Normal distribution

The symmetric, bell-shaped distribution fully described by its mean and standard deviation. Convenient, but real returns have fatter tails, so it understates how often extreme outcomes arrive.

Where you will meet it

Normal distribution appears in 7 learning outcomes on the CFA syllabus. A few of them:

• Explain what skewness and kurtosis say about a return distribution
  CFA Level I · Quantitative Methods

  “Kurtosis measures tail weight relative to the normal distribution: excess kurtosis above zero means fat tails, so extreme outcomes are more likely than a normal distribution implies.”

• Set out how the main asset classes have performed historically in terms of risk and return
  CFA Level I · Portfolio Management

  “Equity returns show fat tails and negative skewness rather than a normal distribution.”

• Explain the inputs and choices a simulation involves and interpret what it produces
  CFA Level II · Portfolio Construction

  “A normal distribution usually understates tail losses compared with a fat-tailed distribution fitted to the same data, so conditional VaR can differ far more than the mean.”

• Explain the difficulties of managing currency exposure in emerging markets
  CFA Level III · Derivatives and Risk Management

  “Risk models built on normal distributions and calm-period data therefore understate losses, so managers should stress-test, size positions conservatively and expect hedging costs to rise in turmoil.”

See also

Standard deviation

Practise it

• Today's practice question One question, with every wrong option explained.
• Free Level I diagnostic test Twelve questions that show which topics to start with.
• Free finance calculators Check your arithmetic on the exam's core formulas.

All terms beginning with N · Glossary