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FRM Part II · FRM Exam Part II · Non-parametric Approaches

A bank uses age-weighted historical simulation on 10 sorted losses. Sorted from worst, the losses and their assigned weights are: 12 (0.05), 9 (0.10), 7 (0.10), 6 (0.15), 5 (0.20), and the rest are smaller losses or gains with the remaining weight of 0.40. The risk manager wants the 1-day VaR at 85% confidence, using the convention that VaR is the loss at which cumulative weight from the worst loss first reaches or exceeds 15%. What is the VaR?

Accumulate weights from the worst loss: 12 carries 5%, then 9 brings the total to exactly 15%. Under the rule that VaR is the first loss where cumulative weight reaches 15%, VaR is 9. Using equal weights or the strictly exceeding rule would give different answers.

  1. A9
  2. B12
  3. C7Correct
  4. D6

Explanation

Cumulative weights from the worst: 12 → 0.05; 9 → 0.15; At 9 the cumulative weight reaches 0.15 exactly, so under the stated 'reaches or exceeds' convention VaR is 9... check: 0.05+0.10 = 0.15, which meets 15%. So VaR is 9. Option 7 would apply an 'exceeds strictly' rule, and 12 ignores the weights.

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