A portfolio has 10% 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

To calculate the standard deviation of the portfolio, we use the following formula:

σportfolio= √((w1^2 × σ1^2) + (w2^2 × σ2^2) + (2 × w1 × w2 × σ1 × σ2 × ρ))

where:
w1 = weight of ASX shares = 10% = 0.1
w2 = weight of WPL = 90% = 0.9
σ1 = volatility of ASX shares = 40%
σ2 = volatility of WPL = 20%
ρ = correlation between ASX and WPL = 0.5

Plugging in these values, we get:

σportfolio= √((0.1^2 × 0.4^2) + (0.9^2 × 0.2^2) + (2 × 0.1 × 0.9 × 0.4 × 0.2 × 0.5))
σportfolio= 0.2030 or 20.30%

Therefore, the answer is C.

A Portfolio Has 10% of Its Value in ASX Shares