Consider the estimation of the CAPM and the Fama-French three-factor model:

r_it r_ft= _i + _i(r_Mt r_ft) + _it,

r_it r_ft= _i + _i(r_Mt r_ft) + s_iSMB_t+ h_iHML_t + _it.

You analyze a stock, run the Fama-French regression above, and obtain the following estimates: _i = 0.5%, _i= 1.3, s_i= 0.3, and h_i= 0.5. Suppose that regardless of which model you use, you obtain the same estimate for _i. In particular, assume that the stock's sensitivity to the market risk, _i , is the same in both the CAPM and the Fama-French model.

Assume that E[r_Mt r_ft] = 8%, E[SMB_t ] = 4%, E[HML_t ] = 6%, and the current risk-free interest rate r_f = 3%.

a) What is the required rate of return on the stock if the Fama-French model holds? What is the expected rate of return on the stock?

b) What is the required rate of return on the stock if the CAPM holds?

c) Explain the reasons for the difference between the stock's required rates of return in the CAPM and the Fama-French model.

d) Suppose that the expected rate of return on the stock is the same as your answer in a). Compute the stock's alpha in the CAPM.

e) Would you buy this stock if you believe in the CAPM? Would your answer be different if you believed in the Fama-French model instead?