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FRM Part II · FRM Exam Part II · Backtesting VaR

A risk manager reviews a 99% one-day VaR model over 500 trading days and finds only 1 exception. The head of trading praises the result. Which interpretation is most consistent with the objectives of VaR backtesting?

With 500 days at 99%, about five exceptions are expected. Only one exception suggests the model may be overly conservative, which misstates risk and ties up capital. Backtesting aims for consistency with the confidence level, so too few exceptions is also a calibration concern.

  1. AThe model is ideal because fewer exceptions always indicate better accuracy
  2. BThe model may be overly conservative, since about 5 exceptions would be expected, so the result still indicates a calibration problemCorrect
  3. CThe model is certainly underestimating risk because exceptions are below the confidence level
  4. DThe backtest is invalid because exceptions must equal exactly 5

Explanation

Expected exceptions are 1% x 500 = 5. Observing 1 is well below expectation, suggesting excessive conservatism, which wastes capital and misstates risk. Backtesting tests for both too many and too few exceptions. Exact equality to 5 is not required, so the last option is wrong.

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