Explanation:

The formula for the unexpected loss (UL) of a single credit asset is: UL = EAD × sqrt( PD × σ²(LGD) + LGD² × σ²(PD) ) where the variance of default probability assuming a binomial distribution is σ²(PD) = PD × (1 - PD).

Given parameters:

EAD = `$30.0` million
PD = 4.0% = 0.04
LGD = 40.0% = 0.40
σ(LGD) = 40.0% = 0.40, so σ²(LGD) = 0.40² = 0.16

Calculate variance of PD: σ²(PD) = 0.04 × (1 - 0.04) = 0.0384

Calculate the terms inside the square root: PD × σ²(LGD) = 0.04 × 0.16 = 0.0064 LGD² × σ²(PD) = 0.40² × 0.0384 = 0.16 × 0.0384 = 0.006144

Sum the variances: Total variance = 0.0064 + 0.006144 = 0.012544 Standard deviation = sqrt(0.012544) = 0.112 = 11.2%

Finally, calculate the Unexpected Loss: UL = ` $30.0` million × 11.2% = \`$ 3.36`0 million. Therefore, the correct answer is B.

921.2. A credit portfolio contains an adjusted exposure of `$30.0` million with a default probability of 4.0%. In regard to loss given default (LGD), the Portfolio Manager estimates an (LGD) of 40.0% with a standard deviation, σ(LGD), of 40.0%. What is the position's unexpected loss (UL)?

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Last updated: July 5, 2026 at 07:03

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921.2. A credit portfolio contains an adjusted exposure of `$30.0` million with a default probability of 4.0%. In regard to loss given default (LGD), the Portfolio Manager estimates an (LGD) of 40.0% with a standard deviation, σ(LGD), of 40.0%. What is the position's unexpected loss (UL)?