Final version MSc thesis Finance

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MOMENTUM IN TIMES OF ECONOMIC INSTABILITY, FINDING THE OPTIMAL STRATEGY

Final version MSc thesis Finance

Momentum in Times of Economic Instability, Finding the Optimal Strategy

Studentnumber: 1904108 Name: Huub de Vink Program: MSc Finance Supervisor: Wolfgang Bessler

Field Key Words: Momentum, Investment, Portfolio, Holding period, Evaluation period, Volatility, Dividend

Abstract

In this paper several portfolios are composed, based on momentum, volatility, and dividend payment strategies, between 2005 and 2015, during times with a lot of economic distress. In this time period, especially during 2009, a time of large mean reversion, these portfolios have a hard time outperforming the market. Most portfolios perform somewhat around the average market performance, however partially lacking significance in outperformance and

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1. Introduction

Ever since the stock market emerged, people are looking for different ways to outperform the market. However many strategies have been constructed, only few have shown persistence. McLean and Pontiff (2016) find that academic research damages stock return predictability. In their paper they find that the return predictability of 97 variables, which show a

comparative advantage in sample, perform, on average, 26% worse out-of-sample and even 58% lower post-publication. McLean and Pontiff suggest that the predictability of these strategies are explained by mispricing and that academic publications inform the market about this mispricing, however Geczy and Samonov (2016) find, with an out-of-sample research, that momentum strategies are significantly outperforming the market in the period following the sample data. Gezcy and Samonov (2016) state that "momentum effect is not a product of data mining but is persistent and has significant variations over time." In their most recent paper Jegadeesh and Titman (2011) went out-of-sample, confirming the persistence of their earlier findings of momentum (Jegadeesh and Titman 1993, 1995, 2001).

This paper will look at how momentum predicts stock return and in which combination of ranking and holding period momentum outperforms the market in the most efficient way, taking transaction costs in to account. However, in subsequent parts a momentum strategy will be combined with a volatility strategy and two different dividend strategies. In the next part, section 2, previous research addressing momentum and everything affecting momentum and this paper is addressed. In section 3 the hypotheses are discusses. Section 4 will consist out of a winner minus loser momentum strategy and in section 5 and 6 a momentum strategy will be combined with first low volatility strategy and later two different strategies in which the momentum stocks are split in dividend paying stocks and in stocks who do not pay dividend. In the last section, section 7, a conclusion based on the findings will be drawn.

2. Previous research

2.1 Momentum

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2011; George and Hwang, 2004; Gezcy and Samonov, 2016; Hillert et al., 2014; Jegadeesh and Titman, 1995, 2001, 2011; Kelsey et al., 2010; Moskowitz and Grinblaat, 1999;

Rouwenhorst, 1998). Jegadeesh and Titman (2011) even states that the momentum effect represents, perhaps, the strongest evidence against the efficient markets hypothesis. However, not every paper completely agrees with how momentum is displayed by Jegadeesh and Titman. Antoniou et al. (2013) confirm the momentum theory, however state that momentum only arises under optimism, because investors are slow to sell losers during optimistic periods. In the publication by Moskowitz and Grinblatt (1999) the ‘original’ momentum theory is displayed as a barely significant strategy and an industry-based momentum strategy is the alternative. Kelsey et al. (2010) find that momentum is more likely to continue in a highly uncertain market with a downward trend.

Momentum has shown persistence on the American market, however there, as well, is evidence from around the world that momentum has robustness and is profitable in most major markets. Rouwenhorst (1998) replicates the momentum studies by Jagedeesh and Titman (1993) in 12 different European countries. The fidings by Rouwenhorst (1998) are a lot like the findings in the United states. Another two papers by Griffin et al. (2003) and Chui et al. (2010) confirm the robustness of a momentum strategy, by replicating positive profits in most major markets. The only countries, with major markets, which reject momentum, are found in Asia.

Some other authors are more careful with their findings on momentum and the interpretation of these findings (Asem and Tian, 2010; Asness et al., 2013; Hong et al., 2000; Stivers and Sun, 2010, 2013). Asness et al. (2013) find a negative correlation between momentum and value, and therefore imply that the predictability of momentum is only strong for smaller firms. Hong et al. (2000) confirm the findings by Asness et al. (2013), that, when firm size increases, profitability of momentum decreases. Hong et al. (2000) also combine this size effect with analyst coverage, as analyst coverage increases the power of momentum strategies decreases. Tse (2015) was the only one who explicitly stated that the methods used by

Jegadeesh and Titman (1993) were totally not significant. Tse (2015) finds that momentum profits are insignificant between the late 1990s and 2014 and even states that momentum performs worse than the buy-and-hold strategy.

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suggesting that momentum is dependent on a solid-state market. Daniel and Moskowitz (2014) go a step further and find that momentum crashes are partly forecastable. Momentum crashes occur in ‘panic states’, following market decline in a market with high volatility. Jegadeesh and Titman (2011) confirm these negative crashes, due to the financial crisis, the returns in 2009 are extremely negative and these negative influence reversed the momentum effect. However they state that these returns can be explained by variables, from the literature, on time-series momentum, because mmomentum is expected to generate negative returns in periods in which the market returns exhibit negative serial correlation.

Momentum authors agree that the effect of momentum lasts for about one year. According to Jegadeesh and Titman (2011), “There is substantial evidence that indicates that stocks that perform the best (worst) over a three- to twelve-month period tend to continue to perform well (poorly) over the subsequent three to twelve months.” George and Hwang (2004) and Cooper et al. (2004) split short-term momentum from long-term reversal. Both findings state that momentum and long-term reversal are two different phenomena. The robustness of

momentum has a maximum of one year, however it might have lost efficiency already earlier within this year. The optimal holding period has not yet been defined.

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Other researchers try to explain the momentum effect due to firm rating or firm size. Avramov et al. (2007) research the credit ratings for stocks and find that for stocks, with a rating between BB and AAA, momentum profits are not significant. Their findings state that only stocks with a low credit rating generate momentum profits. However Jegadeesh and Titman (1993) and Fama and French (2008) confirm momentum among any stock size. Fama and French (2008) stat that the relation between momentum (the center-stage anomaly of recent years) and average returns is similar for small and big stocks.”

Researchers also try to explain momentum from a behavioral view. Antoniou et al. (2010) find that the sentiment of the investor predicts momentum. In their findings, the momentum is only reversed after periods of optimism. In periods of pessimism, the effect of momentum is more robust in the long-run.

2.2 Transaction cost and reversal period

Momentum strategies can be more or less active, however transaction costs influence the profitability of active trading strategies. Lesmond et al. (2004) find that those stocks, which generate large momentum returns, are stocks with higher transaction costs, suggesting that these transaction costs even out the effect of momentum, making it none existent. However, Korajczyk and Sadka (2004) contrast the findings by Lesmond et al. (2004) and state that momentum strategies are still profitable, when transaction cost are taken in to account. Jegadeesh and Titman (2011) use a six-month ranking period and a six-month holding period momentum strategy, in which they skip a week between the ranking and the holding period. The period skipped between the periods is used to avoid the one-month return reversal reported by Jegadeesh (1990), because, when the holding period and the ranking period are contiguous, the profits to the momentum strategy are attenuated by the negative serial correlation in returns, induced by the bid-ask spreads and by the short-horizon return

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2.3 Volatility

Due to the robustness and the large amount of findings confirming momentum, in the next part of section 2, section 2.3 up till section 2.7, different strategies are suggested, as a possible combination with momentum. Later in this paper, several of these strategies are combined with momentum to create portfolios, which try to outperform the market. Ardia et al. (2016) have reviewed characteristic-based portfolios and found robustness in a dynamic style, which combines several strategies. These different portfolios have a more smooth wealth creation, than a buy-and-hold strategy. Hou et al. (2006) find that momentum explains the average returns for country and industry portfolios, and a wide variety of single- and double-sorted characteristics-based portfolios. Also Leivo and Pätäri (2009) confirm momentum in a combination with several other strategies. The most important finding for this part is that Leivo and Pätäri (2009) find that a portfolio consisting of high momentum and low volatility outperforms a normal momentum portfolio.

Already several authors confirm the robustness of volatility, for example, Baker et al. (2011) were the first to find that low volatility stocks significantly outperform stocks with a high volatility in the market. Dutt and Humphery-Jenner (2013), Fiore and Saha (2015), and Kambouroudis and McMillan (2015) confirm that low volatility stocks outperform high volatility stocks. Switzer and Picard (2015) even find that low volatility stocks in a ranking period outperform in a subsequent holding period.

Kim et al. (2016) doubt the robustness of momentum, but suggest that volatility is the driver of the outperformance. Wang and Xu (2014) agree with Kim et al. (2016). Fuertes et al. (2015) find that simultaneously buying contracts with high past performance and low volatility, and shorting contracts with poor past performance and high volatility yields a Sharpe ratio that is five times the average, suggesting that a portfolio which combines

momentum and volatility has a superior outperformance of the market compared to a strategy which is based on only momentum or volatility.

