Duration vs Convexity: Bond Price Sensitivity Explained
Short answer. Duration is a first-order estimate of how much a bond’s price falls for a 1 percentage point rise in yield; a duration of 7 means about a 7% drop. Convexity is the second-order correction: price moves are not a straight line, so convexity improves the estimate for larger yield changes and favours bonds that gain more than they lose.
Side by side
| Duration | Convexity | |
|---|---|---|
| Order of estimate | First order: the slope | Second order: the curvature |
| Measured in | Years (and % price per 1% yield) | Years squared / a small coefficient |
| Example | Duration 7: about -7% for +1% yield | Adds a small gain correction on top of that estimate |
| Accuracy | Good for small yield changes | Matters for large changes |
| Higher value means | More interest-rate sensitivity | Better price behaviour in both directions |
| Typical users | Bond investors, portfolio managers | Fixed-income managers, risk teams |
| Callable bonds | Duration shortens as rates fall | Can be negative convexity |
Which one fits you?
Lean towards Duration if…
- you want a quick read on interest-rate risk
- you compare bond funds by sensitivity
Lean towards Convexity if…
- you are measuring large rate moves
- you hold callable bonds or mortgage-backed securities
Frequently asked questions
Do I need convexity as a regular investor?
Rarely. Duration is the practical number for most investors; convexity matters more for large moves and for managers.
What is negative convexity?
When a bond’s price rises less than expected as rates fall, as with callable bonds that issuers can redeem early.
What is the duration of a zero-coupon bond?
Equal to its maturity, since all cash flow comes at the end.
General education, not personal financial advice. Figures are typical US examples and vary by provider and year.