Lesson 3 of 6 · All lessons in this module
  1. Convexity: measuring the curve
  2. What drives convexity, and why investors value it
  3. Estimating price changes with duration and convexityVideo lesson
  4. Integrated cases: a negative-yield zero priced by hand
  5. Money convexity: the adjustment in currency
  6. Portfolio duration and convexityVideo lesson

Lesson 3 of 6 · 13 min

Estimating price changes with duration and convexity

Add the convexity adjustment, half of convexity times the squared yield change, to the duration estimate, and the price-change estimate moves much closer to the truth.

In short

  • %ΔPVFull≈(−AnnModDur×Δy)+12×AnnConvexity×(Δy)2\%\Delta PV^{Full} \approx (-\text{AnnModDur} \times \Delta y) + \tfrac{1}{2} \times \text{AnnConvexity} \times (\Delta y)^2.
  • The first term is the duration effect; its sign depends on the direction of the yield change.
  • The second term, the convexity adjustment, is always added for an option-free bond, because (Δy)2(\Delta y)^2 is positive.
  • So the estimated gain when yields fall is bigger than the estimated loss when yields rise by the same amount.
  • The improvement matters most for large yield changes, long maturities and low coupons.

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