Bond Duration & Convexity: Interest Rate Price Sensitivity
Macaulay vs. Modified duration, DV01 risk modeling, positive vs. negative convexity, and portfolio duration immunization.
1. Bond Duration: Measuring Interest Rate Risk
Duration measures the sensitivity of a bond's price to changes in benchmark interest rates, expressed in years:
- Macaulay Duration: The weighted average time until all bond cash flows (coupons and principal) are received.
- Modified Duration: The approximate percentage change in bond price for a 100 bps (1.00%) change in yield:
For example, a bond portfolio with a modified duration of 8.0 years will lose approximately 8.0% of its market value if yields rise by 100 bps.
2. Bond Convexity: The Second-Order Derivative
Duration provides a linear approximation, but bond price-yield curves are curved (convex). Convexity measures the rate of change of duration as yields fluctuate.
For standard option-free Treasuries, convexity is positive: as yields fall, prices rise faster than duration predicts; as yields rise, prices fall slower than duration predicts — a structural mathematical advantage for bondholders.