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

A portfolio manager uses a two-factor model in which the expected return on a stock equals the risk-free rate plus factor betas multiplied by factor risk premiums. The risk-free rate is 3%, the stock's beta to factor 1 is 1.2 with a premium of 4%, and its beta to factor 2 is 0.5 with a premium of 6%. What is the stock's expected return?

The expected return is 10.8%. Add the risk-free rate of 3% to the factor contributions of 4.8% (1.2 times 4%) and 3.0% (0.5 times 6%). Leaving out the risk-free rate would give 7.8%, which is incorrect.

  1. A10.8%Correct
  2. B7.8%
  3. C12.0%
  4. D9.0%

Explanation

Expected return = 3% + 1.2×4% + 0.5×6% = 3% + 4.8% + 3.0% = 10.8%. Omitting the risk-free rate gives 7.8%, which is the wrong-base error.

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