MSc Business Economics: Finance track
Master Thesis
Is the value premium driven by the same set of fundamentals
across countries? A study on EURONEXT countries.
Student Name: Andrei Dascalescu
Thesis supervisor: Derya Guler
Statement of originality
This document is written by Student Andrei Dascalescu who declares to take full responsibility for the contents of this document.
I declare that the text and the work presented in this document are original and that no sources other than those mentioned in the text and reference have been used in creating it.
The faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.
Abstract
Value premium, known in literature as the excess return earned by stocks with higher fundamentals, such as Book-to-Market, Earnings-Price, Cash Earnings to Price and Dividend Yield ratios, over the returns generated by the growth stocks, those with common fundamentals. By taking the difference in returns, an investor can apply a rewarding value investing strategy and gain significant profits. This following research analyzes the effects of fundamentals on value premiums across EURONEXT countries and provides possible cross-country value investing strategy based on the results.
Keywords: Value Premium, Cointegration of premiums, Value Premium trend, Value investment strategy
Table of contents
Section 1 - Introduction ...4
Section 2 - Literature Review...6
2.1. - Value Premium and its evidence worldwide ...6
2.2. - EURONEXT Market, the idea behind, Home Bias ...9
2.3. - Literature most related to current research ...10
Section 3 - Research methodology ...11
3.1. - Stationarity. Testing for Stationarity. ...12
3.2. - Lag Selection ...13
3.1. - Cointegration. Johansen method. ...14
Section 4 - Data and descriptive statistics ...15
4.1. - Sample Construction ...15
4.2. - Descriptive Statistics ...17
Section 5 - Results ...20
5.1. - Unit Root Tests ...20
5.2. - Cointegration Relationships ...23
5.2.1. - Cointegration between 2002 and 2015 ...23
5.2.2. - Cointegration during the Financial Crisis ...25
Section 6 - Further Discussion ...26
Section 7 - Robustness Check...29
Section 8 - Conclusion ...30
References ...33
1. Introduction
Value premium is defined in the literature as the excess return earned by stocks with higher fundamentals (Book-to-Market, Earnings-Price, Cash Earnings to Price and Dividend Yield ratios) over the returns earned by "growth" stocks, those with common fundamentals. Current literature, however, is divided when explaining the reasons for this phenomenon. Therefore, Lakanishok, Shleifer and Vishny(1994) agree that this happens due to the investors' overreaction to stocks that have done badly in the past and tend to underprice them, while on the other side, the same investors overreact when "growth" stocks perform very well and tend to overprice those. On the other side, Fama and French (1998) argue in their study that value premium occurs primarily because value stocks are by definition riskier, and accepting more risk in their portfolio, investors have to be rewarded accordingly.
As most of the papers focus on interpreting the value premium from the point of view of returns, this is already an over-used topic. Therefore I will analyze whether there is a behavior in the value premium in a set of countries that have a similar stock market features, that is, countries that use the Euronext platform. For both proximity of the countries, and most important, for using the same trading platform with a harmonized regulatory framework, this study will specifically address to the stock exchanges in Belgium, France, Portugal and the Netherlands.
As the same trading framework and the same trading rules apply to all four countries, one would expect that the value premiums should follow the same trend across the countries. Therefore, the aim of this paper is to investigate whether the value premium responds to the same set of fundamentals within four different countries using the same trading platform and regulatory framework. An initial expected result would be that the value premiums within the four countries are cointegrated, and that they respond to the same set of fundamentals. On the other side, a potential result might be that there is no relationship between the value premiums, or that the relationship is not statistically significant and a potential reason for this is that the value premiums might be different between countries, due to the irrationality of investors or market inefficiency. By
analyzing the size of the cointegrating coefficient of all four ratios across all four countries, the aim of the paper is to see what is the optimal value premium investing strategy in a set of financially identical countries. The study will be conducted for two timeframes: a period between 2002 to 2015 and a second period, entitled in this paper as the period of the Financial Crisis, between September 2007 and September 2009.
The following paper is structured as follows: Part 1 introduces the reader into the main idea and aim of this paper; Part 2 represents the literature review part, where there will be analyzed papers that confirm the existence of the value premium worldwide, a short description of the EURONEXT and the reasons for its creation and an analysis of the most relevant papers for this research. Part 3 of the paper comprises the research methodology used for this study, followed by Part 4, which provides details for the source of the data, analyzes how the sample was constructed and provides a set of descriptive statistics for the data. Part 5 is represented by the results, which are analyzed from both a statistical and economical point of view, for both periods of this analysis (2002 to 2015 and September 2007 to September 2009). Part 6 continues with a further discussions part on the results and interpretation. This part compares a set of papers similar to the current thesis, whose results and findings are in line with those of this paper. Further on, Part 7 of this thesis contains a set of robustness checks that aims to see if the overall research methodology and economic reasoning can be validated when using different set of variables under the same setup. Finally, Part 8 of this paper sums up the findings, draws a set of concluding remarks and suggests further study ideas. Last but not least, this paper concludes with the References and APPENDIX parts.
2. Literature Review
2.1. Value Premium and its evidence worldwide
Fama and French (1992, 1995, 2002, 2007, 2012) find out that indeed, internationally, value stocks do tend to have higher returns than ordinary, "growth" stocks. They show in their study(1997) that for a period between 1975 and 1995, there is value premium of 7.6% per year, and that in twelve out of thirteen countries in their study, the growth stocks are outperformed by the value stocks. However, they argue that this phenomenon cannot be simply explained by the standard Capital Asset Pricing Model (CAPM) , but by a modified CAPM, an Arbitrage Pricing Theory (APT) model that captures the risk factor of value stocks. Basu (1977) shows that low P/E (Price-to-Earnings), or inversed - high Earnings-to-Price- stocks outperform stocks with high P/E values, or lower Earnings-to-Price stocks. This paper represents one of the first papers available to confirm the existence of the value premium. The later paper is then followed by the research of Fama and French (1995) that identify that stocks identified by having a low P/B (Price-to-Book) ratio also outperform high P/B stocks. Petkova and Zhang (2007) continue the study started by Fama and French (1992) and therefore analyze whether the value premium has a constant trend over the years. Their main finding is the existence of a stable value premium of around 6.1% per year for over half a century, during 1945 to 2005, while splitting the value premium in two directions: a dividend-growth component and a dividend-yield component. They use as timing for their portfolio construction the end of December of each year, opposed to the construction method used by Fama and French of forming portfolios at the end of June. This approach is also going to be used further in this current study.
