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The Implication of Attention for the
Profitability of Momentum strategies in the
Dutch Stock Market
Amber Bienfait Msc. Finance Thesis University of Groningen
Abstract: This paper examines the relation between investors’ attention and the profitability of momentum strategies in the Dutch stock market for large-cap and mid-cap stocks from 1990-2016 by conditioning momentum profits on trading volume and market state. The results show that momentum profits are solely derived from “winner” portfolios and that low volume stocks within these portfolios account for a large part of the momentum profits. Furthermore, momentum profits are only significantly present following “up” markets, when defining the market as the lagged market return of the AEX index.
Keywords: Momentum, investors’ attention, trading volume, liquidity, market states JEL classifications: G10, G11, G14, G19
Amber Johanna Elinor Bienfait 06-41215375
s2032996
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1. Introduction
“The momentum effect represents perhaps the strongest evidence against the efficient market hypothesis” ( Jegadeesh and Titman, 2011, pp 507).
Over the last few decades an extensive body of research has shown that stock returns are predictable based on their past returns. Momentum strategies were a reaction to earlier research of e.g. Kahneman and Tversky (1982) and De Bondt and Thaler (1985) who argue that individual people tend to overreact to information. Therefore, they suggest contrarian strategies (buying past losers and selling past winners over a very short or a long time period) would result in abnormal returns. Jegadeesh and Titman (1993) find contradicting results that composing a portfolio of a long-position in past “winners” and a short position in past “losers” (over a short to medium time period) generate higher returns in the US stock market. Other researchers confirm the existence of these profits for different geographical markets (e.g. Rouwenhorst, 1998, Griffin et al., 2003, Doukas and McKnight, 2005, and Forner and Marhuenda, 2003). However, a comprehensive body of research about momentum strategies still lacks for the Dutch stock market. De Haan and Kakes (2011), find that institutional investors in the Netherlands mostly perform contrarian investment strategies instead of momentum strategies. From investors’ perspective no research provides accurate information yet that could provide assistance with the optimisation of momentum investment strategies in the Dutch stock market.
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attention. Hou et al. (2009) argue that investors’ attention has two different roles, where inadequate attention and thus negligence of useful information leads to stock price underreaction. Moreover, behavioural biases, such as self-attribution and extrapolative expectations, can interact with investors’ attention and lead to stock price overreaction. Jegadeesh and Titman (1993) state that if prices either underreact or overreact to information, opportunities exist to exploit momentum strategies.
Inspired by Hou et al. (2009) this paper examines the role of investors’ attention in combination with the frequently discussed anomaly around asset pricing predictability, ‘price momentum’, through investors’ ‘underreaction’ and ‘overreaction’ to new information. Hong and Stein (1999) argue that initial underreaction of investors can lead to momentum profits at the moment when investors correct their expectations based on correct fundamental information. Cooper et al. (2004) and Lee and Swanimathan (2000) confirm that stock price overreaction leads to short-term momentum profits and long-term mean reversals, considering that the prices eventually return to their fundamentals after the stock price overreaction is intensified in the short run through self-attribution bias or overconfidence of investors (Daniel et al., 1998). These theories about investors’ attention towards stocks and the possible interaction with price momentum lead to the following research question of my paper:
To what extent are momentum strategies, conditioned on proxies for investors’ attention, profitable in the Dutch stock market?
To answer this question, I use both cross-sectional and time-series tests across the Dutch stock market for large-cap and mid-cap stocks to see how the momentum profits move along the two different proxies for investors’ attention. Recent research uses the search volume index of the ticker of Google Trends as a proxy for attention of individual retail investors, which provides a direct measure of investors’ attention, considering it represents the search volume on Google for a particular stock (Da et al., 2011). I use indirect measures in my research, based on theories linking these measures to attention, in order to capture a broader base of investors on the Dutch stock market, rather than exclusively individual retail investors.
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attention, they interpret less information about the stock and they are less expected to trade it. Additionally, when they pay more attention to a stock, behavioural biases such as overconfidence and self-attribution can cause investors to form divergent opinions about asset characteristics, which results in more frequent trading (Odean 1998, and Scheinkman and Xiong, 2003). Considering that, the trading volume of a stock is also a widely known measure for the liquidity of the stock, my findings concerning trading volume can be linked to an interpretation of the role of liquidity risk in momentum profits. Considering that, the Dutch stock market generally consists of smaller and more illiquid stocks, than in the UK and the US, I use my research into investors’ attention to point out the role of the illiquidity in Dutch stocks. I use a second widely known measure for liquidity, the bid-ask spread of the stock, as a robustness test for the relationship between liquidity and momentum.
As a time-series proxy for attention I use the state of the economy. Karlsson et al. (2009) report about “the ostrich effect” among investors, which actually means that investors tend to pay more attention towards stocks that are doing well and performing in rising markets, and “put their head in the sands”, when a market is falling and thus not performing well. Therefore, investors tend to pay more attention to stocks following “up” markets, where the overall market is doing well, than following “down” markets.
The main results show that momentum profits are significantly present in the Dutch stock market after controlling for the Carhart four risk factors. However, contradicting existing literature, the profits are exclusively derived from the “winner” portfolios as the “loser” portfolios show short-term mean reversals. Furthermore, after double-sorting the portfolios on trading volume of the stock, the analysis points out that stocks with a lower level of trading volume and thus lower liquidity predict higher future returns. In addition, momentum profits show to be exclusively significant following “up” markets.
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2. Theoretical Framework
This section provides a clear definition of momentum and its possible sources. Furthermore, the section provides a definition of investors’ attention, its indirect proxies used in this paper, trading volume and market state, and elaborates on their possible relation to momentum profits.
2.1. Momentum
The ‘momentum effect’ is explained as the observation that stocks that have performed well in the past, continue to perform well in the future, and vice versa stocks that have performed poorly in the past continue to fall (Jegadeesh and Titman, 1993). Abnormal returns earned with momentum strategies contradict the efficient market hypothesis. This hypothesis claims that whenever news arrives, the impact will immediately be incorporated into the stock prices, without any delay. Therefore, arbitrage opportunities and abnormal returns are impossible (Fama, 1969). Over the past decades, a broad spectrum of literature has documented about momentum theory. De Bondt and Thaler (1985) first examined ‘contrarian strategies’ and found that long-term past losers outperform long-term past winners over the following three to five years. A few years later Jegadeesh (1990) and Lehmann (1990) find the same effect, nevertheless for a very short-term time period. These contrarian studies all generally lead to the conclusion that prices tend to overreact to information.
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have to be rebalanced and this is accompanied with high transaction costs (Lesmond, 2004). Other researches argue that momentum is highly variable over time and experiences large crashes, which makes the strategy unappealing to risk-averse investors (Daniel et Moskowitz, 2013). Baroso and Santa-Clara (2015) however, provide evidence that managing the risk of momentum eliminates crashes and nearly doubles the Sharpe ratio of the strategies. Moreover, Moskowitz et al. (2012) also still document worldwide persistent momentum profits across different asset classes from 1965-2010. They focus on the most liquid instruments in order to avoid illiquidity contaminations that cause high trading costs, and therefore show representative strategies that are easier to implement for investors.
