Contrarian Investment Strategies in European Markets I

Contrarian investment strategies in European markets I. (Ioannis) Soukoulis Student number: 1263130 Supervisor: dr. K.K. (Korhan) Nazliben

Master of Finance University of Tilburg Netherlands 2017

Acknowledgements I would like to express my sincere gratitude to the professors and staff of Tilburg University for a very productive master program. Especially the Finance department who helped me expand my horizons and introduced me to the world of Finance. It was truly a life changing experience that helped me set the foundation for what I hope is a long and prosperous career in Finance. Furthermore I would like to thank my supervisor dr. K.K. Nazliben who was extremely helpful especially since this was the first time I wrote such an extensive thesis. Above all I would like to thank my family who was very supportive and understanding during this long and arduous process. The topic of my thesis is contrarian investment strategies in European markets. Through it I achieved a greater understanding of the financial markets and I was introduced to the field of value investing and gave me the incentive to pursue this subject further.

Contents 1 Introduction ...... 1 1.1 Motivation ...... 2 1.2 Research questions ...... 3 1.3 Contribution ...... 3 1.4 Research Methodology and data ...... 4 2 Literature review ...... 5 2.1 Contrarian and Momentum Strategies...... 5 2.1.1 Long-term return reversal ...... 5 2.1.2 Short term return reversals ...... 6 2.1.3 Medium-term return continuation ...... 6 2.2 Price to Earnings ...... 7 2.3 Book value of equity to Market value equity ...... 10 2.4 Price to Cash flow ...... 13 2.5 CAPM...... 14 2.6 Efficient Markets Hypothesis ...... 15 2.7 Asset price anomalies ...... 18 2.7.1 Explanation for asset pricing anomalies ...... 19 2.7.2 Higher returns as compensation for additional risk ...... 19 2.7.3 Results contrary to the EMH ...... 19 2.7.4 Higher returns due to the design of the research and data biases ...... 20 3 Methodology and Data ...... 22 3.1 Research methodology ...... 22 3.1.1 Portfolio Analysis ...... 23 3.1.2 Cross-sectional regression ...... 25 3.2 Hypothesis ...... 29 3.2.1 Hypothesis test regarding variable P/E ...... 29 3.2.2 Hypothesis test regarding variable P/CF ...... 29 3.2.3 Hypothesis test regarding variable P/B ...... 30 3.2.4 Hypothesis test regarding variable SG ...... 30 3.2.5 Hypothesis test regarding variable ME ...... 31 3.3 Mean reversion ...... 31

3.4 Data ...... 32 4 Empirical study ...... 35 4.1 Analysis of the German stock market ...... 35 4.1.1 Descriptive statistics ...... 35 4.1.2 Mean reversion ...... 35 4.1.3 Ljung-Box Q-Test...... 36 4.1.4 Contrarian investment strategy ...... 39 4.1.5 Cross sectional regression ...... 49 4.2 Analysis of the French stock market ...... 52 4.2.1 Descriptive statistics ...... 52 4.2.2 Mean reversion ...... 52 4.2.4 Ljung-Box Q-Test...... 53 4.2.5 Contrarian investment strategy ...... 55 4.2.6 Cross sectional regression ...... 63 4.3 Analysis of the Dutch stock market ...... 66 4.3.1 Descriptive statistics ...... 66 4.3.2 Mean reversion ...... 67 4.3.3 Ljung-Box Q-Test...... 67 4.3.4 Contrarian investment strategy ...... 69 4.3.5 Cross sectional regression ...... 77 5 Are Value portfolios inherently riskier? ...... 79 5.1 “Bad” states of the world ...... 80 6 Results- Conclusions ...... 83 6.1 Results from the One-dimensional Portfolio analysis approach ...... 83 6.2 Results from the two-dimensional Portfolio analysis approach ...... 84 6.3 Results from the cross sectional regression...... 85 References ...... 87 Appendix A ...... 100 DAX yearly composition ...... 100 CAC yearly composition ...... 101 AEX yearly composition ...... 103 Appendix B ...... 105

Appendix C ...... 108 DAX ...... 108 CAC40 ...... 124 AEX ...... 140

1 Introduction In the modern globalized environment finance is experiencing exponential growth, in an effort by researchers and investors, to interpret the chaotic stock movements throughout time. As long as this effort is successful, the more efficient financial markets become, without ever reaching a level of full efficiency, since the continually changing market conditions give rise to new trends and new ways to achieve abnormal returns. Without a doubt, the complexity of today’s markets has added numerous additional factors that could affect the cross section of equity returns. This fact has put into doubt the Capital Asset Pricing Model (CAPM), which takes into account only one factor a stock’s systemic risk. Among the many strategies trying to exploit the market`s inefficiencies there are the contrarian and momentum investment strategies. Contrarian strategies claim that investors don’t always act rationally, and further overreact to new information in the market moving prices away from their perceived fundamental value. If the contrarian investor believes that a stock’s price is lower than its fundamental value the investor will go long believing this stock to be undervalued. On the other hand, if the contrarian investor believes that a stock is priced higher than its fundamental value, then the investor will go short on the stock believing it to be overvalued. Stocks that are perceived as overvalued are called Growth stocks and stocks that are perceived as undervalued are called Value stocks. (Lakonishok, Shleifer and Vishny 1994)

For the contrarian investment strategy to work it is necessary that the market is mean reverting. Mean reversion is an empirical observation often used in asset investing and is based on the idea that both an asset’s high and low prices are temporary and that stock prices will tend to have an average price over time. (Poterba and Summers 1988) Therefore, when the current market price is less than the average price, the stock is attractive for purchase due to the expectation of an increased price over time and vice versa when the current market price is above the average price, due to the expectations of reversion towards the average

Lakonishok, Shleifer and Vishny (1994), Fama and French (1996a) and Chan and Lakonishok (2004) concluded that value strategies outperform growth strategies in the US stock market. Fama and French (1998) have also investigated markets outside the US testing if the values premium found in past US returns were sample specific. Their findings for non-US markets were similar to those presented previously for the US. In twelve out of thirteen markets value stocks outperformed growth stocks, in the period 1975-1995 including Germany, France and the Netherlands which is

1 relevant for this paper. The consensus is that a buy and hold investment strategy with a long horizon, consistent of a long position in value stocks and a short position in growth stocks has yielded superior returns.

On the other hand, other researchers have found that in the short term stock returns behave quite differently. Jegadeesh and Titman (1993) have found that in the US market buying growth stocks and shorting value stocks gives us positive returns when the portfolio is held between 3 and 12 months. This shows us that in the short term there is a strong trend or momentum effect on stock returns. This find has the opposite implication about stock returns meaning that investors are underreacting to new information and this information are slowly being incorporated into the price. At first glance, the fact that investors may both overreact and underreact to new information might seem like a contradiction but research Barberis, Shleifer and Vishny (1998) has shown that these behaviors can coexist in the market and created models that reflect the investor’s behavior. Barberis, Shleifer and Vishny (1998) propose a model motivated by the idea that investors pay too much attention to the strength of the evidence they are presented with and too little attention too its statistical weight. For example, earnings announcements are information with low strength but significant statistical weight. Also a series of earnings announcements are information with high strength but low statistical significance. From this they predict that stock prices underreact to single earnings announcement but overreact to consistent patterns of good or bad news.

1.1 Motivation These findings challenge the most central hypothesis in finance which is the Efficient Market Hypothesis (EMH). The hypothesis claims that markets are efficient and all available information are incorporated in the price of an asset. Therefore, is impossible to outperform the market with information available to everyone 1 . This is contrary to what advocates of momentum and contrarian strategies claim which is that you can take advantage of the irrationality of investors without exposing yourself to higher risk2. On the other hand proponents of the EMH propose that an explanation for the higher returns of these strategies are the higher risk inherit in these strategies3.

