06. Variance of a 3-Asset Portfolio

Variance of a 3-Asset Portfolio

What is the variance of a portfolio with 3 assets, A, B and C, with weights xA x_A , xB x_B , and xC x_C ?

SOLUTION: xA2σA2+xB2σB2+xC2σC2+2xAxBCov(rA,rB)+2xAxCCov(rA,rC)+2xBxCCov(rB,rC) x_A^2σ_A^2 + x_B^2σ_B^2 + x_C^2σ_C^2 + 2x_Ax_B\mathrm{Cov}(r_A, r_B) + 2x_Ax_C\mathrm{Cov}(r_A, r_C) + 2x_Bx_C\mathrm{Cov}(r_B, r_C)