The following table presents the performance of stock and bond funds under various scenarios.

Scenario	Probability	Rate of return of stock fund (%)	Rate of return of bond fund (%)
Severe recession	0.10	-35	-8
Mild recession	0.20	-10	13
Normal growth	0.50	15	6
Boom	0.20	30	-5

Suppose an investor forms a portfolio with stocks and bonds. Find the investment opportunity set in differing proportions. (10 marks)

Weights in stock fund	Portfolio expected return	Portfolio standard deviation
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0

1

e. Draw the investment opportunity set. (3 marks)

f. Calculate the weight in stock fund, expected return and standard deviation of the minimum-variance portfolio. (6 marks)

g. Given the T-bill rate is 2%. Calculate the weight in stock fund, expected return and standard deviation of the optimal risky portfolio. (6 marks)

h. Calculate the Sharpe ratio for the optimal risky portfolio. (2 marks)

i. Draw the capital allocation line (CAL) on the diagram in part (e). Show the position of the optimal risky portfolio on the CAL. (3 marks)

j. Suppose an investor chooses to invest 80% of his investment fund in the optimal risky portfolio and 20% in a risk-free asset. Calculate the expected return and standard deviation of his portfolio. (4 marks)