You manage a pension fund that will provide retired workers a guaranteed investment contract (GIC) for $1,000 with 3-year maturity, and a guaranteed interest rate of 8%. You plan to fully fund the obligation using 8% annual coupon bonds, selling at par value, with 4 years to maturity. Required (a) (b) What is the duration for the 4-year coupon bond? (5 marks) Suppose that the interest rate could be either 6% or 10% for the following four years and assume that you can do the reinvestment at the corresponding interest rate in either case. Which scenario is unfavorable to you such that you would not be able to pay back the obligation? Explain. (5 marks) Now suppose that you can also investment in 2-year maturity zero coupon bond. How do you immunize the obligation against the unfavorable scenario? Compare the accumulated value of your investment with your obligation at maturity. Assume the interest rate is 10% for the following four years. (5 marks) (c) You manage a pension fund that will provide retired workers a guaranteed investment contract (GIC) for $1,000 with 3-year maturity, and a guaranteed interest rate of 8%. You plan to fully fund the obligation using 8% annual coupon bonds, selling at par value, with 4 years to maturity. Required (a) (b) What is the duration for the 4-year coupon bond? (5 marks) Suppose that the interest rate could be either 6% or 10% for the following four years and assume that you can do the reinvestment at the corresponding interest rate in either case. Which scenario is unfavorable to you such that you would not be able to pay back the obligation? Explain. (5 marks) Now suppose that you can also investment in 2-year maturity zero coupon bond. How do you immunize the obligation against the unfavorable scenario? Compare the accumulated value of your investment with your obligation at maturity. Assume the interest rate is 10% for the following four years. (5 marks) (c)