Consider an investor maximizing expected utility u(r) = ln(r) over returns deciding how much to invest in one risky asset and one risk-free asset. The risky asset will have excess return y > 0 with probability p and excess return y with probability (1 p). The risk-free rate is rf > 0. (a) What are the returns of the risky asset? (b) Find a formula for , the optimal fraction of wealth that the investor will invest in the risky asset, in terms of p, y, and rf . (c) What happens to as y increases? Explain the intuition behind the result.