Fixed Income Securities, 4th Edition

APPENDIX TO CHAPTER 1Prices, Discount Factors, and Arbitrage

A1.1 DERIVING REPLICATING PORTFOLIOS

To replicate the 7.625s of 11/15/2022, Table 1.5 uses the 2.875s of 11/15/2021, the 2.125s of 05/15/2022, and the 1.625s of 11/15/2022. Number these bonds from 1 to 3, and let be the face amount of bond in the replicating portfolio. Then, the following equations express the requirement that the cash flows of the replicating portfolio equal those of the 7.625s on each of the cash flow dates. For the cash flows on November 15, 2021,

(A1.1)

For the cash flows on May, 15, 2022,

(A1.2)

And for the cash flows on November 15, 2022,

(A1.3)

Solving equations (A1.1), (A1.2), and (A1.3) for , , and gives the replicating portfolio's face amounts reported in Table 1.5. Note that, because one bond matures ...