How to Use an F-Test to Compare Stock Return Variances: A Step-by-Step Example
This article walks through a complete F‑test example comparing the monthly return variances of IBM and HP stocks over 36 months, detailing hypothesis formulation, calculation of the test statistic, critical value lookup, and interpretation of results to determine if the variances differ significantly.
The null and alternative hypotheses for both two‑tailed and one‑tailed tests are presented, and the degrees of freedom of the test statistic are specified.
Note: Always place the larger sample variance in the numerator so that the test statistic is greater than 1; then only the right‑hand rejection region needs to be considered, regardless of whether the test is one‑tailed or two‑tailed.
Example 1: We want to test whether the standard deviations of the monthly returns of IBM and HP stocks are equal. Using 36 months of data (2004‑200?), we measured standard deviations of ... and ... . With a significance level of ..., we perform the F‑test.
(1) State the null and alternative hypotheses.
(2) Conduct the F‑test.
(3) Compute the test statistic.
(4) Look up the critical value.
(5) Because the statistic does not fall in the rejection region, we cannot reject the null hypothesis.
(6) Conclude that the standard deviations of IBM and HP stocks are not significantly different.
Reference:
Zhu Shunquan, Economic and Financial Data Analysis and Its Python Application
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