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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 0.8 to a single factor, with a risk-free rate of 2% and a factor risk premium of 5%. The portfolio's expected return is 7%. Which statement best describes the situation and the arbitrage action?

The portfolio is underpriced. Its fair return is 2% plus 0.8 times 5%, or 6%, but it offers 7%. An arbitrageur buys it and shorts a replicating mix with beta 0.8, such as 80% factor portfolio and 20% risk-free asset, locking in a 1% riskless gain.

  1. AThe portfolio is fairly priced because its beta is below 1
  2. BThe portfolio is overpriced; short it and buy a risk-free asset
  3. CThe portfolio is underpriced; buy it and short a combination of the factor portfolio and risk-free asset with beta 0.8Correct
  4. DThe portfolio is underpriced; buy it and short the risk-free asset only

Explanation

The fair expected return is 2% + 0.8 x 5% = 6%. The portfolio offers 7%, so it is underpriced by 1%. The arbitrage buys it and shorts a replicating portfolio with the same beta of 0.8 (80% factor portfolio, 20% risk-free) to remove factor risk. Shorting only the risk-free asset leaves factor exposure.

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