2.2. Sources
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2.3 Attention
The behavioural sources of momentum, in the form of initial underreaction and undue overreaction, can be explained by (limited) investors’ attention. Considering that, attention is a scarce cognitive resource, the brain has limited ability to process a vast amount of incoming information (Kahneman, 1973). This is an important factor to consider, while analysing buying and selling behaviour of investors. Numerous researchers have investigated attention among investors. Peng and Xiong (2006) examine the effects of little attention on investors’ learning behaviour and equilibrium price dynamics and argue that investors tend to act more on sector or industry information instead of firm-specific information, while making investment decisions, due to limited specific attention to the individual stocks. Therefore, crucial firm-specific information might get lost, when investors make important investment decisions, and not all information will be reflected in the stock price. Merton (1987) notes that individual investors only use their limited resources on a few stocks, and therefore only trade stocks that they closely pay attention to. Barber and Odean (2008) examine the matter that noticeable events can seize the investors’ attention and thereby influence their stock buying and selling behaviour. They argue that investors trade more on attention grabbing stocks, and therefore the volume of those stocks is higher. Odean (1998) provides evidence about the fact that overconfident investors trade more often. Karlsson et al. (2009) and Barberis and Xiong (2012) argue that attention and trading volume are greater in rising markets, than in falling markets, due to the fact that people directly derive utility from information. People, and thus investors, will attend to receive good news following rising markets. However, they will not be eager to receive bad news following falling markets. 2.3.1 Momentum, trading volume, and the link to stock liquidity
Considering that, a large amount of attention and thus high trading volume are positively correlated to overconfidence and self-attribution of investors (Daniel et al., 1998), the hypothesis concerning volume and price momentum would be that high volume stocks earn higher momentum returns, which is confirmed by the findings of Hou et al. (2009) and Lee and Swaminathan (2000). However, trading volume is also a widely known liquidity proxy and several existing research papers report contradicting findings about the relationship between liquidity and momentum profits, which raises questions about the hypothesis that should be set in this paper.
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According to Jones (2002), Amihud (2002), and Pastor and Stambaugh (2001), illiquid stocks are expected to receive a higher return. Pastor and Stambaugh (2001) even state that the liquidity risk represents half of the momentum profits. Hence, taking the liquidity characteristics into consideration while forming the momentum portfolios could increase the predictability of the momentum profits. Investors lower their expectations of future stock returns when the stock is frequently traded, and therefore a liquid security yields lower expected returns (Amihud, 2000).
Considering that, liquidity is a difficult phenomenon to define, researchers use more measurements to capture the liquidity of a stock. The market microstructure model (Ho and Stoll, 1980) proposes that trading volume reduces the inventory cost of a trade, which results in a smaller bid-ask spread of a stock, an also widely known measurement for liquidity. Jones (2002) notes that a high bid and ask spread of a stock predict higher returns, as it is followed high transaction costs, which result in a higher price.
2.3.2. Momentum and market state
The theory of Daniel et al. (1998) can be used to predict momentum profits in different states of the economy. The overconfidence of investors is usually greater following market gains (Daniel et al, 1998 and Gervais & Odean, 2001). And therefore, momentum returns should increase, at least in the short run, as a result of an increase in overconfidence in an up market. Hong and Stein (1999) their model also predicts relative changes in price dynamics depending on the state of the market. They examine the change in risk aversion of investors, and they found that decreased risk aversion in rising markets leads to delayed overreaction and thus increased momentum profits.
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Muga and Santamaria (2008) find significant momentum profits following UP markets as well as falling markets, from now on referred to as DOWN markets, for the Spanish stock market. They claim that instead of overreaction the disposition effect1 could be a behavioural explanation of the profitability of momentum strategies. following UP markets show means reversals. Siganos and Chelley-Steeley (2005) find even more contradicting results that momentum profits are exclusively positive following DOWN markets instead of UP markets for the UK stock market. Rey and Schmid (2007) find the same results for the Swiss stock market.
2.3.3. Hypotheses
Basing hypotheses on the theories above, one would expect opposite outcomes, concerning the relationship of trading volume to momentum profits. According to the findings of Lee and Swaminathan (2000) Hou et al. (2009) stocks with a higher trading volume and a higher liquidity level receive more attention from investors, related to overconfidence and self-attribution from investors. Therefore, stocks that are liquid with high trading volumes receive higher momentum returns. However, following the theories of Pastor and Stambaugh (2003) and Amihud (2002), the liquidity risk accounts for a large part of the momentum profits, therefore one would expect that “winner” portfolios mostly consist of low volume stocks.
Considering that, stocks in falling markets receive less attention, and therefore important information might be ignored, the expected returns of momentum strategies are ought to be less in falling markets. Whereas, more attention to stocks in rising markets could interact with behavioural biases that lead to overreaction, such as self-attribution, overconfidence, or extraordinary expectations (e.g. Daniel et al., 1998, De Long et al., 1990), and lead to higher short-term momentum profits following rising markets, compared to falling markets. It is expected that momentum returns reverse in the long run.
1 ‘The disposition effect’ relates to the tendency of investors to sell stocks of which the prices have increased
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3. Data and Methodology 3.1 Data
This paper uses data about stocks listed on the Euronext Amsterdam and is drawn from DataStream. Only large-cap and mid-cap stocks are included in the sample to eliminate highly illiquid stocks with high transaction costs (Moskowitz et al. 2012). The sample period spans 11-11-1990 to 11-12-2015. During 26 years the sample yields a total of 123 stocks with a minimum of 52 stocks, a maximum of 119, and an average of 75 stocks. The double-sorted approach only uses data from 11-01-2001 to 11-12-2015, due to limited availability of trading volume and bid-ask spread data. The raw data includes: the total return index (RI), the stock price (P), turnover by volume (VO), the market capitalisation (MV), and the bid price (PB) and the ask price (PA) of the securities. The market state proxy is partially extracted from DataStream, as the AEX Index. Additionally, data of the total Dutch gross domestic product (GDP) in market prices, used as an alternative indicator for market state, is drawn from the Dutch Centraal Bureau voor Statistiek (CBS) databank2. In conclusion, the Carhart four factors are extracted from Kenneth French’s website3.
3.2 Momentum
First, I use a method almost equal to Jegadeesh and Titman (1993) to form the momentum portfolios, considering that their method has become commonly used in existing literature. The method they use is referred to as the J-month/K-month strategy. The strategies they examine have overlapping holding periods, considering that at the end of every month t they divide stocks into ten equally weighted deciles depending on their prior J-month return (J = 3,6,9,12 months). In my research I use quintiles to form the portfolios, similar to Cooper et al. (2004), considering the smaller size of the AEX stock exchange compared to NYSE used in Jegadeesh and Titman (1993), and the need for a degree of portfolio diversification. The highest return portfolio is called the “winners” portfolio and the lowest return portfolio is called the “losers” portfolio. These portfolios are equally weighted after formation period at time t and, and held for K subsequent months (K = 3,6,9,12 months). Furthermore, similar to Cooper et al. (2004) I sort the stocks at time t based on their prior J-month returns, calculated as the returns from t – J to t -1.
