Optimal portfolio selection for the Dutch

market

Bachelor thesis

Instructor: Korhan Nazliben

Bedrijfseconomie

Faculty of economics

15-05-2011

Thijn van Doorne

S155415

1

Abstract

In this paper is described if it is a option for an small investor to invest in only the dutch

market. Pros and cons of investing in the dutch market only are discussed. Doing that

portfolio theory is used frequently. Futhermore portfolios of stocks from only the AEX are

composed and eventually combined with risk free assets.

2

Contents

Introduction 3

1. Portfolio theory 4

- 1.1 Portfolio size 4

- 1.2 Diversification 5

- 1.3 International diversification 5

- 1.4 Correlation 6

- 1.5 Efficient frontier 6

- 1.6. Diversity of the AEX 6

2. Used methods and data 8

- 2.1. Beta 8

- 2.2. Return 8

- 2.3 Volatility 9

- 2.4 Risk free asset 10

- 2.5 Data 10

3. Composing a portfolio 11

- 3.1 Selecting stocks by using their beta 11

- 3.2 Selecting stocks by using their return 13

- 3.3 The optimal dutch portfolio 14

Conclusion 15

References 17

List of figures and tables 18

3

Introduction

American economist Markowitz was the founder of the modern portfolio theory and a lot of

mathematics and economists did follow him. Clearly there is one thing about an optimal

portfolio that is always the same namely the fact that everything about it is optimal. Optimal

shares, an optimal amount of shares is required, optimal volatility is necessary (here optimal

is as small as possible) and an optimal mean is maybe the most important of the four.

In this paper is shown how to find those four requirements and apply those findings on the

Dutch stock market. Here with the Dutch stock market the AEX is mend. The AEX contains

the 25 biggest listed companies of the Netherlands. Results and changes of the AEX are easy

to follow for Dutch investors. The AEX is the main subject treated on the Dutch business

news. Every day the companies of the AEX are discussed, so there is a lot open information

for everyone. That is why the AEX seems a attractive stock market for a Dutch investor to

invest in. However, is it smart of an investor to invest in only the AEX, are returns high

enough and are there enough possibilities of diversification? Those questions lead us to the

research question of this paper: Is investing in only the AEX an option?

Finding an answer to this question seems interesting, because a lot of papers about optimal

portfolio selection are very theoretical. A practical paper as this one makes the subject more

tangible. A few methods to compose portfolios will be discussed and some small portfolios

will be composed. The results will be useful for, let us say, the ordinary Dutch investor. The

ordinary Dutch investor is characterised in this paper as an investor who wants to make a

profit on the stock market, but does not have a lot time, information and knowledge of

investing. He wants to invest in Dutch stocks, because he is familiar with those stocks and it is

easy to follow the moves of the Dutch companies, because they are Dutch and as result treated

on the Dutch news (RTL Z). That way the investor can make a nice profit and doesn’t need to

invest in markets or products that aren’t familiar to him.

The data which are used, consist of betas, variances, covariances and means of the 25

companies of the AEX.

4

Chapter 1: Portfolio theory

Maximizing return is just a small part of composing a portfolio. Reducing risk is the big part

of it. If the investors goal is to just maximize his return, the only thing he has to do is pick the

stock with the highest return and he’s done (Markowitz [1991]). He would have a portfolio

consisting of only one stock, because every stock he adds lowers the expected return unless he

is able to find a stock with an equal expected return. So optimal portfolio selection is mostly

about reducing risk. Reducing risk is done by diversification. When diversicating you’re

selecting different stocks that together have a lower risk than an individual stock. Reducing

risk can also be done by adding risk free bonds to your portfolio. However that also lowers

the return drastically.

Portfolio size

When an investor is deciding how much stocks he will hold in his portfolio, he’s making a

trade-off between a decreased variance and higher transaction costs. Furthermore his expected

return will drop when he adds more stocks (Elton, Gruber [1977]). It’s important to know how

much stocks you have to put in a portfolio to reduce risk. When having a small portfolio, an

extra security can make a big difference, but having a large portfolio, an extra security may

cost more on transaction costs than it yields.

