You have an obligation to pay $1,000,000 in eight 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 zero-coupon bonds:

Bond Face Value ($) Yield to maturity (% p.a.) Maturity (years)

A 1000 4% 5

B 1000 4% 10

Suppose the yield curve is flat at 4% for all maturities. Use annual compounding in this problem.

(a)What is the present value of the obligation to pay $1,000,000 in eight 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 (approximately) will the value of your hedging portfolio (the bonds only, not the $1,000,000) obligation change? (4 marks)