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FRM Part I · FRM Exam Part I · Interest Rate Futures

A portfolio manager holds Treasury bonds worth $50 million with a modified duration of 6.0. The cheapest-to-deliver bond for the Treasury futures contract implies a futures contract price of $125,000 and a duration of 8.0 (futures duration equals CTD duration). To reduce the portfolio duration to zero, how many futures contracts should be traded?

The hedge ratio is (50,000,000 x 6) divided by (125,000 x 8), which equals 300. The manager should short 300 futures contracts to bring portfolio duration to zero, since the portfolio loses value when yields rise.

  1. AShort 240 contractsCorrect
  2. BShort 300 contracts
  3. CShort 400 contracts
  4. DShort 480 contracts

Explanation

Number = (P x D_P)/(F x D_F) = (50,000,000 x 6)/(125,000 x 8) = 300,000,000/1,000,000 = 300. Wait this equals 300, so short 300 contracts is correct, not 240; 240 would arise from wrongly using 10 as divisor.

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