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The returns of the stocks are calculated as follows:
!!" =!"!(!!!)!!"!(!!!)
!"!(!!!) (1)
Where !!" is the rate of return for period t – J to t-1, !"!(!!!,!) is the total lagged return of stock i at time t – J,K, and !"!(!!!) is the total return of stock i at time t-1.
I use this formula to compute the K-month returns:
!!(!!!) = !"!(!!!)!" !!"!"
!" (2)
Stocks with a price lower than €1 will be excluded from the dataset. This eliminates highly illiquid stocks and high-trading-costs stocks (Cooper et al., 2004). Dividing the stocks into quintiles means that 20% of the average total stocks will be assigned to each quintile, in this case 75 / 5 = 15.
In each month t, the momentum strategy buys the winner portfolio and sells the loser portfolio, holding this position for K months. Hence, different momentum strategies can be used, following different combinations of formation periods (J) and holding periods (K). As the stocks in the portfolio are equally weighted, the monthly returns of the portfolios are calculated as:
!!"!(!, !) = !!"(!,!)
! (3)
Where !!"!(!, !) is the monthly portfolio profit at time t and N is the number of stocks in the
portfolio, in this case 29. J and K represent the different formation periods and holding periods. To calculate the average yearly portfolio profit of the momentum strategies I use this formula:
!!"! !, ! = !! !!"(!,!)
! !
!!! ∗!"! (4)
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and Titman (1993) who report the series of monthly average return of K strategies, starting one month apart each time. An also widely known approach to measure momentum profits is the ‘winner-minus-loser portfolio’ (WML) approach where they measure the ‘winner’ portfolio and subtract the returns of the ‘loser’ portfolio.
In order to test whether the mean profits are significantly different from zero, I will have to determine the standard deviation of the portfolio returns. Newey and West (1987) have developed a variance-covariance estimator that is both consistent in the presence of heteroscedasticity and autocorrelation. Therefore I will use their heteroscedasticity and autocorrelation consistent (HAC) standard errors in my research, to cope with the autocorrelation effect, as the portfolios overlap each other. To measure the significance of the profitability of the different momentum strategies, I use a Newey West regression, where I regress the monthly returns of the different strategies to a constant and the appropriate risk-factors. I test whether the constant of the regression is significantly different from zero.
All the returns in this paper are risk-adjusted. To form the risk-adjusted profits I use the Carhart-four factor model (1997) where I regress the time-series excess momentum returns to a constant and the appropriate factors.
(!!"− !!) = !!+ !!! !!− !! + !!!!"# + !!!!"# + !!!!"! + !!" (5)
Where !!" is the portfolio return and !! is the risk-free rate. (!!"− !!) represents the excess return on the market and additional factors. !"# is the small-minus-big factor for size, !"# the market-to-book factor for value and MOM explains the monthly premium on winners-minus-losers. Therefore, the remaining risk-adjusted returns present a true arbitrage opportunity.
3.3 Attention
3.3.1 Trading volume
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prior J-month trading volume. This results in two “winner” portfolios and two “loser” portfolios for each formation period (J =3,6,9,12) where “high” is an indication of high volume in the prior J-months and “low” is an indication of low volume in the prior J-months. The portfolios now consist of eight stocks each. The momentum strategies where the “loser” portfolios are subtracted from the “winner” portfolios are formed with both high volume and low volume “winner” and “loser” portfolios.
Considering that, trading volume is a commonly used measure for stock liquidity I use my double-sorted portfolio approach to link the results to the relationship between liquidity and momentum profits on the Dutch stock market. Stock liquidity is rather difficult define, and therefore no explicit method exist. Most researchers use several indicators to capture the liquidity of a stock. Therefore, I use a second proxy for liquidity to see if my findings are robust. I use the quoted spread of the stock as Amihud (2000) states that this is a refined measure for liquidity. Considering that, a higher bid-ask spread presents a more illiquid stock I calculate the spread as an illiquidity measure:
!""!#!" = !"!"!!"!"
!"!" (5)
Where !"!" is the ask price of security i at time t and !"!" the bid price of the security at time
t. !"!" is the mid-price between ask price and bid price and is calculated as:
!"!" =!"!"!!"!"
! (6)
This is a measure of illiquidity, therefore the higher the spread is, the lower the liquidity of the stock.
3.2.2. Market state indicators
14 -1 -0,5 0 0,5 1 1,5 2 2,5
n-90 a-91 m-92 f-93 n-93 a-94 -95 m f-96 n-96 a-97 m-98 f-99 n-99 a-00 m-01 f-02 n-02 a-03 m-04 f-05 n-05 a-06 m-07 f-08 n-08 a-09 m-10 f-1
1
n-1
1
a-12 m-13 f-14 n-14 a-15
As discussed earlier, behavioural models and especially the theory of overreaction predict that momentum profits will be greater following market gains (Daniel et al., 1998). To estimate whether momentum profits are higher during an UP state of the economy, I need to determine the UP and DOWN state of the Dutch economy. I do this in two different ways. Firstly, almost similar to Cooper et al. (2004), I look at the 24-month lagged returns of the market at every month t, in this case the AEX index returns. I define the market-state as “UP” when the lagged 2-year return of the market is positive, and the market-state as “DOWN” when the lagged 2-year return of the market is negative. Similar to Cooper et al (2004) I test for lagged 1-year and 3-year market return as well, to see if the determination of an UP of DOWN market plays a large role.
Figure 1. AEX lagged market returns over time.
15 400000 500000 600000 700000 800000 900000 1000000 1100000 1200000 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
Figure 2. Dutch total GDP over time
To test the effect of market state on momentum profits the following regressions are used: !!"− !! = !!+ !!! !!− !! + !!!!"# + !!!!"# + !!!!"! + !!"∗ !!"+ !!!!! (7)
Where !!" is the portfolio return, the same risk factors as in equation 5 are presented and !!" is a generated dummy indicating a positive 24-month lagged market return and thus
following an UP market.
!!"− !! = !!+ !!! !!− !! + !!!!"# + !!!!"# + !!!!"! + !!"∗ (!"#!!"!"" ) + !!!!! (8)
(!"#!!"!"" ) is the difference in percentage of the Hodrick-Prescott filter compared to the trend
of total Dutch GDP in market prices, where a positive percentage indicates the severity of the UP market and a negative percentage the gravity of the DOWN market.
3.3 Sharpe ratio
At last, I perform an in-sample test in my analysis where I use a Sharpe ratio on the returns of the promising momentum strategies to measure the risk-adjusted performance (Sharpe, 1994). The Sharpe ratio is calculated as:
! = !!!!!!
