Is the Amsterdam Exchange Index prone to the overreaction hypothesis?

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Is the Amsterdam Exchange Index prone to the

overreaction hypothesis?

The Winner-Loser Anomaly

Jeanneau Stadegaard

MSc Finance Thesis University of Groningen

Abstract

In this paper, I investigate whether the Amsterdam Exchange Index (AEX) is prone to the overreaction hypothesis during the time period January 1983 to December 2017. No significant evidence for the overreaction effect in the AEX for different formation and test periods for the loser and winner portfolios is found. Loser and winner portfolios cumulated negative abnormal returns. After controlling for time-varying risk, loser portfolios tend to be riskier compared to their counterpart and there is a shift in systematic risk from the formation period to the test period. Further analyses reveal that loser portfolios tend to be smaller size firms and winner portfolios are bigger size firms based on their market values. When controlling for firm size, both loser and winner portfolios cumulated negative abnormal returns. The results from my analyses show that a contrarian investment strategy is not profitable in the AEX.

Keywords: Overreaction hypothesis, market efficiency, contrarian investment strategy, mean reversion, stock market anomaly

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1. Introduction

Nowadays, more and more Dutch people are taking risks with their financial savings due to the low savings rate in the Netherlands (IEX, 2017). In 2017, the number of households that invested in stocks rose by 14%, which means that there are more than 1.4 million Dutch individuals investing in the Amsterdam Exchange Index (AEX). Looking back, the last time that the AEX had more than 1.4 million individuals investing was in the late nineties. However, this prosperous time for investors ended with the collapse of the internet bubble (Volkskrant, 2017). These 1.4 million individuals all have access to mass communication instruments like the internet, and, with the ongoing technological improvements, information can now flow faster and cheaper than ever before.

The cornerstone of modern finance theory is the Efficient Market Hypothesis (EMH), which states that in financial markets all participants are rational and have equal access to information (Fama, 1965). Hence, in these markets it is impossible to get arbitrage profits due to the fact that all information is already incorporated in the stock price (Fama, 1965). Furthermore, the efficient market hypothesis is affiliated with the representation that stock prices follow a random walk, which means that stock prices change randomly (Malkiel, 2003). Combining the EMH and the random walk, a stock price can only change when the stock price has already all the information incorporated and it response to new information (Malkiel, 2003). In the 1990s a new field called behavioural finance developed. This field shows a contradictory view on finance in comparison to the EMH theory. For example, behavioural finance does not only take into account the conventional economics and finance, but it combines behavioural and psychological theory. Particularly, behavioural finance attempts to explain why participants in the world of finance behave irrationally (Shiller, 2002). Based on psychological literature, research indicates that people are prone to limited information processing, rely on the opinion of others and exhibit systematic bias in information processing (Pompian, 2004). This challenges the EMH theory since it explains how the stock price outruns their intrinsic value due to investor excessive optimism or pessimism. Therefore, the stock price reversal should be predictable from their price performance in the past (Dissanaike, 1997). This behaviour indicates inefficiencies in the proposed market form as it is assumed that the stock price returns can be predicted by their historical patterns. As a result, the stock price will not include all the information from the past, hence it is not in line with the EMH.

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value. The overreaction phenomenon of stock markets is by no means new in the world of finance. Well known studies such as De Bondt and Thaler (1985) and Clare and Thomas (1995) have addressed the issue of overreaction in the stock market. With the increase of individuals participating in the AEX (Volkskrant, 2017), new developments related to information and technology and market environments, it is interesting to research the AEX. Interestingly, current research does not illustrate clear evidence on whether there is any significant overreaction effect in the AEX. Therefore, in this paper I am analysing the vulnerability of the AEX to the overreaction hypothesis.

The overreaction hypothesis does not support the weak form of market efficiency. It indicates that stock returns are predictable by analysing their past patterns, where stock prices do not include all information (Dissanaike, 1997). The result of overreaction is that investors overreact to bad or good news that is associated with a particular stock. The consequence of this overreaction is that the stock price will decrease or increase relatively to their true value. Ultimately, it is suggested that the stock price will revert to its true value. Therefore, one could argue that stocks that perform relatively poor to the market in the past will eventually outperform the market in the future. Contrarily, stocks that did well in the past relatively to the market will underperform relatively to the market in the future (Baytas and Cakici, 1999). The conclusion of this overreaction effect is that investors can manifest profitable contrarian strategies. A contrarian strategy is an investment strategy which consist of buying stocks that did poorly and selling short stocks that did well (Chan, 1988).

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The main finding in this paper is that investors cannot make profits implementing a contrarian investment strategy, which buy past losers and sell (short) past winners. The findings in this paper are not suitable for conducting an investment strategy. Furthermore, no transaction costs are implemented.

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2. Literature review

Over the last 30 years, the efficient market hypothesis has been of notable interest to financial economists. Most researches are based on the supposition that financial markets are efficient. The efficient market hypothesis states that it is impossible to earn abnormal returns via trading due to the available information (Fama, 1998). Assuming that the efficient market hypothesis is accepted widely, there is an increasing tendency with academic evidence that appeared to weaken the efficient market hypothesis. One such counterpart against the efficient market hypothesis emerged from researches that examined the overreaction effect. This overreaction effect states that “significant price movements in stock prices will be followed by subsequent price movements in the contrary direction’’ (De Bondt and Thaler, 1985). The definition of the overreaction hypothesis means that stock prices that have gone through a notable downfall with regard to the market in their returns in a certain time period will eventually exceed the market over the same period of time, mostly in a period from one to five years (De Bondt and Thaler, 1985).

Before I analyse the overreaction hypothesis related literature, there will be a short and clear description about the understanding of the overreaction aspect in the field of behavioural finance.

2.1. Behavioural explanation

In the field of behavioural finance there are some explanations that explain the relation between the aspects of overreaction regards to an appropriate reaction. First, the Bayes’ theorem assumes that all investors behave rational, which means that investors update their beliefs in the right direction with appliance of conditional probability to weight both prior and current information. With regard to the overreaction hypothesis, investors tend to interfere the Bayes’ rule due to the fact that they overreact to unexpected news or events, hence, overreaction (De Bondt and Thaler, 1985). An alternative theory called Representativeness Heuristics states that investors tend to rely on restricted number of heuristics, which therefore restrict the amount of assessing values and probabilities to make a decision easier (Kahneman and Tversky, 1973). Kahneman and Tversky (1973) provided a psychological motivation of stock market overreaction. They argue that individuals overweight their recent information and underweight their previous data. Many studies concluded that investors are overreacting in financial markets, both in short and long term. In this paper, the focus is on the long-run stock market overreaction.

