The expected returns for Hickory Inc.and Dickory Inc.are 8.0% and 13.0%, respectively.The standard deviation is 12.0% for Hickory and 18.0% for Dickory.What is the portfolio standard deviation if 40.0% of the portfolio is in Hickory and there is no relationship between the returns on the two securities?
A)0.7108%
B)1.3968%
C)8.4309%
D)11.8186%

Question

Quizplus · Accepted Answer

The portfolio standard deviation when there is no relationship (correlation coefficient = 0) between the returns on two securities can be calculated using the formula for the standard deviation of a two-asset portfolio: $\sigma_p = \sqrt{w_1^2\sigma_1^2 + w_2^2\sigma_2^2}$, where $w_1$ and $w_2$ are the weights of the two assets in the portfolio, and $\sigma_1$ and $\sigma_2$ are the standard deviations of the two assets. Given that 40% of the portfolio is in Hickory and 60% in Dickory (since the total must be 100%), the calculation is as follows:$\sigma_p = \sqrt{(0.4)^2(0.12)^2 + (0.6)^2(0.18)^2}$$\sigma_p = \sqrt{(0.16)(0.0144) + (0.36)(0.0324)}$$\sigma_p = \sqrt{0.002304 + 0.011664}$$\sigma_p = \sqrt{0.013968}$$\sigma_p = 0.118186$To express this as a percentage, we multiply by 100, giving us 11.8186%.

The Expected Returns for Hickory Inc