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.
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 bellshaped 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 valueatrisk (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 overreliance on VaR has been implicated as one of the major causes of the Financial Crisis.

Normal Distribution
A probability distribution that plots all of its values in a ... 
Uniform Distribution
In statistics, a type of probability distribution in which all ... 
T Distribution
A type of probability distribution that is theoretical and resembles ... 
Mesokurtic
A term used in a statistical context where the kurtosis of a ... 
Kurtosis
A statistical measure used to describe the distribution of observed ... 
Bell Curve
The most common type of distribution for a variable. The term ...

Investing
Find The Right Fit With Probability Distributions
Discover a few of the most popular probability distributions and how to calculate them. 
Investing
What a Normal Distribution Means
Normal distribution describes a symmetrical data distribution, where most of the results lie near the mean. 
Trading
Trading With Gaussian Models Of Statistics
The entire study of statistics originated from Gauss and allowed us to understand markets, prices and probabilities, among other applications. 
Managing Wealth
Using Normal Distribution Formula To Optimize Your Portfolio
Normal or bell curve distribution can be used in portfolio theory to help portfolio managers maximize return and minimize risk. 
ETFs & Mutual Funds
Stock Market Risk: Wagging The Tails
The bell curve is an excellent way to evaluate stock market risk over the long term. 
Trading
Bet Smarter With The Monte Carlo Simulation
This technique can reduce uncertainty in estimating future outcomes. 
Managing Wealth
Backtesting ValueatRisk (VaR): The Basics
Learn how to test your VaR model for accuracy. 
Managing Wealth
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. 
Investing
Quantitative Analysis Of Hedge Funds
Hedge fund analysis requires more than just the metrics used to analyze mutual funds. 
Investing
Scenario Analysis Provides Glimpse Of Portfolio Potential
This statistical method estimates how far a stock might fall in a worstcase scenario.

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