrestricted sample. The highest annualized turnover for the winner (loser) portfolio is 1076.7% (1091.2%), the lowest annualized
turnover for the winner (loser) portfolio is 90.5% (85.3%). The higher turnover ratios in the unrestricted sample could be explained by the smaller number of stocks (eight compared to 16) in the portfolios of the restricted sample, since the differences in turnover ratios of the unrestricted and the restricted sample are so small it is unlikely to have a large effect on the transaction costs of the restricted sample.
Table 8 continued Formation
period Portfolio Holding period
Table 9.
Turnover ratios (restricted sample).
This table shows the average percentage turnover of both the winner and loser portfolios for the different J and K periods. For each row, the top number is the average turnover per holding period; the bottom row in italic is the corresponding percentage annualised turnover. The average turnover ratio per formation period and holding period are shown in bold.
Formation period Portfolio Holding period
Table 10 shows the returns net of the effective spreads for the restricted sample, without commission fees or funding premiums of brokerage firms. Again, the same technique is used for the restricted sample as for the unrestricted sample. The highest zero-sum strategy is for strategy J*K 9*6 which could generate a profit of 8.61% significant at the 10% level. The returns in Table 10 are in general much higher for the restricted sample than for the unrestricted sample. This is not surprising when considering the previous three tables. As shown in Table 7, the average effective spread of the restricted sample is considerably lower compared to the unrestricted sample. In addition, Table 8 shows that some strategies in the restricted sample have a higher return without transaction costs and Table 9 shows only a small increase in turnover ratios for the restricted sample. If DeGiro would actually be able to launch a free online-trading platform, a retail investor would be able to execute a profitable strategy when including stocks with higher market capitalization, as shown in Table 10. Again, several of the winner portfolios generate higher returns than the zero-sum investment of going long in the winner portfolio and shorting the loser portfolio.
Table 10.
Average annualized portfolio returns minus spreads, 2000 – 2015 (restricted sample). Each month stocks are ranked in ascending order based on previous J months performance. The stocks in the top decile are assigned to the winner portfolio, the stocks in the bottom decile are assigned to the loser portfolio. The portfolios are restricted by only including half of the stocks that have the highest market value, both winner and loser portfolios contain 8 stocks each. The portfolios are equally weighted and the returns of each portfolio after holding for K months are displayed for each formation period. W-L shows the return of the zero-sum strategy where an investor goes long in the winner portfolio and goes short in the loser portfolio. The returns are adjusted for the effective spread and expressed in percentages. For each return, the t-values of the Newey-West standard errors are shown to test whether the returns of portfolios are significantly different from zero. *, ** and *** denotes significance at the 1%, 5% and 10% level respectively.
Formation period Portfolio Holding period
Table 10 continued
Formation period Portfolio Holding period
K=1 K=3 K=6 K=9 K=12 J=6 Winner 1.347% 7.496%** 10.477%* 10.666%* 9.232%* (t-value) (0.242) (2.043) (3.654) (4.473) (4.756) Loser -14.934% -4.680% -6.511% -5.476% -6.964% (t-value) (1.099) (0.611) (1.150) (1.230) (1.624) W-L -13.587% 2.816% 3.966% 5.190% 2.268% (t-value) (1.114) (0.427) (0.798) (1.234) (0.561) J=9 Winner 5.926% 8.614%* 10.559%* 9.494%* 9.073%* (t-value) (1.161) (2.795) (4.228) (4.708) (5.084) Loser 2.468% -0.581% -1.698% -2.395% -4.698% (t-value) (0.185) (0.076) (0.308) (0.552) (1.123) W-L 8.394% 8.033% 8.861%*** 7.100%*** 4.375% (t-value) (0.702) (1.211) (1.760) (1.752) (1.081) J=12 Winner 12.415%** 11.782%* 11.318%* 10.354%* 10.672%* (t-value) (2.496) (4.047) (5.016) (5.276) (5.434) Loser -8.371% -10.268% -8.960% -8.155% -8.927%*** (t-value) (0.699) (1.265) (1.482) (1.621) (1.858) W-L 4.044% 1.514% 2.358% 2.199% 1.745% (t-value) (0.366) (0.198) (0.413) (0.451) (0.363)
Table 11 shows the average annualized portfolio returns when using Plus500 as a brokerage firm for the restricted sample. Despite the fact that the restricted sample has lower average spreads, there is still not a significant profitable momentum strategy when using Plus500 as a brokerage firm. As expected, the potential losses from executing this investment strategy are lower for the restricted sample than for the unrestricted sample.
Table 11.
Average annualized portfolio returns with Plus500 as brokerage firm, 2000 – 2015 (restricted sample).
Each month stocks are ranked in ascending order based on previous J months performance. The stocks in the top decile are assigned to the winner portfolio, the stocks in the bottom decile are assigned to the loser portfolio. The portfolios are restricted by only including half of the stocks that have the highest market value, both winner and loser portfolios contain 8 stocks each. The portfolios are equally weighted and the annualized returns of each portfolio after holding for K months are displayed for each formation period. W-L shows the return of the zero-sum strategy where an investor goes long in the winner portfolio and goes short in the loser portfolio. For each portfolio the average effective spread is calculated and multiplied with the turnover ratio. The transaction costs are corrected for a daily funding premium charged by Plus500 for holding overnight positions. The returns shown are the net returns adjusted for transaction costs. For each return, the t-values of the Newey-West standard errors test are shown to check whether the returns of the portfolios are significantly different from zero. *, ** and *** denotes significance at the 1%, 5% and 10% level respectively.
Formation
period Portfolio Holding period
Table 12.
Average annualized portfolio returns with DeGiro as brokerage firm, 2000 – 2015 (restricted sample).
Each month stocks are ranked in ascending order based on previous J months performance. The stocks in the top decile are assigned to the winner portfolio, the stocks in the bottom decile are assigned to the loser portfolio. The portfolios are restricted by only including half of the stocks that have the highest market value, both winner and loser portfolios contain 8 stocks each. The portfolios are equally weighted and the returns of each portfolio after holding for K months are displayed for each formation period. W-L shows the return of the zero-sum strategy where an investor goes long in the winner portfolio and goes short in the loser portfolio. For each portfolio the current fixed and variable costs of entering and closing a position through DeGiro are calculated based on a portfolio of €30.000, the average value of Dutch retail investor portfolios in stocks. The returns are adjusted for the transaction costs of DeGiro and the effective spread and expressed in percentages. For each return, the t-values of the Newey-West standard errors are shown to test whether the returns of portfolios are significantly different from zero. *, ** and *** denotes significance at the 1%, 5% and 10% level respectively.
Formation
period Portfolio Holding period
