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

A bank backtests its 99% VaR model using 500 daily PIT values. A histogram of the PIT values shows large excesses in the bins near 0 and near 1, with too few observations in the middle bins (a U-shape). What is the most likely interpretation?

A U-shaped PIT histogram implies realized P&L lands in the extreme tails of the forecast distribution too often, meaning the model's distribution is too narrow and underestimates risk in both tails. A hump shape would indicate the opposite, overstated dispersion.

  1. AThe model understates the dispersion of the P&L distribution, so risk is underestimated in both tailsCorrect
  2. BThe model overstates the dispersion of the P&L distribution, so risk is overestimated
  3. CThe model is systematically biased toward overstating profits
  4. DThe model is correctly specified but suffers from autocorrelated errors

Explanation

A U-shaped PIT histogram means realized outcomes fall in the extreme tails of the predicted distribution more often than expected. This indicates the predicted distribution is too narrow (volatility or tail risk understated). Overstated dispersion would give a hump-shaped histogram with too few tail observations. A bias in the mean would produce a skewed histogram instead.

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