A company owes several debts in the upcoming years: $300 at time 2, and $200 at time 5. The company plans to meet the obligations with investments in three zero-coupon bonds, each paying off at time 1, 3, and 4.
Knowing that the 3-year zero coupon bond is paying off $100, How much payoff should the company purchase from the other two bonds such that the balance sheet is duration-wise matched? Does the suggested portfolio pass the convexity check?