The standard deviation of a two-asset portfolio is calculated using the formula:

$\sigma_P^2 = w_A^2 \sigma_A^2 + w_B^2 \sigma_B^2 + 2w_A w_B \rho_{AB} \sigma_A \sigma_B$

Where:

• $w_A = 0.75$, $w_B = 0.25$
• $\sigma_A = 0.08$ (8% converted to decimal)
• $\sigma_B = 0.14$ (14% converted to decimal)
• $\rho_{AB} = -0.20$

Plugging in the values:

$\sigma_P^2 = (0.75)^2(0.08)^2 + (0.25)^2(0.14)^2 + 2(0.75)(0.25)(-0.20)(0.08)(0.14)$

$= (0.5625)(0.0064) + (0.0625)(0.0196) + 2(0.75)(0.25)(-0.20)(0.0112)$

$= 0.0036 + 0.001225 - 0.00084$

$= 0.003985$

$\sigma_P = \sqrt{0.003985} = 0.06312 = 6.312\%$

This matches option D (6.31%). The negative correlation helps reduce portfolio risk through diversification, but the portfolio standard deviation is still higher than Security A's individual standard deviation due to the higher risk of Security B.