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

A risk manager models returns using a Student's t distribution with 8 degrees of freedom. Given that excess kurtosis equals 6/(ν − 4) for ν > 4, what is the excess kurtosis?

The excess kurtosis is 1.5. Applying the formula 6 divided by (8 minus 4) gives 1.5. The total kurtosis would be 4.5, which exceeds the normal value of 3, reflecting the t distribution's heavier tails.

  1. A1.5Correct
  2. B4.5
  3. C3.0
  4. D0.75

Explanation

Excess kurtosis = 6/(8 − 4) = 1.5. The value 4.5 is the total kurtosis (3 + 1.5), not the excess. The value 3.0 results from using ν − 6 in the denominator, and 0.75 from dividing by ν instead of ν − 4.

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