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FRM Part II · FRM Exam Part II · Backtesting VaR

A regulator-style backtest uses 250 daily observations. A bank's model understates risk, so its true exception probability is 3% rather than the stated 1%. Which statement best describes the power of the backtest?

Power of a backtest is the probability of correctly rejecting an inaccurate model, which equals one minus the Type II error probability. It rises as the true exception rate departs further from the stated rate and as the sample grows.

  1. APower is the probability of correctly rejecting this flawed model, and equals one minus the Type II error probabilityCorrect
  2. BPower is the probability of rejecting an accurate model, and equals the Type I error probability
  3. CPower is the probability of accepting a flawed model, and equals the Type II error probability
  4. DPower depends only on the VaR confidence level and not on the true exception rate

Explanation

Power = 1 - P(Type II error), the chance of rejecting a model that is truly wrong. With a true 3% rate the expected exceptions (7.5) far exceed 2.5, so power is moderate to high, and it depends on how far the true rate departs from 1%.

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