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Explanation:
At a 99% confidence interval, the expected number of exceptions over a year (252 days) is:
Expected exceptions = $252 \times (1 - 0.99) = 2.52$ days.
Observing 8 exceptions in a single year for a 99% VaR model is unusually high. Statistically, using Kupiec's POF test or binomial distributions at a 95% confidence level for the backtest, 8 exceptions falls well outside the non-rejection region (which is typically between 0 and 6 exceptions). Because the observed exceptions are significantly higher than expected, the model is highly likely to be inaccurate and the statistical test should have rejected it.
However, the problem states that the model "is accepted as accurate."
Since we accepted a model that is clearly inaccurate, a Type II error has occurred.
Q.10 A model gives a VaR value of $5 million for a portfolio at a 99% confidence interval. A one-year backtest conducted at the 95% confidence level reveals that losses exceeded $5 million on 8 occasions. The model is accepted as accurate. Assuming 252 days in a year, which of these statements is most likely true?
A
A Type I error has occurred
B
A Type II error has occurred
C
Both Type I and Type II errors have occurred
D
The model has been accepted correctly
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