CFA Level IFixed IncomeHard
A bond has a modified duration of 7.5 and a convexity of 85. If the bond's yield to maturity suddenly increases by 100 basis points, the estimated percentage change in the bond's price, incorporating both duration and convexity effects, is closest to:
- A-7.93%
- B-7.50%
- C-7.08%
- D-6.65%
Show answer & explanationAnswer & explanation
Correct answer: C. -7.08%
%ΔP ≈ −(ModDur × Δy) + 0.5 × Convexity × (Δy)² = −(7.5 × 0.01) + 0.5 × 85 × (0.01)² = −0.0750 + 0.00425 = −0.07075, or approximately −7.08%.
Why the other options are wrong
- A. Incorrectly subtracts the convexity term instead of adding it.
- B. This is the duration-only estimate, omitting the convexity adjustment.
- D. Overstates the convexity adjustment's magnitude.
Duration-Convexity Price Approximation
The full approximation for a bond's percentage price change combines the linear duration effect and the curvature convexity effect: %ΔP ≈ −ModDur×Δy + 0.5×Convexity×(Δy)².
- Convexity term is always added, improving accuracy for large yield changes
- Positive convexity benefits bondholders in both rising and falling yield scenarios
- Duration-only estimates understate price increases and overstate price decreases
Memory trick: Duration is the line, convexity is the curve that saves you.