Suppose there are two independent economic factors, m1 and m2. the risk-free rate is 7%, and all stocks have independent firm-specific components with a standard deviation of 50%. portfolios a and b are both well diversified. what is the expected return–beta relationship in this economy?

The expected return-beta relationship is as follows:

E(rP) = 7% + 4.47βP1 + 11.86βP2

Explanation:

Step 1:

Find the equation

The following equation applies here:

E(rP) = rf + βP1[E(r1) - rf] + βP2[E(r2) - rf]

Step 2:

Find the risk premium for these two factors:

y1 = [E(r1) - rf]

y2 = [E(r2) - rf]

Step 3:

Solve the above two equations with two unknowns to find the values:

40% = 7% + 1.8y1 + 2.1y2

10% = 7% + 2.0y1 + (-0.5)y2

By solving we get

y1 = 4.47%

y2 = 11.86%

Step 4:

Inputting in the equation:

The expected return-beta relationship is as follows:

E(rP) = 7% + 4.47βP1 + 11.86βP2

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