Please show the steps how the risk premiums are calculated for y1=4.22% and y2=10.9%

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 returnbeta relationship in this economy? (Do not round intermediate calculations. Round your answers to 2 decimal places.)

rev: 04_04_2019_QC_CS-164824

Explanation

E(r_P) = r_f + _P1[E(r₁) r_f] + P₂[E(r₂) r_f] We need to find the risk premium for these two factors: 22 = [E(r₁) r_f] and 22 = [E(r₂) r_f]

To find these values, we solve the following two equations with two unknowns:

40% = 6% + 1.6 11 + 2.5 22

10% = 6% + 2.4 11 + (0.7) 22

The solutions are: 22 = 4.22% and 22 = 10.90%

Thus, the expected return-beta relationship is:

E(r_P) = 6% + 4.22_P1 + 10.90_P2