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

A bank's VaR model produces a Berkowitz test with estimated sigma of 1.30 on transformed z_t, with mu near 0 and rho near 0, and the null is rejected. What is the most reasonable interpretation?

The model likely understates risk. An estimated sigma of 1.30 means the transformed outcomes are more dispersed than the standard normal implied by the forecast, so actual P&L moves more than the model predicts, and the rejection reflects this excess variance.

  1. AThe model understates risk, because realized outcomes are more dispersed than forecastCorrect
  2. BThe model overstates risk, because realized outcomes are less dispersed than forecast
  3. CThe model is correctly specified, because the mean is near zero
  4. DThe model has serial correlation in exceedances, since rho is near zero

Explanation

A sigma above 1 means the z_t vary more than a standard normal would, so realized P&L is more dispersed than the forecast distribution implies. That indicates the model understates risk. Mean near zero does not rescue the model, and rho near zero indicates no autocorrelation, not its presence.

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