1 Fama (1965) 2 Lakonishok, Shleifer and Vishny (1994) 3Fama and French (1993, 1996, 1998)

1.2 Research questions What are contrarian investment strategies?

Contrarian investment strategies are going to be introduced showing how they work and use previous studies that confirm their effectiveness4.

Do European markets mean revert?

We will perform an autocorrelation analysis on index returns to see if there is positive or negative serial correlation

Do contrarian investment strategies work in European stock markets?

This paper will perform an empirical study on different European stock markets to see if the theories that are introduced are effective. Especially comparing the findings of this paper to the findings of Lakonishok, Shleifer and Vishny (1994), Chan, Hamao and Lakonishok (1991), Brouwer, van der Put and Veld (1996), Fama and French (1998), Chin, Prevost and Gottesman (2002)

Can the differences between investment strategies be explained by higher risk?

Fama and French (1998) argue that markets are efficient and that the better performance of value investing is due to value stocks being riskier. However in the articles by Lakonishok, Shleifer and Vishny (1994) no evidence is found that value stocks are riskier than growth stocks. This paper will investigate if value strategies are inherently riskier by observing their performance during bad states of the world which in this paper means observing their performance during the 2008 financial crisis. If value stocks still outperform growth stocks in the extreme conditions of the 2008 credit crisis then we can conclude that value stocks aren’t fundamentally riskier. Furthermore we will calculate the beta for both value and growth portfolios and compare them.

1.3 Contribution The research presented so far are performed on the US and International markets and in a large part in bull markets. However, there is a lack of research Europeans markets that’s why this thesis will focus on the markets of Germany, France and Netherlands. Since overreaction plays a

4 Lakonishok, Shleifer and Vishny (1994), (Chan, Hamao and Lakonishok (1991), Brouwer, van der Put and Veld (1996), Fama and French (1998), Chin, Prevost and Gottesman (2002)

3 significant role in contrarian strategies it will be interesting to test these strategies during the recent credit crisis. The high risk in these markets will help us test the hypothesis that contrarian strategies are inherently riskier. If value stocks still outperform growth stocks in the extreme conditions of the 2008 credit crisis then we can conclude that value stocks aren’t fundamentally riskier. Therefore, the purpose of this thesis is to investigate if a value premium exists in the stock markets of Germany, France and Netherlands especially during the credit crisis of 2008.

1.4 Research Methodology and data In order to conduct our research we have chosen firms from different European stock markets from the period 1998-2017 and we collected our data through DataStream. Furthermore we arrived in our result using 2 different methodologies which are:

a) Portfolio Analysis Approach b) Cross Sectional Regressions Approach

According to the Portfolio Analysis Approach we classify firm stock in portfolios based on a particular variable. For example if the variable we are going to use as our basis is firm size then the first portfolio will include the smallest firms and the last portfolio will include the largest firms. For the Cross Sectional Regression Approach we attempt to find if one or all of our variables are statistically significant, if this is true it goes against the CAPM

2 Literature review 2.1 Contrarian and Momentum Strategies One very important parameter in forecasting future equity returns are historic equity returns. In this field research5 varies and tends to conclude that historic returns have the ability to predict the cross-section of future equity returns. However, research in this field are distinguished in three different categories which are:

2.1.1 Long-term return reversal In this category are included researchers6 like De Bondt and Thaler (1985,1987) who noticed return reversals in the long term. This kind of strategies are called contrarian meaning buying stock that have bad past performance (past losers) and sell stock that have good past performance. In their research, they proved that in a holding period of three to five years the stock that had a bad performance in the previous three to five years in the next three to five years performed better than a stock that had who had a good performance in the previous three to five years. However the researchers attribute this fact to markets overreaction which pushed the stock’s price away from its fundamental value.

Nevertheless Chan (1988) and Ball and Kothari (1989) claim that abnormal risk-adjusted returns that turn up in contrarian strategies are due to the failure of returns to adjust to risk. They think that the stocks that are labeled as winners and losers must be subjected to big changes in risk between the period of portfolio formation and the period where Debondt and Thaler apply their methodology.

Furthermore Zarowin (1990) thinks that the reversal phenomenon connected to the size effect because the loser firms tend to be small and the winner firms tend to be large. On the other hand Chopra, Lakonishok and Ritter (1992) showed that reversal doesn’t show up when returns are adjusted for risk and size. However Ball, Kothari and Shanken (1995) and Conrad and Kaul (1993) gave their own explanation about this phenomenon and claimed that it was due to micro-structure induced biases.

5 Ball and Brown (1968), Asquith (1983), Bernard and Thomas (1990), Michaely, Thaler and Womack (1995), Ikenberry, Lakonishok and Vermaelen (1995), Desai and Jain (1997), Rouwenhorst (1998), Grinblatt and Moskowitz (1999), Jegadeesh and Titman (2001), Moskowitz (2003) 6 US: De Bondt and Thaler (1985), Belgium: Vermaelen and Versinge (1986), Japan: Dark and Kato (1986), Brazil: Da Costa (1994), UK: Clare and Thomas (1995), Dissanaike (1996), Loughran and Ritter (1996), Spiess and Afflect- Graves (1995), Canada: Kryzanowski and Zhang (1992)

2.1.2 Short term return reversals More recent research offer evidence for the short-term reversal of returns. For example Lehmann (1990) identified return reversals in a weekly basis and Jegadeesh (1990) and Lo and McKinlay (1990b) report return reversals in a monthly basis. The above researches show that contrarian strategies that pick stocks according to their returns the previous week or month achieve abnormal returns.

Chang, Mcleavey and Rhee (1995) report short-term return reversals in the Japanese stock Market after returns have been adjusted for risk and size. Furthermore Kaul and Nimalendran (1990) and Jegadeesh and Titman (1995) researched in what degree the bid – ask prices spread is able to explain the short-term return reversal.

In addition Lo and McKinlay (1990b) mention in their research that a big part of abnormal returns is caused by a late reaction of the stock’s price to common factors and not to market overreaction. Also Conrad, Hameed and Niden (1994) used weekly data and showed that the size of the volume of past transactions is useful in explaining the phenomenon of short term return reversals. Specifically researchers think that the phenomenon is attributed to high transaction volumes. In other words stocks with high transaction volumes show short-term return reversal while stocks with low transaction volume show return continuation.

2.1.3 Medium-term return continuation In contrast with the results of the two previous categories, Jegadeesh and Titman (1993) state that in the medium term, from three to twelve months, stocks that are past winners on average continue to outperform past losers and so a momentum effect is created in stock prices. Although for the two previous categories a number of competing explanations were formulated for this one not many have been developed. Fama and French (1996a) developed a model that explains the long- term return reversals but cannot explain the medium-term continuation of returns. Furthermore Rouwenhorst (1998) examines medium-term return continuation phenomenon in twelve other countries and proposes that it’s not possible to attribute it to data-snooping bias. Another possible explanation is that the profitability of momentum strategies is that it is a result of overreaction which is caused by positive feedback trading strategies. This explanation is similar to the explanation by Delong, Shleifer, Summers and Waldmann (1990).

Regarding the markets of France, Germany and the Netherland some research has shown that this strategy can succeed. Capaul, Roweley and Sharpe (1993) studied contrarian strategies for France and Germany and found that value strategies outperformed growth strategies for both countries. For the Netherlands Tse and Rijken (1995) and Brouwer, van der Put and Veld (1996) similarly found the existence of a value premium. Mun, Vasconellos and Kish (1999) concluded that for the French and German markets short-term contrarian strategies work best the highest contrarian profits are obtained in the short run and the profits decrease over time. In addition, higher returns are not correlated to increases in the risk coefficients, which is consistent with investor overreaction.