2.2. Overreaction evidence in the USA and UK stock market

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abnormal return methodology. Their research unveiled that stock prices have price reversals over a long period. Two distinctive portfolios of each 35 stocks were created, the best performing stocks were labelled as “winners” and the worst stocks were labelled as “losers”. They tracked each portfolio performance compared to a market index for a time period of three years. De Bondt and Thaler (1985) concluded that the portfolio of the losers outperformed the market index, whereas winners underperformed relatively to the market index. The loser portfolios accumulated positive abnormal returns, however the winner portfolios cumulated negative abnormal returns. They find that the loser portfolios for a formation1_{period of three year, outperformed the market on average}

by 19.6%. The contrarian strategy2_{cumulated a positive abnormal return of 24.6%. They find that}

the longer the formation period the higher the significant of mean reversion is in the test3_period.

Consequently, the findings of De Bondt and Thaler (1985) reflect evidence for overreaction in the US stock market.

In their follow-up paper, De Bondt and Thaler (1987) came up with additional evidence with respect to the overreaction hypothesis. In their paper, they focused on the unresolved findings of their initial paper namely: the January effect, the asymmetry of price correction between the loser and winner portfolios, the influence of market risk and firm size. They propose that losers and winners have excess returns mainly in January. They assume that these excess returns generated in January are mainly reflecting a tax-loss selling pressure for losers and a capital gain tax effect for winners, but there is no empirical evidence for this assumption. Also, variation in the beta of the Capital Asset Pricing Model (CAPM) and firm size fails to explain the overreaction effect. De Bondt and Thaler (1987) found evidence that mean reversion in stock prices results in overreaction in the US stock market. Again, the results from the follow-up paper are in line with the previous study findings on price reversals and overreaction of the stock prices.

Zarowin (1990) re-examines the research of De Bondt and Thaler (1985, 1987) on stock market overreaction. Zarowin (1990) found similar results for the three-year period, showing that losers significantly outperform winners. Neither the January effect nor difference in risk could explain the difference in performance. However, controlling for firm size, Zarowin (1990) found only difference in performance in January. Zarowin (1990) found that when losers are smaller, they outperformed winners. On the other hand, when winners are smaller compared to losers, the winners outperformed losers. Hence, Zarowin (1990) found that the difference between the performance of the loser and winner portfolios is not due to the overreaction, but it is rather explained by the size effect. An explanation for the size effect is hypothesize by Baytas and Cakici

1_{Formation period refers to the period where the stocks are being ranked on prior performance.} 2_{Contrarian means: buying losers stocks and selling short winners stocks.}

3_{Test period refers to the period where portfolios are tested, based on the formation period where loser and winner}

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(1999). They argue that the long-term price reversals are due to that losers tend to be low in market value and price, whereas winners tend to be high in market value and price.

Power et al (1991), examined the overreaction hypothesis in the UK. Their research differs slightly from that of De Bondt and Thaler as they set-up winner and loser portfolios from a list of the top 200 UK firms, whereas De Bondt and Thaler (1985) measured stock excess returns over a formation period to define winner and loser portfolios. The loser and winner portfolios were constructed by selecting the 30 bottom and 30 best stocks. Power et al (1991) found evidence that their results are consistent with the overreaction effect described by De Bondt and Thaler (1985) over a time interval of three to five years. The loser portfolio had a cumulative abnormal return of 86%, where the winner portfolio had a negative cumulative abnormal return of 47% over a five-year period. However, when controlling for change in risk for both equally weighted portfolios, the performance of the contrarian strategy was significantly less. Controlling for risk resulted in an average cumulated abnormal return just under 20% for the loser portfolio and the winner portfolio remain cumulated negative abnormal returns (slightly below zero). Furthermore, MacDonald and Power (1991) conducted also a study for the UK stock market to test for overreaction effect. They used eight three-year test periods and concluded that for the contrarian portfolio it generated an average cumulated abnormal return of 30%.

Clare and Thomas (1995) examined the UK stock market from 1955 to 1990 with respect to the overreaction hypothesis. They formed portfolios by randomly chosen stocks up to 1000 stocks for non-overlapping periods. They find that losers remain losers when the average return is calculated over period of one year. However, they do find evidence of overreaction for the time periods two and three years. Losers tend to outperform winners for a two-year period by an annualised return difference of 1.7%, which is a cumulative difference of 3.43%. For a three-year period, the losers tend to outperform winners by 1.57% per annum, resulting in a cumulative difference of 4.8%. The overreaction results of Clare and Thomas (1995) are much smaller compared to the studies of De Bondt and Thaler (1985, 1987) in the US stock market. When controlling for risk, Clare and Thomas (1995) found no significant difference between the betas of the loser and winner portfolios for periods of two and three years. Their conclusion is that there is a small overreaction effect in the UK stock market, however, in their research they admit they have survival bias, because firms are required to exist of two, four and six years. When controlling for firm size, they find that losers tend to be small in comparison to winners. They argue that the small overreaction effect is probably due to the size effect.

2.3. Overreaction evidence in European countries, Canada and Australia

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winner portfolios were constructed of the five best and five worst stocks. The results of Alonso and Rubio (1990) provide evidence for the overreaction hypothesis for the Spanish stock market. They found that over the last twenty years, loser portfolios outperformed winner portfolios, which resulted in a contrarian profit on average of 7.9% after 12 months after the formation period. At the end of the 36-month test period, the contrarian strategy earned an average cumulative excess return of 36.9%. Additional examinations show that increasing the portfolio of five stocks to ten stocks results in the same conclusion that there is empirical evidence related to the overreaction hypothesis. However, the difference between the loser and winner portfolios declined. They found that the longer the formation and test periods, the more profound evidence is found for the overreaction effect. Moreover, the betas of the winner portfolios increased from the formation period to the test period, the beta increased from 0.75 to 1.08. The beta of the loser portfolios remained on average constant over time. In contrast to the findings of Alonso and Rubio (1990), Forner and Marhuenda (2000) found no significant evidence for the overreaction effect in the Spanish stock market during the period of 1963 to 1997. Forner and Marhuenda (2000) constructed loser and winner portfolios consisting of five stocks for three different horizons namely: 12, 36 and 60 months. The difference in results is mainly due to the fact of different methodologies. Alonso and Rubio used a non-overlapping formation and test period, Forner and Marhuenda used only a non-overlapping test period.

