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

A bank's FX desk has two net delta sensitivities within the same risk-class bucket, after risk weighting: WS1 = 60 and WS2 = 80 (USD millions). The prescribed intra-bucket correlation is 0.50. What is the bucket-level delta capital before any scenario or floor adjustment, using K = sqrt(sum WS² + sum over j≠k of rho·WS_j·WS_k)?

The bucket capital is about 121.7. The squared risk-weighted sensitivities sum to 10,000, and the correlation term adds 2 × 0.5 × 60 × 80 = 4,800. The square root of 14,800 is roughly 121.7. Counting the cross term only once understates the result.

  1. Asqrt(10,000) = 100
  2. Bsqrt(10,000 + 4,800) ≈ 121.7Correct
  3. Csqrt(10,000 + 2,400) ≈ 111.4
  4. D140

Explanation

Sum of squares = 3,600 + 6,400 = 10,000. Cross term counts both j,k and k,j: 2 × 0.5 × 60 × 80 = 4,800. K = sqrt(14,800) ≈ 121.7. Omitting the factor of 2 gives 111.4 (wrong); ignoring correlation gives 100.

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