Question

Suppose there are two independent economic factors, M₁ and M₂. The risk-free rate is 4%, and all stocks have independent firm-specific components with a standard deviation of 53%. Portfolios A and B are both well diversified.

Portfolio	Beta on M1	Beta on M2	Expected Return (%)
A	1.7	1.9	32
B	1.8	-0.7	13

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(r_P) = % + β_P1 + β_P2

Answer 1

Equation 1 is 4%+1.7*P1+1.9*P2=32%

Equation 2 is 4%+1.8*P1-0.7*P2=13%

multiply Equation 1 with 1.8, then Equation 3=4%*1.8+(1.7*1.8)*P1+(1.9*1.8)*P2=32%*1.8

multiply Equation 2 with 1.7, then Equation 4=4%*1.8+(1.7*1.8)*P1-(0.7*1.7)*P2=13%*1.7

subtract equation 4 from equation 3, we get as below

(1.9*1.8)*P2+(0.7*1.7)*P2=32%*1.8-13%*1.7

4.61*P2=0.355

P2=0.355/4.61=7.70%

Put P2 value in equation 1 as below

4%+1.7*P1+1.9*P2=32%

P1=((32%-4%)-(1.9*7.70%))/1.7

=7.86%

Then Expected return–beta relationship E(r_P) = % + β_P1 + β_P2

E(r_P) = 4%+ β*7.86%+ β*7.70%

the above is answer..