Suppose that there are two independent economic factors, F1 and F2. The risk-free rate is 3%, and all stocks have independent firm-specific components with a standard deviation of 42%. Portfolios A and B are both well-diversified with the following properties: Portfolio Beta on F1 Beta on F2 Expected Return A 1.8 2.1 32 % B 2.7 –0.21 27 % 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 + (βP1 × RP1) + (βP2 × RP2)
Re = Rf + [β1 x RP1] + [β2 x RP2]
We have to find the two risk premiums.
Substituting the known numbers for portfolio A in the above expression, we get:
32% = 3% + [1.8 x RP1] + [2.1 x RP2]
29% = [1.8 x RP1] + [2.1 x RP2]
RP2 = [29% - (1.8 x RP1)] / 2.1
Now, we can substitute this in the equation for portfolio B:
27% = 3% + [2.7 x RP1] - [0.21 x RP2]
24% = 2.7[RP1] - [0.21 x {29% - (1.8 x RP1) / 2.1}]
24% = 2.7[RP1] - 2.9% + 0.18[RP1]
24% + 2.9% = 2.88[RP1]
RP1 = 26.9%/2.88 = 9.34%
Therefore,
RP2 = [33% - (1.8 x RP1)] / 2.1
= [29% - (1.8 x 9.34%)] / 2.1 = 12.1875% / 2.1 = 5.80%
The expected return-beta relationship in this economy is:
Re = 3% + [β1 x 9.34%] + [β2 x 5.80%]
Suppose that there are two independent economic factors, F1 and F2. The risk-free rate is 3%,...
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