Dataset
Our dataset consists of the stock prices of 10 companies, of which 5 are Dutch, and 5 are German. The Dutch companies are Aegon, Koninklijke Ahold, Royal Dutch Shell, Unilever and Wolters Kluwer. The German companies are Allianz, Basf, BMW, Man and Siemens. For each company, we collected monthly data from Datastream, starting September 18 1986 and ending September 18 2006.
Assumptions
Expected return is based on the monthly returns of the past 20 years. This means no other information (e.g. future industry information) influences the expected return, and the past is representative for future expectations. The data has not been verified directly but the same set was used in an economics program screened on the BBC last year, it is still accessible currently, see reference for details.

In additional, we do not take into account the dividends paid, but only look at the returns that is realized by stock price movements

The monthly log returns are normally distributed.

Homoskedasticity applies to our dataset. This means that variances are constant over time.

The stock markets are perfect markets. This for example means:

Securities are perfectly divisible

There are no transaction costs

Markets are big enough to buy all desired shares.


Short sales are possible.
Question 1 and 2
We assume to be a European investor in a market portfolio containing all ten assets. In our market portfolio, we have chosen not to invest into risky bad credit loans of corporations with junk bond status, but instead we invest an equal amount of money in each stock of our stock portfolio. This means that we invest € 15,000 in every stock. When calculating the expected returns, we take into account the choice for using log returns or normal returns. When returns are close to 1, these are almost identical. An advantage of using log returns is that returns can be added up. Therefore we will work with log returns instead of normal returns.
After having explained why we use log returns, we now answer question 1 and 2. See table 1.
All 10 stocks 
Dutch stocks 
German stocks 

investment 
€ 150.000 
€ 75.000 
€ 75.000 
expected monthly return 
0,00639 
0,00699 
0,00569 
standard deviation 
0,05462 
0,05638 
0,06569 
95% VaR 
€ 12.518,008 
€ 6.431,754 
€ 7.677,054 
99%VaR 
€ 18.101,519 
€ 9.313,692 
€ 11.034,596 
Table 1: Answers to question 1 and 2
The one month 95% Value at Risk (VaR) for the portfolio with all 10 stocks implies that, with 95% confidence, and with an investment of € 150.000, the maximum loss during a period of one month on this portfolio will be € 12.518,008. For the formula and the assumptions of VaR, and an overview of the other formulas we used, we refer to appendix 2. As can be seen in table 1, the 95% (and 99%) VaR for the portfolio with 10 stocks is smaller than the sum of the 95% (and 99%) VaR of the individual country portfolios. This implies that the returns of these individual portfolios are not perfectly correlated, and thus, that diversification benefits are obtained.
Question 3
The probabilities of losing or gaining a particular amount after a certain period and for a particular portfolio can be calculated with the help of the VaR formula. In appendix 3 this method is shown. Below we have presented our answers to this question in table 2.
Dutch stocks 
German stocks 

Probability of losing more than € 10,000 after 1 year 
13.31% 
18.78% 
Probability of gaining more than € 15,000 after 6 months 
12.62% 
15.13% 
Table 2: Answers to question 3
As can be seen in the results, the probability of losing more than € 10,000 after one year is smaller if you had invested in Dutch stock than in the German stock. The difference is about 5 percent. In the contrary, the probability in gaining more than 15,000 is 2,5 percent higher if you had invested in German Stock. So we can say that investing in Dutch stock is less risky, but the chance of high returns is higher with German stock.
References
BBC Dataset – Accessing BBC iPlayer from Ireland
Masking TCP/IP Addresses – Change IP Address Program