A portfolio has 50% of its value in ASX shares and the rest in Woodside Petroleum (WPL). The volatilities of ASX and WPL are 20% and 20%, respectively, and the correlation between ASX and WPL is 0. What is the standard deviation of the portfolio?

Question

Quizplus · Accepted Answer

The formula for the standard deviation of a portfolio is:

σp = √(w1^2 × σ1^2 + w2^2 × σ2^2 + 2 × w1 × w2 × σ1 × σ2 × ρ12)

where:
w1 and w2 are the weights of the assets in the portfolio
σ1 and σ2 are the volatilities of the assets
ρ12 is the correlation between the assets

In this case:
- w1 = 0.5 (50% in ASX shares)
- w2 = 0.5 (50% in WPL)
- σ1 = 20%
- σ2 = 20%
- ρ12 = 0 (there is no correlation between ASX and WPL)

Substituting the values:

σp = √(0.5^2 × 0.2^2 + 0.5^2 × 0.2^2 + 2 × 0.5 × 0.5 × 0.2 × 0.2 × 0) = 0.1414 or 14.14%

Therefore, the best choice is B, with a standard deviation of 14.14%.

A Portfolio Has 50% of Its Value in ASX Shares