Suppose you are given the following information. The beta of company i, b?i? , i

Question

Suppose you are given the following information. The beta of company i, b?i? , is 1.5, the risk-free rate, r?RF? , is 5 percent, and the expected market premium, r?M???-???r?RF? , is 5.5 percent. (Assume that a?i???=???0.0? .)

b. Because your company is smaller than average and more successful than average (that is, it has a low book-to-market ratio), you think the Fama-French three-factor model might be more appropriate than the CAPM. You estimate the additional coefficients from the Fama-French three-factor model: The coefficient for the size effect, c?i? , is 0.5, and the coefficient for the book-to-market effect, d?i? , is -0.2. If the expected value of the size factor is 6 percent and the expected value of the book-to-market factor is 3 percent, what is the required return using the Fama-French three-factor model? Round your answer to two decimal places.

Explanation / Answer

The Fama-French model:
      ri = rRF + (rm - rBF) bi + (rsmb) ci + (rhmb) dj
      ri = 5% + (5.5%)(1.5) + (6%)(0.5) + (3%)(-0.2) = 13.25% + 3% - 0.6% = 15.65%
      ri = 15.65%

The CAPM:
     ri = rrf + (rm – rrf) bi
     ri = 5% + (5.5%)(1.5) = 13.25%
     ri = 13.25%

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