Suppose that there are two independent economic factors, F 1 and F 2 . The risk-

Question

Suppose that there are two independent economic factors, F1 and F2. The risk-free rate is 6%, and all stocks have independent firm-specific components with a standard deviation of 55%. The following are well-diversified portfolios:

What is the expected return-beta relationship?

Suppose that there are two independent economic factors, F1 and F2. The risk-free rate is 6%, and all stocks have independent firm-specific components with a standard deviation of 55%. The following are well-diversified portfolios:

Explanation / Answer

E(rP) = rf+P1[E(r1)rf] +P2[E(r2) – rf]

We need to find the risk premium for these two factors:

1= [E(r1)rf] and

2= [E(r2)rf]

To find these values, we solve the following two equations with two unknowns:

33% = 6% + 1.7*1+ 2.2*2

0 = 6% + 2.71+ 0*2

The solutions are:1= -2.22% and 2= 16.05%

Thus, the expected return-beta relationship is:

E(rP) = 6% - 2.22 P1+ 16.05 P2

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