On the same idea, Caliskan and Hens (2014) argue that even though there is international value premium, it is different from country to country, and this is due to the difference in risk aversion and time preferences of the investors. These differences automatically lead to affecting the overall volatility and returns, therefore affecting the value premiums. However, they are able to capture the value premium in a study using stock data over 41 countries, including U.S., thus resulting in one of the largest value premium study in literature. They indeed are able to quantify the relationship between
risk aversion and the value premium, by identifying that the highest average value premiums are found in countries from the top fifth of risk aversion and from the bottom quintile of patience countries. Zhang (2005) primarily findings are also in line with Fama and French's findings, and argues that because value stocks posses more risk than ordinary/growth stocks, in the situation of a possible credit crunch will be most affected and will perform badly. Petkova and Zhang (2004) provide a more detailed approach for explaining the risk factor in the value stocks. In their study, they argue that indeed, value stocks do present time-varying risk, but, even after controlling for it using market regressions, the value premiums are still positive and mostly significant. Gulen, Xing and Zhang (2010) continue on Petkova and Zhang's (2004) study, in order to find the magnitude of the time-variations displayed by the value premium. They conclude that, during difficult aggregate economic conditions, the value stocks are more sensitive than the growth stocks and, contrastingly, during favorable economic conditions, the excess returns between value and growth stocks is have mostly insignificant values. They do find that because of the asymmetries of economic conditions, the value premium tends to have an upward spike during high-volatility periods - here including financial crises, or recessions - followed by gradual decreases in the following periods of lower market volatility. As for value firms, the value of equity falls more relative to the average on the market, signaling a higher operation leverage for value firms, it is normally expected that during a recession the value firms to have a higher risk and expected return than growth firms.
However, Lakonishok, Shleifer and Vishny (1994) also argue that strategies involving value stocks outperform strategies involving growth stocks only and assign the value premium mainly to the overestimation of the future growth rates of growth stocks and to the underestimation of the growth rates in the case of value stocks. The authors suggest that growth stocks, or overvalued stocks are more likely to be traded by individual investors. This assumption is made because an institutional investor should be less biased and excited than an individual investor, and thus should trade more value stocks. However, because of various reasons, such as the desire to appear to have prudential investment strategies for their investors, an institutional investor is more likely to invest in growth stocks, because these look less financially distressed. As investing in
value stocks is fundamentally less risky and on the short run it provides higher expected returns, on the short run, from the point of view of a fund administrator or institutional investor, it is safer to invest in growth portfolios. Therefore, due to these reasons, it is unlikely that institutional investors massively invest in value stocks. On the other hand, individual investors do not have the long horizon that a value investing strategy takes to pay off higher returns. Therefore, it is costly for them to hold value stocks for long periods of time and also costly from the point of view of transaction fees. Therefore, as long as these impediments retain investors, both institutional and individual, from investing in value stocks, these stocks will continue to be cheap and look riskier, if not approached. However, as every economical theory works, it is expected that when the moment comes for value stocks to be intensively traded, the spread between value and growth stocks should tighten, therefore reducing the value premium. This, consequently, will lead to the disappearance of the concept of value premium.
Philips (Forthcoming) argues that there is a tendency on the long run that the economy will equalize the growth rates of value and growth stocks to assure that the value stocks do not become a significant fraction of the market. Also, contrary to the findings of Fama and French (1992, 1995, 2002, 2007, 2012), Philips (forthcoming) argues that there is no need to compensate for the risk and therefore the excess return of the value stocks can not be explained by the reward. Also, Philips shows that on the long-run, growth in both the per-share earnings and the price return for any given two stock indices that are rebalanced on a regular basis must be statistically indistinguishable. According to him, this has implications on the free cash flow being practically the mechanism by which the value premium is transferred to the investors. Doukas, Kim and Pantzalis (2002), however, reject the extrapolation hypothesis that states that the excess performance of value stocks is because of investors making errors in predicting future growth in earnings. Therefore, they reject the fact that investors tend to overweight recent information, especially analysts' forecast, a result that is inconsistent to behavioral findings, such as that of La Porta, Lakonishok and Shleifer (1997) who state that investors are overly optimistic with stocks that performed well in the past and overly pessimistic regarding underperforming stocks.
2.2. EURONEXT Market, the idea behind, Home Bias
Euronext has been at the moment of its creation in 2002 and still is one of the largest stock exchange formations in the world. It consists of a conglomerate of four stock exchanges, those of Belgium, France, Portugal and the Netherlands. The idea behind the merger of these four stock markets was to integrate a common trading platform across the four members and to provide the investors a readily available single and influential marketplace. The main advantage that the merged trading platform had was the ability to create large amounts of liquidity, especially as Euronext implemented a set of mechanisms that forced firms to commit more to transparency and comply to better reporting standards that ought to be better than the ones imposed separately by each of the countries back home.
In other words, the main aim of creating the EURONEXT was to reduce the Home Bias, a phenomenon where investors have the tendency to invest in their domestic stock markets and not invest at all or under-invest in foreign markets. The aim was to provide investors a transparent market, the same trading platform and companies complying to the same trading and reporting regulation, in order for them to diversify their global portfolio. However,according to Pownall, Vulcheva and Wang (2012), individual jurisdiction-specific regulations were adopted by each country separately, thus EURONEXT making it possible to have policies implemented as a whole on a cross-country level. Furthermore, as trading fees were and are particularly very high when an investor wants to trade on a foreign market, EURONEXT had the aim to reduce this commission, especially for investors from the EURONEXT countries members. Last but not least, the increased commitment to disclosure and better corporate governance supported by the EURONEXT platform policies, also had the potential and aim to reduce Home Bias and attract investors to gaining more benefits from international diversified portfolios.
2.3. Literature most related to current research
Black, Fraser and McMillan(2007) approach the closest topic to the one in this paper, and most of the methodology, will be inspired by their paper. They are using a cointegration methodology and find that there is indeed a long-run relationship between premiums across the countries in their study.Their main result suggest that even though value and growth stocks are driven by different set of fundamentals, the premium across countries is driven by the same fundamentals. Moreover, they find that information that the cointegration relationships computed using Johansen's Cointegration Test, can be useful tools for predicting future changes and developments in the growth of global production. Furthermore, if it was to specifically analyze the value premiums on each single industry, the decision makers could anticipate recovery of the economy when there is a downturn in the demand curve of value stocks or a downturn in the value premium and an upward trend in the demand of growth stocks, respectively.
