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Answer: USD 5,940
## Explanation Using Equation (3.15), for a large number of loans, the unexpected loss contribution of each loan (ULCi) to the portfolio (ULp) is derived as follows: **ULCi = ULi × √ρ** where: - ULi = USD 10,500 (UL of each loan) - ρ = 0.32 (pairwise default correlation) **Calculation:** ULCi = 10,500 × √0.32 ULCi = 10,500 × 0.5657 ULCi = USD 5,939.70 ≈ USD 5,940 **Why other options are incorrect:** - **A (USD 0)**: ULC of each credit asset is not zero, as there is correlation between loans - **B (USD 1,075)**: This would result from incorrectly using ρ² instead of √ρ in the formula - **C (USD 3,360)**: This ignores the application of the square root of the default correlation in the formula This calculation demonstrates how to determine the UL contribution of individual assets in a diversified portfolio with correlated defaults.
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A credit risk manager at a bank is estimating the unexpected loss (UL) of the bank's portfolio of loans and the UL contributions of the individual loans to the overall portfolio UL. The portfolio consists of a large number of loans and the manager assumes that the loans have approximately the same characteristics and size, with a constant pairwise default correlation of 0.32. Assuming the UL of each loan is USD 10,500, what is the approximate UL contribution of each loan to the portfolio UL?
A
USD 0
B
USD 1,075
C
USD 3,360
D
USD 5,940
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