Business Quantitative Techniques - The Analysis - Business Assignment Help

Assignment Task:

 
The aim of this project is to evaluate different portfolio compositions and financial assets based on time series data. It requires both the statistics and the mathematics components of the unit and you should be able to do parts of the project as the unit progresses. You are strongly encouraged to tackle the project on a weekly basis and complete as many questions as possible.

1 Background
You are an independent consultant and have been approached by a client who wishes to construct a portfolio of four different assets. The client is seeking your advice on the optimal allocation of his investment among these assets. Your tasks are:
To provide analysis on each of these assets
To provide advice on the optimal allocation of his investment in these assets

2 The Analysis
Your report should contain the following elements:
Source of data for your analyses. Daily data is expected for each of the assets for at least the last 10 years.
Plot the prices of each asset separately against time. What do you observe about the movement of these prices during the Global Financial Crisis (late 2008)?
Calculate the return of each asset using the following:
rt=100ln(PtPt−1)rt=100ln?(PtPt−1)
where PtPt is the asset price at time tt. Plot the returns for each asset price.
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 these descriptive statistics in each case?
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.
Assume the returns of each asset are independent of each other; are the mean returns statistically different from each other?
Calculate the correlation matrix of the returns and discuss the directions and strength of the correlations.
Is the assumption of independence realistic? If not, re-test the hypotheses in Question 6 using appropriate test statistics. Compare you result with the results obtained in Question 6.
What are the optimal weights of the portfolio and its optimal expected returns? State clearly your objective function and provide step-by-step derivations.
Bonus question: Why is it not realistic to assume these prices follow a normal distribution? What other distribution would you suggest?

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