Explanation

To calculate the standard deviation of an equally weighted portfolio with two assets, we use the portfolio variance 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:

• $w_1 = w_2 = 0.5$ (equally weighted)
• $\sigma_1 = 0.05$ (5%)
• $\sigma_2 = 0.08$ (8%)
• $\rho_{12} = -1$ (correlation coefficient)

Substituting the values:

$\sigma_p^2 = (0.5)^2(0.05)^2 + (0.5)^2(0.08)^2 + 2(0.5)(0.5)(-1)(0.05)(0.08)$

$\sigma_p^2 = (0.25)(0.0025) + (0.25)(0.0064) + 2(0.25)(-1)(0.004)$

$\sigma_p^2 = 0.000625 + 0.0016 - 0.002$

$\sigma_p^2 = 0.000225$

Taking the square root:

$\sigma_p = \sqrt{0.000225} = 0.015 = 1.5\%$

The closest option to 1.5% is 2% (Option B).

Key Insight: When correlation is -1 (perfect negative correlation), the portfolio standard deviation can be significantly reduced through diversification. In fact, with perfect negative correlation, it's possible to create a portfolio with zero risk if the weights are chosen appropriately. In this case, with equal weights, we get a standard deviation of 1.5%, which demonstrates the power of diversification.