Suppose there are two independent economic factors, M1 and M2. The risk-free rate is 5%, and all stocks have independent firm-specific components with a standard deviation of 44%. Portfolios A and B are both well diversified. Portfolio Beta on M1 Beta on M2 Expected Return (%) A 1.5 1.9 34 B 1.8 -0.6 12 What is the expected return–beta relationship in this economy?
Solution:
We know that
First, we calculate the risk premium, for each of the two factors
and
We get the following equation to be solved
34 = 5 + 1.5 x + 1.9 x ---------------------------------- {A}
12 = 5 + 1.8 x + (-0.6) x ------------------------------ {B}
We multiply equation A by 1.8 and B by 1.5, we get
61.2 = 9 + 2.7 + 3.42
18 = 7.5 + 2.7 -0.9
- - - +
--------------------------------------------------
43.2 = 1.5 + 4.32
= 10%
Substituting the value of in equation A, we get
34 = 5 + 1.5 () +1.9 (10)
= 6.67%
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