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

question 33

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

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Definitions:

Model Contribution

Refers to the impact or influence that a statistical model has in explaining the variability of the observed data.

Negative Correlation

Negative correlation indicates that as one variable increases, the other decreases, and vice versa, demonstrating an inverse relationship.

Null Hypotheses

A hypothesis that stipulates there is no statistical significance between the specified sets of data or that any observed differences are due to chance.

Independent Variable

The variable in an experiment or study that is manipulated to observe its effect on the dependent variable.