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% | 1.567% |
| DB | 0.27 | 0.029 |
| YC | 0.12 | 0.210 |
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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TTanishq
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:
Statistical Significance Test for DB Coefficient
We are testing the following hypothesis:
Test Statistic Calculation
Critical Value
- Significance level: 5% (α = 0.05)
- Degrees of freedom: n - k - 1 = 43 - 2 - 1 = 40
- Critical t-value:
Decision
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. This means the trailing dividend payout ratio has a statistically significant relationship with future 15-year real earnings of the S&P 500._
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