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

A fund's excess return is modeled with the Fama-French three-factor model: alpha = 0.50%, beta on market = 1.10, beta on SMB = 0.40, beta on HML = -0.30. Expected monthly factor premiums are: market excess 0.60%, SMB 0.20%, HML 0.30%. Ignoring the error term and including alpha, the fund's expected monthly excess return is closest to:

The expected excess return is alpha plus the sum of beta times premium: 0.50 + 1.10×0.60 + 0.40×0.20 − 0.30×0.30 = 1.15%, so the closest choice is 1.14%. Leaving out alpha would give about 0.65%.

  1. A1.14%Correct
  2. B0.64%
  3. C1.23%
  4. D1.05%

Explanation

Market: 1.10 x 0.60 = 0.66. SMB: 0.40 x 0.20 = 0.08. HML: -0.30 x 0.30 = -0.09. Sum of factor terms = 0.65; adding alpha 0.50 gives 1.15%. Closest option is 1.14%. Excluding alpha gives 0.65% (option B, the missed-alpha error).

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