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FRM Part II · FRM Exam Part II · Fundamental Review of the Trading Book

A risk manager aggregates two buckets within a risk class under the SbM. Bucket capitals are K1 = 100 and K2 = 50, with net bucket sums S1 = 100 and S2 = -50, and inter-bucket correlation gamma = 0.40. Using sqrt(K1² + K2² + 2·gamma·S1·S2), what is the risk-class delta charge?

The risk-class charge is about 92.2. The squared bucket capitals total 12,500, and the cross term is 2 × 0.4 × 100 × (-50) = -4,000 because the net sums have opposite signs. The square root of 8,500 is roughly 92.2, reflecting diversification benefit between buckets.

  1. Asqrt(12,500 - 4,000) ≈ 92.2Correct
  2. Bsqrt(12,500 + 4,000) ≈ 128.5
  3. Csqrt(12,500) ≈ 111.8
  4. D150

Explanation

K1² + K2² = 10,000 + 2,500 = 12,500. Cross term = 2 × 0.4 × 100 × (-50) = -4,000. Result sqrt(8,500) ≈ 92.2. Using +4,000 ignores the offsetting sign of S2, and ignoring correlation gives 111.8.

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