University Of Amsterdam Faculty of Economics & Business MSc: Finance Master Thesis Contrarian investing & investor attention Tom Hayje 10025332

July 2015 Supervisor: Philippe Versijp

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Statement of Originality This document is written by Student Tom Hayje who declares to take full responsibility for the contents of this document. I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it. The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

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Table of content

1. Introduction 3

2. Literature review 5

3. Data & Methodology 10 3.1 Data 10 3.2 Methodology 10 3.2.1 Portfolio formation process. 10 3.2.2 Attention proxies 11

4. Empirical results 13 4.1 Regular contrarian strategy 13 4.2 Abnormal trade volume strategy 14 4.3 Convexity and concavity of price patterns strategy 18 4.4 Extreme returns strategy 22 4.5 Results summarized 26

5. Conclusion 27

6. References 29

7. Appendix 31

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1. Introduction In certain financial theoretical frameworks and models, such as the capital asset pricing model, the agents involved and the asset prices set by these agents are assumed to be rational (Fama, 2003). In most financial contexts rationality is defined as: Investors update their beliefs correctly upon receiving news and they base their choices on maximizing their utility (Barberis, 2003). However, since there are still several phenomena in the financial markets which cannot be explained by the financial theories and models (Hirshleifer, 1998) it might be that perhaps in practice there it is not so easy to decide for individual investors about which actions are considered the most rational actions, and that in practice there are no perfectly rational investors (Hirshleifer, 2001). This approach to financial theory, in which not all agents are assumed to be fully rational, is referred to as behavioral finance (Barberis 2003) and it is a relatively new field of finance. In recent years behavioral finance has been used to research new problems in the financial markets and to provide a fresh perspective for older problems. Behavioral finance has been used to research a vast range of subjects; from trying to find out if investors trade too much ,what kind of stocks they trade to how individual investors react to news regarding the stock they are paying attention to. In this paper behavioral finance will also be used to tackle a relatively older financial phenomenon: The returns earned by contrarian investment strategies. To be more specific: the effect investor attention has on contrarian investment returns. Contrarian investing is an investment strategy in which the investors buys the stocks that have the relatively worst past performance and sells the stocks that have the relatively best past performance. Contrarian investing has been shown to regularly generate abnormal returns over the long term (Addea- Dappaah, 2009). These abnormal returns are an anomaly in the finance field since it uses past prices to predict future prices, which should not be possible according to the weak form of the efficient market hypothesis (Fama, 1965), and these returns should also eventually be corrected by arbitrage (Chen, 2014). Contrarian investing also works in markets beside, the American financial markets, so it can be ruled out that institutional factors are causing these returns (Schierek, 1999).

Investor attention is the particular behavioral aspect that is going to be used for this research. De Bondt & Thaler theorize that one potential explanatory factor for the abnormal contrarian returns are investors “overreacting” to news and dramatic events (De Bondt, 1985). Two papers regarding investor attention have recently been published (Barber, 2008) Chen, 2014). In the first of these two papers the authors concluded that investors generally tend to buy relatively more of the stocks that have caught their attention in some way (Barber, 2008). The other paper stated that investors cannot react to stocks that they are not paying attention to, and thus cannot overreact to news and events regarding these stocks (Chen, 2014). Thus, if overreactions are the cause for the excess returns earned by contrarian investing then most likely this overreaction effect will be stronger for stocks that receive a lot of attention since, as said before, investors generally purchase more stocks that have grabbed their attention. The theorized overreaction effect will also be smaller for the stocks that receive less attention, or those that nobody pays attention to. This particular subject is relevant because it researches a relatively older financial problem using a more recent theoretical approach. Only a few years ago the first paper dealing with the effect of investor attention on momentum investing was published, while the momentum investing phenomena has been around almost as long as contrarian investing. This research is also original because there currently are no papers combining the two subjects of contrarian investing and investor attention.

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The aim of this thesis is thus to research if investor attention has a significant effect on contrarian investing. The research question that needs to be answered is: Does investor attention have a significant effect on the returns of contrarian investing? To try and answer this question the thesis is set up as follows: First there will be a brief literature review in section two. After which the data used and methodology are described in section three. This section is followed by section four, which contains the empirical results from the tests performed. The paper ends with a quick summary of the entire paper and an answer to the research question, and suggestions for future research.

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2. Literature review In this section the most relevant papers that are used for this thesis research and are referenced throughout this paper are outlined briefly. The paragraph starts off with a brief review of some of the contrarian and investor attention research done so far. This is followed by a discussion of the results and conclusions from each paper. After which the papers their contribution to this research is explained.

Theoretical foundations One of the earliest papers on contrarian investing was published in 1985 and was written by De Bondt and Thaler. Although the word contrarian is not used in this paper the research tests the performance of buying the stocks that have performed the worst and selling the stocks that have performed the best, which is the main principle that contrarian investing is based on. The paper proposes that because not all investors are rational, investors will not update their beliefs according to Bayes’ rules and thus will potentially overreact to certain events. The paper then goes on to state that if stock prices tend to systematically overshoot then the reversals of these prices should be predictable using past data (De Bondt, 1985). To test their theory De Bondt & Thaler introduce two hypotheses: Extreme movements in stock prices will be followed by subsequent price movements in the opposite direction, and the more extreme the initial price movement, the greater will be the subsequent adjustment. Weak market efficiency is violated if either one of these hypotheses turns out to be true (De Bondt, 1985). To test whether these two hypotheses hold, the authors construct portfolios based on the past performance from the NYSE stocks between January 1926 and December 1982. These stocks are sorted based on their past excess returns, the top and bottom stocks are then put into “winners” and “losers” portfolios respectively. The average cumulative abnormal return (CAR) is then calculated for all the portfolios. If the two proposed hypotheses are true then the CAR from the loser’s portfolio minus the CAR from the winner’s portfolio should be above zero. (De Bondt, 1985) Since the abnormal returns that could potentially be achieved by de Bondt & Thaler’s strategy are in violation of the weak efficient market hypothesis (Fama, 1965) the contrarian strategy was going to be tested repeatedly under varying circumstances in order to determine the actual validity of these returns. One of these tests was done by Chan (Chan, 1988). Chan proposed that the returns from contrarian investing were not caused by an overreaction, but that the risks of the winner and loser stocks are not constant over time and if not accounted for causes measurement errors in the betas and could affect the estimation of the abnormal returns (Chen, 1988). After controlling for these possible risk changes and measurement errors, Chan concludes that the abnormal returns earned by contrarian investing are not as significant, and finds no evidence in support of market overreaction (Chan, 1988). A few years later however, the contrarian method was tested again by Lakonishok, Schleifer and Vishny (Lakonishok, 1994). Their research shows that contrarian investing significantly outperforms the market which is caused by investor behavior and not because the strategy is fundamentally riskier of a mismeasurement of risk (Lakonishok, 1994). The authors theorize that loser stocks outperform the winner stock because investors underestimate the future growth rates of loser stocks compared to the growth rates of winners stocks. 15 years later De Bondt again researches contrarian investing strategies, but this time the setting is the German stock market. Contrarian and momentum investment strategies are tested in the Frankfurt stock

6 exchange to test whether or not the results from previous research that was done in the American stock market were caused by institutional factors or a mismeasurement of risk (Schierek, 1999) This paper uses a similar method of constructing the loser and winner portfolios as the previous paper, with stocks being sorted based on the past excess returns over a certain period. In this paper however excess returns is defined in two ways: The first method defines excess returns as the abnormal returns cumulated over a certain period minus the market return while the second method subtracts compounded market return from the compounded abnormal return to calculate the excess return.

