Question

Your portfolio is worth $250,000 and is invested for 14% in equity and the rest in bonds. The risk of equity (as a standard deviation) is 18.2% and the risk of bonds is 9.6%. The correlation between them is 0.8.

What is the risk of this portfolio? express your answer as a standard deviation and in percent without symbol

Please answer using formula and step by step instructions

Answer 1

14% is invested in Equity and the rest (86%) is invested in bonds

Weight of equity in the portfolio = w₁ = 14% = 0.14

Weight of bonds in the portfolio = w₂ = 100% - 14% = 86% = 0.86

Risk or standard deviation of equity = σ₁ = 18.2%

Risk or standard deviation of bonds = σ₂ = 9.6%

Correlation between the two assets (equity and bond) = ρ = 0.8

We will first calculate the variance of the portfolio using the formula and then take the square-root of variance to get the standard deviation (or Risk) of the portfolio

Variance of portfolio

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 = 0.14²*(18.2%)² + 0.86²*(9.6%)² + 2*0.14*0.86*0.8*18.2%*9.6% = 0.0006492304+0.0068161536+0.00336580608 = 0.01083119008

Standard deviation or risk of the portfolio

Standard deviation or risk is square-root of the variance

Standard deviation or risk of the portfolio = σ_P = 0.01083119008^1/2 = 0.104073003608044 = 10.4073003608044 %

Answer -> Risk of the portfolio (in %) = 10.4073003608044