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

A portfolio manager holds a position whose losses in a stress period were far worse than anything in the last 1,000 days of data. She compares historical simulation (HS) VaR and expected shortfall (ES) at 99%. Which conclusion is most accurate?

Historical simulation cannot generate losses beyond the worst observation in its sample, so both VaR and ES understate risk from events more extreme than anything observed. Using actual data does not capture unprecedented scenarios, and ES averages only tail observations from the same limited data.

  1. AHS VaR will capture the stress loss because it uses actual data, so ES is redundant
  2. BHS cannot produce any loss larger than the worst observed in the sample, so both VaR and ES will understate potential losses beyond the historical rangeCorrect
  3. CHS ES will exceed the stress loss because it averages all losses in the sample
  4. DHS VaR is inflated by the stress loss because it is weighted by the covariance matrix

Explanation

Non-parametric estimates cannot exceed the worst loss in the dataset, and events outside the sample are not reflected. Both VaR and ES are bounded by the observed worst loss, so they understate risk from unprecedented events. ES averages only tail losses, not all, and no covariance matrix is used.

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