## What is a 'Probability Distribution'

A probability distribution is a statistical function that describes all the possible values and likelihoods that a random variable can take within a given range. This range will be between the minimum and maximum statistically possible values, but where the possible value is likely to be plotted on the probability distribution depends on a number of factors. These factors include the distribution's mean, standard deviation, skewness and kurtosis.

Next Up

## BREAKING DOWN 'Probability Distribution'

Academics and fund managers alike may determine a particular stock's probability distribution to determine the possible returns that the stock may yield in the future. The stock's history of returns, which can be measured on any time interval, will likely be comprised of only a fraction of the stock's returns, which will subject the analysis to sampling error. By increasing the sample size, this error can be dramatically reduced.

## Types of Probability Distributions

There are many different classifications of probability distributions. Some of them include the normal distribution, chi square distribution, binomial distribution, and Poisson distribution. The different probability distributions serve different purposes. The binomial distribution, for example, evaluates the probability of an event occurring several times over a given number of trials and given the event's probability in each trial. The usual example would use a fair coin and figuring the probability of that coin coming up heads in ten straight flips.

The most commonly used distribution is the normal distribution and it is used frequently in finance, investing, science, and engineering. The normal distribution is fully characterized by its mean and standard deviation, meaning the distribution is not skewed and does exhibit kurtosis. This makes the distribution symmetric and it is depicted as a bell-shaped curve when plotted.

## Probability Distributions Used in Investing

Stock returns are often assumed to be normally distributed but in reality, they exhibit kurtosis with large negative and positive returns seeming to occur more than would be predicted by a normal distribution. This shows up on a plot of stock returns with the tails of the distribution having greater thickness.

Probability distributions are often used in risk management as well to evaluate the probability and amount of losses that an investment portfolio would incur based on a distribution of historical returns. One popular risk management metric used in investing is value-at-risk (VaR). VaR yields the minimum loss that can occur given a probability and timeframe for a portfolio. Alternatively, an investor can get a probability of loss for an amount of loss and time frame using VaR. Misuse and over-reliance on VaR has been implicated as one of the major causes of the Financial Crisis.

RELATED TERMS
1. ### Normal Distribution

A probability distribution that plots all of its values in a ...
2. ### Tail Risk

A form of portfolio risk that arises when the possibility that ...
3. ### Leptokurtic

A statistical distribution where there are extreme points(or ...
4. ### Excess Kurtosis

Excess kurtosis describes a probability distribution with fat ...
5. ### Discrete Distribution

A discrete distribution is a function that gives the probabilities ...
6. ### Distribution Yield

The amount of cash flow received or paid out by an annuity, REIT ...
Related Articles

### Trading with Gaussian models of statistics

The study of statistics originated from Carl Friedrich Gauss and helps us understand markets, prices and probabilities, among other applications.
2. Investing

### Optimize your portfolio using normal distribution

Normal or bell curve distribution can be used in portfolio theory to help portfolio managers maximize return and minimize risk.

### How to Save Clients from RMD Aggregation Mistakes

Advisors can help clients avoid required minimum distribution mistakes in their retirement plans.
4. Personal Finance

### Backtesting Value-at-Risk (VaR): The Basics

Learn how to test your VaR model for accuracy.
5. Investing

### Value at Risk (VaR)

Value at risk, often referred to as VaR, measures the amount of potential loss that could happen in an investment or a portfolio of investments over a given time period.

Staying employed a little longer may allow for a more comfortable retirement.
7. Investing

### Multivariate Models: The Monte Carlo Analysis

This decision-making tool integrates the idea that every decision has an impact on overall risk.
8. Investing

### What's Skewness?

Skewness describes how a data distribution leans.
9. Investing

### Calculating volatility: A simplified approach

Though most investors use standard deviation to determine volatility, there's an easier and more accurate way of doing it: the historical method.
10. Investing

### Expect Big Capital Gains Distributions from These Funds (AGTHX, ACRNX)

The steady rise in the markets since 2009 has led to some outsized gains in a few funds that are finally being realized as long-term winning holdings.
RELATED FAQS
1. ### What does Value at Risk (VaR) say about the "tail" of the loss distribution?

Learn about value at risk and conditional value at risk and how both models interpret the tail ends of an investment portfolio's ... Read Answer >>
Hot Definitions
1. ### Capital Asset Pricing Model - CAPM

Capital Asset Pricing Model (CAPM) is a model that describes the relationship between risk and expected return and that is ...
2. ### Return On Equity - ROE

The profitability returned in direct relation to shareholders' investments is called the return on equity.
3. ### Working Capital

Working capital, also known as net working capital is a measure of a company's liquidity and operational efficiency.
4. ### Bond

A bond is a fixed income investment in which an investor loans money to an entity (corporate or governmental) that borrows ...
5. ### Compound Annual Growth Rate - CAGR

The Compound Annual Growth Rate (CAGR) is the mean annual growth rate of an investment over a specified period of time longer ...
6. ### Net Present Value - NPV

Net Present Value (NPV) is the difference between the present value of cash inflows and the present value of cash outflows ...