- CFA Exams
- CFA Level I Exam
- Study Session 16. Portfolio Management (1)
- Reading 44. Using Multifactor Models
- Subject 1. Arbitrage pricing theory
CFA Practice Question
Suppose we have two well-diversified portfolios (PA and PB) that are sensitive to the same single factor. The risk-free rate is 2%.
A | 0.08 | 2
B | 0.12 | 3
Portfolio | Expected return | Factor sensitivity
A | 0.08 | 2
B | 0.12 | 3
Are there any arbitrage opportunities?
Correct Answer: Yes
λ1 = 0.03
For PA: 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.
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