An investment company is considering three Exchange Traded Funds for one of its clients: ETF Q has an expected return equals 12% and a standard deviation equals 20%. ETF Y has an expected return equals 8% and a standard deviation equals 12%. The third ETF is money market and has an expected return equals to 3%. The first two ETFs, Q and Y are uncorrelated. The client is risk averse with a risk aversion coefficient equals to seven.

1. Find the proportions of each asset, and the expected return and standard deviation of the tangency portfolio. (4 marks)

2. What is the reward-to-variability (Sharpe) ratio of the best feasible capital allocation line? (3 marks)

3. What is the composition of the optimal portfolio in terms of all available funds? (4 marks)

4. What are the expected return and standard deviation of the optimal portfolio in (3)? (4 marks)

5. A less sophisticated investment client would like to use only the Q and Y ETFs, and require an expected return of 10%, what must be the investment proportions of her portfolio in all assets? Compare your result to the optimized portfolio in part 3. What do you conclude? (5 marks)