Testing the predictive power of the CAPM, FF3 and C4F on the Euronext100 stock index

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Testing the predictive power of the

CAPM, FF3 and C4F on the

Euronext100 stock index

Melvin J. H. Welsink

Faculty of Economics and Business

University of Amsterdam Roetersstraat 11, 1018WB Amsterdam

October 15, 2013

Abstract

This empirical study tests the strength of the CAPM, Fama-French three-factor model and Carhart’s four-factor model for the Euronext100 in the period January 2002 to December 2011. Tests are done by running linear time-series regressions on Euronext100 stocks and portfolios. The size-, value- and momentum-effects assigned to the American stock markets in prior research are also found on the Euronext100 within the tested time range. The traditional CAPM is outperformed in explaining these effects by the FF3 and the C4F model. But because of many insignificant betas and close adjusted R2 values, it is not clear which of these models is best in predicting returns. Within the testing period and for the 15 portfolios tested, none of the tested models seems to be linear and convincingly powerful in predicting stock and portfolio returns.

Bachelor Thesis (10 EC) Author: Melvin J. H. Welsink

Student ID: 0582948

First supervisor: drs. S.R. Changoer Second supervisor:

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I. Introduction

It is believed that having a model which can be used to predict the returns of stocks, portfolios and indexes with a particular risk is of great importance. The most common model used for getting these insights is the Capital Asset Pricing Model (CAPM). Well known extensions of this model are the Fama-French three-factor-model and Carhart’s four-factor model.

This empirical research examines if the Capital Asset Pricing Model, the Fama-French three-factor model and Carhart’s four-three-factor model have predictive powe for stocks on the Euronext100 stock market in the period January 2002 to December 2011.

By answering this research question it has to become clear whether using these models gives reliable expected returns. If not, is it interesting to see if there are particular matters that cause these inefficiencies.

Most of the times empirical studies on index markets in the United States (most commonly the S&P 500) are done decades ago. The most recent important papers are from 1993 (Fama and French), 1997 (Carhart) and 2005 (Post and van Vliet). These studies suggest that the model is misspecified relative to portfolios formed on, for example, market value and correlated volatility with the market. Empirical research using more recent data at the European market is relevant because the Euronext100 is a relatively new and young market and thereby differs from the U.S. Stock markets. Thereby, we have recently seen multiple market situations with upward and downward moving markets in Europe within a relative small time period. It is interesting to test whether this has any effect on the predictability of the models.

Fama and French (1992) extended the traditional CAPM model to make it more reliable, based on previous research done by Banz (1981) they introduced the Fama-French three-factor model (FF3). I will check whether adding variables for size and value premium indeed contributes to an increased reliability of the model.

In 1997, Mark Carhart added the momentum factor as a variable to the previous FF3 model. This four-factor model tries to explain the excess return of assets as well. My thesis should test the predictive power of these three models with the Euronext100 index as sample. The time span used to test the sample is the period January 2002 to December 2011. This time range has been chosen because it is the most recent data available for the index over the time span of a decade and it includes the latest recession.

The structure of my paper is as follows. Section II gives a look at the theoretical background of the CAPM, its related models, and its testing. The data and the methodology used are

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explained in section III. In section IV the results of testing the CAPM-models are provided, and finally, section V discusses the results and provides the conclusion of the study.

II. Literature Review

2.1 Introducing the CAPM

Markowitz (1952), following Von Neumann and Morgenstern (1947), developed an analysis based on the expected utility maximum and proposed a general solution for the portfolio selection problem. The portfolio’s risk for a given return cannot be lowered by any added diversification is a Markowitz efficient portfolio. The main idea of Markowitz was that investors could improve the quality of their portfolio by receiving the same or higher expected return as before, but with considerable lower risk. This could be done by eliminating the idiosyncratic risk of the portfolio, this risk should be eliminated by the correlation effect of the different stocks within the portfolio.

In 1964, William F. Sharpe stated that Markowitz’ model did not construct a market equilibrium theory of asset prices under conditions of risk. Sharpe was convinced that such an extension of Markowitz’ analysis would make the relationship between the price of an asset and the components of his overall risk more clear. Sharpe and Lintner (1965) introduced the traditional Capital Asset Pricing Model.

– (1) Where E(Ri) = Expected return for asset i

E(Rf) = Expected risk-free rate

E(Rm) = Expected market return

ßi = Beta, correlation of asset i with the market, level of systematic risk

α = Alpha, unexplained residual

When testing the CAPM four assumptions are made:

- Transactions can be done without transaction costs or taxes,

- Investors prefer the highest expected return for a given level of risk, and therefore prefer the lowest level of risk for a given expected return,

- Investors have homogeneous expectations and information regarding the data used, - Investors can borrow and lend at the given risk free rate of interest,

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The extra assumptions of Sharpe and Lintner in comparison with Markowitz’ model were that all investors should have the same expectations about risk and returns (they should be rational and risk-averse) and that all the lending and borrowing could be done against the risk-free rate. By making this last assumption, the curved efficient frontier could be changed to the straight Security Market Line (SML), this is graphically shown in Figure 1 below. The investors could expect a risk premium on top of the risk-free rate, this risk premium consists of the expected market return minus the expected risk-free rate times beta ([E(Rm) –

E(Rf)] · ßi)

Figure 1. CAPM graphically.

2.2 Testing the CAPM

Some papers in which the CAPM was (empirically) tested, appeared after the CAPM was introduced. The traditional CAPM presumed that the expected excess return on a security should be equal to its level of systematic risk, beta, times the expected excess return on the market portfolio. Fama and MacBeth (1973) concluded, given that the market portfolio is efficient, there did seem to be a positive relation between systematic risk and average returns at the NYSE in the period 1935 to 1968. They could not reject their hypothesises that there was no other risk than portfolio risk influencing the average returns, and that an investor should assume linear expected returns in relation with a security’s portfolio risk.

Black, Jensen and Scholes (1972) stated in their paper that the traditional CAPM was not consistent with the data. In addition there were difficulties to obtain efficient estimates of the mean of the beta factor and its variance. The cross-sectional tests they did were subject to measurement error bias. By expanding the traditional CAPM to a two-factor form of the CAPM, they provided a solution to this bias. Furthermore they showed that the mean of the beta factor had a positive trend over the period they investigated (1931-1965).

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In 1973, Merton seriously doubted the dimension CAPM. He stated that a single-dimension approach was not sufficient to explain asset returns precisely. Menton created the Intertemporal Capital Asset Pricing Model (ICAPM) consisting of multiple independent variables. In addition to the market-premium factor of the traditional CAPM, state variables for proxy the changes in the investors opportunity set should be added.