Finally, Cronqvist, Siegel and Yu (2015) find that if there is a possibility of measuring and explaining the investors' behavior, investment style and economic circumstances, the value premium could be explained both by the risk-based compensation and the under/overestimation of the expected growth rates.
The main objectives of this paper are to analyze whether there exists cointegration between the value premium among the four countries studied. As all four countries are using the same trading platform and comply to the same trading regulations, one would expect that the value premium trend is the same among all four markets. However, as studies have shown, due to behavioral bias, I might even get a result opposed to my expectations. If however this is the result, there might be potential future studies that analyze why there exists this bias between investors having basically the same behavior. As suggested approach, I will be guided by the work of Black, Fraser and McMillan(2007) which have used Johansen (1991) cointegration methodology to find whether there exists a cointegration vector that supports the theory that there is long-run stationary relationship between value price premiums across international countries.
3. Research methodology
The empirical model is based on Black, Fraser and McMillan(2002) paper, that also analyzes if the international value premiums are driven by the same set of fundamentals (value investment ratios) across countries. Also, another key paper for this research is that of Johansen (1991), that helps us to determine if the final value premiums are cointegrated. According to Johansen, if two or multiple variables cointegrate on the long run, this means that they are all determined by the same factors, in our case, by the same set of fundamentals.
A first part of the methodology used in this paper is to determine the value premium in our research data. This is done by deriving an equivalent monthly price series for the data that will be presented in the next part of the thesis. After deriving the price series, which is actually the price series for value and growth portfolios, by subtracting the last from the value series, the value premium can be obtained. By plotting the results, it would reveal how each of the four value premiums (Book to Market premium, Earnings to Price premium, Cash Earnings to Price premium and the Dividend Yield premium) evolved over time and if it had a specific trend. To a more accurate result for the evolution of the value premium, this paper analyzes the value premium by testing its stationarity over time. Stationarity is the state of a variable to have the mean, variance and covariance constant over time, independent of the number of lags. The main benefit of testing for stationarity is the avoidance of any spurious regressions.
The next step of the methodology part will be to decide the ideal number of lags for each variable. This will help also when testing for stationarity and in the next part of the methodology, for providing accurate results. Last, but not least, the last part of the methodology consists in testing the variables for cointegration, or their ability over the long-run to follow identical trends. The cointegration method will reveal the relationship between different variables of this research. Cointegration can be tested either using the Eagle and Granger (1987) method or Johansen (1991) method. Further explanations and description of the methodology is presented in the following parts, with direct references to economic literature. The two final hypotheses of this thesis are the null hypothesis
where there is no cointegration relationship between any of the variables versus the alternative hypothesis of single or multiple cointegration relationships.
3.1. Stationarity. Testing for Stationarity.
Economic literature defines stationarity as the state of a variable which has simultaneously the mean, variance and the covariance constant over time. It is critical to test each time series for stationarity, as a series that is non-stationary might lead to a spurious regression. Thus, a non-stationary time series can reveal high coefficients for its estimates which could be not even revealing the real relationship between different lags of the variable tested.
In order to avoid the situation presented above, there is the need for introducing the concept of unit root testing. The aim of a unit root test is to test whether the variables in this study are stationary or non-stationary and possess a unit root. In order to avoid any spurious regressions, the variables will be checked for stationarity using the Augmented Dickey-Fuller(ADF) test, introduced by Dickey and Fuller (1981). Practically, this test takes into consideration every possible autocorrelations of a variable over time. According to econometrical literature, this test has two hypotheses: the null hypothesis that suggests that the time series has a unit root and therefore is non-stationary, and the alternative hypothesis that suggests that the series is stationary or trend stationary. In order to test for stationarity, the ADF, or Augmented Dickey-Fuller (Dickey and Fuller, 1981) has been used. An ADF test is a test used to determine whether in an autoregressive (AR) model there exists a unit root, or a feature that causes difficulties and statistical issues. Although it might appear a simple approach to test for a unit root, most of financial time series' structure can be capture by an AR model. The ADF regression model is given as follows:
Δyt = c + βtYt-1 - Σ aj Δyt-j + δt + εt (1)
where Δyt is the first difference of the time series, c is the constant term, βt is the
coefficient on a time trend, aj represents the lag order, εt captures the white noise and δt is
constant and a time trend, either one of them, or neither of them two. All regressions in this paper are computing using both a time trend and a constant term. The variable of interest is βt, which will be computed automatically by the econometrical software using
the OLS (Ordinary Least Squares) method.
The null-hypothesis of the ADF test states that the series contains a unit root versus the alternative hypothesis:
H0: β = 0 (2)
H1: β ≠ 0 (3)
3.2. Lag selection
In order to solve the ADF model in the equation above (1) , it first has to be decided what is the ideal number of lags to include into the regression. This can be done by using the BIC (Bayesian Information Criterion), also called SIC (Schwarz Information Criterion), introduced in literature by Schwartz (1978)
BIC/SIC = log(SSR
N )+ log(N)*(K+1)/N (4)
where SSR is the sum squared of residuals, N represents the size of the sample and K the number of independent variables. Alternatively, the Akaike Information Criterion can pe used, introduced by Akaike (1977):
AIC = log(𝑆𝑆𝑅
𝑁 )+2(K+1)/N (5)
where SSR also represent the sum squared of residuals, N the sample size and K the number of independent variables.
In order to select the best lag, econometrical theory suggests that the number of lags that minimizes the value for BIC or AIC to their lowest values. However, current econometrical software does this automatically, by computing the number of lags that
minimizes the value for BIC or AIC. For this research paper, the EViews9 econometrical software was used, and for the sake of economic rationale, both criterions were computed, but overall, the AIC was chosen to be the best criterion to incorporate the lag length.
3.3. Cointegration. Johansen method.
The last step in the methodology part, is to compute the cointegration vectors using the data obtained after applying the unit root test. As many econometric models posses multiple variables, in order to reveal the relationship between them, a researcher has various methods to choose from in order to describe an eventually long-run relationship between variables of a model. The two most widely used cointegration methods in the econometric literature are the Eagle and Granger (1987) cointegration method and the Johansen's (1991) method. However, there is a disadvantage of the Eagle and Granger's method, as it seems impossible for it to detect more than one cointegrating relationship between multiple variables.
