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

A two-factor APT model has a risk-free rate of 3%, a factor 1 risk premium of 5% and a factor 2 risk premium of 2%. A stock has betas of 1.2 on factor 1 and 0.5 on factor 2. What is the stock's expected return under APT?

The expected return is 10%. Add the risk-free rate of 3% to the factor 1 premium of 1.2 times 5%, which is 6%, and the factor 2 premium of 0.5 times 2%, which is 1%. The total is 3% plus 6% plus 1%, equal to 10%.

  1. A10.0%Correct
  2. B9.0%
  3. C7.0%
  4. D6.0%

Explanation

E(R) = 3% + 1.2×5% + 0.5×2% = 3% + 6% + 1% = 10%. Omitting the risk-free rate gives 7%. Ignoring factor 2 gives 9%. Using only the factor 1 premium without the risk-free rate gives 6%.

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