What is the standard deviation of an equally weighted portfolio of two stocks with a covariance of 0.009, if the standard deviation of the first stock is 15% and the standard deviation of the second stock is 20%?
A) 2.0%
B) 2.1%
C) 7.8%
D) 14.2%
E) 14.7%

Question

Quizplus · Accepted Answer

The standard deviation of a two-asset portfolio can be calculated using the formula: $\sigma_p = \sqrt{w_1^2\sigma_1^2 + w_2^2\sigma_2^2 + 2w_1w_2Cov(R_1, R_2)}$, where $w_1$ and $w_2$ are the weights of the two assets in the portfolio, $\sigma_1$ and $\sigma_2$ are the standard deviations of the returns of the two assets, and $Cov(R_1, R_2)$ is the covariance between the returns of the two assets. Given that the portfolio is equally weighted, $w_1 = w_2 = 0.5$, $\sigma_1 = 15\%$, $\sigma_2 = 20\%$, and $Cov(R_1, R_2) = 0.009$, the formula becomes: $\sigma_p = \sqrt{(0.5^2 \times 0.15^2) + (0.5^2 \times 0.20^2) + 2 \times 0.5 \times 0.5 \times 0.009}$. Calculating this gives a standard deviation of approximately 14.2%.

What Is the Standard Deviation of an Equally Weighted Portfolio