Question

You work for an insurance company. You have an obligation to pay $1 mln in exactly 1.5 years from today. Your goal is to provide the company with an immunized portfolio that would hedge the current obligation. The company is only interested in first-order immunization, so you do not have to deal with convexity.

There are two bonds in the market: the first bond has 1 year till maturity, pays 5% coupon rate and is traded at yield 4%. The second one has 2 years to maturity, 3% coupon and is traded at yield 4%. Assume all coupons are paid twice per year. Please provide the approximate quantities invested in every bond (in thousand dollars). Assume one can buy fractions of bonds.