Baytas and Cakici (1999) examined also European countries in light of the overreaction hypothesis. They did research on various stock markets, namely: US, Canada, Japan, France, Italy, Germany and the UK. Interestingly, they found evidence of the overreaction effect in a period of two and three years for Japan, France, Italy, Germany and the UK, but they found no evidence of the overreaction effect in the US and Canada. In line with the research of Baytas and Cakici (1999), Kryzanowski and Zhang (1992) found no evidence of the overreaction effect in the Canadian stock market. Their results were inconsistent with the overreaction effect for formation and test periods of 1, 2, 3, 4, 5, 8 and 10 years.

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2.4. Overreaction effect in emerging markets

Locke and Gupta (2009) examined the Bombay Stock Exchange during the time period of 1991 till 2004. Using a 36-month formation and test period they found that the loser portfolio exceeds the market by a cumulative abnormal return of 78.65%, while the winner portfolio earned significant less 4.26%. After controlling for risk difference, they find positive significant Jensen Alpha’s for the loser portfolios. Hence, loser portfolios outperform winner portfolios after adjusting for risk differences. When controlling for firm size, most of the abnormal returns of both portfolios disappeared.

Da Costa (1994) provide evidence of the overreaction hypothesis in the Brazilian stock market. Using a 24-month formation and test period loser portfolios outperform winner portfolios. The loser portfolio outperformed relatively to the market by 17.63%, whereas the winner portfolio cumulated average abnormal return of -20.25%. When following the methodology by Chan (1988) to adjust for risk differences, Da Costa (1994) found that difference in risk fail to explain the overreaction effect.

2.5. Critics to the Overreaction Hypothesis

The study of De Bondt and Thaler (1985) has generated much attention and controversy. De Bondt and Thaler (1985) suggested that their results provide evidence that investors behave irrationally in stock markets. Furthermore, they suggested that when investors reconsider their expectations, they tend to overweight current information and underweight previous information. This irrational behaviour leads to excessive optimism about positive news and excessive pessimism about negative news. Moreover, this causes stocks to depart from their fundamental value. Despite the evidence of De Bondt and Thaler (1985, 1987) for the overreaction effect, several authors presented other explanations for the overreaction hypothesis. These critics can be divided into three parts: size effect (Zarowin, 1990), bid-ask biases and infrequent trading (Conrad and Kaul, 1993) and time-varying risk (Chan, 1988), (Ball and Kothari, 1989).

As aforementioned, Zarowin (1990) provides evidence that the overreaction effect is mainly due to the size effect, which contributes mainly to less known and smaller size firms. When Zarowin (1990) replicated the study of De Bondt and Thaler (1985), results were consistent with the overreaction hypothesis. When controlling for firm size, Zarowin (1990) found that losers only outperformed winners in the month January. Therefore, Zarowin (1990) concluded that the overreaction effect is a manifestation of the size phenomenon.

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Kothari (1989) provide evidence that the previous performance do changes the level of risk of loser and winner stocks and as a consequence result in a change in expected returns. Hence, the risk of losers and winners does not remain constant. These time-varying risk and expected results is argued to be a result of a change in leverage of these companies and therefore change the market value of these winner and loser portfolios. The beta of the loser portfolios increases after a period of abnormal loss and the beta of the winner portfolio decreases after a period of abnormal gain. These reversals in returns implies changes in equilibrium required returns of investors, which is not controlled in the research of De Bondt and Thaler (1985). When controlling for changes in beta from the formation period to the test period, the contrarian strategy generates only small significant abnormal returns. Ball and Kothari (1989) provide evidence that the betas of loser portfolios surpass the betas of winner portfolios. Ball and Kothari (1989) provide further evidence that the overreaction effect can be explained by the time-varying risk for both the winner and loser portfolios. Using the methodology proposed by Chan (1988) and Ball and Kothari (1989), Dissanaike (1997) provide little evidence for the claim that changes in time-varying risk leads to price reversals. Nevertheless, Chopra et al. (1992) provide counter evidence against Ball and Kothari (1989) because they put down the excess returns by using the CAPM. The CAPM assumes that an increase in the beta risk will reflect directly in a higher excess return. Chopra et al. (1992) provide evidence that the difference in risk between the winner and loser portfolios cannot explain the excess returns in their study and therefore they do accept the overreaction hypothesis.

Conrad and Kaul (1993) state that the overreaction in the long run is based on upwardly biases, because the cumulating single-period returns are calculated over a long-time interval. They changed their methodology by replacing the average cumulated abnormal returns with the average holding period abnormal returns. Conrad and Kaul (1993) conclude that the abnormal returns generated by the contrarian portfolio can all be explained by the January effect. Conrad and Kaul (1993) argue that all the overreaction studies use the same biased methodology of De Bondt and Thaler (1985), due to the arithmetical errors. Therefore, they argue that the process of calculating cumulating single period returns over a long-time interval are prone to the bid-ask spread bias and infrequent trading.

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3. Methodology and data

3.1. Data

The data used in this study consist of monthly stock returns of the current constituents of the Amsterdam Exchange Index (AEX) during the period January 1983 till December 2017. The data is aggregated in twofold. First, because Datastream only has data of the constituents of the AEX from 2009 till December 2017, I used the following document which is attracted from Euronext.com: ‘’The composition of the Amsterdam Exchanges-Index (AEX) from 1983’’, to determine the composition of the constituents from January 1983 till December 2008. From January 2009 till December 2017 the constituents list was obtained from Datastream. Finally, all monthly stock returns were obtained from Datastream. The sample of stocks include both delisted and surviving stocks. Hence, survival bias is minimum. The stock prices are expressed in monthly returns, which is reckon to be most appropriate to avoid the bid-ask effect and the influence of infrequent trading (De Bondt and Thaler, 1985).

To test the overreaction hypothesis, the constituents of the AEX are examined between January 1983 till December 2017 for three different periods, 12, 24 and 36 months, which is 34 years of data. To be included in the sample a stock must have a complete dataset in the formation period and has to be traded at least once in the test period. When a company is delisted before the formation period, the company is excluded from any analysis (De Bondt and Thaler, 1985). If, however, the company is delisted and have traded at least once in the test period, the last trading price will be constant over time. Each formation period has a test period. Hence, for a 12 months formation period, the following 12 months is the test period. Therefore, for a 12 months formation period, there must be 24 months of data, for a formation period of 24 months there must be 48 months of data and finally for a 36 months formation period there must be 72 months of data. The AEX Total Return Index is used for the market returns.