! (9)
where !! is the average monthly portfolio return, !! is the risk free rate, and !! the
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4. Empirical Results
Section 4.1 starts with a discussion of the results of the unrestricted sample of momentum returns in the Dutch stock market from 1990-2015. The sample consists of stocks of the Euronext Amsterdam of large-cap and mid-cap stocks. In addition, Section 4.2 discusses the findings of investors’ attention in relation to momentum returns. It discusses the results of the restricted sample, where a double-sorted approach is used, from 2001 to 2015, to form high volume and low volume portfolios. This section also discusses the relation between liquidity and momentum returns, with a double-sortation on the bid-ask spread as a robustness test. Furthermore, it discusses the empirical findings of the effect of market state on the of large-cap and mid-cap stocks in the period 1990-2015. In conclusion, Section 4.3 discusses an in-sample test of the most promising investment strategies. All returns presented in the analysis are risk-adjusted returns controlled for the Carhart four factors.
4.1 Unrestricted sample 4.1.1. Main results
Table 1 shows the risk-adjusted annualised momentum returns of the different momentum strategies on all large-cap and mid-cap stocks of the Euronext Amsterdam from 1990 to 2016. The t-values associated with the means are presented in Table 1. The superscripts a,b, and c are assigned to the different outcomes of the corresponding p-values and denote the significance level of 1%, 5% or 10%, respectively.
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Tabel 1, where the average size of the stocks is larger in the “winner” portfolios. The average stock price is higher for holding periods J=9 in the “winner” portfolios and lower for holding periods J=3, J=6 and J=12.
4.1.2. Comparison to existing literature
The main results in my sample contradict earlier research of Jegadeesh and Titman (1993), Grinblatt and Moskowitz (2004), Doukas and Mcknight (2005), Griffin et al. (2003), who find that most of the momentum profits are earned with a short position in the “loser” portfolios. This phenomenon could be explained by mean reversion that Wu (2011) also finds in the Chinese Stock Market. The large-cap and mid-cap stocks of the Euronext Amsterdam and thus the relatively more liquid stocks of the Dutch stock market seem not so attractive for short-selling stocks as other markets might be or at least short-selling is not crucial in earning momentum returns, taken into account that this stock market is relatively small compared to other stock market discussed in previous papers about momentum strategies.
Comparing the highest momentum returns to the highest momentum profits of other papers where Jegadeesh and Titman (1993) find a return of 15.72% in the (12;3) strategy for the US stock market, Rouwenhorst (1998) a 16.20% highest momentum returns for the European market and Agyei-Ampomah (2007) finds a substantial high return of 44.46% in momentum strategy (12;1) in the UK stock market in a more recent paper. The highest momentum return presented in my sample is substantially lower with 7.10%4, which could indicate that the exclusion of small-cap stocks and therefore most illiquid stocks could take away high return predictors (Amihud, 2002).
As for the differences in trading volume between the “winner” and “loser” portfolios, the results seem to confirm the findings of Amihud (2002). However, they contradict the findings of Hou et al. (2009), who use trading volume as a measure for investors’ attention and find that the “winner” portfolio returns are driven by higher volume stocks. In the next section the liquidity of the stocks is further examined in terms of trading volume and the bid-ask spread of the stock. Considering that, my sample contains stocks of the period 1990-2016 and the bid and ask prices are not available of that period, it is not possible to define illiquidity as the bid-ask spread of the stock price. The illiquidity factor is presented as the bid-ask spread as part of the double-sorted approach in a later section of this paper.
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Table 1
Risk-adjusted average annualised portfolios returns for various J,K momentum strategies unrestricted sample, 1990-2015.
Each month the stocks are ranked on their past performance in the formation period and assigned to one of the five different quintiles. W is the winner portfolio (the best performing portfolio of stocks) and L is the loser portfolio. The portfolios are held for K months (K=3,6,9,12) for which the weighted overlapping returns are calculated, averaged and annualised. The risk-adjusted mean profits based on the Carhart-four-factor model are presented in the table. The t-values test if the portfolio returns are significantly different from zero. Size represents the average market value of stocks in the portfolios (in millions of euro). Price describes the average stock price (in euros) and volume describes the average turnover by volume also a widely known proxy for liquidity. A, B , or C denote significant levels at 1%, 5% and 10%, respectively based on the (p-values).
Holding periods
Ranking
period Portfolio K=3 K=6 K=9 K=12 Size Price Volume
19 Table 1 continued Holding periods Ranking
period Portfolio K=3 K=6 K=9 K=12 Size Price Volume
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4.2. Attention
4.2.1.1. Risk-adjusted momentum returns within double-sorted portfolio formation conditioned on trading volume
The differences in trading volume between the “winner” and “loser” portfolios in Table 1 confirm the findings of Pastor and Stambaugh (2003), who say that liquidity is priced in a factor, and thus more illiquid stocks generate higher returns. However the differences are not that large. Therefore, the double-sorted portfolio approach further examines this issue. The portfolios in Table 2 are double-sorted into sub-portfolios based on the stocks’ prior J-month trading volume. Several key results appear from the double-sorted approach.
The results show that conditional on trading volume stocks, within the formed “winner” portfolios, with a lower trading volume level generate higher returns. For example in strategy (6;6) the stocks within the “winner” portfolio, that show to have lower volume, earn an average annualised return of 19.18% compared to stocks within the “winner” portfolio of that strategy with a higher trading volume that generate a 16.17% average annualised return. Therefore, the “low-winner” portfolio of this strategy outperforms the winner” portfolio by 3.01%. The “low-loser” portfolio does not outperform the “high-losers” portfolio in this case. The results account for the “winner” portfolios of all formation periods. Therefore, when measuring investors’ attention as the trading volume of the stock, the results point out that overconfidence and self-attribution of investors accompanied by stock price overreaction are not an implication for momentum profits in this case. However, the findings for the “winner” portfolios are in principle consistent with the liquidity theory of Amihud (2002) that stocks with lower liquidity are expected to generate higher returns. For the “loser” portfolios low volume stocks outperform high volume only for formation period J=3 and J=12 (K=6,9,12). In the rest of the holding periods the “high-loser” portfolios outperform the “low-loser” portfolios for almost all holding periods. These findings indicate that half of the bad-performing stocks, to which investors pay less attention, tend to underperform bad-performing stocks that gain more investors’ attention. None of the returns of the “loser” portfolios are statistically significant.
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sortation is also substantially different. Hence, for example, the trading volume, as a liquidity proxy, is lower for the “high-winner” portfolios compared to the “high-loser” portfolios. This does hold for the high trading volume portfolios, however not for the low trading volume portfolios. All the loser” portfolios have a lower average trading volume than the “low-winner” portfolios.
