Question

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 42%. Portfolios A and B are both well diversified.

Portfolio	Beta on M1	Beta on M2	Expected Return (%)
A	1.5	2.4	32
B	2.3	-0.5	10

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

The equation for the expected - beta relationship in this economy can be explained as below:

E(r_p) = R_f + β_P1*(Er₁-R_f) + β_P2 * (Er₂ - R_f)

Let x₁ = Er₁-Rf
x₂ = Er₂ - Rf
now to solve for x₁ and x₂, we need to solve the below two equations epresenting Portfolio A and Portfolio B returns.

therefore, 32% = 6% + 1.5x₁ + 2.4x₂
and 10% = 6% + 2.3x₁ + (-0.5)x₂

Solving for x₁ and x_2.
we get, x₁ = 3.60
      x₂ = 8.58



Putting x₁ and x₂ in the below equation:
E(r_p) = R_f + β_P1*(Er₁-R_f) + β_P2 * (Er₂ - R_f)
E(r_p) = 6% + 3.60*β_P1 + 8.58* β_P2