Fisher and Lorie (1970) investigated what the effect was of putting an extra stock into a

portfolio. Furthermore they show the differences in variance between the smallest and biggest

portfolios. What has to be noticed is that the stocks in their portfolios all had the same

portfolio weights. The result of their investigation shows that, also for the ordinary investor

with a modal income, it’s possible to construct a portfolio with low risk. Reducing the risk of

a portfolio goes fast when you’re expanding your portfolio from 1 to 2 stocks. So it does

when you expand that portfolio from 2 to 3 stocks. But when increasing that portfolio,

reducing risk is going slower. The point where an extra stock does not yield as much as it

costs is hard to find, but Fisher and Lorie prove that ‘portfolio’s containing eight stocks have

frequency distributions strikingly similar to those of portfolio’s containing large numbers of

stocks. Where having 1 stock as your portfolio realizes 0 percent of the maximum variance

reduction, holding 2 stocks in a portfolio realizes over 40 percent of the maximum variance

reduction. If a portfolio contains 8 stocks, over 80 percent of the maximum variance reduction

is achieved (table 1). Considering transaction costs are relatively expensive for the ordinary

investor because of his limited budget he can spend on shares. Holding more than 8 stocks in

5

his portfolio doesn’t seem useful or profitable. So the optimal portfolio of the ordinary Dutch

investor should consist of about 8 stocks.

Diversification

Often the more stocks you have in your portfolio, the smaller your risk. This is the concept of

diversification. Diversification is defined as followed. Diversification strives to smooth out

unsystematic risk events in a portfolio so that the positive performance of some investments

will neutralize the negative performance of others. Especially when the stocks an investor is

adding to his portfolio do not covary with the stocks already in it, risk will be decreased.

(Grinblatt, Titman [2004]). Risk of individual securities differs from risk of those similar

securities combined in a portfolio. The risk of each individual stock is called the independent

or idiosyncratic risk. By combining more different stocks in a portfolio, this independent risk

will get smaller. When putting stocks in a portfolio that belong to companies which are active

in the same industry, you’re dealing with common risk. The volatility of the two stocks is

caused by the same industry, so putting them together will not lessen much risk. (Berk,

DeMarzo [2007])

Unfortunately it is not possible to eliminate all risk. There will always be some risk which is

undiversifiable, called systematic risk.

International diversification

If there’s a way to reduce the systematic risk, then it is done by international diversification.

That international diversification is profitable is been recognized for decades (French,

Poterba, [1991]). Much benefits can be attained by international portfolio diversification in

foreign securities. A international diversified portfolio is likely to carry a much smaller risk

than a typical domestic portfolio (Solnik, [1995]). Solnik says that when securities of one

country are doing bad, securities of another country will probably do good. Indices of the

most countries are unrelated, so investing in more countries will reduce your risk more and

more. Disadvantage of international diversification are exchange rates, but even if an investor

will not hedge this disadvantage, international portfolios still have lower volatility than

national portfolios. Hedging here is taking precautions so fluctuations in the exchange rate

will not effect your cash flows. Naturally there’s a possibility to hedge this risk, but for the

average Dutch investor this may be too much. When an international portfolio is diversified

the perfect way, it’s systematic risk is only 11 percent according to Solnik’s investigation,

while a perfect diversified national portfolio will not get lower than 20 percent. International

6

diversification works well, because of the low correlation between different international

markets. However, international diversification seems to get less and less import. The world

gets smaller. Almost all markets are in contact with and respond to each other. When the Dow

Jones did well one day, the next day the European indices often have a positive opening and

vice versa. So maybe international diversification isn’t that profitable anymore. International

trade is still growing fast as is the amount of international transactions. There is a hypothesis

that says that after every big disaster or world changing happening, correlation of different

stock markets increases (B.F. Yavas [2007]). Stock markets of different countries are moving

more and more together, but there still is enough difference between international markets to

make international diversification profitable.

