Explanation:
At a 99% confidence level over 252 days, the expected number of exceptions is $252 \times 0.01 = 2.52$. Observing 8 exceptions is significantly higher than the expected value, meaning the model is underestimating risk and is highly likely to be flawed or inaccurate.
In statistical hypothesis testing (such as VaR backtesting):
Since the heavily flawed model was "accepted as accurate," we have failed to reject a false null hypothesis, which corresponds to a Type II error.
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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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