CFA Level IFixed IncomeHard
A callable bond currently trades at a price of 100.00. Using a 100 bp yield shock, its price rises to 101.80 when yields fall and falls to 97.90 when yields rise. The bond's effective duration is closest to:
- A4.85
- B2.90
- C1.95
- D3.90
Show answer & explanationAnswer & explanation
Correct answer: C. 1.95
Effective duration = (V₋ − V₊)/(2 × V₀ × Δy) = (101.80 − 97.90)/(2 × 100 × 0.01) = 3.90/2.00 = 1.95. The relatively small price increase when yields fall (versus the larger decline when yields rise) reflects negative convexity from the call feature, which caps upside price appreciation.
Why the other options are wrong
- A. Overstates duration; does not match the correctly applied formula.
- B. Miscalculates the denominator, likely omitting the factor of 2.
- D. This is the numerator alone (price spread), not the duration itself.
Effective Duration & Negative Convexity
Effective duration measures interest rate sensitivity using price shocks and is required for bonds with embedded options, whose cash flows change with yields; callable bonds exhibit negative convexity near the call price, limiting upside price gains.
- Effective duration formula: (V₋−V₊)/(2×V₀×Δy)
- Callable bonds show price compression (negative convexity) as yields fall toward the call price
- Effective duration must be used instead of modified duration for bonds with embedded options
Memory trick: Callable bonds hit a ceiling — upside gets capped.