| name | calculate-bond-duration-convexity |
| description | Use when assessing how sensitive a bond or bond portfolio's price is to a change in interest rates — calculating duration as the first-order approximation of price sensitivity and convexity as the correction for how that sensitivity itself changes as rates move, rather than assuming a bond's rate sensitivity is constant regardless of the size of the rate change. |
| source | Frederick Macaulay, "Some Theoretical Problems Suggested by the Movements of Interest Rates, Bond Yields and Stock Prices in the United States since 1856" (1938) — Macaulay duration; standard fixed-income risk literature |
| tags | ["finance","investing","duration","convexity","interest-rate-risk","fixed-income","bond-risk"] |
| related | ["design-bond-ladder","apply-active-bond-total-return-management","calculate-value-at-risk"] |
Calculate Bond Duration and Convexity
Assess how sensitive a bond or bond portfolio's price is to a change in interest rates by calculating duration — the first-order approximation of price sensitivity to a small rate change — and convexity, the correction accounting for how that sensitivity itself changes as rates move further, rather than assuming a bond's interest-rate sensitivity remains constant regardless of the size of the rate change.
Why This Is Best Practice
Adopted by: Frederick Macaulay introduced the duration concept in his 1938 study of interest rates and bond yields, and Macaulay duration (along with its modified-duration variant) has since become the standard measure of bond interest-rate sensitivity taught and applied throughout fixed-income investment practice, with convexity as its standard companion correction documented across fixed-income risk management literature.
Duration alone provides an accurate approximation of price sensitivity only for small interest-rate changes — for larger rate moves, the actual price change deviates from the duration-based linear approximation, and this deviation (convexity) can be substantial for longer-duration bonds or bonds with embedded options, meaning a risk assessment based on duration alone can meaningfully understate or overstate actual price sensitivity for larger rate moves.
Treating a bond's interest-rate sensitivity as a single constant figure (duration alone) ignores that this sensitivity itself changes as rates move — convexity specifically captures this second-order effect, and combining both measures produces a substantially more accurate estimate of a bond's actual price behavior across a realistic range of rate-change scenarios than duration alone would provide.
