FRM Part I · FRM Exam Part I · Applying Duration, Convexity, and DV01
A 10-year zero-coupon bond with face value $1,000,000 has a yield of 5.00% per year with semiannual compounding. What is its DV01, rounded to the nearest $0.10?
The DV01 is about $595.4. The price is roughly $610,271, and modified duration is 10 divided by 1.025, or 9.756, so DV01 is 610,271 × 9.756 × 0.0001. Using Macaulay duration or annual compounding would give wrong values.
- A$610.3
- B$581.2
- C$297.7
- D$595.4Correct
Explanation
Price = 1,000,000 / 1.025^20 = 610,271. Modified duration = 10 / 1.025 = 9.7561 (Macaulay duration of a zero is its maturity). DV01 = 610,271 × 9.7561 × 0.0001 ≈ $595.4. Using Macaulay duration of 10 gives $610.3, ignoring the yield adjustment; using 10/1.05 gives $581.2, ignoring semiannual compounding.
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