(a) Assuming annual compounding for all bonds and that each bond has a face value of $100, show that the immunization portfolio consists of 317.62 coupon-paying bonds with three years to maturity and 594.95 zero-coupon bonds with 7 year to maturity. Note: You only have to derive a system of equations and then show that the solution given above satisfies both equations. (b) Explain carefully what further transactions are needed, if any, to ensure the liability can be met on the due date. In your answer, refer to interest rate risk, reinvestment risk and rebalancing and any other relevant concepts
Question 1 Assume the yield curve is flat at 6% pa nominal.
Today’s date is 18/7/2011. Suppose we have a liability of $100,000 due in exactly 5 year’s time. We want to immunize the liability by investing in a combination of 3 year coupon-paying bonds paying 10% annual coupons and 7 year zero coupon bonds.
(a) Assuming annual compounding for all bonds and that each bond has a face value of $100, show that the immunization portfolio consists of 317.62 coupon-paying bonds with three years to maturity and 594.95 zero-coupon
bonds with 7 year to maturity.
Note: You only have to derive a system of equations and then show that the solution given above satisfies both equations.
(b) Explain carefully what further transactions are needed, if any, to ensure the liability can be met on the due date. In your answer, refer to interest rate risk, reinvestment risk and rebalancing and any other relevant concepts.
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