Probability Distribution

What Is a Probability Distribution?

A probability distribution describes the possible results of an uncertain quantity, such as a stock's return over the next year, and assigns a probability to each result. The probabilities always add up to 100 percent, so every possible outcome is accounted for. Analysts use distributions to think about risk. Instead of asking what one future price will be, they ask how the range of possible prices is spread out.

How It Works

Distributions come in two broad forms. A discrete distribution covers outcomes that can be counted, such as the number of days in a month a stock closes higher. A continuous distribution covers outcomes that can take any value within a range, such as a daily percentage return. For continuous outcomes, the distribution is often drawn as a curve, and the area under the curve between two points gives the probability that the outcome falls between them.

Several features describe a distribution's shape. The center, often measured by the expected value, shows where outcomes tend to cluster. The spread, measured by standard deviation, shows how far outcomes typically scatter from that center. Skewness describes whether one tail is longer than the other, and kurtosis describes how heavy the tails are overall.

An Example

A common example is the normal distribution, the familiar bell-shaped curve. Many financial models assume that daily returns roughly follow this shape, because it makes calculations simpler. However, real market returns often show fatter tails than a normal distribution predicts, meaning extreme moves happen more often than the bell curve suggests. An investor who relies on a model with a normal shape may underestimate the chance of large losses.

Why It Matters to Investors

Understanding distributions helps investors interpret forecasts. A single average return figure hides how much actual results might vary. Looking at the full distribution, including its spread and tails, gives a more complete picture of what could happen. Distributions are models built largely from past data, so they can become inaccurate when market conditions change.