Msc Thesis: The Three Factor Model for Dutch Equities

Msc Thesis: Luuk Milius

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Msc Thesis:

The Three Factor Model for Dutch Equities

Name: Luuk Milius

Administration number: s613758

Supervisor: Mr R.G.P. Frehen

Second reader: Mr M. Da Rin

Date: 15-11-2012


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Table of contents

Abstract 3

Introduction 4

State of literature 5

Data and methodology 8

Results 10

Conclusion 16

Bibliography 17


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Abstract

The main goal of the paper is to test how suitable the Three Factor Model of Fama &

French (1996) captures cross-sectional differences in returns for Dutch stocks for the period

of 1990-2010. Overall, the model captures most cross-sectional differences (average R2

of

90%). Systematic risk is not priced in the market and a size effect does not seem present for

the sample I used. A value premium does exist. Still, the Three Factor Model has a positive

and significant alpha, so the model can be improved. Therefore a momentum factor is

included. The momentum factor helps explaining cross-sectional differences in returns and

the alpha becomes insignificant after inclusion of this factor.


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Introduction

Since the introduction of the Three Factor Model by Fama & French (1996) many

practitioners accept the model and the implications that follow from it. Important to keep in

mind though, is that Fama & French (1992, 1996) used US data for the development of the

Three Factor Model and the bulk of other existing research relates to US portfolios as well.

There is not as much evidence available on the robustness of the Three Factor Model outside

the US market. As is argued by Bishop et al (2001, p. 192), the Three Factor Model needs

more time and further empirical investigation before it can be accepted as a credible theory-

based model. Furthermore, in response to the data-snooping hypothesis of Black (1993) and

MacKinlay (1995), Barber & Lyon (1997) observe that the best way to evaluate the data-

snooping hypothesis is to test the robustness of the results from Fama & French (1992, 1996)

for different time periods, different countries or a holdout sample. In this paper the Three

Factor Model will be tested for a different country and a different time period. The usefulness

of the Three Factor Model will not be fully known until sufficient new data becomes available

to provide a true out-of-sample check for the performance of this model (Campbell, Lo &

MacKinley, 1997).

Fama & French (1998) opt for a more global version of their Three Factor Model due

to market integration. Applying the implications from international asset pricing theory; if

there is market integration there should be one set of risk factors that explain expected returns

in all countries. In their paper they show that a world factor model leads to lower intercepts

and a higher than a model with a world market factor alone. However, Fama & French

(1998) do not compare this model to a country specific model as Griffin (2002) does. The

explanatory power of world factors could be driven by their country specific components. In

his paper Griffin (2002) finds that domestic models perform better in describing the cross

section of returns and provide more accurate pricing than the world model does.

Since it is better to use a country specific model than a world model, in response to the

data-snooping hypothesis and to provide an additional out-of-sample check to test the

robustness of the Three Factor Model (test the model for a different country and a different

time period) resulted in the development of the research question for this paper:

How well is the Three Factor Model of Fama and French suitable to describe cross-sectional

differences in returns for Dutch stocks listed on the Amsterdam Exchange (AEX)?


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Testing the model for the Dutch market does not only benefit the academic world, but

it will benefit practitioners active in the field of finance as well. It will give insight if

systematic risk, firm size and the book-to-market ratio are priced in the Dutch market. This

has implications for capital budgeting decisions and discount rates (is a small firm premium

necessary for example) for Dutch firms. The results can also influence investment decisions

for people who want to invest in Dutch stocks.

The Three Factor Model is tested using the method of Fama & Macbeth (1973). The

results from the time-series regression (first-pass regression) show that firm size and the ratio

of book-to-market equity seem to have an influence on returns and systematic risk does not

have an influence. The cross-sectional regression (second-pass regression) will show if this

really is the case. The cross-sectional regression shows that systematic risk is not priced in the

market, but firm size is neither. The only factor that seems to matter is the ratio of book-to-

market equity. So the CAPM is insufficient to describe returns for the Dutch market. There is

a small, but insignificant size effect and a value premium does exist. So stocks with a high

book-to-market ratio outperform stocks with a low book-to-market ratio. Furthermore, the

alpha of the model is positive and significant, so part of the returns are not explained.

