Overview — Duration, Convexity, and Rate Sensitivity

Every fixed-income position has a fundamental risk: interest rates move and prices change. This topic is about quantifying, communicating, and hedging that risk. The four lessons move from the most primitive sensitivity measure — DV01, the dollar change in value for one basis point — to progressively richer frameworks: duration as a normalised relative measure, key-rate exposures that break the yield curve into buckets, and regression-based hedging that accounts for the fact that two securities of the same duration can still move differently when rates shift.

These measures are not merely theoretical. A rates desk quotes DV01 on every trade; a portfolio manager reports duration daily; a liability-driven investor immunises a pension fund against the spot curve using key-rate durations. Understanding exactly what each measure assumes — and where it breaks down — separates the practitioners who hedge correctly from those who think they are hedged until rates move in an unusual way.

By the end of this topic you should be able to:

• define DV01, compute it from prices at two nearby rate levels, and use it to determine the hedge ratio for any two rate-sensitive instruments;
• state and derive modified duration and Macaulay duration; relate them to DV01 and explain the coupon and maturity dependence of duration;
• define convexity, explain why it is always positive for fixed-coupon bonds, and use the duration-convexity approximation to price a bond after a large rate move;
• decompose a portfolio's rate exposure into key-rate DV01s across the curve; execute a barbell vs bullet immunisation;
• apply regression-based hedging to construct a tail-hedging ratio when the two-security DV01 hedge fails because their yields don't move one-for-one.

1. Contents
2. The big picture