3.2. Methodology

In line with De Bondt and Thaler (1985), Chan (1988) and among others, I use non-overlapping sample periods with 34 years of data from January 1983 to December 2017. Therefore, to calculate the average returns over a period of 12 months, it empowers to track the returns for both the winner and loser portfolios over 34 non-overlapping periods of one year. For a 24-month time period it will give 16 non-overlapping periods to calculate the portfolio returns and for a 36-month period it will have 10 non-overlapping periods.

3.2.1. Formation of Winner and Loser Portfolios

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market-adjusted model, which is commonly used to test for overreaction effect (De Bondt and Thaler, 1985), (Brailsford, 1992), (Da Costa, 1994), and (Guant, 2000). The market-adjusted abnormal returns are calculated as the difference between the returns of a stock and the market in each month. The market refers in this case to the AEX Total Return Index. The market adjusted return for the three4_{different formation periods are calculated as follow:}

!_",$ = '_",$− '_),$ (1) Where:

!_",$ = Market-adjusted abnormal return for stock i in month t. '_",$ = Continuously compounded return on stock i in month t.

'_),$ = Continuously compounded return on the AEX index in month t.

Where '_",$ and '_),$ is the monthly continuously compounded return calculated as follows:

'_",$ = *+ , '-",$

'-",$./0 (2)

'_),$ = *+ , '-),$ '-),$./0

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Where '-",$ is the stock total return index of the individual constituent on the last day of month t and '-",$./ is the stock total return index of individual constituent on the last trading day in the prior month t. '-),$ is the AEX total return index on the last day of month t and '-),$./ is the AEX total return index of the last trading day in the prior month t. The continuously compounded monthly returns for the constituents and market are computed as monthly total return index, which measures the performance assuming that all other cash distributions, for example dividends, are reinvested. Using the market-adjusted model, no endeavour is being made to particularize the right asset-pricing model for calculating abnormal returns. Therefore, the excess returns over the market are not adjusted for any kind of risk. However, as approved by Brown and Warner (1980) the market-adjusted model performs just as well as more sophisticated models for distinguishing abnormal performance.

All companies in the AEX are ranked based on their market-adjusted cumulative abnormal returns (1!") over their formation period by equation (4). Equation (4) illustrates the

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adjusted cumulative abnormal return for the 36-month period. For the 12 and 24-month period, t is set to t = -12 and t = -24. 1!_" = 3 !_",$ ./ $4.56 = 3 '_",$ ./ $4.56 − 3 '_),$ ./ $4.56 (4)

Where 1!" is the market-adjusted cumulative abnormal return for stock i over a period of 12, 24 and 36 months prior the start of the test period. Then after 12, 24 and 36 months, the market-adjusted cumulative abnormal returns are ranked in order from low to high. Then after calculating the market-adjusted cumulative abnormal return and the ranking for all the individual stocks, winner and loser quintile portfolios are formed. Where the winner portfolio consists of the 20% best performing stocks and the loser portfolio consist of the 20% worst performing stocks of the AEX. The loser and winner portfolios are equally weighted. Most of the overreaction studies use decile portfolios like Brailsford (1992), Gaunt (2000) and Clare and Thomas (1995). Other studies use an equal amount of stocks to form both portfolios, like De Bondt and Thaler (1985, 1987) and Locke and Gupta (2009). The reason I choose for the top and bottom quintile stocks is due to the small amount of stocks in the AEX because the AEX consist of 12 constituents in 1983 and 25 constituents in 2017. Therefore, using quintile portfolios rather than decile portfolios will result in better diversification of both portfolios. Furthermore, the cumulative average abnormal returns in the test period for all securities in the winner and loser portfolios for the non-overlapping three-year, two-year and one-year periods are calculated as follows:

17'_8,9,: = 3 ;<1 >? 3 !",$ @ "4/ A : $4/ (5)

Where 17'8,9,$ is the cumulated average market-adjusted abnormal return in test period n for month t for both the winner and loser portfolios p, N 5_{is the amount of stocks in each portfolio}

and !_",$ is the abnormal return of stock i in month t. The cumulative average abnormal returns for the winner and loser portfolios will be denoted as follows: 17'B,9,$ for winners and 17'C,9,$ for losers. After calculating 17'8,9,$ for all test periods and for the winner and loser portfolios, the average of CAR’s is calculated for both the winner and loser portfolios in each month, which will be calculated as follows:

5_{N will change for each portfolio because the total of number of stocks in each formation period will be different,}

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717'_8,$ = <1

>? 3 17'8,9,$ @

94/

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Where 717'8,$ is the average of CAR for N number of periods for either the winner, loser and contrarian portfolios p. Where p is set to L for the loser portfolio and P is set to W for the winner portfolio.

3.2.2. The Overreaction Hypothesis

To test the overreaction hypothesis in the AEX three hypothesizes will be tested. First, the overreaction hypothesis states that 717'B,$ < 0 and 717'C,$ > 0. Which therefore implies that [717'C,$ - 717'B,$] > 0. The three hypothesis that will be tested are as follows:

D_/: 717'_C,$ = 0 where t = 1…12 and 1…24 and 1…36. D_G: 717'_B,$ = 0 where t = 1…12 and 1…24 and 1…36. D5: 717'C.B,$ = 0 where t = 1…12 and 1…24 and 1…36.

The null hypothesis suggest that an investor should not earn any excess return through investing in a portfolio consisting of past loser stocks and selling short a portfolio consisting of winner stocks of the past, because past returns should not give any indication for future returns. Conformable with the efficient market hypothesis, the abnormal returns for both winner and loser portfolio should be zero. The three hypothesizes will be tested via a t-test on the mean of 717'C,$, 717'B,$ and 717'C,$− 717'B,$.

The test statistics are given by the following formulas:

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Where IC, IL and IC.B are the sample standard deviations of the loser, winner and contrarian portfolios and > is the amount of test periods. The amount of test periods for the 12-month period will be 34. There will be 16 test periods for the 24-month period and for the 36-month period there will be 10 test periods.

