Question

An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 26% and a standard deviation of return of 39%. Stock B has an expected return of 15% and a standard deviation of return of 25%. The correlation coefficient between the returns of A and B is .5. The risk-free rate of return is 6%. The proportion of the optimal risky portfolio that should be invested in stock B is approximately _________.

Answer #1

Answer;

Weight of stock A = 67.32% or 67%

Weight of Stock B = 32.68% or 33%

Explanation;

Optimal Risky Portfolio

Weight stock A= (R1 - RF)(SD stock B)^2 - (R2-RF) Cov Stock A&B / (R1-RF)(SD stock B)^2 + (R2 - RF) - (R1 - RF + R2 - RF) (Cov A& B)

Return Stock A (R1) = 26%

Return Stock B (R2) =15%

Sd of stock A = 39%

Sd of stock B = 25%

Correlation = 0.50

Rf = 6%

Cov A & B = Correlation A & B x SD stock A x SD stock B i.e. =0.5 x0.39 x0.25= 0.04875

Weight of stock A = (0.26-.06)(0.25)^2 - (0.15-.06)(0.04875)/(0.26-0.06)(.25)^2 + (0.15-.06)(.39)^2 - (.26-.06+.15-.06)(0.04875)

= 0.0125 - 0.0043875/ 0.0125 + 0.013689 -0.0141375

= 0.0081125/0.0120515

=.6732 or 67%

Weight of Stock B = 1 - weight of stock

= 1 - 67.32 % =32.68% or 33%

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