Question

What is the standard deviation of a portfolio made up of 50% Stock A and 50% Stock B?

Stock	Expected Return	Beta	Variance	COV A,B
A	19%	2.3	0.08	0.030
B	15%	1.7	0.04

Answer 1

Weight of stock A = WA = 50%

Weight of Stock B = WB = 50%

Standard deviaiton of Stock A = σA = (0.08)^(1/2) = 0.282843

Standard deviaiton of Stock B = σB = (0.04)^(1/2) = 0.2

Covarinace = Cov(A,B) = 0.030

Variance of Portfolio = [(WA)^2 * (σA)^2] + [(WB)^2 * (σB)^2] + [2Cov(A,B) * WA * WB * σA * σA]

= [(50%)^2 * (0.282843)^2] + [(50%)^2 * (0.2)^2] + [2*50%*50%*0.030 *0.282843*0.2]

= 0.02 + 0.01 + 0.000848529

= 0.030848529

Standard deviation of Portfolio = Squareroot of variance

= (0.030848529)^(1/2)

= 0.175637

= 17.56%

Therefore, standard deviation of the portfolio is 17.56%