Suppose there are two independent economic factors, M1 and M2. The risk-free rate is 6%, and all stocks have independent firm-specific components with a standard deviation of 50%. Portfolios A and B are both well diversified. Portfolio Beta on M1 Beta on M2 Expected Return (%) A 1.6 2.5 40 B 2.4 -0.7 10 What is the expected return–beta relationship in this economy? (Do not round intermediate calculations. Round your answers to 2 decimal places.)
E(Rp) = Rf + β(1,p)[E(R1) - Rf] + β(2,p)[E(R2) - Rf]
We need to find the risk premium Rp for each of the two factors:
Rp1 = [E(R1) - Rf]
Rp2 = [E(R2) - Rf]
For Portfolio A;
40% = 6% + 1.6(Rp1) + 2.5(Rp2)
40% - 6% = 1.6(Rp1) + 2.5(Rp2)
Rp1 = [34% - 2.5(Rp2)] / 1.6 ==========> Eq.(1)
For Portfolio B;
10% = 6% + 2.4(Rp1) - 0.7(Rp2)
Put the value of Rp1 from Eq.(1)
10% = 6% + 2.4[{34% - 2.5(Rp2)} / 1.6] - 0.7(Rp2)
10% - 6% = 51% - 3.75(Rp2) - 0.7(Rp2)
4% = 51% - 4.45(Rp2)
4.45(Rp2) = 51% - 4%
Rp2 = 47% / 4.45 = 10.56%
Put the value of Rp2 in Eq.(1);
Rp1 = [34% - (2.5 * 10.56%)] / 1.6
= [34% - 26.40%] / 1.6 = 7.60% / 1.6 = 4.75%
Thus, the expected return-beta relationship is:
E(Rp) = 6% + β(1,p)[4.75%] + β(2,p)[10.56%]
Suppose there are two independent economic factors, M1 and M2. The risk-free rate is 6%, and...
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