Suppose there are two independent economic factors, M1 and M2. The risk-free rat

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. Portfolio Beta on M1 Beta on M2 Expected Return (%) A 1.6 2.5 31 B 2.4 -0.7 12 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% + 1.6?1+ 2.5?2

12% = 5% + 2.4?1+ (?0.7)?2

The solutions are: ?1= 5.01% and ?2= 7.19% Thus, the expected return-beta relationship is: E(rP) = 5% + 5.01?P1+ 7.19?P2.

Thanks

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