Therefore, a momentum factor is added to the model and this model is tested as well.

It follows that inclusion of a momentum factor results in an improvement of the model as

indicated by the alpha of the model. The alpha becomes insignificant. There is no change in

the other factors. Systematic risk and size are still insignificant while the book-to-market ratio

remains its significance. The momentum factor itself is also significant, indicating that past

winners/losers continue to rise/fall even further.

State of literature

For a long time the asset pricing model of Sharpe (1964), Lintner (1965) and Black

(1972) was used to explain differences between returns and risk. The SLB model states that

expected returns on stocks are a linear function of the stocks‟ exposure to market (or

systematic) risk (also known as β). This risk is the only risk that should be priced in the

market, since non-systematic risk can be diversified away. According to this model, market

risk is the only explanatory variable in the cross-section of expected returns.

However, this model is not able to explain the so called „anomalies‟ of stock returns.

Several academics have identified contradictions to the SLB model. Banz (1981) identified a

size effect. Firm size helps in explaining the cross-section of expected returns. Using market


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equity to measure the size of a firm, he finds that small firms have an average return that is

too high given their β and large firms have an expected return that is too small given their β.

Stattman (1980) and Rosenberg, Reid & Lanstein (1985) found another contradiction. They

state that average returns are positively related to the ratio of book equity to market equity.

Evidence for this is also found in the Japanese market by Chan, Hamao & Lakonishok (1991).

Next to this, Bhandari (1988) found that the amount of leverage of a firm is related to risk and

expected return. Finally, Basu (1983) shows that the earnings-price ratio can also help explain

differences in the cross-section of stock returns. According to the SLB model, market risk

should be the only factor that explains the cross-section of expected stock returns, but this is

clearly not the case.

After the establishment of these anomalies Fama & French (1992) tested these

predictions and they found that indeed market risk was not able to explain the cross-section of

expected returns, but other variables helped explaining the cross-section of returns as well.

Beta is insignificant for their sample period, so market risk does not explain the cross-section

of returns. This contradicts the SLB model. They tested the anomalies described above as well.

Their results show that size and book equity to market equity explain most of the variation in

the cross-section of expected returns.

In a later paper of Fama & French (1996) these results lead to the development of the

Three Factor Model. They established a model that is well able to describe the cross-section

of expected returns. The returns are related to three different variables. The excess return on a

market portfolio (Rm-Rf), The difference between the return on a portfolio of small stocks

and the return on a portfolio of large stocks and the difference between the return on a

portfolio of stocks with a high book to market value and the return on a portfolio of stocks

with a low book to market value. This resulted in the development of the following model for

the expected excess return on a security:

Where SMB stands for small minus big and HML for high minus low.

, and are the expected premiums on the small minus big, high

minus low and excess return on the market portfolio and , and are the factor

sensitivities estimated by a time-series regression. This is the Three Factor Model that is able

to explain the anomalies which could not be explained before.


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An explanation why these two new factors help to explain cross-sectional differences

is as follows. The small minus big factor is positive when small firm stocks have

outperformed the stocks of larger companies. This factor is a measure for size risk. Smaller

firms are less diversified and they cannot absorb negative financial events as good as large

firms can. This makes smaller firms riskier, which leads investor to ask a higher risk premium

for these kind of stocks. This is also called the „size effect‟ which is in line with the evidence

of Huberman & Kandel (1987).

The high minus low factor measures the value premium. If it is positive it indicates

that value stocks (high book-to-market ratio) have outperformed growth stocks (low book-to-

market ratio). Before firms go public they need to reach a certain minimum size. If, later they

have a high book-to-market ratio the market value has dropped. This is possible due to

negative events or unfavorable future prospects. Companies with a high book-to-market ratio

face greater risk and thus a higher risk premium is required for these firms. This is also called

the „relative distress effect‟ identified by Chan & Chen (1991). According to these two

explanations smaller firm stocks and value firm stocks are priced in the market.

