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

A bank's PIT backtest over 500 days produces a histogram of PIT values that is U-shaped, with excess frequency near 0 and near 1 and too few values near 0.5. What does this most likely indicate about the VaR model's forecast distributions?

A U-shaped PIT histogram means realized outcomes land in the forecast tails too often, so the model's distributions are too narrow and understate risk. An overly wide forecast would instead produce a hump centered near 0.5.

  1. AThe forecast distributions are too narrow, understating the tails and riskCorrect
  2. BThe forecast distributions are too wide, overstating risk
  3. CThe forecasts are unbiased with correct dispersion
  4. DThe forecasts consistently overestimate profits, causing PIT values to cluster near 0 only

Explanation

Realized outcomes fall in the extreme tails of the forecast distribution more often than expected, so PIT values pile up near 0 and 1. This means the forecast has too little dispersion (underestimates variance). Too-wide forecasts would give a hump-shaped histogram concentrated near 0.5.

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