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

A single-variable regression hedge regresses daily changes in the yield of a bond being hedged (dependent variable) on daily changes in the yield of a hedging instrument. The estimated beta is 1.20. The bond's DV01 is USD 12,000 and the hedging instrument has a DV01 of USD 400 per USD 1 million face. What face amount of the hedging instrument should be sold, ignoring the regression's error term?

Sell USD 36 million face of the hedging instrument. The naive DV01 hedge is 12,000 divided by 400, or 30 million, and it is scaled up by the regression beta of 1.20 because the bond's yield moves 1.2 times as much as the hedge's yield.

  1. AUSD 30 million
  2. BUSD 25 million
  3. CUSD 36 millionCorrect
  4. DUSD 21 million

Explanation

Regression hedge: F = (DV01 of bond / DV01 of hedge) x beta = (12,000/400) x 1.20 = 30 x 1.20 = 36 million. Ignoring beta gives 30 million, the naive DV01 hedge. Dividing by beta gives 25 million, a common inversion error.

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