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 |
Calculate the 95% confidence interval for the estimated coefficient for the independent variable DB. (Number of observations = 43)
Other
Community
NNikitesh
A
(0.27, 0.3286)
B
(0.2, 0.3)
C
(0.2114, 2.0)
D
(0.2114, 0.3286)
Explanation:
The confidence interval is calculated using the formula: CI = βⱼ ± (tₐ,ₙ₋ₖ₋₁ * Se(βⱼ))
Where:
- βⱼ = coefficient for DB = 0.27
- Se(βⱼ) = standard error for DB = 0.029
- n = number of observations = 43
- k = number of regressors = 2 (DB and YC)
- Degrees of freedom = n - k - 1 = 43 - 2 - 1 = 40
- t-value for 95% confidence with 40 degrees of freedom = 2.021 (from t-distribution table)
Calculation: CI_DB = 0.27 ± (2.021 * 0.029) = 0.27 ± 0.05861 = (0.2114, 0.3286)
Therefore, the correct 95% confidence interval is (0.2114, 0.3286).
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