2.2 Price to Earnings A variable that has been used by most researchers as an explanatory variable is the Price to Earnings ratio (P/E). Research7 has shown that stock with low P/E ratio achieve higher returns compared to stocks with low P/E ratio. However, the P/E ratio indicates how many times its earnings per share the market believes the stock to be worth at this moment and usually a firm with good management and hopeful future growth prospects will have high P/E ratio. Furthermore, in case a stocks P/E ratio is higher than the industry average then investors will pick this stock because they will believe it to be the industry’s best firm, either because it’s overvalued either because investors have overstated the firm’s abilities. However, the negative relation between this ratio and returns is confirmed from the study of the Earnings to Price ratio (E/P) which is the reverse of the P/E ratio. The researchers who studied explanatory power of the E/P ratio concluded that there is a positive relation between this variable and stock returns. The research that has been done in this field are presented below

Initially, the first research regarding the E/P ration was performed by Graham and Dodd (1934). Later Nicholson (1960) publish the first comprehensive research regarding the relation of this variable and expected returns of stock and showed that stock with low P/E ratio had higher returns than firms with high P/E ratio. Next Basu (1977) tried explore if the EMH is in effect by testing the explanatory power of the P/E ratio. The sample that he used came from COMPUSTAT and included stock from the NYSE of firms between 1956 and 1971. During the research Basu

7 US: Graham and Dodd (1934), Nicholson (1960), Ball (1978), Basu (1997), Reinganum (1981), Peavy and Goodman (1983), Japan: Aggarwal, Hiraki and Rao (1989), Chan, Hamao and Lakonishok (1991), UK: Strong and Xu (1997), Singapoure: Wong and Lye (1990), New Zealand: Gillan (1990)

7 concluded that from 1957 and 1971 portfolios of stocks with low P/E ratio had, on average, had higher risk adjusted returns compared to portfolios of stocks with high P/E ratio. Also he proved that the explanatory power of this variable regarding expected returns in US markets exceeds that of size effect and systemic risk beta. However, the above result that returns of stock with low P/E ratio tend to be higher than what their risk implies, even if we take into account research and transaction costs and taxes, comes in opposition to the EMH. At the same time, the information of the P/E ratio is not fully reflected in the stock price as fast or as accurately as described by the EMH as there are lags as well as imbalances in the examined period. Ball (1978) concluded that E/P ratio proxies for omitted risk factors and that’s why it explains part of the cross-section of equity returns. In other words when a stock has relative high risk and expected returns their prices are lower relative to earnings and therefore their E/P ratio is higher.

Reinganum (1981) tried to see if some portfolios that he had formulated based on variables size and E/P achieve returns that are different than those predicted than the CAPM. His sample included 566 firms from the NYSE and their quarter earnings, beginning from the last quarter 1975, 8 quarters in total. The results of the t-tests showed that stocks with high E/P ratio achieve higher returns from those with lower E/P ratio even after accounting for the beta coefficient while the most important finding is that the abnormal returns were maintained for at least six months. Also the results of his research showed positive abnormal returns in the two portfolios with the lowest size and furthermore that the effect of the size variable is larger than the effect of the E/P variable. According to the above Reinganum concluded that that the CAPM is inadequate and the size effect includes the E/P effect. Cook and Rozeff (1984) concluded that both the size and the E/P effect are at work. They claim that both effects measure separate aspects of a single underlying effect. Also they found that half of the E/P effect occurs in January and the other half occurs the rest of the year. Banz and Breen (1986) and Rogers (1988) concluded that the E/P effect is a subset to the size effect. However, they found no independent E/P effect throughout the year. Also, they claimed that low P/E ratio becomes more powerful when COMPUSTAT is used as a data source but the low P/E effect is not evident when sequentially collected COMPUSTAT data are used. Which means an ex-post-selection bias (which means that the sample does not use non surviving firms) and look-ahead bias (which means that in the research uses data that are not yet known to the investors) are the causes for the low P/E effect. Using earnings data which are not known to

8 investors to form portfolios tends to put high return (positive earnings surprise) companies in low P/E portfolios and low return (negative earnings surprise) companies in high P/E portfolios.

Jaffe, Keim and Westerfield (1989) tried to study the effect of the variables size and E/P on stock returns. They concluded that the problem that researchers were facing was due the use of small time periods for analysis and also an inability to separate the effects of January from the rest of the months. In addition Jaffe, Keim and Westerfield in an attempt to solve the problem used improved statistical techniques. They used a longer time period in their data, with small survivor biases, applied seemingly unrelated regression (SUR) test and placed emphasis on the differences between January and other months. They collected returns and prices from CRSP, earnings per share from COMPUSTAT8 PST for the years 1967-1986 and from Bankdata for the years 1950-1966. The results showed a significant relation between E/P, size and returns for the period 1951-1986. The coefficients on both E/P and size are significant in January, but only the E/P coefficient is significant outside of January

Levis (1989) showed in his research that both strategies are equally profitable. In other words either if we use size or the P/E ratio we will achieve the same profits. The problem that turned up is that it is often hard to distinguish between the size and share price effects. This evidence lends further credence to the view that these two variables are either proxies for each other or both are just proxies for more fundamental determinants of expected returns for common stocks.

Wong and Lye (1990) examined the effect of size and E/P of the firms in the Singapore stock exchange for the period from 1975 to 1985. What they found is that the high E/P stocks have earned, on average, much higher risk-adjusted returns than the low E/P stocks. This E/P effect is clearly significant even after the size effect, as measured by the market value of firm, was randomized across the high and low E/P portfolios. A further analysis shows that the E/P effect is more significant than size effect but not independent of firm size.

Chang, Hamao and Lakonishok (1991) studied 1570 firms from the Japanese stock exchange from 1971 – 1988 and found there is a significant P/E effect in this market.

8 Data from Compustat are susceptible to two kinds of biases 1) ex-post selection bias which is due to the exclusion of non-surviving firms in the data 2) look ahead bias which is due to inclusion of data that are not yet known to the investors

2.3 Book value of equity to Market value equity A variable that is widely used by researchers is the ratio of Book value to Market value otherwise called book-to-market (B/M) or book equity-to-market equity. Every research9 concluded that this variable is significant in predicting future returns and many claimed that maybe it’s the most important. Furthermore they concluded that stock with a high value of this ratio achieve higher returns than stock with a low value of this ratio. Some researchers even argued that this positive relation between the B/M ratio and stock returns is more pronounced in the long term. However there aren’t many researches that prove the ability of the B/M ratio to predict the cross-section of equity returns. In the US research has been conducted by Stattman (1980), Rosenberg, Reid and Lanstein (1985) and Fama and French (1992). Outside of the US the most prominent researches, and particularly in Tokyo, has been done by Aggarwal, Rao and Hiraki (1989), Chan, Hamao and Lakonishok (1991) and Capaul, Rowley and Sharpe (1993). Regarding the London stock exchange research has been conducted by Capaul, Rowley and Sharpe (1993) and Strong and Xu (1997) while Capaul, Rowley and Sharpe (1993) have also researched the German, French and Swedish stock exchange regarding the ability of the B/M ratio to predict stock returns10. Below there is a more detailed presentation of the research regarding the B/M ratio and also the different explanations that researchers gave. However, in the literature there those that doubt the usefulness of this variable.

