Jill, an elderly investor, has a degree of risk aversion ofA= 3. She is pondering two portfolios, the S&P 500 and a hedge fund. The S&P 500 risk premium is estimated at 5% per year, with a standard deviation of 20%. The hedge fund risk premium is estimated at 10% with a standard deviation of 35%. The return on each of these portfolios in any year is uncorrelated with its return or the return of any other portfolio in any other year. The hedge fund management claims the correlation coefficient between the annual returns on the S&P 500 and the hedge fund in the same year is zero, but Greta believes this is far from certain.

(a) Assuming the correlation between the annual returns on the two portfolios is indeed zero, what would be the optimal asset allocation? (4 marks)

(b) Find the expected return, standard deviation and Sharpe ratio of the optimal risky portfolio. (4 marks)

(c) What are the investment proportions in Greta's optimal complete portfolio that consists of S&P 500, hedge fund and risk-free assets considering his degree of risk aversion