Financial Risk Manager Part 1
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The average return on the Dow Jones Industrial Average for 121 quarterly observations is 1.5%. If the standard deviation of the returns can be assumed to be 8%, then what is the 99% confidence interval for the quarterly returns of the Dow Jones?
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Community
NNikitesh
A
[-0.4%; 3.4%]
B
[0.1%; 2.9%]
C
[-6.5%; 9.5%]
D
[-0.1%; 2.9%]
Explanation:
Calculation Steps:
-
Standard Error Calculation: Standard error = Standard deviation / √Sample size = 8% / √121 = 8% / 11 = 0.727% or 0.00727
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Critical Value for 99% Confidence Interval: For a 99% confidence interval, the z-statistic critical value is 2.575
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Confidence Interval Calculation: Lower bound = Mean - (z × Standard error) = 1.5% - (2.575 × 0.727%) = 1.5% - 1.87% = -0.37% ≈ -0.4%
Upper bound = Mean + (z × Standard error) = 1.5% + (2.575 × 0.727%) = 1.5% + 1.87% = 3.37% ≈ 3.4%
Therefore, the 99% confidence interval is [-0.4%; 3.4%].
Key Concepts:
- The confidence interval provides a range of values within which the true population mean is likely to fall with a specified level of confidence (99% in this case).
- The standard error decreases as sample size increases, making the confidence interval narrower.
- The z-statistic of 2.575 corresponds to the critical value for a two-tailed test at 99% confidence level (0.5% in each tail).
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