Question

Suppose there are two independent economic factors, M 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 My Beta on M2 Expected Return (%) 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(TP) BP2

Answer 1

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;

34% = 5% + 1.5(Rp1) + 1.9(Rp2)

34% - 5% = 1.5(Rp1) + 1.9(Rp2)

Rp1 = [29% - 1.9(Rp2)] / 1.5 ==========> Eq.(1)

For Portfolio B;

12% = 5% + 1.8(Rp1) - 0.6(Rp2)

Put the value of Rp1 from Eq.(1)

12% = 5% + 1.8[{29% - 1.9(Rp2)} / 1.5] - 0.6(Rp2)

12% - 5% = 34.8% - 2.28(Rp2) - 0.6(Rp2)

7% = 34.8% - 2.88(Rp2)

2.88(Rp2) = 34.8% - 7%

Rp2 = 27.8% / 2.88 = 9.65%

Put the value of Rp2 in Eq.(1);

Rp1 = [29% - (1.9 * 9.65%)] / 1.5

= [29% - 18.34%] / 1.5 = 10.66% / 1.5 = 7.11%

Thus, the expected return-beta relationship is:

E(Rp) = Rf + β(1,p)[7.11%] + β(2,p)[9.65%]