Bond Risk Measures and Immunization › Bond Risk Measures and Immunization

A bond portfolio can gain value when rates fall and still leave a pension fund less able to meet its obligations. The liabilities may rise by more than the assets. Managing that mismatch requires a clear choice of what to hedge: a bond's price, the dollar surplus over liabilities, or the funding ratio. These are different quantities, even when all use duration.

This chapter develops duration and convexity as first- and second-order price sensitivities, then uses them to construct and test a portfolio against a future liability. We begin with fixed, nonnegative cash flows and a common yield convention. The approximations describe nearby yield changes; they are not exact repricing rules for arbitrary rate moves.

Immunization matches asset present value and cash-flow timing to a liability under stated assumptions. In the single-liability example, matching Macaulay duration to the payment horizon removes first-order exposure to an immediate persistent change in one flat yield. It does not guarantee payment under every future rate path or remove default and liquidity risk.