Jegadeesh & Titman (1993) discovered another anomaly, the momentum effect. When

stock prices are rising they tend to rise even further and when stock prices are falling they

tend to fall even further. So a strategy involving buying stocks that performed well in the past

and selling stocks that performed poorly in the past generate positive returns. These returns

are not due to systematic risk or delayed stock price reactions to common factors. In a later

paper Carhart (1997) created a factor mimicking portfolio for the momentum effect like Fama

& French (1996) did for the size and value factor. The Three Factor Model can be extended

with the momentum factor resulting in the Four Factor Model for the expected excess return

on a security:

As is explained in the introduction, the model needs more time and further empirical

investigation before it can be accepted as a credible theory-based model. Therefore,

researchers and academics started to test the Three and Four Factor Model for areas other than

the US and for different time periods. There is quite strong evidence that the model describes

expected returns in other countries as well. For example, UK, France & Germany (Malin &

Veeraraghaven, 2004), Japan (Chan, Hamao & Lakonishok, 1991), Australia (Faff, 2004),

Hong Kong (Nartea et al, 2004), Spain (Pena et al, 2010), and also for wider sets of countries


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(Fama & French, 1998), (Rouwenhorst, 1998) (Griffin, 2002), (Moerman, 2005) and (Bauer

et al, 2010). Results differ for several countries and also for different time periods, but in most

instances support for both models is found.

Data and methodology

Fama & French (1992, 1996) suggest that the following model can be used to describe

the cross-section of expected returns on a stock or a portfolio of stocks:

(1)

where i = 1,..,N

Since I would like to test this model for the Dutch market the following hypotheses have been

developed:

H0: The Three Factor Model captures cross-sectional differences in expected returns for

Dutch equities.

H1: The Three Factor Model does not capture cross-sectional differences in expected returns

for Dutch equities.

More specifically, for the model to hold, I expect the coefficient for the alpha to be close to

zero, the beta coefficient should be insignificant and the SMB and HML coefficient should be

statistically different from zero.

To test the Three Factor Model for the Dutch market I gathered data available from

Datastream. I downloaded the monthly stock returns, a proxy for the risk-free rate (the one

month AIBOR), the book-to-market ratios of the equity value and the shares outstanding for

each company from 1990 to 2010. I included delisted stocks to circumvent the survivorship

bias.

From this data the necessary portfolios to test the model are constructed. I proceeded

in the following manner: For the market portfolio I did not use a proxy like the AEX-index,

but I created a market portfolio using all stocks available in my dataset. This results in a

portfolio that resembles the market better than a proxy. To create the SMB and the HML

factors all stocks are allocated at the end of June of each year to two groups (small [S] or big

[B]) based on whether the market equity (stock price times shares outstanding) in June is

higher or smaller than the median for that year. All stocks are also allocated to three groups

(low [L], medium [M] or high [H]) based on their book-to-market equity value in December


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of year t-1. Firms with negative book equity are excluded from this sort. The bottom 30% is

classified as low, the top 30% as high and the 40% in the middle as medium.

In this manner six size/book-to-market equity portfolios are created (S\L, S/M, S\H,

B\L, B\M and B/H). SMB is the difference between the average returns of the S\L, S\M and

S\H portfolios and the average of the returns on the B\L, B\M and B\H portfolios. HML is the

difference between the average returns of the S\H and B\H portfolios and the average returns

of the S\L and B\L portfolios.

Fama & French (1992, 1996) used a 5x5 sorting scheme to construct 25 portfolios

sorted on size and book-to-market equity. However, the Dutch market has far fewer listed

companies than the United States. In order to avoid potential biases I choose to use a 4x4

sorting scheme to construct 16 portfolios instead of 25. These portfolios are created in a

similar fashion as the six size/book-to-market equity portfolios except quartile breakpoints are

used for the allocation of stocks in this case.

