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

Under the FRTB standardised approach default risk charge (DRC) for securitizations, a bank holds a long position with net jump-to-default (JTD) of 40 and a short position in a different tranche with net JTD of -30 (loss to short is a gain). Risk weights are 10% for the long and 10% for the short. Assume the two positions fall in the same bucket and a hedge benefit ratio (HBR) applies: HBR = net long JTD / (net long JTD + |net short JTD|). The bucket capital is: long weighted JTD minus HBR times |short weighted JTD|. What is the bucket capital charge?

Hedge benefit ratio is 40 divided by 70, or 0.571. Long weighted JTD is 4.00 and short weighted JTD is 3.00, so the capital is 4.00 minus 0.571 times 3.00, equal to about 2.29. Using 0.429 instead would wrongly understate the offset.

  1. A4.00 - 3.00 = 1.00
  2. B4.00 - 0.571 × 3.00 = 2.29
  3. C4.00 - 0.429 × 3.00 = 2.71Correct
  4. D4.00 + 3.00 = 7.00

Explanation

HBR = 40 / (40 + 30) = 0.5714. Applying the stated formula gives 4.00 - 0.5714 × 3.00 = 2.286, which is the second option. Checking: 0.5714 × 3.00 = 1.714, and 4.00 - 1.714 = 2.286. So the correct figure is 2.29, not 2.71, which comes from using 1 - HBR (0.429) as the offset. Option 4 ignores netting entirely and option 1 gives full offset.

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