Given the following information on securities E and F, calculate the expected return and standard deviation of returns on a portfolio consisting of 40% invested in E and 60% invested in F. $$\begin{array} { l l l }
& \text { Security E } & \text { Security F } \
\text { Expected Return } & 12 \% & 15 \% \
\text { Standard Deviation of Returns } & 10 \% & 20 \% \
\text { Correlation coefficient of returns } &&{ - 0.50 }
\end{array}$$
A) 13.5%; 15%
B) 13.8%; 14.4%
C) 13.8%; 10.6%
D) 13.5%; 8.7%

Question

Given the following information on securities E and F, calculate the expected return and standard deviation of returns on a portfolio consisting of 40% invested in E and 60% invested in F. $$\begin{array} { l l l } 
& \text { Security E } & \text { Security F } \
\text { Expected Return } & 12 \% & 15 \% \
\text { Standard Deviation of Returns } & 10 \% & 20 \% \
\text { Correlation coefficient of returns } &&{ - 0.50 }
\end{array}$$
A) 13.5%; 15%
B) 13.8%; 14.4%
C) 13.8%; 10.6%
D) 13.5%; 8.7%

Quizplus · Accepted Answer

The expected return of the portfolio is calculated as a weighted average of the expected returns of the individual securities, which is $0.4 \times 12\% + 0.6 \times 15\% = 4.8\% + 9\% = 13.8\%$. The standard deviation of the portfolio is calculated using the formula for the standard deviation of a two-asset portfolio: $\sqrt{w_E^2\sigma_E^2 + w_F^2\sigma_F^2 + 2w_Ew_F\sigma_E\sigma_F\rho_{E,F}}$, where $w$ is the weight, $\sigma$ is the standard deviation, and $\rho$ is the correlation coefficient. Substituting the given values, we get $\sqrt{0.4^2 \times 0.1^2 + 0.6^2 \times 0.2^2 + 2 \times 0.4 \times 0.6 \times 0.1 \times 0.2 \times (-0.5)}$, which calculates to approximately 10.6%.

Given the Following Information on Securities E and F, Calculate