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

A bank uses historical simulation with a 250-day window and equal weights. The 99% VaR is the 3rd worst loss when losses are ranked, and the worst losses in the sample are 9.0, 7.5, 6.0 and 5.5 (USD million). The 2.5 days of data hold no information about losses beyond these. On day 251 the oldest observation, which was the worst loss of 9.0, drops out of the window and the new day's loss is small. What is the most likely effect and the best interpretation?

VaR falls from 6.0 to 5.5 million. When the 9.0 loss leaves the window, the third worst loss becomes 5.5 instead of 6.0. This abrupt change reflects the ghost effect, where an old extreme observation distorts VaR until it drops out, not any change in current risk.

  1. AVaR falls, because the new 3rd worst loss becomes 5.5 and 9.0 disappears; this shows the 'ghost effect' of a single old observationCorrect
  2. BVaR rises, because dropping an old observation increases the sample variance
  3. CVaR is unchanged, because the quantile is determined only by the newest observation
  4. DVaR falls to zero because the window now contains fewer extreme losses

Explanation

Before the drop, the ranked losses are 9.0, 7.5, 6.0 so the 3rd worst is 6.0. After the 9.0 drops out, the ranking is 7.5, 6.0, 5.5, so the 3rd worst becomes 5.5. VaR falls from 6.0 to 5.5 even though nothing changed in current conditions, a ghost effect caused by an old observation leaving the window.

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