You are given $10,000 in cash to invest in a portfolio consisting of a broad stock index fund P, and a portfolio of T-Bills F. You know that the expected return on the stock index is 18%, with a standard deviation of 20%, while the return on the T-Bill portfolio will be 8%. You can borrow funds at a fixed rate of 10% as long as you don't borrow more than $5,000. If you need to borrow more, the lending rate becomes 12%. Assume that your relevant iso-utility curve is given by the equation: E(r) - 202(r) = 0.11125. a) (5 points) How large is the risk premium? b) (5 points) Calculate the three different slopes of the kinked Capital Allocation Line, and draw the Capital Allocation Line (Hint: the CAL has two kinks where the borrowing rates change). c) (5 points) Draw the iso-utility curve into the graph you produced in b). d) (10 points) How much of your portfolio do you optimally invest in the stock index fund? (Hint: at the tangent point/portfolio between the iso-utility curve and CAL, the expected return and standard deviation on the iso-utility curve equals those on the CAL. You need to solve the quadratic equation.) You are given $10,000 in cash to invest in a portfolio consisting of a broad stock index fund P, and a portfolio of T-Bills F. You know that the expected return on the stock index is 18%, with a standard deviation of 20%, while the return on the T-Bill portfolio will be 8%. You can borrow funds at a fixed rate of 10% as long as you don't borrow more than $5,000. If you need to borrow more, the lending rate becomes 12%. Assume that your relevant iso-utility curve is given by the equation: E(r) - 202(r) = 0.11125. a) (5 points) How large is the risk premium? b) (5 points) Calculate the three different slopes of the kinked Capital Allocation Line, and draw the Capital Allocation Line (Hint: the CAL has two kinks where the borrowing rates change). c) (5 points) Draw the iso-utility curve into the graph you produced in b). d) (10 points) How much of your portfolio do you optimally invest in the stock index fund? (Hint: at the tangent point/portfolio between the iso-utility curve and CAL, the expected return and standard deviation on the iso-utility curve equals those on the CAL. You need to solve the quadratic equation.)