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Explanation:
Since the default correlation is 1, all 30 credit positions are perfectly correlated and will either default together or survive together. The portfolio behaves like a single credit with a default probability of 4%.
The total notional value is $4 million, and with a recovery rate of zero, the loss given default is $4 million.
The expected loss (EL) is:
EL = PD × LGD = 4% × $4 million = $0.16 million.
At the 99% confidence level, we look at the 99th percentile of the loss distribution. Since the probability of default is 4% (> 1%), the 99th percentile loss falls in the default region, meaning the gross loss at the 99% confidence level is $4 million.
Credit VaR is defined as the unexpected loss (UL), which is the difference between the gross loss at the given confidence level and the expected loss:
Credit VaR = Gross Loss (99%) - Expected Loss = $4 million - $0.16 million = $3.84 million.
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Q.3072 Zhong Hua is a risk analyst at a Chinese bank having a portfolio that has a notional value of $4 million with 30 credit positions. Each of the credits has a default probability of 4% and a recovery rate of zero. The credit portfolio has a default correlation equal to 1. What is the credit value at risk at the 99% confidence level for this credit portfolio?
A
$3.6 million
B
$0.16 million
C
$4 million
D
$3.84 million