Financial Risk Manager Part 1
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An analyst believes that future 15-year real earnings of the S&P 500 are a function of the trailing dividend payout ratio of the stocks in the index (DB) and the yield curve slope (YC). She collects data and obtains the following multiple regression results:
| Coefficient | Standard error |
|---|---|
| Intercept | -10.8% |
| DB | 0.27 |
| YC | 0.12 |
Test the statistical significance of the independent variable DB at the 5% level of significance, quoting the value of the test statistic and the conclusion. (Number of observations = 43)
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NNikitesh
A
Test statistic = 2.021; DB regression coefficient is statistically different from zero
B
Test statistic = 9.310; DB regression coefficient is statistically different from zero
C
Test statistic = 0.018; DB regression coefficient is not statistically different from zero
D
Test statistic = 9.310; DB regression coefficient has little effect on the returns of S&P 500
Explanation:
Explanation:
We are testing the following hypothesis: H₀: DB = 0 vs H₁: DB ≠ 0
Test Statistic Calculation: The test statistic is calculated as:
Degrees of Freedom: Number of observations (n) = 43 Number of independent variables (k) = 2 (DB and YC) Degrees of freedom = n - k - 1 = 43 - 2 - 1 = 40
Critical Value: For a two-tailed test at 5% significance level with 40 degrees of freedom: t₀.₀₂₅,₄₀ = 2.021
Decision Rule: Since the test statistic (9.310) is greater than the critical value (2.021), we reject the null hypothesis.
Conclusion: The DB regression coefficient is statistically different from zero at the 5% level of significance.
Why other options are incorrect:
- A: Uses the critical value (2.021) as the test statistic
- C: Incorrectly calculates the test statistic (0.27/0.029 ≠ 0.018)
- D: While it has the correct test statistic, the conclusion "has little effect on the returns of S&P 500" is incorrect - statistical significance doesn't necessarily imply economic significance, but the coefficient is statistically significant.
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