The profitability of liquidity based momentum strategies on Euronext Amsterdam

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The profitability of liquidity based momentum strategies on Euronext

Amsterdam

Master Thesis MSc Finance

by C. B. Bongaerts

Supervisor: Dr J.O. Mierau

Abstract

This paper analyses liquidity based momentum strategies on Euronext Amsterdam between 2000-2007. Liquidity of stocks is argued to be an explanation for earing abnormal returns within the momentum strategies. A liquidity based momentum strategy is based on historical returns and historical liquidity of stocks. The results over a time period between 2000-2007 shows that significant liquidity based momentum profits are observable on Euronext Amsterdam. The liquidity concentration of the stocks within different strategies advises to invest in highly liquid stocks. I also test these strategies on Euronext Amsterdam between 2008-2015. Remarkably, this outcome contradicts the previous conclusion, by proposing to invest in illiquid stocks. I analyse the liquidity based momentum strategy during the financial crisis of 2007-2008. The results show that liquidity based momentum strategies are profitable during the financial crisis although, this time period advises to invest in illiquid stocks. Classification: Momentum, Liquidity, Bid-ask spread, investment strategy

Keywords: G10, G11, G14

Author: Caroline Bibi Bongaerts Mail: caroline.bongaerts@hotmail.com Phone: +31652667167

Student number: S2020076

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1. Introduction

Investors and portfolio managers are always exploring new investment strategies that can create significant profits. An investment strategy can be defined as: “different activities to

create an unique and valuable position” (Porter, 1980). Mintzberg (1978), on the other hand

defines strategy as: “a pattern in a stream of decisions”. Kaplan and Norton (1996) describe a strategy as either a theory of cause-and-effect relationship, or an if-then statement. McKeown (2011) notes that: “a strategy is about shaping the future”. These descriptions of strategy point in the same direction, namely that a strategy is an elaborate plan to achieve specific goals under uncertain conditions. A strategy is highly important because of the usual scarcity of available funds for achieving these goals. The present paper focuses on a controversial type of strategies, known as liquidity based momentum strategies (“LIQMS”). These strategies aim to capitalize on the existing trends in the market by selecting stocks based on their historical returns and liquidity. This paper provides a thorough analysis of LIQMS by testing all stocks listed on Euronext Amsterdam.

Over the past decades, many academics have evaluated investment strategies focusing on past stock returns. De Bondt and Thaler (1985), Jegadeesh (1990) and Lehmann (1990), investigated long-term (three to five years) and short-term (one week to one month) past stock returns. These academics invariably reach the conclusion that long- and short-term past losing stocks (“losers”) outperform long- and short-term past winning stocks (“winners”). Their main assumption is that stock prices overreact to external information and suggest that buying past “losers” and selling past “winners” will yield positive returns, known as the contrarian investment strategy.

Since the early 1990s, new theories have been developed which contradict the contrarian strategies and are based on the assumption that stocks which have shown an upward or downward trending price over the previous three- to twelve-months will continue to follow this trend. These are therefore known as the momentum investment strategies. The classic idea of “momentum” is best defined by Sir Isaac Newton in 1687 who described it as “an object in

motion will continue in motion unless acted upon by an external force”. Applying this concept

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(2004) suggest that investing in past “winners” and selling past “losers” within a three- to twelve-month-time horizon will generate excessive profits.

The basis for profiting from abnormal returns is establishing the predictability of equity returns. It is therefore the object of many researchers and valuation models, such as the Capital Asset Pricing Model (CAPM). The fact that these valuation models and investment strategies are based on the predictability of equity returns leads to a conflict with the well-developed efficient market theory literature of Fama (1970), which states that stock returns reflect all available information and since there is no way of knowing future news, historical data cannot be used to predict future stock prices.

The abnormal profits earned by means of momentum strategies are difficult to explain. The most common explanation in the existing literature is that there is a delayed reaction to information (Jegadeesh and Titman, 2011). Investors tend to over- or under-react to information, especially to news about the income of a company (Chan et al. 1996). However, Conrad and Kaul (1998) try to explain momentum profits within the context of the traditional risk based asset-pricing paradigm. They argue that the abnormal returns gained by this strategy are achieved because of bearing higher risks. Other explanations are based on behavioural models. Barberis et al. (1998) discuss how conservatism biases might lead to investors’ under-reaction to information. Daniel et al. (1998) on the other hand, debates that overconfidence of investors can lead to misinterpretation of information. Moreover, Pástor and Stambaugh (2003) present an even more remarkable explanation of the abnormal returns, in particular that the liquidity risk factor accounts for half of the profits to a momentum strategy.

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profitability of different LIQMS. The LIQMS are based on the historical returns and on historical liquidity of stocks. All listed stocks on Euronext Amsterdam are filtered over a time span of seven years, from 2000 to 2007. Furthermore, the LIQMS are also analysed between 2008 and 2015 to test for time-series variation.

Based on the information mentioned above, the main research question of this paper is:

What influence does the liquidity characteristic of stocks have on the momentum profits on Euronext Amsterdam?

To investigate the main research question, I shall first analyse the selected stocks that form part of the momentum portfolios on their past liquidity to determine which types of stocks (liquid or illiquid) show higher momentum profits. Secondly, the different LIQMS are investigated. Thirdly, the strategies are analysed on a different time period to provide a sustainable investment strategy. Fourthly, the financial crisis of 2007-2008 is investigated to give a clear comment on how to adjust an investment strategy during a recession. Finally, the returns are adjusted for risk to analyse if the profits earned within LIQMS disappear when adjusted for common risk factors.

This study contributes to the existing literature on the effects of liquidity on stock price dynamics, for example, Amihud (2000), Lee and Swaminathan (2000), Pástor and Stambaugh (2003) and Sadka (2005). Besides, since the total market capitalization of Euronext Amsterdam is rather small compared to the stock markets in previous studies, the results may differ. Therefore, this paper is of great interest to investors and researchers on Euronext Amsterdam.

The main results show significant positive returns following a LIQMS. However, composing strategies based on liquidity presents contradicting the results over time. Before 2008 liquid stocks performed significantly better, while after 2008 illiquid stocks performing better. These results suggest that that during the financial crisis the outcome reverse. This may implicates that the market state influences the outcome of the LIQMS.

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2. Literature review

2.1 Momentum investing

Table 1 shows a short overview of the existing academic literature on momentum investing.

Table 1: Literature overview

Authors Name article Market(s) Data

Chan, Jegadeesh and

Lakonishok (1996,1999) Momentum strategies The profitability of momentum strategies US 1977-1993 Conrad and Kaul (1998) An anatomy of trading strategies US 1926-1989 Doukas and McKnight (2005) European momentum strategies, information _{diffusion, and investor conservatism} EU 1988-2001 George and Hwang (2004) The 52-week high and momentum investing. US 1963-2001 Griffin, Ji and Martin (2003) Momentum investing and business cycle risk: _{evidence from pole to pole} WO 1928-2000 Hon, Lim and Stein (1999) Bad News Travels Slowly: Size, Analyst Coverage, _{and the Profitability of Momentum Strategies.} US 1980-1996 Jegadeesh and Titman (1993,

2001, 2011)

Returns to buying winners and selling losers: implications for stock market efficiency

Profitability of momentum strategies: an evaluation of alternative explanations Momentum US 1965-1985 1965-1998 1990-2009 Lui, Strong and Xu (1999) The profitability of momentum investing UK 1977-1996 Rouwenhorst (1998, 1999) International momentum strategies. Local return factors and turnover in emerging

markets

EU + EM 1980-1995

The academic literature on momentum investing focuses on strategies that suggest buying past winning stocks and selling past losing stocks to gain excess returns. Levy (1967) was the first who claimed that buying stocks with higher current prices than their past 27 weeks-average created significant abnormal profits. Although this conclusion can be seen as a breakthrough for the market efficiency theory, Levy (1967) also pointed out that his results were not statistically significant. Therefore, Jensen and Bennington (1970) back-tested the profitability of Levy’s trading strategy over a longer time period, mostly outside Levy’s sample period. They concluded that Levy’s trading strategy did not outperform a buy- and hold-strategy and therefore assigned Levy’s result to a selection bias.

