Question

A THREE-ASSET PORTFOLIO PROBLEM
	Stock A	Stock B	Stock C
Mean	-2.92%	6.58%	10.47%
Variance	4.96%	4.57%	3.91%
Standard deviation	22.28%	21.38%	19.77%
Cov(rA,rB)	0.77
Cov(rB,rC)	0.95
Cov(rA,rC)	0.86
Portfolio proportions
xA	25%
xB	35%
xC	40%
Portfolio statistics
Mean
Variance
Sigma

Answer 1

Let the mean of Stock i be denoted by r_i

Let the variance of Stock i be denoted by σ_i²

Mean of portfolio = Σ w_ir_i, where wi is the weight of portfolio i

=> Mean = w_Ar_A + w_Br_B + w_Cr_C = 0.25*(-0.0292) + 0.35*(0.0658) + 0.40*(0.1047) = 0.05761 or 5.761%

Variance of Portfolio = w_A²σ_A² + w_B²σ_B² + w_C²σ_C² + 2w_Aw_BCov(r_A,r_B) + 2w_Bw_CCov(r_B,r_C) + 2w_Aw_CCov(r_A,r_C) = (0.25)²(0.0496)² + (0.35)²(0.0457)² + (0.40)²(0.0391)² + 2(0.25)(0.35)(0.77) + 2(0.35)(0.40)(0.95) + 2(0.25)(0.40)(0.86) = 0.5734 or 57.34% squared

Sigma or standard deviation = √variance = √0.5734 = 0.7572 or 75.72%