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

Two buckets in a risk class have bucket charges Kb1 = 60 and Kb2 = 80, with Sb1 = 40 and Sb2 = -80 (sum of weighted sensitivities in each bucket, floored/capped at Kb). The inter-bucket correlation is 0.25. Under the SBM, what is the delta charge for this scenario, with no alternative needed because the radicand is positive?

The charge is the square root of Kb1 squared plus Kb2 squared plus twice gamma times Sb1 times Sb2. That is the square root of 3,600 plus 6,400 minus 1,600, or about 91.7, closest to 91.4. Ignoring the negative cross term would give 100.

  1. AApproximately 91.4Correct
  2. BApproximately 100.0
  3. CApproximately 105.0
  4. DApproximately 111.4

Explanation

Charge = sqrt(60^2 + 80^2 + 2*0.25*40*(-80)) = sqrt(3600 + 6400 - 1600) = sqrt(8400) = 91.65. Nearest option is 91.4, which is the best match; 100 ignores correlation (sqrt of sum of squares), 105 uses wrong sign on the cross term inflated, and 111.4 adds the cross term with positive sign.

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