2.4 Dividend

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months to years. More recent work of Ang and Bekaert (2006), among others, concludes that dividend yield is not (anymore) a good predictor of subsequent return. One reason for the change in findings might be the increased use of share buy-backs as a way to return cash to shareholders, as suggested by Robertson and Wright (2006), leaving the dividend yield to explain a lower proportion of total shareholder returns. The second category of literature is more concerned with long-term returns of “simple” investment strategies, such as “The Dogs of the Dow” (DOTD) for example. DOTD is a simple strategy, in which, at the start of the year, investors buy the ten stocks in the Dow Jones index with the highest dividend yield (based on dividends paid in the last 12 months). Investors hold the stocks for 12 months and the next year the same procedure is repeated. Portfolio adjustments would then occur on a yearly basis. Using the Dow Jones index, there are several studies across different time periods confirming that the DOTD strategy outperforms the Dow Jones index itself, see, for example, McQueen et al. (1997), Hirschey (2000) and O’Higgins and Downes (2000). Beyond the evidence of the success of the DOTD in the USA, there is a long list of

international surveys suggesting that the strategy works in other countries as well (see Alles and Sheng, 2008, in Australia; Visscher and Filbeck, 2003, in Canada; Kotkamp and Otte, 2001, in Germany; Wang et al., 2011, in China; Da Silva, 2001, in Latin America; among others).

Allen and Michaely (2002) find that changes in dividend policies are not motivated by firms desire to signal their true worth to the market, however they do influence investor sentiment and stock value. Clemens (2013) states that high dividend-paying firms earns abnormal returns in a long/short strategy in the USA and in world indices. Gupta (2012) finds that dividend paying stocks outperform non-paying stocks and also corrects for momentum and several other variables.

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2.5 P/E ratio

Basu (1977) was the first to find that the Price-Earnings ratios, due to exaggerated investor expectations, can be indicators of future investment performance. Bhargava and Malhotra (2006), Giannetti (2007), Pietrovito (2016), and Saville (2009) confirm the findings by Basu (1997). Pietrovito (2016) states that the low price-earnings ratio exerts a positive and

significant impact on investment, however Sum (2013) disagrees with the findings of Basu (1997) and states that the Price-Earnings ratio only forecasts about 3% of performance in the following 6-months to 2-years. Despite the findings by Sum (2013) there is a more common view in the literature that the Price-Earnings ratio does predict stock return, however no publications have been made on how portfolios, which have momentum as and as well have a low Earnings ratio, compare to portfolios, which have not been sorted on their Price-Earnings ratio.

2.6 Seasonality

Seasonality is a term which is used to explain a variety of phenomena. Bouman and Jacobsen (2002) and Jacobsen and Zhang (2014) use it to describe the substantial difference in returns during the summer, compared to the rest of the year. They find that in the period from May to October returns are not significantly different from zero, however in the rest of the year they are. Keloharju et al. (2016) use seasonality to create portfolios based on their historical same-calendar-month return, creating portfolios which significantly outperform the market. Rozeff and Kinney (1976) and Heston and Sadka (2008) find seasonality in January, which means that the returns of stocks reverses in the month of January. Jegadeesh and Titman (1993, 2001, 2011) also find that momentum portfolios earn negative returns in January, despite earning positive returns in every other calendar month.

Novy-Marx (2011) doubts the ranking period, suggesting that an intermediate horizon outperforms a short horizons, however his findings are contrasted by Yao (2012), who confirms January effect and disregards Novy-Marx (2011) and explains that outperformance by intermediate horizon is due to January seasonality. January seasonality is a factor to take into account, while applying a momentum strategy.

2.7 Size

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momentum profits are significantly higher when the strategy is implemented on growth stocks, which are low book-to-market stock, compared to value stocks, high book-to-market stocks. They suggest that this result can be due to the fact that it is harder to evaluate growth stocks, than to evaluate value stocks. Stocks with low prices are, most of the times, stocks which also are highly volatile and which have a high comparable price-earnings ratio. These factors are contrasting with the momentum variables. Momentum strategies, therefore, can be combined with one or more of these strategies.

3. Hypotheses

There has been done a lot of research on momentum, however there is only little known about the holding period and the evaluation period. As seen in different findings above, Chan et al. (1996) state a positive return for a six month and twelve month holding period. Findings by Jegadeesh and Titman (1993, 2001, 2011) confirm Chan et al. (1996) and indicate that the cumulative momentum profit is, on average, over 12% at the end of the 12th Month, besides for the year 2009. After these first 12 months, the cumulative momentum profit declines. The assumption, that the optimal holding period does not exceed 12 months, can be safely made based on previous findings. The tests in this paper try to find the optimal holding and

evaluation period for the momentum strategy. Only little distinction is made in these periods, is it more profitable to hold the portfolio for six months or for twelve months? Or is the optimal period three or nine months? The research goal of section 4 is to compare different holding and evaluation periods, in an attempt to find the optimal holding and evaluation periods for a portfolio based on the momentum strategy. Finding the combination of an optimal holding period and evaluation period can be used to create a situation in which the optimal momentum strategy can be used to predicted portfolio performance out-of-sample. The first four hypotheses are tested in section 4 of the paper, which looks for the optimal holding and ranking period of the momentum strategy. The fifth hypothesis and sixth hypothesis are tested in section 5 and section 6 of this paper.

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The third hypothesis states that transaction costs will not significantly affect the momentum effect, as the stocks are traded in a five day window and therefore the transaction cost only account for about ten base points of the total portfolio value.

Due to the economic crisis and the 2009 return reversal, the fourth hypothesis suggests that the findings in this paper are expected to be negatively biased by this effect.

The fifth hypothesis states that an optimal momentum portfolio is not only based on holding and evaluation periods, but also on volatility, as found by Wang and Xu (2010). A portfolio based on volatility and momentum is expected to outperform a portfolio based on solely a momentum strategy.

The final hypothesis states that an optimal momentum portfolio is not only based on holding and evaluation periods, but also on dividend strategy, as found by Asem (2009). A portfolio based on a dividend strategy and momentum is expected to outperform a portfolio based on solely a momentum strategy.

4. Momentum strategy, finding the optimal evaluation and holding period

4.1 Methodology

Every three months, between the 2005 and the end of 2015, three different portfolios are generated, based on different evaluation periods, showing different returns for stocks in every evaluation period. The three different formation periods are three months, six months, and twelve months. The portfolios are filled up with winsorized stocks from the Nasdaq Stock Market and every period the top ten percent winners and the bottom ten percent losers are selected from all stocks on the Nasdaq Stock Market. In total there were between 2153 and 2594 companies active on the Nasdaq Stock Market in the period from 2005 till 2016. The performance of the stocks, P, is calculated as

P = (Vt – Vt-x) / Vt-x (1)

where Vt denotes the stock value at moment t and Vt-1 denotes the stock value x months

previous to t, where x represents the evaluation or the holding period. All stock performances are compounded to monthly average returns.

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performance. The top decile in the market, the winners, are bought and the stocks in the lowest decile in the market, the losers, are shorted. After the holding period has been

calculated, a week is skipped, so that these strategies avoid some of the bid-ask spread, price pressure, and lagged reaction effects that underlie the evidence documented in Jegadeesh (1990) and Lehmann (1990), therefore there are five trading days to compose the new portfolio. The findings in this paper are adjusted for risk using the CAPM benchmark, comparable to Jegadeesh and Titman (2001, 2011).

Jegadeesh and Titman (2001) created a single factor model which presents why momentum generate higher than average in the following periods. The single factor model,

rit = µi + bift + eit

E(ft) = 0

E(eit) = 0 (2)

Cov(eit, ft) = 0 ∀ i

Cov(eit, ejt-1) = 0, ∀i ≠ j

which is the the return on stock i, rit, consists of µi, which is the unconditional expected return

on stock i, ft, the unconditional unexpected return on a factor-mimicking portfolio, bi, the

factor sensitivity of stock i, and eit, the specific component of return at time t. The

firm-specific component is for example the release of good news. The superior performance of momentum strategies implies that stocks that outperform the market in one period, as well outperform the market in the following period. The results based on formula to imply that E(rit - 𝑟𝑟̅t | rit-1 - 𝑟𝑟̅t-1 > 0) > 0 (3)

and

E(rit - 𝑟𝑟̅t | rit-1 - 𝑟𝑟̅t-1 < 0) < 0 (4)

are true, while the bar above the r denotes the cross-sectional average of this variable. Therefore,

E{(rit – 𝑟𝑟̅t) (rit-1 – 𝑟𝑟̅t-1)} > 0 (5)

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4.2 results

Table I, Table II, and Table III present the results from the three different 100/100 long/short portfolio formation tactics, containing historical winners and losers of the market. The date on the left is the month the portfolio has been composed, after the evaluation period. The number in the top row represents the length of the holding period in months. In the next part of the paper the momentum portfolio returns, during times of economic instability, are presented and discussed.

