You have an obligation to pay $1,000,000 in 3 years from now, and you would like to make an investment now that will enable you to meet this obligation. This investment will be a portfolio containing two of the following bonds:

Bond A: 2-year maturity coupon paying bond. The face value is $1000. Coupon rate 8% p.a. Coupons are paid at the end of each year.

Bond B: 4-year zero coupon bond. The face value is $1000.

Suppose the yield curve is flat at 8% for all maturities. Use annual compounding in this problem.

(a) What is the present value of the obligation to pay $1,000,000 in 3 years? (1 mark)

(b) What are the prices and durations of bond A and B? (4 marks)

(c) How many of bonds A and B should you buy to fully immunise your obligation? (6 marks)

(d) If yields rise by 1% for all maturities, by what percentage will the value of your bond portfolio change using duration approximation? (4 marks)

(e) Will your estimate in the previous question tend to over-state, under-state or perfectly estimate the percentage change in the bond prices? Explain why. (3 marks)