Question

If the financial market consists of only 3 assets and we have the following information on the assets:

Stock	Weight in the market portfolio	Standard deviation (%)
A	50%	20%
B	25%	15%
C	25%	5%

In addition you are given pairwise correlations: ρAB = 0, ρAC = 0, ρBC = 0.5

What is the Standard deviation of the Market?

Answer 1

Weight of Stock A = WA = 50%

Weight of Stock B = WB = 25%

Weight of Stock C = WC = 25%

Standard Deviation of Stock A = σA = 20%

Standard Deviation of Stock B = σB = 15%

Standard Deviation of Stock C = σC = 5%

ρAB = 0

ρAC = 0

ρBC = 0.5

Variance of the market = [(WA)^2 * (σA)^2] + [(WB)^2 * (σB)^2] + [(WC)^2 * (σC)^2] + [2* ρAB * WA * WB *σA * σB ] + [2* ρAC * WA * WC*σA * σC] + [2* ρBC * WC * WB*σC * σB]

= [(50%)^2 * (20%)^2] + [(25%)^2 * (15%)^2] + [(25%)^2 * (5%)^2] + [2*0*50%*25%*20%*15%] + [2*0*50%*25%*20%*5%] + [2*0.5*25%*25%*15%*5%]

= 0.01+ 0.00140625+ 0.00015625 + 0 + 0 + 0.00046875

= 0.01203125

Standard deviaiton of the Market = Square root of the variance of the market

= (0.01203125)^(1/2)

= 0.109687055

= 10.97%

Therefore, Standard deviation of the market is 10.97%