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

A bank backtests 97.5% one-day ES using the tail-loss approach. Over a window, a model forecasts ES of USD 10.0 million each day. On the 5 days when VaR was exceeded, the realized losses were USD 9, 11, 12, 14 and 14 million. Comparing the average exceedance loss with forecast ES, what is the ratio of realized average tail loss to forecast ES?

The average realized loss on the five exceedance days is USD 12 million, from a total of 60 divided by 5. Dividing by the forecast ES of USD 10 million gives a ratio of 1.20, suggesting the model understates tail losses by about 20%.

  1. A1.20Correct
  2. B1.00
  3. C1.40
  4. D1.10

Explanation

Sum of exceedance losses = 9+11+12+14+14 = 60; average = 12.0. Ratio = 12.0/10.0 = 1.20. Using the maximum loss of 14 gives 1.40, and using the median of 12 coincidentally matches the mean here, but 1.00 ignores the realized data.

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