De Bondt & Thaler theorized that investors might be prone to overreacting to certain events, causing an “overreaction” effect. This overreaction effect is linked with investor psychology in a 1999 paper by Hirschleifer, Kent and Subrahmanyam. According to them the overreaction effect, which is also known as long-term reversals, is one of several anomalies that violate the efficient market hypothesis. The authors then introduce two models of two well-known behavioral biases and offer a few propositions which could explain these anomalies. The authors assume that investors are quasi-rational, which means that investors their over assessment of valid private information prohibits them for Bayesian optimizing (Hirshleifer, 1999) The two behavioral biases that are discussed in this paper are: Investor overconfidence and self- attribution bias. Investors are assumed to be overconfident since multiple psychological experiments have shown that individuals tend to overestimate their abilities, this is especially true for tasks which have delayed feedback and require some form of judgment. Stock selection and security trading usually have both of these aspects. Overconfident investors generally give more weight to their own valuations and have a lower estimate of their forecast variance (Hirshleifer, 1998). Self-attribution bias refers to the assumption that investors will react more heavily to public signals that confirm their private information than signals that disagree with the private information (Hirshleifer, 1998). In other words, investor confidence grows after confirming news while disagreeing news only decreases confidence slightly or no decrease at all. Hirshleifer (1998) and the others theorized several propositions based on their model, the propositions that could prove relevant for this thesis are listed below:

1. If investors are overconfident, then price moves resulting from private information arrival are on average partially reversed in the long run. 2. If investors are overconfident then price moves in reaction to the arrival of public information are positively correlated with later price changes. 3. If investors are overconfident, price changes are unconditionally negatively auto correlated at both short and long lags. 4. If investor confidence changes because of biased self-attribution, and if overreaction or correction is sufficiently gradual, then stock price changes exhibit unconditional short-lag positive autocorrelation (“momentum”) and long-lag negative autocorrelation (“reversal”). The previous paper discussed mentioned that investors in general tend to be overconfident and that this overconfidence does not decrease as easily as it increases. Another theorized effect of investor overconfidence is that the overall trading volume of stocks is higher than the optimal value. This theory is argued by Odean in his paper: “Do investors trade too much?” Odean theorizes that because investors are generally overconfident, they will overtrade too much and that this excess trading actually reduces overall

7 value (Odean, 1999). he decides to test this theory by investigating the trading habits of investors with a brokerage discount account since they don’t suffer from agency relationships (Odean, 1999). The author’s method of researching this theory is by testing whether this group of investors is able to cover their trading costs with the profits earned from trading. Also stock return patterns before and after asset purchases and sales are analyzed during varying time periods. Circa 9 years later Odean and Barber wrote an article together detailing the effects investor attention has on the trading habits of investors (Barber, 2008) Investors generally have a limited attention span, meaning that it is nearly impossible for them to be aware of every stock and its price changes. Because individual investors cannot observe all the available stock options, Barber & Odean theorize that investors looking to buy a stock will on average buy more of the stocks that have grabbed their attention somehow (Barber, 2008). The two authors test two hypotheses in their paper, the first hypothesis is that attention influences the buying habits of individual investors more than it affects the selling habits of individual investors. The second hypothesis is that attention affects the buying habits of individual investors more than the buying habits of institutional investors. To try and objectively measure attention, three measurable proxies are used: the abnormal daily trading volume, extreme one-day returns and appearances in the news. Trading volume is used as a proxy since the authors theorize that when significant news about stock has grabbed the attention of a lot of investors, this particular stock will have a higher trading volume than the usual (Barber, 2008). Extreme returns are used as a proxy since if a stock has extreme returns, negative or positive, the extreme returns themselves and the cause of these extreme returns will most likely not go unnoticed by the investing public and will thus grab the investor’s attention (Barber, 2008). The effect of attention on trading habits is combined with an investment strategy by Chen & Yu in 2014. Chen and Yu investigate the effects that investor attention has on the returns of momentum investing. To try and objectively measure attention the authors measure attention through a visual of the convexity or concavity of the price pattern of the stocks. Chen and Yu argue that since overreaction is potentially one of the factors that could cause the high returns of momentum strategies, then this overreaction effect should be stronger for attention stocks; since investors can only overreact to information about stocks they are paying attention to (Chen, 2014). Chen and Yu go on to explain that people are stimulated more by visual stimuli than raw numbers, which could indicate that stocks that have a rapidly decreasing/increasing price pattern will grab the most attention since these stocks are more visually distinctive than relatively constant price pattern (Chen, 2014). This visual attention measure is based on two aspects according to Chen and Yu: The price pattern of a stock will give the investor a verbal and an image code and thus generate a bigger reaction which will grab the investor’s attention more than reading about price changes (Chen, 2014). The second aspect is the law of continuity illusion; this illusion refers to the fact that if people see a price pattern continuously rising/falling then they will expect the price to rise or fall continuously since psychological research has shown that people have the tendency to expect patterns to follow established directions (Chen, 2014).

The following formula is regressed daily for each stock:

푃푖푡  t t ² In this formula the  symbol represents the convexity/concavity of the stock price, so it represents the visual price pattern of the stock. If this value is highly negative then the stock price pattern decreases

8 rapidly, while if it is highly positive then the stock price pattern is rapidly increasing (Chen, 2014). Chen and Yu then construct 9 different portfolios; all with varying levels of convexity/concavity based on the formation period, and will then be held for a certain period. The results & contributions The results of de Bondt & Thaler’s research from 1985 was consistent with their overreaction theory: in violation of Bayes’ rule most people “overreact” to unexpected and dramatic news events (De Bondt, 1985). Loser portfolios earn excess returns of approximately 19.6 percent, while winner portfolios have a negative excess return of 5.0 percent, which means that the market performed 5 percent better than the winner portfolios. Thus the loser minus winner portfolios would have a return of 24.6 percent and has a T- statistic of 2.20. Other findings would be that for loser portfolios the returns are much greater than for the winners, which would imply that the overreaction effect is asymmetrical and is larger for loser stocks (De Bondt, 1985). Secondly, there seems to be some sort of “January effect” present in the returns since most of the excess returns for the loser portfolios are realized in January (De Bondt, 1985). Most of the excess returns are also realized around 2 and 3 years after the formation date, this implies that the reversal effect has the largest effect on the long-term period (De Bondt, 1985). The paper by De Bondt and Thaler relates to this research paper because, as mentioned earlier in this section, it is one of the founding papers on contrarian investing and shows how investor reactions to certain events can influence the profitability of these kinds of strategies. It also contributes to this paper since its investment method is one of the foundations of this research. The results of the contrarian research done in Germany was quite similar to the 1985 done by De Bondt, despite taking place almost fifteen years later and in an entirely different setting (Schierek,1999), the authors go on to state that these results are not accounted for by factors such as risk, beta, or firm size (Schierek, 1999) and suggest that the explanations for these results might be found in the fields of human behavior and psychology (Schierek, 1999). The effects of human behavior and psychology on under and overreactions were researched by Hirschleifer, Kent and Subrahmanyam (Hirschleifer, 1998). The authors concluded that investors overreact to private signals and underreact to public signals and that positive return autocorrelations are the result of continued overreaction by investors, and that the overreaction is gradually reduced over time, causing the long-term reversals (Hirschleifer, 1998). This paper is relevant to the thesis research because it similarly tries to investigate the contrarian returns anomaly (reversals) through the perspective of behavioral finance. Another reason is that any results from the thesis research can be put into perspective using the explanations and models on the behavioral biases. The paper written by Odean in 1999 could prove useful for this thesis because the research shows that assets that are bought by investors tend to have a higher relative return change over a certain period than the assets sold by investors. Assets that have experienced relatively higher returns also are sold more on average. These results could imply that the relatively higher returns of contrarian investing are to be expected. Because assets that have experienced relatively higher returns get sold more on average, this coincides with the contrarian strategy where winner portfolios will be sold. The buying and selling tendencies of investors are also research by Barber & Odean, the main findings of their research is on average, investors are net-buyers of attention (Barber, 2008). Meaning that investors generally tend to buy more stocks that have grabbed their attention than they sell stocks that have

9 caught their attention, with investors sometimes buying approximately 29.45 percent more attention stocks than selling attention stocks for both the abnormal trading volume measure and the extreme one-day returns. Institutional investors are not affected as much by investor attention in their trades, because they have more time and resources to carefully select and monitor the optimal stocks for their portfolios. The attention effects are similar for small and large capitalization stocks (Barber, 2008), so there is no need to account for differences in firm sizes. This paper is relevant to this thesis research because it defines two of the three attention proxies that will be used for this thesis. It also provides a good theoretical background for the effect attention generally has on investors and their stock purchases which is a big part of this thesis research. A different kind of attention proxy was used to research the effects of investor attention on the returns of momentum investing. According to Chen and Yu, winner stocks that are highly convex receive a lot of attention and loser stocks that are highly concave receive a lot of attention. The authors (Chen, 2014) conjectured that a winner’s stock that has a highly convex price pattern will attract more attention since this creates the illusion that the stock’s price will continue on to rise, and thus this stock would receive more attention than a stock in which the price increase speed looks to be slower because it is less convex. The loser stocks that are highly concave have a price pattern that looks to decrease at an accelerated rate and this relatively higher price declining rate will make these particular loser stocks look more attractive (Chen, 2014) The momentum strategy where the winner stocks are highly convex and the loser stocks are highly concave yields an annual raw return of 17.46 percent whereas the conventional momentum strategy generated an annual raw return of 10.46 percent. This paper is thus somewhat similar to the research that will be done for this thesis, but there are a few key differences. The investment strategy for this thesis research is contrarian investing which is the opposite of the momentum strategy analyzed by Chen and Yu. Another difference is that Chen and Yu only use the visual price patterns to define attention, whereas this thesis research will use both the abnormal trading volume and extreme one-day returns from Barber & Odean’s 2008 paper and the visual price pattern as attention proxies. And the final difference is that Chen and Yu construct nine different long-short portfolios to measure the effects, this thesis research will only construct three portfolios: one affected by high attention sorting, one affected by low attention sorting and one regular contrarian investment portfolio. So, because this paper is similar to the thesis research its methods and theories could be used for this thesis research and the results could be useful in terms of comparison. Since momentum and contrarian investing are opposite strategies, it is interesting to see if the results will be the opposite as well.

