Quantitative Techniques for Business

1 Introduction
The aim of this project is to evaluate di↵erent portfolio compositions of financial assets based on time series data. It requires both the statistics and mathematics components of the unit and you should be able to do parts of the project as the unit progresses. I would suggest you tackle the project on a weekly basis and complete as many questions as possible.

2 Data
Download the file "stock201601.xlsx" from Blackboard. The file contains the daily prices of Apple, IBM, Intel and Microsoft for the period 2000.03.06 to 2016.01.29. Note that the prices on weekends and public holidays have been removed.

3 The Analysis
1. Plot the prices of each asset separately against time using software such as EXCEL or Tableau. What do you observe on the movement of these prices during the Global Financial Crisis (late 2008)?

2. Calculate the returns of each asset using the following:
rt = 100 ln ? Pt
Pt!1
?
where Pt is the asset price at time t. Plot the returns for each asset price.

3. Create a histogram for each of the returns series and report their descriptive statistics including mean, median, mode, variance, standard deviation, skewness and kurtosis. What conclusion can you draw by examining the kurtosis in each
case?

4. Under the assumption that the returns of each asset are drawn from an independently and identically distributed normal distribution, are the expected returns statistically di↵erent from zero for each asset? State clearly the null and alternative hypothesis in each case.

5. Assume the returns of each asset are independent from each other, are the mean returns statistically di↵erent from each other?

6. Calculate the correlation matrix of the returns.

7. Is the assumption of independence realistic? If not, re-test the hypotheses in

Question 5 using appropriate test statistics. Compare the results to the results obtained in Question 5.

8. If you can only choose maximum of two assets into a portfolio, which will you choose? What are the optimal weights and the optimal expected returns? State clearly your objective function and provide step-by-step derivations.

9. Bonus question: Why is it not realistic to assume these prices follow a normal distribution?

Please submit your solutions to your local instructor by Friday 3 June 2016 at 5:00pm. Please ensure you show all workings as full mark will not be awarded without showing all essential steps.