Fama and French (1992) were the first that documented empirically that the B/M ratio as well as the market value of equity (MVE) capture the cross-section of average stock returns for the period 1963-1990. According to the researchers stocks with high B/M had higher returns than stock with

9 Rosenberg, Reid and Lanstein (1985), Chan, Hamao and Lakonishok (1991,1993), Penman (1996), Claessens, Dasgupta, Glen (1995), Capaul, Rowley and Sharpe (1993), Fairfield (1994), He and Ng (1994), Lakonishok, Shleifer and Vinshny (1994), Davis (1994), La Porta (1996), Fama and French (1996,1998), Hawawini and Keim (1997), Knez and Ready (1997), Barber and Lyon (1997), Vos and Pepper (1997), Chan. Karceski and Lakonishok (1998), Archour, Harvey Hopkins and Lang (1998), Chui and Wei (1998), Fama and French (1998), Davis, Fama and French (2000), Ho, Strange and Piesse (2000), Li and Pinfold (2000), Trecartin Jr (2000), Bayless and Jay (2001), Lynch (2001), Barry, Goldreyer, Lockwood and Rodriguez (2002), Jensen and Mercer (2002), Caspar G. M. de Groot and Willem F. C. Verschoor (2002), Griffin and Lemmon (2002), Griffin (2002), Keith S. K. Lam (2002), Moskowitz (2003), Chu- Sheng Tai (2003), Lam and Spyrou (2003), Anderson, Korsun and Murell (2003), Ali, Hwang and Trombley (2003), Cooper, Jackson and Patterson 2003) 10 US: Stattman (1980), Rosenberg, Reid and Lanstein (1985), Fama and French (1992), Liew and Vassalou (2000), Tokyo: Aggarwal, Rao and Hiraki (1989), Chan, Hamao and Lakonishok (1991), Capaul, Rowley and Sharpe (1992), Echbo, Masulis and Norli (2000), London: Capaul, Rowely and Sharpe (1993), Strong and Xu (1997), France, Switzerland, Germany: Capaul, Rowely and Sharpe (1993), Japan: Chan et al. (1991) Chui and Wei (1998), Daniel, Titman and Wei (2001), Hong Kong: Lam (2002), New Zealand: Bryant and Eleswarapu (1997), Vos and Perrer (1997), Pinfold, Wilson and Li (2001), Athens: Kousenidis, Negakis and Floropoulos (2000)

10 lower B/M ratio. Fama and French (1995) studied whether the behavior of stock prices, in relation to size11 and book-to-market-equity (BE/ME), reflects the behavior of earnings. Initially they wanted to answer the question if stock prices forecast the reversion of earnings growth observed after firms are ranked on size (MVE) and BE/ME. The stocks they chose came from the US stock market and specifically from the NYSE, AMEX and NASDAQ from the period 1963-1992. Their

12 profitability measure was the variable 퐸퐼(푡)/퐵퐸(푡−1) and concluded that stocks with a low BE/ME ratio are on average more profitable than those with high BE/ME ratio for four years before the portfolio formation and at least five years after. They also concluded that short-term variation in profitability has little effect on stock price and book-to-market-equity; and that the BE/ME variable is associated with long-term differences in profitability. Furthermore, Firms with high BE/ME tend to be persistently distressed. They have low EI/BE ratio for at least 11 years around portfolio formation. Conversely, low BE/ME is associated with sustained strong profitability. Finally they concluded that small stocks tend to be less profitable than big stocks.

Chan, Hamao and Lakonishok (1991) studied the predictability of stock returns in the Japanese stock market using B/M ratio among others13. For their reseach they used monthly data from stocks in the TSE for the period 1971-1988 and they also concluded that stocks with high B/M ratio achieved higher returns compared to stocks with low B/M ratio. In addition, Pontiff and Schall (1998) studied the explanatory power of the BE/ME ratio regarding the prediction of average sock returns. For their research, they used data from the Dow Jones Industrial Average14 (DJIA) for the period 1920-1993 as well as the Standard & Poor’s15 index (S&P). One of the conclusions from this research is that the ability of the BE/ME ratio to predict returns is related with the ability of the book value to predict future cash flows, then book values of the S&P are better cah flow predictors than the book values of the DJIA. In general according to the researchers above, the

11 They proved that BE/ME is a better measure of profitability than size. Proportionally big size low book to market stocks are more profitable than small size high book to market stocks 12 Where 퐸퐼(푡) (equity income) are profits after profits after taxes, interest and dividends 퐵퐸(푡−1) is previous year’s book equity 13 They used the variables E/P, C/P and size 14 The DJIA includes the prices of the largest industrial firms in the US. DJIA’s price is calculated by the sum of the prices of the 30 stocks that are included in the index divided by a special divisor. Every time a stock included in the index performs a split or is replaced by another stock the divisor is adjusted in order for the price of the index to remain unaffected 15 The S&P index is considered a more representative index than the DJIA because it includes 500 stock compared to DJIA’s 30 stock. This results in S&P’s book-to-market ratio doing a better job than DJIA’s book-to-market ratio. S&P data are available after 1940

DJIA B/M ratio has better explanatory power regarding returns from the rest of the independent variables (.interest yield spreads and dividend yields). Furthermore BE/ME explanatory power is due to the book value’s ability to predict future cash flows. However after 1960 the S&P BE/ME ratio is a better predictor of returns from the DJIA BE/ME ratio, therefor the S&P book values are better predictors of future cash flows than DJIA book values.

La porta, Lakonishok, Shleifer and Vishny (1997), Ashiq, Hwang Lee-Seok and Tombley (2003) and Skinner and Sloan (2002) in their research came to the same conclusion that the behavior of the BE/ME variable was due to the mispricing of equity, which had abnormally high BE/ME ratio, while also to the overreaction16 of investors regarding firm performance. Graham and Dodd (1934), DeBondt and Thaler (1987) Lakonishok, Shleifer and Vishny (1994) and La Porta (1996) agreed that the correction of these overreaction causes the book-to-market effect and therefore to the extent that this hypothesis is true proves that the market is inefficient. On the other hand DeChow and Sloan (1997) did not agree with the overreaction theory and proved that stock prices are driven by the naive reliance that investors have in analyst’s forecasts which sometimes could be regarded as biased. Daniel and Titman (1997) in their research showed that the book-to-market effect is a result of investor behavior, who prefer stocks with high BE/ME ratio (growth stocks) while at the same time exclude from their portfolios stocks that their BE/ME ratio is not high enough.

Loughram (1997) and Loughram and Ritter (2000) used data from the period 1963-1995 have completely disputed the explanatory power on the cross-section of equity returns of the BE/ME ratio. Loughram (1997) claimed that professional investors should use liquidity as a tool to form portfolios and not the BE/ME ratio. Kothari, Shanken and Sloan (1995) claimed that the findings Fama and French (1992) are affected by Compustat selection bias and part of the returns of portfolios with high BE/ME ratio is due to survivorship bias in S&P’s Compustat database. On the other hand, Chan, Jegadeesh and Lakonishok (1996) and Davis (1994) disagreed with Kothari, Shanken and Sloan (1995) and claimed that Compustat selection bias has no effect on NYSE and AMEX stocks. Lo and MacKinley (1988), Lo and MacKinlay (1990a), Black (1993a) and MacKinlay (1995) proved in their research that the high returns that are achieved using the BE/ME variable might be a result of data mining. Daniel, Hirshleifer, and Subrahmanyam (1998) theorize

16 Investors overprice stock that exhibit increased returns in the past. This results in investors overestimating each stock’s future growth. On the other hand investors tend to underestimate stock with low returns in previous years.

12 that the high explanatory power of the BE/ME ratio is a result of biases in the way investors make decisions when forming portfolios.

Lakonishok et al. (1994) concluded that the returns of different strategies that use BE/ME are lower for large firms. This is due to arbitrage costs and investor biases that cause mispricing and variables are used as proxy for firm size. Lakonishok et al. (1994) and Haugen and Baker (1996) concluded that the relationship is caused by the fact that markets are inefficient as well as the overreaction of investors. Specifically they claim that investors raise prices of growth firms and lower BE/ME ratios.