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Table 2
Double-sorted on trading volume, 2001-2015
Each month the stocks are ranked based on their past performance in the formation period and assigned to different quintiles. The “winner” portfolio is the best performing portfolio of stocks and the “loser” portfolio contains the worst performing stocks. Within the “winner” and the “loser” portfolio the stocks are double sorted on high volume stocks and low volume stocks based on their prior J-month turnover by volume. This leaves portfolios consisting of eight stocks each. The portfolios are held for K months (K=3,6,9,12) for which the weighted overlapping returns are calculated, averaged, annualized and risk-adjusted to the Carhart four factors. The risk-adjusted mean profits are presented in the table. The t-values test if the portfolio returns are significantly different from zero. Trading volume describes the average trading volume of the portfolio. A, B , or C denote significant levels at 1%, 5% and 10%,
respectively based on the (p-values)
23 Table 2 continued Holding periods Ranking
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4.2.1.2 Risk-adjusted average annualised momentum returns based on double-sortation for trading volume
Table 3. presents a continuation of the double-sorted portfolio approach and shows the returns of the zero-cost momentum portfolios based on the double-sortation on trading volume. The zero-cost portfolios are formed by subtracting the “loser” portfolios from the “winner” portfolios.
The results show that, when the high and low volume portfolios are kept together, meaning that high (low) volume portfolios only get subtracted from high (low) volume portfolios, the low volume zero-cost portfolios outperform the high volume zero-cost portfolios in most cases. For example with strategy (6;12) the exclusively low volume zero-cost portfolio generates a statistically significant return of 9.95% compared to the exclusively high volume zero-cost portfolio in the same strategy that generates 8.04% and outperforms the “high-winners-minus-high-losers” portfolio by 1.91%. The same accounts for the (9;12) strategy where the “low-winners-minus-low-losers” portfolio outperforms the “high-winners-minus-high-losers” portfolio by 2.62% with an average annualised return of 11.35% compared to 8.73%. This return difference between the exclusively low volume portfolios and an exclusively high volume portfolio appears to be the greatest of all holding periods. Almost all momentum strategies increase in return as the holding period increases, which suggests there are almost no observable mean reversals, similar to the previous two Tables. With exception to formation period J=3, where momentum returns decrease from holding period K=3 to K=6 after which they increase again. Remarkably, the combination of “low winner” liquidity portfolios and “high loser” generates higher returns in formation periods J=3 and J=12. Formation period J=12 shows the most statistically significant returns and the highest momentum return of the sample for the (12;12) strategy in the “low-winners-minus-high-losers” portfolio with a return of 12.19% at a 1% significance level.
Comparing these findings to the findings normal momentum returns over this time period5, a higher return is earned combining the momentum strategy of Jegadeesh and Titman (1993) and a double-sortation formation strategy based on trading volume. Apparently, on the Dutch stock market for large-cap and mid-cap stocks the low volume “winners” generate a higher return than the average volume stocks, meaning that a combination strategy earns higher return than a regular momentum strategy. This contradicts with the findings of Lee and Swaminathan (2000) that firms with high past turnover (more illiquid) ratios earn higher
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future returns. However, this only accounts for the “winners” portfolios. The low volume loser portfolios do not earn higher returns compared to the high volume portfolios. Furthermore, note that these more illiquid stocks generating higher returns (“low-winners”) probably are accompanied with substantial high trading costs, when trading these stocks and could diminish momentum profits (Lesmond et al, 2004).
Table 3
Momentum strategies based on trading volume of stocks, 2001-2015
Each month the stocks are ranked on their past performance in the formation period and assigned to different quintiles. The “winner” portfolio is the best performing portfolio of stocks and the “loser” portfolio contains the worst performing stocks. Within the “winner” and the “loser” portfolio the stocks are double sorted on high volume stocks and low volume stocks based on their prior J-month trading volume. This leaves portfolios consisting of 8 stocks each. The portfolios are held for K months (K=3,6,9,12) for which the weighted overlapping returns are calculated, averaged, annualized, and risk-adjusted to the Carhart four factors. Subtracting the different “loser” portfolios from the different “winner” portfolios forms the zero-cost portfolios. The mean profits are presented in the table. The t-values test if the portfolio returns are significantly different from zero. A, B ,or C denote significant levels at 1%, 5% and 10%,
respectively based on the (p-values).
26 Table 3 continued Holding periods Ranking period Portfolio K=3 K=6 K=9 K=12 J=9 LW-HL 0.0072 0.0671 0.0801 0.0894 (t-value) (0.02) (0.80) (1.05) (1.45) LW-LL 0.0537 0.0681 0.0809 0.1135 B (t-value) (0.64) (1.21) (1.49) (2.23) J=12 HW-HL 0.0788 0.1029 C 0.1140 C 0.1219 B (t-value) (0.92) (1.68) (1.96) (2.34) HW-LL 0.0856 0.0941 0.0949 C 0.1083 B (t-value) (1.26) (1.63) (1.80) (2.46) LW-HL 0.0991 0.0941 0.1146 B 0.1219 A (t-value) (1.08) (1.59) (2.00) (2.75) LW-LL 0.1058 0.0853 C 0.0954 C 0..1083 A (t-value) (1.58) (1.66) (1.94) (2.80)
4.2.1.3. Link to the relationship between liquidity momentum profits
The previous sub-sections about trading volume show that stocks with lower trading volume earn higher momentum returns than stocks with higher trading volume, suggesting that stocks, to which investors pay less attention, result in higher returns. Considering that, trading volume is also a widely known measure for liquidity, this subsection tests the robustness of the relationship between liquidity and momentum profits. Lee and Swaminathan (2000) argue that trading volume is not an accurate proxy for liquidity as their results show that trading volume does not show correlation to other proxies for liquidity. To test the robustness of the results, I use the bid and ask spread as a second proxy for liquidity and double sort the momentum portfolios based on the prior J-months spread of the stock. The wider the bid-ask spread of a stock, the higher the appended transaction costs of a possible trade of that stock, which makes a stock less easily accessible, and therefore less liquid (Amihud, 2002). Hence, to compare the results of the double-sorted portfolio approach, “high” portfolios, show a smaller bid-ask spread of the stock, corresponding to high volume of a stock, which also indicates high liquidity.
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than with trading volume. Only “winner” portfolios earn significant returns. The “low winner” portfolio of strategy (9;6) earns the highest momentum return of 19.90% at a 1% significance level. One can conclude that in the Dutch stock market, illiquidity accounts for a part of the momentum returns. Considering that the stocks Dutch stock market are relatively small and illiquid compared to other markets, investors should keep in mind that implementing momentum strategies result in high portfolio rebalancing costs.
Table 4
Double-sorted on bid-ask spread, 2001-2015
Each month the stocks are ranked based on their past performance in the formation period and assigned to different quintiles. The “winner” portfolio is the best performing portfolio of stocks and the “loser” portfolio contains the worst performing stocks. Within the “winner” and the “loser” portfolio the stocks are double sorted on bid-ask spreads of stocks based on their prior J-month illiquidity. In this case, high liquidity stocks (low spread) are “high” portfolios and low liquidity stocks (large spread) are “low” portfolios. This leaves portfolios consisting of eight stocks each. The portfolios are held for K months (K=3,6,9,12) for which the weighted overlapping returns are calculated, averaged, annualised and risk-adjusted for the Carhart four factors. The risk-adjusted mean profits are presented in the table. The t-values test if the portfolio returns are significantly different from zero. Trading volume describes the average trading volume of the portfolio. A, B or C denote significant levels at 1%, 5% and 10%, respectively based on the (p-values).
