A stock fund has a standard deviation of 18 percent and a bond fund has a standard deviation of 11 percent. The correlation of the two funds is .24. What is the approximate weight of the stock fund in the minimum variance portfolio?
A) 16 percent
B) 19 percent
C) 21 percent
D) 24 percent
E) 27 percent

Question

Quizplus · Accepted Answer

To calculate the weight of the stock fund in the minimum variance portfolio, we need to use the formula for the minimum variance portfolio weight, which is:

w(stock fund) = (σ_bond^2 - ρ * σ_stock * σ_bond) / (σ_stock^2 + σ_bond^2 - 2 * ρ * σ_stock * σ_bond)

where:

- σ_stock is the standard deviation of the stock fund
- σ_bond is the standard deviation of the bond fund
- ρ is the correlation between the two funds

Plugging in the numbers, we get:

w(stock fund) = (0.11^2 - 0.24 * 0.18 * 0.11) / (0.18^2 + 0.11^2 - 2 * 0.24 * 0.18 * 0.11) ≈ 21%

Therefore, the weight of the stock fund in the minimum variance portfolio is approximately 21 percent.

A Stock Fund Has a Standard Deviation of 18 Percent