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3. Data & Methodology This section discusses the data & methodology used for this thesis research.

3.1 Data The data used for this research are the daily and monthly stock information from the annually and quarterly updated CRSP database for the period starting from January 2004 up to and including December 2014, so the data used for this research has a timespan of 11 years. The variables from this database that will be used for this research are the following: Permno, daily share volume, daily returns, monthly returns and stock price. Permno is the identifier CRSP used to distinguish between individual companies in the database and allows it to be included in calculations. Daily share volume contains the number of shares traded on a specific date. Daily and monthly returns show the changes in daily and monthly returns and CRSP calculated these returns using the following calculation: ((푃2 / (푃1) -1) = return, where 푃1 represents price for the first observation and 푃2 the price for the second observation. Penny stocks are more susceptible to manipulation, have a few different regulations and are often trade infrequently and thus have reduced liquidity (U.S. Securities And Exchange Commission, 2013) so similar to Chen and Yu’s data, penny stocks will be excluded from the sample, which means that stocks with a price below 5 dollars are not included in the data (Chen, 2014). Contrarian returns are calculated by adding up the returns from the yearly winner portfolios to the returns from the yearly loser portfolios to form the yearly total portfolio return. The average yearly return for each contrarian strategy is calculated by taking the value weighted average of the sum for each yearly total portfolio return. The abnormal returns of each contrarian strategy are calculated by subtracting an average benchmark return from the average contrarian return. There are 3 benchmark indices for the period 2004- 2014 that have been acquired through the CRSP database. These indices are the : Value-weighted market portfolio, the equal-weighted market portfolio and the S&P composite index and table 21 from the appendix contains the relevant information from these indices.

3.2 Methodology To answer the research question of whether or not attention has a significant effect on contrarian returns, two hypotheses will be proposed for each attention strategy:

퐻0: µ푎 - µ푟 = 0 퐻1: µ푎 - µ푟 ≠ 0

Where µ푎 represents the average return for an attention-based contrarian strategy, which can be high or low attention, and µ푟 represents the average return for the regular contrarian strategy. The null hypothesis presumes that there is no significant difference between the average returns of regular and attention-based contrarian approaches. The alternative hypothesis proposes that the returns from regular and attention- based contrarian methods are significantly different.

3.2.1 Portfolio formation This section will elaborate on the process used to form the yearly contrarian portfolios. The portfolio formation process that will be used for this research is based on the method used by Sefton and Scowcroft (Sefton, 2004). While their paper was about momentum research, the formation methods for contrarian and momentum investing are based on the same principles, as evidenced in Schierek & De Bondt’s paper on both investment strategies (De Bondt, 1999). First the regular contrarian portfolio formation method will be

11 explained after which the attention-based contrarian portfolios will be discussed.

The following steps are taken to form each portfolio: 1. For each year of the 10 year sample, the yearly returns are ranked from high to low. 2. For each year, the companies with the ten percent of the highest returns(the winners) and the companies with the lowest ten percent of the returns(losers) are put into a portfolio.

The following three steps are taken to calculate the regular contrarian returns: 3. For each year, a short position is taken in the winner stocks and a long position in the loser stocks. 4. The returns for both the winner and loser stocks are then calculated by taking the returns from the following year. To state it in a formulaic way: Ret(X) = (L(X-1) - W(X-1) Where X represents the year, L represents loser returns and W represents winner return. W is negative because a short position is taken in the winner stocks. 5. The sum of all the yearly winner and loser returns for each year are calculated and then averaged to get the average regular contrarian return.

For the attention based strategies a few different steps will be taken after step 2: 5. The stocks that have been sorted into the yearly winner and loser groups are then ranked and sorted further into a portfolio of either the highest ten percent of the attention proxy or the lowest ten percent. The attention proxies are elaborated on in the following section. 6.. The returns for the stocks with the highest/lowest ten percent are then calculated by taking the returns for the following year. Similar as to the regular strategy the returns for winner stocks are the negative of the returns for the following year. 7. The sum of all the yearly attention based loser and winner’s returns are calculated and the average of this return is average attention based contrarian return.

3.2.2 Attention proxies In order to determine which stocks received the most amount of attention and which stocks received the least amount of attention, this paper will use three proxies as indicators for the amount of attention a certain stock has received. The three attention measures are: the abnormal trading volume of a stock, extreme one day returns and the convexity/concavity of the stock’s price pattern. This section will elaborate on each of the three attention proxies. Abnormal trading volume Abnormal trading volume refers to the daily abnormal trading volume. Barber and Odean (2008) theorized in their paper that stocks that are getting a relatively high amount of attention will also likely have a relatively higher trading volume. Abnormal trading volume is determined by comparing trading volume for a particular day with average trading volume of the previous trading year (Barber, 2008). Thus the formula for abnormal trading volume is:

(1) A푉푖푡 = 푉푖푡 / 푉푖푡

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In this formula, 푉푖푡 is the dollar trading volume for a particular stock (i) on a particular day (t) and 푉푖푡 is the average trading volume for the previous trading year, which is calculated using the following formula: 푉 (2) 푉 = ∑푡−1 푖푑 푖푡 푑=푡−252∗ 252 After calculating the abnormal trading volume for each particular stock, the stocks will then be sorted into ten portfolios based on the abnormal trading volume. Barber and Odean argue that because it is unlikely that the percentage of individual investors that make the purchasing trades are unlikely to cause abnormal trading volume that this particular attention proxy will not suffer from endogeneity issues (Barber, 2008). In their paper Barber and Odean explain that it is unlikely that the percentage of individual investors’ (or institutional investors’) trades that consists of purchases cause abnormal trading volume. This statement is proven by replicating the results using measures that are endogeneity resistant. Extreme one-day returns Extreme one-day returns are used as an attention proxy because daily returns that are either higher or lower than the average/usual daily returns are likely to grab an investor’s attention (Barber, 2008). This particular measure was also used by Barber and Odean in their 2008 paper. They stated that returns that are deemed extreme, either negative or positive, are likely to grab an investor’s attention through the extreme return itself or through a news story reporting the unusual return. The stocks that have experienced the most amounts of relatively extreme returns are then theorized to receive a relatively higher amount of attention than the other stocks. Returns are categorized as extreme returns when these returns can be considered extreme outliers. For each stock, returns are deemed extreme outliers when the returns are either lower than the value of the 1st quartile minus 3 times the interquartile range or higher than the value of the 3rd quartile plus 3 times the interquartile range. Price pattern convexity & concavity the third attention proxy tries to define attention through the pattern of a stock past price movements. This measure was created by Chen and Yu for their research on momentum investing and the effect of attention on the momentum returns. Chen and Yu argue that a stock’s price pattern that is highly convex will indicate that the stock received a lot of attention when it is a “winner” stock and the opposite for a “loser” stock. Whereas a highly concave price pattern for a “loser” stock represents a high amount of investor attention and a low amount of attention for a “winner” stock (Chen, 2014). To calculate the convexity or concavity of a stock’s price pattern the following ordinary least squares regression formula will be performed for each stock from the sample.

(3) 푃푖푡  t t² In this regression the convexity and concavity is represented by variable , positive values represent convexity and negative values represents a concave price pattern. After the stocks are sorted based on their past performance the stocks will be sorted further based on the value of its  to determine which loser and winners stocks scored the highest on the attention proxy used.

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4. Empirical results In this section the results of each contrarian strategy will be discussed. The regular contrarian strategy is discussed first. After this the results of the attention based contrarian strategies are examined. For each attention proxy there are two strategies: One in which the stocks are sorted further based on the highest attention measure and one in which the stocks are sorted further based on the lowest attention measure. Each section will provide a table that displays the yearly average returns earned by the top and bottom portfolios, the standard deviation and the total average return for the strategy. This section will conclude with a short summary of the results and possible explanations for these results. The details of the benchmark indices which these strategies are compared can be found in table 21 from the appendix. Table 22 in the appendix contains the results for every possible strategy comparison.

