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Answer: There is a negative correlation between portfolio return and the value factor, which indicates that the portfolio moves together with growth stocks.
## Explanation **Understanding Fama-French Three-Factor Model:** The Fama-French three-factor model includes: - **Market factor**: Excess return of market over risk-free rate - **SMB (Small Minus Big)**: Size factor measuring performance difference between small-cap and large-cap stocks - **HML (High Minus Low)**: Value factor measuring performance difference between value stocks and growth stocks **Interpreting the Coefficients:** - **SMB coefficient = 0.18 (positive)**: - Positive correlation with size factor - Indicates portfolio moves together with **small-cap stocks** (not large-cap) - A is incorrect because positive SMB means small-cap exposure - **HML coefficient = -0.70 (negative)**: - Negative correlation with value factor - Indicates portfolio moves together with **growth stocks** (not value stocks) - D is correct because negative HML means growth stock exposure **Why Other Options Are Wrong:** - **A**: Incorrect - Positive SMB coefficient indicates small-cap exposure, not large-cap - **B**: Incorrect - Positive HML would indicate value stock exposure, but we have negative HML - **C**: Incorrect - Negative SMB would indicate large-cap exposure, but we have positive SMB **Key Takeaways:** - Positive SMB → Small-cap exposure - Negative SMB → Large-cap exposure - Positive HML → Value stock exposure - Negative HML → Growth stock exposure
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A risk analyst is evaluating an investment portfolio using the Fama-French three-factor model. The analyst regresses thirty years of weekly portfolio returns against the three factors of the model. The analyst obtains the following regression results:
| Alpha | 0.10 |
|---|---|
| Market coefficient | 0.52 |
| SMB coefficient | 0.18 |
| HML coefficient | -0.70 |
Assuming all estimated coefficients are statistically significant, which of the following is correct?
A
There is a positive correlation between portfolio return and the size factor, which indicates that the portfolio moves together with large-cap stocks.
B
There is a positive correlation between portfolio return and the value factor, which indicates that the portfolio moves together with growth stocks.
C
There is a negative correlation between portfolio return and the size factor, which indicates that the portfolio moves together with large-cap stocks.
D
There is a negative correlation between portfolio return and the value factor, which indicates that the portfolio moves together with growth stocks.