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performance during these different formation periods. The “winners” portfolio consisted the best-performing stocks, and the “losers” portfolio consisted the worst performing stocks. To obtain significant profits, long positions were taking in the “winners” portfolio and short positions were taken in the “losers” portfolio. These positions were held for K-month, also known as the J-month/K-month strategy. In the main sample, stocks on the NYSE and AMEX between 1965 and 1989 were examined and displayed significant profits following this trading strategy. The strategy that selected stocks based on the month-formation period and the six-month-holding period, abbreviated as: [6:6] realized an excess return of 12.01% on an average annually basis. Evidence indicates that these abnormal excess returns cannot be explained by systematic risk nor by the different price reactions to common factors. Therefore a more common explanation for momentum profits is, investors common interpretations to released information leading to overreactions. Another interpretation of the results of Jegadeesh and Titman (1993) is that the long- and short- positions taken by investors drive stock prices away from their long-term values.

To create more insights over the predictability of historical returns, Chan et al. (1996) analysed stocks listed on the NYSE, AMEX and NASDAQ over the period 1977 to 1993. They concluded that mid-term investment strategies based on past returns yield significant profits. Comparing the outcome of Jegadeesh and Titman (1993), evidence showed excess returns of 8.80% within [6:6] composition. In addition, ranking stocks according to their past moving average or past earnings growth produced significant excess returns of 7.00% over the next six months. These results clearly invalidate the efficient market theory by illustrating that historical returns can be used to predict future returns. The authors furthermore contradict Jegadeesh and Titman (1993) by arguing that abnormal excess returns are the result of conservatism bias that will lead to market under-reaction instead of over-reaction. Chan et al. (1996) complement the momentum investment strategies literature by constructing portfolios on different historical indicators such as moving averages.

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whereas contrarian strategies usually yield excessive returns over long-term investment periods. Finally, they argue that momentum profits may be entirely due to cross-sectional variance in the mean returns of individual securities instead of time-series patterns in returns of the individual securities.

In 1998, Rouwenhorst expanded Jegadeesh and Titmans’ research on the European market by examining the stock exchange markets of 12 different European countries over the period between 1980 and 1995. Evidence was found that an internationally diversified “winners” portfolio outperforms the “losers” portfolio by around 1.0% after risk corrections. The abnormal returns within the momentum investment strategy are present in all 12 countries, and holds for both large and small firms, although small firms experience stronger return continuations. Furthermore, Rouwenhorst (1998) debates that due to the similarity in result on the U.S stock markets and the European stock markets momentum profits are significantly correlated to common factors across markets. In 1999, consolidating his own research, Rouwenhorst performed a similar investigation within 20 different emerging counties including 1750 firms. The outcome confirmed previous research: emerging markets show momentum profits where small stocks outperform large stocks and value stocks outperform growth stocks. Furthermore, no evidence was found on the relationship between expected returns and share turnover. However, size, beta, momentum and value are found to be positively cross-sectional correlated with turnover, implicating that return premiums do not simply reflect compensations for stock illiquidity.

In 2001, Jegadeesh and Titman conducted further research to evaluate various explanations for momentum profits raised by Conrad and Kaul (1998). In the second research the investment horizon is extended by eight years (1965-1998), but the results remain similar: momentum profits are found on the U.S. stocks markets within the sample horizon. These results prove that momentum profits are not influenced by data snooping biases. In addition, they examined the post-holding period performance and rejected the hypothesis of Conrad and Kaul (1998), who argued that momentum profits exists due to cross-sectional differences rather than time-series patterns. However, the behavioural models presented by Barberis et al. (1998); Daniel et al. (1998); and Hong and Stein (1999), suggesting that the post-holding period returns should be negative was confirmed within their research. This implicated that momentum profits can be explained by a delayed overreaction due to behavioural factor models.

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co-movements among countries. This evidence suggests that if momentum profits are driven by risk, it is largely driven by country specific-risk. In addition, the comparison of momentum portfolios based on macroeconomic factors, GDP and aggregate stock market movements, shows that international momentum profits are generally positive in all economic states. It remains nonetheless unclear whether momentum profits can be explained by a standard set of macroeconomic variables.

2.2 Liquidity

In 2000, Amihud created new tests to narrow the gap between illiquidity and equity pricing. His research simulated effects of illiquidity on stock returns by comparing different holding periods to different bid-ask spreads. Amihud (2000) confirmed that the illiquidity can be measured by the spread between bid- and ask-quotes, which represents the costs of selling a stock. Note, that the use of the spread between the bid- and ask-quotes to determine illiquidity only applies for limited quantities, time periods and the spreads only measures the cost of executing a single trade.1 The paper argues that stocks with higher spreads – low liquidity – earn higher future returns. Furthermore, Amihud (2000) discovered that ex-ante stock excess returns are positively affected by the expected market illiquidity. The paper suggests that the expected excess return partly represents an illiquidity premium.

In contrast to Amihud (2000), Lee and Swaminathan (2000), investigated trading volume as an important link between value and momentum strategies. The use of trading volume as a proxy for liquidity is a widely used measure, because of its simplicity and availability from Thomson Reuters DataStream (DataStream). However, trading volume is highly correlated to volatility, which can block market liquidity.2 Lee and Swaminathan (2000) analysed all stocks listed on the NYSE and AMEX over a period of 30 years (1965-1995), confirming that stocks with high past turnover ratios (high volume stocks) earn lower future returns and exhibit more negative earnings surprises over the future two years. They claim that one may be led to believe that abnormal returns can be explained by the fact that glamour stocks, which tend to be overvalued and overestimated, exhibit the same characteristics as stocks with high turnover ratios. Some of their additional research shows that investors who have a long position in high volume past-winners and a short position in past-losers outperform a strategy singly based on past stock returns. Moreover, their findings show the predictability of the magnitude and persistence of the momentum are affected by trading volume. Contrary to

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the liquidity explanation, the authors claim that high volume stocks earn higher future returns. Lee and Swaminathan (2000) debate that trading volume shows low correlation with firm size or bid-ask spread, and volume is independent of firm size. Therefore they stated that trading volume measured by the turnover ratio is unlikely to be a liquidity proxy. This paper uses the bid-ask spreads as the leading liquidity indicator for performing the research although the turnover by volume is analysed as a robustness test.

