- CFA Exams
- CFA Level I Exam
- Study Session 16. Portfolio Management (1)
- Reading 44. Using Multifactor Models
- Subject 1. Arbitrage pricing theory

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**CFA Practice Question**

Suppose we have two well-diversified portfolios (P

A | 0.08 | 2

B | 0.12 | 3

_{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

λ

For P

_{A}: 0.08 = 0.02 + 2 x λ_{1}λ

_{1}= 0.03If we use the same λ

_{1}to calculate the expected return of portfolio B: 0.02 + λ_{1}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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