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

A portfolio manager has a bond position with a DV01 of 50,000 USD per basis point. She hedges using a level factor whose loadings on the 5-year and 10-year yields are 1.0 and 0.9 respectively (bp of yield change per unit factor move). Her position is exposed at the 10-year point, and she hedges with 5-year instruments only. Based on factor loadings, how many bp of 5-year yield change should she assume to be equivalent to a 1 bp move in the 10-year yield for hedging under a one-factor level model?

A 1 bp move in the 10-year yield corresponds to about 1.11 bp in the 5-year yield. The factor moves 1/0.9 = 1.11 units, and the 5-year loading of 1.0 scales it to 1.11 bp. Using 0.90 inverts the loading ratio.

  1. AAbout 0.90 bp
  2. BAbout 1.11 bpCorrect
  3. CAbout 1.90 bp
  4. DExactly 1.00 bp

Explanation

Under a one-factor model, the 10-year yield change is 0.9 times the factor and the 5-year change is 1.0 times the factor. A 1 bp 10-year move means factor = 1/0.9 = 1.11, so the 5-year moves 1.11 bp. Using 0.90 inverts the ratio.

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