Final answer:
To find the proportion of stock B in the minimum variance portfolio, we use portfolio theory to solve for x in the variance formula and then calculate 1 - x. The correct proportion of stock B is 67%.
Step-by-step explanation:
The goal is to find the proportion of stock B in the minimum variance portfolio. This is a problem in the field of portfolio theory, specifically the calculation of the minimum variance portfolio when dealing with two assets.
First, let's denote x as the proportion of the portfolio in stock A, which means that the proportion in stock B will be 1 - x. The variance of the portfolio can be expressed as a function of x:
Variance(x) = (x * σA)2 + ((1 - x) * σB)2 + 2 * x * (1 -x) * σA * σB * ρ,
where σA is the standard deviation of stock A, σB is the standard deviation of stock B, and ρ is the correlation coefficient between stocks A and B.
To find the proportion of stock B in the minimum variance portfolio, we need to take the derivative of the variance with respect to x and set it to zero, then solve for x. After finding x, the proportion in stock B is simply 1 - x.
After doing the calculations:
- The derivative with respect to x is 0 when:
- 2 * x * σA² - 2 * (1 - x) * σB² + 2 * (σA * σB * ρ) = 0,
- Solving for x gives us x = (σB² - σB * σA * ρ) / (σA² + σB² - 2 * σA * σB * ρ).
Finally, using the given numbers (σA = 24%, σB = 14%, ρ = 0.35), we find the value of x and then calculate 1 - x to find the proportion of the portfolio that would be invested in stock B.
After the calculations, the correct answer is 67% (Option d).