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CMA Final · Strategic Financial Management · Asset Pricing Theories

In a Fama-French three-factor model, the risk-free rate is 6%, the market premium is 7%, the SMB premium is 3% and the HML premium is 4%. A stock has loadings of 1.1 on market, 0.5 on SMB and −0.3 on HML. It is priced at ₹200 and is expected to be worth ₹224 after one year, with a dividend of ₹6 during the year. What is the stock's expected alpha (expected return less model-required return)?

The alpha is +1.0%. The three-factor required return is 6% + 7.7% + 1.5% − 1.2% = 14%. The expected return is (24 + 6)/200 = 15%. Expected return exceeds required return by 1 percentage point, so the stock is slightly underpriced.

  1. A+1.0%Correct
  2. B−1.0%
  3. C+7.0%
  4. D−1.4%

Explanation

Required return = 6 + 1.1×7 + 0.5×3 + (−0.3)×4 = 6 + 7.7 + 1.5 − 1.2 = 14.0%. Expected return = (224 − 200 + 6)/200 = 15%. Alpha = 15 − 14 = +1.0%. Omitting the risk-free rate gives a required return of 8% and an alpha of 7%. Treating the HML term as +1.2 gives a required return of 16.4% and an alpha of −1.4%.

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