Financial Risk Manager Part 1
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A portfolio manager believes that returns on pharmaceutical stocks are more volatile than the returns generated on e-commerce stocks. To check this hypothesis, the portfolio manager collects the data summarized in exhibit 1.
Exhibit 1: Volatility in Pharmaceutical vs. e-Commerce Stocks
| Pharma Stock | e-Commerce Stocks | |
|---|---|---|
| Standard Deviation | 1.50% | 2.10% |
| Sample Size | 20 | 25 |
What is the value of the test statistic?
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TTanishq
A
1.51
B
1.96
C
1.7
D
2.14
Explanation:
Explanation
As the test requires testing the equality of variances of two populations, the appropriate test is the F-test.
Test Statistic Calculation:
[ \text{Test statistic} = \frac{(\text{std. dev. ecommerce})^2}{(\text{std. dev. pharma})^2} ]
[ = \frac{(2.10%)^2}{(1.50%)^2} = \frac{0.000441}{0.000225} = 1.96 ]
Important Note:
A convention, or usual practice, is to use the larger of the two standard deviations on top (in the numerator). When we follow this convention, the value of the test statistic is always greater than or equal to 1; tables of critical values of F then need to include only values greater than or equal to 1. Under this convention, the rejection point for any formulation of hypotheses is a single value on the right-hand side of the relevant F-distribution. However, even without following this convention, we would still arrive at the same conclusion (on whether or not to reject the null).
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