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L.1 · ADVANCED · 2 MIN

Convexity: When Duration Is Not Enough

Duration gives a linear approximation of price sensitivity to rate changes. But bond prices actually move in a curve. Convexity measures this curvature — and it matters most when rates move significantly.

Quiz · 5 questions ↓
§ 01
ΔPrice ≈ −Duration × ΔYield + ½ × Convexity × (ΔYield)²
§ 02

Positive convexity (most bonds) means the bond gains more when rates fall than it loses when rates rise by the same amount. This asymmetry is valuable and is why investors are willing to accept lower yields on high-convexity bonds.

§ 03
Compare the price change of a 10-year bond when rates move ±50bps vs. ±200bps. The larger the rate move, the more convexity matters relative to duration.
§ 04
Two bonds have the same duration but Bond A has higher convexity. Which performs better in a large rate move (either direction)?
§ 05

Mortgage-backed securities have negative convexity — they underperform in both rising rates (duration extends) and falling rates (prepayments accelerate, cutting gains). This is why MBS yields include a convexity premium.

§ 06
Two bonds, same duration 8.0. Bond A has convexity 80, Bond B has convexity 60. Rates fall 1%. Which bond gains MORE?
Five questions · AI feedback

Sit with the ideas.

A bond has duration of 7 years and convexity of 60. Rates drop 2%. What is the approximate price change?

Why:

Other lessons in this course.

  1. 01Convexity: When Duration Is Not Enough— reading now
  2. 02Yield Curve Strategies: Bullets, Barbells, and Ladders
  3. 03Credit Default Swaps: Insurance on Bonds
  4. 04Structured Credit: CLOs, MBS, and ABS
  5. 05Distressed Debt Investing
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