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FRM Part II · FRM Exam Part II · Risk Measurement and Assessment

In an operational risk capital model using a loss distribution approach, the bank aggregates frequency and severity by Monte Carlo simulation. Capital is set at the 99.9th percentile of the simulated annual loss distribution. If 100,000 annual loss scenarios are simulated and sorted from smallest to largest, which scenario approximately gives the capital figure?

With 100,000 simulated years sorted ascending, the 99.9th percentile is the 99,900th scenario, because 0.999 times 100,000 equals 99,900. The average of the largest 100 would be expected shortfall, not the percentile used for capital.

  1. AThe 99,900th ranked scenarioCorrect
  2. BThe 90,000th ranked scenario
  3. CThe 100th ranked scenario
  4. DThe average of the largest 100 scenarios

Explanation

The 99.9th percentile of 100,000 scenarios is at rank 0.999 x 100,000 = 99,900 when sorted ascending. The 100th rank would be the 0.1th percentile. Averaging the largest 100 gives expected shortfall, not VaR.

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