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

Two models forecast 97.5% ES for a portfolio. Model A and Model B both pass a standard exceedance-count test on VaR at 97.5%. Over the sample, Model A's realized average tail loss equals its forecast ES, while Model B's realized average tail loss is 25% above its forecast ES. Which conclusion is best supported?

Model B understates tail severity even though its VaR exceedance frequency is acceptable. Exceedance counts ignore the magnitude of losses beyond VaR, so ES backtesting that compares realized tail losses with forecast ES reveals the shortfall that the frequency test misses.

  1. ABoth models are equally adequate because they pass the VaR exceedance test
  2. BModel B should be preferred because its higher tail loss indicates conservative VaR
  3. CModel B understates tail severity despite adequate exceedance frequency, showing that exceedance counts do not capture the size of tail lossesCorrect
  4. DModel A is rejected because ES equal to realized loss implies overfitting

Explanation

Exceedance tests examine only how often VaR is breached, not how large the losses beyond VaR are. Model B's realized tail loss exceeds forecast ES by 25%, so its ES is underestimated. Model A's tail loss matching ES is the desired result, not overfitting.

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