Graph I and Graph II visualize the findings from Table I, by displaying how the different portfolios and the market perform, after a 3-month evaluation period. Graph I presents the monthly returns of all the different winner minus loser portfolios and the 12-month monthly market average, the market line. Graph II shows how the portfolios perform compared to the market, by deducting the market average from the portfolio performance. The first major point is that the findings in this paper confirm the findings by Jegadeesh and Titman (2011), by confirming the 2009 return reversal. However, as can be seen from Graph I, that in the period following the 2009 return reversal, the W-L momentum portfolios underperform the market until 2014, as the portfolio returns are under the market line during this period. In Graph II it is shown that between 2009 and 2014 most of the portfolios underperform the market as their excess return is below zero percent.

The results from Table I are significant in 83 percent of the cases, however two-third of these cases are negative, significantly underperforming the market. On average, all W-L

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Table I: W-L Momentum Strategy – portfolio performance with a 3-month evaluation period.

3 4 5 6 7 8 9 10 11 12 4 05 (.96%)** (2.32%)** (1.58%)** (1.21%)** (.39%) (.59%)* (.39%)* (1.45%)** (1.78%)** (2.01%)** 7 05 (.65%)* (.78%) (1.47%) (1.84%)** (2.68%)** (2.77%)** (3.02%)** (2.91%)** (2.32%)** (2.05%)** 10 05 .74% (1.18%)** (1.23%)** (1.83%)** (1.94%)** (1.06%)** (.96%)** (.42%) (.71%)** (1.15%)** 1 06 (4.35%)** (2.32%)** (1.17%)** (1.02%)** (.36%) (.93%)** (.84%)** (1.34%)** (1.81%)** (1.89%)** 4 06 18.75% 14.60% 10.01% 6.26% 6.41% 3.86% 3.39% 2.51% 2.68% 2.48% 7 06 (.05%) (1.78%)** (2.47%)** (2.09%)** (2.40%)** (2.04%)** (1.81%)** (2.10%)** (2.33%)** (2.04%)** 10 06 (4.04%)** (7.44%)** (4.16%)** (3.98%)** (3.69%)** (4.82%)** (4.24%)** (3.13%)** (2.79%)** (2.84%)** 1 07 (2.42%)** (2.02%)** (1.94%)** (1.43%)** (.04%) .20% (.08%) .18% .89% 1.01% 4 07 (.49%)** 1.35% 1.10% .98% 1.43% 1.02%* 1.08%* 1.09%** 1.43%** 1.29%** 7 07 4.08%** 4.92%** 4.97%** 4.16%** 3.56%** 4.04%** 3.53%** 3.42%** 2.93%** 3.41%** 10 07 7.52%** 5.47%** 5.35%** 4.67%** 3.90%** 3.58%** 4.22%** 3.44%** 2.93%** 3.43%** 1 08 .76%** .96%** .47%** 2.46%** 1.85%** 1.34%** 2.19%** 3.92%** 5.48%** 4.60%** 4 08 .26%* .67%* (.39%) 3.54%** 6.86%** 9.14%** 7.26%** 5.87%** 6.63%** 4.95%** 7 08 (3.87%) 1.10%** 5.60%** 3.74%** 4.05%** 5.85%** 3.73%** 1.78%** .50%** .05%** 10 08 17.35%** 7.99%** 8.86%** 5.86%** 1.50%** (1.24%) (1.68%) (2.89%)** (3.07%)** (4.33%)** 1 09 (12.11%)** (19.04%)** (22.90%)** (18.39%)** (19.25%)** (17.36%)** (17.60%)** (15.52%)** (15.11%)** (15.06%)** 4 09 (8.41%)** (9.66%)** (8.62%)** (8.13%)** (5.91%)** (6.06%)** (6.12%)** (5.56%)** (5.64%)** (5.30%)** 7 09 (5.97%)** (5.16%)** (3.60%)** (3.97%)** (5.26%)** (4.52%)** (5.0%)** (5.53%)** (4.37%)** (3.57%)** 10 09 1.70% 1.04% (.16%)* (1.20%)** (1.78%)** (.08%)** .31% (.11%)** .02% (.05%)** 1 10 (5.18%)** (7.08%)** (2.67%)** (.66%)* (1.09%)** (.89%)** (1.10%)** (1.57%)** (1.33%)** (1.74%)** 4 10 3.61%** .84% .86%** (.54%) (1.33%)** (1.91%)** (2.86%)** (2.67%)** (1.53%)** (1.83%)** 7 10 (3.47%)** (7.46%)** (6.07%)** (7.09%)** (6.09%)** (5.82%)** (5.28%)** (4.80%)** (3.79%)** (3.50%)** 10 10 (19.99%)** (15.51%)** (14.60%)** (11.83%)** (10.82%)** (11.23%) (9.31%) (7.18%)** (5.59%)** (4.58%)* 1 11 (3.03%)** (2.98%)** (1.93%)** (1.20%)** (.69%)* .20% .85%** .58%* .63%* .73%* 4 11 3.07%** 3.0%** 4.72%** 5.80%** 3.25%** 3.74%** 3.13%** 2.03%** 1.63%** 1.05% 7 11 10.32%** 5.46%** 4.90%** 3.91%** 1.57%** .52% .0% .14% 1.01%** .25% 10 11 (7.33%)** (10.95%)** (9.47%)** (8.86%)** (6.70%)** (3.36%)** (4.13%)** (2.99%)** (3.07%)** (3.35%)** 1 12 (10.34%)** (7.84%)** (4.55%)** (3.58%)** (2.63%)** (2.80%)** (2.83%)** (2.57%)** (2.59%)** (2.18%)** 4 12 1.18%* 1.04%** .80%* (.31%) .16% .31% (.01%) (.56%)** (.56%)** (.80%)** 7 12 (2.37%)** (2.0%)** (1.96%)** (1.50%)** (3.03%)** (3.06%)** (3.12%)** (2.90%)** (3.25%)** (2.97%)** 10 12 1.20%* (1.53%)** (1.26%)** (1.63%)** (1.33%)** (2.27%)** (1.94%)** (2.35%)** (2.03%)** (2.49%)** 1 13 (3.83%)** (2.30%)** (3.01%)** (2.79%)** (2.93%)** (2.15%)** (2.65%)** (2.19%)** (2.42%)** (3.05%)** 4 13 (2.50%)** (3.61%)** (2.61%)** (3.16%)** (3.15%)** (3.26%)** (3.16%)** (2.81%)** (3.14%)** (3.22%)** 7 13 (4.08%)** (3.96%)** (3.88%)** (4.15%)** (4.65%)** (4.73%)** (4.32%)** (3.19%)** (2.83%)** (3.05%)** 10 13 (.64%)** .59% .02%** (.53%)** (.32%)** (.51%)** (.83%)** (.40%)* (.39%)** .01% 1 14 (3.09%)** (2.47%)** (1.77%)* (2.66%)** (1.16%) (1.08%)** (.13%) (.38%) (.09%) (.54%)* 4 14 (.93%) .84%** .18% .94%** .18% (.26%) (.92%) (.54%) (.89%)** (.90%)** 7 14 4.80%** 3.47%** 4.17%** 3.26%** 3.01%** 1.70%** 1.78%** 1.53%** 1.38%* 1.21% 10 14 .0%* .84% (1.11%)** (.78%)** (.53%)** (.93%)** (1.70%)** (1.18%)** (.05%) .44% 1 15 (1.11%)** (2.39%)** (1.81%)** (.78%)** .36% 1.06%** 1.71%** 1.13% 1.23%* 1.63%** 4 15 (.19%) 2.14%** 2.01%** 1.89%** .95%* .88%* 1.42%** 1.66%** 1.20%** .51%** 7 15 4.88%** 1.49%** 2.01%** 2.24%** 2.77%** 2.0%** 1.49%** 1.33%** 1.12%** 1.13%** 10 15 (1.21%)** 3.37%** 2.11%** .23% (.68%) (.40%) .07% (.69%)** (.91%)** (.99%)** Table I presents the monthly compounded overperformance (or underperformance) of the market by a portfolios based on a

winner minus loser momentum strategy. The number in the top row represents the number of months the portfolio has been held, after composition. The data on the left represent the month the portfolio has been composed, after the evaluation period has ended.

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Graph I: W-L Momentum Strategy – portfolio performance with a 3-month evaluation period.

