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

A portfolio manager hedges a bond position using a PCA-based approach with the level and slope factors. The bond has a level factor exposure of +40,000 per unit of factor shock and a slope exposure of +10,000. Hedging instrument A has level exposure of +8,000 and slope exposure of 0. Instrument B has level exposure of +2,000 and slope exposure of +2,000. To neutralize both exposures, which positions are required?

Short 3.75 of instrument A and short 5 of instrument B. The slope exposure is hedged first using B alone, giving -5, and the level exposure remaining after B's contribution of -10,000 is hedged with A, giving -3.75.

  1. AShort 5 of A and short 5 of B
  2. BShort 3.75 of A and short 5 of BCorrect
  3. CShort 5 of A and short 3.75 of B
  4. DShort 6.25 of A and short 5 of B

Explanation

Slope: 10,000 + 2,000 b = 0 gives b = -5 (short 5 of B). Level: 40,000 + 8,000a + 2,000(-5) = 0 gives 8,000a = -30,000, so a = -3.75. Ignoring B's level contribution would give a = -5, which is wrong.

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