Question

A portfolio consists of equity and bonds. The two assets are equally weighted (i.e. equal amounts are invested in each of the two assets). The risk of equity is 17.0%, while the risk of bonds is 8.1%. Given that the correlation between the two assets is 0.2, what is the risk of the portfolio (as a standard deviation)?

Answer 1

Equally weighted portfolio means that the weight of each asset is 50% or 0.5

Weight of equity in the portfolio = w₁ = 0.5

Weight of bonds in the portfolio = w₂ = 0.5

Risk or standard deviation of equity = σ₁ = 17%

Risk or standard deviation of bonds = σ₂ = 8.1%

Correlation between the two assets (equity and bond) = ρ = 0.2

Variance of the portfolio is calculated using the formula:

Variance of the portfolio = σ_P² = w₁²*σ₁² + w₂²*σ₂² + 2*w₁*w₂*ρ*σ₁*σ₂

σ_P² = 0.5²*(17%)² + 0.5²*(8.1%)² + 2*0.5*0.5*0.2*17%*8.1% = 0.007225+0.00164025+0.001377 = 0.01024225

Standard deviation or risk is square-root of the variance

Standard deviation or risk of the portfolio = σ_P = 0.01024225^1/2 = 0.101204001897158 = 10.1204001897158 %

Answer -> Risk of the portfolio = 10.1204001897158 %