Pástor and Stambaugh (2003) investigated whether the market wide liquidity is an important variable for asset pricing, by examining all listed stocks on the NYSE and AMEX between 1966 and 1999. Remarkably, Pástor and Stambaugh (2003) concluded that within their sample period, the liquidity risk factor accounts for half of the profits to a momentum strategy, linking the liquidity exposure to the momentum strategy portfolios. They argue that stocks with high sensitivities to liquidity exceed stocks with low sensitivities by 7.50% on an annual basis, adjusted for exposures to the market return, size and momentum factors. The liquidity measures used are based on the liquidity associated with the volume-related return reversal. In other words, smaller stocks are less liquid and have higher sensitivities to liquidity.

Sadka (2005) focused his research on the liquidity risk components, momentum and post-earnings-announcements, which are important for understanding the asset-pricing anomalies. Data on the NYSE between 1983 and 2001 is investigated where Sadka (2005) subdivided firm-level liquidity into variable- and fixed- price effects. In conclusion, Sadka (2005) confirms the premium for bearing liquidity risk as a compensation for the unexpected variations in the ratio of informed traders to noise traders. It is, therefore, proposed that the asset-pricing model should include an information-based liquidity risk factor.

The main conclusion of the literature is that the momentum investment strategies are highly profitable over time and across countries. The liquidity indicator may be a leading component for earning excessive returns within the momentum investment strategies. Furthermore, most of the researchers ( Amihud, 2000, Brennan and Subrahmanyam 1996 and Sadka, 2000) debate that an illiquidity premium is added when pricing equities, meaning that investing in illiquid stocks will generate higher returns. The hypothesis formulated following the literature is:

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3. Data and Methodology 3.1 Data description

The main data set, which is obtained from the Thomson Reuters DataStream (DataStream), contains all traded stocks on Euronext Amsterdam. The total amount of stock in the main sample of this paper contains 388 stocks, all conducted in euros. The time horizon is set ranging between 2000-2015, due to the limited availability of bid- and ask-prices before 2000. To avoid the survival bias, both non-surviving and surviving stocks are included in the sample. For each stock the following data is extracted from DataStream: Return Index (RI), Market Value (MV), Price (P), Bid Price (PB), Ask Price (PA), Volume (VO) and the industry sector (INDM).

The main data set is adjusted by omitting all stock without available bid- and ask-prices during the research period. Furthermore, all stocks have to be active for at least 24 months to test the maximum holding/formation [12:12] combination. The unadjusted sample is also tested, to confirm the results are not majorly affected by the adjustments. Finally, two months are omitted from the data set because no bid-ask prices were available for any stock.

After cleaning the data, the main data sample contained in total 298 stocks, with a maximum of 231 stock and a minimum of 121 stocks. The average amount of stocks traded in the main sample during the time frame is 158. The stock data originating from the time during the financial crisis is deliberately, maintained in the data set, to identify whether liquidity based momentum strategy remains profitable during a recession period. Discussing the financial crisis separately will help investors learn more about behaving rationally during a recession.

3.2 Momentum investing indicator

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𝑅𝐼_𝑠𝑡 = 𝑅𝑠𝑡−𝑅𝑠𝑡−𝑗

𝑅𝑠𝑡−𝑗 (1)

𝑅𝐼_𝑠𝑡 represents the total return of a stock s at time t. 𝑅𝑠𝑡 represents the total return of stock s at time t and j stands for the formation period. After conducting the “winners” and “losers” portfolios from Formula 1, the portfolios are held for K-months, the holding period. The different holding periods examined have the same length as the formation (J-month) periods, K-3; K-6; K-9 and K-12. For example K-6 months means, the holding period of a stock return is measured over six-month time horizon with time starting at t=1 and ending at t=7. To avoid market microstructure effects, the holding period begins one month later than the formation period ends. The returns of the stocks within the holding period are calculated using Formula 1 except that J has replaced with K.

3.3 Liquidity indictor

Liquidity is a difficult characteristic to capture. There is hence no idealized definition to measure liquidity. Amihud and Mendelson (1986) investigated the influence of illiquidity of equity pricing paradigms by using the bid- and ask-spreads. The ask-price is the price an investor wants to receive for selling his long position in a particular stock. The bid-price is referred to as the price an investor is willing to pay to purchase the stock. The bid-ask spreads, where the bid-price is subtracted from the ask-price, displays positive values, leading to the conclusion that ask-prices are continuously larger than bid-prices. In this paper the liquidity indicator relies on the bid- and ask-spreads defined by Amihud and Mendelson (1968). The reasons for using spreads as the liquidity measurement is: firstly, spreads display the differences between the bid- and ask prices offered in the market and secondly, they can be easily obtained from DataStream. The liquidity indicator is measured following Formula 2.

𝐿𝑖𝐷 =𝑃𝑖,𝑡𝐴−𝑃𝑖,𝑡𝐵

𝑃_𝑖,𝑡𝑀 (2) Where 𝑃_𝑖,𝑡𝐴_{and 𝑃}

𝑖,𝑡𝐵 represents the ask- and bid- prices of a single stock i in the period t, 𝑃_𝑖,𝑡𝑀 represents the mid-price, calculated in the following Formula 3:

𝑃_𝑖,𝑡𝑀 ₌ 𝑃𝑖,𝑡𝐴+𝑃𝑖,𝑡𝐵

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Lee and Swaminathan (2000) on the other hand use turnover by volume (Volume) to determine liquidity. The Volume of stocks is easily obtained from the DataStream. Therefore, the Volume will be presented in the tables and analysed as a robustness test comparing different liquidity indicators.

3.4 Double-sorted approach

To define whether the liquidity component implemented in the sorting phase has an influence on the momentum profits, the investment strategies are constructed following a double-sorted method based on Bandarchuk and Hilscher (2012).

The first level of the sorting process is as mentioned above based on the Jegadeesh and Titman (1993) technique. The stock within the main sample are ranked into deciles based on their past (J-months) returns. The best-performing stocks are placed in the “winners” portfolio and the worst performing stocks are placed in the “losers” portfolio. In this paper, on average 158 stocks are traded in the sample period meaning that the “winners” and “losers” portfolios each contain 16 stocks out of the main sample.

After conducting the first sorting process within the “winners” and “losers” portfolios stocks are ranked based on their past liquidity indicator performance and placed in four different groups: “high winners”, “low winners”, “high losers” and “low losers”. Specifically, high liquidity represents lower value of the liquidity indicator, and low liquidity represent relative high value of the liquidity indicator. To simplify, for example, a stock in the “high winners” portfolio has high past returns and has a high liquidity indicator meaning that the stock are illiquidity during the formation period. On the other hand, a stock in the “low losers” portfolio performed poorly and has a low liquidity indicator meaning that the stock is liquid during the formation period. Taking a long position in “high winners” portfolio and simultaneously a short position in the “low losers” portfolio the liquidity based momentum portfolio can be constructed easily without costs. A portfolio always consists a long position taken in one of the two “winners” portfolios and a short position in the “losers” portfolios.

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and the different strategies (2*2) an investor has 64 (4*16) liquidity based momentum investment strategies (LIQMS).

The total return of the four different portfolios sorted based on the past returns and liquidity is calculated following Formula 4.

π𝑥𝑡[𝐽: 𝐾] = _𝑁1R𝑖𝑡[𝐽: 𝐾] (4)

Where [J:K] stands for the formation and holding period and 𝑅𝑖𝑡 for the return of one of the four different portfolios at time t. Note that the stocks are equally weighted within the portfolios. According to Acharya and Pedersen (2005) computing liquidity based portfolios equally weighted is more appropriate because liquid firms might be overrepresented.