To test the hypothesis the approach of Fama & Macbeth (1973), a two-pass regression,

is used. First, I will run the following time-series regression to obtain the alpha‟s, beta‟s, s‟s

and h‟s:

(2) where I =

1,..,N

Afterwards, I will estimate the following equation using as repressors the betas, s‟s and h‟s

from the first-pass regression:

(3) , where t = 1,..,T

This will tell me whether the Three Factor Model holds for the Dutch market or not.

Furthermore, I will also perform a GRS test as developed by Gibbons, Ross &

Shanken (1989). Each alpha can be tested separately, but the model implies that all alpha‟s are

zero. Therefore, a joint test is much more powerful. The GRS test allows me to test whether

this is the case.

An extension of the Three Factor Model with a momentum factor, identified by

Carhart (1997), can be made. Making it a Four Factor Model. The momentum factor is

constructed as follows. The two size portfolios from the SMB and HML factor are taken and

three new portfolios (low [L], medium [M] and high [H]) are formed every month based on

the prior (2-12) return. The monthly prior (2-12) return breakpoints are the 30th

and 70th

percentiles. In this manner six portfolios (S/L, S/M, S/H, B/L, B/M and B/H) can be formed

to create the momentum factor. It is the average return on the S/H and B/H portfolio minus

the average return on the S/L and B/L portfolio. To be included in a portfolio for month t, a


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stock must have a price for the end of month t-13, a good return for t-2 and the value of the

market equity must be known at the end of month t-1.

To test the Four Factor Model I will follow the same approach as for the Three Factor

Model. I will first run a time-series regression to obtain the alpha‟s, beta‟s, s‟s, h‟s and m‟s:

(4)

where i = 1,..,N

Afterwards, I will estimate the following equation using as repressors the beta‟s, s‟s, h‟s and

m‟s form the first-pass regression:

(5) , where t = 1,..,T

A GRS test to test if all alpha‟s are jointly zero will be applied for the Four Factor Model as

well.

Results

Table 1 shows summary statistics of the 16 portfolios formed on size and book-to-

market equity. What follows from the table is if you move from the portfolio with the lowest

book-to-market ratio to the portfolio with the highest book-to-market ratio the returns of these

portfolios tend to increase. This holds for all book-to-market portfolios irrespective of the size.

The change in returns for portfolios sorted on different sizes is not too evident. The portfolios

formed on size for the second and third book-to-market portfolio show a small decrease in

their returns as firm size becomes bigger. For the fourth book-to-market portfolio this is more

evident. However, the first book-to-market portfolio shows the opposite. Smaller firms have

higher returns in this particular case. From the summary statistics it follows that returns seem

to be higher for value stocks, but a size effect is not too straightforward.

It is also suggested by Fama & French (1992, 1996) that higher returns are associated

with higher levels of risk. Small firms and value firms are supposed to be riskier and therefore

investors require a higher risk premium for these securities (as explained in section 2).

However, this is not straightforward from the table. First of all, a size effect does not seem too

evident, so do investors really require a higher risk premium for smaller firms. Second of all, I

included the standard deviation of each portfolio as a measure of riskiness. Smaller firms are

indeed riskier, but if this is really priced by investors will follow from the cross-sectional

regression later in this paper. For value stocks the evidence is contradictory. The standard

deviations decrease, indicating value stocks are less risky than growth stocks, as opposed to

what Fama & French (1992, 1996) suggest.


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Table 1: Summary statistics

The table displays the average returns and the standard deviations for the different portfolios sorted on

size and book-to-market equity.

Tables 2 and 3 show the results from the first pass, time-series regression without and

with the momentum factor, respectively.

If both models describe expected returns the alpha intercepts should be (close to) zero.

Both tables show that the models leave a large negative return unexplained for portfolios in

the smaller size and lowest book-to-market quartile and a large positive return for stocks in

the biggest size and highest book-to-market portfolio. In the other cases the intercepts are

close to zero. Furthermore, the alpha intercepts of all portfolios are not statistically different

from zero except from the two smallest portfolios in the lowest book-to-market equity quartile.