Therefore, in order to find if there is a cointegration relationship between the value premiums in this study,Johansen's(1991) test for Cointegration will be used. The main difference between the two methods, besides that of the capability of determining multiple cointegrating relationships, is that Eagle and Granger's method used an OLS regression, whereas Johansen's method can be calculated only by using an estimator called the maximum likelihood estimator. This estimator is then used to determine the number of cointegration vectors of the model. However, though, Johansen's method is very sensitive to the number of lags used in the model, therefore the previous part of this paper (Lag Selection) is crucial for testing for cointegration relationships.
The Johansen method is therefore used to determine the exact number of cointegration vectors in a model. Its main equation can be written as follows:
Yt = μ + A1 Yt-1 + ... + Ap Yt-p + εt (6)
where
Y
t represents a vector of variables with size n x 1 that are I(1) (integrated of orderone), μ is a constant term and
ε
tis a vector of the error terms. The above equation can
ΔYt = μ + Π Yt-1 + Σ Γi ΔYt-i + εt (7)
where
Π = Σ A1 - I and Γi = - Σ Aj (8)
If the coefficient for
Π
has a reduced rank r<n, this means that there are n x r matrices, where r is the number of cointegrating relationships. Basically, Johansen test for cointegration suggests two likelihood ratios for the cointegration relationship in order to reduce the rank of the coefficientΠ
: the trace test and maximum EV(eigenvalue) test. The trace test tests the null hypothesis of r cointegrating variables versus the alternative of n cointegrating variables.The formula for the trace test is the following:λtrace(r) = -T Σln(1- λi) (9)
Mathematically, the larger the λi, the larger will the ln(1- λi), but negative and
therefore the trace test will be larger. The interpretation is the a high eigenvalue, larger than zero, will indicate a cointegrating vector. According to Johansen (1991), the cointegration methodology works if the results of the unit root tests suggest non-stationarity of the variables, that is, the unit root test's null hypothesis is not rejected, but there is no evidence by now that stationary variables affect in any way the results of the test.
4. Data and descriptive statistics
4.1. Sample construction
The following empirical analysis in based on growth and value portfolio returns for the four countries in the study: Belgium, France, The Netherlands and Portugal for the time frame of 14 years, between January 2002 and December 2015. The reason why EURONEXT was chosen for this study is the proximity of the countries, and most
framework. As most of the papers focus on interpreting the value premium from the point of view of returns, this is already an over-used topic. Therefore, the intentions of this paper is to analyze whether there is a behavior in the value premium in a set of countries that presumably have identical stock market features.
As the same trading framework and the same trading and reporting rules apply to all four countries, one would expect that the value premiums should follow the same trends across them. The ideal result of this research, according to classical studies, would be that the value premiums are all cointegrated between the four countries. As for the period, the time horizon is chosen in order to capture the effects on all four countries, taking in consideration that Portugal joined the EURONEXT in 2002, almost two years after the creation of the platform.
The data consists in 168 monthly returns for both growth and value portfolios for each country, from which have been compiled the value premiums as it will be presented in the next lines. The source for this data is Kenneth R. French's Data Library, where the owner of the database forms value and growth portfolios in various countries worldwide, using the four ratios that the current thesis is analyzing: Book to Market (BM), Earnings to Price (EP), Cash Earnings to Price (CEP) and the Dividend Yield (DIV). The portfolios are rebalanced at each end of the year by sorting them on each all the four ratios above, followed by computing the returns for the forthcoming 12 months. For a more accurate research, the value portfolios only contain the top 3 percentile of the ratios, whilst the growth portfolios contain the low 3 percentile of them. Furthermore, the database already avoids the survivorship bias in the data, that is, by including newly adding firms, while excluding each year the countries that disappeared that year. Also, by researching on countries that use the same currency, the exchange rate bias is automatically excluded.
Further, in order to apply the methodology, the next step is to find the value premiums. Thus, applying the same strategy used in Black, Fraser and McMillan (2002) paper. Therefore, the returns were not used in order to retrieve the value premium, but to help derive a difference between a price index for both value and growth stocks. Using the data, the study starts by deriving an equivalent price series for the portfolios and then by logging it. After that, the value premium resulted by subtracting the price index of
growth portfolios from the value portfolios. The result obtained is 4 monthly value premiums for each country, that is, value premiums for portfolios formed on the BM ratio, on EP ratio, CEP ratio and DIV ratio, respectively. That is, 2.688 unique monthly value premiums, that are, basically, the frame of this research.
4.2. Descriptive statistics
Figure 1 reports the descriptive statistics for the Value Premium values in all four countries in the research. First, it presents the summary statistics of the Value Premium in Belgium, for each of the four ratios. Therefore, it can be observed that the maximum average value is for the BM ratio, therefore suggesting that, for Belgium, the best value investing strategy is that of creating portfolios using this ratio. However, as it can be seen that the standard deviation is slightly high comparing to the other ratio, this could lead the investors to lose part of their investment. Therefore, a rational investor would choose to create his portfolio by sorting the stocks using the CEP ratio. Even though the return could be half of that provided by BM portfolios, on a historical basis this has proved to be the best strategy, as the minimum return that an investor could get out of this strategy is the only one that is positive out of the four strategies.
Secondly, Figure 1 reports the descriptive statistics for the Value Premiums in France, again for the four ratios. By analyzing the statistics, it can be deducted that the strategy where investors sorted their portfolios by using the BM ratio gains on average the highest return, of almost 6%, and even though it presents the highest standard deviation out of the four ratios (3.75%), in the worst case scenario, investors did get a minimum of 3.06% return over the entire period. This suggests that, in France, the best historical investment strategy is to sort the portfolio using the BM ratio. After only going through two out of four countries it can already be seen that one can not use the same value investment strategy in a group of countries, even though those countries use the same trading platform, the same regulatory framework, etc.
