Skip to content

FRM Part I · FRM Exam Part I · Random Variables

A risk analyst estimates that a return distribution has a variance of 4 and a fourth central moment of 80. Which statement about its kurtosis is correct?

Kurtosis is 5, because the fourth central moment of 80 is divided by the squared variance of 16. Since a normal distribution has kurtosis of 3, excess kurtosis is 2, which indicates heavier tails than the normal distribution.

  1. AKurtosis is 5, so the distribution has heavier tails than a normal distributionCorrect
  2. BKurtosis is 20, so the distribution has heavier tails than a normal distribution
  3. CKurtosis is 2, so the distribution has lighter tails than a normal distribution
  4. DKurtosis is 10, so the distribution has heavier tails than a normal distribution

Explanation

Kurtosis = fourth central moment / variance squared = 80 / 16 = 5. A normal distribution has kurtosis of 3, so excess kurtosis is 2 and the tails are heavier. Dividing by the variance (80/4 = 20) is the wrong scaling, and 10 results from dividing by the cube of the standard deviation (80/8).

Did you get it right without looking?

One question tells you little. A timed set on Random Variables shows your real accuracy, how long you take and where you lose marks.

Practise Random VariablesFree diagnostic mock

More Random Variables questions