4.1 Regular contrarian strategy The regular contrarian approach is the first strategy to be discussed and it is one of the foundations of this research.

Table 1 Regular contrarian investment average returns Period: Top stocks Bottom stocks Combined N 2004-2005 -0,140738 0,071510 -0,069229 625 2005-2006 -0,189289 0,185933 -0,003357 627 2006-2007 -0,096511 0,002556 -0,093955 647 2007-2008 0,364586 -0,127714 0,236872 673 2008-2009 -0,119540 0,782508 0,662968 623 2009-2010 -0,324193 0,129409 -0,194785 554 2010-2011 -0,000870 -0,079246 -0,080116 593 2011-2012 -0,167065 0,200187 0,033121 613 2012-2013 -0,365479 0,234899 -0,130579 607 2013-2014 -0,106642 0,041355 -0,065287 631

Total: 0,017039 12366 Std dev: 0,487044 This table contains the average returns for the regular contrarian top and bottom performing stocks. N refers to the amount of observations for the top stocks and the bottom stocks individually. Std dev refers to the standard deviation of the strategy’s total return. The total average return is calculated by taking the sum of the combined average return multiplied by N and then dividing by this sum by the total amount of observations, which is 12366. The first year in the period column is the year in which the stocks were sorted, the second year is the year in which the returns were realized.

From this table we can see that the regular contrarian strategy earns an average return of approximately 1,70 percent a year. To see whether or not this return has outperformed the market it is compared to a benchmark market index to create the abnormal return. The results of the comparisons with the three benchmark indices are displayed in the table below:

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Table 2 Regular contrarian & benchmark comparisons

Benchmark index Excess ret 푵ퟏ 푵ퟐ t-value P(T > t) Value-weighted index 0,00966 12366 912308 2,2048 0,0137 Equal-weighted index 0,00908 12366 912308 2,0737 0,0191 S&P 500 composite index 0,01166 12366 912308 2,2048 0,0039

This table contains the results from the t-tests performed between the regular contrarian return and the returns from each of the three benchmark indices. 푁1 is the amount of observations for the regular strategy and 푁2 refers to the amount of observations for the particular benchmark index. The T-Value shows the t-score obtained by performing the t-test and P(T>t) shows the accompanying p-values for a one-sided t-test.

As you can see in table 2, the regular contrarian strategy outperforms the benchmark indices by approximately 0,97 percent, 0,91 percent, and 1,17 percent respectively. The t-values from table 2 also indicate that all three of the abnormal returns earned by this strategy are significant at the five percent level, and one of these returns is significant at the one percent level. This level of significance is also confirmed by the low P-values. The t-values for this strategy are similar to the t-values for the contrarian strategies performed in Germany by De Bondt and Thaler (De Bondt, 1985). In their 1985 paper, the t-statistic for buying losers and selling winners earned almost an average of 5 percent but the accompanying t-statistic was also around the 2,20 value which meant it was not statistically significant at the 99 or 98 percent level. This research its contrarian results differ slightly from the contrarian returns that were achieved in the paper by Addea-Dapaah and Peiying where the returns of 0,048 percent were significant at the 99 percent level (Addea,2009)

4.2 Abnormal trading volume strategy The abnormal trading volume is a regular contrarian strategy where the top and bottom performing stocks are sorted further based on their abnormal trading volume.

High abnormal trading volume strategy The returns from the strategy where the winners and losers with the highest abnormal trading volume are sorted further are displayed in table 3 below:

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Table 3 High abnormal trading volume contrarian returns Period: Top stocks Bottom stocks Combined N 2004-2005 -0,214220 0,127816 -0,086404 62 2005-2006 -0,193743 0,139367 -0,054376 63 2006-2007 -0,108677 -0,027765 -0,136442 65 2007-2008 0,357722 -0,222096 0,135626 66 2008-2009 0,084630 0,886192 0,970822 62 2009-2010 -0,109305 -0,087114 -0,196420 55 2010-2011 0,066842 -0,04 0,026842 59 2011-2012 -0,217983 0,141435 - 0,076548 61 2012-2013 -0,351899 0,309967 - 0,041932 61 2013-2014 -0,260115 0,091427 -0,168688 63

Total: 0,019787 1234 Std dev: 0,547066 This table contains the average returns for the high abnormal volume contrarian top and bottom performing stocks. N refers to the amount of observations for the top stocks and the bottom stocks individually. Std dev refers to the standard deviation of the strategy’s total return. The total average return is calculated by taking the sum of the combined average return multiplied by N and then dividing by this sum by the total amount of observations, which is 1234. The first year in the period column is the year in which the stocks were sorted, the second year is the year in which the returns were realized.

The returns from the attention-based strategy have an average of around 1,98 percent. This is only 1,15 times as high as the regular contrarian average return. The standard deviations of the two strategies however differ quite much, with the high abnormal trading volume strategy’s standard deviation being almost twelve percent higher. Table 4 compares the high abnormal trade volume return with the benchmark indices to get the excess returns. The first thing of note is that while the excess returns from this strategy are higher than the ones from the regular strategy, its t-values are actually lower. The lower t-statistic could be explained by the higher standard deviation for the attention strategy or by the considerably lower amount of observations. The lower t-statistic contrasts with the results form Chen and Yu’s paper, where the high attention-based momentum strategy generated a higher return and a higher a t-value (Chen, 2014).

Table 4 High abnormal trading volume & benchmark comparisons

Benchmark index: Excess ret 푵ퟏ 푵ퟐ t-value P(T > t) Value-weighted index 0,01240 1234 912308 0,7965 0,2129 Equal-weighted index 0,01183 1234 912308 0,7596 0,2239 S&P 500 composite index 0,01441 1234 912308 0,9254 0,1774

This table contains the results from the t-tests performed between the high abnormal trading volume contrarian return with the returns from each of the three benchmark indices. 푁1 is the amount of observations for the regular strategy and 푁2 refers to the amount of observations for the particular benchmark index. The T-Value shows the t-score obtained by performing a t-test and P(T>t) shows the accompanying one-sided p-values for the t-values.

Table 5 displays the comparison between the regular contrarian strategy and the high abnormal trading

16 volume strategy. Here it can be seen that the number of observations are very different. The t-test performed on the differences between the two means is not statistically significant at the five percent level for both one-sided and two-sided tests. Again this results contrasts with Chen and Yu’s paper, where the difference between the regular and high attention strategy was significant at the one percent level for a two- sided test (Chen, 2014). These numbers are also not in line with the results from a different paper on price and earnings momentum by Hou, Peng and Xiong. They researched the effects of investor attention, using trading volume as a proxy, on the returns for price and earnings momentum. The authors concluded that price momentum was actually higher for high volume stocks (Hou, 2008). The outcome for the tests performed in table 5 are confirmed by Barber & Odean . They conclude that their attention-driven buying patterns are not capable of generating superior returns (Barber, 2008). Thus a contrarian strategy that is based one of their attention proxies, high abnormal trading volume, is not able to generate a return that is superior to a regular contrarian’s return. The null hypothesis is not rejected for this particular strategy. Table 5 High abnormal volume & regular contrarian compared Strategy: Return 푵 t-value P(T > t) P(|T| > |t|) High abnormal volume 0,019787 1234 Regular contrarian 0,017039 12366 0,7965 0,4326 0,8651

This table contains the results from the t-test performed between the high abnormal trading volume contrarian return and the regular contrarian return. N is the amount of observations for each strategy. The T-Value shows the t-score obtained by from the t-test. P(T>t) shows the accompanying one-sided p-values for the t-value while P(|T| > |t|) shows the p-value for a two-sided t- test.

Low abnormal trading volume strategy The next table displays the return from the strategy where the winners and losers with the lowest abnormal trading volume are sorted further:

Table 6 Low abnormal trading volume contrarian returns Period Top stocks Bottom stocks Combined N 2004-2005 -0,132563 0,107599 -0,024964 62 2005-2006 -0,194624 0,247081 0,052457 63 2006-2007 -0,142257 0,098926 -0,043332 65 2007-2008 0,208005 -0,027694 0,180311 66 2008-2009 -0,285576 0,610744 0,325168 62 2009-2010 -0,521078 -0,082732 -0,403539 55 2010-2011 -0,036319 0,181546 0,119051 59 2011-2012 -0,001628 0,029959 0,033144 61 2012-2013 -0,526797 0,309967 - 0,496839 61 2013-2014 -0,221365 -0,070936 -0,292301 63

Total: -0,0364 1234 Std dev: 0,512511

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This table contains the average returns for the low abnormal volume contrarian top and bottom performing stocks. N refers to the amount of observations for the top stocks and the bottom stocks individually. Period represents the year in which the stocks were sorted and the year the returns were realized. Std dev refers to the standard deviation of the strategy’s total return. The total average return is calculated by multiplying the combined average return with N and multiplying by the total amount of observations, which is 1234.

