What is standard deviation?

What it means

Roughly two thirds of observations fall within one standard deviation of the mean and about 95% within two, provided the distribution is normal. That proviso is doing heavy lifting, because financial returns are not normally distributed.

Why it matters

Real markets have fat tails: extreme moves occur far more often than a normal distribution predicts. A move described as a five-standard-deviation event should happen roughly once in several thousand years and in practice happens every few years, which means models built on normality systematically understate tail risk.

What this changes in practice

It is nonetheless the basis of Bollinger Bands and of most volatility scaling, and it works acceptably for the ordinary middle of the distribution. The mistake is trusting it about the extremes — which are exactly the events that end accounts.