Figure 1: Value Premiums Descriptive Statistics
BELGIUM
No of
Obs. Minimum Maximum Mean Std. Deviation
BM 168 -0,0091 0,1571 0,06991 0,0375 EP 168 -0,3231 0,0199 -0,0311 0,0488 CEP 168 0,0007 0,0617 0,0343 0,0107 DIV 168 -0,0394 0,0883 0,0080 0,0234 FRANCE BM 168 0,0306 0,0998 0,0677 0,0201 EP 168 -0,0218 0,0387 0,0212 0,0095 CEP 168 -0,0451 0,0486 0,0206 0,0095 DIV 168 -0,0029 0,0522 0,0203 0,0143 THE NETHERLANDS BM 168 -0,0055 0,1066 0,0614 0,0293 EP 168 -0,0398 0,1547 0,0546 0,0319 CEP 168 -0,0443 0,0237 0,0047 0,0099 DIV 168 -0,0031 0,1494 0,0794 0,0379 PORTUGAL BM 168 0,0003 0,0429 0,0231 0,0159 EP 168 -0,0130 0,1710 0,0668 0,0504 CEP 168 -0,0374 0,1258 0,0350 0,0375 DIV 168 -0,0153 0,1720 0,0603 0,0554
The table provided above presents the descriptive statistics for the Value Premiums around the countries in this research. The first part presents the descriptive statistics part for Belgium, where the best value investing strategy proves to be the one when the investors have used the CEP ratio when sorting their portfolios. The second part of the table presents the descriptive statistics for France, where
the best value investing strategy proves to be the one where sorting the portfolios was done by choosing the BM ratio. Third part of the table above provides the descriptive statistics for The Netherlands, where a rational investor would have got the most favorable return when sorting the portfolios based on the Dividend Yield ratio. Last, but not least, the final part of the figure provides the statistics for Portugal, where the best value investing strategy was the one of sorting the portfolios using the BM ratios. No of obs. represents the total number of monthly value premiums over the period, 168 for each month, for all the four countries in the study. For the most accurate research, and in line with the Value Investing theory, as well as from the point of view of a rational investor, the best
strategies considered in this study are the ones that guaranteed the investors the minimum loss from the sample.
Going on with the descriptive statistics, it can be observed that for The Netherlands, the best strategy out of the four is to sort the portfolios using the Dividend Yield ratio. Therefore, in the last 14 year, if investors sorted their portfolios accordingly they could have obtained on average returns of 7.9% and, despite the high standard deviation, of almost 3.8%, they would still have lost a maximum of -0.3% of their portfolio value.
To sum up, in Portugal, the highest returns an investor could obtain would have been those of portfolios constructed using the EP ratio. However, due to the standard deviation of more than 5%, he could have lost 1% of his portfolio. Therefore, a risk averse investors would have chosen the BM ratio portfolios, even though he would have got only 2.3% return, but due to the low standard deviation, in the market's worst moments, he would still have got a positive return.In line with the results above, are the plots of the Value Premiums in Figure 5, for each of the four countries. Here, the reader can see that the best investment strategy for Belgium was the BM strategy, being the only one that holds an upward trend over time, despite the downturn it had around the financial crisis. However, due to the high standard deviation, this proves not to be the ideal investment strategy. As for France, the plots confirm that the best investment strategy is that of sorting the portfolio on the BM ratio. Even though the massive downturn during the Financial Crisis, the reader can observe that in the lowest point of the graph, the investor could still get over 3% return. Thirdly, the plots also confirm the strategy for The Netherlands, with a positive minimum return during the Financial Crisis period.
Last, but not least, for Portugal it might look that the best strategy is the one with EP ratio, but, due to a negative minimum reached between 2002 and 2003, and a downwards trend after 2011, this is not the best value investing strategy. On the other hand, the BM ratio portfolios, after a crash at the end of 2008, regain an upwards trend up to the end of the researched period, thus proves to have been the best value investing strategy.
Summing up, depending if the investor is risk averse or not, different strategies might look more plausible than those presented above. However, acting as a rational investor that wants to minimize his risk to the lowest possible value, the best strategies might not be the ones that earn the highest returns, but those who assure the investor a minimum positive gain. Therefore, while choosing the type of investing method is subjective, from the value investing point of view, those presented above are the best possible strategies. Further analyses on this matter are presented in the following part of the thesis.
5. Results
5.1. Unit Root Tests
This section presents the results of the unit root tests applied to each of the four types of value premiums for the four countries in the study. This first part tests the existence of unit roots on the entire time frame between January 2002 and December 2015. Testing for unit roots is done by computing the Augmented Dickey-Fuller (ADF) test using a econometrical software, in our case, EViews9. The two hypotheses for the ADF test are the null hypothesis, or H0, of stationarity, versus the alternative hypothesis, or H1 of non-stationarity. These have 3 test critical value, at the 1%, 5% and 10%. For a series to be non-stationarity, it has to reject the hypothesis at one of the three critical values, and the obtained ADF t-test value to be higher than that of the critical values and the p-Value, or probability value to be lower than 0.05, or 5%. As the most common critical value in economic research is the 5% level, this research also uses the 5% level. Therefore, the critical value at the 5% level is influenced by the number of lags incorporated in the variable and the size of the sample. As in this research, all four variables have the same sample size of 168 units each, only the number of lags determines any differences between the critical value at the 5% level. However, the average critical value in this study is around -3.4370. This implies that if the results of the unit root tests are larger (on the negative scale) than the critical value, the null hypothesis of stationarity is rejected. Also, as it will be seen in the following lines, for Belgium, the test is rejected even at the 1% level, meaning that in 99% of the cases, the variable was non-stationary. The importance of unit root testing has implications on the value premiums, as non-stationarity implies that the analyzed value premium doesn't have the same determinants. Therefore, not rejecting the null hypothesis implies that both the growth portfolios as well as the value portfolios are not sorted on the same ratios. Another implication of the unit root testing is to see how many lags are needed to determine an actual state of the value premium, that is, how many lags influence its current value. The first step in testing for the unit root is to decide what lag length to use. The two most common methods for deciding the lag length are the BIC (Bayesian Information Criterion)/SIC(Schwartz Information Criterion) test and the AIC(Akaike
Information Criterion) test. The formulas for both of these tests are presented in the Methodology part of this paper.These tests are currently automatically computed by the econometrical software, depending on the length of the time series. This paper uses the results of the SIC (Schwartz Information Criterion), as the tables in Appendix regarding the Unit root tests display the results for both the Schwartz Information Criterion and the Akaike Information Criterion. The results of this test will be helpful in the next part of the research, at the Cointegration Relationships. As a summary of the test results of Figure 6 in the APPENDIX, the following situation is presented:
Figure 2: Unit root test results
The table above provides a summary of the test results for the unit root tests. For more details of these tests, the reader is invited to find them in the APPENDIX, in Figure 6. Notes: *p < 0.10, **p < 0.05, *** p < 0.01. ADF critical values with both a constant and linear trend are -3.171 (10%), -3.485 (5%) and -4.116 (1%). Lag lengths have been chosen using the Akaike Information Criterion.
