Final answer:
To find the weight of Portfolio B for the minimum-variance portfolio, we need to use the formula for the minimum-variance portfolio weight. Substituting the given values into the formula, the weight of Portfolio B is approximately 0.879.
Step-by-step explanation:
To find the weight of Portfolio B for the minimum-variance portfolio, we need to use the formula for the minimum-variance portfolio weight:
Weight of B = (σA² - ρABσAσB) / (σA² + σB² - 2ρABσAσB)
Where σA and σB are the standard deviations of Portfolio S and Portfolio B, and ρAB is the correlation between Portfolio S and Portfolio B.
Using the given information:
σA = 0.42
σB = 0.12
ρAB = -0.41
Substituting these values into the formula:
Weight of B = (0.42² - (-0.41)(0.42)(0.12)) / (0.42² + 0.12² - 2(-0.41)(0.42)(0.12))
Weight of B = 0.176 / (0.176 + 0.0144 + 0.0098)
Weight of B = 0.176 / 0.2002
The weight of Portfolio B for the minimum-variance portfolio is approximately 0.879.