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

A portfolio manager uses age-weighted historical simulation with lambda = 0.95 to compute 95% VaR. After sorting losses from largest to smallest, the weights of the largest losses are: loss 12m (weight 0.020), loss 10m (weight 0.031), loss 8m (weight 0.015), loss 7m (weight 0.040), loss 6m (weight 0.012). The next loss is 5m. Using the simple approach of accumulating weights from the worst loss until the tail probability reaches 5%, which loss is the 95% VaR?

The 95% VaR is 10m. Accumulating weights from the largest loss, 12m contributes 0.020 and 10m brings the total to 0.051, which exceeds the 5% tail probability, so the 10m loss is the quantile.

  1. A7mCorrect
  2. B8m
  3. C10m
  4. D6m

Explanation

Cumulative weights from the worst loss: 12m: 0.020; 10m: 0.051. That already exceeds 5% at 10m, so the VaR is 10m under the rule 'first loss where cumulative weight reaches 5%'. Correction needed: 0.020 + 0.031 = 0.051 >= 0.05, so VaR is 10m.

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