Answer: 0.00849

## Explanation To calculate the portfolio standard deviation, we need to compute the portfolio variance first and then take its square root. ### Step 1: Calculate Covariance The covariance between ABC and XYZ is calculated using: $$\text{cov}(R_A, R_B) = \sum P(R_i) [R_i - E(R_i)][R_j - E(R_j)]$$ Given: - ABC: Expected return = 8.2% (0.082), Standard deviation = 1.249% (0.01249) - XYZ: Expected return = 4.975% (0.04975), Standard deviation = 0.46% (0.0046) - Probabilities: 15% (0.15), 60% (0.6), 25% (0.25) $$\text{cov(ABC, XYZ)} = 0.15(0.06 - 0.082)(0.04 - 0.04975) + 0.6(0.08 - 0.082)(0.05 - 0.04975) + 0.25(0.10 - 0.082)(0.055 - 0.04975)$$ $$= 0.15(-0.022)(-0.00975) + 0.6(-0.002)(0.00025) + 0.25(0.018)(0.00525)$$ $$= 0.15(0.0002145) + 0.6(-0.0000005) + 0.25(0.0000945)$$ $$= 0.000032175 + (-0.0000003) + 0.000023625$$ $$= 0.0000555$$ ### Step 2: Calculate Portfolio Variance Since the investment is equally weighted (50% in each): $$W_A = W_B = 0.5$$ $$\sigma_A = 0.01249, \quad \sigma_B = 0.0046$$ Portfolio variance formula: $$\sigma_p^2 = W_A^2 \times \sigma_A^2 + W_B^2 \times \sigma_B^2 + 2 \times W_A \times W_B \times \text{cov}(R_A, R_B)$$ $$\sigma_p^2 = 0.5^2 \times (0.01249)^2 + 0.5^2 \times (0.0046)^2 + 2 \times 0.5 \times 0.5 \times 0.0000555$$ $$= 0.25 \times 0.000156 + 0.25 \times 0.00002116 + 0.5 \times 0.0000555$$ $$= 0.000039 + 0.00000529 + 0.00002775$$ $$= 0.00007204$$ ### Step 3: Calculate Portfolio Standard Deviation $$\sigma_p = \sqrt{0.00007204} = 0.00849$$ Therefore, the portfolio standard deviation is **0.00849** or **0.849%**.

Author: Tanishq Prabhu