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).