Explanation

At a 95% confidence interval, we expect VaR exceedances to occur approximately 5% of the time. Over 100 days, the expected number of exceedances would be:

• Expected exceedances = 100 days × 5% = 5 days

However, the actual number of exceedances observed was 9 days, which is significantly higher than the expected 5 days.

Key Points:

1. 95% confidence interval means we expect losses to exceed VaR only 5% of the time
2. Expected exceedances in 100 days: 100 × 0.05 = 5 days
3. Actual exceedances observed: 9 days
4. Interpretation: When actual exceedances exceed expected exceedances, the model is underestimating risk because it's not capturing the true risk level

Why not the other options:

• A (overestimating risk): Would be true if actual exceedances were LESS than expected
• C (appropriate): Would be true if actual exceedances were close to expected (around 5)
• D (accurate): Same as C - model would be accurate if actual results matched expectations

The model is clearly underestimating risk because it predicted only 5 exceedances but actually experienced 9, indicating the true risk is higher than what the model suggests.