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

A stock has a risk-free rate of 2%, and factor loadings of beta_M = 1.2, beta_SMB = 0.5 and beta_HML = -0.3. Expected factor premiums are market excess return 6%, SMB 2% and HML 4%. Using the Fama-French three-factor model, what is the stock's expected return?

The expected return is 9.0%: 2% risk-free plus 7.2% from market exposure, plus 1.0% from size, minus 1.2% from the negative value loading. The negative HML beta reduces the expected return because the stock behaves like a growth stock.

  1. A9.0%
  2. B10.0%
  3. C9.8%Correct
  4. D11.4%

Explanation

Expected return = 2% + 1.2(6%) + 0.5(2%) + (-0.3)(4%) = 2 + 7.2 + 1.0 - 1.2 = 9.0%. Wait, recheck: 2 + 7.2 = 9.2; +1.0 = 10.2; -1.2 = 9.0%. The correct result is 9.0%; the 9.8% option would result from ignoring the sign of the HML loading incorrectly only partially, so it is wrong.

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