Financial Risk Manager Part 1

Explanation

This question involves testing the equality of variances between two populations (pharmaceutical stocks and e-commerce stocks). The appropriate statistical test for comparing variances is the F-test.

Formula for F-test statistic:

$F = \frac{s_1^2}{s_2^2}$

Where:

• $s_1$ = standard deviation of sample 1
• $s_2$ = standard deviation of sample 2

Given data:

• Pharmaceutical stocks standard deviation = 1.50%
• E-commerce stocks standard deviation = 2.10%

Calculation:

$F = \frac{(2.10\%)^2}{(1.50\%)^2} = \frac{0.021^2}{0.015^2} = \frac{0.000441}{0.000225} = 1.96$

Important convention:

In practice, it's conventional to place the larger variance in the numerator so that the F-statistic is always ≥ 1. This simplifies hypothesis testing since we only need to look at the right tail of the F-distribution.

Why other options are incorrect:

• A. 1.51: This might result from incorrectly calculating $\frac{2.10}{1.50}$ instead of the ratio of variances
• C. 1.70: This doesn't correspond to any logical calculation from the given data
• D. 2.14: This might result from calculating $\frac{1.50}{2.10}$ and then taking the reciprocal incorrectly

The correct test statistic value is 1.96, which corresponds to option B.