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FRM Part I · FRM Exam Part I · Sample Moments

An analyst tests whether 120 monthly returns are normally distributed using the Jarque-Bera statistic, JB = (n/6)[S^2 + (K-3)^2/4]. The sample skewness is -0.5 and the sample kurtosis is 4.0. The 5% critical value of a chi-square distribution with 2 degrees of freedom is 5.99. What is the result?

The Jarque-Bera statistic is 10.0, since 120/6 = 20 multiplied by (0.25 + 0.25) equals 10. This exceeds the 5% chi-square critical value of 5.99 with two degrees of freedom, so the hypothesis of normality is rejected.

  1. AJB = 10.0; reject normality at the 5% levelCorrect
  2. BJB = 10.0; fail to reject normality at the 5% level
  3. CJB = 5.0; fail to reject normality at the 5% level
  4. DJB = 2.5; fail to reject normality at the 5% level

Explanation

S^2 = 0.25 and (K-3)^2/4 = 1/4 = 0.25, sum 0.5. n/6 = 20, so JB = 10.0. This exceeds 5.99, so normality is rejected. JB = 5.0 ignores the kurtosis term; 2.5 uses n/24 in place of n/6; the second option has the right statistic but the wrong conclusion.

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