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Question 2: Return and Risk- 5 marks (3 marks for content and 2 marks for expression)

The share prices of six companies listed on the Australian Securities Exchange (ASX) are provided in the EXCEL Worksheet AssignmentPartIData_2023Spring.xlsx.

(i) In your own words write a brief description of the operations of each of the six companies. Each description cannot be longer than two sentences.

(ii)  Use the data in the EXCEL Worksheet to calculate the expected return and risk of each of the companies and the correlation coefficients for each pair of companies. Summarise your estimates in tables.

(iii) Explain in your own words whether or not you feel that your estimations in (ii) reflect the operations that you described in (i) for each of the six companies.

Note: The following statistics need to be estimated - monthly average continuous returns for each of the entities, the ASX200 and cash rate; sample standard deviations of the monthly continuous returns for each of the companies and the ASX200; and sample correlations based on the monthly continuous returns for each pair of the six (6) companies.

Question 3: Mean-Variance optimisation - 5 marks (3 marks for content and 2 marks for expression) 

You have a risk aversion factor of 2.25 and inherit $1,000,000. Select two of the six companies from the EXCEL spreadsheet to create a two-asset portfolio that allows short selling to occur.

(i) In your own words briefly describe why you chose these two companies.

(ii) Construct the optimum portfolio containing only shares in these two companies. In a table provide your estimates of the expected return and risk of this portfolio and the dollar amount and weights you invest in each of the companies.

(iii) Write a brief description of how trial and error would estimate the weights in the portfolio in (ii).

(iv) Explain in your own words why the weights on each company are different in (ii).

(v) Draw the position of the optimal portfolio you constructed in (ii) on a mean-standard deviation diagram using an efficient frontier and a utility curve. The diagram can be hand drawn.

(vi) Provide a reason in your own words why the portfolio has this position on the diagram in (v).

(vii) Construct the optimum portfolio if you now include a risk-free asset as well as the two companies in your portfolio. In a table provide your estimates of the expected return and risk of this portfolio and the dollar amount and weights you invest in each of the companies and the risk-free asset.

(viii) Write a brief description of how trial and error would estimate the weights in the portfolio in (vii).

(ix) Explain in your own words why the weights on each company and the risk-free asset are different in (vii).

(x) Draw the position of the optimal portfolio you constructed in (ii) on a mean-standard deviation diagram using an efficient frontier and a utility curve. The diagram can be hand drawn.

(xi) Provide a reason in your own words why the portfolio has this position on the diagram in (v).

Note: Use the statistics calculated in Question 2 to estimate the weights, return and risk. Assume the average cash rate will be the return on the risk-free asset.