A stock has a beta of 1.8 and an expected return of 13 percent. A risk-free asset currently earns 3.2 percent.  If a portfolio of the two assets has a beta of 3.6, what are the portfolio weights? (Do not round intermediate calculations. A negative answer should be indicated by a minus sign. Round your answers to the nearest whole number, e.g., 32.)

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Asked Nov 24, 2019
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A stock has a beta of 1.8 and an expected return of 13 percent. A risk-free asset currently earns 3.2 percent.  If a portfolio of the two assets has a beta of 3.6, what are the portfolio weights? (Do not round intermediate calculations. A negative answer should be indicated by a minus sign. Round your answers to the nearest whole number, e.g., 32.)

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Expert Answer

Step 1

Assume that the weight of risk-free asset be y. Thus, the weight of stock be (1-y).

The below expression can be used to calculate the weight of stock.

Weight of stock x Beta of stock
Portfolio beta
Weight of risk-free asset x Beta of risk-free asset
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Weight of stock x Beta of stock Portfolio beta Weight of risk-free asset x Beta of risk-free asset

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Step 2

Substitute (1-y) for weight of stock, 1.8 for beta of stock, y for weight of risk-free asset, 0 for beta of risk-free asset and 3.6 for portfolio beta,

3.6=[(1-y)x1.8]+[yx 0]
3.6
(1-y)
1.8
2 1-y
y 1-2
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3.6=[(1-y)x1.8]+[yx 0] 3.6 (1-y) 1.8 2 1-y y 1-2

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Step 3

Weight for risk-free asset is -1. Thus, weight ...

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