CFA Level II ExamFixed IncomeEasy
A fixed-income analyst is evaluating a non-callable, option-free bond with a 5-year maturity, a 6% annual coupon rate, and a current yield to maturity (YTM) of 5%. If the YTM instantaneously increases by 10 basis points, what is the approximate percentage change in the bond's price, assuming a modified duration of 4.35 years?
- A-0.4350%
- B-4.3500%
- C-0.8700%
- D-0.0435%
Show answer & explanationAnswer & explanation
Correct answer: A. -0.4350%
The approximate percentage change in bond price can be calculated using modified duration: % Change in Price = -Modified Duration × Change in YTM. Given a modified duration of 4.35 and a change in YTM of 0.0010 (10 basis points), the calculation is -4.35 * 0.0010 = -0.00435 or -0.4350%.
Why the other options are wrong
- B. This option implies a 100 basis point change, not 10 basis points, making it too large.
- C. This option likely doubled the change, which is incorrect.
- D. This option incorrectly moves the decimal place; the change in YTM must be expressed as a decimal (0.0010).
Modified Duration Price Change
Modified duration estimates the percentage change in a bond's price for a 1% (100 basis point) change in its yield to maturity. It quantifies interest rate risk.
- Formula: %ΔP ≈ -Modified Duration × ΔYTM
- Higher modified duration implies greater price sensitivity to yield changes.
- It is a linear approximation and works best for small yield changes.
Memory trick: Duration's percentage dip shows price's quick flip.