The spreadsheet Group Report Data.xlsx contains monthly returns on eleven Australian industry portfolios from January 2011 to March 2022. The industry abbreviations are in the table below.

Investor utility is represented by: U = E(R) 12A2. There are two investors with different risk aversion coefficients (A). Gladys has a risk aversion coefficient of 7 and Dominic has a risk aversion coefficient of 3. Investors are able to short-sell each industry throughout the report. Investors are unable to borrow or lend at the risk-free rate except for part 5 of the report. The expected returns per month to be used throughout the report are in the following table. Do not use historical average returns as expected returns. You need to use the historical returns to estimate the covariance matrix.

Calculate the optimal portfolio for both investors that consists of all eleven industries. Compare this to the other portfolios you have already estimated in parts 1, 2 and 3 in terms of diversification benefits. What do you observe? Contrast the differences in what you observe between the two investors. (15 marks)

Now consider the case where both Gladys and Dominic can invest in a risk-free asset. The risk-free rate is 0.75% per month. Estimate the optimal combined portfolio for each investor using the five industries in part 3 and then estimate the optimal combined portfolio for each investor using all eleven industries. How does the existence of the risk-free rate affect your conclusion regarding diversification benefits? Are diversification benefits increased or reduced if the investors can borrow or lend at the risk-free rate? (20 marks)

Your report should conclude with a summary of your findings regarding differences in the benefits of diversification across investors, industries and portfolio size. (10 marks)

Industry Abbreviation Consumer Discretionary Consumer Staples Energy Health Care Industrials Information Technology Materials Telecom Utilities Financials Real Estate COND CONS ENGY HC INDU IT MATL TELE UTIL FIN RE Expected Return (per month) 1.07% 1.00% 1.10% 0.96% 0.99% 1.00% 1.02% 0.90% 0.90% 1.10% 0.98% Industry Abbreviation Consumer Discretionary Consumer Staples Energy Health Care Industrials Information Technology Materials Telecom Utilities Financials Real Estate COND CONS ENGY HC INDU IT MATL TELE UTIL FIN RE Expected Return (per month) 1.07% 1.00% 1.10% 0.96% 0.99% 1.00% 1.02% 0.90% 0.90% 1.10% 0.98%