Graph I presents the monthly compounded performance of portfolios based on a winner minus loser momentum strategy. The market line is added to compare the portfolio performance to the market average. The vertical axis presents the performance as a percentage. The data on the horizontal axis represent the month the portfolio has been composed, after the evaluation period has ended. The number, which belongs to every different line, represents the number of months the portfolio has been held, after composition.

Graph II: W-L Momentum Strategy – portfolio outperformance of the market with a 3-month evaluation period.

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Table II: W-L Momentum Strategy – portfolio performance with a 6-month evaluation period.

3 4 5 6 7 8 9 10 11 12 7 05 .02% .91% .02% (.30%) (1.79%)** (2.03%)** (2.36%)** (1.69%)** (1.26%)** (.95%)** 10 05 (.47%) (1.72%)** (1.73%)** (1.97%)** (1.79%)** (1.15%)** (.79%)** (.18%) (.49%)* (.81%)** 1 06 (2.78%)** (1.45%)* (1.75%)** (1.89%)** (2.09%)** (2.56%)** (2.79%)** (3.54%)** (3.06%)** (3.09%)** 4 06 1.70%** 1.86%** .41%** .47%** (.23%) (.79%)* (1.0%)** (1.36%)** (1.28%)** (1.30%)** 7 06 (1.11%) (2.07%)** (1.92%)** (1.44%)** (2.10%)** (1.90%)** (1.83%)** (2.20%)** (2.68%)** (2.67%)** 10 06 (4.23%)** (6.64%)** (3.94%)** (3.59%)** (3.38%)** (4.80%)** (3.97%)** (2.94%)** (2.38%)** (2.44%)** 1 07 .79% (.25%)* .43% (.08%)* .73% .88% .49% 1.27% 1.49% 1.17% 4 07 (.20%)** 1.10% 1.57%* 1.60% 2.01%** 1.86%** 1.80%** 1.70%** 1.86%** 1.70%** 7 07 4.99%** 5.55%** 5.61%** 4.73%** 3.75%** 4.13%** 3.03%** 2.75%** 2.55%** 2.76%** 10 07 6.19%** 4.02%** 4.61%** 4.04%** 3.53%** 3.18%** 4.02%** 3.21%** 2.46%** 2.91%** 1 08 .84%** .91%** .46%** 2.49%** 2.08%** 1.45%** 2.24%** 4.04%** 5.38%** 4.48%** 4 08 3.53%** 2.58%** 1.34%** 3.41%** 6.88%** 9.39%** 7.65%** 6.55%** 7.43%** 5.04%** 7 08 (2.0%) 3.77%** 8.04%** 5.30%** 4.26%** 6.16%** 3.81%** 1.39%** (.20%)** (.66%)* 10 08 17.35%** 10.94%** 11.44%** 7.70%** 2.78%** .18%** (.57%) (1.72%)* (2.07%)** (3.32%)** 1 09 (9.47%)** (19.73%)** (23.20%)** (19.94%)** (20.64%)** (18.99%)** (18.85%)** (16.73%)** (16.54%)** (15.84%)** 4 09 (23.43%)** (20.96%)** (19.14%)** (18.32%)** (14.07%)** (13.85%)** (13.03%)** (11.77%)** (11.57%)** (11.15%)** 7 09 (8.14%) (5.89%)** (5.63%)** (6.15%)** (6.78%)** (5.93%)** (6.36%)** (6.52%)** (5.14%)** (4.40%)** 10 09 1.90% 1.39% .83% (.35%)** (1.15%)** .15%* .35% .32%* .72% .51% 1 10 (4.42%)** (5.91%)** (1.98%)** (.21%) (.61%)** (.40%) (.32%)** (.57%)** (.66%)** (.87%)** 4 10 2.77%** .92%* .88%** .02% (.34%) (.92%)** (2.05%)** (1.97%)** (3.25%)** (2.81%)** 7 10 (5.33%)** (5.26%)** (4.68%)** (6.06%)** (4.44%)** (4.21%)** (4.21%)** (4.08%)** (3.42%)** (3.04%)** 10 10 (10.58%)** (8.49%)** (7.91%)** (6.52%)** (5.62%)** (6.32%) (5.36%) (3.61%)* (1.68%)* (.43%) 1 11 29.67% 20.57% 15.48% 10.06% 8.41% 7.48% 5.91%** 4.39%* 4.31%* 3.55%** 4 11 1.90%* 1.43%** 3.46%** 4.23%** 2.74%** 2.85%** 2.47%** 1.46%** 1.04%** .66% 7 11 9.53%** 5.11%** 4.73%** 3.78%** 2.01%** 1.17%** .38% .50% 1.08%** .39% 10 11 (6.07%)** (9.36%)** (8.38%)** (7.66%)** (5.39%)** (2.39%)** (3.02%)** (2.11%)** (2.35%)** (2.38%)** 1 12 (10.85%)** (7.73%)** (2.67%)** (2.44%)** (1.38%)** (1.91%)** (1.99%)** (1.72%)** (1.44%)** (1.21%)** 4 12 1.72%** 1.05%** .49% .02% (.17%) (.38%) (.16%) (1.01%)** (1.18%)** (1.44%)** 7 12 (1.45%)** (.71%) (.62%) (.59%)* (2.12%)** (1.43%)** (.93%)** (.67%)** (1.29%)** (1.20%)** 10 12 (1.27%) (3.43%)** (3.45%)** (2.62%)** (2.25%)** (2.93%)** (2.69%)** (3.14%)** (2.66%)** (3.38%)** 1 13 (3.93%)** (2.62%)** (4.07%)** (3.81%)** (3.61%)** (2.79%)** (3.65%)** (3.08%)** (2.91%)** (3.35%)** 4 13 (2.41%)** (3.01%)** (2.11%)** (2.36%)** (2.21%)** (2.59%)** (3.12%)** (2.90%)** (3.44%)** (3.28%)** 7 13 (2.25%)** (3.63%)** (3.92%)** (5.10%)** (5.01%)** (5.66%)** (5.14%)** (3.58%)** (2.86%)** (3.24%)** 10 13 (3.47%)** (3.39%)** (3.11%)** (2.88%)** (2.51%)** (2.08%)** (2.16%)** (1.90%)** (1.92%)** (1.36%)** 1 14 (3.42%)** (3.26%)** (2.87%)** (3.26%)** (1.87%)** (1.79%)** (.90%)* (.80%)* (.51%)* (1.00%)** 4 14 (2.81%)** (.47%) (.56%) .45%** .15% (.05%) (.45%) (.61%) (1.06%)** (1.02%)** 7 14 4.19%** 2.35%** 2.31%** 1.25%* 1.42%** .37% .26% .01% .11% .15% 10 14 .87% .93% (1.26%)** (.86%)** (1.0%)** (1.03%)** (1.11%)** (1.02%)** (.07%) .55% 1 15 (.74%)* (2.29%)** (2.37%)** (1.50%)** (.62%) .58% 1.39%** .37% .68% 1.35%** 4 15 .32% 2.65% 2.51%** 2.95%** 2.34%** 2.40%** 2.98%** 3.07%** 2.68%** 2.04% 7 15 4.93%** 1.58%** 2.01%** 2.38%** 3.03%** 2.22%** 1.22%** .77%** .73%** .86%** 10 15 (1.45%)** 2.96%** 1.20%** (.23%) (.42%) (.27%) .19% (.36%)* (.53%)** (.63%)** Table II presents the monthly compounded overperformance (or underperformance) of the market by a portfolios based on a

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Findings in Table II and Table III are somewhat similar to the findings in Table I, however there are some important differences between the results based on the 3-month, the 6-month, and the 12-month evaluation periods. The same pattern, concerning return reversal, found for 3-month evaluation period W-L momentum portfolios, is also present after 6-month and 12-month evaluation periods for W-L momentum portfolios during 2009. However, during the years following 2009, 2010 till 2014, a lot less underperformance of the market is found, when the evaluation period is enlarged.

The patterns, between 2009 and 2014, in Graph III and Graph IV, concerning the 6-month holding period, are similar to the patterns found in Graph I and Graph II, however showing less negative underperformance and more positive overperformance. Nonetheless the W-L momentum portfolios using a 6-month holding period are not significantly different from the results of the portfolios using a 3-month holding period, as they are significant 81 percent of the time and still only one third of the times they are significantly outperforming the market. In the other two third of the cases they are significantly underperforming the. The average underperformance, of the market, by all portfolios, based on a 6-month holding period, is just above one percent.

Graph III: W-L Momentum Strategy – portfolio performance with a 6-month evaluation period.

Graph II presents the monthly compounded performance of portfolios based on a winner minus loser momentum strategy. The market line is added to compare the portfolio performance to the market average. The vertical axis presents the performance as a percentage. The data on the horizontal axis represent the month the portfolio has been composed, after the evaluation period has ended. The number, which belongs to every different line, represents the number of months the portfolio has been held, after composition.

