Question 2 An individual has a utility function described by U(Y) = ln(Y). There exists a risky asset that is forecasted to pay either of two returns rz >r, with probabilities n and 1-respectively. Let us assume that rz > r >r, and that E() = nr2 + (1 - 1) >r. The individual invests the amount a out of his initial wealth Yo in the risky asset. Write down the expected utility to be maximized by the individual investor. Write down the first order condition solved by the optimal amount invested in the risky asset. Rewrite the FOC such that -(1+0) E[F] - r Y (-)(2-) 10 When would the investor want to borrow at the risk free rate in order to reinvest the proceeds: in the risky asset? Question 2 An individual has a utility function described by U(Y) = ln(Y). There exists a risky asset that is forecasted to pay either of two returns rz >r, with probabilities n and 1-respectively. Let us assume that rz > r >r, and that E() = nr2 + (1 - 1) >r. The individual invests the amount a out of his initial wealth Yo in the risky asset. Write down the expected utility to be maximized by the individual investor. Write down the first order condition solved by the optimal amount invested in the risky asset. Rewrite the FOC such that -(1+0) E[F] - r Y (-)(2-) 10 When would the investor want to borrow at the risk free rate in order to reinvest the proceeds: in the risky asset