Trecartin Jr (2001)proved using data from NASDAQ, AMEX and NYSE that the effect of the BE/ME ratio is weak at times and positive and statistically significant only in the 43% of the monthly regressions tested. The fact that the BE/ME effect is not significant in the short term might be due to two reasons: either the market is inefficient or the variable BE/ME is not an adequate proxy for risk

2.4 Price to Cash flow Another variable that has been found to affect the cross section of equity returns is the ratio of a firms cash flows to its stock price – CF/P (cash flow – to – price). Research has shown a positive relation between stock returns and the CF/P ratio. However the nominator of the CF/P ratio is defined as a firm’s accounting profits plus depreciation. Furthermore a very important point regarding the study and the use of this variable, is that accounting profits might be a biased estimator of economic profits which investors are interested in. Also it’s important to differentiate between reported earnings and cash flows every time we study countries with different accounting practices. These difficulties in accounting profits have driven a number of researchers to study this subject in the US and Japan17. In more detail researchers Chan, Hamao and Lakonishok (1991) studied the cross section of average equity returns of the Japanese stock exchange using among others variables18 the CF/P ratio. For their research, they used monthly data of stock in the Tokyo

17 US: Wilson (1986), Bernard and Stober (1989), Lakonishok, Shleifer and Vishny (1994), Japan: Chan, Hanao and Lakonishok (1991) 18 They also used E/P, B/M and size

Stock Exchange for the period 1971-1988. Their conclusion was that stock with high CF/P ratio achieved higher returns compared to stock with low CF/P ratio.

2.5 CAPM One of the major issue that modern finance tries to solve is the quantification of the relationship between risk and the expected return of stocks. It’s generally accepted that an investment that involves higher risk will have higher returns for the investor, compared with a risk-free investment or even compared with an investment in stocks with lower risk like for example the large blue chips. Nevertheless, until the 50s there was no generally accepted way of measuring investment risk. For this reason, around that time several theories begun to formulate like Markowitz Modern Portfolio Theory that managed to quantify to a degree the concept of risk.

To analyze this phenomenon a number of theories have been developed with the more prevalent being the Capital Asset Pricing Model (CAPM). This Model was developed in the 60s by Sharpe (1964), Lintner (1965) and Mossin (1966), and was expanded upon by Black (1972). According to the CAPM when the market is in equilibrium, the expected return of stocks is a linear function of the stocks beta coefficient and furthermore the stocks beta is enough to explain the cross-section of equity returns. A simple form of the CAPM is as follows:

퐸(푅𝑖) = 푅푓 + 훽𝑖[퐸(푅푚) − 푅푓]

Where:

퐸(푅𝑖) : The expected return of stock i

푅푓 : The risk-free market interest rate

퐸(푅푚) : The expected market return

훽𝑖 : The amount of non-diversifiable risk (the risk that cannot be diversified away) of stock i in a portfolio. According to CAPM it’s the risk of stock i and it’s the slope of the regression of the return of the stock with the market’s excess returns.

퐶표푣(푅𝑖, 푅푓): The covariance between the returns of asset i and the market returns

푉푎푟(푅푚): The variance of the market portfolio

Furthermore, 훽휄 = 퐶표푣(푅𝑖, 푅푚)/푉푎푟(푅푚) If the CAPM applies and the markets are efficient, stock returns should conform to the above relation. One recent research concerning the CAPM is that of Black, Jensen and Scholes (1972).

These economists used data from every stock that were negotiated in the New York Stock Exchange – NYSE for the time period between 1926 and 1965 and created 10 portfolios with different historical estimations of beta. As a result, they found that the cross-sectional data reflect to a degree the predictions of the CAPM.

In addition, another very important research regarding CAPM is that of Fama and Macbeth (1973). This research relies on specific firms and not on creating portfolios. In this research they tested how linear is the relation between beta and expected stock returns. The researchers used monthly data from stock that are negotiated in the NYSE and found that the results of their research support the CAPM.

Another research that supports the validity of the CAPM is that of Fisher Black (1993a). This researcher created 10 portfolios with stocks from NYSE according to their beta. The period that he analyzed was between 1931 and 1991 and every year he rebalanced his portfolio, using monthly data, so that the first portfolio would always include 10% of the stocks with the lowest beta, the second portfolio the next 10% etc. The results of Black’s research showed that there is a positive correlation between expected returns of stock and the undiversifiable beta risk.

2.6 Efficient Markets Hypothesis It’s unquestionable that the basis in which all modern finance theory is based on is the Efficient Markets Hypothesis (EMH). According to Fama and Malkiel (1970) in an efficient market an assets price fully reflects every available information that may affect the price of the asset, in a fast and accurate way, the market prices reflect the assets true value. As a result, in an efficient market an investor cannot use historic or published information to achieve abnormal returns. This happens because this information has already been incorporated in the assets price. Furthermore, in this kind of market there are no undervalued or overvalued stocks and investors can achieve only normal returns, meaning returns that are a function of the investing risk that they have undertaken. All this means that in an efficient market the change in a stock price today, comes only from todays unexpected news, therefore yesterday’s or expected from the market news are no longer relevant. In addition, the fact that the new information reaches the market in a random manner results in a random change in a stock’s therefore making the change unpredictable. The

15 change today in a stock’s price is irrelevant to the change in the stock’s price yesterday. The changes are random variables that follow a random process or putting it differently follow a random walk. If later there are new information that become known to investors they will be examined and if they are deemed crucial they will determine the new price. In addition in the frame of the EMH with the term market we mean all analysts who are in a position to process correctly the available information and all those investors who either on their own or in the cooperation with the analysts are able use this information effectively. Fama (1970) in his research has discerned three different levels of efficiency each one with a different kind of information

 Weak Form EMH. The market is weak form efficient when historical prices of stock do not include important information which could be useful in predicting the assets future prices. Which means that the use of different methods from investors like technical analysis cannot lead to abnormal returns. In this form of efficiency stock prices, stock price changes, transaction volume, index prices etc. cannot be used from investors to increase their abnormal returns  Semi-Strong form EMH. The market has semi-strong efficiency when stock prices reflect all publicly available information. This information might concern the firm itself, the industry where the firm belong, or even the national or global economy. In this kind of efficient market investors use publicly available information or historical prices cannot achieve abnormal returns meaning returns who correspond to higher risk than the risk that they have already undertake.  Strong form EMH. In this case the market is considered efficient when stock prices reflect not only publicly available information but any kind of information either if it’s public or not. In general, no investor under these conditions can use the available information to achieve abnormal returns. When a market is strong form efficient it’s also weak and semi- strong form efficient. With the same logic when a market is efficient in a semi-strong form it’s also efficient in its weak form.

The research that has been conducted to find out if markets are efficient show that the EMH applies in its weak and semi-strong form19. Regarding the strong form research has shown that it does not apply20.

In Finance literature there are a number of assumptions that if true lead to efficient markets. Those assumptions are:

 The existence of many investors that are highly informed about the potential of firms  Homogeneous investor expectations  Information is made public in a random manner  Information is available to all market participants with zero cost  The existence of numerous experts (analysts, stock brokers etc.)  Decisions by investors are made based on advice by experts  Rational investors. In other words investors as a whole must know which information are important and which are not.

The EMH and CAPM had a large impact on finance and that lead many researchers21 to try and find out if they hold true in reality. The empirical research begun during the 60s and has continued to this day. However the vast majority of research until the early 90s was focused on US stock markets as well as industrialized nations like the UK, Japan, Germany, Canada etc. In the 90s many researchers studied developing markets like Brazil, Argentina, Singapure, Hong Kong, etc. There main results that are known to this day completely dispute the validity of the CAPM and put forward new methods of identifying cross sectional average stock returns. The challenge to the CAPM is been made in a financial and accounting level and less in an empirical and statistically significance level. The critics of the CAPM claim that it’s not just one variable the beta coefficient that affects expected stock returns Black, Jensen and Scholes (1972) Fama MacBeth (1973). The research produced models that suggest other firm factors that might explain the cross-section of equity returns. Some notable examples are the following.