Holding periods
Ranking
period Portfolio K=3 K=6 K=9 K=12 Illiquidity
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Table 4 continued Holding periods Ranking
period Portfolio K=3 K=6 K=9 K=12 Illiquidity
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4.4. Market state and momentum
4.3.1. Market state as the lagged return of the market
As a second proxy for investors’ attention I use the market state of the economy. As mentioned in the earlier sections, overreaction theories of Daniel et al . (1998) and Hong and Stein (1999) suggest that short-run momentum profits are greater following UP markets. Similar to Cooper et al. (2004) I first use the lagged return of the AEX Index6 of either 12, 24 or 36 months. The three different market state measures are presented in Table 5. Similar to Cooper et al. (2004), the main focus is the J=6 formation period strategy and holding period of K=47 is added, including months from period t +13 to t +60 to capture the long-term momentum profits and see whether they differ from the short-term momentum profits from Jegadeesh and Titman (1993). The for the Carhart four factors risk-adjusted profits are presented in the table.
The results show that for example the (6;6) strategy shows an average annualised return of 11.14% following an 24-month lagged return UP market at a significance level of 1%. Furthermore, the momentum strategies do not show any significant returns during DOWN markets and show average annualised means to be either negative or substantially small. On the contrary, the momentum returns during UP markets all show to be significantly different from zero after adjusting for risk, via the Carhart-four-factor model. These results support the results of Cooper et al. (2004) and contradict the findings of Griffin et al. (2003) Muga and Santamaria (2008), Rey and Schmid (2007), who state that the profits earned with momentum are higher following DOWN markets. The long-run momentum profits do not show any significant return in any market state for holding period K=47. The profits drop to a lower point or even turn negative, suggesting long-term mean reversal of the momentum returns. If the short-run momentum profits are partially based on overreaction to news these long-term momentum return reversals are in line with the theories of Daniel et al. (1998) and Hong and Stein (1999), who state that investors correct their selves after receiving the correct information. This result is also consistent with the findings of Lee and Swamitnathan (2000) and Jegadeesh and Titman (2001) who find that momentum profits reverse after a period of approximately two years. The findings show to be robust, considering that three measures of momentum states are presented and the results indicate similar outcomes of the tests.
It can be concluded that the momentum profits earned in the Dutch stock market for large-cap and mid-cap stocks is conditioned on the state of the market, when measuring the
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market state as the one-year, two-year or three-year lagged market return and that statistically significant momentum returns are derived exclusively following UP states of the economy. Considering that, the momentum returns following UP markets seem to be caused by behavioural biases such as overconfidence or self-attribution and confirm findings of Hou et al. (2009), it also can be concluded that increased investor attention is an implication for momentum profits.
Table 5
Momentum profits during various definitions of market states
Each month the stocks are ranked based on their past six-month performance (from t-6 to t-1) and assigned to one of the five different quintiles. The returns of the AEX index are measured over the period t-m to t-1 (where m = 12, 24 or 36). Non-negative lagged market returns are defined as "UP" markets and negative lagged market returns are defined as "DOWN" markets. The average annualized risk-adjusted profits of the "winners-minus-losers" portfolios are presented in the table for all holding periods (K= 3,6,9,12,47. The t-values test if the portfolio returns are significantly different from zero during the different market states. . A, B ,or C denote significant levels at 1%, 5% and 10%, respectively based on the (t-values)
Holding periods
Portfolio K=3 K=6 K=9 K=12 K=47
Momentum Profits following 12-month UP market
N 224 221 218 215 173
Mean Profit 0.1887A 0.1114 A 0.1093 A 0.1035 A 0.0315
(t-value) (3.79) (2.44) (2.68) (2.67) (0.93)
Momentum Profits following 12-month DOWN market
N 79 79 79 79 73
Mean Profit 0.1139 -0.0632 0.0105 0.0173 0.0015
(t-value) (1.44) (-0.74) (0.08) (0.22) (0.10)
Momentum Profits following 24-month UP market
N 228 225 222 219 183
Mean Profit 0.2015 A 0.1118 A 0.1210 A 0.0407 A 0.0312
(t-value) (4.16) (2.66) (3.03) (3.04) (1.18)
Momentum Profits following 24-month DOWN market
N 75 75 75 75 63
Mean Profit 0.0451 -0.0888 -0.0399 -0.316 -0.0295
(t-value) (0.42) (-1.03) (-0.54) (-0.56) (-0.54)
Momentum Profits following 36-month UP market
N 226 223 220 217 174
Mean Profit 0.1559A 0.1126A 0.1156 A 0.0970 A 0.0284
(t-value) (2.87) (2.64) (3.15) (2.92) (0.87)
Momentum Profits following 36-month DOWN market
N 78 78 78 78 72
Mean Profit -0.1781 -0.0636 0.0050 0.0258 0.0039
31 -6% -4% -2% 0% 2% 4% 6% 8% 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015
4.3.2. Market state measured as the total Dutch GDP
Simultaneously, I examine another proxy for market state. The relationship between momentum profits and the upswings and downswings of the total Dutch GDP in market prices. A country’s total GDP is a commonly known measure for defining the economical state of a country and therefore serves as an adequate second robustness test to see whether the momentum profits are dependable on the state of the market. The GDP, abbreviation for Gross Domestic Product, can be defined as “The value of all goods and services produced within a country minus the value of any goods and services used in their creation”7. Du and Wei (2004) document that market volatility and thus an unsecure market state is positively correlated to the volatility of the GDP of a country. Figure 1. presents the difference in percentage between the total Dutch GDP and the Hodrick-Prescott filter of the GDP movement. The size of the percentage defines the magnitude of the market states and can therefore give a clearer image of the impact of the state of the economy.
Figure 3. The difference in percentage between the Dutch GDP and the HP-filter
In Table 5 I regress the momentum profits of the “winners-minus-losers” portfolios of all formation periods (J= 3,6,9,12) and all holding periods (K= 3,6,9,12) to the risk-adjusted factors of the Carhart-four-factor model and to either a dummy variable indicating the market as UP or DOWN dependable on the market’s 24-month lagged return or the difference in
32
percentage between the GDP and the trend of the GDP. Thus, two measures of market states are analysed alongside each other, to see if they present coherent results.
