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.