Bond Convexity Calculator
Estimate bond price sensitivity using duration and convexity. Enter your bond assumptions below.
What Is Bond Convexity?
Convexity measures how much a bond’s duration changes as yields move. Duration gives a linear estimate of price sensitivity, while convexity adds the curve. Because bond price/yield relationships are curved, convexity improves your estimate of price changes, especially when rate moves are large.
In practical terms, higher positive convexity is usually desirable: when yields fall, prices rise more than duration alone predicts; when yields rise, prices fall less than duration alone predicts. This asymmetry is one reason many fixed-income investors monitor convexity alongside yield and duration.
How This Convexity Calculator Works
Inputs
- Face Value: Principal paid at maturity.
- Coupon Rate: Annual coupon rate on face value.
- Yield to Maturity: Market discount rate used to price cash flows.
- Years to Maturity: Remaining life of the bond.
- Payments per Year: Coupon frequency (annual, semiannual, etc.).
- Yield Shift: Scenario change in rates for price-impact estimation.
Outputs
- Bond Price based on discounted cash flows.
- Macaulay Duration (years): weighted average time to cash flow receipt.
- Modified Duration (years): first-order price sensitivity to yield changes.
- Convexity (years²): second-order adjustment to improve the duration estimate.
- Scenario Price Impact using duration only, duration + convexity, and exact repricing.
Why Duration Alone Is Not Enough
Modified duration assumes the price/yield curve is a straight line over the change in yield. That is fine for tiny shifts, but accuracy deteriorates when yields move more. Convexity adds curvature and usually narrows the gap between an estimate and the true repriced value.
The common approximation is:
ΔP / P ≈ −Dmod × Δy + 0.5 × Convexity × (Δy)2
where Δy is the yield change in decimal form (for example, +100 bps = +0.01).
Worked Example
Suppose a $1,000 bond has a 5% coupon, 10 years to maturity, semiannual payments, and current yield of 4.5%. If yields rise by 100 basis points:
- Duration-only estimate predicts a price drop.
- Adding convexity slightly offsets that drop.
- Exact repricing is typically closest to the duration+convexity estimate.
You can test this directly in the calculator by changing only the yield shift field and comparing the three scenario outputs.
Interpretation Tips
1) Compare Bonds on Similar Terms
Convexity is most useful when comparing instruments with similar credit quality, maturity range, and liquidity. A higher convexity profile can offer better risk behavior, but yield and spread still matter.
2) Keep Units Consistent
This page annualizes duration and convexity outputs in years and years². Make sure your yield shifts are annual decimal changes when applying formulas outside this tool.
3) Remember the Assumptions
The calculator assumes a plain-vanilla fixed coupon bond and parallel yield shifts. Real portfolios may include callable bonds, non-parallel curve moves, spread changes, and reinvestment effects.
Common Uses for a Convexity Calculator
- Bond portfolio risk analysis and stress testing
- Comparing duration-matched bonds with different curvature
- Interest-rate scenario planning for treasury teams
- Fixed-income education and CFA-style exam practice
Final Thoughts
Convexity is one of the most practical concepts in fixed-income analytics. If you already use duration, adding convexity is the next step toward better risk estimates. Use this calculator as a fast check, then complement it with full curve and spread analysis for investment decisions.