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

Two banks each report 3 exceedances of their 99% one-day VaR over 250 days. Bank A's exceedance losses average 1.1 times VaR; Bank B's average 4 times VaR. Under an exceedance-only backtest, which conclusion is correct?

Both banks look identical to an exceedance-only backtest because it records just a count of three. Bank B's much larger losses beyond VaR signal a heavier tail, which only magnitude-sensitive methods such as expected shortfall comparisons would reveal.

  1. ABoth banks are indistinguishable, although Bank B's model likely has a far heavier unmodelled tailCorrect
  2. BBank B fails the test because its losses are larger
  3. CBank A fails the test because its exceedances are closer to VaR
  4. DBank B passes while Bank A fails since magnitude is weighted inversely

Explanation

The exceedance test uses a binary indicator, so both banks show 3 exceedances and receive identical results. Magnitude information, such as the expected shortfall or loss-severity comparison, would reveal Bank B's heavier tail. Hence the test cannot discriminate between them.

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