This particular contrarian strategy does not seem to yield positive returns. According to table 6, basing a contrarian strategy around the winner and loser stocks with the lowest abnormal trading volume will earn an average loss of nearly 3,64 percent. While this method has a much lower return than the earlier two strategies, its standard deviation is similar, thus the returns for this strategy are not necessarily more spread out than the earlier two strategies. The lower return for the low attention strategy confirms the expectations from Chen & Yu’s paper (Chen, 2014) in which lower attention stocks yield lower returns.

Table 7 Low abnormal trading volume & benchmark comparisons

Benchmark index: Excess ret 푵ퟏ 푵ퟐ t-value P(T < t) Value-weighted index -0,04378 1234 912308 -2,9352 0,0014 Equal-weighted index -0,04436 1234 912308 -2,9754 0,0012 S&P 500 composite index -0,04177 1234 912308 -2,8023 0,0021

This table contains the results from the t-tests performed between the high abnormal trading volume contrarian return and the returns from each of the three benchmark indices. 푁1 is the amount of observations for the regular strategy and 푁2 refers to the amount of observations for the particular benchmark index. The T-Value shows the t-score obtained by performing a t-test and P(T < t) shows the accompanying one-sided p-values for the t-value.

The table depicted above contains the excess returns for the low attention strategy. All three excess returns for this strategy are statistically lower than zero at the 5 percent level. This would lead to the conclusion that this is not a very profitable strategy. These results are similar to Chen and Yu’s results where the low attention strategy has a lower t-value than the regular and high attention strategies (Chen, 2014). However, the results differ in the fact that the low attention momentum strategy did not earn a negative return(Chen, 2014). To see how the low abnormal strategy fares against the regular strategy table 8 is consulted. The t-test performed on the difference between the two means produces a t-value of -2,6551. This would mean that the returns from the two strategies are significantly different at the 99,9 percent level. The low attention counterpart from the momentum research also has a negative return when compared to the original strategy (Chen, 2014). The t-values from the t-test between the two average returns are also statistically significant, with a t-value of -4,54 (Chen, 2014). The lower t-value for the low attention contrarian strategy could indicate that the difference in regular and low attention return is not as extreme as the difference in regular and low attention momentum. For this particular strategy, the null hypothesis is rejected in favor of the alternative hypothesis. A possible explanation for this significantly different result could be that the low abnormal trading volume proxy negatively affected the strategy’s return. According to a paper on trading volume return premiums (Gervais, 2001), stocks that had a particularly low trading volume during a certain period continue to depreciate for the following period. This negative low trading volume premium could have been large enough to negate any high-attention contrarian return premiums. This paper also mentions the

18 fact that volume shocks tend to affect past losers more (Gervais, 2001), thus any negative volume premiums would have a larger effect on a strategy that focuses on purchasing past losers.

Table 8 Low abnormal volume & regular contrarian compared Strategy: Return 푵 t-value P(T < t) P(|T| > |t|) Low abnormal volume -0,0364 1234 Regular contrarian 0,017039 12366 -2,6551 0,0002 0,0005

This table contains the results from the t-test performed between the low abnormal trading volume contrarian return and the regular contrarian return. N is the amount of observations for each strategy. The T-Value shows the t-score obtained by from the t-test. P(T < t) shows the accompanying one-sided p-values for the t-value while P(|T| > |t|) shows the p-value for a two-sided t- test.

The comparisons between the effect of attention on both contrarian and momentum returns so far seem to suggest that attention, when measured using abnormal trading volume, has the opposite effect on the returns of contrarian investing compared to the returns of momentum investing. Where momentum returns, have a high attention based strategy with a higher return and a higher t-value compared to its original counterpart, the contrarian returns have a lower t-value than its regular counterpart. Additionally the low attention based contrarian strategy produces a higher absolute t-value than the high attention based contrarian strategy, while the reverse happens for momentum attention strategies. There is some form of precedent for this, in a paper on contrarian strategies in the London Stock Exchange (Antoniou, 2006) the authors excluded stocks that were traded infrequently from the sample and as a result average returns decreased for most stock sizes along with increases in absolute t-values (Antoniou, 2006). Stocks that are traded infrequently could be considered as stocks that have received the least amount of attention according to Barber and Odean (Barber, 2008)

4.3 Convexity and concavity of price patterns strategy The convexity and concavity strategy is the strategy where stocks will be sorted based on the convexity or concavity of their price pattern. Winner stocks that have a highly convex price pattern are considered stocks that have received a lot of attention, while loser stocks that have received a lot of attention will have a highly negative concave price pattern. As with the other two attention proxies, this section will include the results of a contrarian strategy with high attention stocks, as defined by the convexity or concavity of the price pattern, and one with low attention stocks. Highly convex and highly negative concave trading strategy (high attention)

The returns from this particular strategy are displayed in the table below:

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Table 9 High attention price convexity/concavity contrarian returns Period Top stocks Bottom stocks Combined N 2004-2005 -0,139487 0,144755 0,005268 62 2005-2006 -0,192647 0,191811 -0,000836 63 2006-2007 -0,222186 0,075985 -0,146201 65 2007-2008 0,485884 -0,159616 0,326268 66 2008-2009 -0,053645 0,829434 0,775789 62 2009-2010 -0,172641 -0,072464 -0,245104 55 2010-2011 0,041041 -0,145777 -0,104736 59 2011-2012 -0,120516 0,131411 0,010895 61 2012-2013 -0,239927 0,103175 - 0,136752 61 2013-2014 -0,152816 0,040059 -0,112757 63

Total: 0,021039 1234 Std dev: 0,538028 This table contains the average returns for the high attention price convexity/concavity contrarian top and bottom performing stocks. N refers to the amount of observations for both the top stocks and the bottom stocks. Period represents the year in which the stocks were sorted and the year the returns were realized. Std dev refers to the standard deviation of the strategy’s total return. The total average return is calculated by taking the sum of the combined average return multiplied by N and then dividing by this sum by the total amount of observations, which is 1234.

The average return for this strategy is a bit higher than the regular contrarian return, and slightly higher than the high attention abnormal trading volume strategy. Using this particular strategy to invest would seem to grant the investor a return of approximately 2.1 percent on the investment. Compared to the regular contrarian method, this strategy has more risk involved, but it is less risky than the high abnormal volume approach. The next table depicts the excess returns for the high attention convex and concave method:

Table 10 High attention price convexity/concavity & benchmark comparisons

Benchmark index: Excess ret 푵ퟏ 푵ퟐ t-value P(T > t) Value-weighted index 0,01366 1234 912308 0,8916 0,1863 Equal-weighted index 0,01308 1234 912308 0,8542 0,1967 S&P 500 composite index 0,01566 1234 912308 1,0227 0,1532

This table contains the results from the t-tests performed between the high attention price convexity/concavity contrarian return and the returns from each of the three benchmark indices. 푁1 is the amount of observations for the regular strategy and 푁2 refers to the amount of observations for the particular benchmark index. The T-Value shows the t-score obtained by performing a t-test and P(T > t) shows the accompanying one-sided p-values for the t-value.

According to the table displayed above, a contrarian strategy where the winner stocks are sorted further based on how convex their price patterns are and the loser stocks are sorted further based on the concavity of the price patterns, does not grant the investor significant excess returns. All three t-values are too low to be able to say that the excess returns are statistically different from zero. These results contradict the ones from Chen and Yu. In their paper the strategy with convex winners and concave losers not only yielded the

20 highest returns out of all the strategies, but also was highly significant with a t-value of 6,56 (Chen, 2014). The outcomes of this particular approach are however similar to the previous high attention strategy where the stocks were sorted further based on high abnormal trading volume. For both the high abnormal trading volume and the convex winners/concave losers strategy the returns were not significantly different from zero and both strategies had comparable standard deviations that were higher than the regular contrarian standard deviation. As can be seen in the appendix these two strategies do not differ much from each other, with a t-test producing a t-value of only 0,057.

