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

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. Variance Weight (in the portfolio)

\begin{array} { l l l } \text { Variance } & & \text { Weight (in the portfolio) } \\\hline \text { Security A } & 10 & 0.3 \\\text { Security B } & 20 & 0.7\end{array}

Quizplus · Accepted Answer

The portfolio variance is calculated using the formula: $ \sigma_p^2 = w_A^2 \sigma_A^2 + w_B^2 \sigma_B^2 + 2w_Aw_B\sigma_A\sigma_B\rho_{AB} $. Plugging in the values: $ \sigma_p^2 = (0.3)^2(10) + (0.7)^2(20) + 2(0.3)(0.7)\sqrt{10}\sqrt{20}(0.5) $. Solving this gives a variance of approximately 13.69, and the standard deviation (risk) is the square root of this, approximately 3.7 percent.

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