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FRM Part I · FRM Exam Part I · Modeling Non-Parallel Term Structure Shifts and Hedging

A portfolio has exposures (change in value per 1 bp rise in the rate) to the 2-year, 5-year and 10-year rates of -$40,000, -$10,000 and +$30,000 respectively. A PCA gives level-factor loadings of 1.0, 1.0 and 1.0 for the three rates, and slope-factor loadings of -1.0, 0.0 and +1.0. Using the PCA, what are the portfolio's sensitivities to a 1-unit move in the level factor and in the slope factor?

Level sensitivity is -$20,000 and slope sensitivity is +$70,000. Level equals the sum of exposures times loadings of 1: -40,000-10,000+30,000. Slope uses loadings -1, 0, +1: +40,000 + 0 + 30,000 = 70,000.

  1. ALevel -$20,000; slope +$70,000Correct
  2. BLevel -$20,000; slope -$70,000
  3. CLevel +$20,000; slope +$70,000
  4. DLevel -$80,000; slope +$70,000

Explanation

Level sensitivity = (-40,000)(1)+(-10,000)(1)+(30,000)(1) = -20,000. Slope sensitivity = (-40,000)(-1)+(-10,000)(0)+(30,000)(1) = 40,000+30,000 = +70,000. The sign error on the 2-year loading gives -70,000 or flips signs; summing absolute values gives -80,000.

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