Kurtosis

A measure of how heavy a distribution's tails are relative to its centre. A normal distribution has a kurtosis of 3.

Where you will meet it

Kurtosis comes up in 12 learning outcome notes across the FRM syllabus. A few of them:

• Random Variables
  FRM Part I · Quantitative analysis

  “Kurtosis is the standardised fourth central moment: Kurtosis = E((X − μ)⁴) ÷ σ⁴.”

• Measures of Financial Risk
  FRM Part I · Valuation and risk models

  “The normal distribution is symmetric, with skewness 0 and kurtosis 3, and is fully described by its mean and variance.”

• Volatility Smiles and Volatility Surfaces
  FRM Part II · Market risk measurement and management

  “Both features put more probability than a lognormal in the tails and give a higher peak, which is positive excess kurtosis.”

• Random Variables
  FRM Part I · Quantitative analysis

  “Skewness and kurtosis are standardised moments, so they ignore both a and the size of b.”

See also

Normal distribution

All terms beginning with K · FRM glossary

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