There are two equiprobable states, boom and bust, and two assets, one risk-free and one risky. The risk-free assets total return is Rf = 1.01 and the risky assets 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 , 2 = 2, where and 2 are the mean and variance of the portfolios 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 of his money in the risk-free asset and the rest, 1 , in the risky asset, what will he optimally choose?