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

According to CAPM

Expected return = risk free rate + beta1*risk premium1 + beta2*risk premium 2

Here

we need to find the risk premium for the two factors

RP1 = [E(r1) - rf]

RP2 = [E(r2) - rf]

From the given table,

31% = 5% + 1.6*RP1 + 2.5*RP2

12% = 5% + 2.4*RP1 + (-0.7)*RP2

Solving above two equations, RP1 = 5.01, RP2 = 7.19

Expected return-beta relationship E(rP) = 5% + 5.01P1 + 7.19P2

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