Question

As in previous homework, assume you work for a company that has to pay an obligation of USD 1 mln in 1.5 years from today. There are two bonds on the market - one is a 3%-coupon bond, has one year to maturity and is traded at price 101.7854. Another has 2 years to maturity, has 4% annual coupon rate and is traded at price 104.9214. Assume both principals are 100.

The spot rate curve is given as

6 months 1 year 18 months 2 years
1% 1.2% 1.4% 1.5%

Assume that spot rates follow semi-annual compounding convention, and that coupons are also paid semi-annually.

You want to use the two bonds to construct a portfolio, that would pay off the 1 mln obligation at 1.5 years from today, and would be immunized against parallel shifts in the interest-rate curve (in the sense of quasi-modified duration). Please amounts invested in each bond.