A portfolio has 30% of its value in ASX shares and the rest in Woodside Petroleum (WPL). The volatilities of ASX and WPL are 35% and 30%, respectively, and the correlation between ASX and WPL is 0.3. What is the standard deviation of the portfolio?

Question

Quizplus · Accepted Answer

The standard deviation of a portfolio is calculated using the following formula: 
σᵖ = √(w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ)
where 
σᵢ = standard deviation of asset i 
wᵢ = weight of asset i in the portfolio 
ρ = correlation coefficient between asset 1 and asset 2

In this case, 
w₁ = 0.3 (ASX shares) 
w₂ = 0.7 (WPL) 
σ₁ = 0.35 (volatility of ASX shares) 
σ₂ = 0.3 (volatility of WPL) 
ρ = 0.3 (correlation between ASX and WPL)

Substituting the values, we get: 
σᵖ = √(0.3²(0.35)² + 0.7²(0.3)² + 2(0.3)(0.7)(0.35)(0.3)) 
σᵖ = √(0.00283525 + 0.0441 + 0.012285) 
σᵖ = √0.05922025 
σᵖ = 0.243275

Therefore, the standard deviation of the portfolio is 24.33% or 26.15% rounded to the nearest hundredth. The closest choice is B.

A Portfolio Has 30% of Its Value in ASX Shares