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

An analyst uses a three-factor model to estimate required return. The risk-free rate is 2.0%. Factor sensitivities and premiums are: market 1.0 and 5.0%; size 0.5 and 2.0%; value -0.4 and 3.0%. The required return is closest to:

The required return is about 7.0% (6.8% exactly). Add the risk-free rate of 2.0% to each sensitivity times its premium: 5.0% for market, 1.0% for size, and negative 1.2% for value.

  1. A4.8%
  2. B5.8%Correct
  3. C7.0%

Explanation

Required return = 2.0% + 1.0×5.0% + 0.5×2.0% + (−0.4)×3.0% = 2.0 + 5.0 + 1.0 − 1.2 = 6.8%. Recheck: 2.0+5.0=7.0; +1.0=8.0; −1.2=6.8%. The closest option is therefore 7.0%; 5.8% results from subtracting rather than adding the size term's effect incorrectly, and 4.8% omits the risk-free rate and the size term.

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