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FRM Part II · FRM Exam Part II · Regression Hedging and Principal Component Analysis

A bank holds USD 50 million face of a 10-year bond with a DV01 of USD 0.0800 per USD 100 face value. It hedges with a 5-year bond with a DV01 of USD 0.0400 per USD 100 face value, assuming a parallel yield shift of equal size for both bonds. What face amount of the 5-year bond should be shorted?

The bank should short USD 100 million face of the 5-year bond. The 10-year position has DV01 of USD 40,000, and the 5-year bond has half the DV01 per unit of face, so twice the face amount is required to match sensitivity under a parallel shift.

  1. AUSD 25 million
  2. BUSD 50 million
  3. CUSD 100 millionCorrect
  4. DUSD 75 million

Explanation

Portfolio DV01 = 50,000,000/100 x 0.08 = USD 40,000. Hedge DV01 per USD 100 face is 0.04, so face needed = 40,000/0.04 x 100 = USD 100 million. USD 25 million inverts the ratio.

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