Question

Suppose there are two independent economic factors, M 1 and M 2 . The risk-free rate is 7%, and all stocks have independent firm-specific components with a standard deviation of 50%. Portfolios A and B are both well diversified.

What is the expected return–beta relationship in this economy?

Short answer

Thereturn beta relationship isE (r_P) = 7% + 4.47 β_P1+ 11.86β_P2

Step-by-step solution

Given Information

E(r_P) = 14%

r_f= 7%

β_P1= 1.8

β_P1= 2.0

Calculating the return beta relationship

E(r_P) = r_f +β_P1[E(r₁) - r_f] +β_P1 [E(r₂) – r_f]

Let’s assume,

γ₁=E(r₁) - r_f] and

γ₂=E(r₂) – r_f]

Let’s find the risk premium of these two above factors.

For this, let’s solve these with two unknowns:

40% = 7% + 1.8γ₁ + 2.1γ₂= 4.47%

10% = 7% + 2.0γ₁ + (0.5)γ₂= 11.86%

Therefore the return beta relationship = E (r_P) = 7% + 4.47 β_P1+ 11.86β_P2