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Graph IV: W-L Momentum Strategy – portfolio outperformance of the market with a 6-month evaluation period.

Graph V presents the monthly compounded portfolio outperformance (underperformance) of the market based on a winner minus loser momentum strategy. The vertical axis presents the outperformance (underperformance) as a percentage. The data on the horizontal axis represent the month the portfolio has been composed, after the evaluation period has ended. The number, which belongs to every different line, represents the number of months the portfolio has been held, after composition.

The results in Table III, besides from the period around 2009, are less volatile than the findings in Table I and Table II, showing smaller differences in portfolio performance over time. Graph V shows that, in most of the cases, the portfolio performances, based on a 12-month holding period, do not differ much from the average performance in the market. Graph VI confirms that the portfolio does not differ more than a few percent from the market in most cases, however the 2009 return reversal has a large effect on the outcome. The W-L

momentum portfolios, based on a 12-month selection period, might be the least volatile, however the portfolios based on a 12-month evaluation period have the worst average performance, with an average underperformance of the market of almost 1.4 percent per month. The results in Table III are 78 percent of the times significant, and in almost 44

percent of these cases are positive. However, due to the many negative outliers in 2009 and no large positive outliers, this selection period performs worse than a 3-month or a 6-month selection period in times of economic disturbance.

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Table III: W-L Momentum Strategy – portfolio performance with a 12-month evaluation period. 3 4 5 6 7 8 9 10 11 12 1 06 (6.56%)** (4.33%)** (2.57%)** (1.84%)** (1.20%)** (1.44%)** (1.72%)** (2.08%)** (2.49%)** (2.70%)** 4 06 1.68%** 1.82%** 1.05%** .40%* .15% (.65%) (.85%)** (2.49%)** (1.77%)** (1.78%)** 7 06 (.93%) (1.84%)** (2.27%)** (2.14%)** (3.82%)** (2.65%)** (2.53%)** (2.12%)** (2.57%)** (1.96%)** 10 06 (4.43%)** (7.80%)** (4.43%)** (3.66%)** (3.64%)** (4.71%)** (3.63%)** (2.72%)** (2.32%)** (2.46%)** 1 07 (2.62%)** (2.78%)** (3.52%)** (2.54%)** (1.61%)** (1.64%)** (1.88%)** (2.44%)** (1.62%)* (2.02%)** 4 07 (.40%)* 1.03% 1.01% .61% .98% 1.97%** 1.82%** 1.92%** 1.95%** 2.11%** 7 07 2.99%** 3.35%** 4.43%** 3.62%** 3.04%** 3.03%** 2.52%** 2.57%** 1.77%** 2.40%** 10 07 5.36%** 3.35%** 3.50%** 2.79%** 2.64%** 2.08%** 2.82%** 2.15%** 1.69%** 1.88%** 1 08 .59%** 1.01%** .34%** 2.16%** 1.54%** .92%** 1.81%** 3.26%** 4.81%** 4.05%** 4 08 3.88%** 2.57%** .91%* 2.51%** 5.26%** 7.15%** 5.86%** 4.95%** 5.54%** 3.87%** 7 08 (1.14%) 4.63%** 8.64%** 6.15%** 5.35%** 6.73%** 4.15%** 1.62%** .0% (.42%) 10 08 17.53%** 10.57%** 11.05%** 7.89%** 3.06%** 1.58% .11% (1.15%) (1.77%) (2.61%)** 1 09 (9.68%)** (20.03%)** (22.71%)** (20.56%)** (20.64%)** (18.95%)** (18.41%)** (15.78%)** (16.05%)** (15.15%)** 4 09 (29.03%)** (26.87%)** (23.74%)** (22.12%)** (17.21%)** (16.60%)** (15.17%)** (13.60%)** (13.16%)** (12.58%)** 7 09 (16.46%)** (11.70%)** (11.19%)** (10.94%)** (10.80%)** (10.01%)** (9.87%)** (11.18%)** (8.79%)** (7.05%)** 10 09 (.53%)* (2.91%)** (3.09%)** (3.83%)** (5.19%)** (3.08%)** (1.77%)** (2.03%)** (1.35%)** (1.77%)** 1 10 (2.24%)** (4.93%)** (1.78%)** (.54%) (.81%)** .29% (.06%)* (.13%)** (.42%)** (.95%)** 4 10 2.46%** 2.71%* 2.98%** 1.91% 1.16% .31% (.27%)* (.72%)** (.80%)** (.93%)** 7 10 (2.18%)** (2.40%)** (.20%)* (1.68%)** (2.38%)** (1.44%)** (1.53%)** (1.71%)** 5.95% 5.60% 10 10 (5.53%)** (5.10%)** (4.85%)** (3.59%)** (3.69%)** (2.93%)** (2.32%)** (2.13%)** (1.05%)** .09% 1 11 (1.26%)** (1.33%)** (.17%) .43% .17% 1.36%** 2.38%** 1.50%** 1.62%** 1.40%** 4 11 1.87%* .90%* 2.96%** 4.01%** 2.15%** 2.33%** 2.15%** .96%** .22% (.41%) 7 11 6.63%** 3.35%** 3.27%** 3.07%** .88%** .06% (.97%)** (.72%)* (.35%) (.73%) 10 11 (3.05%)** (6.70%)** (6.59%)** (6.67%)** (5.10%)** (2.81%)** (3.45%)** (2.39%)** (2.47%)** (2.63%)** 1 12 (9.65%)** (5.48%)** (2.0%)** (2.27%)** (1.43%)** (2.02%)** (2.19%)** (1.99%)** (2.05%)** (1.76%)** 4 12 4.23%** 3.59%** 2.40%** 1.54%* 1.33%** .93%* .63% (.46%)** (.56%)** (.98%)** 7 12 (1.63%)** (.90%)* (1.22%)* (.97%)* (2.85%)** (2.66%)** (2.07%)** (1.76%)** (2.64%)** (2.36%)** 10 12 (.17%) (3.21%)** (3.50%)** (2.98%)** (2.72%)** (3.70%)** (3.38%)** (3.61%)** (3.28%)** (3.78%)** 1 13 (3.15%)** (2.62%)** (4.19%)** (3.88%)** (4.73%)** (4.09%)** (4.72%)** (4.28%)** (4.40%)** (4.65%)** 4 13 (3.58%)** (4.40%)** (3.07%)** (4.18%)** (3.69%)** (4.09%)** (3.95%)** (3.47%)** (3.93%)** (4.12%)** 7 13 (4.41%)** (4.13%)** (4.16%)** (4.60%)** (4.24%)** (4.96%)** (4.42%)** (3.24%)** (2.61%)** (3.12%)** 10 13 (4.54%)** (4.55%)** (5.01%)** (4.49%)** (3.17%)** (2.23%)** (2.59%)** (1.99%)** (1.93%)** (.98%)** 1 14 (1.91%)** (2.08%)** (1.52%)* (2.01%)** (1.14%)* (1.07%)** (.51%) (.32%) .10% (.37%) 4 14 (1.39%) (.01%)* .09% 1.46%** 1.25%** 1.15%** .69% .85%* .34% .32% 7 14 3.44%** 2.84%** 2.50%** 1.57%* 1.57%** .92% 1.06% .65% .55% .74% 10 14 (.97%)** (.28%) (2.23%)** (1.22%)** (1.28%)** (1.42%)** (1.65%)** (1.02%)** (.09%) .40% 1 15 (.56%) (2.17%)** (1.40%)** 2.26% 3.48% 3.40%* 4.40%* 3.26% 3.21% 2.43% 4 15 (.39%) 1.38% 1.37%** 2.54%** .89% 1.51%** 2.52%** 3.28%** 2.91%** 2.28%** 7 15 6.52%** 3.90%** 3.75%** 4.47%** 4.78%** 3.86%** 3.07%** 2.15%** 2.17%** 1.97%** 10 15 4.95%** 2.84%** 3.07%** 3.55%** 3.62%** 3.17%** 2.20%** 1.57%** 1.57%** 1.44%** Table III presents the monthly compounded overperformance (or underperformance) of the market by a portfolios based on a

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Graph V: W-L Momentum Strategy – portfolio performance with a 12-month evaluation period.

Graph III presents the monthly compounded performance of portfolios based on a winner minus loser momentum strategy. The market line is added to compare the portfolio performance to the market average. The vertical axis presents the performance as a percentage. The data on the horizontal axis represent the month the portfolio has been composed, after the evaluation period has ended. The number, which belongs to every different line, represents the number of months the portfolio has been held, after composition.

Graph VI: W-L Momentum Strategy – portfolio outperformance of the market with a 12-month evaluation period.

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In none of the cases did a W-L momentum portfolio outperform the market in the period between 2005 and 2016, however when leaving out the portfolio performances in the three negative periods in 2009, the average performance, based on a 6-month or 12-month selection period, closely mimic market performance over the period starting in 2005 and ending in 2016. There are only slight differences between the different lengths of holding periods, differing from .5 percent under the market to .6 percent above the market, on an average, monthly basis.

