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

Two banks each run a 99% one-day VaR model and each record 4 exceedances in 250 days. Bank A's exceedance losses beyond VaR average 1.1 times VaR, while Bank B's average 3.5 times VaR. Bank B's VaR is also more than double Bank A's in the same portfolio. Which conclusion is best supported by exceedance-based backtesting alone?

Exceedance-based backtesting gives both banks the same result because each has four exceedances. It ignores breach magnitude and the level of VaR, so it cannot distinguish a model with mild tail losses from one with severe tail losses. Other tools like expected shortfall or distribution-based tests are needed.

  1. ABank B's model is riskier because its breaches are larger
  2. BBank A's model is better because its VaR is lower
  3. CThe two models are indistinguishable in terms of the backtest result, even though their tail risk and conservatism differ materiallyCorrect
  4. DBank B's model should be rejected and Bank A's accepted

Explanation

Both have 4 exceedances, so the binomial result is identical and a binary test gives the same verdict. Neither the breach magnitudes nor the VaR level enter the test. Tail severity and conservatism need loss-magnitude measures such as expected shortfall backtests or tests on the full distribution.

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