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