Following Jegadeesh and Titman, (1993) the combined performance of the different portfolio is calculated at the end of the holding period. The combined return is calculated following Formula 5.

π𝑝𝑓𝑡[𝐽: 𝐾] = π𝑤𝑡[𝐽: 𝐾] − π𝑙𝑡[𝐽: 𝐾] (5)

π_𝑝𝑓𝑡 stands for the combined return of the momentum portfolio over a time horizon of

[J:K] months, where J and K respectively stand for the holding and formation period.

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4. Empirical Results

Part 1 of Section 4 discusses the results of the average annualized returns, based on the main data sample within the time frame ranging from 2000-2007. Additionally, the average annualized returns of the liquidity based momentum portfolios are discussed. After discussing the results, an out-of-sample data is analysed in Part 2. The time frame of the out-of-sample data is set from 2008-2015. Section 4.3 analyses the liquidity based portfolio returns during the financial crisis of 2007-2008. In Section 4.4 the risk-adjusted returns are discussed to test whether returns disappear when adjusted for common risk factors.

4.1 Averaged annualized liquidity based momentum profits between 2000 and 2007 4.1.1 Averaged annualized portfolio returns

Table 2 presents the average annualized portfolio returns of all traded stocks on Euronext Amsterdam over the period 2000-2007. The Jegadeesh and Titman (1993) approach is used to compose the portfolios. The stocks are ranked based on past returns in the formation (J-month) periods. A decile of the total amount of stocks is placed into the “ winners” and “losers” portfolios. These “winners” and “losers” portfolios are held for different holding periods (K-month). The total return (“winners”– “losers”) is a zero-sum investment, meaning that the total sum of the long position taken in the “winners” portfolio and the short position taken in the “losers” portfolios must be zero. The output of the different portfolios is averaged and annualized to compare the results with other studies. The Newey-West t-test (t-values in Table 2) represents the statistical significance of the results. The liquidity and Volume indicators are shown in Table 2 to compare both indicators.

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paper. Therefore, in conclusion it can be content that short positions taken in “losers” portfolio are less critical on Euronext Amsterdam.

The results show that for most momentum investment strategies the returns show to be significant different from zero and confirm that the market is not efficient as proposed by Fama (1970).3 Table 2 suggests that the momentum strategy is more profitable during the six- and nine-months-formation period. Agyei-Ampomah (2007) argues that the returns increase over time because of a decrease in turnover by volume (Volume). The results in Table 2 confirm that the Volume decreases over time that may cause the observable horizontal trend. The highest return in generated in the [6:9] strategy, 14.61% averaged and annualized, however not significant. In earlier research, Jegadeesh and Titman (1993) found the highest return of 15.72% in the [12:3] strategy, where Chan et al. (1996) found a return of 8.76%, both studies performed on the US stock market. On the European market Rouwenhorst (1998) achieved a return of 16.20%.

Table 2

Average annualized portfolio returns (2000-2007)

Each month all stocks traded on Euronext Amsterdam are ranked, based on their previous J-month performances, and assigned to the “winners” or “losers” portfolio. The “winners” portfolio (PW) contains the 16 best-performing stocks and the “losers” portfolio (PL) contains the 16 worst performing stocks. The stocks within the “winners” and “losers” portfolios are equally weighted in the portfolios where after the overlapping returns are calculated, averaged and annualized for the different (K- 3, K-6, K-9 and K-12) holding periods. The performed Newey-West t-test (t-values in the table) tests whether the returns of the different portfolios significantly differ from zero. ***, ** and * represents the 1%, 5% and 10% significance level of the t-tests.

Holding period (K)

Formation period (J) 3 Months 6 Months 9 Months 12 Months Liquidity Volume 3 Months PW 7.22% 11.08% 14.06%** 12.83%** 3.77% 17735.32 (t-value) (0.896) (1.656) (2.302) (2.106) PL 3.98% 4.97% 0.06% 0.64% 6.57% 19308.66 (t-value) (0.180) (0.296) (0.005) (0.069) PW-PL 3.24% 6.12% 14.00% 12.19% -2.79% -1573.34 (t-value) (0.154) (0.412) (1.648) (1.538) 6 Months PW 11.76% 16.15%** 15.85%** 13.24%** 3.21% 15911.59 (t-value) (1.541) (2.514) (2.649) (2.238) PL 9.21% 5.02% 1.23% 1.60% 6.78% 19047.48 (t-value) (0.333) (0.275) (0.100) (0.150) PW-PL 2.55% 11.13% 14.61% 11.63% -3.57% -3135.89 (t-value) (0.099) (0.675) (1.317) (1.205)

3_{The same results are generated within a sample without any adjustments. Therefore, it can be concluded that the adjustments}

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Table 2 continued

Formation period (J) 3 Months 6 Months 9 Months 12 Months Liquidity Volume 9 Months PW 13.52%** 14.82%** 13.52%** 12.11%** 3.32% 13895.45 (t-value) (1.992) (2.517) (2.409) (2.164) PL 5.13% 3.39% -0.12% 2.25% 7.39% 17374.22 (t-value) (0.178) (0.177) (-0.010) (0.214) PW-PL 8.40% 11.44% 13.64% 9.86% -4.07% -3478.76 (t-value) (0.301) (0.613) (1.165) (0.984) 12 Months PW 12.41%* 13.27%** 12.48%** 11.68%* 3.36% 13106.10 (t-value) (1.754) (2.146) (2.007) (1.829) PL 12.21% 6.84% 3.68% 4.86% 7.71% 17574.77 (t-value) (0.385) (0.345) (0.297) (0.469) PW-PL 0.20% 6.43% 8.81% 6.83% -4.35% -4467.77 (t-value) (0.006) (0.333) (0.740) (0.686)

The liquidity indicator of this paper and average turnover by volume (Volume) are presented in Table 2. The Volume is calculated by the amount of shares traded on average per month. The market averages of Volume and liquidity indicators are 19922.64 and 7.7% respectively. Lee and Swaminathan (2000) used the Volume characteristic as a liquidity indicator, suggesting that low Volume indicates illiquid stocks. The results claim that the “winners” portfolio consists stocks within lower Volume, thus illiquid stocks. The liquidity indicator suggests that illiquid stocks have a higher liquidity indicator, meaning that the “winners” portfolio consists liquid stocks, contradicting previous research. However, Lee and Swaminathan (2000) as well as Thomson Reuters4 debate that Volume measured by the turnover ratio is unlikely to be a liquidity proxy, which is confirmed in this research. The negative liquidity loads of the overall returns can be explained by the Volume, which is pulled away when aggregate liquidity increases (Sadka, 2005).

Figure 1 shows that the liquidity indicator used in this paper as well as the turn over by Volume for the nine-month-formation period. The figure presents evidence that the different liquidity indicators do not move in the same directions. These results confirm the different outcomes of the indicators. Furthermore, it can be argued that indeed Volume is not a good proxy measurement for liquidity compared to the liquidity indicator in this paper.

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Figure 1: Volume and liquidity indicators for the nine-months formation strategy

4.1.2 Average annualized performance of the liquidity indicators

The results above suggest that the Volume and liquidity indicator of stocks differs within the portfolios. Table 3 summarizes the average annualized performance of the “winners” and “losers” portfolios based on the double-sorting approach. The first sorting is based on the Jegadeesh and Titman (1993) method as conducted in Table 2. Within the “winners” and “losers” portfolios, each stock is sub-ranked based on past liquidity performance. The table presents all four sub-ranked portfolios within the different formation and holding periods.

