Question

You are planning to make investment into three stocks, stock A, stock B and stock C. If the following informatiın is given for them (Ka: Rate of return of Stock A)

Variance(Ka)=120

Variance(Kb)=286

Variance(Kc)=125

Covariance(Ka,Kb)=-98

Covariance(Ka,Kc)=260

Covariance(Kb,Kc)=-40

If you from a portfolio investing 30% of your savings into stock A (Wa=30%), 35% of your savings into stock B (Wb=35%) and 35% of your savings into stock C (Wc=35%) what will be the standard deviation of rate of return of your portfolio?

Answer 1

We know that,

Var (Wa Ka+ Wb Kb + Wc Kc) = Wa^2 Var(Ka) + Wb^2 Var(Wb) + Wc^2 Var(Wc) + 2 Wa Wb Cov(Ka,Kb) + 2 Wa Wc Cov(Ka,Kc) + 2 Wb Wc Cov(Kb,Kc)

Var (0.3 Ka+ 0.35 Kb + 0.35 Kc) = 0.3^2 Var(Ka) + 0.35^2 Var(Wb) + 0.35^2 Var(Wc) + 2 * 0.3 * 0.35 Cov(Ka,Kb) + 2* 0.3 * 0.35  Cov(Ka,Kc) + 2 * 0.35 * 0.35 Cov(Kb,Kc)

= 0.3^2 * 120 + 0.35^2 * 286 + 0.35^2 * 125 + 2 * 0.3 * 0.35 * -98 + 2* 0.3 * 0.35 * 260 + 2 * 0.35 * 0.35 * -40

= 85.3675

Standard deviation of rate of return of your portfolio =

= 9.239453447