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Given the returns, risk, and correlation:

E (r) σ rhoSB
Portfolio S 0.145 0.42 -0.41
Portfolio B 0.07 0.12
Risk-free 0.045
What is the weight of Portfolio B for the minimum-variance portfolio?

1 Answer

3 votes

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.

User Massimo Prota
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