Explanation:
Because all 10 credit positions are obligations from the same obligor, they are perfectly correlated (default correlation = 1). The obligor will either default on the entire $1m portfolio or not default at all.
We can determine the loss distribution for the portfolio as follows:
$1,000,000 (since Recovery Rate = 0)$0First, calculate the Expected Loss (EL):
EL = PD × Exposure at Default (EAD) × Loss Given Default (LGD)
EL = 0.05 × $1,000,000 × 1.0 = $50,000
Next, determine the Worst-Case Loss (WCL) at the 99% confidence level. Since there is a 5% chance of losing $1 million and a 95% chance of losing $0, the loss at the 99th percentile (which falls within the worst 5%) is the full $1,000,000.
In risk management, Credit VaR is typically defined as the Unexpected Loss (UL) at a given confidence level.
Credit VaR = WCL at 99% - EL
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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