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

A portfolio has key-rate DV01 exposures of +$40,000 at the 2-year, -$10,000 at the 5-year and -$20,000 at the 10-year (per 1 bp fall in the rate, in dollars). PCA gives a level factor with a shift of 1 bp at each of the three key rates per unit of the factor. Using the 3 key rates only, what is the portfolio's change in value per unit of the level factor? (Treat the stated exposures as the value change per 1 bp fall; the factor is a 1 bp fall in all rates.)

The portfolio gains $10,000 per unit of the level factor. A 1 bp fall in all three key rates changes value by the sum of the key-rate exposures: 40,000 minus 10,000 minus 20,000 equals plus 10,000.

  1. A+$10,000Correct
  2. B+$70,000
  3. C-$10,000
  4. D+$30,000

Explanation

For a 1 bp fall at every key rate, the value change is the sum of key-rate exposures: 40,000 - 10,000 - 20,000 = +10,000. Summing absolute values (70,000) ignores the signs, and -10,000 reverses the sign. The portfolio is therefore only modestly exposed to level shifts.

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