Question

A portfolio constitutes 65% of investments in the shares of Company A and 35% of investments in the shares of Company B. The expected returns for the shares of Company A and Company B are 17% and 20%, respectively. The standard deviations of returns for the shares of Company A and Company B are 5% and 8%, respectively. The correlation coefficient between the returns of the two companies’ shares is 0.85. Determine the risk of that portfolio.

Answer 1

Risk is measured by the standard deviation of the portfolio

Weight of stock A in the portfolio = wA = 65%, Weight of stock B in the portfolio = wB = 35%

Standard deviation of stock A = σA = 5%, Standard deviation of stock B = σB = 8%

Correlation coefficient between stock A and stock B = ρ = 0.85

Variance of the portfolio is calculated using the formula:

Portfolio variance = σP2 = wA2*σA2 + wB2*σB2 + 2*ρ*wA*wB*σA*σB

σP2 = (65%)2*(5%)2 + (35%)2*(8%)2 + 2*0.85*65%*35%*5%*8% = 0.00105625 + 0.000784 + 0.001547 = 0.00338725

Standard deviation is the square-root of variance

Standard deviation of the portfolio = σP = (0.00338725)1/2 = 5.82%

Risk or standard deviation of the portfolio = 5.82%

Answer -> Risk = 5.82%