Table 3 shows that overall the “low winners” portfolios, containing stocks which have high past return and are rather liquid, outperform the “high winners” portfolios. This means that an investor generates higher returns investing in liquid stocks. For example, within the [9:9] combination the averaged annualized “high winners” portfolio generates a return of 12.64%, where the “low winners” portfolio generates a return of 14.43% on an average annualized basis. However, in the twelve-month-formation period the illiquid stocks outperformed the liquid stocks. All results show to be significant and differ from zero.

The “low losers” portfolios, consisting stocks that have low past returns and are liquid, generate higher returns than the “high losers” portfolios. Taking a short position in the liquid or illiquid that “losers” generates overall positive returns in the different holding periods independently of the formation period, meaning that except for the formation and holding periods [3:6], [6:6] and [9:3] the “losers” portfolio is not profitable. In addition, none of the “losers” portfolios (high and low) shows to be significant. Remarkably, the returns of the illiquid “losers” decreases rapidly during the nine- and twelve-month-holding period,

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suggesting illiquid “losers” become profitable over a longer time horizon. Interestingly, a horizon trend in observable within the high and low “losers” portfolio, suggesting that “losers” portfolios move in contrary directions. This means that the profitability of the illiquid “losers” increases over time while the profitability of the liquid “losers” decreases over time.

Overall, it can be concluded that the liquid stocks generate higher returns compared to the illiquid stocks. These results contradict previous research of Amihud (2000) who debates that an investor demands an illiquidity premium for relatively illiquid stocks. To add, Brennan and Subrahmanyam (1996) debate that stocks earn higher returns when they are exposed to higher price impacts. Sadka (2000) also finds an illiquidity premium in pricing equities. The results contradict previous research by arguing that no premium is added for bearing liquidity risk as a compensation for the unexpected variations. The table shows that the liquid stocks ear significantly higher profits compared to the illiquid stocks. However, the illiquid losers become more profitable over time. It can be debated that the “winners” portfolios generate most of the overall performance, since the table shows that most of the “losers” portfolios generate positive returns. These results contradict the previous studies done by Jegadeesh and Titman (1993), Rouwenhorst (2007) Agyei-Ampomah (2007) and Doukas and McKnight (2005). These researchers argue that the “losers” portfolio generated most of the overall portfolio returns though this is not observable in this paper.

Table 3 reports the liquidity indicator used in this paper and Volume of each portfolio. According to Thomson Reuters the research on liquidity over the past 20 years has proven that bid-ask spreads in combination with depth measures such as turnover by Volume provide a good proxy for liquidity.5 Therefore, it can be stated that solely both indicators of liquidity are presenting contradicting arguments. However, when selecting stocks based on liquidity both indicators show similar results, pointing in the same directions. For example the “high winners” portfolio, which are illiquid stocks, have lower Volume than the “low winners” portfolio. The results therefore, confirm the earlier research of Lee and Swaminathan (2000) arguing that both liquidity indicators show that high liquid stocks outperform illiquid stocks.

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Table 3

Average annualized performance of the liquidity indicators (2000-2007)

Each month all stocks traded on Euronext Amsterdam are ranked, based on their previous J-month performances, and assigned to the “winners” or “losers” portfolio. The “winners” portfolio contains the 16 best-performing stocks and the “losers” portfolio contains the 16 worst performing stocks. Secondary, the stocks within the “winners” and “losers” portfolios are sub-ranked on their previous J-month average liquidities. For example the “high winners” portfolio contains the eight best-performed stocks and the most illiquid stocks during the formation period, the “low winners” consists the best-performed stocks but are liquid during the formation period the same sorting is applied within the “losers” portfolio. These portfolio are equally weighted in the portfolios where after the overlapping returns are calculated, averaged and annualized for the different (K-3, K-6, K-9 and K-12) holding periods. The performed Newey-West t-test (the t-values in the table) tests whether the returns of the different portfolios significantly differ from zero. ***, ** and * represents the 1%, 5% and 10% significance level of the t-tests.

Holding period

Formation period 3 Months 6 Months 9 Months 12 Months Liquidity Volume

3 Months High Winner 6.49% 9.49% 12.47%* 11.57%* 6.84% 2653.66

(t-value) (0.692) (1.310) (1.845) (1.722) Low Winner 8.03% 12.50%* 14.91%** 13.64%** 0.55% 32355.87 (t-value) (1.008) (1.748) (2.456) (2.345) High Loser 11.23% 11.59% 0.36% -1.47% 11.77% 1294.81 (t-value) (0.379) (0.521) (0.032) (-0.169) Low Loser -2.89% -3.39% -1.03% 0.03% 1.02% 37008.28 (t-value) -(0.162) -(0.256) -(0.092) (0.489)

6 Months High Winner 7.88% 15.87%** 15.41%** 12.95%** 5.76% 4979.09

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Formation period (J) 3 Months 6 Months 9 Months 12 Months Liquidity Volume

9 Months High Winner 12.32%* 12.98%** 12.64%** 11.63%** 5.97% 2829.47

(t-value) (1.700) (2.169) (2.241) (2.050) Low Winner 14.82%** 16.21%*** 14.43%** 12.63%** 0.50% 24720.22 (t-value) (1.977) (2.511) (2.351) (2.115) High Loser 20.55% 8.65% 0.48% -1.11% 14.00% 1256.77 (t-value) (0.479) (0.347) (0.035) (-0.104) Low Loser -8.19% -4.17% 0.02% 7.18% 1.26% 33090.11 (t-value) -(0.424) -(0.284) (0.002) (0.586)

12 Months High Winner 12.19% 13.40%** 12.71%* 11.40%* 6.13% 1408.82

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4.1.3 Average annualized portfolio returns of the four liquidity based momentum strategies

Table 4 reports the average annualized performance of the “winners” and “losers” portfolios based on the double-sorting approach described in Section 3. In the double-sorting approach in total 64 different portfolios (16*4) are created, based on the different formation and holding periods. The table below shows the output of the different profitability of the zero-sum investment strategies based on past returns and past liquidity.

Table 4 shows that overall portfolios consisting of liquid stocks (“low winners” – “low losers”) outperform the combination of illiquid “winners” and liquid “losers” (“high winners” – “low losers”) except for the twelve-month-holding periods. For example, in the [9:9] combination the return of the liquid stocks (“low winners” – “low losers”) is 14.41% where the return of the combination illiquid “winners” and liquid “losers” is 12.62%. The lowest profits are generated within the illiquid combinations or the combinations of the liquid “winners” and illiquid “losers”. The highest profits are earn is 20.37% in the [9:9] strategy averaged and annualized, however not significant. Jegadeesh and Titman, 1993, Chan et al., 1996 and Rouwenhorst, 1998 found single sorted of 14.61%, 15.72% and 8.76% respectively. This implies that the double-sorted approach, ranking stocks on past returns and past liquidity increased the profits. As mentioned above the illiquid “losers” become profitable over longer time horizon, suggesting that an illiquidity premium needs time to become observable.

Notably, the zero-sum portfolio returns of the illiquid stocks become more profitable over time, however the profitability of the liquid zero-sum portfolio decreases over time. According to Agyei-Ampomah (2007) the profitability for the longer formation and holding periods can be explained by a decrease in Volume over longer time horizons. This means that the Volume in Table 3 should decrease over time, which is indeed observable although in the twelve-month-formation period the Volume slightly increased. The t-statistics suggest that LIQMS are indeed significantly different from zero.

