Convexity
The curvature in the relationship between a bond's price and its yield, correcting duration's straight-line estimate.
Formula
Price Change % = -Modified Duration x Change in Yield + 0.5 x Convexity x (Change in Yield) squared
Unit
ratio (x, times)
In depth
Because the price-yield relationship curves rather than running straight, duration alone overstates losses when yields rise and understates gains when they fall — an asymmetry that favours the bondholder. Positive convexity is therefore a desirable property, and it is greater for longer maturities and lower coupons. Callable bonds and mortgage-backed securities can display negative convexity, where the asymmetry runs the other way and the holder gets the worst of both directions. Convexity matters only for large yield moves; for a 25 basis point change, duration alone is accurate enough.
Worked example
Modified duration 3.95 and convexity 22, with yields rising one point: price change = -3.95 x 1 + 0.5 x 22 x 0.01 x 1 = -3.95 + 0.11 = -3.84%. Duration alone predicted -3.95%, so convexity saved 0.11 points.
Illustrative figures, chosen so the arithmetic is easy to follow. Not a live price and not a valuation of any company.
Educational reference only
This entry explains what “Convexity” means. It is not investment advice and not a recommendation to buy or sell any security. Any numbers above are illustrative, not live prices, and nothing here predicts price direction or rates a stock. Consider your own circumstances and consult a SEBI-registered investment adviser before acting.