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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 the following Carhart four-factor loadings on excess return: market beta 0.90, SMB -0.20, HML 0.50, momentum (UMD) 0.40. Annual factor premiums are: market 6.0%, SMB 2.0%, HML 3.0%, UMD 8.0%. The risk-free rate is 3.0% and alpha is zero. Next, the analyst drops the momentum factor and uses the three-factor model with the same loadings for the first three factors. By how much does the expected return fall, in percentage points?

Dropping momentum removes its contribution of loading times premium, 0.40 × 8.0% = 3.2 percentage points. Expected return falls from 12.7% to 9.5%, because the other factor contributions are unchanged.

  1. A3.2Correct
  2. B5.4
  3. C0.4
  4. D8.0

Explanation

Four-factor expected excess return: 0.90×6 = 5.4; -0.20×2 = -0.4; 0.50×3 = 1.5; 0.40×8 = 3.2; total 9.7%, so expected return 12.7%. Three-factor excess return = 6.5%, expected return 9.5%. The difference is the momentum contribution, 0.40×8 = 3.2 points. Option D ignores the loading.

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