Table 11 High attention price convexity/concavity & regular contrarian compared Strategy: Return 푵 t-value P(T > t) P(|T| > |t|) High attention price pattern 0,021039 1234 Regular contrarian 0,017039 12366 0,2511 0,4009 0,8018

This table contains the results from the t-test performed between the high attention price convexity/concavity contrarian return and the regular contrarian return. N is the amount of observations for each strategy. The T-Value shows the t-score obtained by from the t-test. P(T > t) shows the accompanying one-sided p-values for the t-value while P(|T| > |t|) shows the p-value for a two-sided t-test. The payoff for this approach is also not significantly different from the regular contrarian methods as indicated by table 11. Its P-value of 0,8018 makes it very likely that the alternative hypothesis, that high attention contrarian returns are different from regular contrarian returns, should be rejected. High concave and low convex trading strategy (low attention

Table 12 Low attention price convexity/concavity contrarian returns Period Top stocks Bottom stocks Combined N 2004-2005 -0,143585 0,083081 -0,060505 62 2005-2006 -0,098432 0,100742 0,002310 63 2006-2007 0,056683 0,001316 0,057999 65 2007-2008 0,531739 -0,239282 0,292457 66 2008-2009 0,286598 0,763253 1,049852 62 2009-2010 -0,295769 -0,072464 -0,220552 55 2010-2011 -0,021505 0,075217 -0,137806 59 2011-2012 -0,085440 0,157831 0,072391 61 2012-2013 -0,351063 0,300001 -0,051062 61 2013-2014 -0,011296 -0,03255 -0,043850 63

Total: 0,05092 1234 Std dev: 0,501792 This table contains the average returns for the low attention price convexity/concavity contrarian top and bottom performing stocks. N refers to the amount of observations for both the top stocks and the bottom stocks. Period represents the year in which the stocks were sorted and the year the returns were realized. Std dev refers to the standard deviation of the strategy’s total return. The total average return is calculated by taking the sum of the combined average return multiplied by N and then dividing by this sum by the total amount of observations, which is 1234.

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Table 12 depicted above exhibits the returns from the low attention price pattern method. It notably has the highest return of all the strategies discussed so far, which is in stark contrast to the momentum results from Chen and Yu’s paper where the low attention returns are lower than the regular and high attention returns (Chen, 2014). A comparable kind of result can be found in the paper by Hou, Peng and Xiong, where the earnings momentum were higher for the stocks that received relatively less attention (Hou 2008). Although in terms of price momentum the results for this strategy the results do contrast with Hou’s results. The standard deviation of the returns is also considerably lower than most of the previous strategies that have been done so far, with the regular contrarian method being the only exception. Whereas the low attention abnormal volume method yielded a negative average return, this version of a low attention approach surprisingly has a very high average return of almost 5,1 percent. The next table shows how this low attention strategy fares against the market benchmarks:

Table 13 Low attention price convexity/concavity & benchmark comparisons

Benchmark index: Excess ret 푵ퟏ 푵ퟐ t-value P(T > t) Value-weighted index 0,04354 1234 912308 3,0478 0,0012 Equally-weighted index 0,04296 1234 912308 3,0077 0,0013 S&P 500 composite index 0,04554 1234 912308 3,1884 0,0007

This table contains the results from the t-tests performed between the low attention price convexity/concavity contrarian return and the returns from each of the three benchmark indices. 푁1 is the amount of observations for the regular strategy and 푁2 refers to the amount of observations for the particular benchmark index. The T-Value shows the t-score obtained by performing a t-test and P(T > t) shows the accompanying one-sided p-values for the t-value.

As expected based on the average return that this strategy yielded, the t-values of the low attention price pattern strategy seem to indicate that the strategy significantly outperform the benchmark indices. Again the results are the opposite of the momentum paper (Chen, 2014). In that paper the low attention strategy also has a statistically significant return at the 99 percent level, but the low attention momentum strategy does not outperform both the regular and the high attention contrarian strategies, while this low attention contrarian strategy does outperform the regular and high attention methods.

Table 14 Low attention price convexity/concavity & regular contrarian compared Strategy: Return 푵 t-value P(T > t) P(|T| > |t|) Low attention price pattern 0,05092 1234 Regular contrarian 0,017039 12366 2,2677 0,0117 0,0235

This table contains the results from the t-test performed between the high attention price convexity/concavity contrarian return and the regular contrarian return. N is the amount of observations for each strategy. The T-Value shows the t-score obtained by from the t-test. P(T > t) shows the accompanying one-sided p-values for the t-value while P(|T| > |t|) shows the p-value for a two-sided t-test. Table 14 reports that the low attention price pattern method is significantly different from the regular contrarian approach at the five percent level. The high t-value and low P-values lead to the conclusion that for this strategy the null hypothesis should be rejected in favor of the alternative hypothesis. A possible explanation for this superior return could be that investors are more likely to have a biased valuation when valuating stocks for which not a lot of of information is available (Hirshleifer, 2001). Thus

22 for the low-attention stocks the investor misperceptions are the highest (Hirshleifer, 2001), which can possibly allow this particular low attention strategy to generate such superior returns. In the appendix table 22 it can be seen that this strategy outperforms all the high attention strategies, however the differences are only significant at the ten percent level. The two low attention approaches discussed so far have yielded highly different results, with the P value of the t-test done of the two returns producing a value that shows the difference in returns is significant 99,9 percent level with a P-value of 0,000005. Thus so far the effects of low attention on the returns of contrarian investing have yielded mixed results.

4.4 Extreme returns strategy In the extreme return strategies, stocks will be further sorted based on the relative amount of extreme returns a particular stock had during the year. Barber and Odean (Barber, 2008) theorized that stocks that have returns that are unusual will catch more investor attention than stocks that have less extreme returns or stocks that have no extreme returns. The first strategy of this section will be about the stocks that have the highest relative amount of extreme returns and the second strategy will detail the results of the stocks with the lowest relative amount of extreme returns.

High attention extreme returns strategy Table 15 High extreme contrarian returns Period Top stocks Bottom stocks Combined N 2004-2005 0,053422 -0,117620 -0,064198 62 2005-2006 -0,071877 0,065082 -0,006794 63 2006-2007 -0,007901 -0,155050 -0,162951 65 2007-2008 0,258875 -0,653231 -0,394355 66 2008-2009 -0,175330 0,941090 0,765760 62 2009-2010 -0,163880 0,175686 0,011805 55 2010-2011 0,116363 -0,209834 -0,093471 59 2011-2012 -0,016778 0,045363 0,028585 61 2012-2013 -0,140832 0,480141 0,339309 61 2013-2014 -0,047007 0,023494 -0,023513 63

Total: 0,018269 1234 Std dev: 0,612708 This table contains the average returns for the High extreme returns contrarian top and bottom performing stocks. N refers to the amount of observations for both the top stocks and the bottom stocks. Period represents the year in which the stocks were sorted and the year the returns were realized. Std dev refers to the standard deviation of the strategy’s total return. The total average return is calculated by taking the sum of the combined average return multiplied by N and then dividing by this sum by the total amount of observations, which is 1234.

The above table contains the results of the high attention extreme returns strategy. With a return of approximately 1,83 percent this strategy is the third least profitable strategy of all the strategies that have been discussed, with only the low abnormal trading volume and the regular contrarian strategies earning a lower return. The relatively low returns combined with its relatively high standard deviation make this

23 particular sorting method a poor choice compared to most the alternatives offered in this paper. How the high extreme returns hold up against the benchmark indices is displayed in the next table:

Table 16 High extreme contrarian & benchmark comparisons

Benchmark index: Excess ret 푵ퟏ 푵ퟐ t-value P(T > t) Value-weighted index 0,01089 1234 912308 0,6196 0,2678 Equally-weighted index 0,01031 1234 912308 0,5869 0,2787 S&P 500 composite index 0,01289 1234 912308 0,7388 0,2315

This table contains the results from the t-tests performed between the High extreme contrarian return and the returns from each of the three benchmark indices. 푁1 is the amount of observations for the regular strategy and 푁2 refers to the amount of observations for the particular benchmark index. The T-Value shows the t-score obtained by performing a t-test and P(T > t) shows the accompanying one-sided p-values for the t-value.

The results from the table do not leave much room for discussion, this particular strategy does not grant the investor abnormal returns that are statistically different from zero. All three p values are above 0,2 which indicates the returns are not significant at the twenty percent level. The results for the high attention sorting methods continue to contrast with related literature (Chen, 2014) (Hou, 2008), with this third and final high attention strategy also having lower t-values than the regular approach. From the next table it can also be seen that this strategy is not significantly different from the regular contrarian method. The resulting t-test between the two average returns produces a low t-value of 0,0694 with an accompanying one-sided p-value of 0,4791 and that indicates that the null hypothesis should not be rejected. As mentioned earlier in this section this means that all three of the high attention strategies tested did not manage to achieve superior returns compared to the regular approach. This could also be explained by the fact that the attention proxies developed by barber & Odean (Barber, 2008) are not capable of generating superior returns. Table 22 in the appendix shows the comparison between the high extreme returns strategy with all the other attention strategies and the regular contrarian method.