BELGIUM ADF test statistic: P(Prob.): Lag Length:
BM -14,7703* 0,0000 0 EP -7,1120* 0,0000 5 CEP -12,8710* 0,0000 0 DIV -4,6388* 0,0013 6 FRANCE BM -1,8809 0,6600 0 EP -3,6292** 0,0303 0 CEP -2,5576 0,3004 6 DIV -3,6041** 0,0324 0 THE NETHERLANDS BM -3,6500** 0,0287 1 EP -2,4518 0,3517 0 CEP -3,8004** 0,0188 0 DIV -1,9029 0,6486 0 PORTUGAL BM -2,0591 0,5463 0 EP -1,2891 0,8871 0 CEP -0,8192 0,9610 0 DIV -0,3209 0,9895 0
The reader can observe that for Belgium, each of the four ratios reject the null hypothesis on stationarity at the 1% level (-4.116 value). However, two out of for ratios, EP and DIV respectively require a number of 5 and 6 lags to reject the null hypothesis, while the other two don't require any lag length to reject the null hypothesis. By rejecting the null hypothesis at the 1% level, I assume that both the value and the growth portfolios are determined by the same set of fundamentals, or ratios, therefore the value premium is correctly defined and the difference between the two portfolios is statistically significant. Therefore, by judging after the ADF test statistic values, it is confirmed that both the BM value investing strategy and CEP investing strategy have been the most profitable strategies during the time horizon. Therefore, if investors decided to buy value portfolios sorted on the BM ratio, while selling growth portfolios constructed on the same ratio, and bought value portfolios sorted on the CEP ratio and selling growth the portfolios, respectively, would have maximized their returns.
Going on, looking at France, it can be observed that only two of the ratios - BM and DIV did slightly reject the null hypothesis of stationarity at the 5% level, while the other two - EP and CEP- did not reject it, not even at the 10% level, also confirming that two of the most viable investment strategies were those of sorting the portfolios based on either the Book to Market or Dividend Yield ratios. The results suggest that in France, companies that were undervalued (or had their book price close or higher to their market price) or offered high dividends compared to their market price (or had high dividend yields) were more profitable than companies that were slightly or highly overvalued or those that offered small or no dividends.
As for The Netherlands, the results of the unit root testing confirm that only two series - BM and CEP - out of four ratios can reject the null hypothesis and are non-stationary.Although, these two series slightly reject at the 5% value. However, following the initial result that portfolios based on the DIV ratio were the most profitable, the results suggest that BM and CEP portfolios were profitable. Last, but not least, for Portugal, the results suggest that none of the ratios can reject the null hypothesis, every single one of them not being able to reject the hypothesis of non-stationarity during the entire time horizon.
Going further on, in Figure 7, the ADF Test Equations are represented for each variable, for each of the four countries in the study. The equations have been automatically computed by the Econometrical Software and helps the reader better understand how much is the current value of a certain ratio affected by its past. Therefore, by using the Least Squares method, each lag has been computed to better represent the model. Furthermore, the constant term and the time trend have also been atuomatically calculated. Last but not least, the equations helped us in finding the value for the Akaike Information Criterion and Schwartz criterion, which indicated the best possible number of lags for each of the ratios.
However, even though some of the time series did not reject the null hypothesis, the next part of the analysis - testing for cointegration relationships - is not affected, as Johansen's (1991) Cointegration Method allows for analyzing multiple cointegration relationship, both between non-stationarity series, stationary series and different combinations of the two.
5.2. Cointegration relationships
5.2.1. Cointegration between 2002 and 2015
This current part of the research presents the cointegration relationships during the entire time horizon. The aim of this part is to analyze what is the best strategy when compiling a portfolio based on stocks in the four countries. Therefore, by computing the cointegration relationships, one investor can decide what is the best combination of value investing strategy in Belgium, France, The Netherlands and Portugal all together. Therefore, last step of this research is to compute cointegration vectors using the data obtained above. Therefore, if the
Π
matrix, described in the Methodology section of this paper, has a reduced rank r < n, this implies there exist n x r matrices, where r represents the number of cointegrating relationships. Theoretically, Johansen test for cointegration suggests two likelihood values for the cointegration relationship in order to minimize the rank of theΠ
matrix: the trace test and maximum EV(eigenvalue) test. The critical valuethe Maximum eigenvalue, the critical value is 27,5843 for at least one cointegration equation at the 5% critical level be rejected, but there is no inference if stationary variables are included. These critical values are practically the maximum likelihood estimators of the cointegration vectors for the model. If there proves not to be any cointegration relationships, the results will be insignificantly different from zero. As there will be four variables analyzed for cointegration, the maximum number of cointegration relationship will be at most 3. Therefore, the maximum likelihood ratios are equal to those presented above.
Therefore, for this research paper, a total number of 8 cointegration relationships are computed, as it follows: four cointegration equations for the same variable across the countries ( eg. BM for Belgium, BM for France, BM for The Netherlands and BM for Portugal, etc.) for both the entire period of the study and the period during the Financial Crisis, which in this research is represented by the period between Sep-07 to Sep-09, in order to see could have been the best value investing strategy by only using the same set of fundamentals(ratios).
Summing up the results in Figure 8 in APPENDIX, the following results represent the result of the cointegration tests:
Figure 3: Johansen Cointegration Relationships between 2002-2015
SERIES: Trace Test Prob Max-Eigen Stat. Prob
BM 54,7979 0,0097 32,6114 0,0053
EP 72,6354 0,0001 50,3094 0,0000
CEP 68,8776 0,0002 39,7415 0,0009
DIV 49,5342 0,0345 27,0241 0,0583
The table above summarizes the results for the Johansen Cointegration Relationships between 2002-2015, results that can be found in APPENDIX, Figure 7.
The results of the Johansen' cointegration test suggest that if using the same ratio or fundamental across the four countries, all four ratios are able to reject the null hypotheses of non-existence of a cointegration relationship if using the Trace Test, while only three - BM, EP and CEP - out of the four ratios can reject the same null hypothesis if
using the Maximum Eigenvalue test. However, for maximizing the results, the best cross-country value investing strategy is the one that has the maximum Trace Test value and Maximum Eigenvalue Statistic value. Therefore, according to the results, the best strategy an investor could have chosen at the beginning of the period is the one based on the EP ratio, with the value for the Trace Test of 72,6354 and 50,30944 for the Maximum Eigenvalue Statistic. This result suggests that across all the four countries, the portfolios formed by companies that had high EP ratios, or had earnings per book value of share above 1 proved to be the most profitable. This result also confirms that, contrary to studies that suggested that no matter the ratio chosen the result should be the same and even though that all four countries operate under the same framework and regulation, the best possible strategies could be applied only while sorting the portfolios by BM, EP and CEP ratios.
