Probability

Standard Deviation

Also known as: SD, Sigma, Volatility

The square root of variance, expressing dispersion in the same units as the data.

sigma = sqrt(Var(X)).

In finance this is volatility. Annualising assumes independent returns and uses the square-root-of-time rule: multiply a daily figure by sqrt(252) ≈ 15.9. A 1% daily standard deviation is roughly 16% annualised, which is a conversion worth being able to do instantly.

For a normal distribution, about 68% of outcomes fall within one standard deviation, 95% within two and 99.7% within three.

The trap. Those percentages assume normality. Financial returns have fat tails, so "a five-sigma event" occurs far more often than the normal distribution implies - which is why the phrase is usually a sign the model is wrong rather than that something remarkable happened.

Related terms

Practise this

Put it into practice

Knowing the definition is not the same as spotting where it applies under time pressure. Work the question bank free.

Start practising free

Browse the full quant interview glossary