MA7008 Financial Mathematics Assignment

The tasks:

1. Download the historical prices of any five stocks previously selected in your portfolio. The historical prices should go back a sufficient period in time from the date that you obtain the data in order to yield positive average returns. Give a brief description of each company and the type of business they are in. Calculate the expected return and the volatility for each company as well as the correlations between the asset returns.
   (10 marks)
2. Use an appropriate Solver function to determine the portfolio risk and the percentage of investment in each asset in your portfolio for a target return of your choice. Repeat this process for different portfolio target returns and hence, draw the efficient frontier curve.
   (20 marks)
3. Calculate the Sharpe ratios for a range of expected portfolio returns and volatilities that you calculated in parts (ii), and by using a risk free investment guaranteeing a return of 1.5%, determine the equation of the Capital Market Line. Discuss the economic significance of the Capital market Line.
   (20 marks)
4. Using linear regression analysis, calculate the beta for each asset in the portfolio and discuss the significance of this quantity. Estimate Value at Risk (5%) for your portfolio and discuss how much each asset contributes to your estimated VaR.
   (20 marks)
5. Estimate the volatility of a single asset in your portfolio using ARCH/GARCH and its extensions using R. Identify the best model and provide an explanation of your chosen model.
   (15 marks)
6. Give a summary of your findings in a non-technical language that could inform a potential investor choosing the best efficient portfolio and discuss the implication of other relevant performance measurements.
   (15 marks)

Up to 5 marks will be awarded for clarity of presentation as described in the instructions.

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