5.2.2. Cointegration during the financial crisis
The current part of the thesis provides an answer to what was the best value investing strategy during the Financial Crisis period between Sep-07 to Sep-09, when all the markets were in turmoil, given the fact that little or no investors did manage to obtain significant profits above the market, except Hedge Funds. The research wants to analyze what could be the best strategy during a credit crisis, so that investors that are anticipating future Financial Crisis can apply to their portfolio
.
The setup is the same as in the previous part of this paper, the only variable that differs is the time span. Therefore, after applying the same procedure as in the previous analysis, the following sum up of results in Figure 9 from APPENDIX are presented:Figure 4: Johansen Cointegration Relationships between Sep-07 to Sep-09
SERIES: Trace Test Prob Max-Eigen Stat. Prob
BM 79,5473 0,0000 38,5087 0,0014
EP 58,2889 0,0039 26,9154 0,0607
CEP 64,6760 0,0006 38,7291 0,0012
DIV 43,1885 0,1281 23,7014 0,1455
Following the interpretations in the previous part, the results of Johansen's cointegration test suggests that only three - BM, EP and CEP - out of the four ratios can reject the null hypothesis of non-existence of a cointegration relationship if only using the Trace Test, while only few as two - BM and CEP - out of the four ratios can reject the same null hypothesis if using the Maximum Eigenvalue Statistic, therefore limiting the best possible value investing strategies during the Financial Crisis to those of sorting the portfolios based on the BM and CEP ratios. However, because earnings during the Crisis suffered a downturn, based on these results, the best possible strategy would have been that of choosing undervalued stocks, based on the Book to Market ratio. Even though this results have strong statistical backups, there might not be much economical reasoning behind them. Therefore, there is a large proportion of certainty that the value premiums might appear due to the pessimism of the investors, and that there might be a cyclical investors' behavior that leads to the appearance of this premium.
6.Further Discussion
The following part of the thesis aims to further discuss the results previously obtained in relation to related papers that confirm the existence of value premium and apply studies on various countries. As shown in previous parts of this thesis, value premiums exist under various forms and the debate is still open. Therefore, portfolio managers or even individual traders wishing to capture these higher expected returns, or premiums, still face challenges. Of course, implementation of strategies that capture the value premium can be costly and timely. For these individuals to be completely satisfied, there is an acute need of strategies that reduce the trading needs and can be done with low trading costs. Further on, a set of studies that are in line with the results and conclusions of this current research paper are presented and compared to the actual thesis. As a start, Dimson, Nagel and Quigley (2003), perform an analysis on the UK stock market between 1955 and 2001 in order to capture the value premiums. However, they only analyze this by sorting on the Book-to-Market and Dividend Yield ratio. Their findings suggest that the value premium can be captured from small-cap sized companies as well as large-cap companies. They also find that portfolios sorted on the Dividend
Yield ratio yield approximately equal value premiums to those of portfolios sorted on the Book-to-Market ratio. However, they do suggest that managers willing to capture the value premium should be very aware about the need to rebalance their portfolios yearly. Also, they emphasize the high risk that illiquidity among small-cap stocks present, as an impediment. Therefore, illiquidity might lead to higher trading costs, therefore making a certain value investing strategy not appealing to investors.
Further on, a paper of Andrikopoulos and Daynes (2004) continues the study on the existence of the value premium on the British stock market, by investigating a period between 1998 and 2002. The setup is identical to the one in Dimson, Nagel and Quigley's (2003) paper, only that they decide to sort the portfolios on four ratios, three out of which are also found in this paper: Book-to-Market, Dividend Yield, Earnings to Price and Weighted Average Sales Growth Rank (WASG)1. They do find strong evidence on the persistence of the value premium over the years and suggest that further studies should focus on combinations of the ratios when sorting out the portfolios. Therefore, they suggest that investors should either use different value investing scenarios from the pointview of selecting the ideal ratio or take into consideration multiple ratios at once when setting up a value portfolio.
Further on, the paper of Chaves, Kalesnik, Hsu and Shim (2012) is in line with this current research. Their paper analyzes the value premium only by sorting the portfolios on the Book-to-Market ratio, on a time horizon of 30 years. Even though the limitation of only one ratio, the results are in line with those obtained here, each of the four countries proving to have a value premium through the entire period, with values similar to those in this paper. However, they suggest that a large component of this value premium is due to the mispricing theory, which according to them, it has important implication for portfolio managers and individual investors.
As in this current paper, the reader can observe that there is value premium confirmed through the entire period of the analysis, it can be deducted that there is a time horizon effect. A confirmatory paper for this is the paper of In, Kim and Gencay's (2010)
1 By Weighted Average Sales Growth Rank, the authors define the expectations of
"Investment Horizon Effect on Asset Allocation between Value and Growth Strategies". In their paper, the authors use Fama-French portfolios and confirm that, as the investment horizon increases, there is a tendency of investors to migrate from investing in growth stocks to investing in value stocks. As this current paper suggests that on the long run, no matter the value investing strategy chosen by an individual, there will always be an extra return over the growth stocks, so does their paper, suggesting that, on the long run, value stocks even become less risky than growth stocks.
According to the results in this paper suggesting that during a market turmoil, the best value investing strategy might be the one based on the Book-to-market ratio, an extra argument for the results of the cointegration relationships during the financial crisis, obtained in this current paper, stands the research of Sykes (2007). They use the same classical setup when sorting the portfolios, this time using only the Book-to-Market ratio. Their main finding is that, the high returns for the value stocks, occurs mainly due to the investors' undervaluation under conditions of pessimism, rather than uncertainty about the stocks. They suggest that the cyclicity of investor enthusiasm can be a reasonable explanation for the high value premiums during various time periods, especially during a financial crisis. Therefore, as the BM ratio has the largest cointegration coefficient for all the four countries, compared to the other three ratios, this is also a confirmation of validity for the obtained results.
The paper that mostly emphasizes the results obtained in this current research is the paper that guided the entire thesis, that of Black, Fraser and McMillan (2002). Further to the fact that the results obtained here are in line with their results, there is an important finding of their paper. The authors suggest that the cointegration relationships computed using Johansen's Cointegration Test, can be useful tools for predicting future changes and developments in the growth of global production. Furthermore, if it was to specifically analyze the value premiums on each single industry, the decision makers could anticipate recovery of the economy when there is a downturn in the demand curve of value stocks or a downturn in the value premium and an upward trend in the demand of growth stocks, respectively.
7.Robustness check
The current study can be of course subject of robustness checks. Therefore, in order to assess the sensitivity of these results, I have decided to replicate several analyses, primarily Johansen's cointegration relationships, by using different combinations of value premiums in the equation.
