Question 3 (15 points)

Assume all the coupon bonds have just paid out their respective semi-annual interest payments today. Assume further that all the bonds have a par value of $100 and are perfectly divisible (i.e., buying or selling any fraction of a bond unit is possible).

You have a fixed liability of $1,000,000 at the end of the fifth year. Assume that you can only invest in two bonds: Bond 1 carries 10% coupon with 10 years to maturity and Bond 2 carries 13% coupon with 5 years to maturity.

(a)(10 points) The term structure is flat and the yield (expressed as bond-equivalent yield) is 8 percent. Construct an immunization portfolio today.

(b)(5 points) Assume the term structure shifts to 9% flat in six months, check if you are able to meet your obligation, then rebalance your portfolio.