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FRM Part I · FRM Exam Part I · Common Univariate Random Variables

A student t distribution with 5 degrees of freedom is used to model standardized returns instead of a normal distribution. Which statement is correct?

For a t distribution with 5 degrees of freedom, variance is v/(v-2) = 5/3 and excess kurtosis is 6/(v-4) = 6. The heavy tails come from low degrees of freedom, and both moments converge to normal values as the degrees of freedom grow large.

  1. AIts variance is 5/3 and its excess kurtosis is 6Correct
  2. BIts variance is 5/3 and its excess kurtosis is 3
  3. CIts variance is 1 and its excess kurtosis is 6
  4. DIts variance is 3/5 and its excess kurtosis is 3

Explanation

For a t distribution, variance = v/(v-2) = 5/3 for v = 5. Excess kurtosis = 6/(v-4) = 6/1 = 6 (defined for v > 4). Variance of 1 would apply only as v approaches infinity, and 3/5 inverts the formula.

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