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CFA Level I · CFA Level I Exam · The Capital Asset Pricing Model, Market Model, and Other Factor-Based Equity Models

A Carhart four-factor model gives these inputs: risk-free rate 2.0%, market risk premium 6.0%, SMB premium 2.0%, HML premium 3.0%, WML premium 4.0%. A stock has betas of 1.10 (market), 0.50 (SMB), -0.20 (HML) and 0.30 (WML). The stock's expected return is closest to:

The expected return is about 10.2%. The risk premiums contribute 6.6% from the market, 1.0% from size, -0.6% from value and 1.2% from momentum, totaling 8.2%. Adding the 2.0% risk-free rate gives 10.2%.

  1. A8.2%
  2. B10.2%Correct
  3. C11.2%

Explanation

Market: 1.10 x 6.0 = 6.6. SMB: 0.5 x 2 = 1.0. HML: -0.2 x 3 = -0.6. WML: 0.3 x 4 = 1.2. Sum of premiums = 8.2. Adding the 2.0% risk-free rate gives 10.2%. Omitting the risk-free rate gives 8.2%, the first option.

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