Question

Stock A has a standard deviation of returns of 48% and Stock B has a standard deviation of returns of 49%. Suppose you decide to invest all of your investment funds in these two stocks, and 65% is invested in Stock A. The correlation coefficient of returns for these two stocks is 0.18. What is the standard deviation of returns for the combined investment in these two stocks?

Answer 1

Ans.  Portfolio Variance = w²_A*σ²(R_A) + w²_B*σ²(R_B) + 2*(w_A)*(w_B)*Cov(R_A, R_B)

where cov (X,Y) = covariance between X and Y

σ_X = standard deviation of X

σ_Y = standard deviation of Y

P_XY = correlation coefficient between X and Y

Portfolio Variance = w²_A*σ²(R_A) + w²_B*σ²(R_B) + 2*(w_A)*(w_B)*P_AB*σ(R_A)*σ(R_B)

Standard deviation of combined investment = Portolio Variance

Variance = (.48)²(.65)² + (.35)²(.49)² + 2*(0.65)*(0.35)*(0.18)*(0.48)*(0.49)

Variance = 0.15

Standard Deviation = Variance

Standard Deviation = 0.39