Lognormal Distribution

A lognormal distribution is a statistical shape describing a set of numbers where the LOGARITHM of those numbers, not the numbers themselves, forms a normal distribution (the familiar symmetric "bell curve"). In trading, it is the shape often used to describe stock prices or the returns compounded over time, rather than the day-to-day percentage changes themselves.

Here is why it fits prices reasonably well: a normal distribution is symmetric and stretches equally in both directions, including into negative numbers. A stock price cannot go below zero, so a symmetric bell curve is a poor model for the price itself. If instead you look at the price's logarithm, or equivalently think in terms of percentage moves compounded over many periods, the resulting distribution is skewed to the right, has a long tail toward high values, and never dips below zero. That matches how prices actually behave: a stock can rise without any theoretical ceiling but can only fall to zero, never past it.

The nuance that trips people up is the difference between the distribution of PRICES and the distribution of RETURNS (the period-to-period percentage changes). Simple percentage returns over short, discrete periods are often modeled as roughly normal for convenience, while the price level itself, or continuously compounded returns over a longer horizon, are modeled as lognormal. Traders and analysts sometimes use the terms loosely, so it is worth checking which one a given model or tool is actually assuming.

It is also worth remembering this is a simplifying assumption, not a law of nature. Real markets show fatter tails and more extreme jumps than a clean lognormal curve predicts, especially around news events, earnings, or panics. Models like Black-Scholes option pricing lean on the lognormal assumption because it is mathematically tractable, but that assumption is a known weak point of those models, not an empirical guarantee.