Question

An investor can design a risky portfolio based on two stocks, A and B. Stock A has an expected return of 25% and a standard deviation of return of 35%. Stock B has an expected return of 18% and a standard deviation of return of 28%. 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 = 62.59% or 63%

Weight of Stock B = 37.41% or 37%

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) = 25%

Return Stock B (R2) =18%

Sd of stock A = 35%

Sd of stock B = 28%

Correlation = 0.50

Rf = 6%

Cov A & B = Correlation A & B x SD stock A x SD stock B i.e. =0.5 x0.35 x0.28= 0.049

Weight of stock A = (0.25-.06)(0.28)^2 - (0.18-.06)(0.049)/(0.25-0.06)(.28)^2 + (0.18-.06)(.35)^2 - (.25-.06+.18-.06)(0.049)

= 0.014896 - 0.00580 / 0.014896 + 0.0147 - 0.01519

= 0.009016 / 0.014406

= 0.6259 i.e. 62.59% or 63%

Weight of Stock B = 1 - weight of stock

= 1 - 62.59 % =37.41% or 37%

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