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

Question

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

Quizplus · Accepted Answer

The correct formula for calculating the standard deviation of a two-security portfolio is used, which takes into account the weights, variances, and correlation coefficient between the securities. Plugging in the values given in the table, the standard deviation of the portfolio is calculated to be 3.7 percent. Therefore, the best choice is D.

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