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

A risk analyst backtests a bank's daily VaR model using the probability integral transform (PIT). For each day, she evaluates the model's forecast cumulative distribution function at the realized P&L. If the model's forecast distributions are correct, which statement describes the resulting PIT series?

Under a correctly specified model, the PIT values are independent and identically distributed uniform on the interval from zero to one. Normality arises only if the uniform values are additionally transformed by the inverse standard normal CDF.

  1. AThe values are independent and identically distributed uniform on [0,1]Correct
  2. BThe values are independent and identically distributed standard normal
  3. CThe values are exactly equal to the VaR confidence level on every day
  4. DThe values are positively autocorrelated with mean equal to 0.5

Explanation

The PIT applies the forecast CDF to the realized outcome. If the forecast distribution is the true conditional distribution, the transformed values are i.i.d. U(0,1). The normal option describes the series only after a further inverse-normal transformation, which is a separate step.

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