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Table 6
Momentum profits and different measurements for market state
Each month the stocks are ranked on their past six-month performance (from t-6 to t-1) and assigned to one of the five different quintiles. The returns of the AEX index are measured over the period t-m to t-1 (where m = 12, 24 or 36). Non-negative lagged market returns are defined as "UP" markets and negative lagged market returns are defined as "DOWN" markets. The average annualised profits of the "winners-minus-losers" portfolios are presented in the table for all holding periods (K= 3,6,9,12,47), along the side of the CAPM alphas and Carhart alphas. The t-values test if the portfolio returns are significantly different from zero during the different market states. . A, B ,
or Cdenote significant levels at 1%, 5% and 10%, respectively based on the (t-values)
Holding period K=3 K=6 K=9 K=12 Mean NW-Std t-value Mean NW-Std
t-value Mean NW-Std t-value Mean
34 Table 6 continued Holding period K=3 K=6 K=9 K=12 Ranking Period Mean
NW-Std t-value Mean NW-Std t-value Mean
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4.3 In-sample test
From investors’ perspective the previous results have given useful information, for the implementation of possible momentum investment strategies on the Ducth stock market. In this Section I take a few promising strategies and perform an in-sample performance test to see whether these strategies were actually profitable during a smaller time period within my sample. Many researches argue that in-sample significance does not guarantee out-of-sample significance, however Rapach and Wohmar (2006) find that both tests are susceptible for possible data-minig and both have a predictive abilitiy. I choose the time period 2010-2015, considering that the economic crisis also might have interfered and it is interesting to see whether the most promising momentum strategies derived from information over a 26 year time span, were also of substantive worth during a more recent time period.
The first strategy I test is the (6;12) strategy of the single-sorted portfolio formation. The “loser” portfolio shows a short-term mean reversal with a significant positive return for holding period K=12. Therefore, I combine momentum strategies with contrarian strategies in this case and mimic a long-position in the “winner” portfolio together with a long position in the “loser” portfolio, which results in an average annualised return of 19.75% between 2010-2015 and a Sharpe ratio of 1.90. This result shows that in the Dutch stock market, where short selling is apparently not attractive for investors, a combination of two strategies predicting stock returns based on past performance appears to be very lucrative.
Secondly, I test the (12;3) strategy of the double-sorted approach for both trading volume and the bid-ask spread. Considering that none of the loser portfolios show any significant returns this strategy exclusively holds a long position in the “low winners” portfolio. This portfolio earns the highest returns over the whole sample period. The “low winner” portfolio double-sorted on volume earns an average annualised return of 16.46% with a Sharpe ratio of 1.77 and the “low winner” portfolio double-sorted on the bid-ask spread of a stock earns an average annualised return of 17.10% with a Sharpe ratio of 1.91, therefore it is more effective to double-sort momentum portfolios in this strategy on the bid-ask spread of stocks.
All three promising strategies appear to earn significant return with a relatively high Sharpe ratio8. These outcomes confirm that the research has presented valuable investment opportunities.
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5. Conclusion and discussion
In this paper I examine the effect of two different proxies for investors’ attention, trading volume and market state, on momentum profits on the Dutch stock market for large-cap and mid-large-cap stocks during various time periods between 1990-2016.
5.1 Conclusion
The results show that momentum profits show to be statistically significant in the Dutch market for large-cap and mid-cap stocks, however all the momentum returns are derived from the “winner” portfolios and taking a short position in the “loser” portfolio actually only lowers the momentum returns.
In time period 2001-2016 the low volume stocks generate a higher return in the “winner” portfolio, leading to an overall higher return of the low liquidity momentum strategy. These findings are robust, after using bid-ask spread as a second proxy for liquidity. The findings are in line with the results of Pastor and Stambaugh (2003) and Amihud (2000, 2002), who report that stocks with a lower level of liquidity generate higher returns. It contradicts the research of Hou et al. (2009) and Lee and Swaminathan (2000), who state that portfolios with a higher turnover, also a proxy for liquidity generate higher returns. It should be taken into account that the portfolios used in the double-sorted approach are smaller than in the unrestricted sample, which results in more limited stock diversification. It appears that the difference in liquidity of the stocks on the Dutch stock market compared to those in the UK in and the US, results in different results. The presence of smaller and more illiquid stocks on the Euronext Amsterdam, even after excluding small-cap stocks, causes the effect of liquidity risk to overshadow the effect of increased investor attention measured by trading volume. Therefore, trading volume, used in this paper, appears to be an inadequate proxy for investors’ attention in the Dutch stock market.
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considering upswings and downswings of total Dutch GDP as a proxy for market state the results do not correspond, which suggest that only stock market indices have an effect on momentum profits.
5.2 Recommendations for future research
A proposition for further research would be to focus on optimal measurements of investors’ attention and to establish a measurement of institutional investors’ attention as well, next to the Google search Volume Index that can proxy retail investors’ attention.
Furthermore, future research could examine the optimisation of momentum strategies. Especially, considering that “loser” portfolios in the Dutch stock markets for large-cap and mid-cap stocks do not earn any significant return and therefore a standard momentum strategy does not suffice in maximising momentum profits. Following Moskowitz et al. (2012) for instance find significant return for a diversified portfolio of momentum strategies across different asset classes without being exposed to standard asset pricing factors.
Considering that, momentum profits are not profitable during DOWN markets, it is interesting to examine whether DOWN markets might influence momentum profits in a harmful way. Bohl et al. (2016) show that during volatile market recoveries in Germany momentum strategies suffer such tremendous losses that, it takes decades to recover from those losses. Further research, examining the relationship between market rebounds and momentum strategies could eliminate risk factors involved.
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6. Literature
Agyei-Ampomah, S., 2007. The post-cost profitability of momentum trading strategies: Further evidence from the UK. European Financial Management, 134, 776-802. Amihud, Y., Mendelson, H. 2000. The liquidity route to a lower cost of capital. Journal of
Applied Corporate Finance, 12(4), 8-25.
Amihud, Y., 2002. Illiquidity and stock returns: Cross-section and time-series effects. Journal of financial markets, 5(1), 31-56.
Aouadi, A., Arouri, M., Teulon, F., 2013. Investor attention and stock market activity: Evidence from France. Economic Modelling, 35, 674-681.
Barber, B., Odean, T. 2008. All that glitters: The effect of attention and news on the buying behavior of individual and institutional investors. Review of Financial Studies, 21(2), 785-818.
Barberis, N., Xiong, W. 2012. Realization utility. Journal of Financial Economics, 104(2), 251-271.
Barroso, P., Santa-Clara, P., 2015. Momentum has its moments. Journal of Financial Economics, 116(1), 111-120.
Bohl, M., Czaja, M., Kaufmann, P., 2016. Momentum profits, market cycles, and rebounds: Evidence from Germany. The Quarterly Review of Economics and Finance.
Carhart, M., 1997. On persistence in mutual fund performance. The Journal of finance, 52(1), 57-82.
Chordia, T., Shivakumar, L., 2002. Momentum, business cycle and time-varying expected returns. Journal of Finance, 57, 985-1019.
Cooper, M., Gutierrez, J., Hameed, A., 2004. Market states and momentum. Journal of Finance, 59, 1345-1365.
Corwin, S, Coughenour, J., 2008. Limited attention and the allocation of effort in securities trading. The Journal of Finance, 63(6), 3031-3067.
Da, Z., Engelberg, J., Gao, P., 2011. In search of attention. The Journal of Finance, 66(5), 1461-1499.
Daniel, K., Hirshleifer, D., Subrahmanyam, A., 1998. Investor psychology and security market under- and overreactions. The Journal of Finance, 53, 1839-1885.
