Optimal Risky Portfolio Proportion Calculation

The proportion of the optimal risky portfolio that should be invested in stock B can be calculated using a specific formula. In this case, we are given the expected return, standard deviation of return, and correlation coefficient between stocks A and B, along with the risk-free rate of return.

Calculation Process

To find the proportion invested in stock B (WB), we can use the following formula:

WB = [(E(RA) - Rf) * σB^2 - (E(RB) - Rf) * σA * σB * ρAB] / [(E(RA) - Rf) * σB^2 + (E(RB) - Rf) * σA^2 - (E(RA) - Rf + E(RB) - Rf) * σA * σB * ρAB]

Where:

• WB = proportion invested in stock B
• E(RA) = expected return of stock A (21%)
• E(RB) = expected return of stock B (14%)
• Rf = risk-free rate of return (5%)
• σA = standard deviation of return for stock A (39%)
• σB = standard deviation of return for stock B (20%)
• ρAB = correlation coefficient between returns of A and B (0.4)

By plugging in the given values into the formula and performing the calculations, we get:

WB ≈ 0.71 or 71%

Therefore, the proportion of the optimal risky portfolio that should be invested in stock B is approximately 71% (Option D).