2.3 Multifactor Models

2.3.1 Size effect

Rolf W. Banz (1981) studied the relationship between return and market value of common stocks at the New York Stock Exchange. The study suggests that the CAPM is misspecified, over the forty year period (1936-1975) Banz did research about. It became clear that smaller NYSE firms had significant larger risk adjusted returns than bigger firms at that same NYSE and the conclusion could be drawn that this size effect is not linear in the market proportion. It is most pronounced for the smaller firms at the NYSE. Banz (1981) states that there is proof that a size effect exists, but he cannot make clear why. There is consensus that a possible explanation for the size effect could be that smaller companies/stocks are less liquid in comparison with greater sized companies/stocks. As a compensation for the higher liquidity risk of these smaller stocks, investors should be compensated with a higher expected return. While Banz (1981) noticed the size effects at the CAPM for stocks at the NYSE but could not make clear why this exists, Fama and French (1993) where able to explain the size effect by adding a SMB (Small Minus Big) variable. Fama and French did cross-sectional time-regression tests comparable with Banz for the NYSE, Amex and the NASDAQ for the 1963-1991 period with portfolios controlling for other effects and stated that value premiums vary with firms size and could be explained by SMB.

2.3.2 Value effect

Besides the size effect Banz mentioned, other effects on the CAPM became clear by testing the original CAPM. Basu (1977) sorted all the NYSE stocks in the period between 1957 and 1971 on earnings-price ratios. He stated an effect could be found, stocks with a high E/P-ratio (growth stocks) had significant higher returns than stocks with a low E/P-E/P-ratio (value stocks). After Stattman (1980) and Rosenberg, Reid, and Lanstein (1985) already mentioned different returns for stocks with different book-to-market ratios which could not be explained by the betas of the stocks and Chan, Hamao and Lakonishok (1992) stated that book-to-market ratios have a strong role in explaining the differences of average returns on the

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Japanese Tokyo Stock Exchange stocks between 1971 and 1988. Fama and French (1992) did identify a value premium for the U.S. stock markets. Stocks with high ratios of the book value of equity to the market value of equity, value stocks, had higher average returns than stocks with low book-to-market ratios, growth stocks in the testing period of 1962 to 1989. According to Fama and French, this value premium was left unexplained by the earlier discussed CAPM of Sharpe and Lintner. They proved the existence of the value effect by adding the HML (High Minus Low) variable. This HML variable in addition to the earlier mentioned SMB variable, led to the introduction of the Fama-French three-factor model. They stated that the FF3 should replace the traditional CAPM of Sharpe (1964) and Lintner (1965).

2.3.3 Three-factor model

The three-factor model of Fama and French, from now on called FF3, contains the market beta, a variable for size (SMB), and a variable for value (HML):

– (2)

In a more recent paper, Thierry Post and Pim van Vliet (2004) stated that this multiple factor model helps explaining value- and size portfolios in the post-1963 period (1963-2002), especially for the market segment with the small caps. But they also concluded that the model Fama and French provided in 1993 did not help to explain the fit for beta and reversal portfolios. Using this model for this benchmark did not improve the results compared with the traditional CAPM. And despite the good fit for the post-1963 period, there were no significant improvements for the size portfolios, and the results were even worse compared to the CAPM model for book-to-market equity (BE/ME) portfolios in the period before 1963. In their concluding remarks Post and van Vliet serious doubted the use of the Fama and French multiple factor model of the CAPM (compared with the traditional CAPM), especially for large cap stocks. In their opinion the results of the FF3 model are highly specific to the sample period and the set of benchmark portfolios.

2.3.4 Momentum effect

In 1985, De Bondt and Thaler first noticed what they called the “overreaction effect”. For the period of 1926 to 1982, the stocks at the NYSE with the highest returns for the ranking period of respectively one, two, three or five years were marked as winners, and the stocks with the lowest returns as losers. These winners and losers portfolios where tested against the NYSE

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for a holding period equal to their ranking period. They concluded that most people overreact to unexpected and dramatic news events and therefore the loser portfolios outperformed the NYSE in the long run and the winner portfolios underperformed the NYSE in the long run. In other words, prior losers outperform prior winners, and the overreaction effect was observed to be larger for prior losers than for prior winners.

Based on the research of De Bondt and Thaler (1985), Jegadeesh and Titman (1993) tested whether past returns provided useful information when trying to predict the stock prices for the NYSE and the AMEX in the time range from 1965 to 1989. A time-horizon of three to twelve months was chosen to rank stocks and Jegadeesh and Titman concluded that the winners of the past outperformed the losers of the past when having a holding period equal to the time-horizon of the ranking period. So where in the long run prior winners underperform prior losers, in the short term prior winners outperform prior losers. A momentum strategy was created by holding long positions of the past winners, and holding short positions of the past losers. An important assumption for the (no cost) momentum strategy is assuming no transaction costs. The momentum strategy can be seen as a momentum effect which is useful to help predicting stock prices. Chan, Jegadeesh and Lakonishok (1996) examined why the momentum effect occurs, it is difficult to find explicit reasons for the appearance of momentum. Their explanation is that momentum occurs most of the times around earning announcements, and they conclude that the most logical explanation of the momentum effect is the responds of the market when new information occurs.

2.3.5 Carhart’s four-factor model

The momentum effect is not covered by the FF3 of Fama and French. Carhart (1997) used the FF3 model and added the one-year momentum anomaly provided by the research of Jegadeesh and Titman (1993), with a four-factor model, from now on called C4F, as a result:

– (3)

On January 1 of each year (1962-1993) Carhart formed ten equally weighted portfolios using ranked returns and subdivided the top and bottom portfolio further in 3 equally weighted portfolios. Taking a long position in the highest portfolio (top 3,33% of sample) and a short position in the lowest portfolio explains the PR1YR variable (Carhart 1993). Post and van Vliet (2004) stated that the model of Carhart could not be rejected for size- value- and

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momentum portfolios in the 1931-1962 period. For the post-1963 (till 2002) period the model predicted the returns less accurate and could not be rejected for size- and value-based portfolios, but should be rejected for the momentum portfolios.

III. Data and Methodology

3.1 Data description

3.1.1 Date

The data used and tested in this thesis is all from the time range January 2002 till December 2011, this is the most recent data and includes the most accurate information. Expanding the time range could make the data less reliable because the Euronext100 has been listed only since December 31, 1999 and using data of a more settled index with (at least) two years of historical data is to be preferred.

3.1.2 Euronext100 index and returns

My sample consists of all individual stocks of the Euronext100 index. The Euronext100 is an index containing the hundred largest and most liquid stocks of Euronext Paris, Brussels, Amsterdam, Lisbon, and Luxembourg. Each quarter the index is reviewed and adjusted due to size and liquidity. The Euronext100 should be a useful representation of the European market. The data source for the returns of the Euronext100 and the returns for the stocks quoted at the Euronext100 is Datastream. The data for the Euronext100 itself could be found with the Datastream-code EUNX100, and the data for the stocks listed at the Euronext100 were acquired with the Datastream-code LEUNX100. Stocks not listed on the Euronext100 at January 1 of the year 2012 have not been taken into account for testing in this thesis. Therefore, the number of stocks tested on, increased from 82 stocks in January 2002 to 100 stocks in July 2011 and after. All the single stocks of the Euronext100 used in this empirical research can be seen in Appendix A.

