USING THE PRIOR 12 MONTHLY RETURNS, AN ANALYST ESTIMATES THE MEAN M...
2.
Using the prior 12 monthly returns, an analyst estimates the mean monthly return of stock XYZ to be -0.75%
with a standard error of 2.70%.
ONE-TAILED T-DISTRIBUTION TABLE
Degrees of Freedom
α
0.10
0.05
0.025
8
1.397
1.860
2.306
9
1.383
1.833
2.262
10
1.372
1.812
2.228
11
1.363
1.796
2.201
12
1.356
1.782
2.179
Using the t-table above, the 95% confidence interval for the mean return is between:
a.
-6.69% and 5.19%
b.
-6.63% and 5.15%
c.
-5.60% and 4.10%
d.
-5.56% and 4.06%
Correct Answer: a
Rationale:
The confidence interval is equal to the mean monthly return plus or minus the t-statistic times the stan-
dard error. To get the proper t-statistic, the 0.025 column must be used since this is a two-tailed interval. Since the
mean return is being estimated using the sample observations, the appropriate degrees of freedom to use is equal
to the number of sample observations minus 1. Therefore we must use 11 degrees of freedom and therefore the
proper statistic to use from the t-distribution is 2.201.
The proper confidence interval is: -0.75% +/- (2.201 * 2.70%) or -6.69% to +5.19%.
Section:
Quantitative Analysis
Reference: Michael Miller, Mathematics and Statistics for Financial Risk Management, 2nd Edition
(Hoboken, NJ:
John Wiley & Sons, 2013). Chapter 7, “Hypothesis Testing and Confidence Intervals.”
Learning Objective:
Construct and interpret a confidence interval.
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2015 Financial Risk Manager (FRM®) Practice Exam