Answer: 0.04172

## Explanation To calculate the standard deviation of loss on a single loan, we use the formula for variance of a Bernoulli distribution: **Given:** - Probability of Default (PD) = 1.1% = 0.011 - Loss Given Default (LGD) = 1 - Recovery Rate = 1 - 0.40 = 0.60 - Exposure at Default (EAD) = USD 1 million (but since we're calculating per unit, we can use L=1) **Variance of loss per loan:** \[ \sigma^2 = PD \times (1 - PD) \times LGD^2 \] **Calculation:** \[ \sigma^2 = 0.011 \times (1 - 0.011) \times (0.60)^2 \] \[ \sigma^2 = 0.011 \times 0.989 \times 0.36 \] \[ \sigma^2 = 0.010879 \times 0.36 \] \[ \sigma^2 = 0.00391644 \] **Standard deviation:** \[ \sigma = \sqrt{0.00391644} \] \[ \sigma = 0.06258 \] However, this is the standard deviation of the **loss amount**. The question asks for the standard deviation of the **loss on a loan**, which is typically expressed as a percentage of the exposure. Since L=1, we need to calculate the standard deviation of the **loss rate**. **Standard deviation of loss rate:** \[ \sigma_{loss\ rate} = \sqrt{PD \times (1 - PD)} \times LGD \] \[ \sigma_{loss\ rate} = \sqrt{0.011 \times 0.989} \times 0.60 \] \[ \sigma_{loss\ rate} = \sqrt{0.010879} \times 0.60 \] \[ \sigma_{loss\ rate} = 0.1043 \times 0.60 \] \[ \sigma_{loss\ rate} = 0.06258 \] Wait, this gives us 0.06258, which matches option D. But let me reconsider the question. Actually, the standard deviation of loss on a loan is: \[ \sigma = \sqrt{PD \times (1 - PD)} \times LGD \] \[ \sigma = \sqrt{0.011 \times 0.989} \times 0.60 \] \[ \sigma = \sqrt{0.010879} \times 0.60 \] \[ \sigma = 0.1043 \times 0.60 = 0.06258 \] This matches option D. However, I notice that 0.04172 (option C) is exactly: \[ \sqrt{PD \times (1 - PD)} = \sqrt{0.011 \times 0.989} = \sqrt{0.010879} = 0.1043 \] But this is the standard deviation of the **default indicator**, not the loss. The loss standard deviation should be multiplied by LGD. **Therefore, the correct answer is D (0.06258)**, which represents the standard deviation of the loss rate on a single loan. **Verification:** - Expected loss = PD × LGD = 0.011 × 0.60 = 0.0066 - Variance = PD × (1-PD) × LGD² = 0.011 × 0.989 × 0.36 = 0.003916 - Standard deviation = √0.003916 = 0.06258 This confirms that option D (0.06258) is correct.

Author: LeetQuiz .