Explanation

To calculate the credit VaR at the 95% confidence level:

Step 1: Understand the portfolio structure

• Portfolio value: $1,000,000
• Number of credits: n = 50
• Each credit value: $1,000,000 / 50 = $20,000
• Default probability: π = 0.02
• Recovery rate: 0%
• Default correlation: 0

Step 2: Use the binomial distribution information

• The 95th percentile of defaults is 3
• This means at the 95% confidence level, we expect up to 3 defaults

Step 3: Calculate the worst-case loss

• With 3 defaults, the loss = 3 × $20,000 = $60,000
• However, this is the absolute loss, not the VaR

Step 4: Calculate credit VaR

• Credit VaR = Worst-case loss - Expected loss
• Expected loss = n × π × credit value = 50 × 0.02 × $20,000 = $20,000
• Credit VaR = $60,000 - $20,000 = $40,000

Step 5: Verify the calculation

• Portfolio value: $1,000,000
• Expected portfolio value: $1,000,000 - $20,000 = $980,000
• 95th percentile portfolio value: $1,000,000 - $60,000 = $940,000
• Credit VaR = Expected portfolio value - Worst-case portfolio value = $980,000 - $940,000 = $40,000

Therefore, the credit VaR at the 95% confidence level is $40,000.