This should not be the case, since all intercepts should be zero. However, this also occurs in

the work of Fama & French (1996) and other empirical tests of the Three and Four Factor

Model. In that sense my results do not deviate from other papers.

Furthermore, the GRS test for the Three Factor Model has a test statistic of 3.779 with

a p-value of 0.000003141. This indicates, at a significant level, that not all alpha‟s are equal to

zero. Thus, there is still a part of expected returns that is not explained by the model. The

same holds for the Four Factor Model. The GRS test statistic has a value of 3.225 with a p-

value of 0.0000482 for the Four Factor Model.

Even though the models do not capture all the variation in the returns on the portfolios,

both models still capture most of the variation as indicated by the R2‟s of the regressions. In

one particular case the R2 is 95%. The average R

2 of the Three Factor Model is 90.15% while

the average R2 for the Four Factor Model is 90.24%. So the inclusion of the momentum factor

contributes only little to the explanatory power of the Four Factor Model.

Size Low 2 3 High Low 2 3 High

Small 0.488 1.200 1.285 1.409 8.514 7.158 5.803 5.465

2 0.821 1.023 1.267 1.193 7.428 5.816 5.168 5.305

3 0.848 1.104 1.180 1.113 6.917 5.368 4.859 5.002

Big 1.072 1.059 1.016 1.166 6.124 4.976 5.310 4.842

Book-to-market equity

Means Standard deviations


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Table 2: Results from time-series regression (first-pass regression) for the Three Factor Model

The table displays the results from the time-series regression of the 16 portfolios excess returns over the

excess market return, SMB and HML factor ( β ,

where i = 1,..,N).


Small -0.721 -0.012 0.099 0.193 -4.20 -0.10 1.02 1.86

2 -0.298 -0.141 0.080 -0.065 -2.76 -1.34 0.84 -0.66

3 -0.141 0.002 0.059 -0.064 -1.32 0.02 0.51 -0.51

Big 0.164 -0.008 -0.137 0.057 1.59 -0.07 -1.04 0.48


Small 1.119 0.939 0.866 0.830 28.77 32.59 39.37 35.40

2 1.119 0.974 0.909 0.937 45.78 40.82 42.00 41.46

3 1.087 1.022 0.961 0.971 44.86 36.09 36.75 34.07

Big 1.058 1.024 1.096 0.986 45.26 38.75 36.64 36.58


Small 1.314 1.292 1.025 0.973 25.17 33.41 34.71 30.92

2 0.983 0.821 0.720 0.731 29.95 25.63 24.78 24.10

3 0.717 0.448 0.339 0.331 22.04 11.78 9.67 8.66

Big 0.424 0.200 0.135 0.186 13.52 5.63 3.37 5.13


Small -0.347 -0.007 0.265 0.469 -6.36 -0.16 8.61 14.29

2 -0.340 0.189 0.460 0.623 -9.93 5.65 15.17 19.68

3 -0.460 0.239 0.496 0.658 -13.56 6.01 13.55 16.46

Big -0.408 0.338 0.539 0.547 -12.47 9.14 12.85 14.46

Size Low 2 3 High

Small 0.903 0.925 0.934 0.915

2 0.950 0.922 0.919 0.916

3 0.943 0.871 0.866 0.850

Big 0.933 0.870 0.853 0.857

R squared



s T-statistic


h T-statistic


Alpha T-statistic


Beta T-statistic


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Table 3: Results from time-series regression (first-pass regression) for the Four Factor Model

The table displays the results from the time-series regression of the 16 portfolios excess returns over the

excess market return, SMB, HML and MOM factor ( β

, where i = 1,..,N).


