QUESTION 1

Assume annual compounding and that the yield curve is flat at 8.50% pa nominal. Suppose we have a liability of $700,000 due in exactly 7 years' time. We want to immunize the liability by investing in a combination of 3-year coupon-paying bonds paying 9.50% annual coupons and 10-year zero coupon bonds

(a) What is the price of the 3-year bond?

(b) What is the price of the 10-year bond?

(c) What is the present value of the liability?

(d) What is the Macaulay Duration of the 3-year bond (in years)?

(e) What is the Macaulay Duration of the 10-year bond (in years)?

(f) What is the Macaulay Duration of the liability (in years)?

(g) What is the first equation in the system of equations that needs to be solved to find the immunizing portfolio, where q_Z is the number of zero-coupon bonds and q_C is the number of coupon-paying bonds in the immunizing portfolio?

(h) What is the second equation in the system of equations that needs to be solved to find the immunizing portfolio, where q_Z is the number of zero-coupon bonds and q_C is the number of coupon-paying bonds in the immunizing portfolio?