Answer: 0.0280

## Explanation For a portfolio with correlated loans, the standard deviation of portfolio loss as a percentage of portfolio size is given by: **σ_portfolio = √[ρ × σ_loan² + (1 - ρ) × σ_loan² / N]** Where: - ρ = correlation = 0.2 - σ_loan = standard deviation of loss on a single loan (from previous question) - N = number of loans = 50,000 From the previous question, the standard deviation of loss on a single loan is approximately 0.06258. **Calculation:** - σ_loan² = (0.06258)² = 0.003917 - First term: ρ × σ_loan² = 0.2 × 0.003917 = 0.0007834 - Second term: (1 - ρ) × σ_loan² / N = (0.8 × 0.003917) / 50,000 = 0.0031336 / 50,000 = 0.00000006267 **σ_portfolio = √[0.0007834 + 0.00000006267] = √0.00078346267 = 0.02799 ≈ 0.0280** Therefore, the standard deviation of the loss from the loan portfolio as a percentage of its size is **0.0280** or **2.80%**, which matches option B.

Author: LeetQuiz Editorial Team