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FRM Part I · FRM Exam Part I · The Arbitrage Pricing Theory and Multifactor Models of Risk and Return

A well-diversified portfolio has a beta of 1.2 to a single factor. The risk-free rate is 3% and the factor risk premium is 5%. Under a one-factor APT, the portfolio is observed to offer an expected return of 10%. What is the expected-return mispricing and the implied arbitrage action?

The APT required return is 3% plus 1.2 times 5%, which equals 9%. The portfolio offers 10%, so it is underpriced by 1.0%. An arbitrageur would buy it and short a factor-matched portfolio with the same beta to lock in the excess return.

  1. AThe portfolio is underpriced by 1.0%; buy it and short a factor-matched portfolioCorrect
  2. BThe portfolio is overpriced by 1.0%; short it and buy a factor-matched portfolio
  3. CThe portfolio is underpriced by 4.0%; buy it and short a factor-matched portfolio
  4. DThe portfolio is fairly priced; no arbitrage exists

Explanation

APT required return = 3% + 1.2 x 5% = 9%. The portfolio offers 10%, which is 1.0% above the required return, so it is underpriced. An arbitrageur buys it and shorts a combination with the same factor beta (1.2) to remove factor risk. Using 7% as the required return would wrongly omit the risk-free rate, and 4% is a different error.

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