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 are1.13 and 0.97 during a boom and duringa bust, respectively.

Consider an investor with preferences over portfolios represented bythe 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 ofthat makes the investor indifferent between therisk-free and the risky asset.

c.Now assume that= 6.25. If the investor puts a proportionof hismoney in the risk-free asset and the rest,1, in the risky asset,what will he optimally choose?