3.2.3. Bonferroni correction

In this paper several statistical tests are performed on the same data set simultaneously, which increases the change to reject a null hypothesis incorrectly. Therefore, to eliminate this problem I will use the Bonferroni correction, where the p-value is adjusted by equation (10), which test each hypothesis individually by dividing the significance level with the amount of comparisons being made by the following formula (Goeman et al, 2014):

M =N_O (10)

Where: P = The significance level

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4. Results

Table 1 presents the average cumulative abnormal returns for three different non-overlapping test periods for the loser, winner and contrarian portfolios. The portfolios consist of all constituents of the AEX from January 1983 to December 2017. The performance of all stocks in the formation period determines which stocks belongs to the loser or winner portfolios. The loser portfolio consists of the 20% worst performing stocks and the winner portfolio consists of the 20% best performing stocks. Both portfolios are held for three different holding periods namely, 12, 24 and 36 months, depending on their formation period. This means for a 12-month formation period, the portfolio is held for another 12 months into the test period, a 24-month formation period is held for another 24 months in the test period and finally, a 36-month formation period is held for another 36 months in the test period. The t-statistics are reported to conclude if any of the results are statistical significant, which in this case tests the hypothesis if the return of the three different portfolios is significantly different from zero. The returns that are significant different from zero are denoted by *** (1%), ** (5%) and * (10%). The Bonferroni correction is indicated by B, which reports if the return on the portfolio is significant different from zero adjusted by the Bonferroni correction.

Table 1

Differences between Average Cumulative Abnormal Return (ACAR) in test periods

All AEX constituents with a complete dataset in the formation period of 12, 24, and 36 months in the period 1983-2017 are identified. The market-adjusted abnormal returns are calculated for each stock and are ranked based on their cumulative abnormal return. The 20% worst performing stocks shape the loser portfolio and 20% best performing stocks shape the winner portfolio. For each portfolio the cumulative market-adjusted abnormal returns are calculated over three different test periods namely: 12, 24 and 36 months. This table represents the average market-adjusted abnormal returns (ACAR) for each test period for the loser, winner and the contrarian portfolio (loser-winner) as well and their t-statistic respectively, which test whether the returns of the portfolios are significantly different form zero. The contrarian portfolio has a long position in the loser portfolio and a short position in the winner portfolio. The Overreaction Hypothesis states that 717'C,$ >

0 and 717'B,$ < 0, which therefore implies that (717'C,$− 717'B,$) > 0. To test the profitability of the contrarian strategy, the null hypothesis is tested via D/:717'C,$= 0, DG:717'B,$ = 0 and D5: (717'C,$−

717'_B,$) = 0. The hypotheses are tested via a t-test on the means of ACAR. The significance levels 1%, 5% and 10%

are denoted by ***, **, *. The Bonferroni correction is denoted as B, which denote whether the returns of the portfolios are significantly different from zero adjusted by the Bonferroni correction.

Portfolio formation period and number of non-overlapping

independent replications

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In Table 1 the average cumulative abnormal returns for the loser and winner portfolios at the end of the one-year period are -6.18% (t-statistic: -2.1782) and -5.04% (t-statistic: -1.7184). The winner portfolio tends to perform better than the loser portfolio, however, there are no significant positive returns generated in the one-year period, resulting in a contrarian portfolio that generates an average cumulative abnormal return of -1.14%. In the two-year period the loser portfolio tends to perform better than the winner portfolio but again there is no positive significant performance of both portfolios. However, in the two-year period there is a positive contrarian portfolio but this result is not statically significant. For the three-year period there are no significant positive performance of both portfolios, resulting in an average cumulative abnormal return for the loser portfolio of -18.69% (t-statistic: -2.7051) and for the winner portfolio -0.80% (t-statistic: -0.1499). After controlling for the Bonferroni correction, none of the results are statistically significant. The results in Table 1 suggests there is no significant overreaction effect in the AEX, meaning that a contrarian trading strategy in the AEX is not profitable. The results presented in Table 1 are not in line with the studies done by De Bondt and Thaler (1985, 1987) and Clare and Thomas (1995) who found significant overreaction results after a three-year test period. On the other hand, the results in Table 1 are extensively consistent with studies of Brailsford (1992) and Gaunt (2000) which both found negative cumulative abnormal returns in the Australian equity market at the end of the three-year test period. For example, Brailsford (1992) found that the winner portfolio undergoes a price reversal during the test period. At the end of the 36-month test period the winner portfolio cumulated an average abnormal return of -69.6%. However, the loser portfolio does not undergo any price reversal, it rather cumulated negative abnormal returns at the end of the 36-month test period which results in an average cumulated abnormal return of -52.6%.

Table 1 shows only the end result of the three different test periods. However, it is interesting to look at different holding periods within the three different non-overlapping test periods to identify any price reversals. Table 2 presents the monthly average cumulative abnormal returns between the loser, winner and contrarian portfolios over 12 months into the test period. The results show that the loser portfolio continues to cumulate negative abnormal returns. This result is expected when taking into account the overreaction literature, where De Bondt and Thaler (1985) and Clare and Thomas (1995) found no overreaction effect for a 12-month horizon. Only in the 4th_{month into the test period, the loser portfolio outperformed the winner portfolio, which}

cumulated an abnormal return of 0.56%. But this result is not statistically significant. The winner portfolio cumulates positive abnormal returns up to the 3rd_{month in the test period of 0.85%, and}

thereafter continue to cumulate negative abnormal returns, resulting in significant negative abnormal returns for the last three months into the test period. The last column of Table 1 shows the contrarian portfolio. In the first three months in the test period it cumulated negative abnormal returns. However, after the end of month four up to the end of month ten, it cumulated an average abnormal return of 0.74%. After the 10th_{month the contrarian portfolio cumulated negative}

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statistically significant. After controlling for the Bonferroni correction, none of the results are statistically significant, meaning that there is no significant overreaction effect for the 12-month test period in the AEX.

Table 2

Differences between Average Cumulative Abnormal Return (ACAR) over 12 months into the test period.

All AEX constituents with a complete dataset in the formation period of 12 months in the period 1983-2017 are identified. The market-adjusted abnormal returns are calculated for each stock and are ranked based on their cumulative abnormal return. The 20% worst performing stocks shape the loser portfolio and 20% best performing stocks shape the winner portfolio. For each portfolio the cumulative market-adjusted abnormal returns are calculated over 12 months. This table represents the average market-adjusted abnormal returns (ACAR) for each test period for the loser, winner and the contrarian portfolio (loser-winner) as well and their t-statistic respectively, which test whether the returns of the portfolios are significantly different form zero. The contrarian portfolio has a long position in the loser portfolio and a short position in the winner portfolio. The Overreaction Hypothesis states that 717'C,$ > 0 and 717'B,$< 0, which therefore implies that (717'C,$− 717'B,$) >

0. To test the profitability of the contrarian strategy, the null hypothesis is tested via D/:717'C,$= 0, DG:717'B,$= 0 and D5: (717'C,$− 717'B,$) = 0. The hypotheses are tested via a t-test on the means of ACAR. The significance levels 1%, 5% and 10% are denoted by ***, **, *. The Bonferroni correction is denoted as B, which denote whether the returns of the portfolios are significantly different from zero adjusted by the Bonferroni correction.

