Skip to content

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

A risk manager wants to bootstrap an estimate of expected shortfall (ES) from a historical simulation sample, rather than only VaR. Which approach is consistent with the bootstrap method?

Compute ES in every resample, as the average of losses beyond the VaR quantile, and then use the distribution of those ES estimates for inference. The bootstrap works for any statistic, provided resampling is done with replacement from the original data.

  1. AIn each resample, compute ES as the average of losses beyond the VaR quantile, then use the distribution of these ES values for inferenceCorrect
  2. BCompute ES once from the original sample and multiply by the square root of the number of resamples
  3. CReplace the tail observations with values from a fitted normal distribution before resampling
  4. DResample without replacement so each observation appears exactly once in every resample

Explanation

The bootstrap applies to any statistic: for each resample with replacement, compute the statistic (here ES, the average loss beyond VaR) and study the resulting distribution. The other options use an arbitrary scaling, introduce a parametric assumption, or sample without replacement, which would just reproduce the original sample.

Did you get it right without looking?

One question tells you little. A timed set on Non-parametric Approaches shows your real accuracy, how long you take and where you lose marks.

Practise Non-parametric ApproachesFree diagnostic mock

More Non-parametric Approaches questions