CFA Level I · CFA Level I Exam · Estimation and Hypothesis Testing
An analyst compares the return volatility of two independent portfolios. Portfolio X has a sample variance of 0.0090 from 21 observations, and Portfolio Y has a sample variance of 0.0045 from 31 observations. Assuming normal returns, the F-statistic for testing equality of the variances, with the larger variance in the numerator, is closest to:
The F-statistic is about 2.00, found by dividing the larger sample variance, 0.0090, by the smaller, 0.0045. Degrees of freedom are 20 in the numerator and 30 in the denominator, and the sample sizes do not alter the ratio.
- A0.50
- B2.00Correct
- C2.10
Explanation
F = larger sample variance / smaller sample variance = 0.0090/0.0045 = 2.00, with 20 numerator and 30 denominator degrees of freedom. Inverting gives 0.50, which would put the smaller variance on top. Sample sizes do not enter the statistic itself.
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