Explanation

Key Information:

• Confidence Level: 99% VaR
• Number of Observations: 1,000
• Observed Exceptions: 25
• Null Hypothesis (H₀): VaR model is accurate
• Expected Exceptions: At 99% confidence level, we expect 1% exceptions = 10 exceptions out of 1,000 observations

Analysis:

1. Expected vs. Actual Exceptions:

   • Expected: 10 exceptions (1% of 1,000)
   • Actual: 25 exceptions
   • The actual exceptions (25) are significantly higher than expected (10)

2. Statistical Testing:

   • With 25 exceptions vs. expected 10, this is statistically significant
   • We would likely reject the null hypothesis that the VaR model is accurate
   • Therefore, we would probably call the model bad (inaccurate)

3. Type I vs. Type II Error:

   • Type I Error (False Positive): Rejecting a true null hypothesis
     • Risk: We might reject an actually accurate model
   • Type II Error (False Negative): Failing to reject a false null hypothesis
     • Risk: We might accept an actually inaccurate model

4. Conclusion:

   • Since we're rejecting H₀ (model is accurate), we risk making a Type I error
   • We might be rejecting an actually good model
   • This corresponds to Option C: "We will probably call the model bad (inaccurate) but we risk a Type I error"

Basel II Backtesting Framework:

The Basel Committee uses a traffic light approach where:

• Green Zone: 0-4 exceptions (model acceptable)
• Yellow Zone: 5-9 exceptions (model may need improvement)
• Red Zone: 10+ exceptions (model likely inadequate)

With 25 exceptions, the model is clearly in the red zone and would be considered inadequate.