The portfolio manager of Alpha, an asset management firm, needs to create a portfolio containing two stocks - Gamma and Rho, which have a correlation coefficient of 0.3 with each other. Based on historical data, the average annual return of Gamma in the past 4 years has been 5% p.a. with a risk (standard deviation) of 8% p.a. As for Rho, the stock generated an average annual return of 10% p.a. with a risk of 16% p.a. The current risk-free rate is 4% p.a.
a) What is the allocation (%) of Gamma in the optimal risky portfolio? [3 marks]
b) What is the expected return and standard deviation of the optimal risky portfolio? [3 marks]
c) What is the maximum Sharpe ratio possible? [2 marks]
d) If the optimal complete portfolio of an investor has an allocation of 20% in the risk-free asset, what would be the investor’s coefficient of risk aversion? [2 marks]