Table 17 High extreme & regular contrarian compared Strategy: Return 푵 t-value P(T > t) P(|T| > |t|) High extreme 0,018269 1234 Regular contrarian 0,017039 12366 0,0694 0,4729 0,9459

This table contains the results from the t-test performed between the high extreme contrarian return and the regular contrarian return. N is the amount of observations for each strategy. The T-Value shows the t-score obtained by from the t-test. P(T > t) shows the accompanying one-sided p-values for the t-value while P(|T| > |t|) shows the p-value for a two-sided t-test.

Low attention extreme returns strategy The final strategy discussed in this paper is the extreme returns strategy with the lowest amount of attention, and its results are displayed in the following table:

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Table 18 Low extreme contrarian returns Period Top stocks Bottom stocks Combined N 2004-2005 -0,165878 0,031699 -0,134179 62 2005-2006 -0,146278 0,162728 0,016450 63 2006-2007 -0,057942 -0,05556 -0,113507 65 2007-2008 0,668196 -0,1243 -0,113507 66 2008-2009 -0,021587 0,872909 0,851322 62 2009-2010 -0,268459 0,103526 -0,164933 55 2010-2011 -0,018515 -0,054737 -0,073253 59 2011-2012 -0,141964 0,197486 0,055522 61 2012-2013 -0,339673 0,291414 -0,048259 61 2013-2014 -0,108211 -0,034232 -0,142443 63

Total: 0,042216 1234 Std dev: 0,469347 This table contains the average returns for the low extreme returns contrarian top and bottom performing stocks. N refers to the amount of observations for both the top stocks and the bottom stocks. Period represents the year in which the stocks were sorted and the year the returns were realized. Std dev refers to the standard deviation of the strategy’s total return. The total average return is calculated by taking the sum of the combined average return multiplied by N and then dividing by this sum by the total amount of observations, which is 1234.

This strategy seems to perform much better than its high attention counterpart, with its return being almost 2.5 times higher. The average return of 4,22 percent is one of the highest out of all discussed strategies. Similar to the previous low attention strategy that was discussed, the results of this particular strategy contrast somewhat to Hou’s (Hou, 2008) results in terms of price momentum, and they contrast fully to Chen’s (Chen, 2014) results on momentum investing.

Table 19 Low extreme contrarian & benchmark comparisons

Benchmark index: Excess ret 푵ퟏ 푵ퟐ t-value P(T > t) Value-weighted index 0,03483 1234 912308 2,6071 0,0046 Equally-weighted index 0,03426 1234 912308 2,5641 0,0052 S&P 500 composite index 0,03684 1234 912308 2,7573 0,003

This table contains the results from the t-tests performed between the low extreme contrarian return and the returns from each of the three benchmark indices. 푁1 is the amount of observations for the regular strategy and 푁2 refers to the amount of observations for the particular benchmark index. The T-Value shows the t-score obtained by performing a t-test and P(T > t) shows the accompanying one-sided p-values for the t-value.

The benchmark comparisons are reported in table 19. The t-values and one-sided p-values, which range from 2,56 to 2,75 and 0,003 to 0,0052, are all in full support rejecting the idea that these excess returns are statistically equal to zero. In terms of raw returns this strategy seems to perform much better than the market, since its average return is notably higher than the returns offered by the market through its benchmark indices. This is the second low attention strategy that manages to outperform the market, with the low attention price pattern strategy being the first.

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The next table shows how this method compares to the regular contrarian strategy:

Table 20 High extreme & regular contrarian compared Strategy: Return 푵 t-value P(T > t) P(|T| > |t|) High extreme 0,042216 1234 Regular contrarian 0,017039 12366 1,7906 0,0368 0,0736

This table contains the results from the t-test performed between the low extreme contrarian return and the regular contrarian return. N is the amount of observations for each strategy. The T-Value shows the t-score obtained by from the t-test. P(T > t) shows the accompanying one-sided p-values for the t-value while P(|T| > |t|) shows the p-value for a two-sided t-test.

The low attention extreme returns strategy seems to outperform the regular method when considering the returns and the difference in returns is large enough to consider it a significantly better performance. The strategy is significantly larger at the five percent level, and the strategy is significantly different at the ten percent level when a two-sided t-test is done. The ten percent level however is not quite high enough to conclude that the alternative hypothesis should hold on a consistent basis. So it cannot be stated with absolute certainty that this particular attention proxy has a significant different effect on the returns of contrarian investing. The null hypothesis can only be rejected if a one-sided hypothesis is considered. As with the previous low attention strategy, this particular strategy could have outperformed the regular contrarian method because investors have a lot more misconceptions about low attention stocks, which clouds their valuations (Hirshleifer, 2001). These misconceptions about the low-attention stocks could have caused this low attention strategy to do better than its regular contrarian counterparty.

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4.5 Results summarized In this section the results from all the strategies and possible explanations for these results will be briefly summarized. [Insert table 22]

In the appendix table 22 displays the comparisons between each strategy discussed in this paper. The strategies are numbered from 1 to 7, with the numbers representing the order in which they are discussed in this paper, with the regular contrarian approach being number 1, and so forth. Throughout this paper seven different contrarian strategies are discussed and tested; one regular, three high attention and three low attention strategies. The regular strategy earned an average return of around 1,70 percent and its abnormal returns were all statistically significant. All three high attention strategies earned slightly higher returns than the regular one with the average returns being 1,97, 2,1 and 1,82 percent. However, not one of the three high attention approaches managed to significantly outperform the regular contrarian strategy The t-values for the three strategies ranged from around 0,07 to 0,25 and this means these excess returns cannot be considered significantly different from the regular method. All three attention proxies thus have a similar effect on the returns on contrarian investing when sorted for high attention. Possible explanations for these insignificant high attention results could be explained by the fact that according to Barber & Odean, attention-driven buying cannot generate superior returns on its own (Barber, 2008), which would mean that buying based on attention alone does not grant the investor significant excess returns. Thus attention-driven contrarian strategies would not generate a return that is superior to the regular contrarian, since attention-driven purchasing does not add significant superior returns. The low attention strategies however have more mixed results. The first of the low attention methods, which is based on a low trading volume attention proxy has a negative effect on the returns, with this strategy earning a negative return of approximately -3,1 percent which is statistically different from the regular approach. This negative difference could be explained by Gervais’s negative trading volume premium combined with volume shocks being stronger for loser stocks (Gervais, 2001) The second approach has a positive effect on the returns, this strategy performed the best of all the strategies discussed with an average return of 5, 1 percent and is also significantly different from the regular method at the five percent level, indicated by its two-sided p-value of 0,0235. The third low attention strategy however, while having a relatively high return of 4,22 percent and a relatively high t- score of 1,7906, only differs significantly from the regular contrarian method at the five percent level when a one-sided hypothesis is considered. For a two-sided hypothesis the difference has a P-value of 0,0736, which is not significant at the five percent level. These two positive differences could potentially be caused by the common misperceptions investors have about low-attention stocks (Hirshleifer, 2001), which could give these two low attention strategies better circumstances to produce superior returns than the regular contrarian method.

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5. Conclusion The purpose of this research paper was to answer the question of: Does investor attention have a significant effect on the returns of contrarian investing? Here contrarian investing is defined as buying the stocks that have relatively performed the worst and selling the stocks that have relatively performed the best. This particular investment method has generated significant excess returns which are potentially caused by investor overreactions to news or events regarding the stock market. Investor attention refers to the fact that investors only have a limited attention span, and because of this cannot pay attention to every stock on the market. Because of this attention scarcity investors are more likely to purchase the stocks that have grabbed their attention in some form. Stocks that receive a relatively higher amount of attention are referred to as attention stocks If overreaction is the cause of the high contrarian returns, then these returns should be higher for attention stocks, and an attention-based contrarian strategy should, in theory at least, have a larger overreaction effect. To test this theory, the following two hypotheses were constructed:

퐻0: µ푎 - µ푟 = 0 퐻1: µ푎 - µ푟 ≠ 0

Furthermore, to test these hypotheses, seven different contrarian portfolios were constructed; one regular, three high attention and three low attention portfolios. The attention portfolios are sorted based on one of three proxies used to try measure stock attention objectively. The first is abnormal trading volume, the second is the convexity and concavity of the stock’s their price pattern and the third proxy is the amount of extreme returns. Each of these attention strategies would then be compared to the regular contrarian approach to test for significant differences. The tests performed on the contrarian portfolios produced the following: Not one of the three high attention strategies managed to outperform the regular contrarian method. The low attention strategy based on abnormal trading volume had a significantly lower return than the regular approach. The low attention approach based on the price pattern of stocks was significantly larger and different than the regular contrarian strategy at the five percent level. The low attention strategy based on extreme returns had a significantly larger return than the regular strategy, but the average returns between the two were not significantly different at the five percent level. In terms of the high attention strategies the results are all in line with each other, with all strategies being statistically similar to the regular approach. However, for the low attention methods the results are slightly mixed. One is significantly smaller, the second is significantly larger and the third has a result that is significantly larger than the regular contrarian return but it is not extreme enough to be able to reject the proposed null hypothesis. These results lead to the following conclusion:

- High investor attention has no significant effect on the returns of contrarian investing - Low investor attention has a slightly positive effect on the returns of contrarian investing

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Because for the third low attention strategy it cannot be said with a 95 percent certainty that low investor attention contrarian investing is significantly different the returns of regular contrarian investing, it can only be concluded, with 95 percent certainty, that low attention contrarian investing has larger returns than regular contrarian investing. Possible limitations of this research could be that due to time limitations it was too much work to perform these tests on a sample from a larger time-period, the time period used in this research is smaller than most time periods used in comparable research. I would recommend for future research to use a comparable timeframe as the other papers. Another recommendation I would make for future research is to test the effects of attention for both contrarian and momentum in the same paper. This would allow the researcher to make better comparisons between the effects attention has on the two strategies. Since this research had to compare the effects of attention on contrarian returns to the effects of attention on momentum returns while both momentum researches are set in a much bigger time-frame and do not use the exact same attention proxies.

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6. References

Addae-dapaah, K., L. Peiying (2009) Investing in REITS: Contrarian versus Momentum Paper presented at PRRES 2009 Conference, Sydney, Australia.

Antoniou, A., Galariotis, E.C. and Spyrou, S.I. (2006). Short-term Contrarian Strategies in the London Stock Exchange: Are They Profitable? Which Factors Affect Them? Journal of Business Finance & Accounting, 33(5&6), 839-867.

Asness, C.S.,. Moskowitz, T.J. & Pedersen, L.H. (2013), Value and momentum everywhere, Journal of Finance 68, 929-985. Barber, B. M. & 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, Vol. 21, Issue 2, pp. 785- 818

Barberis, N. & Thaler, R. (2003), A survey of behavioral finance, Handbook of the Economics of Finance, edition 1, volume 1, chapter 18, pages 1053-1128 Elsevier. Chan, K. C. (1988),On the contrarian investment strategy, The Journal of Business Vol. 61, No. 2 pp. 147- 163

Chen, L. & Yu, H. (2014), Investor Attention, Visual Price Pattern, and Momentum Investing. 27th Australasian Finance and Banking Conference 2014 Paper De Bondt, W. F. M. and Thaler, R. (1985), Does the Stock Market Overreact? The Journal of Finance, 40: 793–805.

Fama, E.F., (1965), Random Walks in Stock Market Prices, Financial Analysts Journal, Vol. 21, (5), p55- 59.

Fama, F., French, K R (2003), The Capital Asset Pricing Model: Theory and Evidence. CRSP Working Paper No. 550

Gervais, S, Kaniel R., Mingelgrin,D.H. (2001). The high-volume return premium. Journal of Finance Vol. 56, p877–919.

Harrison, H.& Stein, J.C. (1999), A unified theory of underreaction, momentum trading and overreaction in asset markets, Journal of Finance 54, 2143-2184.

Hirshleifer, D. (2001) Investor Psychology and Asset Pricing The Journal of Finance Vol. 56, No. 4 pp. 1533-1597

Hou, K., L. Peng, and W. Xiong, (2009), A Tale of Two Anomalies: The Implications of Investor Attention for Price and Earnings Momentum, Working Paper, Princeton University

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Kent, D. Hirshleifer, D. & Subrahmanyam, A. (1998) Investor psychology and security market under- and overreactions, Journal of Finance 53, 1839-1885.

Lakonishok, J., Shleifer, A. and Vishny, R. (1994). Contrarian Investment, Extrapolation, and Risk. Journal of Finance, 49(5), 1541-1578.

Odean, T. (1999) Do investors trade too much? American Economic Review 1279–98.

Penny Stock Rules (2013) U.S. Securites And Exchange Commision website http://www.sec.gov/answers/penny.htm Schierek, D, De Bondt, W. and Weber, M. (1999), Contrarian and Momentum Strategies in Germany. Financial Analysts Journal Vol. 55, No. 6, Behavioral Finance pp. 104-116

Sefton, J. & Scowcroft (2005) A, Understanding Momentum. Financial Analysts Journal, Vol. 61, No. 2, pp. 64-82,

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7. Appendix

Table 21 Benchmark indices information Benchmark index: Average return Standard deviation N Value-weighted index 0,00738 0,04276 912308 Equally-weighted index 0,00796 0,05092 912308 S&P 500 composite index 0,00537 0,04062 912308

This table contains the information about the benchmark indices used to compare with the contrarian strategies. Average return represents the returns earned by these indices during the 2004-2014 period. The standard deviation shows the spread of the returns for each index. N refers to the amount of observations the index had during the 2004-2014 period.

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Table 22 1 2 3 4 5 6 7 Strategy: 1 Excess ret: -0,0027 0,0534 -0,004 -0,0339 -0,0012 -0,0252 t-value: -0,1699 2,6551 -0,2511 -2,2676 0,0679 -1,7925 P(T > t): 0,5674 0,0002 0,5991 0,9883 0,5271 0,9632 P(|T| > |t|): 0,8651 0,0005 0,8018 0,0235 0,9459 0,0736

2 Excess ret: 0,0027 0,0561 -0,0013 -0,0311 0,0015 -0,0224 t-value: 0,1699 2,6329 -0,0573 -1,4732 0,0647 -1,0931 P(T > t): 0,4326 0,0043 0,4711 0,9296 0,4742 0,8628 P(|T| > |t|): 0,8651 0,0085 0,9543 0,1408 0,9485 0,2745

3 Excess ret: -0,0534 -0,0561 -0,0574 -0,0873 -0,0547 -0,7862 t-value: -2,6551 -2,6329 -2,7154 -4,2765 -2,3938 -3,9739 P(T > t):) 0,9998 0,9957 0,9957 1,0000 0,9916 1,0000 P(|T| > |t|): 0,0005 0,0085 0,0067 0,0000 0,0168 0,0001

4 Excess ret: 0,004 0,0013 0,0574 -0,0298 0,0028 -0,0212 t-value: 0,2511 0,0573 2,7154 -1,4267 0,1193 -1,0419 P(T > t): 0,4009 0,5229 0,0033 0,9231 0,4525 0,8512 P(|T| > |t|): 0,8018 0,9543 0,0067 0,1538 0,9050 0,2975

5 Excess ret: 0,0339 0,0311 0,08732 0,0298 0,0326 0,0087 t-value: 2,2677 1,4732 4,2766 1,4267 1,4419 0,4450 P(T > t): 0,0117 0,0704 0,0000 0,0769 0,0747 0,3282 P(|T| > |t|): 0,0235 0,1408 0,0000 0,1538 0,1495 0,6564

6 Excess ret: 0,0012 -0,0015 0,0547 -0,0028 -0,0326 -0,0239 t-value: 0,0679 -0,0647 2,3938 -0,1193 -1,4419 -1,0849 P(T > t): 0,4729 0,5258 0,0084 0,5475 0,9253 0,8610 P(|T| > |t|): 0,9459 0,9485 0,0168 0,9050 0,1495 0,2781

7 Excess ret: 0,0252 0,0224 0,7862 0,0212 -0,0087 0,0239 t-value: 1,7906 1,0391 3,9739 1,0419 -0,4450 1,0849 P(T > t): 0,0368 0,1372 0 0,1488 0,6718 0,1390 P(|T| > |t|): 0,0736 0,2745 0,0001 0,2975 0,6564 0,2781

This table contains the comparisons between each strategy discussed in this paper. The table displays the results of a two sample t-test performed on all the combinations of strategies done in Stata. The numbers all represent a strategy in the order in which they are discussed in this paper, with 1 being the regular contrarian strategy and 7 being the low extreme returns strategy. Excess return represents the differences in returns and is calculated by taking the returns from the strategy number from the left- hand side of the table and subtracting the return from the strategy number from the upper-side of the table. P(T > t) represents the probability of obtaining a particular average return from the upper-hand side that is higher than the return from a particular average return from the left-hand side when the null hypothesis of differences in returns equals 0 is assumed. P(|T| > |t|) represents the probability of obtaining an excess that is at least as extreme as the when the null hypothesis of excess return equal zero is assumed.

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