Question

Your portfolio has a beta of 1.28. The portfolio consists of 35 percent U.S. Treasury bills, 31 percent Stock A, and 34 percent Stock B. Stock A has a risk-level equivalent to that of the overall market. What is the beta of Stock B?

Answer 1

Answer:

2.85

Explanation:

U.S. Treasury bills are a risk-free asset, and thus have a beta of zero. Since Stock A has a risk-level equivalent to that of the overall market, its beta is one. Therefore, the beta for Stock B can be found by:

$1.28=0.35\beta_{T}+0.31\beta_{A}+0.34\beta_{B}\\1.28 = 0.35*0+0.31*1+0.34\beta_{B}\\\beta_{B}=\frac{1.28-0.31}{0.34}\\ \beta_{B}=2.85$

The beta of Stock B is 2.85.

Answer 2

The beta of Stock B is 2.85.

Portfolio beta = Respective beta*Respective weight

1.28 = (0.35*0) + (0.31*1) + (0.34*Beta of Stock B) [Where Beta of market=1 and Beta of risk-free assets=0]

1.28 = 0.31 + (0.34*Beta of Stock B)

Beta of Stock B = (1.28 - 0.31) / 0.34

Beta of Stock B = 0.97 / 0.34

Beta of Stock B = 2.85294117647

Beta of Stock B =2.85

In conclusion, the beta of Stock B is 2.85

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