Groundlearn / Calculators / Duration and convexity
Duration and convexity calculator
Price a fixed-coupon bond, measure its duration and convexity, and see how well the approximation tracks the exact price change.
Calculator
- Price
- 100.0000
- Macaulay duration
- 8.1078
- Modified duration
- 7.7217
- Convexity
- 75.00
- Duration effect
- −7.72%
- Convexity effect
- +0.37%
- Estimated price change
- −7.35%
- Exact (repriced)
- −7.36%
- Estimate error
- 0.013 pp
−7.7217 × +0.0100 × 100 = −7.72%, plus ½ × 75.00 × 0.0100² × 100 = +0.37%, giving −7.35%.
| Shock | Duration only | With convexity | Exact |
|---|---|---|---|
| −200 bp | +15.44% | +16.94% | +17.06% |
| −100 bp | +7.72% | +8.10% | +8.11% |
| −50 bp | +3.86% | +3.95% | +3.96% |
| +50 bp | −3.86% | −3.77% | −3.77% |
| +100 bp | −7.72% | −7.35% | −7.36% |
| +200 bp | −15.44% | −13.94% | −14.05% |
How it works
The calculator prices the bond from its cash flows, then measures how sensitive that price is to the yield. Macaulay duration is the present-value-weighted average time to the cash flows. Modified duration divides it by one plus the periodic yield and gives the percentage price change for a one-unit change in yield. Convexity captures the curvature that duration misses.
%ΔP ≈ −Dmod × Δy + ½ × C × (Δy)²
Δy is in decimals, so 100 bp is 0.01. Duration alone always overstates the fall when yields rise and understates the gain when they fall, for an option-free bond. Adding convexity closes most of the gap; the exact column reprices the bond at the new yield so you can see what is left. Convexity here is quoted in years squared, on the same annual basis as duration.
The calculator assumes the price falls on a coupon date (no accrued interest), a flat yield and no embedded options. For callable or mortgage-backed bonds, use effective duration and convexity instead.
Worked example
A 10-year bond with a 5% annual coupon, yielding 5%, prices at par. Modified duration is 7.7217 and convexity 75.00. For a +100 bp shock, duration gives −7.72% and convexity adds +0.37%, an estimate of −7.35% against an exact −7.36%. The duration and convexity guide walks through the same bond.
Related
- Duration and convexityThe full guide with a shock table.
- Bond price on the BA II PlusKeystrokes for pricing the same bond.
- Modified durationGlossary definition with the exam angle.
- ConvexityGlossary definition with the exam angle.
- Effective durationFor bonds with embedded options.
- All calculatorsVaR scaling, swap valuation.
Educational content only. This is not financial, investment, legal or regulatory advice. Results are illustrations under the stated assumptions, not a valuation of any real security.
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