How this calculator works
Duration gives the first-order change in a bond's price when the yield moves. Convexity captures the curvature that remains: price rises more when yields fall than it loses when yields rise by the same amount. This calculator prices the bond at the current yield, at the yield plus the shift and at the yield minus the shift, then applies the standard finite-difference second derivative. All shifts are in periodic terms, so an annual shift of 1% on a semi-annual bond is applied as 0.5% per period. A higher convexity is favourable to the holder, and longer maturities and lower coupons generally produce more of it.
Formula
Convexity = (P- + P+ - 2 P0) / (P0 x (change in yield)^2), where P0, P+ and P- are prices at the current yield, the yield plus the shift, and the yield minus the shift. The yield change is per coupon period: annual shift / frequency.
Worked example
A $1,000 bond with a 5% semi-annual coupon and 10 years left is priced at a 5% yield. A 1% annual yield shift means pricing the bond at 4% and 6%, which gives $1,081.76 at the lower yield and $925.61 at the higher one against a $1,000 base price. The convexity is (1,081.76 + 925.61 - 2,000) / (1,000 x 0.005^2) = 294.79 in period-squared units.
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Frequently asked questions
What is convexity used for?
It improves the estimate of a price change for a larger yield move. Duration alone is linear; adding half of convexity times the squared yield change captures the curve of the price-yield relationship.
Why is convexity not shown as a percentage?
It is a second-order sensitivity with units of periods squared. Analysts usually combine it with duration: percentage price change is about -duration x change in yield + 0.5 x convexity x (change in yield)^2.
Does a bigger yield shift change the answer?
Yes. Convexity is a local measure, and a finite difference over a wider shift samples the curve further from the point and produces a different estimate. Use the same shift when comparing bonds.
What about callable bonds?
A callable bond's price-yield curve can bend the other way near the call price, giving negative convexity. The plain discounting used here assumes the bond runs to maturity.