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

A portfolio has a DV01 of $50,000 to a 2-year loading and $30,000 to a 10-year loading, both expressed as dollar loss per 1bp rise. Factor 1 (level) loads +1 and +1 on the 2-year and 10-year rates. Factor 2 (slope) loads -1 on the 2-year and +1 on the 10-year. What is the portfolio's loss per one-unit shock to each factor, (level, slope)?

The level exposure is a loss of $80,000 per unit and the slope exposure has magnitude $20,000. Level adds the two DV01s, 50,000 plus 30,000. Slope loads -1 on the 2-year and +1 on the 10-year, giving -50,000 plus 30,000, a net gain of $20,000 for steepening.

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

Explanation

Loss for factor k = sum of DV01 times loading. Level: 50,000(1)+30,000(1) = 80,000. Slope: 50,000(-1)+30,000(1) = -20,000, meaning a gain of $20,000 for a steepening shock; the magnitude is 20,000. Option with 80,000 for slope ignores the sign of the loading, and the reversed options swap the factors.

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