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

A trader hedges a bond position against level and slope PCA factors using two hedging instruments. The bond has factor exposures of level 800 and slope 200 (USD per unit factor move). Hedge A has exposures level 100 and slope 50 per contract; Hedge B has level 100 and slope -50 per contract. How many contracts of A and B (long) should be sold to neutralize both exposures?

Set level hedge equal to 800: a plus b equals 8, and slope hedge equal to 200: a minus b equals 4. Solving gives 6 contracts of A and 2 of B. Only that combination neutralizes both level and slope exposures at once.

  1. ASell 5 of A and 3 of BCorrect
  2. BSell 4 of A and 4 of B
  3. CSell 6 of A and 2 of B
  4. DSell 3 of A and 5 of B

Explanation

Solve 100a+100b=800 and 50a-50b=200. So a+b=8 and a-b=4, giving a=6 and b=2. Therefore sell 6 of A and 2 of B. Option 5/3 gives slope 100 and the 4/4 gives slope 0; neither neutralizes slope 200.

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