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

In a single-factor APT model, the risk-free rate is 3%, and the expected return on a well-diversified portfolio with factor beta 1.0 is 9%. A well-diversified portfolio A has beta 1.5. If no arbitrage holds, what is the expected return of portfolio A?

The expected return is 12.0%. The factor risk premium is 9% minus 3%, or 6% per unit of beta. Multiplying by beta of 1.5 gives a 9% premium, which added to the 3% risk-free rate gives 12.0% under no-arbitrage pricing.

  1. A12.0%Correct
  2. B13.5%
  3. C9.0%
  4. D10.5%

Explanation

The factor risk premium is 9% - 3% = 6% per unit of beta. Portfolio A expected return = 3% + 1.5 x 6% = 12.0%. The 13.5% option wrongly applies beta to the total return (1.5 x 9%), and 10.5% adds only 1.5% of beta to risk-free incorrectly.

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