Small -0.644 -0.019 0.085 0.160 -3.74 -0.14 0.86 1.53

2 -0.239 -0.112 0.092 -0.062 -2.22 -1.05 0.94 -0.61

3 -0.102 0.042 0.065 -0.070 -0.95 0.34 0.55 -0.55

Big 0.149 0.013 -0.083 0.048 1.42 0.11 -0.63 0.4


Small 1.086 0.942 0.872 0.844 26.81 30.98 37.61 34.34

2 1.094 0.961 0.904 0.936 43.25 38.37 39.61 39.22

3 1.071 1.004 0.958 0.974 42.22 33.84 34.72 32.38

Big 1.064 1.015 1.073 0.990 43.2 36.47 34.36 34.8


Small 1.321 1.291 1.023 0.970 25.56 33.28 34.59 30.92

2 0.988 0.824 0.721 0.731 30.61 25.76 24.75 24.03

3 0.721 0.451 0.340 0.331 22.28 11.92 9.66 8.61

Big 0.423 0.202 0.141 0.185 13.45 5.68 3.53 5.09


Small -0.375 -0.004 0.271 0.482 -6.82 -0.1 8.59 14.43

2 -0.362 0.178 0.456 0.622 -10.54 5.23 14.7 19.2

3 -0.475 0.224 0.494 0.660 -13.79 5.55 13.18 16.15

Big -0.403 0.331 0.518 0.550 -12.04 8.75 12.22 14.23


Small -0.087 0.007 0.016 0.037 -2.58 0.29 0.84 1.83

2 -0.066 -0.033 -0.013 -0.004 -3.14 -1.58 -0.7 -0.2

3 -0.044 -0.045 -0.007 0.008 -2.1 -1.84 -0.3 0.3

Big 0.017 -0.023 -0.061 0.010 0.82 -1 -2.35 0.43

Size Low 2 3 High

Small 0.906 0.925 0.934 0.916

2 0.952 0.923 0.919 0.916

3 0.944 0.873 0.866 0.850

Big 0.933 0.870 0.856 0.857


m T-statistic


R squared


s T-statistic


h T-statistic


Alpha T-statistic


Beta T-statistic


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The results show furthermore that the beta coefficient does not change that much for

different portfolios. Though the changes in the SMB and HML factors are more evident. The

SMB factor declines for bigger firms and for firms that have a higher book-to-market ratio.

The HML factor increases for portfolios that have higher book-to-market ratios. For the

momentum factor a clear pattern cannot be found. This indicates that systematic risk does not

have an influence on average returns, but other factors have. Since the beta coefficient

remains close to constant for different portfolios, but the coefficient of the SMB and HML

factors change considerably for different portfolios sorted on size and book-to-market equity.

The HML coefficients are negative for the first book-to-market equity quartile and

positive for the other quartiles (except for the smallest firms in the second quartile). This is in

line with the results of Fama & French (1996) and other papers. However, the SMB

coefficients are not completely in line with other academic research. The coefficients for the

biggest firms are negative in the results of Fama & French (1996). A possible explanation for

this can be that Fama & French (1996) use breakpoints of market equity of NYSE stocks to

allocate all US stocks (NYSE, AMEX and Nasdaq) to a certain size portfolio. Another

explanation can be that in the US more “super sized” firms (firms with a big amount of

market equity) exist than in The Netherlands. This may influence the results. Furthermore,

Rouwenhorst (1998) reports that the momentum effect is stronger for small firms than for

large firms, so I expect to find higher coefficients for smaller firms. The results show support

for the findings of Rouwenhorst (1998). The coefficients of the second, third and fourth book-

to-market equity quartiles become smaller as size increases. These results need to be

interpreted with caution since most of the test-statistics indicate that the results are

insignificant.

The results of the cross-sectional regression for the Three and Four Factor Model are

displayed in tables 4 and 5, respectively. What follows from the Three Factor Model is that

beta and SMB are insignificant. So systematic risk, as stated by the CAPM, does not explain

average returns for the sample period. A similar argument can be made for firms that differ in

size. The coefficient is positive, indicating that smaller firms earn higher returns than larger

ones, but the size coefficient is insignificant though. The value premium is positive, so high

book-to-market firms earn higher returns and this is also priced in the market. The alpha is

positive and significant, indicating that the model can be improved, since part of the returns

are left unexplained.


