Question 3 [20 marks] There are two equiprobable states, boom and bust, and two assets, one risk-free and one risky. The risk-free asset's total return is Rj = 1.01 and the risky asset's total returns are 1.13 and 0.97 during a boom and during a bust, respectively. Consider an investor with preferences over portfolios represented by the utility function U (4, 02) = u do?, where u and o are the mean and variance of the portfolio's returns, respectively. a. Find the mean and variance of the returns of the two assets. b. Find the value of that makes the investor indifferent between the risk-free and the risky asset. c. Now assume that . = 6.25. If the investor puts a proportion a of his money in the risk-free asset and the rest, 1 - a, in the risky asset, what a will he optimally choose? Question 3 [20 marks] There are two equiprobable states, boom and bust, and two assets, one risk-free and one risky. The risk-free asset's total return is Rj = 1.01 and the risky asset's total returns are 1.13 and 0.97 during a boom and during a bust, respectively. Consider an investor with preferences over portfolios represented by the utility function U (4, 02) = u do?, where u and o are the mean and variance of the portfolio's returns, respectively. a. Find the mean and variance of the returns of the two assets. b. Find the value of that makes the investor indifferent between the risk-free and the risky asset. c. Now assume that . = 6.25. If the investor puts a proportion a of his money in the risk-free asset and the rest, 1 - a, in the risky asset, what a will he optimally choose