FRM Part I · FRM Exam Part I · Interest Rates
A bond with a market value of USD 1,000,000 has a Macaulay duration of 7.2 years and a yield of 4% per year, compounded semiannually. What is the approximate DV01 of the position?
DV01 is about USD 705.88. Convert Macaulay duration to modified duration by dividing by one plus the periodic yield (1.02 for semiannual compounding), giving 7.0588. Multiplying by the USD 1,000,000 value and by one basis point (0.0001) gives the dollar change per basis point.
- AUSD 705.88Correct
- BUSD 720.00
- CUSD 692.31
- DUSD 7,058.80
Explanation
With semiannual compounding, modified duration = 7.2 / (1 + 0.04/2) = 7.2 / 1.02 = 7.0588. DV01 = 7.0588 × 1,000,000 × 0.0001 = USD 705.88. Dividing by 1.04 (annual compounding) gives 692.31, which is wrong because the yield is compounded semiannually. Using Macaulay duration directly gives 720.00, and 7,058.80 is off by a factor of ten.
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