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Table 4

Average annualized portfolio returns of the four liquidity based momentum strategies (2000-2007) Each month all stocks traded on Euronext Amsterdam are ranked, based on their previous J-month performances, and assigned to the “winners” or “losers” portfolio. Secondly, within the “winners” and “losers” portfolios are ranked according to their previous J-month average liquidities. Table 4 shows the zero-sum investments strategies. All these portfolios are equally weighted in the portfolios, after which the overlapping returns are calculated, averaged and annualized for the different (K-3, K-6, K-9 and K-12) holding periods. The performed Newey-West t-test (the t-values in the table) tests whether the returns of the different portfolios significantly differ from zero. ***, ** and * represents the 1%, 5% and 10% significance level of the t-tests.

Formation period (J) Portfolios 3 Months 6 Months 9 Months 12 Months

3 Months High Winner - High Loser -4.74% -2.10% 12.11% 13.05%

(t-value) -(0.159) -(0.097) (1.147) (1.569)

High Winner - Low Loser 9.38% 12.88% 13.49% 9.43%

(t-value) (0.560) (1.115) (1.416) (1.033)

Low Winner - High Loser -3.20% 0.91% 14.55% 15.11%*

(t-value) -(0.111) (0.044) (1.463) (1.902)

Low Winner - Low Loser 10.92% 15.88% 15.94%* 0.03%

(t-value) (0.699) (1.610) (1.985) (0.489)

6 Months High Winner - High Loser -18.99% 0.39% 12.43% 14.14%

(t-value) -(0.445) (0.016) (0.908) (1.453)

High Winner - Low Loser 9.92% 20.17%* 16.67% 9.65%

(t-value) (0.565) (1.740) (1.541) (0.948)

Low Winner - High Loser -12.58% 0.51% 13.25% 14.64%

(t-value) -(0.287) (0.019) (0.944) (1.458)

Low Winner - Low Loser 16.33% 20.29%* 17.50%* 10.14%

(t-value) (0.922) (1.724) (1.707) (0.992)

(t-value) -(0.195) (0.177) (0.897) (1.268)

(t-value) (1.168) (1.269) (1.050) (0.392)

(t-value) -(0.133) (0.298) (0.972) (1.223)

Low Winner - Low Loser 23.00% 20.37% 14.41% 5.45%

(t-value) (1.291) (1.453) (1.174) (0.450)

(t-value) -(0.222) (0.071) (0.557) (0.955)

(t-value) (0.664) (0.7930 (0.596) (0.116)

(t-value) -(0.227) (0.035) (0.459) (0.906)

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4.2 Averaged annualized liquidity based momentum profits between 2008 and 2015

Section 4.2 back-tests the previous results over a different time horizon, between 2008 and 2015. This out-of-sample test period is implemented to test whether LIQMS are independent over time. To add, this sample period can be used as a robustness test. In both sub-time horizons the financial crisis is maintained. Within this section the same analyses, as Section 4.1 are discussed.

4.2.1 Averaged annualized portfolio returns

The results of the averaged annualized portfolio returns in the time frame ranging from 2008 until 2015 are presented in Appendix 1 and 2. The out-of-sample period also presents momentum profits on Euronext Amsterdam, similar to the main sample period. Additionally, the “winners” still generates most of the overall performance, contradicting Jegadeesh and Titman (1993), Rouwenhorst (2007) Agyei-Ampomah (2007) and Doukas and McKnight (2005). The “losers” portfolio in this time frame is however profitable, contributing to the overall performance. The results show to be significantly different from zero. Furthermore, the liquidity indicator and the Volume also contradict each other in this sample period.

Table 5 summarizes the average annualized performance of the “winners” and “losers” portfolios based on the double-sorting approach. The portfolios are first sorted on historical returns where after each of the stocks within the “winners” and “losers” portfolios are sub-ranked based on historical liquidity. Table 5 presents all four sub-sub-ranked portfolios within the different formation and holding periods.

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The Volume indicator shows similar arguments as the liquidity indicator in this paper, low Volume stocks are more illiquid. However, the results contradict Lee and Swaminathan (2000) by arguing that illiquid stocks, low Volume stocks, earn higher returns. Furthermore, as stated before when testing two liquidity indicators combined they are debated to be good proxies for liquidity and therefore should point in the same direction. According to Thomson Reuters, combining different liquidity indicators such as bid-ask spreads and turnover by Volume, are significantly better proxies than single use of the indicators.

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Table 5

Average annualized performance of the liquidity indicators (2008-2015)

Each month all stocks traded on Euronext Amsterdam are ranked, based on their previous J-month performances, and assigned to the “winners” or “losers” portfolio. The “winners” portfolio contains the 16 best-performing stocks and the “losers” portfolio contains the 16 worst performing stocks. Secondly, within the “winners” and “losers” portfolios the stocks are ranked on their previous J-month average liquidities. For example the “high winners” portfolio contains the eight best-performed stocks and the most illiquid stocks during the formation period, the “low winners” consists the best-performed stocks but are liquid during the formation period as the same sorting is applied within the “losers” portfolio. These portfolio are equally weighted in the portfolios where after the overlapping returns are calculated, averaged and annualized for the different (K-3, K-6, K-9 and K-12) holding periods. The performed Newey-West (the t-values in the table) tests whether the returns of the different portfolios significantly differ from zero. ***, ** and * represents the 1%, 5% and 10% significance level of the t-tests.

3 Months High Winner 14.50%* 11.93% 10.54%* 10.31%** 9.37% 8432.68

(t-value) (1.657) (1.537) (1.822) (2.055) Low Winner 5.80% 9.01% 11.94%** 10.38%** 0.25% 41536.38 (t-value) (0.630) (1.278) (1.963) (2.128) High Loser -11.55% -11.32% -10.25% -5.03% 14.37% 3086.07 (t-value) -(1.031) -(1.486) -(1.611) -(0.915) Low Loser 1.84% 4.43% 4.77% 0.03% 0.49% 53353.53 (t-value) (0.164) (0.528) (0.665) (0.489)

6 Months High Winner 25.26%** 15.78%** 12.95%** 10.84%** 9.88% 6150.05

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9 Months High Winner 19.30%** 14.02%* 11.32%* 8.63%* 9.71% 6027.30

(t-value) (2.230) (1.898) (1.842) (1.862) Low Winner 7.72% 8.44% 8.60%* 8.86%** 0.28% 31739.27 (t-value) (0.957) (1.379) (1.766) (2.313) High Loser -20.65%* -15.27%* -11.21% -6.70% 13.60% 3302.05 (t-value) -(1.802) -(1.786) -(1.472) -(1.090) Low Loser 2.80% 9.72% 6.36% 3.08% 0.53% 46341.26 (t-value) (0.203) (0.844) (0.735) (0.470)

12 Months High Winner 18.73%*** 13.00%** 10.29%** 9.45%** 9.34% 5029.03

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Table 6 reports the average annualized performance of the zero-sum portfolio returns based on the double-sorting approach. In the double-sorting approach in total 64 different portfolios (16*4) are created, based on the different formation and holding periods. The Table below shows the output of the different “winners” and “losers” portfolio strategies to investigate the profitability of the zero-sum investment strategies based on past returns and past liquidity.