Returns are calculated by:

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Where Ri is the return on a certain asset Dt is the dividend in month t, Pt is the closing price

(end of the month) of an asset and Pt-1 is the closing price of an asset one month earlier. These

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3.1.3 Risk-free rate

The risk-free rate per month used will be defined by the three month rate of the Euro Interbank Offered Rate (Euribor) during that same period adjusted to one month. The Euribor is used because the testing has been done at the European market and the rates were available at Datastream. Instead of the Euribor it is also possible to use the German government bills for the risk-free rate. There is no significant difference between these two proxy risk-free rates.

In Datastream, the Euribor three-month-rates are given by the EIBOR3M code, but the rates have been converted to the associated yearly interest rates. To obtain the monthly risk-free rate, the average of the daily Euribor three-month rates in a month has been calculated (rf3M,yearly) and then converted with the following formula:

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Where Rf is the risk-free rate per month. All the monthly risk-free rate percentages per month are listed in Table 17 in Appendix . 3.2 Methodology 3.2.1 Testing Testing in this thesis has been done with the original CAPM model, the FF3 model of Fama and French and the C4F model of Carhart. Linear time-series regressions have been done to test the three different models of the CAPM. To be able to generate correct regressions, the risk-free rates have been subtracted from the dependent variables (Ri), which led to the following formulas: CAPM: – (6)

FF3: – (7)

C4F: – (8)

Where (9)

For testing the traditional CAPM, formula (6) is used, for testing the FF3 formula (7) and for testing the C4F, there have been regressions on formula (8).

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For the statistical testing of these models, IBM SPSS Statistics has been used. By running regressions in SPSS, alphas have been calculated and tested for significance with a 95% confidence interval. It has been taken for granted that a model is misspecified for a stock or portfolio if the alpha was significant different from zero in the testing period. For the complete Euronext100 the models are quoted as misspecified when the number of stocks with a significant alpha within the index, divided by the total number of stocks within the index, were above 5%.

3.2.2 Explanatory variables

3.2.2.1 Market factor variable: (Rm-Rf)

The explanatory variable for the market risk is the explanatory variable that has been used in all three types of the CAPM. The Euribor risk-free rates per month have been subtracted from the monthly Eauronext100 returns. In the traditional CAPM, it was stated that the beta of the market factor variable should capture the risk of an asset with respect to the market. The higher the beta, the higher the expected return in the CAPM. Beta is calculated by:

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3.2.2.2 Size and Value variables: SMB and HML

To be able to compute the explanatory variables for size and value, it has been necessary to form portfolios of stocks on size and value. To compare the stocks for size, the market values of all the Euronext100 firms have been used, the market values could be retrieved from Datastream (with the MV-code). The values of the Euronext100 firms have been judged based on Book-To-Market value. The BTM values have been generated by taking the inverse of the Market-To-Book-Values that were exported from Datastream (MTBV-code).

Forming the portfolios has been done using the same method Fama and French used (1993). In January of each year t from 2002 to 2012, all Euronext100 stocks available at Datastream have been ranked on market value. At the median market value, the stocks have been split into two groups, Small (S) and Big (B). In the same way, three equal groups based on book-to-market values were created, High (H), Middle (M) and low (L). The reason for dividing the firms in two different groups for size, but in three different groups for book-to-market is the predicted role in average monthly stock returns. Fama and French (1992) stated that the role of book-to-market was believed to be stronger.

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After the stocks were divided in the different groups, six portfolios have been formed by taking the intersects of the size and value groups, generating six portfolios: SL, SM, SH, BL,

BM and BH. For example, when a firm has a Big market value, and a Low BTM-ratio, it

should be allocated to the BL portfolio.

The Small-Minus-Big (SMB) explanatory variable has been constructed by subtracting the average of the returns of the big-sized firms (BL, BM, BH) from the average of the portfolios with the relative small-sized firms (SL, SM, SH). In this way both of these groups have more or less equal book-to-market ratios, which should ensure that the value-factor has no influence on SMB.

Following the literature of Banz (1981) and Fama and French (1992 and 1993), SMB should have a significant positive coefficient. They have all been endorsing the argument that small firms should have considerable higher (expected) returns in comparison with big firms because of the size factor.

The High-Minus-Low (HML) explanatory variable has been formed using the same roadmap as used for SMB. The average returns of the low book-to-market groups have been subtracted from the average returns of the high book-to-market groups to make sure the size-effect does not affect the HML factor.

Stattman (1980), Rosenberg, Reid and Lanstein (1985) and again Fama and French (1992) showed that stocks with high book-to-market values have higher returns compared with low book-to-market firms. The prediction is that the Eurnonext100 data for the time range between 2002 and 2012 endorses these empirical findings, and has a significant positive HML coefficient.

3.2.2.3 Momentum variable: MOM

The explanatory momentum variable (MOM) used in the C4F variant of the CAPM is about predicting the average returns of portfolios based on their previous returns. To construct this MOM, six portfolios were formed. Every six months, starting in July 2002 and ending July 2011, the average returns per firm of the last six months were calculated, ranked and thereafter divided in six portfolios (mom1, mom2, mom3, mom4, mom5, mom6). In which case

mom1 is the 16.67% of the Euronext100 firms with the highest average past returns, and mom6 is the portfolio covering the 16.67% of the firms with the lowest average past returns.

The MOM was generated by subtracting the average monthly returns of portfolio mom6 from the average monthly returns of portfolio mom1. The MOM represents the momentum

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strategy: buying the past winners, mom1, and going short in the past losers, mom6. It is important to realise that the assumption was made that there were no transaction costs.

Testing for momentum effect is relatively new, in 1993 it was done for the first time by Jegadeesh and Titman. They concluded losers were outperformed by winners when the holding period was equal to the ranking period. Carhart (1997) extended the empirical research of Jegadeesh and Titman and introduced the PR1YR factor, which is comparable to the MOM factor that was used in this research. Most important difference between the two factors is the ranking and holding period of one year in Carhart’s research where the ranking and holding period in this empirical paper is six months. When the momentum effect is considered to be present at the Euronext100, coefficients on MOM should be positive and significant.

3.2.3 Dependent variables: Portfolios and stocks

First, all available Euronext100 stocks have been tested with linear time-series regressions. For the CAPM and FF3 a time range of 120 monthly periods has been used, and for testing the C4F model a time range of 114 monthly periods has been used. This difference in time range exists because there was a lack of data regarding past monthly returns necessary for the ranking period of the MOM. The alphas generated, representing the mistake of a model, when regressing were tested for significance at a 95% confidence interval with a t-test. Because evidence for the reliability of a model and his explanatory variables cannot always be displayed correctly when using single stocks (Carhart, 1997) the focus of this empirical research has been at testing on portfolios.

All of the portfolios used for testing are based on equally weighted data. Twelve portfolios have been constructed, nine portfolios based on size and book-to-market, and six portfolios based on momentum. As far as the size and book-to-market portfolios are concerned , it was investigated whether the mimicking portfolios of the explanatory variables SMB and HML capture the factors in monthly returns related to size and book-to-market. And with the momentum portfolios it was tested if the mimicking portfolio for the explanatory variable MOM captures the factors related to the momentum effect.

