Definition
Convexity is a measure of how the price sensitivity of a bond changes as interest rates change, capturing the curvature in the price-yield relationship that duration alone misses.
Why it matters
Convexity is the second-order refinement to duration in the analysis of interest rate risk. Where duration provides a linear approximation of how a bond's price responds to rate changes, convexity captures the fact that the response is actually curved, with the correction becoming material when rate moves are large.
How it works
Convexity is calculated from the same set of a bond's cash flows that duration uses, but it emphasizes flows that occur further in the future, because those flows are more sensitive to how the discounting curves. Higher convexity is favorable for a bondholder: when rates fall, a bond with high convexity gains more than duration alone predicts; when rates rise, the same bond falls less than duration alone predicts. A bond with duration of five years and moderate convexity might rise 5.2 percent when rates fall by one percentage point and fall only 4.8 percent when rates rise by one percentage point, where duration alone would predict a symmetric five percent move in either direction. The size of the convexity correction grows with the maturity of the bond and with the size of the rate change being analyzed.
In practice
For an individual holding bonds directly, convexity is usually not necessary to analyze in isolation. It becomes visible in comparative choices between bonds with similar durations: a bond with higher convexity is preferable when rates are expected to move by a large amount in either direction. For an individual evaluating a lifetime income product, convexity is not a quoted metric but is part of the insurer's asset-liability management. A well-managed general account matches not only the duration of assets to liabilities but also convexity, so that the two sides move together across both small and large rate changes.
Related terms
- Duration
- Yield curve
- Term structure of interest rates
- Present value
- Discount rate
- Asset-liability management
- Duration matching
- Bond