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

A trader holds a position with a DV01 of USD 50,000 per basis point. She hedges with a Treasury futures contract with a DV01 of USD 80 per contract per basis point. A regression of the position's yield changes on the hedge instrument's yield changes gives a beta of 1.20. How many futures contracts should she short to minimise variance using the regression hedge?

She should short 750 contracts. The unadjusted DV01 hedge is 50,000 divided by 80, or 625 contracts, and multiplying by the regression beta of 1.20 gives 750. Beta scales the hedge because the position's yield moves 1.2 basis points per basis point of the hedge instrument.

  1. A750Correct
  2. B625
  3. C520
  4. D900

Explanation

Regression hedge: contracts = (position DV01 / contract DV01) x beta = (50,000/80) x 1.20 = 625 x 1.2 = 750. Ignoring beta gives 625. Dividing by beta gives 520.8, about 521, which is the inverted-beta mistake. 900 would come from multiplying by beta twice (625 x 1.2 x 1.2).

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