An investor holds 100 three-year zero coupon bonds with a face value of 100 which trades for 92.5. The investor wants to use a one-year zero coupon bond, face value of 100, which trades at 95 and a five-year zero-coupon bond with a face value of 200, which trades at 180, to immunise the portfolio.

a) How many one-year and five-year bonds should the investor buy or short of immunising the portfolio using both duration and convexity of the bonds?

b) If the investor has shorted the one-year and the five-year bonds where has she invested the money received? Why has she chosen these forms of assets?

b) Suppose that the one-year discount factor falls to 0.94106, the three-year discount factor declines to 0.89848 and the five-year discount factor falls to 0.857204. Calculate the value of the portfolio of 1-year, 3-year and 5-year bonds before and after the change in interest rates and explain why the immunization is not perfect. (Ignore rounding errors).