A stock has a beta of 1.40 and an expected return of 12 percent. A risk-free ass
ID: 2653147 • Letter: A
Question
A stock has a beta of 1.40 and an expected return of 12 percent. A risk-free asset currently earns 3.8 percent.
What is the expected return on a portfolio that is equally invested in the two assets? (Round your answer to 2 decimal places. (e.g., 32.16))
If a portfolio of the two assets has a beta of 0.91, what are the portfolio weights? (Round your answer to 4 decimal places. (e.g., 32.1616))
If a portfolio of the two assets has an expected return of 8 percent, what is its beta? (Do not round intermediate calculations and round your answer to 3 decimal places. (e.g., 32.161))
If a portfolio of the two assets has a beta of 2.80, what are the portfolio weights? (Negative amount should be indicated by a minus sign.)
A stock has a beta of 1.40 and an expected return of 12 percent. A risk-free asset currently earns 3.8 percent.
Explanation / Answer
1)
2)Let the weight of Risk free security be X
Weight of equity = 1- X
1.40(1-X) +0 = .91
1.40 -1.40 X = .91
1.40X = .49
X(weight of risk free security) = .49/1.40 = .35
(1-X) = (Weight of stock) = 1-.35 = .65
3)Let weight of Stock be X , So weight of risk free security = 1-X
Return on portfolio =( return on stock *weight of stock ) + (return on risk free security * weight of risk free security)
8 = (12 * X) +( 3.80 *[1-X])
8 = 12X + 3.80 - 3.80 X
8 = 8.20 X +3.8
8.20 X = 4.20
X (Weight of stock ) = 4.20 / 8.20 = .51
weight of risk free security = (1 - X ) = 1-.51 = .49
Beta of portfolio= .714
4)Let the weight of stock be X , So weight of risk free security = (1-X)
1.40 X +0 = 2.80
X(weight of stock) = 2.80 /1.4 = 2
weight of risk free security = (1-X) = ( 1-2 ) = -1
weight Return weighted return stock .50 12 6 Risk free security .50 3.80 1.90 Expected return on portfolio 7.90%Related Questions
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