老师，需要计算步骤

问题如下：

Question Consider a portfolio with two assets. Asset A comprises 25% of the portfolio and has a standard deviation of 17.9%. Asset B comprises 75% of the portfolio and has a standard deviation of 6.2%. If the correlation of these two investments is 0.5, the portfolio standard deviation is closest to:

选项：

A.6.45%. B.7.90%. C.9.13%.

解释：

Solution

B is correct. The standard deviation of a two-asset portfolio is given by the square root of the portfolio’s variance:

${\sigma }_p=\sqrt{w_1^2{\sigma }_1^2+w_2^2{\sigma }_2^2+2w_1{w}_2{\rho }_{1,2}{\sigma }_1{\sigma }_2}$

Using this formula, the existing standard deviation is calculated as follows:

$\sqrt{{0.25}^2\times {0.179}^2+{0.75}^2\times {0.062}^2+2\times 0.75\times 0.25\times 0.5\times 0.179\times 0.062}=7.90\%$

A is incorrect because it leaves off the correlation term in the equation:

$\sqrt{{0.25}^2\times {0.179}^2+{0.75}^2\times {0.062}^2}=6.45\%$

C is incorrect because it is the weighted average standard deviation of the two assets given: (0.25 × 0.179 + 0.75 × 0.062) = 9.125%.

Portfolio Risk and Return: Part I