Question: Your fund has an obligation to pay out $4,000 in 5 years $9,000 in 7 years. You want to immunize this liability with zero-coupon bonds that have a maturity of 2years and a perpetuity that makes annual payments. The current market interest rate is 8.00%.
a. Calculate the duration of the liability.
b. What is the duration of the bond? What is the duration of the perpetuity?
c. What proportion of your investment should you put into the zero-coupon bond and what proportion in the perpetuity to immunize your position?
d. How much, in dollars, should you invest in each of the assets?
e. What is the face value of your investment in the zero-coupon bond?