Explanation

Step 1: Calculate the variance of one loan

• Loss given default (LGD) = 1 - Recovery Rate = 1 - 0.55 = 0.45
• Loss amount per default = L × LGD = 125,000 × 0.45 = USD 56,250
• Variance of one loan = p(1-p) × (Loss amount)² = 0.06 × 0.94 × (56,250)²
• Variance of one loan = 0.0564 × 3,164,062,500 = 178,453,125

Step 2: Calculate the portfolio variance

For a portfolio with n loans and pairwise correlation ρ:

• Portfolio variance = n × σ² + n(n-1) × ρ × σ²
• Portfolio variance = 7 × 178,453,125 + 7 × 6 × 0.35 × 178,453,125
• Portfolio variance = 1,249,171,875 + 2,623,260,938 = 3,872,432,813

Step 3: Calculate portfolio standard deviation

• σₚ = √3,872,432,813 = USD 62,228.87

Step 4: Calculate the ratio

• Portfolio size = n × L = 7 × 125,000 = USD 875,000
• Ratio = σₚ / Portfolio size = 62,228.87 / 875,000 = 0.0711 ≈ 0.07

Therefore, the closest ratio is 0.07 (Option A).

This calculation shows how correlation significantly increases portfolio risk, as the standard deviation of losses relative to portfolio size is 7.11%, which is much higher than what would be expected with uncorrelated defaults.