Answer: 8.7%

## Explanation To calculate the portfolio standard deviation, we need to use the portfolio variance formula for a two-asset portfolio: **Portfolio Variance Formula:** \[ \sigma_p^2 = w_1^2 \sigma_1^2 + w_2^2 \sigma_2^2 + 2w_1w_2 \text{Cov}(1,2) \] Where: - \( w_1 = w_2 = 0.5 \) (equal weighting) - \( \sigma_1^2 = \sigma_2^2 = 100 \%^2 \) (variance of returns) - \( \text{Cov}(1,2) = 50 \%^2 \) (covariance) **Step-by-step calculation:** 1. Calculate the portfolio variance: \[ \sigma_p^2 = (0.5)^2 \times 100 + (0.5)^2 \times 100 + 2 \times 0.5 \times 0.5 \times 50 \] \[ \sigma_p^2 = 0.25 \times 100 + 0.25 \times 100 + 2 \times 0.25 \times 50 \] \[ \sigma_p^2 = 25 + 25 + 25 \] \[ \sigma_p^2 = 75 \%^2 \] 2. Calculate the portfolio standard deviation: \[ \sigma_p = \sqrt{\sigma_p^2} = \sqrt{75} \] \[ \sigma_p \approx 8.66\% \] **Result:** The portfolio standard deviation is approximately 8.66%, which is closest to **8.7%** (Option B). **Why the other options are incorrect:** - **A. 7.9%**: This is too low and would correspond to a portfolio variance of about 62.4%², which doesn't match our calculation. - **C. 75.0%**: This is the portfolio variance (75%²), not the standard deviation. The standard deviation is the square root of variance. **Key Concept:** Portfolio standard deviation is calculated as the square root of portfolio variance. For equally weighted assets, the portfolio variance depends on both individual variances and their covariance.

Author: LeetQuiz .