Christy is considering investing in the common stock of One Liberty and Heico. The following data are available for these two securities: $$\begin{array} { l l l }
& \text { One Liberty } & \text { Heico } \
\text { Expected return } & 0.12 & 0.16 \
\text { Standard deviation of returns } & 0.08 & 0.20
\end{array}$$ If she invests 30% of her funds in Heico and 70% in One Liberty, and if the correlation of returns between these securities is +0.65, what is the portfolio's expected return and standard deviation?
A) 14% and 15.67%
B) 14.8% and 9.44%
C) 13.2% and 10.54%
D) 13.1% and 9.67%

Question

Christy is considering investing in the common stock of One Liberty and Heico. The following data are available for these two securities: $$\begin{array} { l l l } 
& \text { One Liberty } & \text { Heico } \
\text { Expected return } & 0.12 & 0.16 \
\text { Standard deviation of returns } & 0.08 & 0.20
\end{array}$$ If she invests 30% of her funds in Heico and 70% in One Liberty, and if the correlation of returns between these securities is +0.65, what is the portfolio's expected return and standard deviation?
A) 14% and 15.67%
B) 14.8% and 9.44%
C) 13.2% and 10.54%
D) 13.1% and 9.67%

Quizplus · Accepted Answer

The portfolio's expected return is calculated as a weighted average of the expected returns of the individual investments, which is $0.3 \times 0.16 + 0.7 \times 0.12 = 0.132$ or 13.2%. The portfolio's standard deviation is calculated using the formula for the standard deviation of a two-asset portfolio: $\sqrt{w_1^2\sigma_1^2 + w_2^2\sigma_2^2 + 2w_1w_2\sigma_1\sigma_2\rho}$, where $w_1$ and $w_2$ are the weights of the investments, $\sigma_1$ and $\sigma_2$ are the standard deviations of the investments, and $\rho$ is the correlation coefficient between the returns of the two investments. Plugging in the given values, we get a standard deviation of approximately 10.54%.

Christy Is Considering Investing in the Common Stock of One