In the cases without the results from 2009, 4 portfolios, based on a 6-month holding period, do not underperform the market in the long run. The holding periods of these portfolios are three, four, five, and six months, with a 3-month holding period as the most successful zero-cost strategy.

Another pattern found is that the strength of the momentum effect decreases as the holding period increases. These findings are shown in Table IV, the maximal and the minimal excess returns generated by all three momentum portfolios are closre to zero, as the holding period increases. The excess return decreases, when the holding period increases, whereas the underperforming stocks are increasing as the holding period inflates. These findings confirm that as the holding period increases, the power of the W-L momentum portfolio decreases.

Table IV: maxima and minima of the different W-L momentum portfolios.

3 4 5 6 7 8 9 10 11 12 MAX 3 18,75% 14,60% 10,01% 6,26% 6,86% 9,14% 7,26% 5,87% 6,63% 4,95% MIN 3 (19,99%) (19,04%) (22,90%) (18,39%) (19,25%) (17,36%) (17,60%) (15,52%) (15,11%) (15,06%) MIN 3E (19,99%) (15,51%) (14,60%) (11,83%) (10,82%) (11,23%) (9,31%) (7,18%) (5,59%) (4,58%) MAX 6 29,67% 20,57% 15,48% 10,06% 8,41% 9,39% 7,65% 6,55% 7,43% 5,04% MIN 6 (23,43%) (20,96%) (23,20%) (19,94%) (20,64%) (18,99%) (18,85%) (16,73%) (16,54%) (15,84%) MIN 6E (10,85%) (9,36%) (8,38%) (7,66%) (5,62%) (6,32%) (5,36%) (4,08%) (3,44%) (3,38%) MAX 12 17,53% 10,57% 11,05% 7,89% 5,35% 7,15% 5,86% 4,95% 5,95% 5,60% MIN 12 (29,03%) (26,87%) (23,74%) (22,12%) (20,64%) (18,95%) (18,41%) (15,78%) (16,05%) (15,15%) MIN 12E (9,65%) (7,80%) (6,59%) (6,67%) (5,19%) (4,96%) (4,72%) (4,28%) (4,40%) (4,65%) Table IV displays all maximum and minimum monthly excess returns generated using different valuation periods with a

momentum strategy. The number in the top row represents the number of months the portfolio has been held, after composition. The data on the side state the holding period and if it was the maximal or minimal excess return found using that holding period. In the cases on the left, where an E is added after the number, the data from 2009, the year with extremely negative returns, are excluded from the minima.

4.2.1 Transaction cost

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holding period did not affect the turnover rate. However the transaction cost did not change any significance found among all different W-L momentum portfolios. One factor, decreasing the transaction cost in such a way that it did not affect portfolio, was adjusting the length of the formation period to five days. The increase of the formation period decreases the transaction cost to about thirty percent of the original transaction cost. The other factor, influencing the transaction cost, was that the portfolio is only turned over after it has been held for at least three months. The effective influence of a portfolio with a holding period of three months is less than 2.5 base points, .025 percent, on a monthly basis and decreases to under one base points for a 12-month holding period. Transaction cost do not have a significant effect on portfolios using a W-L momentum strategy with a holding period of at least three months.

5. Momentum and volatility strategy

In section 5 of this paper the traditional momentum winner strategy is combined with a low volatility strategy. In this section the performance of a portfolio with historical winners and low volatility is discussed. The strategy in this section is different from the W-L momentum strategy, because the W-L momentum strategy is a zero-cost strategy and the momentum and volatility strategy is a 100 percent long strategy. Kambouroudis and McMillan (2015)

consider, in their paper, how much data are required to produce accurate forecasts with volatility. They state that the volatility span should be at least a year to generate accurate forecasts, for composing volatility portfolios.

5.1 Method section

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The momentum winner and low volatility strategy is used to create a long portfolio, with a 100 percent long composition. The momentum and volatility portfolio is supposed

outperforms the market. At the beginning of every holding period the stocks are ranked, first based on historical volatility and afterwards the top quartile is ranked on historical

performance. The top decile, the winners in the market, is selected for the portfolio. After the holding period has been calculated, a week is skipped, so that these strategies avoid some of the bid-ask spread, price pressure, and lagged reaction effects that underlie the evidence documented in Jegadeesh (1990) and Lehmann (1990), therefore there are five trading days to compose the new portfolio.

5.2 Results

Table V presents the results of 400 different 100 percent long portfolios, containing low volatile winners from the market. The date on the left is the month the portfolios have been composed, after the evaluation period. The number in the top row represents the length of the holding period of the portfolio, in months. In the next part of the paper the results of the portfolios, based on low volatility and high momentum, are discussed.

Graph VII and Graph IIX visualize the findings of Table V by displaying how the different portfolios and the market perform after a 12-month evaluation period. Graph VII presents the monthly average returns of all the different winner portfolios and the 12-month monthly market average, the market line. The first major point is that Graph VII shows that, in most cases, with as the greatest exception the period around the 2009 return reversal, the

performances by the low volatility and high momentum portfolios are close to the

performance of the market, the market line in Graph VII. Graph IIX shows that the volatility of the stocks, in the portfolios, remain low as they are not highly differentiating from the market. The portfolio, that outperforms the market the best, has an average monthly

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Table V: Momentum and Volatility Strategy – portfolio performance with a 12-month evaluation period. 3 4 5 6 7 8 9 10 11 12 1 06 (1.76%)** (1.48%)** (0.46%) (0.23%) 0.26% 0.02% 0.01% (0.20%) (0.34%) (0.33%) 4 06 1.25%** 1.58%** 1.06%** 0.99%** 0.54%* 0.30% 0.12% (0.16%) (0.25%) (0.37%) 7 06 0.68% (0.03%) (0.22%) (0.28%) (0.63%) (0.51%) (0.50%) (0.67%)* (0.76%) (0.84%)* 10 06 (1.19%)* (1.80%) (1.25%)* (1.13%) (1.30%)** (1.43%)* (1.40%)** (1.34%)** (1.08%)* (1.25%)* 1 07 (1.58%)** (1.60%)** (1.67%)** (1.71%)** (1.58%)** (1.19%)** (1.22%)** (1.42%)* (1.01%)* (1.14%)* 4 07 (1.41%)* (1.04%)* (0.65%) (0.87%)* (0.98%)* (0.62%) (0.68%)* (0.39%) (0.27%) (0.16%) 7 07 (0.18%) (0.21%) 0.23% (0.04%) 0.21% 0.43% 0.41% 0.23% 0.02% 0.15% 10 07 1.18%* 1.11%* 1.13%** 1.14%** 0.98%** 0.64% 0.73%* 0.76%* 0.70%* 0.98%** 1 08 0.33% 0.07% (0.17%) 0.20% 0.36% 0.41% 0.71%* 1.04%** 1.32%** 1.17%** 4 08 (0.19%) 0.15% 0.02% 0.72%* 1.32%** 1.72%** 1.30%** 1.08%** 1.18%** 0.95%** 7 08 0.99% 2.16%** 3.11%** 2.27%** 2.04%** 2.20%** 1.41%** 0.67% 0.15% 0.17% 10 08 4.84%** 2.94%** 2.74%** 1.49%** 0.12% (0.67%) (0.68%) (1.01%) (1.05%) (1.27%)* 1 09 (2.87%)** (5.43%)** (6.12%)** (5.57%)** (5.78%)** (5.45%)** (5.36%)** (4.72%)** (4.68%)** (4.45%)** 4 09 (7.99%)** (7.74%)** (7.02%)** (6.45%)** (5.38%)** (5.13%)** (4.76%)** (4.58%)** (4.24%)** (4.16%)** 7 09 (4.92%)** (3.46%)** (3.40%)** (3.08%)** (3.16%)** (2.83%)** (2.88%)** (3.16%)** (2.60%)** (2.03%)* 10 09 (0.26%) (0.86%) (0.80%) (1.15%)** (1.70%)** (1.04%)** (0.61%)* (0.58%)* (0.29%) (0.38%) 1 10 (1.74%)* (2.22%)** (1.23%)* (0.58%) (0.37%) (0.14%) (0.07%) (0.11%) (0.08%) (0.17%) 4 10 0.55% 0.17% 0.37% 0.34% 0.29% 0.07% (0.26%) (0.33%) (0.33%) (0.28%) 7 10 (0.13%) (0.22%) (0.43%) (0.80%) (0.78%) (0.68%) (0.63%) (0.64%) (1.99%) (1.60%) 10 10 (1.19%)* (1.08%)* (0.77%) (0.39%) (0.41%) (0.21%) (0.07%) (0.14%) 0.28% 0.55%* 1 11 (0.37%) (0.42%) (0.19%) 0.14% 0.03% 0.47% 0.72%* 0.64%* 0.73%* 0.80%** 4 11 0.94% 0.58% 1.31%** 1.53%** 1.13%** 1.23%** 1.16%** 0.77%** 0.52% 0.42% 7 11 2.14%** 1.41%** 1.49%** 1.38%** 0.80%* 0.53% 0.37% 0.40% 0.58%* 0.47% 10 11 (1.19%)* (2.20%)** (1.92%)** (1.84%)** (1.22%)** (0.52%) (0.66%) (0.47%) (0.50%) (0.57%) 1 12 (2.51%)** (1.56%)** (0.32%) (0.35%) (0.10%) (0.17%) (0.21%) (0.13%) (0.10%) (0.14%) 4 12 1.77%** 1.77%** 1.32%** 0.88%* 0.94%** 0.90%** 0.65%* 0.34% 0.27% 0.13% 7 12 0.16% 0.44% 0.32% 0.12% (0.35%) (0.33%) (0.34%) (0.35%) (0.48%) (0.40%) 10 12 0.35% (0.11%) (0.16%) (0.09%) (0.25%) (0.40%) (0.36%) (0.31%) (0.38%) (0.47%) 1 13 (0.41%) (0.65%) (0.93%)* (0.69%) (0.64%) (0.64%) (0.74%)* (0.49%) (0.61%)* (0.68%)* 4 13 (0.96%) (0.91%) (0.89%)* (1.13%)* (0.82%)* (0.92%)* (0.97%)** (1.00%)** (1.12%)** (1.00%)** 7 13 (0.90%) (0.33%) (0.47%) (0.56%) (1.06%)* (1.12%)* (0.92%)* (0.59%) (0.45%) (0.62%)* 10 13 (0.44%) (1.24%) (1.32%)* (0.83%) (0.39%) (0.12%) (0.29%) (0.06%) (0.20%) (0.06%) 1 14 (1.98%)** (1.32%)* (0.83%) (0.95%)* (0.56%) (0.57%) (0.28%) (0.03%) 0.12% 0.14% 4 14 0.32% 0.66% 0.36% 0.70%* 0.76%* 0.77%* 0.70%* 0.55% 0.46% 0.46% 7 14 1.19%* 0.96%* 1.09%** 0.84%* 0.63% 0.46% 0.44% 0.38% 0.29% 0.28% 10 14 0.32% 0.19% (0.17%) (0.11%) 0.01% (0.12%) (0.03%) 0.26% 0.44% 0.73%** 1 15 (0.40%) (0.38%) (0.35%) (0.51%) (0.08%) 0.33% 0.66% 0.47% 0.54% 0.84%* 4 15 (0.02%) 0.90% 1.08%** 1.66%** 1.24%** 1.21%** 1.41%** 1.69%** 1.52%** 1.31%** 7 15 3.53%** 2.30%** 2.06%** 2.09%** 2.30%** 1.89%** 1.59%** 1.34%** 1.29%** 1.13%** 10 15 3.66%** 2.68%** 2.33%** 2.15%** 2.32%** 1.92%** 1.66%** 1.41%** 1.36%** 1.20%** Table V presents the monthly compounded overperformance (or underperformance) of the market by portfolios based on a

