you are advising your clients to spread their risk across an equity mutual fund with the following information

state of economy	Probability	Fund a	Fund b	0.6FundA + 0.4FundB
Recession	0.2	0.08	-0.15
normal	0.5	0.15	0.10
boom	0.3	0.03	0.20

Assume are considering a portfolio that invests 60% and 40% in Fund A and Fund B, respectively. (a) What are the portfolio returns in each scenario? What are the expected returns for each fund and portfolio? (b) What is the average volatility of the two funds? (c) What is the correlation between the two funds? (d) Can you reduce the volatility by holding the portfolio, and why? How much risk can you cut when comparing with the average volatility?