Correlation

Correlation shows how two assets move in relation to each other. Correlation does not have

an effect on the expected return on a portfolio, but is very important for the amount of risk the

portfolio carries. When correlation is lower, volatility is lower (Berk, DeMarzo [2007]).

When the correlation of a portfolio is low, you can bear less risk and have the same expected

return as a portfolio with a higher correlation. A portfolio with low correlation is directly well

diversified.

Efficient frontier

The efficient frontier is the most efficient risk-return trade-off (Grinblatt, Titman [2004]). If a

portfolio is not on the efficient frontier it wastes risk by not maximizing the mean return. The

efficient frontier gives the optimal risk and return combinations. That is why an investor

wants his portfolio to be on the efficient frontier. As seen in figure 1 an individual asset will

not be on the efficient frontier. It is necessary to combine different combinations to get on the

efficient frontier. The portfolio with the best risk-return trade-off is called the tangency

portfolio and has the most attractive sharpe ratio. The sharpe ratio is calculated by:

(Expected return portfolio – risk free rate) / standard deviation portfolio. The higher the

sharpe ratio, the more attractive the portfolio. Often portfolios include risk free assets,

because they could reduce much risk.

7

Diversity of the AEX

How difficult is it to diversify within the AEX? Is it a problem that de AEX contains only 25

different companies? At first sight 25 seems very small, but when we take a closer look at it,

maybe it is not that big a problem.

As became clear earlier it is very important to diversify. Especially for the small investor,

because he can not afford to bear much risk and risk big losses. When taking a closer look at

the companies of the AEX, diversification by investing in only the AEX seems possible. The

25 companies of the AEX are active in a big amount of industries, which is good. Industries

tend to move together, so you need a variety of industries in your portfolio (Grinblatt, Titman

[2004]).

The general assumption is that there are tree sectors: the primary sector contains agriculture

and mining (Fugro), secondary sector contains all different kinds of industry (Arcelor Mittal,

Philips), and the tertiary sector contains services (Randstad). The AEX has companies in all

those sectors. The secondary sector is under divided in more parts as for example basic

materials, technology and financials, also in those parts are Dutch companies existing.

So a portfolio is diversified the best way when it contains stocks coming from different

industries. Ahold and KPN are complete different companies, so for example putting them

together would give a low portfolio volatility. However those companies are both Dutch, so

when the Dutch market is doing worse, both stocks are not doing good either. What is

considered as important is that you should not just choose companies that are active in

different industries, but also in different regions too. Is lessens your risk.

8

Chapter 2. Used methods and data

When deciding which stocks to put in one portfolio, the betas and correlations of the stocks

are used. Not every possible portfolio with eight stocks is considered, because there are too

many portfolio’s of eight different stocks ( to be precise: 25! / (8! x 17!) = 1081575

possibilities).

Beta

The beta coefficient of the market model has gained wide acceptance as a relevant measure of

risk in portfolio and security analysis (Klemkosky, Martin [1975]. The beta shows the return

of a specific stock with respect to the market index. Generally prices of stocks go up when the

market index grows. That is why most betas are positive. As seen in table 3, Aegon reacts

strongly to growth of the AEX, while KPN does not.

Putting stocks with high beta’s in one portfolio seems reasonable, because then the portfolio

will have a high beta too and probably a high return. Investors as Black, Jenson and Scholes

(1972) do not agree with this. High betas mean high volatilities and high risk. Furthermore

found Klemkosky and Martin [1975] in their investigation that portfolios containing stocks

with low betas sometimes have higher returns than portfolios containing stocks with high

betas. Overall portfolios with higher betas have higher returns, but the difference with

portfolios with low betas is much less than generally assumed. In this paper portfolio’s of

stocks with high betas, stocks with low betas, and stocks with beta’s close to one will be

composed to find out which portfolio has the highest return and lowest variance.

Return

When a portfolio holder is going to diversify, he has to deal with the risk-return trade-off. Is

he choosing for a portfolio with a high return and a high risk or does he prefer a portfolio with

al lower return which is less risky. In this paper, portfolios of stocks with high returns only

and stocks with low returns only will be composed. Also combinations are made. The goal is

to find the perfect balance. Returns used are the yearly returns calculated by use of the past

two years.

