Explanation

Conditional VaR (CVaR), also known as Expected Shortfall, is the average of all losses that exceed the VaR level.

Given:

• VaR at 99th percentile = USD 8 million
• Losses beyond VaR level: USD 9, 10, 11, 13, 15, 18, 21, 24, 32 million

Calculation: CVaR = Average of all losses beyond VaR level

Sum of losses beyond VaR = 9 + 10 + 11 + 13 + 15 + 18 + 21 + 24 + 32 = 153 million

Number of observations beyond VaR = 9

CVaR = 153 / 9 = USD 17 million

Key Points:

• CVaR provides the expected loss given that the loss exceeds the VaR level
• It's calculated as the simple average of all losses in the tail beyond the VaR threshold
• With 1,000 days of data and 99% VaR, we expect 10 worst-case scenarios (1% of 1,000), but only 9 are provided in this case
• The CVaR of USD 17 million represents the average loss on the worst 0.9% of days