### Recent Question/Assignment

Exhibit 1: Monthly Share prices for Three Traded Stocks and the monthly Share Price Index.
Month Market index Carbon Ltd (\$) Oxygen Ltd (\$) Helium Ltd (\$)
1 4650 13.05 8.00 20.55
2 4770 13.40 7.60 21.15
3 4840 13.87 7.00 20.95
4 4940 13.12 7.70 18.75
5 4815 13.37 8.10 17.10
6 4788 13.00 8.60 19.35
7 5055 13.50 8.30 20.10
8 5125 13.90 8.90 21.05
9 5035 14.12 9.70 22.15
10 5115 14.87 10.20 23.85
11 5200 15.25 10.65 22.90
12 5255 16.05 11.05 21.85
13 5305 16.40 11.45 23.80
14 5408 16.00 10.95 25.05
15 5510 16.25 10.55 26.25
16 5430 16.50 11.00 25.00
17 5360 17.00 10.55 26.65
18 5420 17.35 10.10 28.15
19 5490 18.00 10.70 32.80
20 5555 18.35 9.45 35.70
21 5500 18.55 10.12 32.55
22 5575 19.20 10.45 30.30
23 5645 18.70 10.05 32.90
24 5695 18.20 10.85 34.50
25 5770 18.75 11.15 35.75
Exhibit 2
Dividend History: Annual dividends paid for the last 6 years.
Carbon Ltd (\$) Oxygen Ltd (\$) Helium Ltd (\$)
1.00 0.60 1.50
1.05 0.63 1.60
1.10 0.66 1.70
1.15 0.70 1.80
1.20 0.74 1.90
1.25 0.77 2.00

Questions
Your lecturer has instructed each team to specifically address all of the following questions:
1. Using the information given in Exhibit 1, calculate the historical monthly returns for each company and the market index.
2. With the use of the excel functions calculate the average monthly return and standard deviation of returns for each company and the market index.
3. Using your answers to question 1, above, and assuming that investors can only invest in one of the three alternatives in Exhibit 1, use both the average return and standard deviation to determine which share would be the most appropriate for a risk-averse investor. Provide numerical justification for your selection.
4. Calculate the covariance of returns and correlation coefficients between all shares. Provide an explanation of your results and the implications for diversification.
5. Determine the expected return and standard deviation of a two-asset portfolios comprised of Carbon and Oxygen; Carbon and Helium; and Oxygen and Helium. Assume equal weightings of each share within each portfolio. Interpret your results and comment and illustrate the impact on risk when combining shares into a portfolio.
6. Determine the expected return and standard deviation of a three-asset portfolio comprising all three shares. Assume equal weightings of each share within the portfolio. Why is the computation more complex than a portfolio comprising of only two shares? Is this portfolio more efficient than the portfolios constructed in question 5? Provide numerical evidence to support your answer.
7. Determine the systematic risk (Beta) of all three shares. Interpret your answers. The use of excel functions is acceptable to calculate Beta.
8. Calculate the required rate of return for all three shares. Assume the risk-free rate of return is 4%. You will need to provide an explanation for all your workings given the method of approach you have adopted.
9. Utilising the required rates of return calculated in question 8 above and the historical dividend information in exhibit 2; calculate the present value for all three shares. You will need to state any assumptions that you have made and a justification for your approach to each valuation.