Suppose that there are two independent economic factors, F1 and F2. The risk-fre

Question

Suppose that there are two independent economic factors, F1 and F2. The risk-free rate is 5%, and all stocks have independent firm-specific components with a standard deviation of 54%.Portfolios A and B are both well-diversified with the following properties:

Portfolio Beta on F1 Beta on F2 Expected Return A 1.6 2.0 32 % B 2.6 –0.20 29 %

What is the expected return-beta relationship in this economy? Calculate the risk-free rate, rf, and the factor risk premiums, RP1 and RP2, to complete the equation below. (Do not round intermediate calculations. Round your answers to two decimal places.) E(rP) = rf + (P1 × RP1) + (P2 × RP2)

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,

32% = 5% + 1.6*RP1 + 2*RP2

29% = 5% + 2.6*RP1 + (-0.2)*RP2

Solving above two equations, RP1 = 9.67, RP2 = 5.76

Expected return-beta relationship E(rP) = 5% + 9.67P1 + 5.76P2

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