**Probability Distributions for Stocks**

We list here a few links that might be of interest and will continue to add
to this page as time permits

Suggest Google Search on "Probability distributions for stocks"

http://www.investopedia.com/terms/p/probabilitydistribution.asp

Typical, but not very good definition...

http://www.investopedia.com/articles/06/probabilitydistribution.asp

Find The Right Fit With Probability Distributions

Discusses discrete and continuous distributions

An attempt to chart uncertainty

Some common distributions: uniform, normal, lognormal, (many of the most popular
models of stocks assume that the prices are distributed lognormally).

Poisson, student's t, beta, ..

The normal distribution is omnipresent and elegant and it only requires two parameters (mean and distribution). Many other distributions converge toward the normal (e.g., binomial and Poisson). However, many situations, such as hedge fund returns, credit portfolios and severe loss events, don't deserve the normal distributions.

http://demonstrations.wolfram.com/StockPriceProbabilityWithStableDistributions/

This Demonstration calculates the probability that the random price of the
exchange-traded fund, SPY, will be higher or lower after one month than a
particular future possibility.
It uses some 'model' with four parameters and shows what the cumulative
distribution looks like with different parameters.

http://www.ehow.com/info_7982047_normal-probability-distribution-stocks.html

**Normal Probability Distribution in Stocks **

Stock market analysts try to make predictions about the behavior of stocks. The
more data that they have about the stocks, the better their predictions will be.
One of the most important pieces of information that analysts have is the
distribution of stock returns, because it tells them how likely each possible
scenario is. The normal distribution is commonly used in analyses of the stock
market, but some analysts
have questioned its applicability.

Limitations

The normal distribution may fit much of the data, but it has limitations in its
relevance to investors' choices. Portfolio choices are influenced by investors'
perceptions of risk. Because the normal distribution is symmetrical, the
possibility of gains is treated in the same way as the risk of losses when
calculating the variance of a portfolio. However, investors see only losses as
risks, so only downward movements should negatively affect a portfolio's
volatility.

Our comment: This is true, but relates to the use of the distribution in efficient
portfolio theory where 'risk' is represented by the variance/co-variance matrix
of possible investments. This criticism is more relevant to distributions
that are not symmetric, rather than to those that are, such as the normal
distribution because the 'risk' of gain is mirrored by the risk of loss in
symmetric distributions.