Bond Convexity, explained.
Bond convexity measures the curvature of the price–yield relationship, supplementing duration’s first-order sensitivity.
Why it happens
A face-100 annual bond pays coupons of five. Exact discounted cash flows are compared with a linear duration approximation and a quadratic approximation using the second derivative at a 5% baseline yield.
Bond convexity measures the curvature of the price–yield relationship, supplementing duration’s first-order sensitivity.
Read the result
Compare exact price and both approximations at the selected yield shift. A convexity measure is a sensitivity, not a return forecast.
A worked example
Reprice a fixed-coupon bond
Start with the face-one-hundred bond paying five annually at a five-percent yield.
Move the yield by one percentage point and compare linear and quadratic estimates with exact discounting.
Try a larger move or longer maturity to inspect where a local approximation becomes less accurate.
OPTIONAL DEEPER DETAILGo deeper: inside the model
Inside this model
A face-100 annual bond pays coupons of five. Exact discounted cash flows are compared with a linear duration approximation and a quadratic approximation using the second derivative at a 5% baseline yield.
Where this idea is useful
A practical use
When a yield move is large, inspect approximation error instead of extending a local linear sensitivity without qualification.
A common misconception
“Duration exactly predicts every yield-driven price change.”
Duration is a first derivative evaluated locally. Convexity adds curvature, and even the second-order approximation can diverge for larger changes.
What this explanation leaves out
- This annual-pay option-free bond omits default, embedded options, day-count conventions and nonparallel yield changes.
Do all bonds have this same positive curvature?
No. Embedded options and changing cash flows can alter the relationship; this board uses an option-free fixed-payment bond.
How large a move can your local sensitivity reasonably approximate?
Associated thinkers
Associations marked provisional are awaiting source review.
Further reading
Explore the original research or the teaching reference behind this experiment.