39
Du, J., Wei, S., 2004. Does insider trading raise market volatility? The Economic Journal, 114(498), 916-942.
De Long, J., Shleifer, A., Summers, H., Waldmann, R., 1990. Noise trader risk in financial markets. Journal of political Economy, 703-738.
De Bondt, W., Thaler, R., 1985. Does the stock market overreact? The Journal of Finance, 40, 793-805.
Doukas, J., McKnight, P., 2005. European momentum strategies, information diffusion, and investor conservatism. European Financial Management, 113, 313 338.
Fama, E., 1969. Efficient capital markets: A review of theory and empirical work. Journal of Finance, 25, 383-417
Forner, C., Marhuenda, J., 2003. Contrarian and momentum strategies in the Spanish stock market. European Financial Management, 9, 67-88.
Gervais, S., Odean, T., 2001. Learning to be overconfident. Review of Financial studies, 14(1), 1-27.
Griffin, J., Ji, X., Martin, J., 2003. Momentum investing and business cycle risk: Evidence from pole to pole. The Journal of Finance, 58, 2515-2547.
Grinblatt, M., Moskowitz, T., 2004. Predicting stock price movements from past returns: The role of consistency and tax-loss selling. Journal of Financial Economics, 71(3), 541-579.
Grundy, B., Martin, J., 2001. Understanding the nature of the risks and the source of the rewards to momentum investing. Review of Financial Studies, 14, 29-78. de Haan, L., Kakes, J., 2011. Momentum or contrarian investment strategies: evidence
from Dutch institutional investors. Journal of Banking & Finance, 35(9), 2245-2251. Hodrick, R., Prescott, E., 1997. Postwar US business cycles: an empirical investigation.
Journal of Money, credit, and Banking, 1-16.
Ho, T., Stoll, H., 1980. On dealer markets under competition. The Journal of Finance, 35(2), 259-267.
Hong, H., Stein, J., 1999. A unified theory of underreaction, momentum trading, and overreaction in asset markets. The Journal of Finance, 54, 2143-2184.
Hou, K., Xiong, W., and Peng, L. 2009. A tale of two anomalies: The implications of investor attention for price and earnings momentum. Available at SSRN 976394.
Huang, D., 2006. Market states and international momentum strategies. Quarterly Review of Economics and Finance, 46, 437-446.
40
Kahneman, D., & Tversky, A. (1982). The psychology of preferences. Scientific American. Karlsson, N., Loewenstein, G., Seppi, D., 2009. The ostrich effect: Selective attention to
information. Journal of Risk and uncertainty, 38(2), 95-115.
Jegadeesh, N., 1990. Evidence of predictable behavior of security returns. The Journal of Finance, 45(3), 881-898.
Jegadeesh, N., Titman, S., 1993. Returns to buying winners and selling losers: Implications for stock market efficiency. The Journal of Finance, 48, 65-91. Jegadeesh, N., Titman, S., 2001. Profitability of momentum strategies: An evaluation of
alternative explanations. The Journal of Finance, 562, 699-720.
Jegadeesh, N., Titman, S., 2011. Momentum. Annual Review of Financial Economics, 3, 493-509.
Jones, C., Lamont, O., 2002. Short-sale constraints and stock returns. Journal of Financial Economics, 66, 207-239. .
Lehmann, B., 1990. Fads, martingales and market efficiency. Quarterly Journal of Economics, 105, 128
Lee, C., Swaminathan, B., 2000. Price momentum and trading volume. the Journal of Finance, 55(5), 2017-2069.
Lesmond, D., Schill, M., Zhou, C., 2004. The illusory nature of momentum profits. Journal of Financial Economics, 71, 349-380.
Liu, W., Strong, N., Xu, X., 1999. The profitability of momentum investing. Journal of Business Finance and Accounting, 26, 1043-1091.
Moskowitz, T., Ooi, Y., Pedersen, L., 2012. Time series momentum. Journal of Financial Economics, 104(2), 228-250.
Muga, L., and Santamaria, R., 2008. Momentum, market states and investor behavior. Empirical Economics, 37, 105-130.
Newey, W., West, K., 1987. A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix.
Odean, T., 1998. Volume, volatility, price, and profit when all traders are above average. ` The Journal of Finance, 53(6), 1887-1934.
Pastor, L., Stambaugh, R., 2001. Liquidity risk and expected stock returns (No. w8462). National Bureau of Economic Research.
41
Rey, D., Schmid, M., 2007. Feasible momentum strategies: Evidence from the Swiss stock market. Financial Markets and Portfolio Management, 21, 32 352.
Rouwenhorst, K., 1998. International momentum strategies. Journal of Finance, 53, 267 284.
Scheinkman, J., Xiong, W., 2003. Overconfidence and speculative bubbles. Journal of political Economy, 111(6), 1183-1220.
Sharpe, W., 1994. The sharpe ratio. The journal of portfolio management, 21(1), 49-58.
Shefrin, H., Statman, M., 1985. The disposition to sell winners too early and ride losers too long: theory and evidence. Journal of Finance, 40, 777–790
Siganos, A., Chelley-Steeley, P., 2005. Momentum profits following bull and bear markets. Journal of Asset Management, 6, 381-388.
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Appendix
Appendix 1: the risk-adjusted annualised average returns over the period 2001-2015 Table Appendix 1
Average annualised portfolios returns for various J,K momentum strategies restricted sample, 2001-2015.
Each month the stocks are ranked on their past performance in the formation period and assigned to one of the five different quintiles. W is the winner portfolio (the best performing portfolio of stocks) and L is the loser portfolio. The portfolios are held for K months (K=3,6,9,12) for which the weighted overlapping returns are calculated, averaged and annualised. The risk-adjusted mean profits based on the Carhart-four-factor model are presented in the table. The t-values test if the portfolio returns are significantly different from zero. A, B , or C denote significant levels at 1%, 5% and 10%, respectively based on the
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Appendix 2: Momentum portfolios, double sorted on bid-ask spread over the period 2001-2015
Table Appendix 2
Momentum strategies based on liquidity of stocks
Each month the stocks are ranked based on their past performance in the formation period and assigned to different quintiles. The “winner” portfolio is the best performing portfolio of stocks and the “loser” portfolio contains the worst performing stocks. Within the “winner” and the “loser” portfolio the stocks are double sorted on bid-ask spreads of stocks based on their prior J-month illiquidity. In this case, high liquidity stocks (low spread) are “high” portfolios and low liquidity stocks (large spread) are “low” portfolios. This leaves portfolios consisting of eight stocks each. The portfolios are held for K months (K=3,6,9,12) for which the weighted overlapping returns are calculated, averaged, annualised and adjusted for the Carhart four factors. The risk-adjusted mean profits are presented in the table. The t-values test if the portfolio returns are significantly different from zero. Trading volume describes the average trading volume of the portfolio. A, B , or C denote significant levels at 1%, 5% and 10%, respectively based on the (t-values).
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Table Appendix 2 continued