In Table 3 the results are presented for the monthly average cumulative abnormal returns for the loser, winner and contrarian portfolio over 24 months into the test period. There is a clear price reversal after the third month in to the test period for both the loser, winner and the contrarian portfolios. The loser portfolio cumulated after three months positive abnormal returns, however, none of these results are significant. After 24 months in the test period the loser portfolio cumulated a negative abnormal return of -0.15% (t-statistic: -0.0249). This negative cumulated abnormal return is smaller than the cumulated abnormal return for the 12-month horizon, where it generates an average cumulated abnormal return of -6.18%. The winner portfolio cumulated negative abnormal returns after the third month in the test period. The winner portfolio generates a negative average cumulated abnormal return at the end of the 24-month test period of -12.48% (t-statistic: -2.4613). It seems that the loser portfolio in the 24-month test period tend to do better than the winner portfolio, although they both have cumulated negative abnormal returns. The

Months in test

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contrarian portfolio cumulated positive abnormal returns after the third month in the test period. It cumulated a positive abnormal return at the end of the 24 months of 12.32% (t-statistic: 1.1909). However, this result is not statistical significant which means that in the 24-month test period there is no statistical significant evidence for the overreaction hypothesis in the AEX. After controlling for the Bonferroni correction, no results were statistically significant.

Table 3

Months in test

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Table 4

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Table 4 represents the monthly average cumulative abnormal returns between the loser, winner and contrarian portfolio over 36 months into the test period. The loser portfolio continues to cumulate negative abnormal returns during the whole test period. The loser cumulated a negative average abnormal return of -18.69% (t-statistic: -2.7051). This result is consistent with the study of Brailsford (1992) who found no price reversals for loser portfolios after 36 months into the test period. Brailsford (1992) found at the end of the 36 months in the test period, the loser portfolio cumulated a negative abnormal return of -52.6%. Only in the second test period the loser portfolio has a positive cumulated abnormal return, but it is not significant. Surprisingly, the winner portfolios earn positive cumulated abnormal returns up to the 21st_{month into the test period, but}

after the 21st_{month it continues to cumulate negative abnormal returns, resulting in -0.80%}

(t-statistic: -0.1499) cumulative average abnormal return at the end of the 36-month test period. In Table 4 it seems that the winner portfolio performed better than the loser portfolio, even though the cumulated abnormal returns are negative for both portfolios. There are no statistically significant results for the 36-month test period. Table 2, 3 and 4 are graphically illustrated in Appendix B.

To conclude, there is no significant overreaction effect in the AEX for the test periods of 12, 24 and 36 months. Noticeably, buying stocks that performed worst in the past and selling stocks short that performed great in the past will not be profitable in the AEX. These findings are similar to that of Brailsford (1992) who founds no significant overreaction effect in the Australian equity market for the 36-month test period in the period of 1958 to 1987.

5. Further analyses

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5.1. Robustness to time-varying risk

From a methodological point of view, it is assumed that an equally weighted market-adjusted return is used for calculating average cumulative abnormal returns. This assumption implies that α = 0 and β= 1 for all stocks in the AEX, which therefore implies that risk has to be constant overtime. However, there are several studies that have been criticised for the use of this method. Chan (1998), Vermaelen and Verstringe (1986) and Lauterbach and Vu (1992) suggested that the overreaction hypothesis can be explained by the risk differences among the loser and winner portfolios. In order to investigate whether the risk of loser portfolios is more risky than that of winner portfolios I use a methodology which is on cognizance with the critiscms of Chan (1988), Vermaelen and Vestringe (1986) and Lauterbach and Vu (1992). To control for time-varying risk, I will use the same following model used by De Bondt and Thaler (1987), Clare and Thomas (1995), Chen and Sauer (1997) and Zarrowin (1990):

'8,$ − 'V,$ = P + XY'),$− 'V,$Z + [$ (11)

'_C,$− '_B,$ = P + XY'_),$− '_V,$Z + [_$ (12)

Where \ is either the continuously compounded return of the loser portfolio 'C,$ or the continiously compounded return of the winner portfolio 'B,$. The Jensen performance index is denoted by P, which measures the abnormal performance of the portfolio. The slope coeffcient is denoted by X, which measures the CAPM beta risk difference between the two portfolios. '),$− '_V,$ is the market risk premium, were '),$ is the continuously compounded return on the AEX and 'V,$ is the three-month Dutch Interbank offered rate. Unfortunately, there was no suitable one-month risk free rate. Equation 11 and 12 are both regressed for the 36-month formation and test periods. Evidence of overreation implies when the Jensen performance index is significant and positive. A significant postive X for the contrarian portfolio indicates that losers have more systematic risk than winners (Locke and Gupta, 2009).

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out of ten periods higher compared to the beta of the winner portfolio. Hence, it can be concluded that losers are significantly riskier in the formation period and less risky in the test period. The results are contrary to the findings of Chan (1988), Forner and Marhuenda (2000) and Guant (2000) who found that the beta of losers was significantly smaller compared to winners during the formation period and the beta of the loser portfolios tends to be higher in the test period compared to the beta of the winner portfolios. In Table 5, the beta of the loser portfolio is in the test period lower in seven out of ten periods compared to the formation period beta. This pattern is also observed for the winner portfolios. The beta of the loser portfolio in the formation period is on average 1.3055, which means it is theoretically 30% more volatile than the AEX. Moreover, there is a change in risk coefficient from the formation period to the test period. For loser portfolios, the average beta in the formation period equals 1.3055 and decrease in the test period to 1.0567. For the winner portfolio, the beta decrease in the test period to 0.9394. Worth mentioning, the beta of the loser and winner portfolios in the test period is on average close to 1, which means they follow the price movements of the AEX. Overall, Table 5 suggest that both the loser and the winner portfolio are less risky in the test period compared to their formation period.

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Table 5

Excess returns and betas for the Loser and Winner portfolios relative to the CAPM

The performance of the ten non-overlapping three-year periods with robustness to time-varying risk are regressed by the following equation:

!",$− !&$ = ) + +,!-,$− !&,$. + /$. !",$ is either the continuous compounded return for the loser portfolios or the continuous compounded return for the winner portfolios, ) is the Jensen performance index, + is the CAPM beta of respectively the loser and winner portfolio, ,!-,$− !&,$. is the market risk premium, where !&,$ is the three-month Dutch Interbank offered rate and !-,$ is the continuously compounded return of the AEX. The Jensen performance index and beta for the formation period is denoted by )0 and +0. The Jensen performance index and beta for the test period is denoted by )1 and +1. The t-statistics are shown in brackets. The significance levels 1%, 5% and 10% are denoted by ***, **, *. The Bonferroni correction is denoted as B, which denote whether the returns of the portfolios are significantly different from zero adjusted by the Bonferroni correction.

