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

An analyst regresses daily changes in the yield of a 10-year bond (dependent variable) on daily changes in the 10-year swap rate (independent variable) and obtains a slope of 0.90 and an R-squared of 0.80. The bond position has DV01 of USD 100,000 and the swap DV01 is USD 900 per unit. Using the regression hedge, how many swap units should be traded (in absolute terms)?

The hedge requires 100 swap units. Multiply the DV01 ratio of about 111.1 by the regression beta of 0.90. The beta adjusts for the bond yield moving 0.90 bp per 1 bp swap move; R-squared only indicates hedge effectiveness, not size.

  1. A100.0Correct
  2. B111.1
  3. C123.5
  4. D100.0 scaled by 0.80, i.e. 80.0

Explanation

Hedge units = (position DV01 / swap DV01) × beta = (100,000 / 900) × 0.90 = 111.11 × 0.90 = 100.0. Using no beta gives 111.1, dividing by beta gives 123.5, and multiplying by R-squared is incorrect because R-squared measures fit, not sensitivity.

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