Explanation:
A 99% daily VaR implies an expected exceedance rate of 1%. Over 224 trading days in a year, the expected number of exceedances is:
$1% \times 224 = 2.24$ days.
Observing 12 exceedances is significantly higher than the expected 2.24. This indicates that the model is likely underestimating the true risk. The null hypothesis in this context is that the model is accurate. If the model is accepted despite strong evidence that it is inaccurate (underestimating risk), the bank is failing to reject a false null hypothesis. Failing to reject a false null hypothesis constitutes a Type II error.
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Q.11 A model gives an annual VaR value of $9.5 million for a portfolio at a 99% confidence interval. A one-year backtest conducted at the 95% confidence level reveals that losses exceeded $9.5 million on 12 occasions. The model is accepted as accurate. Assuming 224 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.