Explanation:
The correct answer to the question is option D: USD 5,940. This is determined by using Equation (3.15) to calculate the unexpected loss contribution (ULCi) of each loan to the portfolio's unexpected loss (ULp). The formula for this calculation is ULCi = UL * sqrt(p), where UL is the unexpected loss of each loan and p is the pairwise default correlation.
In the given scenario, the unexpected loss (UL) of each loan is USD 10,500, and the pairwise default correlation (p) is 0.32. Plugging these values into the formula yields:
ULCi = 10,500 * sqrt(0.32) = USD 5,939.70
This result is rounded to USD 5,940, which corresponds to option D. The other options are incorrect for the following reasons:
The reference for this information is from Gerhard Schroeck's book "Risk Management and Value Creation in Financial Institutions", specifically Chapter 5, "Capital Structure in Banks" (pages 170-186 only).
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A bank's credit risk manager is in the process of determining both the unexpected loss (UL) for an entire loan portfolio and the UL contributed by each individual loan to the total portfolio UL. The loan portfolio consists of several loans that are presumed to have similar characteristics and dimensions. The pairwise default correlation between these loans is consistently 0.32. If the unexpected loss for each individual loan is USD 10,500, how can the contribution of each loan to the overall portfolio UL be estimated?
A
USD 0
B
USD 1,075
C
USD 3,360
D
USD 5,940