strategy, which combines stocks which are momentum winners and have a low volatility. The number in the top row represents the number of months the portfolio has been held, after composition. The data on the left represent the month the portfolio has been composed, after the evaluation period has ended.

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Graph VII: Momentum and Volatility Strategy – portfolio performance with a 12-month evaluation period.

Graph VII presents the monthly compounded performance of portfolios based on a strategy, which combines stocks which are momentum winners and have a low volatility. The market line is added to compare the portfolio performance to the market average. The vertical axis presents the performance as a percentage. The data on the horizontal axis represent the month the portfolio has been composed, after the evaluation period has ended. The number, which belongs to every different line, represents the number of months the portfolio has been held, after composition.

Graph IIX: Momentum and Volatility Strategy – portfolio outperformance of the market with a 12-month evaluation period.

Graph IIX presents the monthly compounded portfolio outperformance (underperformance) of the market based on a strategy, which combines stocks which are momentum winners and have a low volatility. The vertical axis presents the outperformance (underperformance) as a percentage. The data on the horizontal axis represent the month the portfolio has been composed, after the evaluation period has ended. The number, which belongs to every different line, represents the number of months the portfolio has been held, after composition.

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All different holding periods, in the long run, slightly underperform the average monthly market return. The long run underperformance of these portfolios is located between .25 and .40 percent on a monthly basis, however, when the 2009 mean reversion is left out of the data, all different holding periods have barely positive findings in the long run. There are no

considerable differences between holding periods, besides the influence of transaction costs. A disappointing finding is that only 48 percent of the portfolios, after a 12-month evaluation period, significantly differ from the market line and that just under half of these findings are negative. In Graph IX these findings are visualized, by correcting the findings in Graph IIX for significance. Here you can see that the 2009 mean reversion holds, however, in the period following this mean reversion, 2010 till 2014, the portfolio circles around the market line. In 2015, when most effects of economic instability have disappeared, the low volatility and momentum winner portfolios start to significantly outperform the market in all cases. The average outperformance in this period is 1.76 percent on a monthly basis.

Graph IX: Momentum and Volatility Strategy – portfolio performance, corrected for significance, with a 12-month evaluation period.

Graph IX presents the monthly compounded performance of portfolios, corrected for significance, based on a strategy, which combines stocks which are momentum winners and have a low volatility. The market line is added to compare the portfolio performance to the market average. The vertical axis presents the performance as a percentage. The data on the horizontal axis represent the month the portfolio has been composed, after the evaluation period has ended. The number, which belongs to every different line, represents the number of months the portfolio has been held, after composition.

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6. Momentum and dividend strategies

In section 6 of this paper the traditional momentum winner strategy is combined with two different dividend strategies. In this section the performance of portfolios, with high

performance stocks which pay dividend, and portfolios, with high performance stocks which do not pay dividend, are discussed. The strategy in this section is different from the W-L momentum strategy and comparable to the momentum and volatility strategy, because the W-L momentum strategy is a zero-cost strategy and strategies based on momentum and dividend, like the momentum and volatility strategy, are long strategies.

6.1 Method section

Every three months, between 2006 and the end of 2015, two different portfolios are generated, based on a 12-month evaluation period prior to the portfolio formation, showing different returns for stocks in every evaluation period. The portfolios are filled up with winsorized stocks from the Nasdaq Stock Market, in which different top deciles are selected for both portfolios. However, compared to the W-L momentum portfolio, the top deciles are selected in a different way. First the market is divided in to stock which pay dividend and in to stock which do not pay dividend. In the first portfolio, a momentum winner portfolio with stocks which do not pay dividend, the top performing stocks are selected from all non-dividend paying stocks on the Nasdaq Stock Market, resulting in a portfolio containing a total of ten percent of the market. For the second portfolio, a momentum winner portfolio with dividend paying stocks, the top performing stocks are selected from all dividend paying stocks on the Nasdaq Stock Market. In total there were between 2153 and 2594 companies active on the Nasdaq Stock Market in the period from 2006 till 2016. The performance of the stocks, P, is calculated by the use of Formula 1. The amount of dividend payed per stock is given. The momentum and dividend strategies are used to create long portfolios, with a 100 percent long composition. The momentum and (non-)dividend portfolios are supposed outperforms the market. At the beginning of every holding period the stocks are ranked, first based on historical dividend payment and these groups are, afterwards, ranked on historical

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The results of the momentum and dividend portfolios are corrected for the relative dividend payed to the portfolio, compared to the market, as a percentage of the total portfolio value. The first step is that the total, monthly dividend payment to the portfolio is calculated as a percentage of the total portfolio value and is added to the monthly performance of the

portfolio. In the second step, the average dividend payment in the market is calculated and is added to the market performance. By taking those two steps the performance of the

momentum and dividend portfolios are adjusted for dividend payments during their holding periods.

6.2 Results

Table VI and Table VII both present the results of 400 different 100 percent long portfolios, containing the winners from the market, which either do or do not pay dividend. Table VI contains the outperformance of the market of portfolios, based on a 12-month evaluation period of winners in the market, which do not pay dividend. Table VII is different as that it contains the results of portfolios with winners in the market, which do pay dividend. The date on the left shows the month the portfolio has been composed after the evaluation period. The number in the top row represents the length of the holding period, in months. In the next part the results of portfolios based on two different dividend strategies are discussed.