19 Fama and Blume (1966), Fama, Fisher and Roll (1969) 20 Fama (1991) 21Fisher and Lorie (1968, 1970, 1977) Ibbotson and Sinquefield (1976), Siegel and Montgomery (1995)

 Size: Banz (1981) Fama and French (1992)  Earnings to Price ratio: Basu (1983)  Leverage: Bhandari (1988)  Book to Market equity ratio: Fama and French (1992)  Cash Flow to Price ratio: Chan, Hamao and Lakonishok (1991)  Past sales growth: Lakonishok Shleifer and Vishny (1994)  Trading Volume: Roll (1981)  Momentum: Brennan et al. (1998)  Share price: Blume and Stambaugh (1983)  Price to book value ratio: Rosenberg et al (1985), Fama and French (1992)

With the emergence of many models such as these it’s a very important goal for researchers to explain which of these models explain the cross-section of equity returns better. The regression methodologies that are used by researchers are Cross Sectional Regressions and more specifically the one which originated from Farma and Macbeth (1973) where they examine if one or many variables have the ability to explain the cross-section of equity returns, while the power of these variables is not captured from the CAPM. This is also the method we are going to use for our empirical analysis in chapter 4. Finally, in the dispute regarding the validity of the CAPM the main point of dispute was whether the market beta and the variables that are specialized to each individual firm are statistically significant. However, it wasn’t paid attention to what degree these variables were economically significant in explaining the cross- section of equity returns.

2.7 Asset price anomalies The first blow to the EMH and the CAPM came from anomalies concerning the pricing of assets. In recent years researchers discovered a number of variables that are company specific and which can help explain the cross-section of equity returns. Some of them are

 The past returns effect ( Contrarian and Momentum Strategies)  The Book to Market effect  The Earnings to Price effect  The Cash Flow to Price effect  The Sales Growth effect

 The Size effect

2.7.1 Explanation for asset pricing anomalies In academic literature there are many disagreements about the explanation given regarding the ability of some variables to explain the cross section of equity returns. The explanations that have been given by different scientists vary and are divided in three different categories presented below

2.7.2 Higher returns as compensation for additional risk Fama and French (1992) gave an explanation regarding the fact that some variables achieve higher returns and that was that these variables are riskier. Therefore, these variables measure the risk of the stock so that the correlation between these variables and the following return reflect a compensation for risk.22 Furthermore, Fama and French (1993) suggested that size and book-to-market equity proxy for sensitivity to common risk factors in stock returns. Lakonishok, Shleifer and Vishny (1994) concluded that this indication is due to wrong expectations from investors. Davis, Fama and French (1998) found that explanations that are based on risk factor provide a better explanation regarding the correlation between variables and average stock returns

2.7.3 Results contrary to the EMH Academic literature includes a substantial number of research which conclude that abnormal stock returns are a result of an inefficient market. For example, there are researchers who claim that these variables allow investors to select stocks that are mispriced. That way opportunities turn up to make returns which are greater than those expected by investors for the risk they have taken. 23 Particularly Lakonishok, Shleifer and Vishny (1994) claimed that the high returns attributed to stocks with high BE/ME ratios are due investor wrong conclusions based on past earnings growth. This category of investor is excessively optimistic for the future earnings growth of firms with high earnings growth in the past and at the same time they are excessively pessimistic about the future earnings growth of stocks with low earnings growth in the past. In addition, they suggested that stocks with low BE/ME ratio are more attractive to

22 Fama and French (1993, 1995, 1996a) 23 Lakonishok, Shleifer and Vishny (1994), Haugen and Baker (1996) and Daniel and Titman (1997)

investors compared to stock with high BE/ME which means that they attract naïve investors who raise stock prices and lower their expected returns

2.7.4 Higher returns due to the design of the research and data biases A significant number of articles that attempt to interpret the explanatory power of different variables on average stock returns focus on data snooping biases and sample selection biases. Data snooping bias is related to a bias when surveying the data meaning the bias that arises when we use the information from the data to drive further research with the same or related data. This bias is difficult to avoid due to non-experimental nature of economics. In academic literature there is a significant number of researches tried to narrow the chance of appearance of data snooping bias. Those researches for example used out of sample data and different time period data, but also hold out sample data. Black (1993a, 1993b) and MacKinlay (1995) claimed that the relation between firm specific variables and average stock returns cannot be observed in out of sample data. Specifically Black (1993a, 1993b) claimed that the size effect that was observed by Banz (1981) could be the result of the period selection of the sample because the size effect is observed in some periods and not in others. However Chan, Hamao and Lakonishok (1991), Capaul, Rowley and Sharpe (1993) and Fama and French (1998) proved that there is strong correlation between average stock returns and variables outside the US stock market. Sample selection bias is about the bias that appears while picking a sample. Particularly is a result of excluding some stock from the sample.

Kothari, Shanken and Sloan (1995) claimed that when the beta coefficient is calculated using yearly and not monthly returns there is a strong relation between this coefficient and returns. In addition they found that the relation between book to market equity and returns that was observed by Fama and French (1992) is due to survivorship bias in the COMPUSTAT data. Kothari, Shanken and Sloan (1995) note that there are two types of survivorship bias in the COMPUSTAT sample, which may lead to false relations between returns and variables. The first kind of bias is known in the academic literature as back-filling bias which appears because COMPUSTAT includes historical data when firms are included in the data. Specifically, COMPUSTAT was created in 1991 but the data were collected from 1982. Which means that firms that did not survive after 1991 are probably not included in the database. Therefore,

winner firms that had low returns in the past but increased their returns later will be included in the database but loser firms with high book to market equity that were later liquefied are not included in the database. The second kind of bias is the distressed firm bias and is a result of firms in COMPUSTAT that face financial trouble and do not publicize their data. These firms sometimes overcome their trouble and sometimes do not. The firms that manage to overcome their trouble send all their missing accounting data to COMPUSTAT on the other hand firms that do not manage to overcome their financial troubles do not publicize their missing data and this happens because the sampling procedure tends to exclude this kind of troubled firms. Which means that if the first are included in the sample while a lot of the second are excluded, the firms with high book to market will present high returns precisely because firms that did not survive were excluded from the sample and were not examined. Nevertheless Chan, Jegadeesh and Lakonishok (1995) showed that the sample selection bias is not large. Also Cohen and Polk (1995) formed portfolios that significantly limited the COMPUSTAT selection bias and found similar results. Fama and French (1996b)agreed that survivorship bias does not explain the relation between book to market and average stock returns. Davis (1996) and Kim (1997) show proof that conflict with the survivorship bias hypothesis. Particularly Davis (1996) discovered book to market, cash flow to price earnings to price effect in a sample from July 1963 to June 1978 that had no survivorship bias. Finally Amihud, Christensen and Mendelson (1992) when they used different statistical methods the relation between average returns and market beta is positive and significant

3 Methodology and Data 3.1 Research methodology The relation between specific company variables like market value, sales, book value and stock returns which is contrary to the CAPM is the focus of many scientists in the US and the rest of the world. However, it’s evident from the last chapter that the research conducted on the US stock market far outnumbers research conducted on the European stock markets. Particularly the objective of this thesis is to test the contrarian investment strategies on European market using the methodologies developed by Lakonishok, Shleifer and Vishny (1994). Contrarian investment strategies include going long on stock that are undervalued and going short on stock that are overvalued in the eyes of contrarian investor24. Overreaction about a stocks prospects will force the stock away from its fundamental value and as a result over or understate the stocks risk and misrepresent the firm’s future prospects. The goal of the contrarian investor is to take advantage of these mispricings and go against the herd of investors. Crucial for a contrarian investment strategy is to clearly identify what are value and growth stock. Lakonishok, Shleifer and Vishny (1994) use the following definitions:

 Value stocks are characterized by low past growth and low expected future growth in sales, earnings and cash flows.  Growth stocks are characterized by high past growth and expected high future growth in sales, earnings and cash flows

Identifying what consists a value and what a growth stock is crucial for our methodology. There are two methodologies used in the papers presented. One is selecting stocks based on their stock returns in the previous year’s Jegadeesh and Titman (1993) which are momentum based strategies and the other is by selecting stocks based on different accounting variables Lakonishok, Shleifer and Vishny (1994). For our purposes the second method will be chosen since the first one relies on the markets short term failure to recognize a trend in contrast with the accounting variables method which is driven by the markets unwarranted belief in the continuation of a long term trend. There are several variables that can be used, but in this paper the focus of attention will be on the market to book (M/B), sales growth (GS), price-to-cash flow (P/CF) and price-earnings (P/E) variables. The purpose of these variables is to be proxy

24 Lakonishok, Shleifer, & Vishny (1994)

for past and future expected growth. We use P/CF and P/E as proxies of future growth because they are ratios of price to a measure of profitability and we use SG and M/B as proxies for past growth (Lakonishok, Shleifer and Vishny 1994). A low P/E ratio indicates low expected growth rates and a high P/E ratio indicates high expected growth by the market hence growth stocks. However high P/E ratio may be due to temporarily depressed earnings and therefore cannot be a growth stock. The idea behind this is Gordon’s formula (Gordon and Shapiro 1956) which states that:

퐷 (1 + 𝑔) 푃 = 푡 푡 푟 − 𝑔

Where 퐷푡(1 + 𝑔) is next period’s dividend and 푃푡 is current stock price, r is required rate of return on the stock and g is the expected growth rate of dividends. For example to get an

expression in terms of earnings, we write 퐷푡(1 + 𝑔) = 휌퐸(1 + 𝑔), where 퐸(1 + 𝑔) is next periods earnings and ρ, the payout ratio, is the constant fraction of earnings paid out as dividend. We can then write

푃 휌(1 + 𝑔) 푡 = 퐸푡 푟 − 𝑔

Where the growth rate g for dividends is also the growth rate for earnings on the assumption that dividends are proportional to earnings. According to this expression holding ρ and r constant a high Price-to-Earnings (P/E) firm has a high expected growth rate of earnings while a low P/E firm has a low expected growth rate of earnings and similarly for the ratio of Price- to- Cash flow (P/CF). While the assumption of a constant growth rate for dividends and strict proportionality between earnings (or cash flow) and dividends are restrictive, the intuition behind Gordon's formula is quite general. Differences in P/CF or P/E ratios across stocks should proxy for differences in expected growth rates. Growth stocks are characterized by high P/CF, P/E SG and M/B ratios while value stocks are characterized by low P/CF, P/E SG and M/B ratios.

3.1.1 Portfolio Analysis The plan for this research is to implement a simple buy and hold strategy. The holding periods are one, two, three and five years. At the start of each period the stocks will be ranked according to the ratios. Then the stock will be divided into portfolios, each portfolio containing 20% of

the stock, and calculate for returns for each portfolio. The purpose of this is to see if the portfolios with low ratios (value stock) will outperform portfolios with high ratios (growth stock). Returns are calculated by assuming that investors weight their portfolios according to the stocks’ individual market values. The value-weighted returns ensure that a potential size effect does not occur. In this paper, it will also be reported the returns in the case that investors invest equally in all stocks, as this approach is used in many former studies. The portfolios are rebalanced each year to reflect changes in the relative ratios. For each portfolio we calculate its returns using the following formula:

푅푝 = 푤′ ∗ 푅

푤′ is the column vector of the relevant portfolio weights R is the row vector of the relevant asset returns.

The previous classification of stock relies on a single measure of either past growth or future growth. Next, we classify our stocks by using two multiples at the same time measuring both past and future growth. The contrarian investors should sell stocks with high past growth as well as high expected future growth and buy stocks with low past growth as well as low expected future growth. The prices of these stocks should be overvalued because investors naively extrapolate good past performance into the future. Therefore Growth stocks are defined as stocks with high past growth and high expected future growth. The opposite is assumed for value stocks. In this next step we continue to use P/CF and P/E as proxies for future growth and GS and M/B as proxies for past growth. At the beginning of each period the stocks are independently sorted in 3 groups (1) top 30 percent (2) middle 40 percent (3) bottom 30 percent based on each of the two variables. The sorts are for 5 pairs of variables: P/CF and BG, M/B and SG, P/E and GS, P/E and M/B, and M/B and P/CF. For our purposes, the value portfolio refers to the portfolio containing stocks ranked in the bottom group on both variables among P/CF, P/E, M/B and GS. The growth portfolio has the opposite rankings. Again, for each portfolio we calculate returns and see if value portfolios outperform growth portfolios

To be able to make conclusions from the results obtained, it is necessary to make a statistically significant test. The most common way to do this is by using a t-test, which tests whether the difference in returns between the two strategies is equal to zero. A t-test’s test statistic follows

a t distribution instead of a normal distribution and an assumption of normality is used for our data. The return differences are tested by a paired two sample t-test. This procedure tries to determine if the mean of the return differences is statistically significant. This test pairs the return from the value strategy with the return for the growth strategy in each year. The purpose of this testing method is to see whether the variation in the return from year-to-year is the same for each strategy. This will make it possible to get an insight into whether the level of return is the same for both strategies.

The null hypothesis for the comparison of the two populations is that the level of the returns is the same for both strategies:

퐻0: µ푣푎푙푢푒 − µ푔푟표푤푡ℎ = 0

This null hypothesis has no direction and is two-sided, whereas the alternative hypothesis has a direction and is one-sided. The alternative hypothesis states that the difference in the returns is larger than zero, indicating that the value strategy by definition earns a higher return that the growth strategy:

퐻퐴: µ푣푎푙푢푒 − µ푔푟표푤푡ℎ > 0

The t-statistics are calculated from the following equation:

퐷√푛 푇퐷 = 푆퐷

Where 퐷 represents the mean return difference between the two tested strategies, n is the

number of observations and 푆퐷 is the standard variance, which is calculated from the return

differences. 푇퐷 is t-distributed with n-1 degrees of freedom. The test performed is testing the null hypothesis and thus is two sided. Therefore the critical value that the t-test value has to exceed for each test performed is 1.960 for 푛 ==> ∞.

