Question

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 ReturnA 1.6 2.0 32%B 2.6 -0.20 29%What is the expected return-beta relationship in this economy?

Answer 1

Answer:

Rp = 3% + BP1 * 10.42% + BP2 * 6.1%

Explanation:

Portfolio A:

R_p = R_f + Beta1*Factor1 + Beta2*Factor2

32% = 3% + 1.6*F1 + 2*F2

Portfolio B

29% = 3% + 2.6*F1 - 0.2*F2

Solvig the equatios

3% = -F1 + 2.2*F2

F1 = 2.2F2 - 3%

F1 = 2.2F2 - 0.03

Substituting

29% = 3% + 2.6*(2.2F2 - 0.03) - 0.2F2

29% = 3% + 5.72F2 - 0.078 - 0.2F2

5.52F2 = 29% - 3% +0.078

5.52F2 = 0.26 +0.078

5.52F2= 0.338

F2 = 0.338/5.52 = 0.061

F1 = 2.2F2 - 0.03 = 2.2(0.061) - 0.03

    = 0.1042

The return Beta relationship in this economy  Rp = 3% + BP1 * 10.42% + BP2 * 6.1%