Suppose there are two independent economic factors, M 1 and M 2 . The risk-free

Question

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 52%. Portfolios A and B are both well diversified.

What is the expected return–beta relationship in this economy? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

Expected return–beta relationship E(rP) =  % +  P1 +  P2

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:

31% = 5% + 1.61+ 2.52

12% = 5% + 2.41+ (0.7)2

Solving for the two equations. The solutions are:1= 10.49% and 2= 25.97%

Thus, the expected return-beta relationship is:E(rP) = 5%+10.49 P1+ 25.97P2

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