Example:

The stock price of electronics manufacturer Philips at the beginning of May 2009 was €14.48.

Two years later at the same date, the price is €20.55. The yearly return of Philips is:

((20.55 – 14.48) / 14.48) / 2 = 0.21.

9

One of the features an optimal portfolio has to meet is an optimal return. An optimal return is

a return that is as high as possible. Computing the return of a portfolio is done by the formula:

N

i 1

wi E(Ri) = Portfolio return.

Where:

N = the number of shares.

Wi = The weight of share i in the portfolio.

E(Ri) = The expected return of share i.

Volatility

An optimal volatility is low. When the volatility of the return of a portfolio is low, the risk of

a portfolio is low. The volatility of the return of a portfolio is the square root of the variance

of a portfolio which is computed by the formula:

N

i 1

wi2 σ i

2 +

N

i 1

N

i 1

wiwjCov(Ri,Rj) = Variance of portfolio ij

Where:

σ i = The volatility of share i.

Cov(Ri,Rj) = The covariance of share i and j.

This covariance is computed by use of the correlation between two stocks. The correlation of

al stocks of the AEX is already given (table 2).

Corr(i,j) * σ(i) x* σ(j) = Covariance I and J.

Where:

Corr(i,j) = Correlation of I and J. Correlation hereafter given by ‘ρ’ .

When the volatility of a portfolio with more than 2 stocks is computed, obviously the prior

function of volatility of portfolio return is used. This function is however, is a lot bigger than

the function of a portfolio with only 2 stocks. The variance formula of a portfolio with 3

stocks for example is designed as followed:

wi2σ i

2 + wj

2σ j

2 + wk

2σ k

2 + 2 wi wj σ i σ j ρij + 2 wi wk σ i σ k ρik + 2 wj wk σ j σ jk ρjk =

Variance of portfolio ijk.

10

Risk free asset

Adding a risk free asset to a portfolio reduces risk. Of course it reduces the expected return

too.

The expected return of the portfolio including a risk free asset is calculated by:

E(R) = Rf + Ws (E(Rs) – Rf )

Rf = Risk free rate

Ws = Weight

E(Rs) = Expected return portfolio containing only stocks

The volatility of the portfolio including a risk free asset is calculated by:

σ = Ws * σs

σ = Volatility of portfolio

σs = Volatility of portfolio containing only stocks

Data

The means of the stocks used in the calculations are found by calculating their average yearly

returns. The height of the stock rates in may 2009 and may 2011 of every individual stock are

summed up and divided by two to find the average yearly return. This average yearly return is

used as a mean in the calculations. By calculating the mean, it didn’t seem useful to go further

back in time than two years, because of the financial crisis almost all stocks would show a

negative average yearly return then. Means of the stocks are in table 2.

The volatility of the individual shares of the AEX are found by using the Datastream program

provided by Tilburg university. Those are used in the calculations. The volatilities are

calculated by using the rates of the stocks of the last 280 days. Volatilities of the stocks are

also in table 2.

The correlations used are found by Van Antwerpen, a master student from the Erasmus

university of Rotterdam. He used the correlation function in excel on all the daily returns of

2010 to calculate the correlation matrix. The correlations are in table 3.

Van Antwerpen did also calculate the beta of the AEX. He used a regression for his

calculations and used the daily returns of the companies and of the AEX.

11

Chapter 3. Composing a portfolio

Because not all investors are equally risk averse, optimal porftolios differ. There are investors

who see an optimal portfolio as a risky portfolio, but with great returns. Other investors are

more risk averse and just want to be sure about their future earnings. They prefer a less risky

portfolio. What those two have in common though, is that they have the lowest possible

variance for a specific expected return (so they are both mean-variance optimizers and want

their portfolio to be on the efficient frontier) and that they are compose their portfolios the

same way (Grinblatt, Titman [2004]).

