CFA Level IFixed IncomeMedium
A bond currently priced at 100.00 is analyzed using a 50 bp yield shock in each direction. If yields fall by 50 bps, the price rises to 104.50; if yields rise by 50 bps, the price falls to 96.00. The bond's approximate modified duration is closest to:
- A8.50
- B6.75
- C4.50
- D9.00
Show answer & explanationAnswer & explanation
Correct answer: A. 8.50
Approximate modified duration = (V₋ − V₊)/(2 × V₀ × Δy) = (104.50 − 96.00)/(2 × 100 × 0.005) = 8.50/1.00 = 8.50.
Why the other options are wrong
- B. Incorrect; does not match the correct symmetric duration formula result.
- C. Too low; likely a miscalculation using only one price change instead of the symmetric difference.
- D. Overstates duration; check the denominator (2 × V₀ × Δy) calculation.
Approximate Modified Duration
A duration estimate calculated from bond prices after small upward and downward yield shocks: (V₋ − V₊)/(2 × V₀ × Δy).
- Requires prices at yield up and yield down scenarios
- V₀ is the initial (base) price
- Widely used for bonds without closed-form duration formulas, e.g., callable bonds
Memory trick: Shock it up, shock it down, split the difference.