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Table 6

Excess returns and betas for the contrarian portfolios relative to the CAPM

The performance of the ten non-overlapping three-year periods with robustness to time-varying risk are regressed by the following equation: !_",$− !_&,$= ) + +,!_-,$− !_.,$/ + 0$. !",$ is the continuous compounded return for the loser portfolios and

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5.2. Controlling for firm size

Loser stocks are likely to me smaller size firms compared to winner stocks due to the fact that loser stocks have lost market value compared to winner stocks (Zarowin, 1990). Table 7 summarizes the results of average size of the loser and winner portfolios for the ten non-overlapping 36-month periods. Size is a proxy for market value and it is expressed in millions. Additionally, the average size of each portfolio is measured at the end of the formation period.

As derived from Table 7, the average size of the loser portfolio is always lower compared to the winner portfolio, except for the first formation period 1983-1985. This result is in consonance with the findings of Zarowin (1990), Gaunt (2000), Locke and Gupta (2009) and De Bondt and Thaler (1987). It is expected that the loser portfolios are smaller than the winner portfolios because size is measured at the end of an excessive performance period (Zarowin, 1990). Zarowin (1990) presumed that difference in size between the loser and winner portfolios may be a consequence of the difference in performance between the loser and winner portfolio. After controlling for firm size, Zarowin (1990) found that there was no evidence of overreaction effect. Locke and Gupta (2009), who examined the Bombay stock exchange, also found no overreaction effect when they compared losers and winners with equal size. In order to investigate the role of size, each stock in their ascending formation period is ranked based on their market value. Additionally, size is measured at the end of the formation period which is consistent with De Bondt and Thaler (1987), Fama and French (1986) and Zarowin (1990). The market value is used as proxy for firm size. To classify whether a stock is either small or big, at the end of each formation period the sample is split into half based on their market values, so each stock is either big or small relatively to their market value. After classifying which stocks are small or big, each stock is then ranked based on their prior period performance.

Table 7

Portfolio size of Loser and Winner portfolios at the end of the formation period

The average size of each portfolio at the end of the 36-month formation period. Size is measured as the market value displayed in millions for the ten non-overlapping 36-month formation periods.

Formation period Loser Portfolio Winner Portfolio

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Table 8

Average Cumulative Abnormal Returns for portfolios based on their market size and prior performance

All AEX constituents with a complete dataset in the formation period of 36 months in the period 1983-2017 are identified. First, all stocks are ranked based on their market value, which is a proxy for size. In each formation period a stock is either small or big. Second, within the size categories small and big, all stocks are then ranked on their prior performance. For each portfolio the cumulative market-adjusted abnormal returns are calculated over 36 months. This table represents the average market-adjusted abnormal returns (ACAR) for each test period for the small loser, small winner, big loser, big winner and the contrarian portfolio (loser-winner) and their t-statistic respectively, which test whether the returns of the portfolios are significantly different form zero. The contrarian portfolio has a long position in the loser portfolio and a short position in the winner portfolio. The Overreaction Hypothesis states that !"!#$,&> 0 and !"!#*,&< 0, which therefore implies that (!"!#$,&− !"!#*,&) > 0. To test the profitability of the contrarian strategy, the null hypothesis is tested via 01:!"!#$,& = 0, 03:!"!#*,& = 0 and

04: (!"!#$,&− !"!#*,&) = 0. The hypotheses are tested via a t-test on the means of ACAR. The significance levels 1%, 5% and 10% are denoted by ***, **, *. The Bonferroni correction is denoted as B, which denote whether the returns of the portfolios are significantly different from zero adjusted by the Bonferroni correction.

ACAR in the months after the 36-month formation period

6 12 18 24 30 36

Portfolio Mean t-statistic Mean t-statistic Mean t-statistic Mean t-statistic Mean t-statistic Mean t-statistic

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This results in portfolios of Small-Losers, Small-Winners, Big-Losers and Big-Winners. The number of stocks in each portfolio are based on the number of stocks used for testing overreaction for the month test period. The main feature of this process is that for each non-overlapping 36-month period, stocks are selected independently by their market value and their prior performance. This results in, for example, that the Small-Loser portfolio are truly small losers (Zarowin, 1990). Table 8 presents the average cumulative abnormal returns for the ten 36-month non-overlapping test periods adjusted by size and prior performance and with different holding periods in to the test period namely: 6, 12, 18, 24, 30 and 36 months. Panel A consist of Loser and Small-Winner portfolios. The Small-Loser portfolio consist of stocks with the smallest market values and lowest prior performance. The Small-Winner portfolio consist of stocks with the smallest market values and highest prior performance. The contrarian portfolio for the small portfolios is denoted by SL-SW (Small Losers - Small Winners). Panel B consist of Big-Loser and Big-Winner portfolios. The Big-Loser portfolio consist of stocks with the highest market values and lowest prior performance. The Big-Winner portfolio consist of stocks with the highest market values and highest prior performance. The contrarian portfolio is denoted by BL-BW (Big Losers - Big Winners).

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5.3. Increasing the length of the formation and test period

De Bondt and Thaler (1985) found in their research that extending the formation period to five years leads to results with higher significance levels. Yet, this five-year period is more prone to mean reversion literature than our previous used formation periods of one, two and three-year (Brailsford, 1992). In line with the findings of De Bondt and Thaler, the study of Fama and French (1988) found that mean reversion takes place among three to five years. If the AEX has a mean reversion characteristic, then overreaction will be found more likely for a five-year formation period, if however, overreaction exist at all in the AEX. Accordingly, I run an additional test using a five-year formation and test periods. The results are presented in table 9.

Table 9

Differences between Average Cumulative Abnormal Return (ACAR) over 60 months into the test period.