Table 6 shows that portfolios, which contain of illiquid stocks (“high winners” – “high losers”) in general outperforms the liquid stocks portfolios. These results contradict previous results of the time frame between 2000-2007. These outcomes show that the overall results are highly influenced by the illiquid “loser”. However, these results show that the illiquidity premium as presented by Amihud (2000) and Sadka (2005) when equity pricing is not observable in this time frame because all results in the table decrease over the longer time periods. Although, the illiquid stocks still generate significantly higher profits compared to the liquid stocks. Furthermore, the results show that the illiquid “losers” create most of the overall performance. These results complement Jegadeesh and Titman (1993), Rouwenhorst (2007) Agyei-Ampomah (2007) and Doukas and McKnight (2005) by debating that indeed the “losers” portfolios create most of the overall zero-sum investment.

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Table 6

Average annualized portfolio returns of the four liquidity based momentum strategies (2008-20015)

Each month all stocks traded on Euronext Amsterdam are ranked, based on their previous J-month performances, and assigned to the “winners” or “losers” portfolio. Secondly, the stocks are ranked on their previous J-month average liquidities. Table 6 shows the zero-sum investment strategies. All these portfolios are equally weighted in the portfolios the overlapping returns are calculated averaged and annualized for the different (K-3, K-6, K-9 and K-12) holding periods. The performed Newey-West t-test tests whether the returns of the different portfolios significantly differ from zero. ***, ** and * represents the 1%, 5% and 10% significance level of the t-tests.

Formation period (J) Portfolios 3 Months 6 Months 9 Months 12 Months 3 Months High Winner - High Loser 26.05%*** 23.25%*** 20.79%*** 15.34%***

(t-value) (2.573) (3.012) (3.303) (2.617)

High Winner - Low Loser 12.66%* 7.50% 5.78% 6.37%

(t-value) (1.764) (1.576) (1.044) (1.431)

Low Winner - High Loser 17.36%* 20.33%*** 22.19%*** 15.41%***

(t-value) (1.824) (2.762) (3.794) (3.215)

(t-value) (0.545) (0.995) (1.477) (0.489)

6 Months High Winner - High Loser 43.07%*** 30.67%*** 21.84%*** 17.09%***

(t-value) (4.417) (4.118) (2.869) (2.861)

High Winner - Low Loser 21.94%** 5.45% 6.15% 4.54%

(t-value) (2.169) (0.600) (0.773) (0.6550

Low Winner - High Loser 24.40%*** 26.51%*** 21.42%*** 16.91%***

(t-value) (2.811) (3.552) (3.060) (3.233)

(t-value) (0.498) (0.189) (1.053) (0.996)

(t-value) (4.530) (4.151) (3.368) (3.046)

High Winner - Low Loser 16.51%* 4.30% 4.96% 5.55%

(t-value) (1.747) (0.498) (0.698) (0.977)

(t-value) (3.155) (3.687) (3.539) (3.198)

Low Winner - Low Loser 4.93% -1.28% 2.25% 5.78%

(t-value) (0.541) (-0.167) (0.433) (1.359)

(t-value) (3.730) (3.902) (4.135) (3.327)

High Winner - Low Loser 16.93% 9.28% 9.01% 11.12%***

(t-value) (1.487) (1.202) (1.547) (2.751)

(t-value) (2.734) (3.378) (3.661) (3.192)

Low Winner - Low Loser 6.97% 6.03% 8.64%** 11.50%***

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4.3 Average annualized portfolio returns during the financial crisis

The results in 4.1 and 4.2 suggest that the liquidity based momentum strategy reverses in a downward market movement. This section analyses the average annualized returns during the financial crisis between January 2007 and December 2008.

The financial crisis of 2007-2008 is widely assumed to be the worst global financial crisis since the Great Depression in the 1930s. This crisis had catastrophic impact on stock markets around the world. Since the crisis investors are more than ever seeking for investment strategies, which generate significant returns by providing predictability under uncertain conditions.

Table 7 summarizes the average annualized performance of the “winners” and “losers” portfolios based on the double-sorting approach, the portfolios are ranked based on historical return and historical liquidity. Table 7 presents all four sub-ranked portfolios within the different formation and holding periods.

From Table 7 it can be concluded that all returns decreased dramatically and even all became negative during the financial crisis, no exceptions. This illustrates the major impact of the financial crisis on Euronext Amsterdam. It should be mentioned that during the financial crisis in 2007-2008, the Netherlands Authority for the Financial Markets adopted emergency measures to restrict conditions on short selling, meaning that the high returns which should have been earned taken a short position in the “losers” portfolio are not representative.

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Table 7

Average annualized performance of the indicators during the financial crisis

Each month all stocks traded on Euronext Amsterdam are ranked, based on their previous J-month performances, and assigned to the “winners” or “losers” portfolio. Secondly, within the “winners” and “losers” portfolios the stocks are ranked on their previous J-month average liquidities. For example the “high winners” portfolio contains the eight best-performed stocks and the most illiquid stocks during the formation period, the “low winners” consists the best-performed stocks but are liquid during the formation period as the same sorting is applied within the “losers” portfolio. The portfolios are equally weighted where after the overlapping returns are calculated, averaged and annualized for the different (K-3, K-6, K-9 and K-12) holding periods. The performed Newey-West t-test (the t-values in the table) tests whether the returns of the different portfolios significantly differ from zero. ***, ** and * represents the 1%, 5% and 10% significance level of the t-tests.

3 Months High Winner -26.81%*** -17.19%* -15.48%* -15.74%** 9.26% 2301.73

(t-value) -(2.715) -(1.727) -(1.994) -(2.373) Low Winner -36.82%*** -25.33%*** -14.36%** -12.17%** 0.26% 55281.63 (t-value) -(2.914) -(2.806) -(2.090) -(2.053) High Loser -42.11%*** -34.36%*** -31.28%*** -27.26%*** 6.92% 857.39 (t-value) -(2.995) -(3.131) -(3.509) -(3.693) Low Loser -47.15%*** -26.36%* -17.23% 0.03% 0.49% 42591.89 (t-value) -(2.957) -(1.806) -(1.051) (0.489)

6 Months High Winner -20.90% -16.38% -15.64%** -17.23%** 8.38% 11858.39

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9 Months High Winner -20.28%** -15.38% -15.66%** -16.25%** 8.41% 4305.55

(t-value) -(2.214) -(1.593) -(1.975) -(2.623) Low Winner -25.09%* -17.67%* -15.84%** -14.23%** 0.27% 46238.02 (t-value) -(1.883) -(1.712) -(2.049) -(2.088) High Loser -69.23%*** -50.29%*** -42.28%*** -37.20%*** 7.74% 775.19 (t-value) -(6.177) -(4.112) -(4.820) -(5.604) Low Loser -58.35%*** -41.48%*** -26.14%* -21.59%** 0.62% 16459.19 (t-value) -(3.350) -(3.092) -(1.772) -(2.192)

12 Months High Winner -13.16%* -14.36% -17.10%* -16.61%** 8.60% 1585.56

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Table 8 presents the average annualized performance of the “winners” and “losers” portfolios based on the double-sorting approach described in Section 3. Each of the portfolios consists eight (5%) stocks out of the main restricted sample.

