
Answer-first summary for fast verification
Answer: CNY 51,701
## Explanation **C is correct.** Using Equation (3.15), the unexpected loss contribution for a single credit asset (ULCᵢ) is derived as follows: \[ ULC_i = UL_i * \sqrt{p} \] where \( p = \) pairwise default correlation = 0.25, and, \[ UL_i = \text{unexpected loss of each loan} = EA * \sqrt{(PD * \sigma_{LR}^2 + LR^2 * \sigma_{PD}^2)} \] where, - EA = loan exposure amount = CNY 3,000,000 - PD = 0.04 - \(\sigma^2(PD) = 0.196^2 = 0.0384\) - \(LR^2 = 0.15^2 = 0.0225\) - \(\sigma^2(LR) = 0.09^2 = 0.0081\) Therefore, \[ UL_i = \text{CNY } 3,000,000 * \sqrt{0.04 * 0.0081 + 0.0225 * 0.0384} \] \[ = \text{CNY } 3,000,000 * \sqrt{0.000324 + 0.000864} = \text{CNY } 103,402.13 \] Thus, \[ ULC_i = 103,402.13 * \sqrt{0.25} = \text{CNY } 51,701.07 \] **A is incorrect.** CNY 18,000 is not related to the calculation. **B is incorrect.** CNY 25,851 is the result obtained by incorrectly getting the product of ULᵢ and p. **D is incorrect.** CNY 103,402 is the unexpected loss (ULᵢ) itself, not the unexpected loss contribution (ULCᵢ).
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An analyst in the credit risk department of a bank is estimating the unexpected loss contributions (ULC) of individual loans to overall credit portfolio risk. The portfolio consists of many loans that have approximately the same characteristics and size. Additional information about each loan is provided below:
What is the correct estimate of the ULC of a single loan to the overall credit portfolio risk?
A
CNY 18,000
B
CNY 25,851
C
CNY 51,701
D
CNY 103,402