The six momentum portfolios discussed at the “MOM explanatory variable”, minus the risk-free rates for every month, were used as dependent momentum portfolios in the regressions. With mom1 as portfolio with the highest average past returns and mom6 as portfolio with

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lowest average past returns1. As before with the MOM factor, the momentum portfolios have been tested for 114 months instead of 120 because of a lack of data.

As discussed in paragraph 3.2.2.2, the size and book-to-market portfolios were formed by taking the intercepts of stocks within the two different measurement factors (so stocks both ranked in for example Big market size and High book-to-market ratio tertiles would end up in portfolio BH). Contrary to the portfolios formed for creating the SMB and HML, not only the ranked book-to-market stocks were divided in three groups (Low, Middle, High), but the ranked size stocks were divided in three groups (Small, Middle, Big) as well. Thus, nine portfolios were formed: SL, SM, SH, ML, MM, MH, BL, BM, BH. Where the first letter refers to the relative size, and the second letter refers to the relative book-to-market ratio of the stocks in the portfolio2.

1

When it was not possible to divide the total number of firms equally over the six portfolios, the firms were been divided in a certain order. The first firm remaining was placed in the portfolio mom4, the second firm in portfolio mom3, the third firm in portfolio mom5, the fourth firm in portfolio mom2 and when there was a fifth firm remaining this stock was allocated to portfolio mom6.

2

When the ranked market values or market-to-book values of the firms could not be divided by three, the first firm remaining was allocated to the Middle group and in case of a second firm remaining this firm was allocated to the Small (for size) or Low (for book-to-market) group.

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3.2.4 Subsamples: Time range

So far, all the testing was done using the complete time range of 2002 to 2012, regarding 120 or 114 monthly periods. Because the complete time range captures the economic crisis in Europe starting in 2007, three subsamples with respect to the economic situation within Europe were chosen. Three models were tested in the chosen subsample periods during a positive market situation, a market situation of economic depression and an instable market situation after a depression. In this empirical research the assumption was made that the economic depression within Europe started in the second week of July 2007, indicated by the red dot in Figure 2 below. Figure 2 shows the trends of the Euronex100.

Figure 2. Chart of the Euronext 100 in the time range January 2, 2002 till January 2, 2012. (from finance.yahoo.com)

For optimal representation of the three different states of the European market, subsample time ranges of two years, with 24 monthly periods, were used.

The subsample time ranges are:

July 2005 – June 2007 (positive Euronext100 trend) July 2007 – June 2009 (negative Euronext100 trend)

July 2009 – June 2011 (period of uncertainty at the Euronext100)

These three different time ranges were tested to see whether different market trends are related to the reliability of the different models tested and if there is a difference between the three models within the subsample time ranges.

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IV. Results

4.1 Descriptive statistics

When looking at the descriptive statistics of the explanatory variables, the summary statistics regarding the mean of the monthly excess returns and the associated standard deviation (volatility) in table 4 for the complete testing period immediately show an interesting pattern. Where the mean of the excess market return was always positive for the total time range in empirical research of Black, Jensen and Scholes (1973), Fama and French (1993) and Carhart (1997) a mean excess monthly return of -0.288 percent for the explanatory variable for market risk, Rm-Rf, can be detected here. All other explanatory variables have a positive mean for the excess returns per month.

_Mean monthly return Standard deviation First quartile Second quartile (median) Third quartile N Rm-Rf -0,288 5,541 -3,610 0,482 3,371 120 SMB 0,864 1,708 0,059 0,871 1,946 120 HML 0,285 3,887 -1,847 0,021 1,944 120 MOM 0,456 6,236 -1,474 0,899 3,694 114

Table 2. Mean monthly returns (%), volatility, quartiles and number of periods.

Another remarkable data descriptive is the volatility of the SMB factor. Where higher standard deviations are expected when the excess return increases, SMB has the highest mean excess return of all explanatory variables but the associated standard deviation is the smallest of all variables. It is difficult to derive a conclusion for the variable MOM because fewer monthly periods are taken into account when testing on MOM. Appendix B (table 18) shows that volatility of the other variables increases when accounting for 114 periods and there are fluctuations in the mean of excess return as well. When regressing the C4F model, the complete time range consisted of 114 months. In appendix B the descriptive statistics for Rm-Rf, SMB and HML for this time range can be found.

Table 3 at the next page shows the mean monthly returns and their associated volatility of the explanatory variables per year. Market situations can be observed more properly in this table. There is shown that the mean of the excess market return is lowest during the beginning of the recession in 2008, and while the mean monthly returns were again positive for the year 2009 high volatilities still make clear the situation of economic distress.

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15 2002 2003 2004 2005 2006 Mean St. Dev Mean St. Dev Mean St. Dev Mean St. Dev Mean St. Dev Rm-rf -3,186 8,028 0,943 5,431 0,568 2,269 1,611 3,188 1,173 3,081 SMB 0,978 2,515 0,420 2,125 1,393 1,342 0,727 1,166 0,731 1,541 HML 1,223 4,271 0,421 3,445 1,121 2,037 0,628 1,403 0,449 1,537 MOM -0,852 14,126 1,198 9,364 1,831 4,118 0,440 3,064 1,118 2,888 2007 2008 2009 2010 2011 Mean St. Dev Mean St. Dev Mean St. Dev Mean St. Dev Mean St. Dev Rm-rf -0,024 3,297 -5,011 7,399 2,025 6,854 0,326 5,454 -1,310 4,626 SMB -0,073 1,323 1,397 1,780 1,489 1,903 1,251 1,506 0,323 1,268 HML -1,367 1,598 -1,026 2,880 3,146 8,390 -0,415 3,474 -1,328 3,537 MOM 1,686 3,282 0,285 4,953 -3,442 10,210 1,222 4,288 0,423 2,337

Table 3. Mean of the monthly returns (in %) and their volatility, per year.

In table 4a and 4b, a strong correlation between the explanatory variables is shown. The Pearson correlations of SMB, HML and MOM are all significant with Rm-Rf, a strong relation exists. The correlations of MOM with SMB and HML are also significant, which results in the observation that the only correlation not significant is the correlation between SMB and HML. Rm-Rf SMB HML MOM Rm-Rf SMB HML MOM Rm-Rf 1,000 Rm-Rf SMB -,383 1,000 SMB ,000 HML ,537 -,022 1,000 HML ,000 ,407 MOM -,496 ,241 -,410 1,000 MOM ,000 ,005 ,000

Table 4a. Pearson Correlations of Table 4b. Significance of Pearson Correlations explanatory variables. of explanatory variables (at a 5% level).

Strong correlations between explanatory variables suggest there could be multicollinearity. Multicollinearity leads to higher standard errors, which enlarges the confidence intervals for the coefficient of the variables and small t-values. Then coefficients have to be larger to be significant and it is harder to reject the hypothesis of coefficients being equal to zero.

