Convexity.

In plain English

Convexity captures the curvature in the relationship between a bond's price and its yield, correcting the straight-line estimate that modified duration provides on its own. Most ordinary bonds have positive convexity, which means prices rise a bit more when rates fall than they drop when rates rise by the same amount. That asymmetry works in the holder's favor and is one reason two bonds with identical duration can behave differently in a large rate move. Mortgage-backed securities can show negative convexity, because homeowners refinance when rates fall, cutting short the bonds that would otherwise have gained the most. The effect is small for tiny rate changes and grows with the size of the move.

01Why it matters

Duration alone understates a bond's gain when rates fall and overstates its loss when rates rise, and convexity is the correction that makes the estimate honest for large moves.

02The math, step by step

A bond has a modified duration of 8. Duration alone predicts that a 2 point rate rise costs 16 percent and a 2 point drop gains 16 percent. With positive convexity the actual result might be a 14.5 percent loss and a 17.5 percent gain. The curve is worth about 1.5 points in each direction.

Illustrative example. The amounts here are hypothetical, chosen to show how the math works, not real quoted rates or figures.

03What this is NOT

04Receipts

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