Year 2 · Core Finance · Markets & Instruments
Duration & Convexity
Measure and manage interest-rate risk using Macaulay duration, modified duration, DV01/PVBP, convexity, key-rate duration, portfolio aggregation and immunization.
LEARNING OBJECTIVES
What you should be able to explain after this lesson
01
Explain why maturity alone is not enough to measure bond interest-rate risk.
02
Calculate and interpret Macaulay and modified duration.
03
Use DV01/PVBP to express dollar sensitivity to a one-basis-point yield move.
04
Add convexity to improve price-change estimates for larger yield moves.
05
Aggregate duration risk across a portfolio and distinguish parallel from non-parallel curve risk.
06
Understand key-rate duration, effective duration and immunization as professional risk-management tools.
CONCEPT MAPFrom bond price to rate-risk management
Maturity tells you when principal is repaid; duration tells you more about price sensitivity
CORE FACTS · SAME IN EVERY MODE
Two bonds with the same maturity can have different interest-rate sensitivity because their coupon cash flows arrive at different effective timings.
All else equal, longer maturity generally increases duration.
All else equal, a lower coupon generally increases duration because more value is concentrated in the final principal payment.
A zero-coupon bond's Macaulay duration equals its maturity under the standard definition.
BeginnerTeaching style changes, knowledge does not.
Imagine two five-year bonds. One pays a large coupon every year; the other pays no coupon and gives you everything at year five. The second bond keeps more of your economic value locked in the distant future, so its price reacts more strongly when discount rates change.
COMPARISON
What tends to increase duration?
| Feature | Typical effect, all else equal |
|---|---|
| Longer maturity | Higher duration |
| Lower coupon | Higher duration |
| Zero coupon | Macaulay duration = maturity |
PROFESSIONAL VOCABULARYInterest-rate risk / risque de taux / interest-rate risk First-order sensitivity / sensibilité de premier ordre / first-order sensitivity
Risk that a position's value changes because interest rates or yields change.
Linear approximation of value change for a small change in a risk factor.