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Answer: USD 17 million
## Explanation **Conditional VaR (CVaR) Calculation**: Conditional VaR represents the average loss given that the loss exceeds the VaR threshold. **Given**: - VaR at 99th percentile: USD 8 million - Losses beyond VaR level: 9, 10, 11, 13, 15, 18, 21, 24, 32 (all in millions) **CVaR formula**: \[ \text{CVaR} = \frac{\text{Sum of all losses exceeding VaR}}{\text{Number of losses exceeding VaR}} \] \[ \text{Sum of losses} = 9 + 10 + 11 + 13 + 15 + 18 + 21 + 24 + 32 = 153 \] \[ \text{Number of losses} = 9 \] \[ \text{CVaR} = \frac{153}{9} = 17 \] Therefore, the conditional VaR is **USD 17 million** **Key points**: - CVaR is also known as Expected Shortfall (ES) - It provides the average loss in the worst 1% of cases - CVaR is always greater than or equal to VaR - This measure is more sensitive to extreme losses in the tail of the distribution
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A market risk manager uses historical information on 1,000 days of profit/loss information to calculate a daily VaR at the 99th percentile, of USD 8 million. Loss observations beyond the 99th percentile are then used to estimate the conditional VaR. If the losses beyond the VaR level, in millions, are USD 9, USD 10, USD 11, USD 13, USD 15, USD 18, USD 21, USD24, and USD 32, then what is the conditional VaR?
A
USD 9 million
B
USD 32 million
C
USD 15 million
D
USD 17 million
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