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FRM Part II · FRM Exam Part II · Beyond Exceedance-Based Backtesting of Value-at-Risk Models

A bank backtests ES with a method that compares the realised average of losses beyond VaR to forecast ES, using a bootstrap or simulation under the model's own distribution to get a p-value. Under which condition does this approach become most unreliable, as discussed in the ES backtesting literature?

The approach is least reliable when there are few exceedances, because the average tail loss is then estimated from very limited data and the test has low power. Higher confidence levels worsen this. Currency choice and linear exposures are not the main problem.

  1. AWhen the sample contains very few exceedances, so the tail-loss average is estimated from limited dataCorrect
  2. BWhen VaR is computed at a 95% rather than 99% level, which removes all tail observations
  3. CWhen the portfolio has only linear exposures
  4. DWhen losses are measured in USD rather than local currency

Explanation

Tail-based ES tests rely on the exceedances, and at high confidence levels there are few of them, so the average tail loss is noisy and tests have low power. Lower confidence levels give more tail data, not none. Linear exposures and the currency of measurement do not undermine the method.

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