Jensen (2003) indicates that it should be a rule of thumb to assume multicollinearity if the Pearson-correlations are higher than 0,5, or lower than -0,5, Mason and Lind (1996) stated that correlations between -0,70 and 0,70 do not cause problems regarding multicollinearity. Based on this literature, there is possible (small) multicollinearity between Rm-Rf and HML and no significant multicollinearity between the other explanatory variables.

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4.2 Euronext100 stocks 4.2.1 CAPM

Table 5 shows a summary of the regression results for testing the Euronext100 single stocks for the traditional CAPM.

N n stocks average α average lαl n of sign α n of sign β 120 100 0,610 0,793 18 98

Table 5. Summary of CAPM regression results: Euronext100 stocks.

Significance of the alpha of 18 stocks out of the total sample of 100 stocks is proven by regressing the single stocks on the traditional CAPM model with a confidence interval of 95% in the time range of January 2002 to December 2011.

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Using formula (11) we get: (18/100) ∙ 100% = 18% of the stocks is significant.

Because 18 percent is larger than 5 percent, the conclusion can be drawn that the traditional CAPM is misspecified for the single Euronext100 stocks within the sample time range.

4.2.2 FF3

Regressing the Euronext100 single stocks with the FF3 model, summary of output is given in table 6, makes clear that 8 percent of the alphas is significant different from zero. Because 8 percent exceeds 5 percent, it can be concluded that the FF3 model is misspecified for the single stocks at the Euronext100 during the sample time range.

N n stocks average α average lαl n of sign α n of sign βrm-rf n of sign βSMB n of sign βHML 120 100 0,162 0,828 8 100 29 35

Table 6. Summary of FF3 regression results: Euronext100 stocks.

In comparison to the traditional CAPM, it can be assumed that the FF3 model has greater predictive power. Although the average of the absolute alpha is slightly higher using the FF3 model instead of the CAPM, the number of significant alphas is considerably lower when regressing with the FF3.

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4.2.3 C4F

The four-factor model of Carter was tested in the time range July 2002 to December 2011. The percentage of significant alphas after regressing the Euronext100 stocks on the C4F model is 6,13 percent. Therefore the conclusion can be drawn that the C4F is misspecified for the Euronext100 single stocks.

N n stocks average α average lαl n of sign α n of sign βrm-rf n of sign βSMB n of sign βHML n of sign βMOM 114 98 0,162 0,801 6 95 25 33 14

Table 7. Summary of C4F regression results: Euronext100 stocks.

Compared to the CAPM it seems that returns of Euronext100 stocks are better explained by the C4F model. The percentage of significant alphas is 11,87 percent lower when using the C4F model where the difference in the average of the absolute alpha is negligible. In comparison to the FF3 model there does not seem to be a considerable difference.

The information given in tables 5, 6 and 7 regarding the different betas indicate that only the beta regarding the market risk has significant explanatory value. This pattern can be explained by looking at the composition of the betas. As discussed before the betas of SMB, HML and MOM were created after ranking the available data and forming portfolios. This makes it possible to test if the size-effect, value-effect and momentum-effect are captured by relatively SMB, HML and MOM. In absence of these portfolios the explanatory value of the variables is difficult to measure and there is a lot of non-systematic risk.

4.3 Portfolios

4.3.1 Descriptive statistics of portfolios

To be able to test the three different versions of the CAPM on size-effect, value-effect and momentum-effect, 15 portfolios consisting of Euronext100 stocks were formed. These portfolios can be divided into two groups, one group of portfolios based on multiple combinations of size and book-to-market ratios (above the line in table 8) and one group based on returns of the last six months, the momentum portfolios shown below the line in table 8. In both groups every firm is represented only once. In table 8 below can be seen that for the momentum portfolios, the number of firms accounted for in a portfolio is about equal. An average of 17 firms is represented by the four middle portfolios, and an average of 16 firms per portfolio for the most extreme portfolios. The variance in the number of firms in the

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portfolios formed on size and book-to-market is higher, with a minimum average of eight firms in the portfolio with Middle size and High book-to-market value and a maximum average of 10,8 firms in the portfolio of Small size and High book-to-market.

When looking at the mean of the monthly excess return and the volatility, one can conclude that no positive linear relationship between these factors exists in the sample, the portfolios with the highest monthly returns do not have the highest volatility. This indicates that not all idiosyncratic risk is diversified away by the portfolios. Remarkable are the relative high standard deviations of the portfolios BH and mom6.

Indications of a size effect can already be noticed when looking at the mean returns, Small firm portfolios have an obvious higher monthly mean return than middle-sized and especially big-sized firm portfolios. The average difference between the mean return of the small and big size portfolios is 1,509%. Less indication is noticed for the value-effect, although there is a difference between high book-to-market and low book-to-market portfolios of 0,156%. No (positive) linear relation between the mean of the monthly excess returns and the associated volatility for the momentum portfolios can be found. There can not be stated that volatility increases when monthly returns are high, in fact the highest volatility is for portfolio

mom6 which provides the second lowest returns taking the complete testing period into

account3.

Portfolio mom1, the past winners, has the highest mean excess return which is in accordance with the literature of Jegadeesh and Titman (1993) and Carhart (1997), but the mean returns of the other momentum portfolios do not show a particular pattern of a relationship between past performance and current performance.

3

The mean excess returns and volatility of the size and book-to-market portfolios associated with testing the C4F, 114 monthly periods, can be seen in Appendix B (table 19).

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19 Mean Excess Return (monthly) Standard Deviation N avg. number of firms SL 0,94022 6,75621 120 8,7 SM 1,14972 6,32883 120 9,7 SH 1,17583 6,76213 120 10,8 ML -0,08415 5,56506 120 10,1 MM -0,12199 5,77582 120 9,6 MH 0,01758 7,43104 120 8 BL -0,26008 4,99430 120 10,4 BM -0,29133 6,84987 120 9,4 BH -0,12940 9,16736 120 10,1 mom1 0,69255 6,05289 114 16 mom2 0,41776 5,54849 114 17 mom3 0,09588 5,26327 114 17 mom4 0,44383 5,93936 114 17 mom5 0,45930 6,98594 114 17 mom6 0,23614 9,21293 114 16

Table 8. Mean of excess monthly return (%), volatility, number of periods and average number of firms in portfolio.

4.3.2 CAPM

The empirical results of testing the portfolios for the traditional CAPM are shown in table 9 and 10, significant t-values of betas are denoted by asterisks (*) and significant t-values of alpha are denoted by double asterisks (**).

For the portfolios based on size and book-to-market there are three significant alphas. All these significant alphas are associated with portfolios of small-sized firms, and the value of alpha is positive. As shown in table 8, the mean excess returns of these portfolios where higher relative to the other portfolios. When assuming the CAPM model good in predicting returns, a higher (absolute) beta should explain these higher returns but the empirical results clearly reject this statement. The existence of a size-effect not explained by the CAPM is a possible explanation for these findings, the FF3 model could possible provide more evidence for this size-effect. The adjusted R2 of the small-sized portfolios is lower than the adjusted R2 of the other portfolios as well, which suggests that the returns of the small-sized portfolios are less precisely predicted by the used explanatory variables.

