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 48%. 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(r) = rf + 1*P1 + 2*P2

38 = 5 + 1.6*P1 + 2.3*P2; 1.6*P1 + 2.3*P2 = 33 equation (1)

8 = 5 + 2.2*P1 – 0.6*P2; 2.2*P1 – 0.6*P2 = 3 equation (2)

Multiplied by certain number to eliminate one variable

1.6*P1 + 2.3*P2 = 33 equation (1) multiplied by 11

2.2*P1 – 0.6*P2 = 3 equation (2) multiplied by 8

17.6 P1 + 25.3 P2 = 363

17.6 P1 – 4.8 P2 = 24

Subtract (1) – (2)

(25.3 + 4.8) P2 = (363 – 24)

P2 = 11.26

Now from equation 2,

P2 = (0.6 P2 + 3)/2.2 = (0.6*11.26 + 3)/2.2 = 4.43

E(r) = 5% + 11.26*1 + 4.43*2

This is the return-beta relationship

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