Explanation:
Since all 10 credit positions are from the same obligor, they are perfectly correlated. Thus, if the obligor defaults, all 10 positions will default simultaneously. The probability of default is 5%.
Since the confidence level is 99%, we are looking at the worst 1% of cases. The default probability (5%) is greater than the tail probability (1%). Therefore, at the 99% confidence level, the obligor will have defaulted.
If the obligor defaults, the loss is the entire portfolio value ($1 million) because the recovery rate is zero.
Expected Loss (EL) = Probability of Default × Loss Given Default × Exposure at Default
EL = 0.05 × 1 × $1,000,000 = $50,000
Credit VaR is defined as the unexpected loss at the given confidence level.
Credit VaR = Worst-case loss at 99% - Expected Loss
Worst-case loss at 99% = $1,000,000 (since 5% > 1%, default happens in the 99th percentile worst case).
Unexpected Loss (Credit VaR) = $1,000,000 - $50,000 = $950,000.
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Q.3 A $1m portfolio of credits is divided into 10 credit positions. Each credit position in the portfolio has a default probability of 5% and a recovery rate of zero. Each credit position is an obligation from the same obligor. What is the credit VaR at 99% confidence for this portfolio?
A
$50,000
B
$950,000
C
$1 million
D
$0
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