Bond A is a 4-year bond with a 10% coupon rate and Bond B is a 2-year bond with a 20% coupon rate. Both bonds have a face value of 100, and all coupons are paid annually, starting in year 1. Consider a portfolio that consists of one unit of Bond A and one unit of Bond B. The yield curve is flat at = 5%.

a) What is the Macaulay duration of this portfolio?

b) Compute the approximate percentage change in the value of the portfolio if the interest rate increases by 200 basis points.

c) Suppose a pension fund holds this portfolio and is worried about fluctuations in its price. Explain how the fund can hedge its interest rate risk using 3-year zero-coupon bonds with a face value of 100.

[20 marks]