Posted: September 13th, 2017

Quantitative Techniques for Business

Quantitative Techniques for Business
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 di?erent 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: rt = 100 ln Pt Pt-1

where Pt 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 di?erent 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 di?erent 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?
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