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

A bank's risk manager wants to report the uncertainty in expected shortfall (ES) as well as VaR using historical data. Which is a valid use of the bootstrap in this context?

Compute ES on every bootstrap resample and study the distribution of those values to estimate its standard error or confidence interval. The bootstrap works for any statistic, including coherent measures like expected shortfall, not just VaR.

  1. ACompute ES on each resampled dataset and use the distribution of ES values to gauge its standard errorCorrect
  2. BUse the bootstrap only for VaR because it cannot be applied to coherent risk measures
  3. CReplace each observation by its volatility-adjusted value and compute ES once
  4. DDiscard the lowest 5% of observations and recompute ES

Explanation

The bootstrap can be applied to any statistic of the data, including ES, by recomputing it on each resample and examining the spread. It is not restricted to VaR. Volatility adjustment and trimming are different techniques that do not measure estimation uncertainty.

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