Invests in a market-value weighted portfolio

Suppose you are German investor that invests in a market-value weighted portfolio P1 that contains the 7 German companies that you collected. Calculate the returns of this portfolio. Create three different sample. First, the Full Sample (FS) that contains all your data. Second, the Early Sample (ES) that contains the first half of your FS dataset. Third, the Late Sample (LS) that contains the second half of you FS dataset.
Use the FS dataset to answer the following questions:

1. Suppose you are a European investor that invests in portfolio P1. Calculate the monthly returns of this portfolio. Hint: the market value of a company changes monthly, so take this into account. Like what we have seen in class, make a histogram for the market-value weighted portfolio P1 returns.
2. Calculate the average monthly return and the risk as measured by the standard deviation and – like what we have seen in class - make a graph that contains the (empirical) cumulative distribution function of portfolio P1, together with the cumulative normal distribution function assuming that the expected return and variance are estimated by the average return and standard deviation (squared) from the previous question. Compare!
3. Calculate the monthly 99% Value at Risk for an investment of €100,000 in portfolio P1. Explain how!
4. Using the FS dataset, draw the mean-variance frontier based on the seven assets when short sales are allowed. In addition, in the same figure, draw the mean-variance frontier when short sales are NOT allowed. Moreover, put these seven assets and the market value-weighted portfolio of those assets in the figure as well (note that these are single points.).1 Explain the results.
5. Using the FS dataset, consider the case when short sales are allowed. Assume that the investor is maximizing the mean-variance utility function which we have seen in class with a risk aversion level A = 4 and a constant risk-free rate that is equal to 𝑟𝑓 = 0.25 × 𝐸{𝑟𝐺𝑀𝑉}. Calculate and draw the Capital Allocation Line, together with its mean variance frontier for the cases of the previous question. Discuss your findings.
6. Download an all-share index (for example Dax) and corresponding short term interest rate series for Germany and calculate returns (note: determine and motivate which short term rate and which return measure are appropriate.). Next, using the time series returns of each company, the short-term interest rate as a proxy for risk fee and the all-share index as a proxy for the market, estimate the CAPM model for the samples ES and LS separately. (so in total there will be 14 regressions). Discuss!
7. Using the estimates of the previous question draw the Security Market Line for the samples ES and LS in separate graphs. Put in each graph also the individual assets and the German market-value weighted portfolio (note that these are points). Discuss and motivate your results. Importantly, discuss the differences between the graphs and how they relate to the theory, that is, are your findings in line with the theory or not and motivate why this is the case in your opinion.

Sample Solution