Suppose there are two independent economic factors, M1 and M2. The risk-free rate is 4%, and all stocks have independent firm-specific components with a standard deviation of 49%. Portfolios A and B are both well diversified. Portfolio Beta on M1 Beta on M2 Expected Return (%) A 1.6 2.4 39 B 2.3 -0.7 9

E(rP) = 4% + 5.50% x β(M1) + 10.92% x β(M2)

Step-by-step explanation:

let us recall from the following statement:

The  two independent economic factors are M1 and M2

Th risk free rate = 4%

The standard deviation of all stocks of  independent firm specific components is =49%

P = portfolios for A and B

Now,

What is the expected relationship of return-beta

The Expected return-beta relationship E(rP) =  % +  βp₁ +  βp₂

E(rA) = 4% + 1.6 * M1 + 2.4* M2 = 39%

E(rB) = 4% + 2.3 * M1 + (-0.7)* M2 = 9%

Therefore

Solving for M1 and M2 using excel solver, we have M1 = 5.50% and M2 = 10.92%

E(rP) = 4% + 5.50% x β(M1) + 10.92% x β(M2)