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After inclusion of the momentum factor the beta coefficient and the SMB coefficient

remain insignificant and the HML coefficient remains significant. However, the alpha

coefficient becomes smaller and loses its significance. So the Four Factor Model does a better

job in explaining cross-sectional differences in returns than the Three Factor Model does. The

momentum factor itself is also positive and significant. Stocks that have outperformed other

stocks tend to do so the next period as well and vice versa.

Table 4: Results from cross-sectional regression (second-pass regression) for the Three Factor Model

The table displays the results from the cross-sectional regression of the portfolios excess returns over

the excess market return coefficient, SMB coefficient and HML coefficient (

, where t = 1,..,T).

Table 5: Results from cross-sectional regression (second-pass regression) for the Four Factor Model

The table displays the results from the cross-sectional regression of the portfolios excess returns over

the excess market return coefficient, SMB coefficient, HML coefficient and MOM coefficient (

, where t = 1,..,T).

The value premium is also persistent in other countries for different periods. This can

explain why the value premium still exists for the current sample. Fama & French (1998)

found that value stocks outperform growth stocks in twelve of thirteen major markets,

including the Dutch market for the 1975-1995 period. In a later paper by Bauer et al (2010) is

shown that the value premium is persistent in a later sample period for US stocks as well

(1985-2002).

In the same paper of Bauer et al (2010) is shown that the size effect disappeared for

the US market. Van Dijk (2011) states that recent empirical studies assert that the size effect

disappeared after the early 1980‟s. The size effect for the Dutch market has been tested by

Doeswijk (1997). He found a small size effect (0.13) but it is not statistically significant.

Carhart (1997) shows that momentum is present in the US market and afterwards

Rouwenhorst (1998) tested this for the European market. In a sample of 12 European

Alpha Beta SMB HMLλ 1.265 -0.485 0.025 0.472

Test statistic 2.602 -0.870 0.132 2.605

Alpha Beta SMB HML MOMλ 0.933 -0.182 0.008 0.442 2.863

Test statistic 1.844 -0.316 0.040 2.395 3.583


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countries (including The Netherlands) during the period 1980-1995 he found that momentum

is present in all countries. This is in line with the results I found for my dataset. The value

premium and momentum seems persistent while the size effect has disappeared.

Conclusion

I tested the Three Factor Model as developed by Fama & French (1992, 1996) for the

Dutch market. It provides an out-of-sample check since it is tested for a different market and a

different time period (1990-2010). I found that beta is insignificant and thus systematic risk is

not priced. So the CAPM does not hold for the Dutch market. The same holds for the size

effect, smaller firms do not earn a significant higher return than larger firms. A value

premium does exist. Value stocks earn a higher return than growth stocks. After testing the

Three Factor Model I included a fourth factor, the momentum factor. After inclusion of this

factor, beta and the size factor remain insignificant and the value factor remains significant.

The momentum factor itself is significant as well and improves the model as is indicated by

the alpha. The alpha coefficient loses its significance and thus is not statistically different

from zero.

These findings are important for professionals active in the field of corporate finance

and investments. For capital budgeting, setting the discount rate and investment decisions for

example. To determine the correct discount rate the CAPM is insufficient. Not only a firms‟

sensitivity to market risk matters. Furthermore, many practitioners add a small firm premium

to the discount rate, but it is not clear whether a size effect really exists (at least not for the

sample period I choose). For investment decisions a similar argument can be made. Small

firms do not necessarily outperform larger firms. However, value firms do outperform growth

firms and a momentum strategy seems to work as well.

There is one important limitation of the method used that needs to be taken into

account. The model assumes that the loadings on market risk, SMB, HML and the momentum

factor are roughly constant over time. This can be an issue, since variation through time in

these coefficients can occur, because companies (and the constructed portfolios as well) can

wander between growth and distress. It is possible that a model which allows for time

variation of the factor loadings does a better job in explaining the cross-section of expected

returns and maybe the Three Factor Model will suffice to capture differences in the cross-

section of expected returns in that particular instance.


17

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Msc Thesis: The Three Factor Model for Dutch Equities