All AEX constituents with a complete dataset in the formation period of 60 months in the period 1983-2017 are identified. The market-adjusted abnormal returns are calculated for each stock and are ranked based on their cumulative abnormal return. The 20% worst performing stocks shape the loser portfolio and 20% best performing stocks shape the winner portfolio. For each portfolio the cumulative market-adjusted abnormal returns are calculated over 60 months. This table represents the average market-adjusted abnormal returns (ACAR) for each test period for the loser, winner and the contrarian portfolio (loser-winner) as well and their t-statistic respectively, which test whether the returns of the portfolios are significantly different form zero. The contrarian portfolio has a long position in the loser portfolio and a short position in the winner portfolio. The Overreaction Hypothesis states that !"!#$,&> 0 and !"!#*,& < 0, which therefore implies that (!"!#$,&− !"!#*,&) > 0. To test the profitability of the contrarian strategy, the null hypothesis is tested via 01:!"!#$,&= 0, 03:!"!#*,&= 0 and 04: (!"!#$,&−

!"!#*,&) = 0. The hypotheses are tested via a t-test on the means of ACAR. The significance levels 1%, 5% and 10% are denoted by ***, **, *. The Bonferroni correction is denoted as B, which denote whether the returns of the portfolios are significantly different from zero adjusted by the Bonferroni correction.

Formation period Test period ACAR for Loser ACAR for Winner ACAR for Loser-Winner 1983-1987 1988-1992 _-0.7795 _0.0067 _-0.7862 1988-1992 1993-1997 _0.2724 _0.3662 _-0.0938 1993-1997 1998-2002 _-0.0756 _0.0787 _-0.1543 1998-2002 2003-2007 _-0.1997 _-0.1078 _-0.0919 2003-2007 2008-2012 _0.2674 _-0.2846 _0.5520 2008-2012 2013-2017 _0.1973 _-0.0663 _0.2636 Average _-0.0318 _-0.0007 _-0.0311 t-statistic _-0.1920 _-0.0081 _-0.1686

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-3.11% (t-statistic: -0.1686). In line with the preceding results, the differences between the average cumulative abnormal returns between the two portfolios is not statistically significant. The results in Table 9 are similar to those of Brailsford (1992). Brailsford (1992) found after increasing the formation and test period to five years no evidence of overreaction in the Australian equity market. The average cumulative abnormal returns of the loser portfolio were -104.6% and for the winner portfolio -72.9%. Moreover, Braildford (1992) found no difference in cumulative abnormal returns between the winner and loser portfolio that were statistically significant. Although the results in Table 9 are not that big of that of Brailsford, the conclusion is identical. The composition regards to the amount of stocks in each portfolio of Table 9 can be found in Appendix C.

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6. Conclusions

This paper examines whether the AEX is prone to the overreaction hypothesis. The overreaction hypothesis is based on the findings of De Bondt and Thaler (1985, 1987), which found evidence that stocks which performed poorly in the past tend to outperform stocks that performed good in the past. If there is any significant overreaction, then stock prices will outrun their intrinsic value and reversals for these stocks should be predictable from data of the past (De Bondt and Thaler, 1985). I investigate the potential overreaction hypothesis, time-varying beta, size effect and different formation and test periods for the AEX, using monthly stock data from January 1983 to December 2017. To do so, different formation and test periods have been considered namely, 12-month, 24-12-month, 36-month and 60-months. The 60-month formation and test period were used for further analysis. The results show no significant overreaction effect in the AEX for all formation and test periods. In all test periods losers and winners cumulated negative abnormal returns. These findings conclude that a contrarian portfolio, which buy past losers and selling short past winners, will not be profitable. These findings are contradictory to the findings of De Bondt and Thaler (1985, 1987), Clare and Thomas (1995) and others, which found significant evidence of the overreaction hypothesis, meaning that a contrarian portfolio earned positive abnormal returns. However, the findings in this paper are extensively in line with the findings of Brailsford (1992), who found no overreaction effect in the Australian equity market during the time period 1958 to 1987.

Additionally, I investigate whether loser portfolios are on average riskier than winner portfolios. Based on the methodology used by Chan (1988), I find that loser portfolios are on average riskier in the formation and test period than their counterpart. Noticeably, these findings are not in line with the findings of Chan (1988), Forner and Marhuenda (2000) and Guant (2000) who found that the betas for the loser portfolios are smaller in the formation period and bigger in the test period. Furthermore, there is a shift in systematic risk from the formation period to the test period, resulting in less risky portfolios for both the loser portfolio and the winner portfolio. Regards to the contrarian portfolio, there was no significant evidence of overreaction via the Jensen performance index. The beta in the contrarian portfolio is on average positive, which mean that losers are riskier in the contrarian portfolio. This is in line with the findings of Clare and Thomas (1995) who found indeed that losers are riskier than the winner stocks.

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Big-Winners. There are no significant positive average abnormal returns found for the four classifications. Small-Losers and Small-Winners tend to cumulated negative abnormal returns. Small-Losers performed even worse than their counterparts. Big-Losers and Big-Winners cumulated both negative abnormal returns. Whereas losers performed better than Big-Winners. Furthermore, the contrarian portfolio of the Big-Losers and Big-Winners cumulated positive average abnormal return. However, the results are not statistically significant.

Fama and French (1988) argued that a five-year period is more prone to mean reversion behaviour than the previous formation and test periods. Additionally, De Bondt and Thaler (1985) found that their overreaction results were increased when they increased their formation and test period to 60-months (five years). Additional analyses are made in which the formation and test period are increased to 60-months. The results indicate that there is still no overreaction effect in the AEX. The loser and winner portfolio cumulated negative average abnormal returns. Therefore, this result is not in line with De Bondt and Thaler (1985) and Fama and French (1988). However, Brailsford (1992) found no overreaction effect when increasing the formation and test period to 60-months. Accordingly, the results from my analyses are in line with the findings of Brailsford (1992).

In conclusion, this paper contributes to the existing literature due to the fact that the AEX is not widely analysed. In particular, research on the overreaction hypothesis in the AEX is sparse. These findings have implications for investing strategies for investors in the AEX. This mean that investors cannot solely earn arbitrage profits by conducting a contrarian investment strategy, where they buy past losers and selling past winners. Worth mentioning, the results are not adjusted for transaction costs.

6.1. Limitations and suggestions for further research

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One of the most critical assumption in this research is to deal with delisted firms. In this paper I make an assumption that firms have to have a complete dataset in the formation period and have to be traded at least once in the test period. If, for some reason, a company is delisted in the test period and it had trade at least for one day in the test period, I assumed that the last traded price will be constant over time. However, there are other solutions which are interesting to research how it affects the results with respect to the overreaction hypothesis. First, when a firm is delisted the proceeds can be reinvested equally among other stocks in the portfolio. Second, when a firm is delisted, the proceeds can be reinvested in the market index. Finally, when a firm is delisted the stock will be excluded from any analyses. However, the last solution will increase the survival bias.

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