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:
Calculation: ULCi = 10,500 × √0.32 ULCi = 10,500 × 0.5657 ULCi = USD 5,939.70 ≈ USD 5,940
Why other options are incorrect:
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