Bond Risk Measures and Immunization › Summary

This chapter developed the core quantitative tools for measuring and managing bond interest rate risk:

Duration measures a bond's sensitivity to interest rate changes. Macaulay duration represents the weighted average time to receive cash flows. Modified duration directly quantifies the percentage price change for a given yield change. For example, a bond with a modified duration of 7 will lose approximately 7% of its value for each 1% increase in yields.

Convexity adds the second-order price term omitted by duration. It improves the approximation in the worked examples, but finite-shock errors remain. For positive convexity the term is positive for a nonzero yield change and zero at the expansion point.

Portfolio measures aggregate individual bond durations and convexities using market-value weights. DV01 and dollar duration express risk in dollar terms useful for hedging.

Immunization against a single payment matches present value and Macaulay duration to the payment horizon under a consistent yield convention. It removes first-order exposure to the stated immediate persistent parallel shock in the fixed-cash-flow model, not every possible rate path or source of risk.

Liability-driven investing extends immunization concepts to manage complex streams of future obligations. The duration gap measures the mismatch between asset and liability sensitivities, guiding portfolio construction for pension funds and insurers.

Own-YTM duration and convexity are local price sensitivities, not assumptions that a benchmark yield curve moves in parallel. The common-yield portfolio and immunization scenarios here do not cover arbitrary curve-shape changes. These measures have other limitations, but they remain essential tools that every fixed income practitioner must master. More advanced techniques build upon this foundation by adding sensitivity to curve shape changes, credit spreads, and embedded options.