A portfolio has 25% of its value in ASX shares and the rest in Woodside Petroleum (WPL). The volatilities of ASX and WPL are 40% and 20%, respectively, and the correlation between ASX and WPL is -0.5. What is the standard deviation of the portfolio?

Question

Quizplus · Accepted Answer

The standard deviation of the portfolio can be calculated using the formula for the standard deviation of a two-asset portfolio: $\sigma_p = \sqrt{w_1^2\sigma_1^2 + w_2^2\sigma_2^2 + 2w_1w_2\sigma_1\sigma_2\rho}$, 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 (volatilities) of the two assets, and $\rho$ is the correlation coefficient between the returns of the two assets. Plugging in the given values: $w_1 = 0.25$, $w_2 = 0.75$, $\sigma_1 = 0.40$, $\sigma_2 = 0.20$, and $\rho = -0.5$, we get $\sigma_p = \sqrt{(0.25^2)(0.40^2) + (0.75^2)(0.20^2) + 2(0.25)(0.75)(0.40)(0.20)(-0.5)} = 13.23\%$.

A Portfolio Has 25% of Its Value in ASX Shares