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

A bank has a 99% one-day VaR backtest with only 100 observations. The model shows 0 exceptions. A validator says the low power of exceedance-based tests with short samples is a concern. What is the best interpretation?

With only 100 observations at 99% confidence, zero exceptions occurs about 37% of the time even for a correct model. The test has low power to separate good from bad models, so the result is weak evidence either way.

  1. AZero exceptions proves the VaR is exactly calibrated
  2. BZero exceptions is statistically impossible at 99% confidence
  3. CWith few observations, the test has little ability to distinguish a correct model from one that is too conservative or even moderately too low, so the evidence is weakCorrect
  4. DZero exceptions means the model underestimates risk and must be rejected immediately

Explanation

At 99% with 100 days, expected exceptions are 1. Observing 0 has probability 0.99^100, about 37%, so it is entirely consistent with a correct model. Equally, a mis-specified model could produce few exceptions in a short sample, so the test has low power and the result is weak evidence.

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