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

Why is backtesting ES generally considered more demanding in data terms than backtesting VaR at the same confidence level?

ES is the average loss in the tail, and only a few observations fall there. With so little tail data, estimates are noisy and statistical tests have low power, making ES backtesting harder than simply counting VaR exceedances.

  1. AES is computed at a higher confidence level than VaR by regulation
  2. BES requires normality of returns, which VaR does not
  3. CES depends on the average of losses in the tail, so few tail observations leave the estimate and tests with low statistical powerCorrect
  4. DES cannot be computed using historical simulation

Explanation

ES averages losses beyond VaR, and tail observations are scarce, so test statistics are noisy and have low power. ES does not require normality and can be computed by historical simulation. The confidence level is a separate choice.

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