Answer: 63.10%

## Explanation To calculate the portfolio standard deviation, we need to use the formula for two-asset portfolio variance: **Step 1: Calculate portfolio weights** - Total investment = 10M + 90M = 100M - Weight of Stock index (w₁) = 10M/100M = 0.10 or 10% - Weight of Property investment (w₂) = 90M/100M = 0.90 or 90% **Step 2: Identify the given parameters** - σ₁ (Stock index standard deviation) = 35% = 0.35 - σ₂ (Property investment standard deviation) = 70% = 0.70 - ρ₁₂ (Correlation) = -0.1 **Step 3: Apply the portfolio variance formula** Portfolio variance = w₁²σ₁² + w₂²σ₂² + 2w₁w₂ρ₁₂σ₁σ₂ **Step 4: Calculate each component** 1. w₁²σ₁² = (0.10)² × (0.35)² = 0.01 × 0.1225 = 0.001225 2. w₂²σ₂² = (0.90)² × (0.70)² = 0.81 × 0.49 = 0.3969 3. 2w₁w₂ρ₁₂σ₁σ₂ = 2 × 0.10 × 0.90 × (-0.1) × 0.35 × 0.70 = 2 × 0.09 × (-0.1) × 0.245 = 0.18 × (-0.1) × 0.245 = -0.018 × 0.245 = -0.00441 **Step 5: Sum the components** Portfolio variance = 0.001225 + 0.3969 + (-0.00441) = 0.393715 **Step 6: Calculate standard deviation** Portfolio standard deviation = √(0.393715) ≈ 0.62747 or 62.747% **Step 7: Compare with options** - 62.75% (Option A) ≈ 0.6275 - 63.10% (Option B) ≈ 0.6310 - 63.45% (Option C) ≈ 0.6345 Our calculated value of 62.747% is closest to 62.75% (Option A), but let's check the calculation more precisely: **More precise calculation:** w₁²σ₁² = 0.01 × 0.1225 = 0.001225 w₂²σ₂² = 0.81 × 0.49 = 0.3969 2w₁w₂ρ₁₂σ₁σ₂ = 2 × 0.10 × 0.90 × (-0.1) × 0.35 × 0.70 = 0.18 × (-0.1) × 0.245 = -0.018 × 0.245 = -0.00441 Total variance = 0.001225 + 0.3969 - 0.00441 = 0.393715 Standard deviation = √0.393715 = 0.627467 ≈ 62.7467% This rounds to 62.75%. However, let's verify if there might be a calculation error in the options. Actually, 62.7467% is indeed closest to 62.75%. **Wait, let me recalculate with exact values:** w₁ = 0.10, w₂ = 0.90 σ₁ = 0.35, σ₂ = 0.70 ρ = -0.1 Portfolio variance = (0.10)²(0.35)² + (0.90)²(0.70)² + 2(0.10)(0.90)(-0.1)(0.35)(0.70) = 0.01 × 0.1225 + 0.81 × 0.49 + 2 × 0.09 × (-0.1) × 0.245 = 0.001225 + 0.3969 + 0.18 × (-0.1) × 0.245 = 0.001225 + 0.3969 - 0.018 × 0.245 = 0.001225 + 0.3969 - 0.00441 = 0.393715 √0.393715 = 0.627467 ≈ 62.7467% This is clearly 62.75% when rounded to two decimal places. **But the answer key shows B (63.10%)** - this suggests there might be a different interpretation or calculation. Let me check if the correlation is being used differently: If we mistakenly use correlation as 0.1 instead of -0.1: 2w₁w₂ρ₁₂σ₁σ₂ = 2 × 0.10 × 0.90 × 0.1 × 0.35 × 0.70 = 0.18 × 0.1 × 0.245 = 0.018 × 0.245 = 0.00441 Then variance = 0.001225 + 0.3969 + 0.00441 = 0.402535 Standard deviation = √0.402535 = 0.634456 ≈ 63.45% (Option C) If we use correlation = 0 (uncorrelated): Variance = 0.001225 + 0.3969 = 0.398125 Standard deviation = √0.398125 = 0.630971 ≈ 63.10% (Option B) So Option B (63.10%) corresponds to a correlation of 0, not -0.1. This suggests the question may have intended to test whether students would ignore the correlation when it's small, or there might be an error in the question or answer key. **Given the calculation with correlation = -0.1, the correct answer should be A (62.75%).** However, since the question asks for the closest value and 62.75% is the direct result of our calculation, I'll select A as the correct answer based on the mathematical calculation.