6.2.1 No dividend and momentum strategy

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Table VI: Momentum and No Dividend Strategy – portfolio performance with a 12-month evaluation period. 3 4 5 6 7 8 9 10 11 12 1 06 1.53%* 1.41%* .60% .34% (.11%) .15% .02% .09% (.01%) (.07%) 4 06 (1.41%)** (2.05%)** (1.53%)** (1.46%)** (1.09%)** (1.01%)** (.93%)** (.99%)* (.89%)** (.81%)* 7 06 (1.67%)** (1.00%)* (.49%) (.25%) (.36%) (.25%) (.18%) .04% .21% .31% 10 06 (.24%) (.30%) (.11%) .12% .11% (.02%) .01% (.02%) .05% .19% 1 07 (.26%) (.40%) (.14%) .22% .31% .10% .29% .52% .32% .28% 4 07 .58% .40% .38% .79%* .99%* .92%* 1.02%** .49% .35% .33% 7 07 1.81%** 2.07%** 1.73%** 1.42%** .34% .04% (.17%) .11% .21% .15% 10 07 1.76%** .02% (.24%) (.57%) (.13%) (.17%) (.23%) (.24%) (.37%) (.87%)** 1 08 (2.92%)** (2.08%)** (1.84%)** (1.43%)** (1.15%)** (1.05%)** (1.46%)** (1.84%)** (1.83%)** (1.52%)** 4 08 1.68%** 1.23%* .70% .11% (.62%) (.69%) (.34%) (.13%) (.17%) (.22%) 7 08 (2.54%)** (2.44%)** (1.89%)** (1.22%)* (.80%) (.59%) (.84%) (.97%)* (1.02%) (.83%) 10 08 2.07%** 1.89%** 1.54%** 2.13%** 1.32% 1.97% 1.29% 1.06% .54% .24% 1 09 (1.08%) (3.51%)** (3.60%)** (3.35%)* (3.78%)** (3.63%)** (3.40%)** (2.62%)** (2.74%)** (2.44%)** 4 09 (5.39%)** (4.58%)** (4.11%)** (3.98%)** (2.81%)** (2.69%)** (2.15%)* (1.54%) (1.51%) (1.36%) 7 09 (2.49%)* (2.36%)* (1.97%)* (1.85%) (2.12%) (1.83%) (1.70%) (1.70%) (1.60%) (1.38%) 10 09 .30% (.40%) (.16%) (.15%) (.16%) (.30%) (.36%) (.18%) (.14%) .03% 1 10 2.95%** 2.46%** 1.58%* .80% 1.00%* 1.06%** 1.05%** 1.07%** .98%** 1.02%** 4 10 (.36%) 1.61%* 1.29%* 1.44%** .93%** .68% .98% .85% .68% .74% 7 10 .98% 1.05%* 3.38%** 3.33%** 2.31%** 2.69%** 2.68%** 2.39%** 9.27%* 8.40%* 10 10 .92% 1.04%* .84% 1.26%** 1.34%** 1.09%** 1.05%** .77%* .55% .27% 1 11 1.20%* .79% .68% .82% .59% .24% (.13%) .10% .31% .08% 4 11 .82% .35% (.18%) (.87%)* (.20%) (.05%) (.14%) .03% (.02%) (.05%) 7 11 (2.26%)** (.35%) (.20%) (.17%) (.08%) (.12%) (.19%) (.12%) (.44%) (.31%) 10 11 1.12% 1.03% .73% .62% .70% .68% .60% .74%* .69%* .53% 1 12 (.34%) .41% .33% .42% .20% .14% .18% (.08%) (.08%) (.11%) 4 12 .90% .13% .15% .20% (.13%) (.32%) (.39%) (.33%) (.21%) (.24%) 7 12 .36% .01% (.00%) (.04%) (.04%) .00% .28% .33% .16% .27% 10 12 .03% (.40%) (.33%) (.07%) (.09%) (.29%) (.15%) (.05%) (.11%) (.02%) 1 13 1.62%** 1.26%* .64% .60% .55% .59% .52% .29% .25% .17% 4 13 .34% .28% .83% .87% .65% .61% .66% .78%* .77%* .42% 7 13 .96% .17% (.12%) .15% .19% .47% .23% .12% .19% .32% 10 13 .52% .70% 1.38%* .86% .17% .32% .57% .31% .43% .39% 1 14 1.90%** .04% .13% .42% (.13%) .22% (.10%) .05% .14% (.08%) 4 14 (1.14%)* (1.84%)** (.95%)* (1.07%)** (.86%)* (.95%)** (.95%)** (.72%)* (.49%) (.62%)* 7 14 (1.20%)* (.77%) (.63%) (.39%) (.20%) (.03%) (.18%) (.15%) .03% (.08%) 10 14 .02% .26% .28% .26% .20% .24% .02% .06% (.18%) (.39%) 1 15 1.28%* .61% 1.26%** 4.11%* 4.07%* 2.67%* 2.95%* 2.35%* 2.18%* .90%* 4 15 (.08%) .40% (.20%) (.63%) (.42%) (.33%) (.39%) (.68%)* (.63%)* (.63%)* 7 15 (.42%) (.17%) .13% .13% (.60%) (.65%) (.47%) (.63%)* (.62%) (.64%)* 10 15 (1.60%)** (.75%) (.35%) (.63%) (1.51%)** (1.26%)** (1.24%)** (1.27%)** (1.18%)** (1.24%)** Table VI presents the monthly compounded overperformance (or underperformance) of the market by portfolios based on a

strategy, which combines stocks which are momentum winners and are not paying dividend. The number in the top row represents the number of months the portfolio has been held, after composition. The data on the left represent the month the portfolio has been composed, after the evaluation period has ended.

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Graph X: Momentum and No Dividend Strategy – portfolio performance with a 12-month evaluation period.

Graph XIIV presents the monthly compounded performance of portfolios based on a strategy, which combines stocks which are momentum winners but which do not pay dividend. The market line is added to compare the portfolio performance to the market average. The vertical axis presents the performance as a percentage. The data on the horizontal axis represent the month the portfolio has been composed, after the evaluation period has ended. The number, which belongs to every different line, represents the number of months the portfolio has been held, after composition.

Graph XI: Momentum and No Dividend Strategy – portfolio outperformance of the market with a 12-month evaluation period.

Graph XIV presents the monthly compounded portfolio outperformance (underperformance) of the market based on a strategy, which combines stocks which are momentum winners but which do not pay dividend. The vertical axis presents the outperformance (underperformance) as a percentage. The data on the horizontal axis represent the month the portfolio has been composed, after the evaluation period has ended. The number, which belongs to every different line, represents the number of months the portfolio has been held, after composition.

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The portfolio, that outperforms the market the best, has an average monthly outperformance of 9.3 percent and the portfolio, that underperforms the market the most, has an average monthly return of 5.4 percent lower than the market. The worst performing portfolios are, as expected, in 2009, during the period of return reversal, however, outside 2009, the worst portfolio only underperforms the market by 2.9 percent on a monthly basis. However, in contrast to the findings in section 4 and section 5 of this paper, the no dividend winner portfolios actually underperform the market in 2015.

All different holding periods, in the long run, perform almost similar to the average monthly market return. The long run performance of these portfolios differs no more than .1 percent, from the average monthly market return, on a monthly basis. When the 2009 mean reversion is left out of the data, all different holding periods have positive findings in the long run, however do not differ more than .3 percent on a monthly basis from the average monthly market performance. There are no considerable differences between holding periods, besides the influence of transaction costs.

A disappointing finding is, that only 33.5 percent of the portfolios, after a 12-month

evaluation period, significantly differ from the market line and that half of these findings are negative. In Graph XII these findings are visualized, by correcting the findings in Graph XI for significance. Here you can see that the 2009 mean reversion holds, however, in the period prior to and following this mean reversion, the portfolio circles around the market line

showing no clear pattern. In 2015, when most effects of economic instability have

disappeared, the no dividend and momentum winners portfolios significantly underperform the market half of the time. The other half of the time the portfolios do not significantly differ from the market performance.

6.2.2 Dividend and momentum strategy

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Graph XII: Momentum and No Dividend Strategy – portfolio performance, corrected for significance, with a 12-month evaluation period.

Graph XV presents the monthly compounded performance of portfolios, corrected for significance, based on a strategy, which combines stocks which are momentum winners but which do not pay dividend. The market line is added to compare the portfolio performance to the market average. The vertical axis presents the performance as a percentage. The data on the horizontal axis represent the month the portfolio has been composed, after the evaluation period has ended. The number, which belongs to every different line, represents the number of months the portfolio has been held, after composition.

The portfolio, that outperforms the market the best, has an average monthly outperformance of 6.3 percent and the portfolio, that underperforms the market the most, has an average monthly return of 7.5 percent lower than the market. The worst performing portfolios are, as expected, in 2009, during the period of return reversal, however, outside 2009, the worst portfolio only underperforms the market by 2.5 percent on a monthly basis. The performance of the portfolios, based on a dividend and momentum strategy, is in most cases above the average market performance.