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

A bank uses BRW-weighted historical simulation. Sorted losses (largest first) and their weights are: 12m (weight 0.02), 9m (0.02), 7m (0.03), 5m (0.04), 4m (0.05), 3m (0.84). What is the 95% VaR if the chosen convention is the smallest loss whose cumulative weight from the worst loss reaches at least 5%?

VaR is 7 million. Accumulating weights from the largest loss gives 2%, 4%, then 7% at the 7 million loss. That is the first point where tail weight reaches at least 5%, so it is the 95% VaR under this convention.

  1. A9m
  2. B7mCorrect
  3. C5m
  4. D12m

Explanation

Cumulative weights from the worst loss: 12m = 0.02, 9m = 0.04, 7m = 0.07. The 5% tail threshold is first reached at the 7m loss (0.07 >= 0.05). The 9m loss is wrong because cumulative weight there is only 4%, below 5%.

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