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;
30% = 5% + 1.8(Rp1) + 2.2(Rp2)
30% - 5% = 1.8(Rp1) + 2.2(Rp2)
Rp1 = [25% - 2.2(Rp2)] / 1.8
For Portfolio B;
8% = 5% + 2.1(Rp1) - 0.5(Rp2)
Put the value of Rp1 calculated above in Portfolio A,
8% = 5% + 2.1[{25% - 2.2(Rp2)} / 1.8] - 0.5(Rp2)
8% - 5% = 29.16% - 2.56(Rp2) - 0.5(Rp2)
3% = 29.16% - 3.06(Rp2)
3.06(Rp2) = 29.16% - 3%
Rp2 = 26.16% / 3.06 = 8.53%
Put the value of Rp2 in the equation,
Rp1 = [25% - (2.2 * 8.60%)] / 1.8
= [25% - 18.92%] / 1.8 = 3.46%
Thus, the expected return-beta relationship is:
E(Rp) = 5% +(3.46%)*β(1,p) +(8.53%)*β(2,p)
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