Composing and selecting a portfolio consists of two stages. At first an investor starts with

observing and experiencing, then he formulates beliefs about the future performances of, in

this case, the stocks of the AEX. The second stage the investor uses those relevant beliefs

about future performances to select the portfolio. (Markowitz [1952]).

In this paper portfolios are composed by looking at data of different stocks. Investigated is

what is the best method for a ordinary investor to collect stocks to put in his portfolio. Stocks

are composed using their beta or return. Earlier we have seen that a portfolio of a ordinary

Dutch investor should consist of maximal eight stocks, because transaction costs are high and

eight seems enough to diversify. In this chapter we select portfolios of just 3 stocks, because

differences between different portfolios will probably be bigger then. The portfolio that is the

most attractive will be combined with a risk free bond. For calculations, formulas of the

previous chapter are used.

Selecting stocks by using their beta

As mentioned in chapter 2, 3 portfolios are made. (1) A portfolio with high-beta stocks; (2) a

portfolio with low-beta stocks; (3) a portfolio with stocks having betas near 1.

High beta

companies

Low beta

companies

Companies having

a beta near 1.

Aegon Ahold Akzo Nobel

ING KPN Philips

Randstad Unilever TNT

12

The return and volatility of those three portfolios will be calculated. Every stock has an equal

weight in the portfolio, which is 0.33% (1/3).

- Return of portfolio 1: 0.2363 or 23.36 % which is rather high compared to the AEX.

The AEX showed over the last two years a yearly return of 21.67 %. The fact that

those stocks achieved a higher return than the AEX sounds logical, because the

average beta of the tree stocks is 1.669. When the AEX achieves a positive return, this

portfolio should achieve a return which is even 70% higher.

- Return of portfolio 2: 0.0720 or 7.2 % which is lower that the yearly return of the

AEX. This sounds reasonable, because those companies all have low betas and did

react less stronger on the growth of the AEX than the companies with high betas.

klemkosky and Martin (1975) noted that the difference between portfolios with low

betas and high betas is much less than generally assumed. In this case however the

difference is really big though.

- Return of portfolio 3: 0.1922 or 19.22% which is close to the yearly return of the AEX

as expected because of their mean beta of 0.997.

It seems clear that when the market acts normal stocks with high betas give high returns. That

was also the expectation. Now the variances of the portfolios will be computed. You might

say that the portfolio with the highest return has the highest variance, but maybe this case is

different, because de portfolios are composed by use of their beta instead of by use of their

return.

- Variance of portfolio 1. 0.2037 or 20.37%. Maybe this seems high, but a portfolio with

a return of over 23% it’s not that much although it is more than the volatility of the

AEX (0.19%)

- Variance of portfolio 2. 0.1034 or 10.34%. This is a very low volatility. Much lower

than the volatility of the AEX and the volatility of portfolio 1. It is also expected,

because less risk means often less return.

- Variance of portfolio 3. 0.1657 or 16.57%. This volatility also has more or less it’s

expected value. The return of portfolio 3 is lower than the return of the AEX or the

return of portfolio 1, so a lower volatility fits.

Selecting stocks by use of their beta does not show impressive results. Returns and volatility

are as expected. Selecting stocks by their beta seems like a good method if you are looking for

a portfolio with a high return of a low volatility. Portfolios with a high return and low

volatility will not be found using this method. At least not within the AEX.

13

Selecting stocks by using their return

To see if selecting portfolios by using return is a good method, here two portfolios are

computed. (1)Stocks with the highest return are combined and (2) stocks having the single

highest return are combined. Expected is that portfolio 1 will have a much volatility, but it’s

interesting to see the difference between the volatilities of the two portfolio’s. Maybe here it’s

not the case and portfolio’s with a high return in the AEX don’t have a volatility that is as

high as expected.

High return

companies

Less high

return

companies

DSM ASML

Fugro Boskalis

Randstad Heineken

Return of portfolio 1: 0.4839 or 48.39%. This is a very high return which is expected, because

this portfolio contains the best three stocks of the past 2 years.

