Bond convexity calculator
Duration tells you roughly how much a bond's price moves when yields change; convexity corrects that estimate for the curve of the price–yield relationship. Enter the face value, coupon rate, yield to maturity, years left and coupon frequency, then a yield shift in percentage points. You get the price, both durations, convexity, the estimated price change and the exact change from repricing the bond.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Enter the face value, the yearly coupon rate and the yield to maturity.
- Enter the years to maturity and the coupons per year.
- Enter a yield change in percentage points, for example 1 or −0.5.
With f coupons a year, N periods, a yield per period i = y ÷ f and cash flows CF_k:
- Price P = Σ CF_k ÷ (1 + i)^k
- Macaulay duration = Σ k × PV_k ÷ P ÷ f; modified = Macaulay ÷ (1 + i)
- Convexity = Σ CF_k × k(k + 1) ÷ (1 + i)^(k+2) ÷ P ÷ f²
- ΔP ÷ P ≈ −modified × Δy + ½ × convexity × Δy²
The exact change reprices the bond at the new yield. The bond is valued on a coupon date.
Worked example
A 10-year bond with a 5 % semiannual coupon at a 6 % yield:
- Price 925.61, Macaulay duration 7.895 years, modified 7.665, convexity 71.7854.
- For +1 point: duration alone says −7.665 %; with convexity −7.3061 %.
- Repricing at 7 % gives −7.318 % and a price of 857.88.
A 2-year 10 % annual bond at par has a price of 1,000, a Macaulay duration of 1.9091 and a convexity of 4.6582.
Tips
- Zero-coupon and long bonds have the most convexity; callable bonds can have negative convexity, which this plain-bond formula does not show.
- For small yield moves duration alone is enough; convexity matters for moves of a point or more.
- Some sources quote convexity divided by 100 or by 2; check the convention before comparing numbers.
Frequently asked questions
What is bond convexity?
It measures how duration itself changes as yields move. Price falls less when yields rise and gains more when they fall than duration alone predicts; convexity captures that bend. For a 10-year zero-coupon bond at 5 % with annual compounding it is 10 × 11 ÷ 1.05² = 99.77.
How do I estimate a price change with convexity?
% change ≈ −modified duration × Δy + ½ × convexity × Δy², with Δy as a decimal. For the 10-year zero at 5 % and +1 point: −9.5238 % + ½ × 99.7732 × 0.0001 = −9.0249 %, close to the exact −9.0434 %.
Why is convexity good for the holder?
The convexity term ½ × C × Δy² is positive whichever way yields move, so a bond with more convexity loses less when yields rise and gains more when they fall than a bond with the same duration and less convexity.
What units is convexity in?
Years squared, like duration in years. The calculator works per coupon period and divides by the frequency squared, so results for annual and semiannual bonds are comparable.