[Verse 1] When bond prices move, they don't move straight Duration tells us the approximate rate But there's a curve that duration can't see A bend in the line called convexity Price goes up when yields fall down But the relationship's not linear all around There's a bow, a curve, a gentle bend That makes price changes accelerate in the end [Chorus] Convex curve, convex curve Price and yield don't move on a straight preserve When yields drop low, prices jump up high More than duration would imply Convex curve, convex curve Positive bend that investors observe The longer the bond, the bigger the bow Convexity's the extra boost we need to know [Verse 2] Duration gives us the first degree But convexity adds what we really need to see It's the second-order effect that matters most When interest rates change, it gives us a boost Imagine a smile drawn on a chart Yield on the x, price on the y-part The curve bends up, that's positive sign More gain when rates fall, protection when they climb [Chorus] Convex curve, convex curve Price and yield don't move on a straight preserve When yields drop low, prices jump up high More than duration would imply Convex curve, convex curve Positive bend that investors observe The longer the bond, the bigger the bow Convexity's the extra boost we need to know [Bridge] Duration estimates but can't be precise Convexity adds the mathematical spice For larger yield changes, duration falls short Convexity gives us the full report The curve gets steeper as maturity grows The bow gets bigger, that's how it goes Price sensitivity with an upward bend Convexity's the bond investor's friend [Chorus] Convex curve, convex curve Price and yield don't move on a straight preserve When yields drop low, prices jump up high More than duration would imply Convex curve, convex curve Positive bend that investors observe The longer the bond, the bigger the bow Convexity's the extra boost we need to know [Outro] Remember the curve, remember the bow Convexity's the secret that pros all know Duration plus convex gives the full view Bond price changes, now you know what to do
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