Explanation:

For a two-asset portfolio, the variance is calculated using the formula:

$$\sigma_p^2 = w_1^2 \sigma_1^2 + w_2^2 \sigma_2^2 + 2w_1w_2\rho_{12}\sigma_1\sigma_2$$

Where:

• $w_1$ and $w_2$ are the weights of Asset 1 and Asset 2, respectively (both 0.5 for an equally weighted portfolio).
• $\sigma_1^2$ and $\sigma_2^2$ are the variances of Asset 1 and Asset 2, respectively.
• $\rho_{12}$ is the correlation between the returns of the two assets.

Plugging in the values:

$$\sigma_p^2 = (0.5)^2(0.05) + (0.5)^2(0.06) + 2(0.5)(0.5)(0.75)\sqrt{0.05}\sqrt{0.06}$$

Simplifying:

$$\sigma_p^2 = 0.0125 + 0.015 + 0.0205396 = 0.04804 \approx 0.048$$

Option A (0.038) is incorrect because it omits the doubling of the covariance term. Option C (0.055) is incorrect as it represents the weighted average of the variances, which is not applicable here since the correlation is not 1.