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FRM Part I · FRM Exam Part I · Applying Duration, Convexity, and DV01

A manager holds a $80 million bond portfolio with modified duration 6.25. She hedges the DV01 by shorting a Treasury bond that trades at 125 per 100 face value with modified duration 4.0. What face amount of the hedge bond must be sold short?

Short $100 million face of the hedge bond. The portfolio DV01 is $50,000, while the hedge bond has a DV01 of $500 per $1 million face because it trades at 125 with duration 4.0. Dividing 50,000 by 500 gives 100 million face.

  1. A$100 millionCorrect
  2. B$125 million
  3. C$80 million
  4. D$64 million

Explanation

Portfolio DV01 = 80m x 6.25 x 0.0001 = $50,000. Hedge bond DV01 per $100 face = 125 x 4.0 x 0.0001 = 0.05, i.e. $500 per $1 million face. Required face = 50,000 / 500 = $100 million. Using $125 million ignores that the bond trades at 125 and treats face as market value.

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