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

A risk manager notes that a historical simulation VaR at the 99% level using 250 daily observations is determined essentially by the 2nd or 3rd worst loss. Which is the most appropriate concern about this estimate?

The estimate suffers from high sampling error, because a 99% VaR from 250 observations depends on only two or three tail data points. A single extra or missing extreme loss can move VaR materially, making the estimate unstable.

  1. AIt is biased upward because it uses only losses beyond the mean
  2. BIt is subject to high sampling error because the estimate depends on very few tail observationsCorrect
  3. CIt will always be lower than the parametric normal VaR
  4. DIt cannot be computed because the sample is smaller than 500 observations

Explanation

At 99% with 250 observations, only about 2.5 observations lie in the tail, so the quantile estimate rests on very few points and is noisy. There is no rule that it is lower than normal VaR, and it can be computed with a smaller sample.

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