3.1.2 Cross-sectional regression The next method we are going to use in order to measure the relation between the cross section of average returns and our company specific variables is the Cross Sectional Regressions Analysis. According to this method the analysis is based on individual firms and there is no

formation of portfolios like the first method. This method is based on Fama and Macbeth (1973) and it was first used as a way to explain abnormal returns, meaning returns that are not justified by the stocks systemic risk (beta). However there is a number of academic studies25 that have established this methods credibility but also there are some that either questioned its credibility or outright rejected it26. Specifically we regress each firms yearly returns from 1998 to 2017 with the variables we are interested in meaning M/B, P/E, P/CF and GS. However the regressions residuals might by cross-sectional correlated and heteroskedastic27. Furthermore the ordinary least squares estimators that come out of the regressions are tested if they are statistically significant with a t-statistic which follows a t-student distribution. The problem that may turn out at this point is that due to the correlation and heteroscedasticity in the residuals it is very possible that the t-test might present as statistically significant some variables even though those variables aren’t statistically significant. In other words there is a tendency to overestimate the true statistical significance of the estimated coefficients. For this reason according to the methodology of Fama and Macbeth (1973) from each cross sectional regression we perform we keep the least square estimator of the coefficient of each explanatory variable. Next we suppose that these yearly estimators of the coefficient of each variable which are a time series of 19 observations are independent from each other and follow a normal distribution. Which means that as the final estimator of the coefficient of each variable we use the average of the coefficients that we have estimated in each time series. Finally to test the significance of this estimator we use a t-statistic which is calculated by dividing the time series average with the ratio of the standard deviation of the average estimation divided by the root of the number of observations of each time series. (Brooks 2008)

At this point we must point out that this methodology exhibits both advantages and disadvantages. At first a disadvantage of this method is that while calculating the t-statistic, in order to determine if the final estimator of the coefficient of each explanatory variable is statistically significant, the standards errors of the estimators for each cross sectional regression are not taken into account, but the standard error of the mean value of the time series is used

25 Chan, Hamao and Lakonishok (1991), Davis (1994, 1996), Fama and French (1992, 1996b), Kothari, Shanken and Sloan (1995), Chan, Jegadeesh and Lakonishok (1996), Loughram (1997) 26 Shanken (1992, 1996) 27 Jagannathan and Wang (1998) determined that the Fama-Macbeth estimator can be unbiased but only under certain conditions

instead. At the same time this is also this methods advantage because it simplifies data research on a large cross section of individual stocks because we do not have to estimate the covariance matrix of asset returns. Another advantage of this methodology is that it allows for the coefficients of the explanatory variables to vary through time. Specifically the Fama and Macbeth method is divided in the following parts: 1) We collect the yearly returns for the stocks of our sample as well as the yearly values of our variables meaning the variables M/B, P/E, P/CF, GS and we form panel data 2) In this part we perform cross sectional regressions for each year separately. Specifically for each year we run a cross sectional regression over the four variables. For each of the eleven models that we are going to use we are going to run the regression 19 times one for every year. The estimated coefficients of each model will form a time series We use the following model Single variable models

푅𝑖,푡 = 푎0,푡 + 푎1,푡(푀𝑖,푡⁄퐵) + 휀𝑖,푡 (1)

푅𝑖,푡 = 푎0,푡 + 푎2,푡(푃𝑖,푡⁄퐶퐹) + 휀𝑖,푡 (2)

푅𝑖,푡 = 푎0,푡 + 푎3,푡(푃𝑖,푡⁄퐸) + 휀𝑖,푡 (3)

푅𝑖,푡 = 푎0,푡 + 푎4,푡(퐺푆𝑖,푡) + 휀𝑖,푡 (4)

푅𝑖,푡 = 푎0,푡 + 푎5,푡 ln(푀퐸𝑖,푡) + 휀𝑖,푡 (5)

Multivariate models

푅𝑖,푡 = 푎0,푡 + 푎1,푡(푀𝑖,푡⁄퐵) + 푎2,푡(푃𝑖,푡⁄퐶퐹) + 푎3,푡(푃𝑖,푡⁄퐸) + 푎4,푡(퐺푆𝑖,푡) + 휀𝑖,푡 (6)

푅𝑖,푡 = 푎0,푡 + 푎1,푡(푀𝑖,푡⁄퐵) + 푎2,푡(푃𝑖,푡⁄퐶퐹) + 푎3,푡(푃𝑖,푡⁄퐸) + 푎5,푡 ln(푀퐸𝑖,푡) + 휀𝑖,푡 (7)

푅𝑖,푡 = 푎0,푡 + 푎1,푡(푀𝑖,푡⁄퐵) + 푎2,푡(푃𝑖,푡⁄퐶퐹) + 푎4,푡(퐺푆𝑖,푡) + 푎5,푡 ln(푀퐸𝑖,푡) + 휀𝑖,푡 (8)

푅𝑖,푡 = 푎0,푡 + 푎1,푡(푀𝑖,푡⁄퐵) + 푎3,푡(푃𝑖,푡⁄퐸) + 푎4,푡(퐺푆𝑖,푡) + 푎5,푡 ln(푀퐸𝑖,푡) + 휀𝑖,푡 (9)

푅𝑖,푡 = 푎0,푡 + 푎2,푡(푃𝑖,푡⁄퐶퐹) + 푎3,푡(푃𝑖,푡⁄퐸) + 푎4,푡(퐺푆𝑖,푡) + 푎5,푡 ln(푀퐸𝑖,푡) + 휀𝑖,푡 (10)

푅𝑖,푡 = 푎0,푡 + 푎1,푡(푀𝑖,푡⁄퐵) + 푎2,푡(푃𝑖,푡⁄퐶퐹) + 푎3,푡(푃𝑖,푡⁄퐸) + 푎4,푡(퐺푆𝑖,푡) + 푎5,푡 ln(푀퐸𝑖,푡) + 휀𝑖,푡 (11)

With:

푅𝑖,푡= the one year return on stock i starting at the last trading day of April;

푀𝑖,푡⁄퐵= the M/B ratio;

푃𝑖,푡⁄퐶퐹= the P/CF ratio;

푃𝑖,푡⁄퐸= the P/E ratio;

퐺푆𝑖,푡= the Sales growth ratio

ln(푀퐸𝑖,푡)= the natural logarithm of the market value of stock i;

푎0,푡, 푎1,푡, 푎2,푡, 푎3,푡, 푎4,푡, 푎5,푡 are the coefficients of the variables M/B, P/CF, P/E, Sales Growth and Market Value

휀𝑖,푡= the error term;

The coefficients 푎0,푡, 푎1,푡, 푎2,푡, 푎3,푡, 푎4,푡, 푎5,푡 of the variables M/B, P/CF, P/E, GS and ME are estimated using the Ordinary Least Squares method. For example after we perform the 19

regressions for the model 푅𝑖,푡 = 푎0,푡 + 푎1,푡(푀𝑖,푡⁄퐵) + 휀𝑖,푡 in the end we will have a time series that

will include the estimations 푎1,1, 푎1,2, 푎1,3 … 푎1,19 where the first indicator refers to variable 1 meaning M/B and the second indicator to year t. After we have for each model a time series of coefficient estimators we can calculate our final estimator of the coefficient of our variable according to the following formula

∑19 푎 푎̅ = 푡=1 푖,푡 푖 19

Therefore for example the final estimator of the coefficient of the variable M/B will be 푎̅̅1̅ =

∑19 푎 푡=1 1,푡 . Which means that the final estimator of the coefficient of the variable M/B is equal 19 to the arithmetic average of the individual estimated coefficients. However this estimator has different value for each model since it originates from different time series

3)In the final part, which can be called the empirical test, it is tested at what degree the estimators that have been previously calculated are statistically significant. In order to perform this test we use a t-statistic that comes out of the formula below (Brooks 2008)

푎̅̅̅𝑖 푡 = 푠 √푛

푎̅푖 : The final estimator of the i variable as it was calculated in part 2 s : The standard deviation of the final estimator of the coefficient of variable i

Since we have 1,2,3,5 year holding periods we are going to run regressions for every holding period. For example for 1 year holding period we run 19 separate cross sectional regressions, one for each holding period, in which the dependent variable is the return index of stock i and the independent variable is the characteristics of the stock. Then using the Fama and MacBeth (1973) method the coefficients for these 19 cross-sectional regressions are averaged and the t- statistics are computed. We do the same for 2, 3, 5 year holding periods.

3.2 Hypothesis The hypothesis that we are going to make to find out if the variables P/B, P/E, P/CF and GS are capable of explaining the cross section of equity returns in European stock markets, meaning if the variables are statistically significant, and therefore can be used to implement a contrarian investment strategy are the following:

3.2.1 Hypothesis test regarding variable P/E 퐻0: The ratio stock price to earnings does not affect a stocks expected return