FRM Part I · FRM Exam Part I · Interest Rates
A manager holds a $50 million bond portfolio with a modified duration of 6.0 and wants to reduce its duration to 2.0 using Treasury bond futures. Each futures contract is priced at $120,000 and has a duration of 8.0. Which position is closest to the required hedge?
Short about 208 contracts. The duration-based hedge is (2 - 6) x $50 million divided by (8 x $120,000), which is about -208.3. The negative sign means selling futures. Shorting 313 would remove all duration, which overshoots the target of 2.
- ALong 208 contracts
- BShort 104 contracts
- CShort 208 contractsCorrect
- DShort 313 contracts
Explanation
Contracts = (target duration - current duration) x P / (futures duration x futures price) = (2 - 6) x 50,000,000 / (8 x 120,000) = -200,000,000 / 960,000 = -208.3, so short about 208. Short 313 is the full hedge to zero duration (6 x 50m / 960,000 = 312.5). Short 104 uses the target duration instead of the change.
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