Question

# Suppose there are two independent economic factors, M1 and M2. The risk-free rate is 6%, and...

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(rP) =  % +  βP1 +  βP2

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

E(rp) = Rf + βP1*(Er1-Rf) + βP2 * (Er2 - Rf)

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 x2.
we get, x1 = 3.60
x2 = 8.58

Putting x1 and x2 in the below equation:
E(rp) = Rf + βP1*(Er1-Rf) + βP2 * (Er2 - Rf)
E(rp) = 6% + 3.60*βP1 + 8.58* βP2