Financial Risk Manager Part 1
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A market analyst has established that future 10-year growth of earnings in the S&P 500 can be explained by a combination of two factors: the slope of the yield curve (YCS) and the preceding dividend payout ratio (PR) of stocks that have been featured in the index.
The analyst carries out a regression and obtains the following results:
| Coefficient | Standard Error |
|---|---|
| Intercept | -10.6% |
| YCS | 0.20 |
| PR | 0.12 |
Test the statistical significance of YCS at the 10% level of significance, quoting the t-statistic and the conclusion if .
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NNikitesh
A
16.60; The YCS coefficient is statistically significantly different from zero
B
16.60; The PR coefficient is statistically significantly different from zero
C
8.333; The YCS coefficient is statistically significantly different from zero
D
1.68; The YCS coefficient is not statistically significantly different from zero
Explanation:
Explanation
To test the statistical significance of the YCS coefficient at the 10% significance level:
-
Calculate the t-statistic:
- Coefficient for YCS = 0.20
- Standard error for YCS = 0.024
- t-statistic = Coefficient / Standard Error = 0.20 / 0.024 = 8.333
-
Determine degrees of freedom:
- Sample size n = 46
- Number of independent variables (excluding intercept) = 2 (YCS and PR)
- Degrees of freedom = n - k - 1 = 46 - 2 - 1 = 43
-
Find critical t-value:
- For a two-tailed test at 10% significance level (α = 0.10)
- With 43 degrees of freedom, the critical t-value ≈ 1.68
-
Decision rule:
- Reject the null hypothesis if |t-statistic| > critical t-value
- 8.333 > 1.68, so we reject the null hypothesis
-
Conclusion:
- The YCS coefficient is statistically significantly different from zero at the 10% significance level
Note: The text incorrectly states to test H₀: PR = 0 vs H₁: PR ≠ 0, but the question asks to test YCS, not PR. The correct hypothesis test should be: H₀: YCS coefficient = 0 vs H₁: YCS coefficient ≠ 0
The t-statistic calculation and conclusion remain correct despite this minor error in the explanation text.
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