1. INTRODUCTION
Quantitative Techniques for Business Project
School of Economics and Finance
Curtin University
School of Economics and Finance
Curtin University
Felix Chan
March 6, 2018
1 Introduction
The aim of this project is to evaluate different 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 “stock201801-Sem1.csv” from Blackboard. The file contains the
daily prices of Apple, Hewlett Packward (Inc.), Intel and Microsoft for the period
XXXXXXXXXXto XXXXXXXXXXNote that the prices on weekends and public holidays have
een removed.
3 The Analysis
1. Plot the prices of each asset separately against time using software such as EX-
CEL or Tableau. What do you observe on the movement of these prices during
the Global Financial Crisis (late 2008)?
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3. THE ANALYSIS
2. Calculate the returns of each asset using the following:
t = 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 indepen-
dently and identically distributed normal distribution, are the expected returns
statistically different from zero for each asset? State clearly the null and alter-
native hypothesis in each case.
5. Assume the returns of each asset are independent from each other, are the mean
eturns statistically different from each other?
6. Calculate the co
elation 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?
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4. SUBMISSION
4 Submission
Please submit your solutions to your local instructor by Monday 4 June 2018 at
1:00pm. Please ensure you show all workings as full mark will not be awarded without
showing all essential steps.
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