Question

Stocks X, Y, Z are currently traded at PX = $10, PY = $8, and PZ = $15. Their standard deviations of the returns are σX = 30%, σY = 15%, and σZ = 20%. The return correlations between: [1]XandYis-0.7,[2]XandZis0.2,and[3]YandZis0.5.

a. What is the standard deviation of the returns of the equal-weighted portfolio of Stock X and Y?

b. What is the standard deviation of the returns of the value-weighted portfolio of Stock X and Z?

Answer 1

a. Standard Deviation of X and Y = ((Weight of X * σX)² + (Weight of Y * σY)² + 2*Weight of X * Weight of Y * σX * σY * Correlation(X,Y))^0.5 = ((50%*30%)²+(50%*15%)² + 2* 50%*50%*30%*15%*0.7)^0.5 = 20.94%

b. Standard Deviation of X and Z = ((Weight of X * σX)² + (Weight of Z * σZ)² + 2*Weight of X * Weight of Z * σX * σZ * Correlation(X,Z))^0.5 = ((50%*30%)²+(50%*20%)² + 2* 50%*50%*30%*20%*0.5)^0.5 = 21.79%

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