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

An analyst estimates 99.9% one-day VaR from 500 daily historical returns. Which concern is most relevant to this estimate?

With only 500 observations, a 99.9% quantile has about half an observation beyond it, so the estimate is very imprecise and cannot exceed the worst loss in the sample. Non-parametric methods cannot extrapolate beyond observed data, unlike extreme value approaches.

  1. AVery few observations lie beyond the 99.9% quantile, so the estimate is highly imprecise and cannot exceed the worst observed lossCorrect
  2. BThe method will overstate VaR because it assumes fat tails
  3. CThe estimate depends on a correlation matrix that is hard to calibrate
  4. DThe estimate will automatically reflect scenarios worse than any in the sample

Explanation

At 99.9% with 500 observations, the expected number of tail observations is 0.5, so the estimate relies on one or zero data points and is bounded by the worst observed loss. Historical simulation cannot produce losses beyond those in the sample, which is why extreme value theory is often used for extreme quantiles.

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