Answer-first summary for fast verification
Answer: –0.30%
## Explanation The Fama-French three-factor model equation is: \[R_{GRI} - R_f = \alpha + \beta_{MKT} \times (R_{mkt} - R_f) + \beta_{HML} \times R_{HML} + \beta_{SMB} \times R_{SMB}\] **Given values:** - Stock GRI return (R_GRI) = 7.8% - Risk-free rate (R_f) = 1.50% - Market return (R_mkt) = 6.00% - Market beta (β_MKT) = 1.25 - HML beta (β_HML) = -0.45 - HML factor return (R_HML) = 2.50% - SMB beta (β_SMB) = 2.10 - SMB factor return (R_SMB) = 1.00% **Calculation:** \[7.8\% - 1.50\% = \alpha + 1.25 \times (6.00\% - 1.50\%) + (-0.45) \times 2.50\% + 2.10 \times 1.00\%\] \[6.30\% = \alpha + 1.25 \times 4.50\% + (-1.125\%) + 2.10\%\] \[6.30\% = \alpha + 5.625\% - 1.125\% + 2.10\%\] \[6.30\% = \alpha + 6.60\%\] \[\alpha = 6.30\% - 6.60\% = -0.30\%\] **Why other options are incorrect:** - **A (-2.55%)**: Uses absolute value of negative HML beta - **B (-2.18%)**: Forgets to subtract risk-free rate from market return before multiplying by beta - **D (1.20%)**: Forgets to subtract risk-free rate on the left side of the equation
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A portfolio manager at a mutual fund is evaluating the end-of-year returns of the stocks in the portfolio and comparing them to those predicted by the Fama-French model. The manager considers stock GRI, which had a return of 7.8% over the previous year and had a beta to the market of 1.25. The factor betas for the stock and the returns of each factor are presented in the following table:
| Factor | Factor beta | 1-year factor return |
|---|---|---|
| HML factor | –0.45 | 2.50% |
| SMB factor | 2.10 | 1.00% |
The market had a return of 6.00% over the previous year and the risk-free rate of interest remained constant at 1.50%. What was the alpha of stock GRI for the previous year?
A
–2.55%
B
–2.18%
C
–0.30%
D
1.20%
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