With respect to the value-effect it can be seen (table 9) that the indications for this effect described earlier in the descriptive statistics are present in the empirical results of testing the CAPM as well. The portfolios consisting of the high book-to-market firms seem to have higher t-values for alpha than the other portfolios based on the same sized firms accounting

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for the middle or low book-to-market ratios. The slightly higher means of the monthly excess returns mentioned in the descriptive statistics (table 8) for high book-to-market portfolios indicating a possible value-effect are probably partly captured by the market-factor coefficients in the CAPM. Looking at the betas in table 9, higher betas can be observed for high book-to-market portfolios relative to the other portfolios.

Adj. R2 α β t (α) t (β) SL ,724 1,240 1,039 3,819** 17,681* SM ,755 1,436 ,994 5,014** 19,168* SH ,748 1,481 1,057 4,768** 18,803* ML ,792 ,174 ,895 ,750 21,301* MM ,904 ,164 ,992 1,005 33,549* MH ,810 ,366 1,208 1,237 22,552* BL ,840 -,022 ,827 -,118 25,003* BM ,860 ,040 1,147 ,169 27,013* BH ,868 ,316 1,542 1,037 27,998*

Table 9. Empirical results CAPM: Size and b-t-m portfolios.

Table 10 shows that 66,67% of the alphas retrieved from the regression of momentum portfolios with the traditional CAPM are significant. The empirical results do not provide any prove of the existence or possibility of a momentum-effect. Significant alphas are shown for both high past-performance portfolios as low past-performance portfolios. A pattern that can be derived from these results is that portfolios with lower past returns over the last six months have higher betas relative to the portfolios formed with high past-performance firms.

Adj. R2 α β t (α) t (β) mom1 ,752 ,846 ,942 2,993** 18,531* mom2 ,835 ,566 ,910 2,681** 23,962* mom3 ,873 ,239 ,882 1,362 27,921* mom4 ,916 ,609 1,020 3,784** 35,177* mom5 ,868 ,649 1,168 2,733** 27,324* mom6 ,820 ,479 1,497 1,308 22,706*

Table 10. Empirical results CAPM: Momentum portfolios.

To summarize the empirical results of the traditional CAPM, with exception of the BL portfolio, all the portfolio returns were underestimated by the CAPM and the beta of each portfolio was strongly significant. Regarding size and book-to-market portfolios three alphas were significantly different from zero and the average adjusted R2 observed is 0,811. When

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testing the momentum portfolios four out of six alphas of the portfolios regressed on were significant and the average adjusted R2 of the momentum portfolios is 0,844.

4.3.3 FF3

As described in the previous paragraph, a probable size-effect and a possible value-effect could be distinguished in the empirical results of the CAPM model. Using the Fama and French three-factor model should therefore improve the empirical results in comparison to the CAPM. In table 11 and 12, the empirical results of testing the portfolios for the FF3 model are presented. Adj. R2 α βRm-rf βSMB βHML t (α) t (βRm-rf) t (βSMB) t (βHML) SL ,784 1,097 1,270 ,413 -,516 3,376** 18,840 2,177* -5,864* SM ,837 ,560 1,031 ,950 ,231 2,120** 18,796 6,159* 3,226* SH ,914 ,383 1,002 1,075 ,537 1,863 23,486 8,953* 9,642* ML ,837 ,199 1,042 ,142 -,370 ,856 21,594 1,048 -5,879* MM ,914 -,141 1,021 ,350 ,040 -,803 27,996 3,410* ,841 MH ,878 ,099 1,014 ,055 ,576 ,368 18,229 ,349 7,929* BL ,890 ,096 ,947 ,016 -,338 ,561 26,632 ,155 -7,290* BM ,871 ,367 1,160 -,325 -,151 1,442 21,974 -2,187* -2,194* BH ,938 ,685 1,194 -,782 ,720 2,906** 24,420 -5,680* 11,273*

Table 11. Empirical results FF3: Size and b-t-m portfolios.

The empirical results of the size and book-to-market portfolios considered in table 11 show that there are three significant alphas. Compared with table 9 of the CAPM there can be seen that portfolios SL and SM were significant for testing on the CAPM as well. Contrary, where the alpha of SH was significant for the traditional CAPM it is not significant for the FF3 model anymore, but the alpha of BH is significant for the FF3 and not for the CAPM.

When the FF3 model would be linear, the size and book-to-market portfolios should be fully explained by the model and its coefficients. Considering the significant alphas of three out of nine portfolios it can be stated that when testing the FF3, no linearity of the model was observed and the average level of the values of alpha is lower compared to the average t-values for the alphas of the CAPM.

Observing the betas, the conclusion can be drawn that all the betas associated with the market premiums are still significant, but changed a lot because of the high correlations between the market factor and the SMB and HML factors. The betas for SMB are three times, and the betas for HML are once, not proven to be significant different from zero. These betas, denoted

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without an asterisk, have no explanatory power for the returns of the portfolios they are associated with. Looking at the betas of SMB it can be seen that portfolios considering smaller firms have higher SMB betas than portfolios considering bigger firms, which have negative or zero betas. This is a logical observation considering SMB is the Small-Minus-Big firms portfolio, mimicking the size-effect. The same conclusion can be drawn for the High-Minus-Low book-to-market variable, where high book-to-market portfolios have higher returns than subsequently middle and low book-to-market portfolios.

Adj. R2 α βRm-rf βSMB βHML t (α) t (βRm-rf) t (βSMB) t (βHML) mom1 ,773 ,358 1,031 ,622 -,042 1,182 16,081* 3,534* -,497 mom2 ,838 ,397 ,906 ,191 ,071 1,691 18,241* 1,402 1,086 mom3 ,883 -,029 ,899 ,320 ,057 -,155 22,468* 2,912* 1,073 mom4 ,930 ,282 1,036 ,387 ,078 1,706 29,567* 4,023* 1,673 mom5 ,868 ,776 1,127 -,174 ,053 2,907** 19,944* -1,125 ,708 mom6 ,834 ,226 1,401 ,223 ,327 ,573 16,783* ,975 2,954*

Table 12. Empirical results FF3: Momentum portfolios.

When comparing the empirical results of the momentum portfolios of testing the CAPM in table 10 with the empirical results of the momentum portfolios associated with testing the FF3 in table 12, an obvious difference can be observed. Four of the six momentum portfolios had significant t-values for alpha when testing the CAPM, where only one of the six momentum portfolios has a significant t-value for alpha when testing the FF3 model. The significant momentum portfolios alphas of the CAPM regression seem to be explained by the size-effect factor, SMB, when testing these momentum portfolios for the FF3 model. In table 12 is shown that when the coefficient of SMB is significant different from zero for a momentum portfolio, the alpha associated with this portfolio is decreased to a level not significant different from zero. Thereby the levels of the adjusted R2 of these portfolios are increased compared to the CAPM when testing for the FF3.

