Macro & Micro economics

Quantitative Techniques for Business

Project description
Quantitative Techniques for Business 203
Project
School of Economics and Finance
Curtin University
Felix Chan
March 2014
1 Introduction
The aim of this project is to evaluate dierent portfolio compositions of nancial
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 le \stocks.xlsx” from Blackboard. The le contains the daily stock
prices of Microsoft, Apple, Intel and Hewlett-Packard for the period 1988.07.20 to
2009.07.20. Note that the prices on weekends and public holidays have been removed.
3 The Analysis
1. Plot the stock prices separately against time on EXCEL. What do you observe
on the movement of these prices during the Global Financial Crisis (late 2008)?
2. Calculate the returns of each stock price using the following:
r
t
= 100 ln
P
t
P
t
1
where
P
t
is the stock price at time
t
. Plot the returns for each stock 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 stock returns of each asset are drawn from an
independently and identically distributed normal distribution, are the expected
returns statistically dierent from zero for each asset? State clearly the null and
alternative hypothesis in each case.
5. Assume the stock returns from each asset are independent from each other, are
the mean returns statistically dierent from each other?
6. Calculate the correlation matrix of the stock 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 stocks 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 stock prices follow a
normal distribution?
2
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