Explanation

To calculate the standard deviation of portfolio losses, we need to compute:

Step 1: Calculate individual loan standard deviations

The formula for standard deviation of losses for each loan is:

σᵢ = √[pᵢ − pᵢ²] × [Lᵢ(1 − Rᵢ)]

Where:

• pᵢ = probability of default
• Lᵢ = exposure at default (amount borrowed)
• Rᵢ = recovery rate

For Loan 1:

• p₁ = 2% = 0.02
• L₁ = CNY 15 million
• R₁ = 40% = 0.40
• L₁(1 − R₁) = 15 × (1 − 0.40) = 15 × 0.60 = CNY 9 million
• σ₁ = √[0.02 − 0.02²] × 9 = √[0.02 − 0.0004] × 9 = √0.0196 × 9 = 0.14 × 9 = CNY 1.26 million

For Loan 2:

• p₂ = 2% = 0.02
• L₂ = CNY 20 million
• R₂ = 25% = 0.25
• L₂(1 − R₂) = 20 × (1 − 0.25) = 20 × 0.75 = CNY 15 million
• σ₂ = √[0.02 − 0.02²] × 15 = √[0.02 − 0.0004] × 15 = √0.0196 × 15 = 0.14 × 15 = CNY 2.1 million

Step 2: Calculate portfolio variance

The portfolio variance formula is:

σₚ² = Σ(i=1 to n) Σ(j=1 to n) ρᵢⱼ σᵢ σⱼ

For two loans: σₚ² = σ₁² + ρ₁₂ σ₁ σ₂ + ρ₁₂ σ₂ σ₁ + σ₂² = σ₁² + 2ρ₁₂ σ₁ σ₂ + σ₂²

Where ρ₁₂ = 0.6

σₚ² = (1.26)² + 2 × 0.6 × 1.26 × 2.1 + (2.1)² = 1.5876 + 3.1752 + 4.41 = 9.1728

Step 3: Calculate portfolio standard deviation

σₚ = √σₚ² = √9.1728 = CNY 3.0287 million ≈ CNY 3.03 million

Therefore, the correct answer is CNY 3.03 million.