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% | 1.525% |
| YCS | 0.20 | 0.024 |
| PR | 0.12 | 0.230 |
Test the statistical significance of YCS at the 10% level of significance, quoting the t-statistic and the conclusion if n = 46.
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TTanishq
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% level of significance:
Step 1: Calculate the t-statistic
The t-statistic for the YCS coefficient is calculated as:
Step 2: Determine the critical t-value
- Sample size (n) = 46
- Number of independent variables (excluding intercept) = 2 (YCS and PR)
- Degrees of freedom = n - k - 1 = 46 - 2 - 1 = 43
- For a two-tailed test at 10% significance level, the critical t-value is approximately 1.68
Step 3: Compare and conclude
Since the calculated t-statistic (8.333) > critical t-value (1.68), we reject the null hypothesis that the YCS coefficient equals zero.
Conclusion: The YCS coefficient is statistically significantly different from zero at the 10% level of significance.
Note: The question specifically asks to test YCS, not PR. The t-statistic for PR would be 0.12/0.230 = 0.522, which is not statistically significant.
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