Return of portfolio 2: 0.3909 or 39.09%. Still a high return, but obviously much less than the

return of portfolio one.

Now the expectation is that portfolio 2 has a lower volatility. If not, portfolio 1 contains a

combination of stocks that maybe is attractive to the ordinary Dutch investor.

Volatility of portfolio 1: 0.1643 or 16.43%. This is not a high volatility compared to the

volatilities of the portfolios composed by beta. Also because the return is so high, the

portfolio expectation was that this portfolio is very risky. The risk return trade-off of this

portfolio seems very good. It is striking that the three stock combined here do not have the

highest individual volatility while they do have the highest return. That is why the portfolio

volatility is not high either.

Volatility of portfolio 2: 0.1722 or 17.22%. Also this volatility is not very high. However,

because the return of this portfolio is almost 10 percent less than the return of portfolio 1, a

lower volatility was expected. Compared to the portfolios composed by their betas, this

volatility is not that high. At least the risk return trade-off of this portfolio seems very good.

14

The optimal Dutch portfolio

DSM, Fugro and Randstad should form a nice portfolio, although with a volatility of 16.43%

you are not very certain about your future earnings. It is obvious that those three stocks

toghether do better than other combinations made. There is a way to decrease the volatility of

a porftolio consisting of only those three stocks drastic and that is by using risk free bonds

(Berk, Demarzo, 2007). Of course expected return will drop too. Because an optimal portfolio

for only the Dutch market is composed, also here Dutch assets are used. A Dutch risk free

government bond that yields 10 year, purchased in may 2011 is giving a return of 3.35% per

year (figure 2), which is not very high but do not forget this bond is risk free.

Because this bond does not have volatility, requested volatility and return of the above three

assets in combination with the risk free bond is easy to calculate. Now it is possible to

approach that efficient frontier and that tangency portfolio. Futhermore it is possible to

compose portfolios that fit every investor. When an investor does not want to bear much risk,

he invests relatively more in the risk free bond. When he is willing to take much risk, he

invests relatively more in the stocks.

Different porftfolios are composed by just adjusting the weights of the portfolio. Results are

shown in the table below.

Weight Portfolio return Portfolio volatility

0,1 7,854 % 1,643

0,2 12,358 % 3,286

0,3 16,862 % 4,929

0,4 21,366 % 6,572

0,5 25,87 % 8,215

0,6 30,374 % 9,858

0,7 34,878 % 11,501

0,8 39,382 % 13,144

0,9 43,886 % 14,787

1 48,39 % 16,43

In this table there is a portfolio for almost every investor. There is no portfolio better than the

other, because volatility and return relatively change equally. That is why using a method as

the sharpe ratio to find the best portfolio of those ten will not work. The only way for an

investor to find the optimal portfolio is by asking himself the question: How risk-averse am I?

15

Conclusion

As shown in this paper there are arguments for and against investing in only the AEX. When

looking at portfolio size, investing in only the AEX would not give any problems. A portfolio

containing 8 stocks could achieve over 80 percent of the risk reduction. Furthermore

diversification looks possible within the AEX. The AEX contains a lot companies that are

active in separate industries and are because of that not influencing each others results.

When looking at the results of portfolio selection and calculations, it seems possible to

construct a portfolio with a high return and a low volatility. It should at least be possible to

defeat the AEX returns with a well composed portfolio. Especially by just looking at return a

nice portfolio could be constructed. Often stocks with the highest return accompany a high

return. The AEX proves there are exceptions.

It is obvious there are not just arguments in favour of investing in only the AEX. The concept

of diversification does not say that investing in only the AEX is no option, but it says that it’s

possible to reduce your risk more by also investing abroad. You should not just invest in

companies that are active in different industries, difference in region is also important.

Correlation will often be lower between companies of different countries than between

companies which are active in the same country. By investing internationally benefits could

be achieved that can not be achieved by just investing nationally. There is a expression that

says that the world gets smaller. However, this does not mean that investing nationally

becomes more profitable, only the difference with investing internationally gets smaller.