Specifically, I have reran the Johansen's test for two different specifications for the entire period and for the period during the Financial Crisis: BM for Belgium, EP for France, EP for Portugal and BM for the Netherlands. The ratios combination for the test has been randomly chosen. The same specifications were used when testing and the results can be observed by the reader in Figure 10 (Check #1 for the entire period of the study and Check #2 for the period of the Financial Crisis) from APPENDIX.
First, when testing for the cointegration relationships for the entire period, the result still displays one cointegration relationship at the 5% level, therefore rejecting the trace test's null hypothesis critical value of 47.8561 with a value of 53.9986 and Maximum eigenvalue's null hypothesis critical value of 27.5843 with a value of 33.6833. Not surprisingly, the result of Johansen's Cointegration Test suggests that, even when randomizing the ratios in the model, the model is still statistically significant and plausible. On the other hand, rerunning the same analysis for the period of, while yet again randomizing the ratios used as variables, the model is slightly able to reject the null hypothesis of Maximum eigenvalue at the 0.05 level.
Secondly, replicating the primary analysis of this paper, this time for the reduced period of the Financial Crisis, the results can be observed in the second part of the Figure 10 in APPENDIX, entitled "Johansen Cointegration Test for Robustness Check - Check #2". Thus, despite the expectation, the test slightly fails to reject the null hypothesis both for the trace test and for the Maximum eigenvalue test. Possible reasons for this failure might be both the small sample included in the sample (only 24 observations for each ratio), and, due to this small size of the sample, the randomization of the ratios. Therefore, after rerunning the regressions, the results suggest that different specifications to those initially used in the study can be used and will lead to positive but smaller results. However, these results can be highly affected by behavioral biases that have not
been included in the analysis. The results of the replications support the same inferences as those in the previous part of this study.
Additional robustness checks can be done, by simply randomizing the variables, changing the sample period either by increasing it or decreasing it. Additionally, the existence of the value premium could be tested using a difference-in-difference model, before and after the Financial Crisis of 2007 to 2009.
8. Conclusion
This research analyzes the various value investing strategies based on ratios such as Book to Market (BM), Earnings to Price (EP), Cash Earnings to Price (CEP) and Dividend Yield (DIV) ratios. The value investing strategies are based on the value premium, defined in the literature as the difference between value and growth portfolios. The research is done on members of the EURONEXT market: Belgium, France, The Netherlands and Portugal, on a time horizon between 2002, when Portugal joined the market up to 2015 and consists on index prices of portfolios constructed using the four different ratios. Therefore, there are 168 monthly unique data points for each ratio, for all four countries, thus resulting a total of 2688 monthly returns. To a more accurate for the evolution of the value premium, beside simple descriptive statistics, the evolution is graphically plotted and unit root tests are performed through the Augmented Dickey-Fuller (ADF) test. The aim of unit root testing is to see whether the variables in the study are stationary of non-stationarity. The unit root testing is done at the 5% critical level and for Belgium all ratios are able to reject the null hypothesis of stationarity, for France two out of four, two for The Netherlands and none for Portugal. The next step in the research was to see if the value premiums are cointegrated. The aim of this part is to analyze what is the best strategy when compiling a portfolio based on stocks in different countries. Therefore, by analyzing the cointegrating relationship, one investor can decide what is the best combination of value investing strategy in Belgium, France, The Netherlands and Portugal all together. The research identifies the number of cointegrating relationship
between the four ratios, and this is confirmed or infirmed through the two likelihood ratios the Johansen's test has: the trace test and the maximum eigenvalue test.
Therefore, for this research paper, a total of 8 cointegration relationship have been computed, as follows: 4 cointegration relationships for the same variable across all four countries in two time horizons - during the entire period between 2002 and 2015 and during the Financial Crisis. The best results are taken in consideration only if both likelihood ratios can reject the null hypothesis at the 5% level, with critical values of 47, 8562 for the trace test and 27,5843 for the Maximum eigenvalue.
Therefore, the results of the cointegration testing suggest that for the period between 2002 and 2015, BM, EP and CEP all can reject the null hypotheses, but for maximizing the result, the best cross-country value investing strategy is the one that has the maximum Trace Test value and Maximum Eigenvalue Statistic value. Therefore, for this time horizon, the portfolios formed of companies that had high EP ratios, or had earnings per book value of share above 1 proved to be the most profitable. As for the period during the Financial Crisis, only BM, EP and CEP ratios can reject the null hypothesis of non-existence of cointegrating relationship if only using the Trace Test and only BM and CEP ratios reject the same null hypothesis is using Maximum Eigenvalue Statistic, therefore limiting possible value investing strategies during the Financial Crisis to those of stocks sorted based on the BM and CEP ratio.
However, because earnings during the Crisis suffered a downturn among all industries, due to lack of credit and low purchase power, based on the results, the best possible strategy would have been that of choosing undervalued stocks, based on the Book to Market ratio.
To conclude, it can become costly for an individual to hold a long position on value stocks, due to the lack of liquidity and higher transaction fees and also difficult for an institutional investor to hold any position in value stocks, which are considered to be riskier then growth stocks. Therefore, as long as these impediments retain investors, both institutional and individual, from investing in value stocks, these stocks will continue to be cheap and look riskier, if not approached. However, as every economical theory works, it is expected that when the moment comes for value stocks to be intensively traded, the spread between value and growth stocks should tighten, therefore reducing the
value premium. This, consequently, will lead to the disappearance of the concept of value premium.
I encourage further studies that can continue this research, by enlarging the database to the entire European Union or a specific global region, or on companies that depend on certain industries, such as Oil or Mining Industry. I also support future papers that aim at improving the current research. Also, approaching this research from the pointview of behavioral science could provide new answers to the topic. As Book-to-Market, Earnings to Price, Cash Earnings to Price and the Dividend Yield might all be, at some extent, reasons for underpricing the stocks, further studies should take into consideration the speculative demand and investors' behavior. Also, a possible further research that enables a study on a matrix form of the value premiums, resulting in various combinations between them, for example: BM for Belgium, DIV for France, DIV for Portugal and CEP for the Netherlands and so on, is highly encouraged. Also, further studies that compare the results obtained in this research to the rest of Europe are welcomed. Therefore, the real impact of creating Euronext could be measured by comparing these results to results in other countries, stock market mergers and so on. Last but not least, new discoveries of other significant types of value premium, apart from those in the literature are welcomed.
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