FRM Part I · FRM Exam Part I · Hypothesis Testing
A risk analyst tests whether the variance of a portfolio's monthly returns differs from a benchmark value. H0: σ² = 16 (in %²). A random sample of 21 monthly returns gives a sample variance of 25 (%²). What is the chi-square test statistic?
The chi-square statistic is 31.25. It equals the degrees of freedom (20) times the sample variance (25) divided by the hypothesized variance (16). Using n rather than n−1, or inverting the ratio, gives wrong values.
- A31.25Correct
- B32.81
- C25.00
- D12.80
Explanation
The statistic is (n−1)s²/σ0² = 20 × 25 / 16 = 31.25, with 20 degrees of freedom. Using n instead of n−1 gives 32.81. Using the ratio of standard deviations times df gives 25. Inverting the ratio gives 12.80.
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