The value-factor HML has explanatory power (significant beta) for the mom6 portfolio only, resulting in a slight increase in the adjusted R2 for this portfolio compared with table 10 of the CAPM.

All the empirical results of testing for the FF3 model taken into account it can be concluded that the FF3 model predicts the portfolio returns better than the CAPM does. Where the number of significant alphas for the size and book-to-market portfolios is equal for both models, the number of significant alphas for the momentum portfolios has obviously

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decreased. The average goodness of fit of the explanatory variables explaining the model, measured with the adjusted R2, has increased from 0,811 to 0,874 for size and book-to-market portfolios and slightly increased from 0,844 to 0.854 for explaining momentum portfolios. The betas concerning market risk are significant for al portfolios. The betas concerning the size-effect and the value-effect are significant for 60% of the portfolios. The nonlinearity of the CAPM seems to be explained partially by the FF3 factors, with the important note that the FF3 model is not linear for the Euronext100 portfolios in the period of 2002 to 2011 as well.

4.3.4 C4F

The empirical results of testing for the C4F model in table 13 show only minor changes in comparison with table 11 for the FF3. The alpha for the SM portfolio was significant before and when testing for the C4F not anymore, but the p-value is still very close to significance with a p-value of 5,3% and a confidence interval of [-0,006 , 1,073]. Furthermore this improvement regarding significance is reached by adding the beta for momentum, which is not significant from zero itself for portfolio SM.

The beta for momentum is significant for only 33,33% of the size and book-to-market portfolios, and adding the MOM factor results in an extra coefficient of SMB not different from zero. This can be explained by the significant correlation between MOM and SMB. The high correlation between MOM and Rm-rf and HML results in negative values for all MOM coefficients of the size and book-to-market portfolios. The average adjusted R2 for these portfolios is 0.879 which is not significantly different from the adjusted R2 of the same portfolios for the FF3 model (0,874).

Adj. R2 α βRm-rf βSMB βHML βMOM t (α) t (βRm-rf) t (βSMB) t (βHML) t (βMOM) SL ,792 1,058 1,198 ,409 -,469 -,054 3,409** 17,484* 2,251* -5,260* -1,031 SM ,838 ,533 1,035 ,986 ,185 -,035 1,959 17,224* 6,194* 2,364* -,761 SH ,915 ,379 ,984 1,104 ,499 -,069 1,799 21,159* 8,961* 8,239* -1,920 ML ,854 ,189 1,004 ,196 -,443 -,137 ,844 20,273* 1,492 -6,876* -3,609* MM ,915 -,136 1,003 ,362 ,028 -,044 -,760 25,347* 3,450* ,540 -1,445 MH ,880 ,028 1,039 ,065 ,534 -,008 ,102 17,075* ,404 6,746* -,166 BL ,894 ,074 ,960 ,031 -,385 -,028 ,430 25,134* ,309 -7,753* -,970 BM ,882 ,325 1,120 -,276 -,212 -,132 1,306 20,386* -1,894 -2,967* -3,131* BH ,945 ,735 1,121 -,769 ,724 -,110 3,222** 22,255* -5,767* 11,050* -2,839*

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Table 14 shows a remarkable pattern, the MOM factor should be very helpful in explaining momentum portfolios but, taken into account that only six momentum portfolios were tested, the results do not endorse this statement within the tested time-range. Compared to the FF3 model, the number of significant alphas did not change and the level of the associated t-values became larger. There is one coefficient of the SMB factor which was not significant when testing the FF3 model which is significant when testing the C4F model, and 33,33% of the MOM coefficients is not significantly different from zero for the momentum portfolios. Despite of these facts, the goodness of fit for the momentum portfolios measured by the adjusted R2 has increased from 0,854 to 0,905. This increase is mainly due to the improved goodness of fit for the mom1 and mom 6 portfolios.

Adj. R2 α βRm-rf βSMB βHML βMOM t (α) t (βRm-rf) t (βSMB) t (βHML) t (βMOM) mom1 ,897 ,305 1,179 ,463 ,105 ,399 1,492 26,088* 3,867* 1,785 11,491* mom2 ,860 ,376 ,964 ,128 ,130 ,158 1,722 20,026* 1,003 2,071* 4,274* mom3 ,886 -,038 ,922 ,295 ,080 ,063 -,201 22,388* 2,702* 1,492 1,978 mom4 ,931 ,290 1,016 ,408 ,058 -,054 1,771 28,152* 4,271* 1,229 -1,944 mom5 ,900 ,808 1,039 -,079 -,035 -,239 3,485** 20,304* -,583 -,530 -6,088* mom6 ,955 ,305 1,179 ,463 ,105 -,601 1,492 26,088* 3,867* 1,785 -17,30*

Table 14. Empirical results C4F: Momentum portfolios.

Summarized the C4F model does not seem to be a linear and reliable model. In comparison to the CAPM most of the empirical results are better in predicting the portfolio returns and there are less significant t-values for alpha observed. Compared to the FF3 model it is difficult to conclude which of these models has more predicting power for the Euronext100 portfolios in the period of 2002 to 2011. The average t-value of the alphas rises when using the C4F model instead of the FF3 model, but the total number of significant alphas decreases from a total number of four to a total of three. A very important note to the C4F results and comparisons with the other models is that the time range where size and book-to-market portfolios are tested for is different from the time ranges used for testing these portfolios in the other models, so testing for subsamples with the same time span could help when comparing these two models with each other.

The high correlations between the explanatory variables and the many insignificant betas observed suggest that omitting the HML factor (accounting for the highest correlations) could provide a more reliable model for predicting the portfolio returns. In appendix E, a regression output for such a model can be seen, but further testing for this alternative model will not be done in this paper.

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4.4 Subsamples

Because the time range tested consists of periods with rising markets as well as recession, it is interesting to see if there are any changes in the three models tested and relative to each other within these different economic markets. Three subsamples are taken, all consisting of 24 monthly periods, but within different economic situations (see figure 2, page 13). The first subsample time range is a period of positive market sentiment, July 2005 to June 2007. The second subsample is during economic distress, July 2007 to June 2009. And the last subsample time range is from July 2009 to June 2011, with the European market still in recession and trying to recover. The descriptive statistics and empirical results can be found in Appendix C.