Investing in only the AEX seems like an option to an ordinary Dutch investor. Of course he

would bear less risk if he would invest internationally but this way he keeps transaction costs

low and he does not to invest in markets and products that are not familiar to him.

Furthermore he can decide the size of his own risk by combining stocks with risk free bonds.

Calculations showed that it is possible to construct a attractive portfolio with only 3 stocks.

For a big company that invests billions however, investing in international markets is

recommended, because 1 percent difference in profit could be huge.

16

There was a plan to prove that volatility would indeed be lower when stocks of the AEX

would be combined with stocks of the Dow Jones. Returns and volatilities of the Dow Jones

are available, but correlations between stocks of the AEX and the Dow Jones are not. It would

be interesting to see what the difference is between an international and national portfolio.

17

References

- J.Y. Campbell, L.M. Viceira. The term structure of risk return trade-off.

- M. Grinblatt, S. Titman. 2004, 2nd

edition. Mc. Graw Hill. Financial markets and corporate

strategy. Ch. 4. Valuing financial assets.

- H. M. Markowitz. 1952. The journal of finance, Portfolio selection. Pages 77-91

- R. Jeurissen. October, 2005. A Hybrid Genetic Algorithm to track the Dutch AEX-index

- R. M. Stulz, 2003. Risk Management and Derivatives. Thomson South West

- H. M. Markowitz. June 1991. Foundations of portfolio theory.

- E.J. Elton, M.J. Gruber. October 1977. Risk reduction and portfolio size: An analytical

solution.

- L. Fisher, J.H. Lorie. April 1970. Some Studies of Variability of Returns on Investments in

Common Stocks

- P.L. Bernstein, F.J. Fabozzi. Streetwise: the best of the journal of portfolio management.

- R.C. Klemkosky, J.D. Martin. September 1975. The adjustment of beta forecast.

- K.R. French, J.M. Poterba. January 1991. Investor Diversification and International Equity

Markets

- B.H. Solnik. 1995. Why not diversify internationally rather than domestically?

- B.H. Yavas. 2007. Benefits of international portfolio diversification.

- B. Benning. July 2009. Levert international investeren nog steeds grote voordelen op?

- J. Berk, P. Demarzo. 2007. Corporate finance.

18

Appendix

Table 1

* L. Fisher, J.H. Lorie. April 1970. Some Studies of Variability of Returns on Investments in Common Stocks

Figure 1.

19

Table 2.

mei-09 mei-11 Yearly return Volatility

Ahold 8,47 9,506 0,061157 0,16

Aegon 4,24 5,3369 0,129351 0,33

Air France KLM 9,19 11,67 0,134929 0,35

Akzo Nobel 32,79 52,17 0,295517 0,22

Aperam*

Arcelor Mital 20,71 24,69 0,096089 0,34

AMSL 16,22 27,925 0,36082 0,33

BAM 6,05 5,44 -0,05041 0,34

Boskalis 19,47 36,165 0,428737 0,33

Corio 33,99 48,05 0,206826 0,22

DSM 24,66 46,01 0,432887 0,23

Fugro 29,07 62,35 0,572411 0,26

Heineken 23,11 40,815 0,383059 0,18

ING groep 7,68 8,947 0,082487 0,34

KPN 9,22 10,76 0,083514 0,18

Philips 14,48 20,55 0,209599 0,31

Randstad 18,78 37,415 0,49614 0,32

RD Shell A 17,99 25,84 0,218177 0,19

Reed Elsevier 8,61 8,928 0,018467 0,19

SBM Offshore 12,99 19,45 0,248653 0,29

TNT 14,29 16,33 0,071379 0,29

TomTom 4,26 6,061 0,211385 0,4 Unibail Rodamco 139,45 158,5 0,068304 0,26

Unilever 15,64 22,39 0,215793 0,19

Wereldhave 53,26 70,88 0,165415 0,18

Wolterskluwer 13,05 15,88 0,108429 0,2

AEX 251,47 360,42 0,216626 0,19

*No data of Aperam, because Aperam is listed since january 2011.

20

Table 3.

21

Table 4.

Figure 2