Positive & Negative Convexity
Whether rate moves work for you or against you — and why mortgages are the classic trap.
Duration is a straight-line estimate of price change; convexity is the curvature it misses. The sign of convexity tells you whether that curvature helps or hurts.
Positive convexity (good)
Prices rise more when rates fall than they drop when rates rise by the same amount — a favorable asymmetry. Plain (option-free) bonds have positive convexity. You'd happily own it for free.
Negative convexity (the trap)
Prices rise less when rates fall and drop more when rates rise. This comes from embedded options held by the borrower — most importantly prepayment in mortgages and MBS, and call features. When rates fall, borrowers refinance and your high-yield asset disappears just when you'd want to keep it; when rates rise, prepayments slow and your duration extends into the selloff. Heads you lose, tails you lose less.
Why it matters for a balance sheet
A book heavy in MBS, callable bonds, or prepayable mortgages behaves worse than its duration suggests in both directions — a critical thing to model in rate-shock scenarios.
How PhxIQ relates
The mortgage rate vs. the 10Y on the dashboard is the spread that drives prepayment incentive — when it compresses and rates fall, negative convexity bites.