4.4.1 Positive Euronext100 sentiment

Between July 2005 and June 2007 the Euronext100 performed well with an average monthly return of 1,85%. Table 15 below shows a summary of the empirical results for this time range. Two out of 15 portfolios regressed on for the CAPM have a significant alpha and measured with the adjusted R2, the market premium beta explains 74,4% of the returns of the portfolios. Adding the explanatory variables for the Fama and French model, the variables together have a higher explaining value and there is only one significant alpha left. When subsequently the MOM factor is added, adjusted R2 just slightly increases and the significant alpha is still present. The significant coefficient of SMB for the MH portfolio (based on size and book-to-market) is not significant anymore for the C4F model. This shows the FF3 model is nonlinear, supported by the fact that only eight of the 18 betas for the size and book-to-market factors SMB and HML for portfolios based on these same factors for the FF3 model regressions are significant. While the adjusted R2 increases when adding variables, these increases are small and furthermore lots of the coefficients of these variables are not proven to be significant differently from zero. None of the three tested models seems to be a reliable and linear model for explaining the Euronext100 portfolio returns in the period from July 2005 to June 2007

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portfolios (Jul05-Jun07) Size/btm Momentum Total CAPM Significant alphas 2 0 2 Adjusted R2 0,735 0,759 0,744 FF3 Significant alphas 1 0 1 Adjusted R2 0,791 0,798 0,794 Significant betas SMB 5 1 6 Significant betas HML ₃ ₀ ₃ C4F Significant alphas ₁ ₀ ₁ Adjusted R2 _0,795 _0,851 _0,817 Significant betas SMB ₄ ₂ ₆ Significant betas HML 3 0 3

Significant betas MOM 2 2 4

Table 15. Summary empirical results subsample 1.

4.4.2 Negative Euronext100 sentiment

In July 2007, many markets, including the European market, collapsed and it was the beginning of a worldwide recession. During the two year period of July 2007 to June 2009, the average monthly return of the Euronext100 was -2,09%. Where portfolios based on small firms size, high book-to-market values and the best performing firms of the last six months generate higher returns for the other subsample periods and the total time range tested for. The opposite seems to be true for high book-to-market and best past performance firms in a market of economic distress. Within this time range, these portfolios underperform the other portfolios where portfolios of small sized firms still perform better relative to the other portfolio.

For the CAPM, the explanatory value of the market premium variable calculated by the adjusted R2 is almost 14% higher compared to the adjusted R2 for the same model in a positive market sentiment. Despite of this high value, five of the portfolios alphas are significant, as shown in table 16.

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portfolios (Jul07-Jun09) Size/btm Momentum Total CAPM Significant alphas 2 3 5 Adjusted R2 0,870 0,896 0,881 FF3 Significant alphas 0 0 0 Adjusted R2 0,917 0,916 0,916 Significant betas SMB 3 1 4 Significant betas HML ₅ ₂ ₇ C4F Significant alphas ₁ ₀ ₁ Adjusted R2 _0,917 _0,937 _0,925 Significant betas SMB ₃ ₁ ₄ Significant betas HML 4 0 4

When testing for the FF3 model, all significant alphas disappear. This is remarkable because three of the significant alphas were associated with momentum portfolios, and the explanatory variables added focus on size and book-to-market ratios. High correlation between HML and MOM (table 26 in appendix C) could explain this observation. Adding the MOM explanatory variable to test for the C4F model does not improve the empirical results compared to the FF3 model. The adjusted R2 increases but not significantly and there is one (instead of zero) significant alpha. There are also less betas significantly different from zero, while the opposite would be expected after adding an extra variable. None of the tested models seems to be linear for the tested time range, but the FF3 model seems to predict the portfolio returns best in this negative market segment. There are no significant alphas when testing for the FF3 model, the model has the most significant betas of all models and the adjusted R2 is not significant lower than the adjusted R2 of the C4F model.

4.4.3 Recovering Euronext100

In the period of July 2009 to June 2011 the European market was insecure and volatile and trying to get out of the recession, the average monthly return of the Euronext100 was 1,41% during this time range.

The results of regressing for the CAPM in table 17 show seven significant alphas for the 15 portfolios tested on. When testing for the FF3 model, none of these alphas remain significant. Possibly, the three significant alphas of the momentum have disappeared because the CAPM has no time dummies and, even though there are no time dummies in the FF3 model as well,

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the book-to-market factor in the FF3 model could be a control factor for the time-effect. This effect is partly included in the stock price which is part of the book-to-market ratio. The goodness of fit of the model, the adjusted R2, increases significantly and most of the betas are significantly different from zero.

Adding the MOM factor to the FF3 model again increases the adjusted R2, although this increase is smaller compared to the increase after adding the SMB and HML variables. More significant values for the betas are observed and the C4F seems to be the best in predicting portfolio returns of the three models tested for the time range between July 2009 and June 2011.

portfolios (Jul09-Jun11) Size/btm Momentum Total CAPM Significant alphas 4 3 7 Adjusted R2 0,799 0,831 0,812 FF3 Significant alphas ₀ ₀ ₀ Adjusted R2 _0,880 _0,873 _0,877 Significant betas SMB 4 3 7 Significant betas HML 4 1 5 C4F Significant alphas ₀ ₀ 0 Adjusted R2 _0,876 _0,923 0,895 Significant betas SMB ₄ ₄ ₈ Significant betas HML 4 3 7

Considering the three different models in the subsample periods there can be concluded that all three of the models had higher values of adjusted R2 for the time range in the period of economic market distress and the FF3 model is an improvement compared to the traditional CAPM for every time range. The MOM factor seems to have explanatory power for the extreme momentum portfolios only, the mom1 and mom6 portfolios are the only portfolios where the coefficient of MOM is always significant for. Many betas not significant different from zero indicate that none of the three models are linear.

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V. Conclusion

This thesis tested if the traditional CAPM, the Fama-French three-factor model, and Carter’s four-factor model have high predictive power for portfolio and stock returns. It is tested on the Euronext100 stocks and portfolios formed from these stocks on size, book-to-market ratio and momentum in the period of January 2002 to December 2011.

The strength of the models is determined by the adjusted R2, the number of significant alphas, and the number of betas significantly different from zero.

Descriptive statistics confirm higher returns for portfolios based on small firms, high book-to-market ratios and highest past returns firms. These returns are not explained by the book-to-market premium factor of the CAPM and seem to prove the existence of the size-, value- and momentum-effect. Exception for these findings is the period of economic distress in Europe from July 2007 till June 2009. Small-sized firms still performed better in this period, but high book-to-market firms and firms with high past performance returns performed worse compared with the other portfolios in market situation of economic distress.

The FF3 and C4F model both outperform the traditional CAPM in terms of adjusted R2, less

significant alphas and lower average t-values for the alphas.

While the adjusted R2 is higher for C4F model compared to the FF3 model, it is difficult to state C4F outperforms FF3. Difference in R2 is not always significant, and adding the explanatory variable MOM sometimes increases the number of significant alphas and insignificant betas.

All the models seem to be nonlinear for the Euronext100 stocks and portfolios in the tested time range. Significant alphas for the portfolios when testing the CAPM can be explained by adding the size-, value- and momentum-effect variables of the FF3 and C4F model and many betas of these explanatory variables are not significantly different from zero. Especially the explanatory power of MOM and HML are questionable. The MOM factor seems to have significant influence for extreme past return portfolios mom1 and mom6 and to a lesser extent portfolios mom2 and mom5. However, values of MOM coefficients for momentum portfolios

mom3 and mom4 are never significantly different from zero and therefore unreliable.

Since the CAPM, FF3 and C4F models are possible not linear, it is recommended to use characteristics-adjusted returns when testing for return predictability.

Testing the predictive power of the CAPM, FF3 and C4F on the Euronext100 stock index