Analysing the results, it can be concluded that in all formation and holding combinations the portfolios containing high illiquid stocks (“high winners” – “high losers”), outperform the combinations of high liquid stocks (“low winners” – “low losers”). The highest return is earned going long in the high winners and short in the high losers, earning a return of 57.76% averaged annualized [12:3] combination.

The portfolio combinations consisting liquid “winners” and illiquid “losers” (“low-winners” – “high-losers”) shows higher returns than the combination of illiquid “(“low-winners” and liquid “losers” within all different holding and formation periods except for the three-months holding period. For example, within the nine-month-formation and nine-month-holding period [9:9] the return of the liquid ‘winners” and illiquid “losers” generates a return of 26.44% and the return of the combination consisting illiquid “winners” and liquid “losers” is 10.48% averaged and annualized, arguing that illiquid losers generate most of the overall zero-sum portfolio returns.

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Table 8

Average annualized portfolio returns of the four liquidity based momentum strategies (2007-2008)

Each month all stocks traded on Euronext Amsterdam are ranked, based on their previous J-month performances, and assigned to the “winners” or “losers” portfolio. Secondly, within the “winners” and “losers” portfolios the stocks are ranked on their previous J-month average liquidities. Table 8 shows the zero-sum investment strategies. All these portfolios are equally weighted in the portfolios where after the overlapping returns are calculated, averaged and annualized for the different (K-3, K-6, K-9 and K-12) holding periods. The performed Newey-West t-test (the t-values in the table) tests whether the returns of the different portfolios significantly differ from zero. ***, ** and * represents the 1%, 5% and 10% significance level of the t-tests.

Formation period (J) Portfolios 3 Months 6 Months 9 Months 12 Months 3 Months High Winner - High Loser 15.30% 17.17%*** 15.80%*** 11.51%**

(t-value) (1.075) (2.702) (2.788) (2.316)

High Winner - Low Loser 20.34%* 9.18% 1.75% -0.50%

(t-value) (1.733) (1.057) (0.145) -(0.059)

Low Winner - High Loser 5.28% 9.03% 16.92%*** 15.09%***

(t-value) (0.677) (1.429) (3.057) (2.701)

(t-value) (1.108) (0.139) (0.278) (0.398)

6 Months High Winner - High Loser 38.30%** 30.92%*** 21.79%*** 15.21%***

(t-value) (2.591) (6.062) (4.176) (3.244)

High Winner - Low Loser 28.46%** 15.92%* 9.29% 4.03%

(t-value) (2.602) (1.699) (0.836) (0.597)

Low Winner - High Loser 26.59%** 30.20%*** 25.11%*** 22.18%***

(t-value) (2.240) (5.635) (5.145) (4.893)

Low Winner - Low Loser 16.74%* 15.20%* 12.62% 11.00%

(t-value) (1.857) (2.001) (1.117) (1.570)

(t-value) (5.884) (5.838) (7.904) (9.018)

High Winner - Low Loser 38.07%*** 26.10%*** 10.48% 5.35%

(t-value) (3.421) (3.161) (1.175) (1.088)

(t-value) (4.462) (4.970) (7.332) (6.229)

Low Winner - Low Loser 33.27%*** 23.80%*** 10.30% 7.36%*

(t-value) (4.468) (5.441) (1.385) (1.762)

(t-value) (5.120) (5.492) (4.003) (4.237)

High Winner - Low Loser 48.51%*** 22.03%* 6.95% 2.80%

(t-value) (3.251) (1.941) (0.737) (0.481)

(t-value) (4.143) (4.387) (4.931) (5.172)

Low Winner - Low Loser 33.19%*** 15.69%*** 5.78% 4.54%

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4.4 Liquidity based momentum strategies adjusted for risk

Agyei-Ampomah (2007) argues that in general different risk in returns of the portfolios could be allocated the different expected returns between the portfolios above. Therefore, in this paper the risk-adjusted abnormal returns of the various liquidity based momentum strategies (LIQMS) are examined following Agyei-Ampomah (2007). The three-factor model of Fama and French (1996) is used to adjust the various returns of the different “winners” and “losers” portfolios. The three-factor model is presented in following Formula 6:

Rpt − RFt = αp + β1P (RMt − RFt ) + β2PSMB + β3PHML + εPt (6)

The Rpt represents the portfolio return and RFt stands for the risk-free rate, SMB and

HML are the factors for size and book-to-market respectively. To perform this regression the

values needed are downloaded from the Fama website, where the European values are used because since the Euronext Amsterdam is part of a European chain of stock exchanges and has strong correlations with other European countries, which makes it a good proxy. It is expected that if the returns of the portfolios are compensated for higher risk, the abnormal returns of Table 4 and Table 6 would disappear when adjusting them for common risk factors (Agyei-Ampomah, 2007). The outcome of the risk-adjusted portfolios is presented in Appendix 3.

The results (2000-2007) show that significant risk-adjusted returns for almost all the zero-sum investments strategies. Remarkably, in the zero-sum risk-adjusted returns the “losers” portfolio becomes increasingly important in generating the overall returns, for example in [9:9] strategy the “high losers” portfolio generates -12.43%, the “high winners” portfolio generates 7.11%, and the zero-sum portfolio return is 19.54%. These results suggest that the short positions taken in the “losers” portfolios are increasingly important to obtain the abnormal profits.6

6_{The results of the risk-adjusted returns over the time frame ranging from 2008-2015 are similar to the results presented in}

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5. Conclusion

This paper examines the profitability of various liquidity based momentum strategies (LIQMS) applied to the stocks listed on Euronext Amsterdam over a period of 15 years. By analysing LIQMS this paper seeks to create a link between two past indicators, historical returns and the historical liquidity of stocks. To create a solid investment strategy based on past returns and past liquidity of the stocks the total sample period is sub-divided into three sample periods. Firstly, a period between 2000 and 2007 is analysed in addition, as robustness test a sub-period ranging from 2008 to 2015 is analysed. Since the first two sub-periods are in a less turbulent market state the third sub-period is set during the financial crisis of 2007-2008.

The statistical results over the sub-periods present evidence of profitable momentum strategies based on the single sorted approach on Euronext Amsterdam. The results obviously contradict Jegadeesh and Titman (1993), Rouwenhorst (2007), Agyei-Ampomah (2007), and Doukas and McKnight (2005) by concluding that overall the short position in the “losers” portfolios do not generate most of the overall performance. Instead the “winners” portfolios generate most of the overall performances within the time period of this paper.

The results on the double-sorting approach, based on both historical returns and historical liquidity, indicate that liquidity influence the profitability of the momentum profits. The first sub-period (2000-2007) concludes, that portfolios which contain highly liquid stock, “low-winners” and “low-losers”, generate higher returns than any other combination based on liquidity. These results contradict previous research done by Amihud’s (2000) Brennan and Subrahmanyam (1996) and Sadka (2000). They suggest that an illiquidity premium is added in equity pricing mechanisms, although this premium is observable over a longer time horizon. Furthermore, the results are complementary to the outcome of Lee and Swaminathan (2000), arguing that liquid (high Volume) stocks outperform illiquid (low Volume) stocks.

The results of the out-of-sample data (2008-2015) contradict the main sample period results, by arguing that investors should invest in illiquid stocks. The results therefore contradict Lee and Swaminathan (2000), by arguing to invest in low Volume stock rather than in high Volume stocks. However, the results are complementary to Amihud (2000), Brennan and Subrahmanyam (1996)and Sadka (2005) implying that an illiquidity premium is added when pricing equities.