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.