Financial Risk Manager Part 1
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At a 95% confidence interval, the value at risk (VaR) of a portfolio is approximately $10 million. During 100 days, the VaR was exceeded on 9 different occasions. Based on this information:
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NNikitesh
A
This model is overestimating risk
B
This model is underestimating risk
C
This model is appropriate for estimating the risk
D
The model is accurate
Explanation:
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:
- 95% confidence interval means we expect losses to exceed VaR only 5% of the time
- Expected exceedances in 100 days: 100 × 0.05 = 5 days
- Actual exceedances observed: 9 days
- 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.
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