******* Please answer part b only

Problem 4 - Managing Bond Portfolios [14 marks] a) You are a financial consultant and an expert in contingent immunization strategies. A client has hired you to make sure her portfolio has a value of at least $750,000 at the end of six years. The current value of her portfolio is $545,000. The bonds at your disposal currently yield an effective annual rate of 6.00%. i. Given the current interest rate, what amount would you need to invest today to achieve the requested goal? [1 mark] ii. Suppose that three years have passed (so there are three years left to meet the original goal) and the interest rate is 7.00%. What is the trigger point of your client's portfolio? That is, how low can the value of the portfolio get before you are forced to immunize your strategy to achieve the requested goal? [2 marks] iii. As in part (ii) assume three years have passed (so there are three years left to meet the original goal) and the interest rate is 7.00%. You see that the portfolio value is $581,600. What should you do? What effective annual rate is required to meet the original goal? [2 marks] b) You are about to purchase a 10-year par bond with a 4.50% coupon rate paid annually. i. What are the duration and the convexity of this bond? [4 marks] ii. Assume that right after you purchase the bond an economic announcement drives the YTM to 6.00%. What is the new price of the bond? [1 mark] iii. What price would be predicted by the duration rule after the YTM increases to the amount stated in part (ii)? Is this price the same as the one reported in part (ii)? Why? [2 marks] iv. What price would be predicted by the duration-with-convexity rule after the YTM increases to the amount stated in part (ii)? Is this price the same as that reported in part (ii)? Why? [2 marks]