The expected return on VZ next year is 12% with a standard deviation of 20%. The expected return on ANT next year is 24% with a standard deviation of 30%. The correlation between the two stocks is .6. If Emily makes equal investments in VZ and ANT, what is the standard deviation of her portfolio?
A) 22.47%
B) 25.00%
C) 5.05%
D) 15.00%

Question

Quizplus · Accepted Answer

The standard deviation of a two-asset portfolio is calculated using the formula: $\sqrt{w_1^2\sigma_1^2 + w_2^2\sigma_2^2 + 2w_1w_2\sigma_1\sigma_2\rho}$, where $w_1$ and $w_2$ are the weights of the two assets in the portfolio (0.5 each for equal investments), $\sigma_1$ and $\sigma_2$ are the standard deviations of the assets (20% and 30%, respectively), and $\rho$ is the correlation coefficient between the returns of the two assets (0.6). Plugging in the values: $\sqrt{0.5^2*0.2^2 + 0.5^2*0.3^2 + 2*0.5*0.5*0.2*0.3*0.6}$ gives approximately 22.47%.

The Expected Return on VZ Next Year Is 12% with a Standard