Calculate the Risk (Standard Deviation)of the Following Two-Security Portfolio If

Multiple Choice

Calculate the risk (standard deviation) of the following two-security portfolio if the correlation coefficient between the two securities is equal to 0.5.
$\begin{array}{cc}&\text { Variance } & \text { Weight (in the portfolio) } \\\hline \text { Security A } &10 & 0.3 \\ \text { Security B } &20 & 0.7\end{array}$

A) 17.0 percent
B) 5.4 percent
C) 2.0 percent
D) 3.7 percent
$\begin{aligned}\sigma_{\mathrm{p}} & =\left[\mathrm{wl}^{2} \sigma_{1}^{2}+\mathrm{w}_{2}^{2} \sigma_{2}^{2}+2\left(\mathrm{w}_{1}\right) \left(\mathrm{w}_{2}\right) \left(\rho_{1,2}\right) \sigma_{1} \sigma_{2}\right]^{1 / 2} \\& =\left[(0.3) ^{2}(10) +(0.7) ^{2}(20) +\right. \\& \left.=2(0.3) (0.7) (0.5) (10) ^{1 / 2}(20) ^{1 / 2}\right]^{1 / 2}=3.7 \%\end{aligned}$