The data for this coursework is found in the Excel file ‘EC3114 Portfolio Diversification Coursework’ in Moodle, just above ‘Submission Boxes’.
Please submit your individual coursework in Turnitin by 10:00h on Monday 11 December 2023. The Turnitin link appears in Moodle in the slot for that week. The coursework report should be in either Word or PDF format only (do not post Excel worksheets or worse, zipped files). Do not collaborate. Do not use AI to do your work.
The Excel spreadsheet has data on beginning of the month adjusted closing price of stocks on four firms trading on the LSE: Shell, Sainsbury, National Grid and Easy Jet, and on the FTSE100 Index. The data covers the period 01-09-2019 to 01-11-2023.
Assume that the risk-free rate of return is constant at 0.04% per month throughout the period.
Demonstrate clearly all the methods you are using for these tasks.
Use the price data to find the monthly returns for each firm’s stock and the FTSE 100.
Now combine two firms from the given four to form a portfolio that will give you the best diversification opportunities. Justify why you choose these two stocks for your portfolio. Explain all the assumptions you have made.
Once you have formed this portfolio, write a presentable report of about 1,500 words (word count excludes tables, figures, charts and equations) that covers all the tasks below. Calculate the following and demonstrate all your work, clearly explaining the process. If you are showing summary statistics, please present this in a nice clearly labelled table. Charts or diagrams need to be properly labelled. Do not include the raw data in your report – I already have this.
a) Find the expected return and the level of risk exhibited by the Global Minimum-Variance Portfolio. What proportions of your wealth are invested in each of the two stocks?
b) Plot the investment opportunity set of the two risky assets (You can do this either on Excel, or manually). Use increments of 10% over the range 0-100% in the weights (or investment proportions) for w1.
c) Draw and label the Capital Allocation Line (CAL) that is just tangential to the opportunity set. Label this point of tangency P. Explain what P is.
d) Use the solution derived from the maximization problem of the Sharpe Ratio (or slope of the CAL) to find the weights invested in each asset at P. You do not have to show the derivation here – simply use the results from the maximization problem from the textbook or the slides from the lecture.
e) Calculate the expected return and the standard deviation at P. Calculate the Sharpe Ratio for this CAL.
f) If your risk aversion parameter has a value of A = 3, find the composition of the complete portfolio C you would invest in.
Comment on your answer and compare with what you would have earned if you were to invest all your wealth in either one of the single stock.
g) Calculate the standard deviation and the expected return of your complete portfolio C.
h) Explain how your answers to part g) above change when the investor is:
1) risk loving
2) risk neutral
3) more risk averse than in part (f) above.
i) Is it worth investing in the FTSE 100 instead of a two-asset portfolio in our case here?
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