Optimal Risky Portfolio Proportion Calculation

What is the proportion of the optimal risky portfolio that should be invested in stock B?

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).

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