1. You are given the performance of stock and bond funds under various scenarios, as shown in the table below:

Scenario	Probability	Rate of return of stock fund (%)	Rate of return of bond fund (%)
Crash	0.1	-30	-5
Poor	0.4	-2	12
Good	0.3	15	4
Excellent	0.2	40	2

a. Calculate the expected returns of the stock and bond funds. (4 marks) b. Calculate the standard deviations of the stock and bond funds. (4 marks) c. Calculate the correlation coefficient of the stock and bond funds. (4 marks) d. Suppose an investor forms a portfolio with stock and bond funds. Find the investment opportunity set in differing proportions. (8 marks)

Weights in stock fund	Portfolio expected return	Portfolio standard deviation
0.0
0.2
0.4
0.6
0.8
1.0

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