Duration of zero coupon bonds
1. Suppose you invest in zero coupon bonds. One matures in 1 year, paying $100, and its price is $56.93. The other matures in 2 years, paying $1100, and its price is $943.07.
a) Compute the yield-to-maturity on each bond.
b) Compute the duration for each bond.
2: Immunization: A pension fund manager must provide a payment to a policyholder in the amount of $1,600 in 5 years. To ensure that the pension fund will be able to meet its future obligation, the fund manager purchases a 5 year coupon bond ($1000 par value) that pays a 10% coupon rate.
a) Will the pension fund have sufficient funds to meet its future obligation if it purchases the 5-year coupon bond? You may assume for Part(a) that the YTM is constant at 10% throughout the period and any coupon payments are re-invested at this rate. You may also assume that coupon payments are made annually.
b) The pension fund manager believes that by purchasing a 5-year coupon bond which exactly matches the investment horizon of the fund she has been able to immunize her portfolio. Is her logic correct? For Part (b) you may assume that coupon payments are made annually and are re-invested.