ECOM2001 Quantitative Techniques For Business 3 aim of this project is to prepare, evaluate and analyse portfolios composed of four financial assets

Introduction

The aim of this project is to prepare, evaluate and analyse portfolios composed of four financial assets. It requires deep understanding of both the statistics and the mathematics components of the unit. You should be able to do parts of the project as the unit progresses. It is recommended that you work on a weekly basis.

Data

Download the stockprices_sem2_2018.csv from Blackboard. The file contains daily stock prices for Apple (AAPL), Hewlett Packard (HQP), Intel (INTC) and Microsoft (MSFT), sourced from www.nasdaq.com.

The Analysis

1. Plot the prices of each asset separately against time using software such as EXCEL or Tableau. Succinctly describe in words the historical time evolution of each of the four time series (limit: 100 words for each series). 
2. Calculate the returns of each asset using thefollowing:

r  = 100ln (  Pt/t Pt–1 )

Where P_t is the asset price at time t. Plot the returns for each asset.

3. Create a histogram for each of the returns series. Also, report their descriptive statistics in a table 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 of 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 prices follow a normal distribution?

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