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Answer: $8,000
## Explanation To calculate the Credit VaR at the 95% confidence level: **Given:** - Portfolio value: $1,000,000 - Number of credits (n): 1,000 - Default probability (π): 2% (0.02) - Recovery rate: 0% - Default correlation: 0 - 95th percentile defaults: 28 **Calculation:** 1. Each credit has equal exposure since the portfolio is equally distributed among 1,000 credits 2. Value per credit = $1,000,000 / 1,000 = $1,000 3. At the 95th percentile, we expect 28 defaults 4. Loss at 95th percentile = 28 defaults × $1,000 per credit = $28,000 **Expected Loss Calculation:** - Expected defaults = n × π = 1,000 × 0.02 = 20 defaults - Expected loss = 20 defaults × $1,000 = $20,000 **Credit VaR Calculation:** - Credit VaR = Unexpected Loss = Loss at 95th percentile - Expected Loss - Credit VaR = $28,000 - $20,000 = $8,000 Therefore, the Credit VaR at the 95% confidence level is **$8,000**, which corresponds to option B.
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Suppose there is a $1,000,000 portfolio with n credits that each have a default probability, π = 2% and a zero recovery rate. The default correlation is 0 and n = 1,000. There is a probability of 28 defaults at the 95th percentile based on the binomial distribution with the parameters of n = 1,000 and π = 0.02. What is the credit VaR at the 95% confidence level based on these parameters?
A
$7,000
B
$8,000
C
$9,000
D
$10,000