School of Economics and Finance
Curtin University
Felix Chan
July 28, 2015
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 “exchange.xlsx” from Blackboard. The file contains the daily spot
exchange rates between Australia and Japan, UK and US. It also has US Treasury Bill
rate for the period 1992.08.07 to 2012.08.09. Note that the data on weekends and
public holidays have been removed.
3 The Analysis
1. Plot the exchange and bill rates separately against time on EXCEL. What do
you observe on the movement of these assets 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 rate at time t. Plot the returns for each rate.
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 different from zero for each asset? State clearly the null and alternative
hypothesis in each case.
5. Assume the returns from each asset are independent from each other, are the
mean returns statistically different 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 rates follow a normal
distribution? Moreover, is Treasury Bill safer than the other three exchange
rates?
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4 Submission
Please submit your solution to your tutor by Friday 2015.11.06. Please ensure you
show all workings as full mark will not be awarded without showing all essential steps.
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