Question

Suppose that there are two independent economic factors F1 and F2. The risk-free rate is 5%,...

Suppose that there are two independent economic factors F1 and F2. The risk-free rate is 5%, and all stocks have independent firm-specific components with a standard deviation of 45%. The following are well-diversified portfolios:

Portfolio

Beta on F1

Beta on F2

Expected Return

A 1 2 19%
B 2 1 24%

What is the expected return-beta relationship in this economy?

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Answer #1
Expected return = risk free rate+M1 beta*M1 risk premium+M2 beta*M2 risk premium
19=5+1*M1 risk premium + 2*M2 risk premium
14=1*M1 risk premium + 2*M2 risk premium……(1)
24=5+2*M1 risk premium + 1*M2 risk premium
19=2*M1 risk premium + 1*M2 risk premium……(2)
Solving (1) & (2) simultaneously we get
M1 risk premium=8
M2 risk premium=3
Expected return Beta relationship is:
E{r}=5% + Beta M1*8 + Beta M2*3
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