Convexity
Definition
Convexity is the second-order measure of a bond's price sensitivity to yields — it captures how duration itself changes as rates move. Because the price/yield relationship is curved, duration alone underestimates price gains when yields fall and overestimates losses when yields rise for a standard bond.
Plain-vanilla bonds have positive convexity, which is favorable: prices rise more for a given yield drop than they fall for the same yield rise. Callable bonds and mortgage-backed securities can exhibit negative convexity — when yields fall, the issuer's call option (or homeowners' refinancing) caps price appreciation, so the bond underperforms exactly when rates rally.
Practically: price change ≈ (−duration × Δy) + (½ × convexity × Δy²), so convexity matters most for large rate moves.
Why interviewers ask
This is the natural follow-up after you nail a duration question — 'why isn't duration enough?' or 'why do MBS have negative convexity?' Being able to explain that positive convexity means asymmetric, favorable price behavior, and that embedded call/prepayment options flip the sign, distinguishes candidates in markets and FIG interviews.
Related terms
Interviews don't test definitions — they test recall under pressure.
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