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 44%. Portfolios A
and B are both well diversified.
Portfolio | Beta on M1 | Beta on M2 | Expected Return (%) |
A | 1.5 | 1.9 | 34 |
B | 1.8 | -0.6 | 12 |
What is the expected return–beta relationship in this economy?
(Do not round intermediate calculations. Round your answers
to 2 decimal places.)
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:
34% = 5% + [1.5 x RP1] + [1.9 x RP2]
29% = [1.5 x RP1] + [1.9 x RP2]
RP2 = [29% - (1.5 x RP1)] / 1.9
Now, we can substitute this in the equation for portfolio B:
12% = 5% + [1.8 x RP1] - [0.6 x RP2]
7% = 1.8RP1 - [0.6 x {29% - (1.5 x RP1) / 1.9}]
7% = 1.8RP1 - 9.16% + 0.47RP1
16.16% = 2.27RP1
RP1 = 16.16%/2.27 = 7.11%
Therefore,
RP2 = [29% - (1.5 x RP1)] / 1.9
= [29% - (1.5 x 7.11%)] / 1.9 = 18.34% / 1.9 = 9.65%
The expected return-beta relationship in this economy is:
Re = 5% + [β1 x 7.11%] + [β2 x 9.65%]
Suppose there are two independent economic factors, M1 and M2. The risk-free rate is 5%, and...
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