An investor's utility from wealth is given by u(w)=ln(w). The investor has initial wealth w=100 and is considering invest an amount x between 0 and 100 in a risky asset. In a good state, the rate of return is rg = 0.3 per dollar invested with probability 0.6. In a bad state, the rate of return is rb = -0.3 per dollar invested with probability 0.4. The risk-free rate of return is rf = 0.1 per dollar invested in a risk-free asset.

(a) Is this investor risk-averse? risk-neutral? or risk-loving? What is the relationship between EU and U(EV)? (Which one is larger?). Explain.

(b) What is the expected rate of return per dollar in the risky asset?

(c) Suppose you invest x = 60 into risky asset and invest the rest of wealth into riskfree asset. What is your expected utility from this portfolio? Hint: There are two possible outcomes of ending wealth you can get.