Suppose we have two well-diversified portfolios (P_A and P_B) that are sensitive to the same single factor. The risk-free rate is 2%.

Portfolio | Expected return | Factor sensitivity
A | 0.08 | 2
B | 0.12 | 3

Are there any arbitrage opportunities?

Correct Answer: Yes

For P_A: 0.08 = 0.02 + 2 x λ₁
λ₁ = 0.03

If we use the same λ₁ to calculate the expected return of portfolio B: 0.02 + λ₁ x 3 = 0.02 + 0.03 x 3 = 11%.

However the expected return for portfolio B is 12%. This means that portfolio B is under-valued or portfolio A is over-valued. There is an arbitrage opportunity in this case.