Consider the following probability distribution for a stock fund:

State of the Economy	Probability	Return
Boom	0.35	20%
Normal growth	0.50	4.5%
Recession	0.15	-9%

a. What are the expected return and the standard deviation of the stock fund? (10 points)

b. Suppose the expected return and standard deviation of a bond fund is 4% and 5%. The correlation between the stock fund and the bond fund is 0.71. And the optimal risky portfolio, P*, comprising the stock and bond fund, is investing 50% in each. What are the optimal risky portfolios expected return and standard deviation? (10 points)

c. Assume that you have a risk aversion parameter A = 4, and the risk-free rate is 4.4%. What is your optimal investment in P*? What are your optimal investment proportions in the stock fund, the bond fund, and the risk-free asset, respectively? What are the expected return and standard deviation of your complete portfolio (the portfolio constructed with P* and the risk-free asset)? (10 points)